Effects of eliminating the unfunded social security system in an economy with entrepreneurs

PDF

Download

Open document

Flip pages

Summarize

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content EFFECTS OF ELIMINATING THE UNFUNDED SOCIAL SECURITY SYSTEM IN AN ECONOMY WITH ENTREPRENEURS by Okan Eren A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2008 Copyright 2008 Okan Eren Dedication I dedicate my PhD thesis to my parents, Mrs. Fatma Eren and Mr. Osman Eren. ii Acknowledgements I am very indebted to my advisor, Professor Selahattin Imrohoroglu, for his continuous support, encouragement, and invaluable comments on the subject. This dissertation would not have been possible without him. I am also very thankful to the committee members- Professor Vincenzo Quadrini, Professor Ayse Imrohoroglu, Professor Caroline Betts, and Professor Guillaume Van- denbroucke for their support, numerous comments, and suggestions. iii Table of Contents Dedication ii Acknowledgements iii List of Tables vi List of Figures viii Abstract ix 1 Introduction 1 2 The Infinite Horizon Model 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.2 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.3 Intermediation . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.4 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.5 Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.6 Utility Maximization . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 Benchmark Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4.1 Preferences and Demographics . . . . . . . . . . . . . . . . . . 36 2.4.2 Intermediation . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.3 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.4 Labor Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.4.5 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.5 Benchmark Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5.1 Aggregate Effects . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5.2 Non-Corporate Sector . . . . . . . . . . . . . . . . . . . . . . 44 2.5.3 Distributional Effects on Wealth and Income . . . . . . . . . . 47 iv 2.5.4 Welfare Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.6.1 Coefficient of Relative Risk Aversion, . . . . . . . . . . . . . 51 2.6.2 Share of Capital, . . . . . . . . . . . . . . . . . . . . . . . . 56 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3 The Pure Life Cycle Overlapping Generations Model 63 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2 The Model Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . 69 3.2.3 Financial Intermediaries . . . . . . . . . . . . . . . . . . . . . 70 3.2.4 Role of the Government . . . . . . . . . . . . . . . . . . . . . 71 3.2.5 Profit Maximization of the Firms . . . . . . . . . . . . . . . . . 74 3.2.6 Utility Maximization of the Household . . . . . . . . . . . . . 75 3.3 Stationary Competitive Equilibrium . . . . . . . . . . . . . . . . . . . 79 3.4 Benchmark Calibration of the Model . . . . . . . . . . . . . . . . . . . 81 3.4.1 Demographics and Preference Parameters . . . . . . . . . . . . 81 3.4.2 Parameters of the Intermediation Sector . . . . . . . . . . . . . 82 3.4.3 Technological Parameters . . . . . . . . . . . . . . . . . . . . 83 3.4.4 Parameters of Labor Process . . . . . . . . . . . . . . . . . . . 86 3.4.5 Parameters of the Government Sector . . . . . . . . . . . . . . 87 3.5 Quantitative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.5.1 Macroeconomic Aggregates . . . . . . . . . . . . . . . . . . . 92 3.5.2 Non-Corporate Sector . . . . . . . . . . . . . . . . . . . . . . 94 3.5.3 Wealth and Income Distributions . . . . . . . . . . . . . . . . . 97 3.5.4 Welfare Comparisons . . . . . . . . . . . . . . . . . . . . . . . 99 3.6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.6.1 Coefficient of Relative Risk Aversion, . . . . . . . . . . . . . 101 3.6.2 Share of Capital, . . . . . . . . . . . . . . . . . . . . . . . . 106 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Bibliography 112 v List of Tables 2.1 Target Moments and Model Results . . . . . . . . . . . . . . . . . . . 38 2.2 Calibrated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3 The Long-run Aggregate Effects of the Policy Change . . . . . . . . . . 44 2.4 The Long-run Effects of the Policy Change on the Non-corporate Firm Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.5 The Long-run Effects of the Policy Change on Non-corporate Sector . . 46 2.6 The Long-run Effects of the Policy Change on Wealth Distribution . . . 48 2.7 The Long-run Effects of the Policy Change on Income Distribution . . . 49 2.8 Welfare Effects of the Policy Change in the Long Run . . . . . . . . . . 50 2.9 The Long-run Effects on the Non-corporate Firm Size, . . . . . . . . 52 2.10 The Long-run Effects of the Policy Change on Non-corporate Sector, 53 2.11 The Long-run Aggregate Effects, . . . . . . . . . . . . . . . . . . . . 54 2.12 Wealth and Income Distribution, . . . . . . . . . . . . . . . . . . . . 55 2.13 Consumption Compensation, . . . . . . . . . . . . . . . . . . . . . . 56 2.14 The Long-run Effects on the Non-corporate Firm Size, . . . . . . . . 57 2.15 The Long-run Effects of the Policy Change on Non-corporate Sector, 57 2.16 The Long-run Aggregate Effects, . . . . . . . . . . . . . . . . . . . . 58 2.17 Wealth and Income Distribution, . . . . . . . . . . . . . . . . . . . . 59 2.18 Consumption Compensations, . . . . . . . . . . . . . . . . . . . . . 60 vi 3.1 Target Moments and Model Results in Overlapping Generations (OG) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.2 Calibrated Parameters in OG Model . . . . . . . . . . . . . . . . . . . 90 3.3 The Long-run Aggregate Effects of the Policy Change, OG . . . . . . . 93 3.4 The Long-run Effects of the Policy Change on the Non-corporate Firm Size, OG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.5 The Long-run Effects of the Policy Change on Non-corporate Sector, OG 95 3.6 The Long-run Effects of the Policy Change on Wealth Distribution, OG 98 3.7 The Long-run Effects of the Policy Change on Income Distribution, OG 99 3.8 Welfare Effects of the Policy Change in the Long Run, OG . . . . . . . 100 3.9 The Long-run Effects on the Non-corporate Firm Size with OG, . . . 102 3.10 The Long-run Effects of the Policy Change on Non-corporate Sector with OG, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.11 The Long-run Aggregate Effects with OG, . . . . . . . . . . . . . . . 104 3.12 Wealth and Income Distribution with OG, . . . . . . . . . . . . . . . 104 3.13 Consumption Compensation with OG, . . . . . . . . . . . . . . . . . 105 3.14 The Long-run Effects on the Non-corporate Firm Size with OG, . . . 106 3.15 The Long-run Effects of the Policy Change on Non-corporate Sector with OG, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.16 The Long-run Aggregate Effects with OG, . . . . . . . . . . . . . . 108 3.17 Wealth and Income Distribution with OG, . . . . . . . . . . . . . . . 108 3.18 Consumption Compensation with OG, . . . . . . . . . . . . . . . . . 109 vii List of Figures 3.1 Cross-Section Consumption . . . . . . . . . . . . . . . . . . . . . . . 91 3.2 Profile of Intertemporal Wealth Transfers . . . . . . . . . . . . . . . . 92 3.3 Fraction of Young Entrepreneurs . . . . . . . . . . . . . . . . . . . . . 96 viii Abstract This study investigates the effects of eliminating the unfunded social security on an economy with entrepreneurs in the presence of individual income and lifespan uncer- tainties by using two different models, an infinite horizon and a pure life cycle over- lapping generations (OG) model. Both models are very successful in replicating the dispersion of the wealth observed in the U.S. data. According to the quantitative results in both frameworks, the removal of the unfunded social security creates a significantly more equal distribution of wealth in the long run. More specifically, the wealth Gini, a commonly used measure of wealth inequality, falls from 0:807 to 0:521 and 0:765 to 0:684 in the infinite horizon and OG models, respectively. A mechanism, designed to guarantee a certain level of income for the households who fail to save adequately for their retirement years, generates a wealth distribution that is highly concentrated in the top tail. The first model, the infinite horizon model, reports a 39% increase in the frac- tion of entrepreneurs after privatization while the increase stays very low in the second model, around 4%. Unlike their fraction in the total population, their share in total net worth and income is considerably reduced after the policy change in both models. The stock of physical capital, aggregate output, and aggregate consumption are observed to increase after the privatization. However, the percentage increases in aggregate output and consumption in an economy with entrepreneurs are lower than those observed in an ix economy without them regardless of the choice of the model. The results also indicate a more unequal distribution of income, even if the share of the richest households is lowered after the removal of the unfunded social security. x Chapter 1 Introduction The unfunded pension system partially insures people against income and mortality risks in their elderly years by providing a certain flow of income. It is financed by taxing the current young or more specifically working population who also expect that they will be collecting the retirement benefits. This system creates an externality in the market mechanism which distorts the optimal saving and labor supply decisions of individuals. Most of the people especially who lack the foresight and resources to save against future uncertainties greatly benefit from the unfunded social security during their retirement period. The benefits and costs of this system have been analyzed by many researchers from different perspectives. Particularly, the effects of eliminating the unfunded social security on the behaviors of individuals as well as the economy as a whole have been a vital research topic in the recent decades. These studies mostly focus on the effects of the unfunded social security on aggre- gate capital formation and the welfare. So far, there has been a little work on the effects of the privatization on the wealth distribution given the fact that the models having been used in those studies do not generate a wealth distribution that is close to the one observed in the U.S. data. At this point, this study deviates from the previous literature and tries to match the U.S. wealth distribution by introducing occupational heterogeneity and then analyzes the effects of removing the unfunded pension system on the economy and mainly wealth distribution. Occupational heterogeneity is obtained by introducing entrepreneurship as an alternative occupation to being a worker. In this way, the effects 1 of the privatization on the decisions of entrepreneurs can also be investigated. This is particularly important considering the fact that entrepreneurs own forty percent of the total net worth in the U.S. even though they constitute a small fraction of the population. Therefore, this study is related to literature on two separate topics; the unfunded social security and the entrepreneurship. In this study, the effects of eliminating the pay-as-you-go social security in an econ- omy with entrepreneurs are analyzed by using two different frameworks. The first model is an infinite horizon model and used by the papers in the literature on the entrepreneur- ship such as [23], [4], and [20]. On the other hand, the other one is a pure life cycle overlapping generations model and adopted by most of the papers in the literature on the unfunded social security, for instance [2], [19], [16], and [7]. In both frameworks, entrepreneurship is modeled as an alternative occupation through which households can accumulate big amounts of wealth so that the wealth distributions generated by the model economies are very close to the one observed in the U.S. data. In this sense, this paper is the first to analyze the effects of eliminating the unfunded social security on occupational choice, entrepreneurs, wealth and income distributions. Although households may realize death in the first model, it is still named as infi- nite horizon model because each household is replaced with a young household, his descendant, upon his death thereby forming a dynasty that has an infinite lifespan. The households in this framework are assumed to live through two phases of life cycle, more specifically young age and old age. Every young household faces a constant probability of aging at the end of each period but never realizes mortality shock. Unlike the young, there is a positive probability of death in each period for every old household. Those probabilities are assumed to be constant and not allowed to vary across households so as to obtain a stationary distribution of households over the two demographic states. When 2 a young household replaces an old upon his death, he also receives his assets in the form of bequests. Since every household is assumed to be altruistic towards his descendants, he values his own consumption and the consumption of his descendant equally. Households are further assumed to be heterogenous with respect to their labor and entrepreneurial abilities. Both labor and entrepreneurial efficiencies of a household fol- low a stationary finite state Markov process. The retirement is mandatory if a young household realizes aging shock and does not choose to begin or continue his own busi- ness. If an old entrepreneur decides to retire in any period, he is not allowed to be entrepreneur in the remaining of his lifetime. A household in this setting optimally chooses his occupation at the very beginning of every period knowing his labor and entrepreneurial ability. A worker inelastically supplies his labor into the market in return for wage income. On the other hand, an entrepreneur manages his own business and can only supply his labor into it. If the labor demand of his business is in short of his labor supply, the foregone labor income is the cost of being entrepreneur. If he demands more labor than his own, he is allowed to hire as much labor as he needs at the market wage rate. There are two sectors of production which are named as corporate and non-corporate sectors following [23]. The corporate sector is populated by many firms whose produc- tion technology exhibits constant returns to scale with respect to the factors of produc- tion, labor and physical capital. All corporate firms have access to the same technol- ogy. On the contrary, the production technology of the entrepreneurial firms is char- acterized by decreasing returns to scale the degree of which determines the share of entrepreneurial profit in the output. All entrepreneurial firms benefit from the same pro- duction technology but they differ from each other with respect to their entrepreneurial 3 efficiencies. The wage rate and rental rate of physical capital are determined in the cor- porate sector by the forces of supply and demand. Entrepreneurs take those prices as granted when combining labor and capital in the process of maximizing their profits. Besides the two sectors of production, there is an intermediary sector which consists of many financial institutions. Those institutions collect the savings of households at the market interest rate and provide the firms in the production sectors with the funds that they need in their productive activities. The financial firms in this sector are not involved in productive activities, and they only transfer resources from households to firms in both corporate and non-corporate sectors. Corporate firms are allowed to borrow as much as they need at the prevailing market interest rate. Conversely, non-corporate firms are borrowing constrained and can only borrow up to a certain amount. The maximum amount up to which an entrepreneur can borrow depends on his current wealth but not on his entrepreneurial ability or future profits. Entrepreneurs also pay an extra cost per unit of resources that they borrow in excess of their asset holdings. These resources are simply taken away from the economy, and therefore the extra cost of entrepreneurial borrowing is a deadweight loss. Because entrepreneurs are borrowing constrained and pay an extra cost for borrowing in excess of their wealth, not only entrepreneurs but also workers have an extra incentive for saving besides insurance and altruistic motives. In this environment, the government ensures the continuation of the unfunded social security and is responsible for taxation of consumption expenditures and income. The social security system is unfunded in the sense that the amount of social security taxes collected from the current working population, entrepreneurs or workers, is just equal to the total benefits paid to the retired in a given period. In other words, the public pension system is self-financing. It is the government’s duty to set the social security tax rates that balances the social security budget in any period. It is worth to note that the presence 4 of the unfunded social security creates a negative externality in the economy. It distorts the saving decisions of young households by taking away a part of their income in the form of social security taxes and guaranteeing a certain income throughout their senior years. If not taken away, these resources could have been used by those households more efficiently and productively. Since the social security provides partial insurance against income and mortality risks in the elderly years, it also depresses the savings for insurance purposes. Returning to the unfunded social security, every household who is actively working pays the social security taxes for their labor income regardless of the occupation or demographic state. There are three types of income for an entrepreneur- labor income, profit income, and interest income. Only his labor income is subject to the social security taxation. In an effort to replicate the regressiveness of U.S. social security system, it is assumed that the part of the labor income above a certain level is not subject to the social security taxation. In other words, there is a maximum level of labor income above which social security taxes do not apply. The amount of benefit that a retiree receives is a constant fraction of the average lifetime labor earnings subject to the social security taxation. Hence, the retired are homogenous with respect to the retirement benefits. This assumes away the heterogeneity observed in the U.S. economy in terms of pension payments due to the lack of ability of the model to keep track of the age of a household. The second responsibility of the government is the taxation of consumption expen- ditures and income in order to finance its purchases. The government is assumed to purchase an exogenously given fraction of goods and services produced in the economy, and those are not used in any productive activity. The government uses the revenues gen- erated from income and consumption taxation to finance its purchases. All consumption expenditures done by workers, entrepreneurs, and the retired are taxed at a constant rate 5 which is equal to the average tax rate on consumption in the U.S. estimated by [22]. On the other hand, income is assumed to be taxed both progressively and proportionally. The definition of income here encompasses the labor earnings, profits of entrepreneurs, rental income from capital, and pension payments to the retired. All types of income are thoroughly subject to the income taxation except the social security transfers made to the retired. In reference with the taxation of social security benefits in the U.S., the income taxes are assumed to apply to a certain portion of the pension payments only if this portion is greater than a certain level together with the income from all other sources. Otherwise, the pension payments are exempt from income taxation. The policy experiment in this model is conducted by removing the unfunded public pension system without any compensation. Then, the two steady states of this economy before and after the policy change are examined and compared so as to study the quan- titative effects of the policy reform on the economy and households. The policy reform 1 is assumed to be revenue neutral so that the level of the government purchases is fixed at its steady state value with the social security. Moreover, the progressiveness of the income taxation is also preserved by allowing the relevant parameters of the model to adjust to the changes that take place following the privatization of the pension system. All other parameter values are kept unchanged after the privatization and new steady state of the economy is quantitatively computed. The two steady states are numerically compared in order to derive some conclusions about the effects of privatization on the key macroeconomic aggregates, such as aggregate output, capital, and consumption, occupational choices of households, and wealth and income distributions. 1 Throughout the thesis, policy reform, policy change, policy abandonment, privatization, and policy alteration are interchangeably used to refer to the instant elimination of the unfunded social security in the economy. 6 Quantitative findings are mostly in line with the results documented by the previous papers in the literature on the unfunded social security. When the depressing effect of the pension system on the household saving is removed, the physical capital accumula- tion is observed to increase substantially when the steady states with and without social security are compared. This can be attributed to the absence of the partial insurance that used to be provided by the unfunded social security. In the absence of such an insurance mechanism, the households optimally raise their savings and begin to accumulate more wealth to insure themselves against the possible risks in the future, especially when they are retired. Numerically, the steady state capital stock after the policy switch is found to be sixty three percent higher than what it used to be. Even though such a big rise in the stock of physical capital may imply big changes in the aggregate output and consump- tion, the percentage increases in those are surprisingly observed to stay relatively very low compared to the increase in the stock of physical capital. This difference might be explained by studying the behavior of the entrepreneurs and the non-corporate sector as a whole in more detail. In the new steady state after the policy reform, more households are observed to choose entrepreneurship over being worker. More specifically, the fraction of business owners in the whole population increases by almost forty percent in the steady state following the privatization. The distribution of households across occupational states changes in favor of the entrepreneurs. On the contrary, the non-corporate output and labor demand are significantly reduced implying a significant fall in the income and profit of entrepreneurs. The removal of the depressing effect of the unfunded social secu- rity on the savings of households has a positive effect on the entrepreneurs. Neverthe- less, the general equilibrium effect via factor prices reduces the levels of entrepreneurial profit and makes it more difficult for the households to start off their own businesses. As 7 a result of these two opposing forces, the fraction of entrepreneurs essentially increases while the output and labor demand in the non-corporate sector fall in the long run. The most important contribution of this paper to the literature is about the effect of the reform on the distribution of wealth. Most of the previous papers in the literature on the unfunded social security system are able to replicate the bottom tail of the wealth distribution observed in the U.S. data while having difficulty in the top tail of the distri- bution. Unlike those papers , the infinite horizon model is very successful to match the both tails of the wealth distribution observed in the data. In the wealth distribution gen- erated by a model without entrepreneurs, the share of the wealthiest one percent in total wealth is roughly four percent, a very small value when compared to thirty five percent, which is the value observed in the data. Inclusion of the entrepreneurs into this very same model enables the model to generate a more concentrated distribution of wealth in which the wealthiest one percent holds almost thirty one percent of the total net worth or the stock of physical capital. The elimination of the unfunded social security in the model economy is observed to create a less concentrated distribution of wealth in the long run. This conclusion is not new to the literature. There are several papers such as [11], and [13] which report that privatizing the pension system results in a more equal wealth distribution. However, they do not show how the shares of the households in different wealth percentiles change after the privatization. A more equal distribution of wealth might be obtained by a decrease in the fraction of household with zero wealth or in the share of the wealthiest households in the total wealth or both. According to quantitative results, the latter is the case in a model with entrepreneurs. For example, the share of the wealthiest one percent falls by approximately sixty percent in the new steady state of the model economy. Meanwhile, it seems that almost all of the households hold positive levels of wealth in the economy 8 without the unfunded social security. This is a huge change when compared to the fraction of households with zero wealth, fifteen percent, with the social security. Even if the unfunded social security is intended to protect the households who have very little income or lack the foresight to save against future uncertainties, it creates a more unequal wealth distribution in favor of the wealthiest. The infinite horizon model is a common choice among the papers in the literature on the entrepreneurship. Despite the ease of computational solution with this type of modeling, it is not the choice of the papers that have studied the effects of the elimina- tion of the unfunded social security in the literature. Most of these papers use a version of the pure life cycle overlapping generations model in which the social security system can be built more realistically than the infinite horizon model. In the infinite horizon model, there is a positive probability of observing a household who lives a single period of working stage while living a very long retirement for instance two hundred periods (years). This creates an unrealistically high lifespan uncertainty in which case house- holds increase their savings so much that almost none of the households is observed to hold zero wealth after the privatization. This is one of the reasons for a more equal wealth distribution obtained in the new steady state of the economy, and this result might be criticized given the extremely high lifespan uncertainty in the model. In order to take these criticisms into account and be able to model the unfunded social security more realistically, a pure life cycle overlapping generations model is also used to study the effects of the privatization in an economy with entrepreneurs as a separate paper. In the second model, the economy is populated by overlapping generations of house- holds of different ages. Every household is assumed to live up to a maximum age condi- tional on survival. Unlike the infinite horizon model, there is an exogenously determined maximum age up to which households might live, and households face the risk of death 9 at each age of the life cycle. The survival probabilities are age dependent and the same for all households of the same cohort. They are further assumed to be independent of time in order for the distribution of households across cohorts to be stationary. Dif- ferent from the assumption of zero population growth rate in the previous model, the population is assumed to grow at a constant rate and this rate is equated to the average population growth rate in the U.S. The share of each cohort in the total population is then determined by the age-dependent survival probabilities and the constant growth rate of population. When a household dies before reaching the maximum possible age with positive asset holdings, all of his wealth is confiscated by the government and equally distributed to the surviving households at the very end of each period. Unlike the infi- nite horizon model, the households are assumed to have no descendants and thus they have no intention of leaving some bequests upon their death. In this manner, an incen- tive mechanism, bequest, for household saving is assumed away in the pure life cycle setting. Similar to the first model, each household is endowed with a finite amount of time and they either spend this time managing and working in their own business or inelasti- cally supplying their labor into the market conditional on the occupational choice. The market wage rate is not allowed to vary across different sectors of production. The labor efficiency per unit of time of a household is characterized by his age and a stochastic pro- cess which does not depend on the age of the household. The age dependent component of the labor efficiency is obtained by using the estimates of [15]. The other component, stochastic process, is assumed to follow a finite-state Markov process that generates the Gini coefficient of labor earnings observed in the data. The labor efficiency of every young household is given by the product of these two independent components regard- less of his current occupation. The labor efficiency of every old household who chooses 10 to run and work in his own business is set to unity. Moreover, the entrepreneurial effi- ciency is also assumed to follow a finite state Markov process in the steady state. An entrepreneur can work in his own business by supplying his labor endowments into it. If the optimal amount of labor demanded by his own firm is lower than his labor endow- ments, he does not have the option of working in the market in the remaining of his time. The production technology here is slightly different from the first model. The pro- duction technology in the corporate sector is identified by a labor augmenting Cobb- Douglas function. In the steady state, it reduces to the form of the production func- tion used in the infinite horizon model. The factor productivity in the corporate sec- tor is assumed to grow at a constant rate in contrast to the no technological growth assumption in the first framework. The form of the entrepreneurial production func- tion in steady state is the same as the one in the first model. It still exhibits decreasing returns to scale and its strength signifies the share of profit in the entrepreneurial output. The entrepreneurial ability is assumed to grow at a constant but different rate from that of the corporate factor productivity outside the steady state. The factor shares in the non-corporate sector are constantly proportional to the corporate share and their sum is strictly less than unity. Even though all corporate firms are identical in all respects, non-corporate firms differ from each other with respect to the efficiency of its owner. Nevertheless, both corporate and non-corporate capital is assumed to depreciate at a constant exogenously specified rate throughout the production process. Meanwhile, the government is still responsible for the unfunded social security sys- tem and the taxation of consumption expenditures and the household income. Similarly, labor earnings, entrepreneurial profits, and interest income are subject to the income taxation. In case of the taxation of the pension payments of the retired, the rule that is 11 early explained in the description of the infinite horizon model exactly applies to this model either. The government does not discriminate among the sources of income and the total income of a household from all various sources are taxed as a whole. The total income is taxed both proportionally and progressively. A progressive income tax formula is adopted when analyzing the effects of the elimination of the unfunded social security on the economy and especially on the wealth distribution. Another duty of the government is to maintain the balance in the budget of the unfunded pension system. Hence the government sets the rate of the social security pay- roll tax that equates the the total amount of benefit payments to the total social security taxes collected from the working population. Since the model distinguishes the house- holds with respect to their ages, the benefit that a household receives in his retirement can be calculated more realistically. The amount of the benefit depends on the average of the indexed lifetime labor earnings of the household. When indexing the labor earn- ings of a household, the growth rate of the technology is used as the indexation factor. After calculating the average indexed lifetime labor earnings of a household, the amount of benefit is found by applying a piecewise linear benefit formula, a formula that is used by the Social Security Administration of the U.S. In this formulation, the lower the aver- age indexed income, the higher the replacement ratio. For a household with a average indexed lifetime income that is equal to the average labor earnings in the economy, the replacement ratio implied by this formula is approximately forty four percent. Even though the quantitative results of the pure life cycle overlapping generations model do slightly differ from those with the infinite horizon model, they provide addi- tional information about the effects of the privatization. Unlike the first model, the effects on the consumption and wealth profiles across cohorts can be quantified and 12 analyzed in the overlapping generations framework. According to the numerical find- ings, the consumption profile shifts in favor of the younger cohorts in the new long-run equilibrium. More importantly, it is possible to study the pattern of the change in the distribution of entrepreneurs across cohorts following the privatization. Such an analysis reveals that the the distribution of young entrepreneurs changes in a way that the fraction of them at the younger ages decreases while increasing in the older cohorts. Different from the results of the first model, the rate of increase in the ratio of entrepreneurs in the whole population increases by a much lower percentage, four percent only. Comparing to forty percent increase in the ratio of entrepreneurs in the infinite horizon model, this can be considered as a very small change. Correspondingly, the overlapping generations model also does very well in replicat- ing the wealth distribution observed in the data. The model generates a distribution of wealth that matches the wealth shares of the top percentiles and the lower percentiles as well. The removal of the unfunded social security causes the wealth distribution to be more equal as in the infinite horizon model. Here, the fall in the fraction of households with zero wealth or the increase in the share of the lowest percentiles are comparably small, and the contribution of those changes to the improvement in the equality of the wealth distribution remains very little. In this environment, the wealth distribution is becoming more equal after the policy change mostly because of the subsequent fall in the share of the wealthiest. Another interesting observation is the increase in the frac- tion of households with zero wealth after the policy change in the same economy without entrepreneurs. As a consequence, the wealth distribution is observed to be slightly more unequal after the privatization in this economy. In this study, the effects of eliminating the unfunded social security on key macroe- conomic aggregates, welfare, occupational choice and especially wealth distribution 13 are comprehensively studied in an economy in which households are heterogenous with respect to their occupations. Two different frameworks- namely a model with an infinitely living dynasty and another with households of overlapping generations, are used during the quantitative analysis. The remainder of the thesis is organized in the following way. Chapter 2 includes the paper that uses the infinite horizon framework and Chapter 3 is the paper with the pure life cycle overlapping generations model. 14 Chapter 2 The Infinite Horizon Model 2.1 Introduction The unfunded social security system is a mechanism that provides households with par- tial insurance against the income shocks related to the old age and longevity risks. Since it guarantees a certain flow of income during the retirement, households, especially the ones who lack the resources or foresight or are too impatient to save for their retirement, mostly benefit from this system. Besides its benefits, the public pension system cre- ates distortions in the optimal saving and work decisions of the working households by imposing payroll taxes on their labor income and discouraging them from saving against future uncertainties. This two-sided nature of the unfunded social security system raises questions about whether its costs or benefits outweigh the other. Hence, the effects of eliminating the unfunded social security on the stock of physical capital, aggregate out- put, and the welfare of the households have been studied in different environments by many researchers. Most of the papers in the literature on the unfunded pension system focus on the effects of the privatization on the aggregate capital formation and the welfare of the households. They pay little or no attention to its effects on the wealth distribution, occu- pational choice, and the entrepreneurs. Because entrepreneurs hold the 40% of the total net worth in the U.S. and models of entrepreneurship are very successful in replicating the distribution of wealth observed in the U.S. data, it is important to examine the effects 15 of removing the unfunded social security in such an economy. Examples of the papers that models entrepreneurship in a general equilibrium framework include [23], [4], and [20]. A model that incorporates entrepreneurship and matches the both tails of the U.S. wealth distribution enables a more detailed analysis of the effects of the unfunded social security on wealth distribution, occupational choice, and entrepreneurial decisions. One of the previous papers in the literature on the unfunded social security, [3] shows that the social security reform has no effect on the capital accumulation when the bequests are taken into account in an overlapping generations model. On the contrary, [2] reports a 24% increase in the capital stock following the removal of the unfunded public pension system in a pure life-cycle framework with complete markets and per- fect foresight. Similarly, the quantitative findings of [16] documents a 40% rise in the capital stock. The results of [7] not only confirm an increase in the capital stock in an overlapping generations model with idiosyncratic income shocks and endogenous labor supply decision but also show that even though a household would prefer to be born in an economy without social security, the majority of existing households oppose to the social security reform. In a similar way, [17] shows that the unfunded social secu- rity reduces the capital stock and welfare again in an overlapping generations model in which households are borrowing constrained and face an uncertain lifetime. [11] examines the effects of the policy change in an overlapping generations model (OLG) with two-sided altruism in which households enjoy a partial family insurance against lifespan and income uncertainty. In such an environment, the family insurance may perform the role of the unfunded social security after the privatization and its effects on the aggregate capital and welfare might be different from a pure life cycle model. According to [11], the physical capital accumulation with the unfunded social security is 8% less than what it would be otherwise. In a similar setting, [12] reports 6% rise in 16 the capital stock following the policy reform. In case of welfare, [12] reports that the welfare of the most households decreases in the steady state without social security. In [13], they allow the households to choose the amount of the labor that they supply into the market in the same model and show that households would like to be born into an economy without social security and the privatization is supported by 52% of the current households. The unfunded social security system affects the wealth distribution by creating sav- ing disincentives for the households thereby reducing the wealth accumulation. Only few papers talk about how wealth inequality reshapes after the policy change. One of those few studies, [1] analyzes the effects of the social security on the wealth inequal- ity in a model with life-span uncertainty. The findings of [1] indicate a less concen- trated wealth after the introduction of the unfunded social security. On the contrary, [11] reports that wealth Gini decreases from 0:58 to 0:46 in the steady state without the social security in a model without life-time uncertainty. Even though these two studies reach some results concerning the wealth distribution, they fail to match the U.S. wealth distribution observed in the data especially the top tail of it. Therefore, they do not explain how the wealth distribution is becoming more equal because of whether a rise in the assets of the households in the bottom tail or the fall in the share of those in the top tail of the distribution. This paper mainly studies the effects of eliminating the unfunded social security on the wealth distribution, occupational choice, and entrepreneurial decisions in an infi- nite horizon life-cycle model in which households face both mortality and income risks. It differs from the papers in the literature on the unfunded social security in several 17 aspects. First, it explicitly models entrepreneurship in a general equilibrium frame- work and successfully matches the both tails of the U.S. wealth distribution. The pres- ence of entrepreneurship creates occupational heterogeneity new incentives for saving by offering huge amounts of profit income. There are some other models that match the distribution of the wealth in U.S. data but they do not investigate the effects of the pri- vatization 1 . Second, households, contrary to the models of two-sided altruism, are only altruistic towards their descendants. This enables households to transfer wealth to their descendants in the form bequests. Finally, the household income is assumed to be taxed progressively by using the formula developed by [27] and estimated by [14]. Since pro- gressive taxation creates disincentives for the saving of the households with high income and discourages the accumulation of wealth, inclusion of which strengthens the model’s results about matching the wealth distribution observed in the data. The ability of a model to match the skewness in U.S. wealth distribution is very important and gives great confidence when studying the effects of the privatization on the wealth distribution. The benchmark model successfully generates a wealth Gini of 0:807 that is very close to the one in the data, 0:803 which is reported by [24]. Having a Gini coefficient of wealth that is very close the one in the data does not necessarily mean that the model successfully replicate the one in the data. A very high wealth Gini can also be obtained by a distribution mostly concentrated in the bottom tail. The benchmark model very closely match the wealth distribution observed in U.S. data. For example, the share of the wealthiest 1% is found to be 30:47% comparing to the one in data, 34:70%. Even though is not intended, the model is also very successful in replicating the income distribution observed in the U.S. data. The income Gini in the model economy, 0:501, is very close to the U.S. income Gini of 0:553. 1 For example, [21] assumes stochastic time discount factors in replicating the U.S. wealth distribution. Another is [6] who calibrate the model economy to the Lorenz curves of U.S. earnings and wealth. 18 After the removal of the social security system, the wealth Gini is observed to fall from 0:807 to 0:521 in the new steady state indicating a more equal wealth distribution. This drop reflects the changes that take place in the two tails of the wealth distribution following the policy change. Since households increase their savings on average for insurance purposes, the share of the households in the bottom tail significantly increases after the reform. The share of the lowest 40% increases from 1% to 11%. There are nearly no households with zero wealth in the new steady state thanks to extremely high uncertainty in the lifespan by the design of the model. Meanwhile, the share of the wealthiest 1% decreases by almost 60% because of the fall in the entrepreneurial profits as they optimally react to the changes in the relative factor prices. In contrast to the wealth distribution, income distribution becomes more concentrated in the economy without social security even though the income share of the top 1% falls from 15% to 12%. In case of occupational choice, more households prefer to be entrepreneur in the steady state without the unfunded social security. The ratio of entrepreneurs in the whole population increases by 39% after the reform because it is more likely that a house- hold who realizes a good entrepreneurial shock does have the required initial wealth for entrepreneurial business. Unlike the ratio of entrepreneurs, their share in the total wealth and income are observed to jump down by 36%, and 5%, respectively. The over- all average size of the entrepreneurial firms is also reported to fall by 24%. To be more specific, the firms operated by entrepreneurs with low factor productivity experience an increase while those of the most efficient entrepreneurs contrarily suffer a reduction in their average firm size. If the non-corporate sector 2 is analyzed as a whole, the total 2 Following [23], the two sectors of production in the economy are named as corporate and non- corporate sectors. The non-corporate sector refers to the entrepreneurial sector which consists of the small and medium size firms of entrepreneurs. 19 capital employed in the sector is observed to increase by 11% while the total labor and total output go down by 21% and 9%, respectively. The quantitative results also reveal that the aggregate output, consumption, and cap- ital increase in the new steady state of the economy after the policy change in line with the most of the previous results in the literature. These aggregates also increase when the same experiment is conducted in an economy without entrepreneurs for compar- ison purposes. If the two experiments are compared, a robust and interesting obser- vation is that the percentage changes in the aggregate output and consumption in the economy without entrepreneurs are found to be 50% and 125% higher than those with entrepreneurs, respectively. In case of welfare, the two steady states of the same econ- omy are compared, and it is found that an unborn household prefer to be born into an economy without the unfunded social security. However, the required compensation for this household to be indifferent between two steady states is significantly lower with entrepreneurs. This reflects the loss of entrepreneurial income due to the lower profit levels in the new steady state. The rest of the paper is organized in the following way. Section 2.2 talks about the benchmark model in detail. Section 2.3 and 2.4 explain the competitive equilibrium and the calibration methods. Section 2.5 reports the benchmark results. A sensitivity analysis is conducted in section 2.6. Finally, section 2.7 concludes the paper. 2.2 The Model The model used in this paper is somewhat similar to those developed by [23], [4], and [20] in certain aspects. The model economy is comprehensively explained in this sec- tion. 20 2.2.1 Households A continuum of households of measure one lives in the model economy. Households are assumed to go through two phases of lifetime- young age and old age. The population is assumed to be constant over time by abstracting from population growth rate. At the end of every period, every household realizes a demographic shock that determines his demographic state in the next period or survival to the next period. A young household may realize the demographic shock of aging with a positive probability, denoted by p o 2 (0; 1), and continues his life as an old while an old household faces the risk of death, probability of which is denoted byp d 2 (0; 1) 3 . In this setup, a household never dies as long as he remains in the demographic state of the young age. If an old household realizes the mortality shock, he is replaced with his descendant, a young household, and his assets are transferred to his descendant in the form of bequests. Households are assumed to be perfectly altruistic towards their descendants in the sense that a household derives the same utility from the consumption of his offspring as his own consumption. In other words, he puts the same weight on the utility from his own consumption and his offspring’s. Hence, the bequest mechanism creates an addi- tional incentive for household to save encourages the accumulation of wealth. Given that a household values his own consumption and his descendant’s equally, his preferences over the consumption sequencefc t g 1 t=1 can generally be represented by the following expected discounted lifetime utility: E 0 ( 1 X t=1 t u(c t ) ) (2.1) 3 Constant probabilities of aging and death create a stationary distribution across demographic states. 21 where2 (0:1) is the subjective time discount factor, E 0 is the expectation operator, andu(:) is the period utility function which is identical for all households. To be more specific,u(:) takes the following Constant Elasticity of Substitution (CES) form: u(c t ) = c 1 t 1 (2.2) where is the coefficient of relative risk aversion and> 0 4 . Moreover, households are heterogenous with respect to their labor and entrepreneurial ability endowments. Labor efficiency or labor productivity per unit of work time of a household,l, is assumed to followN l -state Markov process. The state space of the labor efficiency process is given by the set,L =fl 1 ;l 2 ;:::;l N l g. A house- hold’s labor productivity is drawn from L according to the conditional probabilities defined asp(l t ;l t+1 ) =prob(l t+1 =l t ) before he makes his occupational or consumption- saving decisions. But, a newborn household picks a value from this set according to the corresponding unconditional probabilities as well as an old entrepreneur. A retired household is assumed to have no labor productivity and, thus, can not supply any labor into the market. An old household is only allowed to supply his labor endowments into his own business at the market rate of wages only if he is an entrepreneur. In a similar manner, the values that the entrepreneurial factor productivity,, might take forms the setT =f 1 ; 2 ;:::; N g. The process that governs the entrepreneurial ability is anN -state Markov process and completely independent from the labor ability process. The random variable takes values from the set, according to the condi- tional probabilities denoted byp( t ; t+1 ) = prob( t+1 = t ). When an old entrepreneur dies, his descendant is assumed to draw a value from conditional on his parent’s 4 1 is the elasticity of intertemporal substitution 22 entrepreneurial state in order to exploit the fact that children can benefit from their par- ents’ experiences and knowledge. If an old entrepreneur decides to get retired, he fore- goes this opportunity forever and never realizes another entrepreneurial shock. There- fore, his entrepreneurial state is automatically set to 1 , the state in which households have zero entrepreneurial productivity. A worker inelastically and arbitrarily supplies his labor into corporate and non- corporate sectors in return for a wage per efficiency unit of labor. The market wage rate does not vary across sectors. On the other hand, an entrepreneur can only supply his labor into his own business and does simultaneously manage his own business. He can always hire labor at the prevailing wage rate when the labor demand of his business is in excess of his own endowment. This assumption makes entrepreneurship extremely attractive when the entrepreneurial idea that a household draws is very productive and so he can get his full labor income as well as the entrepreneurial profit. 2.2.2 Technology The production in this economy is conducted by the aforementioned two sectors- corporate and non-corporate sectors. Corporate sector consists of large competitive firms while the non-corporate sector consists of relatively small firms operated by entrepreneurs. Corporate Sector : All corporate firms are assumed to have access to the same produc- tion technology. This common technology is represented by a standard Cobb-Douglas production function: F (K c ;H c ) =AK c H (1) c (2.3) 23 whereK c andH c are the total capital and labor employed in the corporate sector, respec- tively, A is the total factor productivity in the corporate industry, and is the income share of the capital. Capital is assumed to depreciate at the constant rate of. The mar- ket return on physical capital and labor wage rate are settled in this sector by the forces of supply and demand. Since this specific technology exhibits constant returns to scale, both the aggregate and the firm level profits in the corporate sector are zero. Non-corporate Sector : Each entrepreneurial state has its own production efficiency denoted by . Given the value of , an entrepreneur employs labor and capital in the production process. The production technology in this sector is similar to its corporate counterpart and characterized by f(k;h;) =k u 1 h u 2 (2.4) whereu 1 > 0 andu 2 > 0 are the income shares of capital and labor in non-corporate sector, respectively.u 1 andu 2 are constant fractions,, of the income shares of the cap- ital and labor in the corporate sector 5 . The profit or the income share of the entrepreneur is then given by (1) where = (u 1 +u 2 ). (1) is assumed to be strictly positive so that the technology exhibits decreasing returns to scale such that entrepreneurs enjoy positive profits. The income shares of capital and labor do not vary across entrepreneurs. Nonetheless, entrepreneurs are heterogenous in terms of profit and firm size because entrepreneurial productivity varies across entrepreneurs and they are borrowing con- strained. The capital used in the entrepreneurial sector 6 depreciates at the same constant rate of as the corporate capital does. 5 u 1 = andu 2 = (1) 6 Entrepreneurial and non-corporate sector are interchangeably used throughout the paper 24 2.2.3 Intermediation The intermediary sector finances the projects in both corporate and non-corporate sec- tors by transferring the necessary funds from the households to the firms. Households except entrepreneurs are borrowing constrained and can not borrow from the financial institutions in the intermediary sector. Households earn interest income per unit of funds that they transfer to the production sectors via the intermediary sector. The rate of return on savings of the households is assumed to be equal to the risk free rate of return on cap- ital,r. Firms in the corporate sector are allowed to borrow as much as they need at this rate. Unlike corporate firms, an entrepreneur can only borrow up to a certain amount that depends on his leverage ratio, denoted by , and current asset holdings. The entrepreneur pays the risk-free interest rate plus a fixed cost of intermediation, , per unit of resources borrowed in excess of the value of his assets. This cost is neither con- sumed nor invested by the financial institutions. It is just taken away from the economy. An entrepreneur with asset holdings,a, pays the rate,r +, to the financial institutions per unit of resources borrowed in excess ofa and can borrow up toa . 2.2.4 Government The government in this model guarantees the continuation of the pay-as-you-go social security system and is responsible for the government purchases and taxation of the consumption expenditures and income. Social Security System Social security system functions as an insurance mechanism against the old age income shocks and longevity risks. It ensures that households with low income who are less 25 likely to save enough for their retirement obtain a certain flow of income in their elderly years. Households pay payroll taxes when working and collects benefits during their retirement. It is the government’s task to collect payroll taxes from working popula- tion and to make the benefit payments to the retired. In compliant with the U.S. social security system, only the labor income is subject to the social security taxation. Hence, entrepreneurs pay the payroll taxes levied on their labor income excluding the profit and interest income. The government sets the payroll tax rate, s that balances the social security budget. All workers and entrepreneurs are obliged to pay social security taxes as long as they work. The part of the income abovey m s , is exempt from social security taxes. In other words,y m s is the maximum amount of labor income that is subject to the social security taxation. The social security tax that a working household pays is computed by T s (y) = s minfy;y m s g (2.5) wherey is the household’s income that is subject to social security taxation. The benefit that a retiree or an old entrepreneur gets is a fixed fraction of his average lifetime taxable income. The heterogeneity in the social security benefits is assumed away because the model has the lack of ability to keep track of the average labor earnings over the life cycle. Thus, the benefit a retired household receives is assumed to be a fixed fraction of the average of the individual average lifetime labor earnings which is denoted byI The amount of the benefit,b s is given by b s = s I (2.6) where s is the replacement ratio. 26 Government Purchases and Taxation The level of government purchases,G, is assumed to be given exogenously as a constant fraction of the aggregate output. It is financed by the revenue generated from taxes on consumption expenditures and income. Consumption expenditures of households are assumed to be taxed at the constant rate of c . In the case of income taxation, labor earning, entrepreneurial profit, and interest income are subject to the taxation. Social security transfer payments to the retired are partly taxable conditional on a certain criterion. Only a fraction of the social security benefits,f o b , is taxable if the total income of the household from all other sources together with this particular fraction exceedsy o b . Otherwise, pension payments are exempt from income taxation. A progressive income tax formula is used so as to capture the progressive nature of the U.S. income taxation. The progressiveness of income taxes is supposed to reduce the inequality in the wealth and income distribution 7 . The income tax formula derived by [27] is used when calculating the amount of tax that a household with taxable income, y tx , has to pay: t(y tx ) = 0 h y tx ( 1 +y 2 tx ) 1 2 i (2.7) where 0 ; 1 ; 2 > 0 are the constant parameters of the tax formula. Since there are other sources of tax revenue for a government, household income is also assumed to be tax proportionally. As a result, the total income tax,T (:), is given by the following generalized progressive tax formula: T y (y tx ) =t(y tx ) + 3 y tx (2.8) 7 For a discussion of this issue, see [5] 27 where 3 is the constant tax rate on the income signifying the non-progressive portion of the income taxation. 2.2.5 Profit Maximization In this section, the profit maximization problems of a representative corporate firm and of a non-corporate firm are explained. There are two inputs of production; capital and labor in both sectors of production. Corporate Sector A typical firm in the corporate sector solves the following maximization problem taking the gross interest rate, (R) and the wage rate (w) as given: max Kc;Hc>0 AK c H 1 c + (1)K c RK c wH c (2.9) where A represents total factor productivity, K c is the capital demand, and H c is the labor demand by the firm. The gross output of the firm is the sum of the newly produced goods and the part of the capital remaining after production. A constant fraction, , of the capital depreciates during the process. Furthermore, aggregate corporate capital evolves according to the following rule K 0 c = (1)K c +I c (2.10) where I c is the gross investment in the corporate sector, and K 0 c is the next period’s capital. 28 Non-Corporate Sector The non-corporate firms exploit a decreasing returns to scale technology so that entrepreneurs can enjoy positive amounts of profit. An entrepreneur in the non-corporate sector is characterized by his beginning of period asset holdingsa and entrepreneurial productivity. A household with a high may choose to be a worker if he does have very little wealth to start off because of the borrowing restrictions that he faces. Com- bined with the possibility of high entrepreneurial revenues, the strictness of borrowing conditions creates an additional saving motive for households. The maximization problem of an entrepreneur with (a;) is depicted by (a;) = max ( 0k (1+)a h 0 ) n k u 1 h u 2 ~ R(ka)Rawh + (1)k o (2.11) and ~ R = 8 > < > : R + if k>a R if ka 9 > = > ; (2.12) where is the extra cost of borrowing for entrepreneurs,k is the entrepreneur’s capital demand andh is the entrepreneur’s labor demand. 2.2.6 Utility Maximization The expected discounted lifetime utility of a household can be written as a convex com- bination of the relevant value functions, weights computed by using the probabilities 29 assigned to the various possible states of the nature. There are six different value func- tions denoted byV r (:),V oe (:;:;:),V o (:;:;:),V w (:;:;:),V ye (:;:;:), andV y (:;:;:)- explic- itly, the value function of the retired, the old entrepreneur, the old before occupational choice, the worker, the young entrepreneur, and the young before occupational choice, respectively. In the following two subsections, the corresponding utility maximization problems are presented in more detail. The Old A household may always choose to be either an entrepreneur or a retiree when he reaches the retirement age. If he becomes an entrepreneur, he always makes an occupational choice in the beginning of every period until he get retired. If he gets retired, then he is not allowed to return to entrepreneurship in the rest of his life. All old households are assumed to receive pension benefits regardless of their occupational status. The value function of a retired household is the simplest of all six value functions. The retired have only one state variable,fag, that represents wealth transferred from the previous period. Given the state vectors r =fag and =fa;;lg, the decision problem that a retiree faces can be formulated as follows V r ( r ) = max c;a 0 0 c 1 1 + (1p d )V r ( 0 r ) +p d E l 0E 0 == 1 V y ( 0 ) s:t: (1 + c )c +a 0 = a +yT y (y tx ) y = (R 1)a +b s y tx = 8 > < > : y (1f o b )b s if (y (1f o b )b s )y o b (R 1)a otherwise 9 > = > ; 30 wherey o b is the amount of taxable income below which the pension payments are tax- free,f o b is the fraction of pension transfers that enters the calculation of taxable income, 0 denotes the state vector in the next period,b s is the social security benefits received, E 0 = is the expectation operator over 0 conditional on current, andE l 0 is the uncon- ditional expectation operator with respect to labor efficiency. It can be seen from the objective function of the retired that he does not have an occupational choice in the next period. On the other hand, the old entrepreneur has three state variables,fa;;lg; beginning of period asset holdings, entrepreneurial efficiency, and labor productivity, respectively. His maximization problem is expressed below, V oe () = max c;a 0 0 c 1 1 + (1p d )E l 0E 0 = V o ( 0 ; 0 ) +p d E l 0E 0 = V y ( 0 ) s:t: (1 + c )c +a 0 = a +yT y (y tx )T s (y e ) y = (R 1)a +b s +(a;) +y e y e = w minfh e ;l hg y tx = 8 > < > : y (1f o b )b s if y (1f o b )b s >y o b yb s otherwise 9 > = > ; wherey e is the total income of the household from entrepreneurial activities,h e is the labor demand by the entrepreneur’s firm, andh is the time endowment of the household. 31 An old household makes his occupational decision at the very beginning of each period after observing his labor and entrepreneurial abilities. The household has three state variables,fa;;lg. The value function of an old household is given by V o () = 8 > < > : V r ( r ) if = 1 max i2f0;1g f(1i)V r ( r ) +iV oe ()g otherwise 9 > = > ; : (2.13) If an entrepreneur realizes the lowest efficiency shock, 1 , he automatically gets retired; that means,i is automatically set to zero. The Young Likewise, a young household chooses his occupation at the very beginning of every period knowing his labor and entrepreneurial efficiency states. New entrepreneurial shock is drawn conditional on the entrepreneurial state in the preceding period not the occupational status. In other words, an entrepreneur and a worker with the same level of entrepreneurial productivity have identical probabilities of drawing a particular in the next period. A household who chooses to be a worker has three state variables,fa;;lg. The decision problem of a worker is represented by V w () = max c;a 0 0 c 1 1 + (1P o )E l 0 =l E 0 = V y ( 0 ) +P o E l 0E 0 = V o ( 0 ) s:t: (1 + c )c +a 0 = a +yT y (y tx )T s (y w ) y = (R 1)a +y w y w = wl h y tx = y 32 whereE l 0 =l is the conditional expectation operator with respect to labor efficiency, and y w is the labor income. A young entrepreneur’s state space also consists of three variables,fa;;lg. His value function is given by V ye () = max c;a 0 0 c 1 1 + (1P o )E 0 = E l 0 =l V y ( 0 ) +P o E l 0E 0 = V o ( 0 ) s:t: (1 + c )c +a 0 = a +yT y (y tx )T s (y e ) y = (R 1)a +(a;) +y e y e = w minfh e ;l hg y tx = y: wherey e is the labor income of the entrepreneur. A young household chooses either to run his own business or to supply his labor into the market given his state variables,fa;;lg. The corresponding value function is given below: V y () = 8 > < > : V w () if = 1 max i2f0;1g f(1i)V w () +iV ye ()g otherwise 9 > = > ; : (2.14) 2.3 Competitive Equilibrium A state vector, s = (a;;l;), specifies the asset holdings, labor efficiency, entrepreneurial efficiency, and age of a household at the very beginning of every period wherea2R whereR =R + [f0g,2T,l2L,2E =fyoung; oldg, ands2S = RTLE. ~ s = (a;;l; o)2 ~ S is a state vector of a household just after occupational choice and o2O =fyoung entrepreneur; worker; old entrepreneur; retiredg, 33 and ~ s2 ~ S =RTLO. A stationary competitive equilibrium is defined as a set of pricesfR;wg, value functionsfV (s); ~ V (~ s)g, allocationsfa(~ s);c(~ s);k(~ s);h(~ s);o(s)g, a government tax system,f s ; 3 g, social security transfers,fb s (~ s)g, aggregate demands fK c ;H c ;K e ;H e g wheree andc refer to entrepreneurial and corporate sectors, respec- tively, the stationary distribution of the households over the state space,(~ s) such that: 1. Given the prices, government tax system and transfer payments, allocations solve the maximization problem of the household. 2. Capital and labor markets clear K c + Z ~ S k(~ s)d(~ s) = Z ~ S a(~ s)d(~ s) =K H c + Z ~ S h(~ s)d(~ s) = Z ~ S n(~ s)d(~ s) =H wheren(~ s) is the labor supply of the household. 3. The prices are given by R =A K c H c 1 + (1) w =A(1) K c H c 4. The intermediary sector is perfectly competitive and financial institutions make zero profit. Banks collect deposits from households and transfer these funds to the firms. They charge the risk-free interest rate to the firms, r = R 1, and pay it to the households. The extra per-unit cost of intermediating funds to the non-corporate sector is and paid by entrepreneurs. 34 5. The social security system is self-financing: R ~ S b s (~ s)d(~ s) = R ~ S T s (y l (~ s)d(~ s)) wherefy l g refers to the labor income. 6. The government budget is balanced G = R ~ S f c c(~ s) +T y (y tx (~ s))gd(~ s) = c C + R ~ S fT y (y tx (~ s))gd(~ s) where C is the aggregate consumption. 7. The distribution of households over the state ~ s is time-invariant (~ s) =P (~ s) whereP is the transition matrix from one period to the next. 8. The good market clears C +G +K + R ~ S (k(~ s)a(~ s))d(~ s) =AK c H 1 c + R ~ S y e (~ s)d(~ s) 2.4 Benchmark Calibration This section explains the methods used in calibrating the five sets of parameters; demo- graphic and preference, intermediation, technology, labor productivity, and government sector parameters. Table 2.2 gives a list of the calibrated parameters at the end of the 35 section. One model period is taken to be one year when calibrating the model parame- ters. 2.4.1 Preferences and Demographics There are two preference parameters to be calibrated, the relative risk aversion coeffi- cient,, and the subjective time discount factor,. The relative risk aversion coefficient is set to 1:5, a value that is common in the literature. The subjective time discount fac- tor is calibrated in such a way that the capital-output ratio becomes 2:66 in steady state equilibrium. The probability of aging,p o is set to a value that leads to 46 model periods of average duration of working time. In a similar way, the value ofp d is chosen to have the average duration of the old age be 14 periods. Population growth rate is assumed to be zero. 2.4.2 Intermediation There are two parameters that has to be calibrated in the intermediation sector. The first parameter is the leverage ratio, , the maximum amount that entrepreneurs can borrow up to, and is set to 40% following [10]. The operational or extra cost, , of intermediating funds to the non-corporate firms is fixed at 5% following [20] and [8]. 2.4.3 Technology Corporate Sector The production technology in the corporate sector is presented by a Cobb-Douglas pro- duction function,F (K;H) =AK H 1 . The productivity parameter is normalized to unity implying a zero rate of growth of the total factor productivity. Capital’s share of 36 output takes 0:36 which is a value consistent with data. The depreciation rate,, is given by = I Y K Y (2.15) where K Y and I Y is the steady state ratios of capital to output and investment to output, respectively. The latter is fixed at 0:133. The definition of capital in this model does not include the public capital. Non-Corporate Sector The share parameters,u 1 andu 2 , are assumed to be proportional to the shares of capital and labor in the corporate sector so thatu 1 = andu 2 = (1). The proportion- ality constant, determines the degree of decreasing returns to scale and2 (0; 1). This parameter is calibrated together with rest of the entrepreneurial parameters. The entrepreneurial ability,, takesN = 4 values. The first value corresponds to the case in which the household has no entrepreneurial project to implement and 1 is set to zero. The vector of entrepreneurial efficiency points is given by T = [0 2 3 4 ]: (2.16) The associated transition probabilities of the entrepreneurial productivity is given by a transition matrix. In order to decrease the number of unknown parameters, a house- hold’s entrepreneurial state is assumed to evolve gradually in the sense that a household with i may only get i1 if i6= 1 or i+1 if i6= 4 in the next period. For all other possibilities transition probabilities are set to zero. The transition probability from state i to state j is denoted by p ij = prob( t+1 = j = t = i). It is further assumed that 37 p 1;2 =p 23 =p 34 ; p 43 = 1 2 p 32 andp 12 =p 1 ; p 21 =p 2 ; ;p 32 =p 3 . Then, the matrix of transition probabilities is state as P = 2 6 6 6 6 6 6 6 6 6 4 1p 1 p 1 0 0 p 2 1p 1 p 2 p 1 0 0 p 3 1p 1 p 3 p 1 0 0 1 2 p 3 1 1 2 p 3 3 7 7 7 7 7 7 7 7 7 5 (2.17) Above assumptions that reduces the number of unknown parameters are standard in the literature on the entrepreneurship. Table 2.1: Target Moments and Model Results Moment Name Model Value Target Value Fraction of entrepreneurs 7:6% 7:6% Overall exit rate 20:9% 20:0% New entrants’ exit rate 42:0% 40:0% Entrepreneurs share in wealth 43:2% 40:0% Entrepreneurs share in income 28:3% 27:0% Ratio of median wealth of entrepreneurs to the rest 8:05 8:00 Wealth Gini 0:807 0:803 * The percentage deviations from the target values are less than or equal to 8% There are seven non-corporate parameters to be calibrated. The values of , 2 , 3 , 4 , p 1 , p 2 , and p 3 , are calibrated to match the seven moments from the U.S. data. The fraction of entrepreneurs, the share of entrepreneur’s income, the wealth held by the entrepreneur, ratio of median assets of entrepreneurs to that of workers, overall exit rate from entrepreneurship, new entrepreneur’s exit rate, and wealth Gini coefficient are used as target moments. Table 2.1 compares the target values and the values generated 38 by the benchmark calibration. The resulting vector of entrepreneurial productivity and transition matrix are given by T = [0 1:21 1:46 2:47]; P = 2 6 6 6 6 6 6 6 6 4 0:92 0:08 0:00 0:00 0:38 0:54 0:08 0:00 0:00 0:23 0:69 0:08 0:00 0:00 0:13 0:87 3 7 7 7 7 7 7 7 7 5 : 2.4.4 Labor Efficiency First, the logarithm of the labor earnings is assumed to follow an AR(1) process. The persistence parameter of the process is taken to be 0.95, a number that is consistent with the estimates in the literature such as [18], and [25]. The variance of the process is chosen such that the Gini coefficient of the labor earnings in the equilibrium is 0:38 following [4]. Then, the continuous AR(1) process is transformed into aN l = 5-state discrete one by using the quadrature-based method of [26]. Then, the labor productivity grid points are calculated as L = [0:25 0:45 0:77 1:31 2:36] (2.18) 39 The following transition matrix is also obtained P l = 2 6 6 6 6 6 6 6 6 6 6 6 6 4 0:7376 0:2473 0:0149 0:0002 0:0000 0:1947 0:5555 0:2328 0:0169 0:0001 0:0112 0:2221 0:5334 0:2221 0:0112 0:0001 0:0169 0:2328 0:5555 0:1947 0:0000 0:0002 0:0149 0:2473 0:7376 3 7 7 7 7 7 7 7 7 7 7 7 7 5 : (2.19) 2.4.5 Government Social Security System The public pension system in the model is self financing. Hence, the government deter- mines the constant rate of social security tax that balances the budget of the social secu- rity system. The replacement rate, s , is taken to be 0:44. This number is the average replacement rate of a household with an average life-time income that is equal to the average labor earnings in the U.S. economy. Average labor earnings, y l per year in the U.S. economy is $38; 000 in 2006. The income level,y m s above which no social security tax is collected is given by the Social Security Administration (SSA) as $94; 000 in the same year. The ratio of this maximum income to the average labor earnings is used to find the maximum income in the model that is subject to the social security taxation. The fraction of social security benefit, f o b , that is conditionally subject to income tax- ation is taken as 0:5. The limit of income, y o b , below which the benefit payments are exempt from income taxation is set to $32; 000 which is also taken from the SSA. 40 Income Taxation The progressive income taxation formula derived by [27] depends on three parameters; tau 0 , 1 , and 2 . [14] estimate these parameters by using the U.S. data. Their estimates for 0 , 1 , and 2 are 0:258, 0:031, and 0:768, respectively. Since the second estimate, 1 , is unit dependent, the value of this parameter is found within the model. 1 is computed by model 1 = 1 y US 1989 y model 2 (2.20) where y US 1989 is the average total household income in the U.S. in 1989, and y model is the average total household income in the model. In this way the average tax rate on a household with average income in the U.S. economy in 1989 is equated to the average tax rate on a household with average income in the model. Following [9], I fix y US 1989 at 50 which corresponds to an income of $50; 000. [22] find the average tax rate on consumption to be 5.5%. The only remaining tax parameter is the non-progressive income tax rate,t 3 . It is computed within the model so that the government budget is balanced. Government purchases are assumed to equal to 21.5% of the total output as in [13]. 41 Table 2.2: Calibrated Parameters Parameter Value Source Household p o 0:022 p d 0:071 1:500 0:924 Intermediation 0:400 [10] 0:050 [8] Corporate Technology A 1:000 0:360 0:050 Non-Corporate Technology 0:880 [u 1 u 2 ] [0:317 0:563] [ 1 2 3 4 ] in text P in text Labor Efficiency h 1.000 [l 1 l 2 l 3 l 4 l 5 ] in text P l in text Social Security System s 0:440 SSA y m s y l 2:470 SSA f o b 0:500 SSA Taxation G Y 0:215 [13] c 0:055 [22] 0 0:258 [14] 1 0:397 2 0:768 [14] 3 0:058 y o b y l 0:842 SSA 42 2.5 Benchmark Results In this section, the quantitative properties of the benchmark model economy before and after the elimination of the unfunded social security are discussed. The same experiment is also conducted in an economy without entrepreneurs, named as the standard model, and results of which are also presented for comparison reasons. The policy experiment is assumed to be revenue neutral in the sense that the level of government purchases in the initial economy is supposed to remain unchanged during transition and after the new steady-state of the economy is reached. The degree of progressiveness of the income taxation is preserved in the new economy by allowing the relevant tax parameters to adjust in the process. 2.5.1 Aggregate Effects The unfunded social security system, especially for the low-income households, serves as an insurance mechanism against the income and longevity shocks by collecting pro- ductive resources from the working households and transferring them to the retired. All households, guaranteeing a certain flow of income in their retirement, feel less need to save against the future uncertainties associated with old age. In essence, it discourages the young households from saving and creates a downward pressure on the stock of physical capital. After the removal of such a mechanism, households would increase their savings and channel some of the resources, that have been being collected in the form of social security taxes, into the productive sectors in return for interest income. As a natural consequence, the aggregate capital, output and consumption would climb up in the new steady state of the economy. Table 2.3 reports the long-run effects of the social security reform on some impor- tant aggregate variables in the benchmark and standard economies. When there is an 43 Table 2.3: The Long-run Aggregate Effects of the Policy Change With Entrepreneurs s t s r w K Y C K Y SSS* 0:44 13% 3:18% 1:47 5:17 1:94 1:24 2:66 No SSS 0:00 0% 1:33% 1:70 8:44 2:21 1:34 3:83 % 58% 16% 63% 14% 8% 44% Without Entrepreneurs s t s r w K Y C K Y SSS 0:44 13% 8:54% 1:11 3:53 1:33 0:87 2:66 No SSS 0:00 0:00 4:62% 1:35 6:02 1:61 1:02 3:74 % 46% 21% 71% 21% 18% 41% unfunded social security system, the replacement rate and the resultant social security tax rates in the two economies are identical, and 0:44 and 13%, respectively. The cap- ital stock in the economy with entrepreneurs increases by 63%, a rate slightly lower than the one without entrepreneurs which is 71%. Similarly the aggregate output with entrepreneurs increases by 14%, which is a significantly lower rate when compared to 21%, the one without entrepreneurs. The aggregate consumption is observed to increase by 8% with entrepreneurs, while it rises by 18% in the standard model. The smaller percentage change in the aggregate consumption with entrepreneurs can be attributed to the fall in the total output and profit of the entrepreneurs. This is going to be analyzed in more detail in the next section. 2.5.2 Non-Corporate Sector The effects of the policy change on the non-corporate sector are separately argued in order to focus on the new dynamics generated by the entrepreneurial activities and incentives. The possibility of very high revenue when a household realizes the high- est entrepreneurial productivity shock makes saving more attractive for the households. 44 Having a high entrepreneurial efficiency is not enough by itself to generate a high level of profit because a household with a high but very low asset holdings may not be able to commence his own business. Even though this household becomes an entrepreneur, he can still increase his entrepreneurial profit by a huge amount employing more capital, and in order to do so he needs to save more. Table 2.4: The Long-run Effects of the Policy Change on the Non-corporate Firm Size SSS No SSS % Average Firm Size 2 = 1:21 4:8 6:5 35% 3 = 1:46 13:6 15:0 10% 4 = 2:47 60:9 57:2 6% Overall 29:8 22:7 24% Maximum Firm Size 2 = 1:21 7:5 9:7 29% 3 = 1:46 35:8 46:2 29% 4 = 2:47 615:3 440:9 28% Table 2.4 presents the average and maximum firm sizes to each entrepreneurial effi- ciency state in the two long-run equilibria. Average firm sizes with 2 and 3 increase in the new steady state by 35% and 10%, respectively, while the average size for the most productive entrepreneurs decreases by 6%. The overall average of the firm size in the non-corporate sector also decreases by 24%. This result can mostly be attributed to the relatively higher increase in the fraction of low ability entrepreneurs in the final steady state. In the same way, the maximum firm sizes in the second and third entrepreneurial states increase while the maximum firm size falls by 28% for the highest entrepreneurial efficiency. There are two factors that can explain the increase in the average firm sizes. First, all households increase their savings and so accumulate more wealth that can be employed 45 by their own firms if they choose to be entrepreneur. Second, the threshold amount of capital to start off a business is higher after the reform. Moreover, if an entrepreneur is able to operate at the profit maximizing levels without borrowing in both states, he employs more capital without social security in order to take advantage of the relatively lower interest rate. Of the most productive entrepreneurs, none is observed to reach the profit maximizing levels without borrowing. Hence, an entrepreneur lowers his capital demand after the policy change given that he has the same level of wealth in both steady states. When this is combined with the lower profit levels, those households employ less capital on average in the equilibrium without the pension system. Table 2.5: The Long-run Effects of the Policy Change on Non-corporate Sector SSS* No SSS % Ratio of Entrepreneurs 7:62% 10:57% 39% Wealth held by Entrepreneurs 2:23 2:34 5% Share of Entrepreneurs’ Wealth in Total 43:19% 27:68% 36% Share of Entrepreneurs’ Income in Total 28:33% 26:84% 5% Median Wealth Entrep.-to-Non-entrep. ratio 8:05 1:98 75% Non-Corporate Capital (K e ) 2:26 2:51 11% Non-Corporate Labor (H e ) 0:49 0:39 21% Non-Corporate Output (Y e ) 1:28 1:16 9% Corporate Capital (K c ) 2:91 5:93 104% Corporate Labor (H c ) 0:29 0:39 37% Corporate Output (Y c ) 0:66 1:04 58% * SSS stands for Social Security System Table 2.5 quantitatively shows how some key moments in the non-corporate sector change after the elimination of unfunded social security in the long run. These find- ings indicate a lower rate of increase in the amount of capital employed by the non- corporate sector comparing to the corporate sector- 11% to 104%. The total labor hired by the entrepreneurs drops by 21% due to the higher costs of labor. The total output produced by this sector also decreases by 9% pointing to a substantial decrease in the 46 total entrepreneurial income. This clearly explains the lower percentage increase in the aggregate output and consumption in the benchmark model compared to the stan- dard model. Though the level of wealth held by entrepreneurs slightly increases, the share of the entrepreneurs in the total wealth is reduced from 43% to 28%. The share of entrepreneurs income in total also experiences a 5% fall. Similarly, the ratio of the median wealth of entrepreneurs to that of non-entrepreneurs greatly decreases from 8 to 2. Most importantly, the ratio of entrepreneurs rises from 7:62% to 10:57% in the long-run, because households accumulate more wealth in the absence of the unfunded social security and there are very few of them with zero wealth 8 . 2.5.3 Distributional Effects on Wealth and Income The benchmark model does a great job in matching not only the wealth Gini but also the wealth distribution observed in the U.S. data. In the literature on the social security reform, two opposing results have been reported regarding the distribution of wealth but a model matching the U.S. wealth distribution has not been implemented in the anal- ysis of the privatization. [11] and [13] state that the policy reform reduces the wealth inequality across individuals, while [1] argues that the introduction of the pension sys- tem results in a less concentrated wealth distribution. The findings of both the bench- mark and standard model exhibit the economy with social security has a more unequal wealth distribution. Table 2.6 depicts the wealth distributions in the economy pre and post social security reform. In the benchmark economy, there is a big mass of households at the bottom of the wealth distribution who have zero wealth, more specifically 15% of the whole pop- ulation. Of those with zero wealth, 62% consist of the retired who have no income and 8 This is going to be explained in more detail in the next section. 47 Table 2.6: The Long-run Effects of the Policy Change on Wealth Distribution % of the wealth owned by the top % with Wealth 1% 5% 10% 20% 40% 60% a 0 Gini Data 34:70 57:80 69:10 81:70 93:90 98:90 6:9-12:9 0:803 Entrep. and SSS 30:47 60:87 70:74 82:06 94:42 99:03 15:11 0:807 Entrep. and no SSS 13:36 30:39 40:26 55:39 76:31 89:29 0:00 0:521 No Entrep. but SSS 4:17 16:88 29:52 49:45 76:63 92:04 1:71 0:492 No Entrep. and no SSS 3:18 13:61 24:55 42:57 68:59 85:40 0:00 0:388 * The wealth shares and wealth Gini are taken from [24]. are dependent on the pension payments. One peculiarity of the model is that households may work for a few periods not long enough to save adequately for retirement, but live for many years in their retirement state. This oddness of the model has the potential to generate more retired households with zero wealth than what it would be otherwise 9 . After the policy change, the wealth Gini is lowered by 35% indicating a more equal wealth distribution. In a similar manner but differently, the wealth Gini decreases at a lower rate, 23%, in the second economy. The fall in the share of the wealthiest and the rise in the share of the poorest in total wealth mainly contribute to the changes observed in the wealth distribution in both benchmark and standard economies. The fraction of wealth that belongs to the wealth- iest 1% is roughly halved in the new steady state as well as that of the top 5% and 10%. When the same experiment is conducted in an economy without entrepreneurs, the results are in the same direction but the percentage changes are much lower. The introduction of entrepreneurship as an additional motive of saving enables us to gen- erate a wealth distribution that very close matches the U.S. data, and thus, the effects of the policy alteration can be studied without facing the criticisms, that previous mod- els in the literature experienced, regarding the model’s lack to match the U.S. wealth 9 This peculiarity can be removed by using an overlapping generations model. 48 distribution. The social security system, a system designed to protect the low-income households against income and longevity risks, seems to create a more concentrated wealth distribution in favor of the wealthiest. Table 2.7: The Long-run Effects of the Policy Change on Income Distribution % of the income of the top Income 1% 5% 10% 20% 40% 60% Gini Data 17:50 32:80 43:10 58:00 78:00 90:50 0:553 Entrep. and SSS 15:14 28:93 39:10 56:24 76:05 87:20 0:501 Entrep. and no SSS 11:51 25:77 37:69 57:16 80:06 92:98 0:560 No Entrep. but SSS 2:97 13:56 25:55 44:03 67:87 82:89 0:370 No Entrep. and no SSS 3:07 14:67 28:36 48:61 74:74 89:86 0:468 * Income distribution data is taken from [24]. The income distributions in the two economies are presented by Table 2.7. The income distribution, as shown on the table, is fairly close to the one observed in the U.S. data. The income Gini, 0:501, that is generated by the model is very close to one in the data, 0:553. After the policy reform, the income Gini rises to 0:560, by 12%. The income Gini increases because more people are pushed to the bottom tail of the income distribution even though the shares of high-income households shrink. The effect of the loss of pension payments outweighs that of the lower shares of the top on the income distribution. The income Gini obtained in the standard model, 0:370, is much lower than the value in data. Nevertheless, the percentage increase in the income Gini in the second economy is 27%, more than twice as large as the change in the first economy. The low-income group loses a considerable share of their income in total which seriously increases the income inequality. The deteriorating effect of the policy reform on the income inequality in a world with entrepreneurs is much smaller than without them. In this sense, the presence of entrepreneurs in an economy, can somewhat lessen the 49 negative effects of the policy reform on the income distribution by providing the old with extra income through business activities. 2.5.4 Welfare Effects The pay-as-you-go social security system distorts the optimal consumption-saving behavior of every household by providing partial insurance against future shocks and taxing their labor income. In the absence of these taxes, households would be able to split the resources taken away from them between consumption and saving optimally thereby either getting more utility or obtaining extra income in the form of interest in the future. When investigating the welfare effects of the privatization, the expected util- ity of an unborn household is used as a unit of measure. This measure of welfare is computed and compared in the two steady states of the two model economies. Table 2.8: Welfare Effects of the Policy Change in the Long Run SSS No SSS CC (%) Expected Utility at Birth with Entrepreneurs 28:26 26:70 11:99% Expected Utility at Birth Without Entrepreneurs 29:17 26:82 18:26% * CC is the consumption compensation. Table 2.8 separately lists the steady-state values of this welfare measure in the two economies before and after the policy change. Expected utility at birth is simply taken as the expected utility of a young household since there is no age-dependency in the model economy. The corresponding consumption compensations 10 are also reported in the last column of the table. Consumption compensation is the necessary percentage 10 CC = " V NS V S 1 1 1 # whereV S andV NS are the expected value functions of the young with and without the social security, respectively. 50 change in the amount of consumption of a household and his descendants in every period before the policy switch in order for this household to have the same expected utility as in the final steady state of the same economy. In the absence of entrepreneurs, the compensation is found to be 18% reflecting a valuable welfare gain. The introduction of entrepreneurial activities into this basic model pulls this number down to 12%. The adverse effect of the policy reform on the entrepreneurial wealth and income through the rental rate and wage rate reduces the average consumption of the entrepreneurs creating a certain amount of welfare loss. This outcome is in line with the findings regarding the aggregate consumption (see Section 2.5.1). 2.6 Sensitivity Analysis In this section, a sensitivity analysis is performed regarding the coefficient of relative risk aversion,, and the shares of capital in the non-corporate sector,, and corporate sector, . The coefficient of relative risk aversion measures the relative strength of a household’s reaction against the risks. The higher this coefficient is, the more the household saves against future uncertainties. The parameter of the income share of capital,, determines the ratio of capital to labor given the corresponding factor prices. 2.6.1 Coefficient of Relative Risk Aversion, The unfunded social security system provides a partial insurance against the longevity and income risks, a household faces. The removal of such a system triggers a limited boom in the savings of the households, the amount of which is dependent on how risk averse they are. Since a wealthy household is highly likely to be an entrepreneur by starting off his own business if he realizes a non-zero efficiency shock, the value of the 51 coefficient of relative risk aversion plays an important role how entrepreneurs react to the social security reform and how this affects the economy overall. Thus, the persistence of the results derived in the previous section is analyzed as the the coefficient of relative risk aversion deviates from its benchmark value. is allowed to take two different values; 1 (period utility function reduces to the logarithmic form) and 2. A value of greater than 2 generates an interest rate that is either too close to zero or negative after the removal of the social security system in an economy with entrepreneurs. The maximum value of at which I was able to get a positive interest rate after the policy change was 2:15. For convenience, the values of above 2 are considered as extreme cases, and 2 is assumed to be the upper bound of the feasible choices for the parameter in the sensitivity analysis. Table 2.9: The Long-run Effects on the Non-corporate Firm Size, Percentage Change Following the Reform = 1:0 = 1:5 = 2:0 Average Firm Size 2 14% 35% 45% 3 11% 10% 25% 4 6% 6% 1% Overall 25% 24% 17% Maximum Firm Size 2 18% 29% 41% 3 18% 29% 41% 4 32% 28% 23% * Benchmark calibration. First, the changes in the average and maximum firm sizes in the non-corporate sector are studied for the values of mentioned in the previous paragraph, and the findings are reported in Table 2.9. The table gives the percentage changes in the corresponding firm size definitions when the economy is moving from the initial steady state with the public 52 pension system to the final steady state without it. When the efficiency specific firm sizes are considered, the percentage rise in both average and maximum firm sizes increases by the coefficient of relative risk aversion for 2 and 3 . For the highest efficiency level, 4 , the percentage fall in firm sizes seems to be inversely related to. The overall average of the firm sizes also decreases for the different values of in the new steady state. In this context, the benchmark conclusion about the firm sizes seems fairly robust for the given set of values of. However, it is worth to note that the fall in the overall average firm size is mostly due to the increasing fraction of entrepreneurs with low efficiencies rather than the decrease in the size with 4 . Table 2.10: The Long-run Effects of the Policy Change on Non-corporate Sector, Percentage Change after the Reform = 1:0 = 1:5 = 2:0 Ratio of Entrepreneurs 33% 39% 35% Wealth held by Entrepreneurs 1% 5% 8% Share of Entrepreneurs’ Wealth in Total 28% 36% 44% Share of Entrepreneurs’ Income in Total 3% 5% 9% Median Wealth Entrep.-to-Non-entrep. ratio 74% 75% 79% Non-Corporate Capital (K e ) 4% 11% 17% Non-Corporate Labor (H e ) 16% 21% 26% Non-Corporate Output (Y e ) 8% 9% 11% * Benchmark calibration. Table 2.10 summarizes further results on non-corporate sector. The fraction of entrepreneurs, following the elimination of the unfunded social security, significantly rises for each choice of listed on the table. The effect of the policy change on the the amount of wealth held by entrepreneurs is contingent upon the value of and it reverses for = 1:0. The effect reverses in case of logarithmic utility, because all of the most productive entrepreneurs are producing below the profit maximizing levels 53 without borrowing, and hence they obtain lower profit income on average after the priva- tization. This effect dominates the increase in the capital employed by the less efficient entrepreneurs. However, the share of entrepreneurs in both total wealth and income and the ratio of median wealth of entrepreneurs to that of non-entrepreneurs fall regardless of the value of. The results also reveal that the physical capital demanded by the non- corporate sector increases while the labor demand and aggregate output fall adjusting to the changes in the corresponding prices for all values of. Table 2.11: The Long-run Aggregate Effects, Percentage Change after the Removal of the SSS = 1:0 = 1:5 = 2:0 Entrep No Entrep Entrep No Entrep Entrep No Entrep K 37% 37% 63% 71% 95% 115% Y 9% 12% 14% 21% 19% 32% C 6% 11% 8% 18% 10% 25% K Y 26% 22% 44% 41% 64% 63% * Benchmark calibration. Next, Table 2.11 reports the the sensitivity results for the macroeconomic aggregates. The increases in the capital stock, aggregate output, and consumption seem very robust to the changes in the value of . The percentage increases in the aggregate output and consumption still stay very low in an economy with entrepreneurs when compared to the standard model. Especially, the change in the aggregate consumption without entrepreneurs is at least 85% higher than the one with entrepreneurs for the values of that are considered here. The presence of entrepreneurs lowers the positive effect of the privatization on aggregate output and aggregate consumption because of the lower entrepreneurial profit levels in the latter steady state of the economy. 54 Table 2.12: Wealth and Income Distribution, = 1:0 = 1:5 = 2:0 SSS No SSS SSS No SSS SSS No SSS Wealth Gini 0:800 0:574 0:807 0:521 0:803 0:477 Share of top 1% 26:92% 14:89% 30:47% 13:36% 30:57% 10:91% Share of lowest 40% 00:91% 08:41% 00:97% 10:71% 01:11% 12:49% Income Gini 0:493 0:556 0:501 0:560 0:506 0:567 Share of top 1% 13:48% 11:24% 15:14% 11:51% 15:23% 10:57% Share of lowest 40% 13:02% 07:24% 12:80% 07:02% 12:80% 06:58% * Benchmark calibration. According to Table 2.12, the wealth Gini is significantly reduced at all values of in the new steady state indicating a less concentrated wealth distribution. The share of the wealthiest 1% is observed to fall regardless of the value of leading to a more equal distribution of wealth. Another observation that greatly contributes to the reduction in the wealth inequality is the huge jump in the wealth of the poorest which is also observed for all specifications of . These results strongly suggest that the changes related to the wealth distribution are not sensitive to the value of. On the other hand, the privatization considerably increases the income inequality reflected by a significant increase in income Gini for all values of. This can primarily be attributed to the big fall in the share of the bottom 40% in total income after the removal. This movement is also robust to the changes in the coefficient of relative risk aversion. Similar conclusions are reached when the effects of the reform on the welfare are taken into account. Table 2.13 exhibits the percentage change in consumption compen- sation corresponding to each in both benchmark and standard economies. A lower compensation is required in an economy with entrepreneurs than the one without them for all values of. Consumption compensations are higher for the higher values of in 55 both economies. However, the difference between two economies become more signif- icant as the value of gets higher. Specifically, the consumption compensation is 35% and 77% higher without entrepreneurs for = 1 and 2, respectively. Table 2.13: Consumption Compensation, = 1:0 = 1:5 = 2:0 CC with Entrep 9:75% 11:99% 13:20% CC Without Entrep 13:19% 18:26% 23:40% * Benchmark calibration. 2.6.2 Share of Capital, The income share of capital in the non-corporate sector is determined byu 1 = e . In the benchmark calibration, e is set equal to, the share of capital in the corporate sec- tor, following the literature on entrepreneurship. In this part, this assumption is relaxed in two directions. First, the corporate share is fixed at the benchmark value and e is allowed to take two additional values, 0:30 and 0:42. Second, the assumption of both ’s having the same value is unchanged, but quantitative results for 2f0:33; 0:42g are also obtained. The interest rate in the steady state without unfunded social security becomes negative if< 0:33. So, it is not allowed to take values lower than this number even though e takes a lower value in the first case. The first table here, Table 2.14, shows how firm sizes change after privatization for new specifications of ’s. The benchmark results concerning whether the firm sizes increase or decrease in the new steady state of the economy are robust to the changes in the capital shares in both sectors. Nonetheless, the magnitude of change varies across different specifications. For instance, the percentage fall in the maximum firm size with 56 Table 2.14: The Long-run Effects on the Non-corporate Firm Size, Percentage Change Following the Reform e = 0:30 e = 0:36 e = 0:42 = 0:33 = 0:42 Average Firm Size 2 22% 35% 43% 42% 20% 3 10% 10% 7% 14% 10% 4 7% 6% 2% 6% 4% Overall 22% 24% 19% 24% 19% Maximum Firm Size 2 8% 29% 60% 34% 23% 3 8% 29% 60% 34% 23% 4 41% 28% 7% 34% 19% * Benchmark calibration. ** = 0:36 ande6= in the first three columns. ***e = holds in the last two columns. 4 is inversely related to e when is fixed at its benchmark value or to when both are identical. This highlights the fact that the values of the share parameters significantly affects how much firm sizes adjust after privatization, but they do not alter the direction of the change. In this sense the benchmark results are very robust to the value of the parameters of capital shares in both sectors. Table 2.15: The Long-run Effects of the Policy Change on Non-corporate Sector, Percentage Change after the Reform e = 0:30 e = 0:36 e = 0:42 = 0:33 = 0:42 Ratio of Entrepreneurs 31% 39% 36% 43% 27% Wealth held by Entrepreneurs 0% 5% 8% 6% 1% Share of Entrepreneurs’ Wealth in Total 43% 36% 32% 38% 35% Share of Entrepreneurs’ Income in Total 7% 5% 3% 4% 9% Median Wealth Ratio 79% 75% 73% 77% 75% Non-Corporate Capital (Ke) 6% 11% 16% 14% 7% Non-Corporate Labor (He) 24% 21% 18% 22% 20% Non-Corporate Output (Ye) 13% 9% 4% 10% 8% * Benchmark calibration. More results on the non-corporate sector are listed by Table 2.15 for the same set of parameter values. The benchmark findings for the variables listed in this table, except 57 the wealth held by the entrepreneurs, are obviously robust to the different choices of share parameters. The fraction of entrepreneurs significantly increases while the share of entrepreneurs in income and wealth, and the ratio of entrepreneur’s median wealth to that of the rest decrease after the privatization for all parameter specifications con- sidered. The level of entrepreneurial wealth is negatively affected by the privatization via the the lower rates of profits in the new steady state and hence, it even remains unchanged when e = 0:30 and = 0:36. The non-corporate capital demand is observed to go up at significantly non-zero rates for the values of ’s shown on the table. On the contrary, the total labor demand in non-corporate sector always decreases regardless of the values of’s, and there is an inverse relationship between the percent- age change in it and the share of capital. Similarly, the fall in the non-corporate output is robust to the changes in the share parameters. Table 2.16: The Long-run Aggregate Effects, Percentage Change after the Removal of the SSS, = 0:33 = 0:36 = 0:42 Entrep No Entrep Entrep No Entrep Entrep No Entrep K 71% 78% 63% 71% 52% 59% Y 14% 21% 14% 21% 14% 21% C 6% 16% 8% 18% 12% 21% e = 0:30 e = 0:42 K 75% 58% Y 14% 15% C 6% 11% * Benchmark calibration. As shown in Table 2.16, aggregate capital, output, and consumption significantly and robustly increase for e =2f0:33; 0:42g, results of which are listed in the upper half of the table, and = 0:36 plus e 2f0:30; 0:42g, results shown in the lower half. The benchmark observation that the percentage increases in aggregate consumption and 58 output with entrepreneurs are notably lower than those in an economy without them. When the values of both share parameters are changed simultaneously maintaining their equality, percentage increase in the aggregate consumption is proportional to the com- mon value of share parameters. This is also observed in the other experiment where the corporate share is fixed at its benchmark value and non-corporate share is allowed to vary. A similar observation can be reached for the stock of physical capital, but the relationship is inverse. Table 2.17: Wealth and Income Distribution, e = 0:30 e = 0:36 e = 0:42 SSS No SSS SSS No SSS SSS No SSS Wealth Gini 0:804 0:502 0:807 0:521 0:807 0:542 Share of the top 1% 29:23% 11:56% 30:47% 13:36% 31:07% 14:95% Income Gini 0:490 0:562 0:501 0:560 0:513 0:564 Share of the top 1% 13:81% 10:25% 15:14% 11:51% 16:05% 12:68% = 0:33 = 0:42 Wealth Gini 0:803 0:506 0:806 0:545 Share of the top 1% 29:87% 12:28% 30:40% 15:04% Income Gini 0:491 0:563 0:521 0:556 Share of the top 1% 14:23% 10:74% 16:50% 12:71% * Benchmark calibration. The results of both experiments regarding the wealth and income distribution in an economy with entrepreneurs are illustrated by Table 2.17. For all parameter specifi- cations that are shown on this table, the wealth Gini significantly decreases after the privatization while the income Gini increases. Similarly, the share of the wealthiest 1% in total wealth is at least halved after the removal of the unfunded social security con- tributing the fall in the wealth Gini. As an additional information that is not on the table, the fraction of the households with zero wealth becomes nearly zero in the new steady state in all of the cases considered. On the other hand, the share of the richest 1% in total 59 income is also observed to fall by considerable amounts. Since its effect on the income Gini is outperformed by the decrease in the share of the poorest, the income Gini is found to fall in all cases. To summarize these observation, it can confidently be stated that the removal of unfunded social security robustly improves the wealth equality while deepening the problem of income inequality in the long-run. Table 2.18: Consumption Compensations, e = 0:30 e = 0:36 e = 0:42 = 0:33 = 0:42 CC with Entrep 6:24% 11:99% 13:20% 7:03% 21:49% CC Without Entrep 18:26% 18:26% 18:26% 14:02% 24:81% % 192% 52% 38% 99% 16% * Benchmark calibration. The last table, Table 2.18, presents the effects of the policy alteration upon the wel- fare as measured by the consumption compensations for the given values of’s. When is fixed at its benchmark value and e is relaxed, the required consumption com- pensation still remains below the one without entrepreneurs indicating the robustness of the benchmark conclusion. But, the difference between the compensation amounts becomes larger as the values of e gets smaller. Particularly, the consumption compen- sation without entrepreneurs is almost three times larger than the one with them, when e = 0:30. When both’s are relaxed, the consumption compensation in the standard model is at least 16% higher than its counterpart in the benchmark economy . An inverse relationship between consumption compensation and the value of continues to exist. 60 2.7 Conclusion This paper mainly examines the effects of eliminating the unfunded social security sys- tem on key macroeconomic aggregates, welfare, income and wealth distributions and deviates from the existing literature by allowing occupational heterogeneity. The inclu- sion of entrepreneurship into an infinite horizon life-cycle model brings in an additional saving motive for households. The results of the benchmark calibration indicate that aggregate capital, output and consumption increase at positive rates, but the percentage changes in aggregate output and consumption are significantly lower than those reported in economies without entrepreneurs. The subsequent sensitivity analysis discloses that this conclusion is robust to the changes in relevant parameters of the model only for aggregate output and consumption. In all of the different parameter choices, the non- corporate output is observed to fall significantly and, consequently, to bring about a lower rate of increase in the aggregate output than what it would be otherwise. The findings about the occupational choice and the behavior of the entrepreneurs in response to the removal of the public pension are new to the literature. Even though the occupational distribution changes in favor of the entrepreneurs, the share of entrepreneurs in the total wealth is almost halved in the new steady state of the model economy. The share of entrepreneurs in total income notably decreases either. Like- wise, average firm size, capital demand, and total output in the non-corporate sector are shown to go down while the capital demand in this sector increases at a relatively low rate comparing to the corporate sector. In the light of those findings, entrepreneurship, an additional saving incentive, is observed to limit the benefits of the privatization in case of aggregate consumption and output. The benchmark model successfully matches the U.S. wealth distribution by generat- ing extremely wealthy households by introducing occupational heterogeneity. The most 61 important finding of this paper is that the elimination of the unfunded social security generates a less concentrated wealth distribution by increasing the average wealth and decreasing the share of the wealthiest in total wealth. It is interesting that a system that is designed to insure households with low income against the future uncertainties pro- duces a wealth distribution in favor of the wealthiest. Furthermore, the model generates an income Gini that is very close to the one in the U.S. data, though it is not intended. The income Gini in the economy with entrepreneurs increases after the policy change but at a rate that is much lower than the rate at which it increases without entrepreneurs. The positive effect of the policy change on the wealth equality is greater in the presence of entrepreneurs, while its deteriorating effect on the income equality is smaller with them. Finally, the policy reform removes the social security taxes and benefits that dis- tort the optimal consumption-saving decisions of households resulting in higher income and consumption on average. The rise in the aggregate consumption is lower with entrepreneurs in the benchmark model because they significantly lose income in total compared to the initial steady state. Consequently the associated welfare gain is found to be higher in an economy without entrepreneurs than what it would be with them. Thus, a model that does exclude the entrepreneurial dynamics in an economy may over- estimate the welfare benefits associated with the removal of the unfunded social security system. The change in the welfare measure, consumption compensation, in an economy with only workers is 52% higher than the benchmark economy. 62 Chapter 3 The Pure Life Cycle Overlapping Generations Model 3.1 Introduction The unfunded social security system is a mechanism through which especially the peo- ple who have very low income or lack the foresight to save are partially insured against mortality, lifespan, and old-age income shocks. This insurance benefit is provided at the cost of distorting the optimal saving and labor supply decisions. Since it transfers a particular fraction of the productive resources which are at the disposable of the working population to the retired, it has serious welfare effects for both groups of people as well as aggregate effects on the economy overall. The benefits and the costs of the unfunded social security have been a vital subject for many researchers. However, very little or no emphasis has been given to the effects of the unfunded social security on the wealth distribution. There are mainly two types of modeling, life-cycle and dynastic, that are used in the literature to study the privatization of the unfunded social security. The dynastic models with two-sided altruism, such as [11], and [12], emphasize the importance of the family insurance in assessing the effects of eliminating the unfunded social security. On the other hand, the pure life-cycle models, such as [2], [19], [16], and [7], mostly assume away the other incentives such as bequests and focuses on the role of the social security 63 as an insurance mechanism against future uncertainties. Event though this paper adopts a pure life-cycle model, it obviously differs from both types of models by introducing occupational heterogeneity, more specifically entrepreneurship as an alternative incen- tive mechanism for saving. By doing so, the model successfully matches the wealth and income distribution observed in the U.S. data as other papers such as [23], [4], and [20]. In such a model, the effects of the privatization on the wealth and income distribution can be studied in more detail and by more confidence. New to the literature, its effects on the occupational choice and the behavior of the business owners can be analyzed. Moreover, the robustness of the previous results on the key macroeconomic aggregates and welfare can be checked in the presence of entrepreneurial incentives for saving. The model of this paper is simply a standard pure life-cycle overlapping generations (OG) model that incorporates the entrepreneurship. In this sense, this is the first OG model in the literature that incorporates the entrepreneurship. Households are heteroge- nous with respect to labor productivity and entrepreneurial efficiency. The presence of entrepreneurial opportunities creates another incentive for saving, other than insurance purposes, by offering possibility of very high income in the form of profits when they have a productive entrepreneurial project. Since the borrowing of the entrepreneurs is limited by their wealth, households have to increase their savings in order to be able to take advantage of highly productive entrepreneurial opportunities. They keep accu- mulating wealth as long as they can increase their profits by employing more physical capital. Finally, the household income is assumed to be taxed progressively following [27] and [14]. The quantitative findings exhibit that the fraction of entrepreneurs increases by 4% in the steady state after the policy change. The main reason for the rise in the num- ber of entrepreneurs is the expansion in the wealth accumulated by households in an 64 effort to compensate for the partial insurance that used to be provided by the social security. To be more specific, only the number of entrepreneurs in the cohort of age 24 and older increases, while the effect for the younger cohorts is reversed. The privati- zation of the unfunded social security changes the distribution of entrepreneurs across cohorts in the favor of the older ages. The increase in the fraction of entrepreneurs is not robust to the choice of the risk aversion coefficient. Meanwhile, non-corporate capital demand increases by 6%, while the non-corporate output and labor demand are reduced by 7% and 15%, respectively. This can be interpreted as a big loss of income for the entrepreneurs especially when their number is higher in the final steady state. The benchmark findings reveal that the aggregate capital, output, and consumption climb up by 39%, 8%, and 1% which are in line with some of the previous papers. For instance, [2] and [16] report 24% and 40% increases in the capital stock, respectively. In the version of the benchmark model without entrepreneurs, the standard OG model, those percentages are observed to be 36%, 12%, and 9%, respectively. The percentage change in aggregate output is 50% higher with the standard model. For the aggregate consumption, the percentage increase in the standard model is nine times bigger than the benchmark model as result of the fall in the entrepreneurial income. It even becomes negative when the share of capital in the non-corporate sector is set to 0:30. This differ- ence is also reflected in the consumption compensation that is percentage change in the consumption levels of the initial economy in all periods and contingencies in order for an unborn household to be indifferent between two steady states of the same economy. The consumption compensation is 10% and 21% for the benchmark and standard mod- els, respectively. Similarly, [7], [12], and [13] show that an unborn household would like to be born in an economy without social security. 65 The benchmark model generates a wealth Gini of 0:765 with social security. After the privatization, it becomes 0:684 implying a more equal wealth distribution. [13] and [11] also report a more equal wealth distribution without the social security. On the contrary, [1] argues that the introduction of the unfunded social security causes a less concentrated wealth distribution. Even though it is not intended, the model is also successful in matching the income distribution observed in the U.S. data. The model generated income Gini is 0:533 which is very close to the one in the U.S. data, 0:553. The removal of the unfunded social security pushes up the income Gini to 0:563 pointing to a more unequal income distribution. In the remainder of the paper, Section 3.2 explains the model economy, Section 3.3 defines a stationary competitive equilibrium, the benchmark calibration of the model parameters are done in Section 3.4, the quantitative results are presented in Section 3.5, Section 3.6 contains a thorough sensitivity analysis regarding the relevant parameters, and finally, Section 3.7 lists the concluding remarks. 3.2 The Model Economy A standard overlapping generations (OG) model is altered to include occupational het- erogeneity by introducing the entrepreneurship as an alternative, yet very effective occupation. It is similar to models developed by [23], [4], and [20] in modeling the entrepreneurship. 3.2.1 Households There is a continuum of overlapping generations of households of measure one in the model economy at a given time. Households in this economy may live up to a maximum 66 age ofi m depending on survival. The probability of survival from the current period to the next is contingent upon the current age. In order for the cohort shares to be stationary, the survival probabilities are assumed to be time-independent and a constant population growth is assumed. Moreover, households are assumed to get retired automatically at the age ofi r unless they choose to run their own businesses. The survival probability of a household from agei toi+1 is denoted bys i . Constant cohort shares,f i g im i=1 , are computed by using these probabilities. Specifically, the share of cohort 1 is given by 1 = ( 1 + im X i=1 Q i1 j=1 s j n i1 ) 1 (3.1) wheren is the constant population growth factor. Accordingly, the stationary shares of the other cohorts are given by the following expression: i = i1 s i n (3.2) fori = 2;:::;i m . Each household is endowed with h units of time which is inelastically supplied into the market. However, households are heterogenous with respect to their labor abilities. Labor efficiency or labor productivity per unit of work time of a household,l, is assumed to follow N l -state Markov process. The state space of the labor efficiency process is given byL =fl 1 ;l 2 ;:::;l N l g. Labor productivity is drawn from the set, L, according to the conditional probabilities that are defined asp(l i+1 ;l i ) =prob(l i+1 =l i ) wherel i+1 is the next period’s value. But, a newborn household picks a value from this set in conjunction with the corresponding unconditional probabilities. A retired household is assumed to have no labor productivity and, though, can not supply any labor into the 67 market. In addition to this stochastic component of labor supply, the labor efficiency of a young household is assumed to vary with his age and the process is identical for all households. This process is denoted byf i g ir1 i=1 . Households also differ from each other regarding their ability to run their own busi- nesses efficiently. The entrepreneurial efficiency is a key element characterizing the productivity of the associated business. Similar to the labor ability, the entrepreneurial factor productivity, , realizes a value from the set, T =f 1 ; 2 ;:::; N g, according to the conditional probabilities denoted by p( i+1 ; i ) = prob( i+1 = i ). A household of cohort 1 draws his entrepreneurial efficiency from the same set but along with the corresponding unconditional probabilities. If an old entrepreneur decides to get retired, he foregoes this opportunity forever and never realizes another entrepreneurial shock in the remaining years of his lifetime. Accordingly, his entrepreneurial state is set to 1 , the state in which households have zero entrepreneurial productivity and destined to be worker. An old entrepreneur is only allowed to supply his labor endowments into his own business at the market rate of wages and his labor efficiency per unit of work time is set to unity for simplicity. A worker inelastically supplies his labor into both corporate and entrepreneurial sectors in return for a wage per efficiency unit of labor. The market wage rate does not vary across sectors. On the other hand, an entrepreneur can only supply his labor into his own business and does manage it at the same time. He can always hire more labor at the prevailing wage rate in the market when his business demands labor in excess of his own endowments. This assumption makes entrepreneurship extremely attractive when the entrepreneurial idea that a household possesses is noticeably productive and he can get his full labor income in addition to the profit. 68 3.2.2 Production Technology The production in this economy is conducted by the aforementioned two sectors; corpo- rate and entrepreneurial sectors. The second one is also called as non-corporate sector. Corporate sector consists of many competitive firms while the non-corporate sector con- sists of relatively small-sized firms owned and operated by entrepreneurs. Corporate Sector : All of the corporate firms have access to the same technology which is represented by a standard Cobb-Douglas production function: F (K c;t ;H c;t ) =K c;t (A c;t H c;t ) (1) (3.3) where K c;t and H c;t are the total capital and labor employed in the corporate sector, respectively,A c;t is the total factor productivity at time t, and is the income share of the capital. A c;t is assumed to grow at the constant gross rate of g. The steady-state equivalent of this production function is given by F (K c ;H c ) =K c H (1) c : (3.4) Capital is assumed to depreciate at a constant rate, . The market return on physical capital and the wage rate are settled in this sector by the forces of supply and demand. Since this specific technology exhibits constant returns to scale, both the aggregate and the firm-level profits in the corporate sector are zero. Non-corporate Sector : The production technology in the entrepreneurial sector is somewhat similar to the corporate technology. This production technology combines 69 capital and labor together with the entrepreneurial productivity and produces the only physical good in the economy. The technology in this sector is characterized by f(k;h;) =k u 1 h u 2 (3.5) where u 1 > 0 and u 2 > 0 are the income shares of capital and labor, respectively. u 1 andu 2 are constant fraction,, of the income shares of the capital and labor in the corporate sector 1 . The profit or the income share of the entrepreneur is then given by (1) where = (u 1 +u 2 ). (1) is assumed to be strictly positive so that the technology exhibits decreasing returns to scale such that entrepreneurs enjoy non-zero levels of profit. The income shares of capital and labor do not vary across entrepreneurs. Nonetheless, entrepreneurs are heterogenous in terms of profit and firm size because entrepreneurial productivity varies across entrepreneurs and they are borrowing con- strained. The capital used in the entrepreneurial sector depreciates at the same constant rate of as the corporate capital does. 3.2.3 Financial Intermediaries The intermediary sector finances the projects in both corporate and non-corporate sec- tors by transferring the funds from the households to the firms. Households except entrepreneurs are completely borrowing constrained and can not borrow from the finan- cial institutions in the economy. Households earn interest income per unit of funds that they transfer to the production sectors via the intermediary sector. The rate of return on saving is assumed to be equal to the risk free rate of return on capital,r. 1 u 1 = andu 2 = (1) 70 Firms in the corporate sector are allowed to borrow as much as they need at the risk free rate of interest. Unlike corporate firms, an entrepreneur can only borrow up to an amount that depends on his leverage ratio and his current asset holdings. The leverage ratio for an entrepreneur is denoted by and constant across households. The entrepreneur pays the risk-free interest rate as well as a fixed cost of intermediation,, per unit of funds borrowed in excess of the value of his assets to the financial institutions. This cost is neither consumed nor invested by the financial institutions. It is just taken away from the economy. An entrepreneur with asset holdings,a, pays the rate,r +, to the financial institutions per unit of resources borrowed in excess ofa and can borrow up toa . 3.2.4 Role of the Government Social Security System There is an unfunded social security system that is designed to mimic certain features of the U.S. social security system. The system is unfunded in the sense that the cost of the pension transfers made to the current retired is financed by the taxes collected from the current workers. The government is responsible for setting the tax rate, s , that balances the social security budget. Only the labor income is subject to the social security taxation regardless of the occupation. The part of the labor income that is above y m s is exempt from social security taxation. Thus, the social security tax that a household pays is calculated by T s (y l ) = s minfy l ;y m s g (3.6) wherey l is the household’s income that is subject to social security taxation. 71 The benefit of a household who reaches the retirement age,i r , is calculated by using a piecewise linear function: b ir = ( e ir1 ) (3.7) where e ir1 is the average lifetime labor earnings at the end of age ofi r 1 in the steady state of the model economy 2 . The average labor earnings at agei is given by e ir1 = e ir2 (i r 2) +wl ir1 ir1 h i r 1 (3.8) where h is the time endowment of a worker and ir1 is the age dependent efficiency fac- tor. The second term in the numerator is replaced with the entrepreneur’s labor income when the household chooses to be an entrepreneur. The amount of benefit is assumed to remain constant throughout the retirement once it is calculated. The age-dependent benefit formula in steady state is shown below: b i+1 = b i g i =i r ;:::;i im1 (3.9) wherei m is the maximum possible age. Government Purchases and Taxation Besides the unfunded social security system, the government in this model purchases an exogenously determined amount of goods and immediately consumes them up. The level of government purchases,G, is assumed to be a constant fraction of the aggregate 2 The explicit form of is given in Section 3.4.5 72 output. The cost of government purchases is financed by the tax revenue from consump- tion and income. Consumption expenditures of households are taxed at the constant rate of c . Those taxes are also included in the model, because knowing the marginal effects of the unfunded social security on household behavior and aggregate economy might be more realistic and intuitive when replicating a real economy. The household income is not only taxed proportionally but also progressively so as to take into account its effect on the wealth distribution. The progressiveness of income taxes is supposed to reduce the inequality in the wealth distribution. The earnings that is subject to the income taxation comprise of labor income, entrepreneurial profit, and interest income. The pension payments to the retired are either partly taxable or not tax- able. Only a fraction,f o b , of the social security benefit is subject to the income taxation if the total income of the household from all other sources together with this fraction exceedsy o b . Otherwise, pension payments are exempt from income taxation. The progressive income tax formula that is developed by [27] is adopted in order to capture the degree of progressiveness the U.S. income taxation. The following progres- sive formula is applied when calculating the income tax: t(y tx ) = 0 h y tx ( 1 +y 2 tx ) 1 2 i (3.10) where y tx is the household’s total taxable income and 0 ; 1 ; 2 > 0 are the constant parameters of the formula. The total income tax that a household with taxable income, y tx , has to pay is calculated by the following generalized progressive tax formula: T y (y tx ) =t(y tx ) + 3 y tx (3.11) 73 where 3 is the constant tax rate in the formula signifying the non-progressive portion of the income taxation. 3.2.5 Profit Maximization of the Firms Corporate Firms A typical firm in the corporate sector solves the following maximization problem in the steady state after taking the gross interest rate, (R) and the wage rate (w) as given: max Kc;Hc>0 K c H 1 c + (1)K c RK c wH c (3.12) whereK c andH c are the capital and labor demand of the firm, respectively. The gross output of the firm is the sum of the newly produced goods and the capital remaining after the production process. A certain amount of the capital used in the production depreciates during the process. A constant fraction, , of the capital entering into the production is used up during the process and the cost of depreciation is paid by the firm. Entrepreneurial Firms The profit maximization problem of an entrepreneurial firm is similar to that of a cor- porate firm. Unlike corporate firms, the non-corporate firms are not allowed to borrow as much as they need. The maximum amount of capital that an entrepreneur can borrow is determined by his asset holdings. Specifically, an entrepreneur with asset holdings of a can borrow resources up to (1 +)a and pays an extra cost of borrowing,, for the amounts exceeding his asset holdings. The maximization problem of an entrepreneur with (a;) is formulated as 74 (a;) = max ( 0k (1+)a h 0 ) n k u 1 h u 2 ~ R(ka)Rawh + (1)k o (3.13) and ~ R = 8 > < > : R + if k>a R if ka 9 > = > ; (3.14) where is the extra cost of borrowing for entrepreneurs,k is the entrepreneur’s capital demand andh is the entrepreneur’s labor demand. 3.2.6 Utility Maximization of the Household When defining the preferences of a household over the consumption and saving, six types of value functions are used. Those are denoted byV r (:;:;:),V oe (:;:;:;:),V o (:;:;:; ), V w (:;:;:;:;:),V ye (:;:;:), andV y (:;:;:); more specifically, those are the value function of the retired, the old entrepreneur, the old before occupational choice, the worker, the young entrepreneur, and the young before occupational choice, respectively. In the fol- lowing two subsections, the corresponding utility maximization problems are presented in more detail. The Problem of the Old An old household is not allowed to be entrepreneur once he chooses to get retired. This assumption is essential in obtaining a low mass of entrepreneurs in the right tail of the age distribution. The occupational decision of an old entrepreneur involves choosing either to continue managing his own business or to get retired for his remaining years. 75 All old households are assumed to receive pension payments regardless of their occupa- tional status. The retired have only three state variables, i r =fi;a i ;e i g; age, wealth transferred from the previous period and average lifetime labor earnings, respectively. The corre- sponding utility maximization problem of a retiree is formulated as follows V r ( i r ) = max c i ;a i+1 0 n u(c i ) + ~ s i V r ( i+1 r ) o s:t: (1 + c )c i +ga i+1 = Rq +a i +y i T y (y tx;i ) y i = (R 1)a i +b i y tx;i = ( y i (1f o b )b i if (y i (1f o b )b i )y o b (R 1)a i otherwise ) where ~ = g 1 is the adjusted time discount factor, q is the amount of accidental bequests received, y o b is the amount of taxable income below which the pension pay- ments are tax-free,f o b is the fraction of pension transfers that enters the calculation of taxable income, a i+1 denotes the wealth being transferred to the next period, b i is the social security benefits received at age i, and s i is the probability that the household survives from agei toi + 1. On the other hand, an old entrepreneur has four state variables, i oe =fi;a i ; i ;e i g; beginning of period asset holdings, entrepreneurial efficiency, and average lifetime labor 76 earnings, respectively. A typical old entrepreneur solves the following maximization problem: V oe ( i oe ) = max c i ;a i+1 0 n u(c i ) + ~ s i E i+1 = iV o ( i+1 o ) o s:t: (1 + c )c i +ga i+1 = Rq +a i +y i T y (y tx;i )T s (y e i ) y i = (R 1)a i +b i +(a i ; i ) +y e i y e i = w minfh e i ; hg y tx;i = ( y i (1f o b )b i if y i (1f o b )b i >y o b y i b i otherwise ) wherey e i is the total income of the household from entrepreneurial activities,h e i is the labor demand by the entrepreneur’s firm, h is the time endowment of the household, and E i+1 = i is the conditional expectation operator. Here, it is implicitly assumed that the labor efficiency of an old entrepreneur in his own business is unity. The state of average lifetime earnings,e, of an old household is determined at the age ofi r and is unaltered in the rest of his life. Hence,e i =e ir fori =i r ;:::;i m . The occupational decision is done at the very beginning of every period by the house- holds after entrepreneurial opportunities are observed and realized. The household has four state variables, i o =fi;a i ; i ;e i g. The value function of an old household before occupational choice is given by V o (i;a i ; i ;e i ) = ( V r ( i r ) if i = 1 maxfV r ( i r );V oe ( i oe )g otherwise ) : (3.15) If an entrepreneur realizes the lowest efficiency shock, 1 , he optimally decides to get retired. Occupational decision is made at the very beginning of each period. 77 The Problem of the Young A young household also chooses between being a worker and managing his own firm. He realizes entrepreneurial ability shock at the beginning of every period conditional on his previous efficiency and independent from his previous occupation. In other words, an entrepreneur and a worker with the same level of entrepreneurial productivity have identical probabilities of drawing a particular in the next period. A household who chooses to be a worker has five state variables, i y = fi;a i ; i ;l i ;e i g. The decision problem of a worker is represented by V w i y = max c i ;a i+1 0 n u(c i ) + ~ s i E i+1 = iE l i+1 =l iV y i+1 y o s:t: (1 + c )c i +ga i+1 = Rq +a i +y i T y (y tx;i )T s (y w i ) y i = (R 1)a i +y w i y w i = w i l i h y tx;i = y i where i is the age dependent labor efficiency, E l i+1 =l i is the conditional expectation operator with respect to labor efficiency. A young entrepreneur has the same set of state variables, i y . The value function of a young entrepreneur is given by V ye i y = max c i ;a i+1 0 n u(c i ) + ~ s i E i+1 = iE l i+1 =l iV y i+1 y o s:t: (1 + c )c i +ga i+1 = Rq +a i +y i T y (y tx;i )T s (y e i ) y i = (R 1)a i +(a i ; i ) +y e i y e i = w minfh e i ; i l i hg y tx;i = y i : The young makes an occupational decision very early in a given period after observ- ing his labor and entrepreneurial shocks. The set of state variables of a young household 78 before occupational choice consists offi;a i ; i ;l i ;e i g. The corresponding value func- tion is given as follows V y i y = ( V w i y if i = 1 max V w i y ;V ye i y otherwise ) : (3.16) 3.3 Stationary Competitive Equilibrium The state vector of a household before occupational choice,x = (a;;l;e), specifies asset holdings, entrepreneurial efficiency, labor efficiency, and average lifetime earn- ings of the household anda2R,2T,l2L,e2R whereR =fR + [f0gg, andx2 S =RTLR. Similarly but slightly differently, ~ x = (a;;l;e; o)2 ~ S is the state vector of a household just after occupational choice and o2O =f young entrepreneur, worker, old entrepreneur, retiredg, and ~ x2 ~ S =RTLRO. A stationary com- petitive equilibrium is a set of pricesfR;wg, value functionsfV i (x); ~ V i ( ~ x)g im i=1 , allo- cations n a i+1 ( ~ x);c i ( ~ x);k i ( ~ x);h i ( ~ x);o i (x) o im i=1 , a government tax system,f s ; 3 g, social security transfers,fb i ( ~ x)g im i=ir , aggregate demandsfK c ;H c ;K e ;H e g wheree andc stand for entrepreneurial and corporate sectors, respectively, the stationary distribution of the households over the state space,f i ( ~ x)g im i=1 such that: 1. Given the prices, government tax system and transfer payments, allocations solve the maximization problem of the household. 2. The prices are given by R = K c H c 1 + (1) w = (1) K c H c 79 3. The amount of accidental bequests, q, is given by nq = P i; ~ x a i+1 ( ~ x) i ( ~ x)n 1i 4. Capital and labor markets clear K c + X i; ~ x k i ( ~ x) i ( ~ x)n 1i = X i; ~ x a i ( ~ x) i ( ~ x)n 1i +q =K H c + X i; ~ x h i ( ~ x) i ( ~ x)n 1i = X i; ~ x h s i ( ~ x) i ( ~ x)n 1i =H whereh s i ( ~ x) is the supply of the labor by a household of agei and given by h s i ( ~ x) = 8 > > > < > > > : minfh i ( ~ x); i l i hg if youngentrepreneur i l i h if worker minfh i ( ~ x); hg if oldentrepreneur 0 if retiree 9 > > > = > > > ; . 5. The intermediary sector is perfectly competitive and financial institutions make zero profit. 6. The social security system is self-financing: P im i=ir P ~ x b i ( ~ x) i ( ~ x) = P i; ~ x T s (y l;i ( ~ x)) i ( ~ x) wherey l;i refers to the corresponding labor income. 7. The government budget is balanced G = P i; ~ x n c c i ( ~ x)n 1i +T y (y tx;i ( ~ x)) o i ( ~ x) 80 G = c C + P i; ~ x T y (y tx;i ( ~ x)) i ( ~ x) where C is the aggregate consumption. 8. The distribution of households over the state ~ x satisfies i+1 ( ~ x 0 ) = P ~ x i ( ~ x)s i P ~ x 0 = ~ x i = 1;:::;i m 1 whereP ~ x 0 = ~ x is the matrix of transition probabilities. 9. The good market clears C +G +K + P i; ~ x k i ( ~ x)a i ( ~ x) i ( ~ x)n 1i =K c H 1 c + P i; ~ x y e i ( ~ x) i ( ~ x)n 1i 3.4 Benchmark Calibration of the Model This section illustrates the calibration of the parameters that characterize the demograph- ics and preferences of the households, intermediary sector, technology, labor process, and the government sector. Table 3.2 summarizes the calibrated parameters at the end of the section. 3.4.1 Demographics and Preference Parameters One period in the model corresponds to one year. The households are assumed to start living on their own at the age of 21 which corresponds to the age of 1 in the model economy. They are allowed to work until the age of 66 at which they automatically retire. So, the mandatory retirement age,i r , in the model becomes 46. The households younger thani r are considered to be young and the others are called as old. Depending 81 on survival, a household can live up to 80 periods or years. Following this, the maximum possible age,i m , is set to 80. The conditional survival probabilities are taken from the Social Security Administration (SSA) for the cohort of 1950. The constant population growth rate in the model is calibrated to 1:2%, the average of the annual population growth rate in the U.S. economy. Then, the population growth factor,n, becomes 1:012. The period utility function of a household is a standard constant-elasticity-of- substitution (CES) utility function and given by u(c i ) = c 1 i 1 (3.17) where is the relative risk aversion coefficient. This parameter is set to 1:5, a number that is used by many such as [4]. Following [23], the subjective time discount factor, is chosen so that the ratio of capital to output in the steady state equilibrium is 2:66, the post-war average observed in the U.S. excluding the public capital. 3.4.2 Parameters of the Intermediation Sector Entrepreneurs’ leverage ratio limits the amount that they can borrow from the financial institutions in the intermediary sector. This ratio is assumed to be independent from the entrepreneur’s wealth and unaltered across entrepreneurs. The maximum amount of borrowing for an entrepreneur is calculated by multiplying his asset holdings with the constant leverage ratio. The leverage ratio, , is set to 37% that is consistent with findings of [10]. The other parameter specifies the operational or extra cost,, of inter- mediating funds to the entrepreneurs by financial institutions. It is fixed at 5% following [20] and [8]. 82 3.4.3 Technological Parameters Corporate Sector The technology in the corporate sector is identified by a labor augmenting Cobb- Douglas production function, F (K t ;H t ) = K t (A t H t ) 1 . The share of capital, , in the corporate sector is assumed to be equal to 0:36, a number that is consistent with the U.S. data. The productivity growth rate is set to 1:65%. Then, the corresponding productivity growth factor,g, becomes 1:0165. The depreciation rate,, is assumed to be identical across both sectors of production. When calibrating the depreciation rate, the law of motion for aggregate capital in steady state is exploited. The depreciation rate is given by = (I=Y ) (K=Y ) + 1gn (3.18) where K Y is the capital-output ratio, and I Y is the investment-output ratio. The steady state ratio of aggregate investment to the aggregate output is fixed at 0:18 that is consis- tent with the U.S. data. Non-Corporate Sector The parameters that determine the shares of capital and labor areu 1 andu 2 . When cal- ibrating these parameters, the production technology is allowed to exhibit decreasing returns to scale thereby permitting entrepreneurs to collect positive profits. However, 83 these parameters are assumed to be proportional to the corresponding shares in the cor- porate sector with the same degree of proportionality,2 (0; 1). This parameter speci- fies the share of output that goes to the entrepreneur in the form of profits. Consequently, the corresponding share parameters are formulated as folows u 1 = ; u 2 = (1): The process that governs the entrepreneurial efficiency,, is assumed to followN = 4-state Markov process. The associated vector of values of is shown as follows T = [0 2 3 4 ]: (3.19) where the first value, zero, stands for the case in which the household possesses no entrepreneurial project or idea. The corresponding matrix of transition probabilities is obtained after making a couple of simplifying assumptions. In order to decrease the number of unknown parameters, a household’s entrepreneurial state is assumed to change gradually in the sense that a household with j may only get j1 ifj6= 1 or j+1 ifj6= 4 in the next period and transition probabilities are set to zero for all other possibilities. p jz denotes the transition probability from statej to statez and defined as p jz = prob( i+1 = z = i = j). It is also assumed thatp 12 = p 23 = p 34 ; that is, the probability that a household draws a better entrepreneurial efficiency in the next period is independent from his current realization. A further assumption states thatp 43 = 1 2 p 32 implying that the the likelihood of realizing a worse efficiency is lower in the highest 84 state than the third state. For notational simplicity,p 12 = p 1 ; p 21 = p 2 ; ;p 32 = p 3 are also specified. As a result, the matrix of transition probabilities is written as P = 2 6 6 6 6 6 6 6 6 6 4 1p 1 p 1 0 0 p 2 1p 2 p 1 p 1 0 0 p 3 1p 3 p 1 p 1 0 0 1 2 p 3 1 1 2 p 3 3 7 7 7 7 7 7 7 7 7 5 (3.20) Together with the three parameters in the transition matrix, the set of entrepreneurial parameters that is to be calibrated are , 2 , 3 , 4 , p 1 , p 2 , and p 3 . These seven parameters are calibrated so that the model generated fraction of entrepreneurs, share of entrepreneur’s income, wealth held by the entrepreneurs, ratio of median assets of entrepreneurs to that of workers, overall exit rate from entrepreneurship, new entrepreneur’s exit rate, and wealth Gini coefficient match to those observed in the U.S. data. Table 3.1 reports the target and benchmark model values of these moments. Table 3.1: Target Moments and Model Results in Overlapping Generations (OG) Model Moment Name Model Value Target Value Fraction of entrepreneurs 7:6% 7:6% Overall exit rate 19:5% 20:0% New entrants’ exit rate 41:7% 40:0% Entrepreneurs’ share in total wealth 40:9% 40:0% Entrepreneurs’ share in total income 31:2% 27:0% Ratio of median assets of entreps to the others 7:36 8:00 Wealth Gini 0:765 0:803 * The percentage deviations from the target values are less than or equal to 9% except entrepreneur’s share in income 85 The following vector of entrepreneurial productivity and transition matrix are obtained after calibration: T = [0 1:27 1:50 2:66]; P = 2 6 6 6 6 6 6 6 6 4 0:91 0:09 0:00 0:00 0:48 0:43 0:09 0:00 0:00 0:24 0:67 0:09 0:00 0:00 0:12 0:88 3 7 7 7 7 7 7 7 7 5 : 3.4.4 Parameters of Labor Process There are two efficiency parameters that determine the labor supply of a young house- hold in efficiency units as mentioned before. The first one is age-dependent efficiency vector,fg ir1 i=1 . This vector is obtained by using the estimates of [15]. Stochastic labor efficiency,l is assumed to follow an AR(1) process. The persistence parameter of this process is taken as 0:95 that is consistent with its estimates given by [18], and [25]. Its variance is calibrated to hit an earnings Gini of 0:38 as [4]. Next, the continuous AR(1) process characterized by these parameters is transformed into a N l = 5-state discrete process by using the quadrature-based method developed by [26]. The grid points of the labor productivity are given by L = [0:25 0:45 0:77 1:31 2:36]: 86 The following is the corresponding transition matrix of the labor productivity from one period to the next P l = 2 6 6 6 6 6 6 6 6 6 6 6 6 4 0:7376 0:2473 0:0149 0:0002 0:0000 0:1947 0:5555 0:2328 0:0169 0:0001 0:0112 0:2221 0:5334 0:2221 0:0112 0:0001 0:0169 0:2328 0:5555 0:1947 0:0000 0:0002 0:0149 0:2473 0:7376 3 7 7 7 7 7 7 7 7 7 7 7 7 5 : 3.4.5 Parameters of the Government Sector Social Security System The parameters that characterize the pension system are calibrated in line with the U.S. social security system. The maximum amount of labor income,y m s , that is subject to the social security taxation is a multiple of the model generated average labor earnings of the workers. The multiplication factor,m s , is taken to be the ratio of the maximum taxable labor income, $94; 000, given by the SSA to the average labor earnings, $38; 000, in 2006. Then, the labor income above which no social security taxation is applied is calculated by y m s =m s e l (3.21) where e l is the average labor earnings of the workers in the model economy. 87 The benefit that a newly retired household receives is calculated by using a piecewise linear formula. The bend points in this formula are given by b 1 = 0:20 e l ; b 2 = 1:25 e l ; b 3 = 2:47 e l : The formula that calculates the benefit of a retiree at the age of i r in the steady state equilibrium is demonstrated by ( e ir1 ) = 8 > > > > < > > > > : 0:9 e ir1 if e ir1 <b 1 0:9b 1 + 0:32( e ir1 b 1 ) if b 1 e ir1 <b 2 0:9b 1 + 0:32b 2 + 0:15( e ir1 b 2 ) if b 2 e ir1 <b 3 0:9b 1 + 0:32b 2 + 0:15b 3 if e ir1 b 3 9 > > > > = > > > > ; (3.22) where e ir1 is the average indexed lifetime labor earnings at the end of age ofi r 1 in the steady state. The technological growth rate,g is used when indexing the earnings. Income Taxation The progressiveness of the income taxation is captured by using the formula given by Equation 3.10 which is derived by [27]. This formulation depends on three parameters; tau 0 , 1 , and 2 . When calibrating these parameters for the U.S. economy, the estimates provided by [14] are used. These are 0:258, 0:031, and 0:768, respectively. Since the second parameter, 1 , is unit dependent, its value is computed within the model by model 1 = 1 y U:S: 1989 y model 2 (3.23) where y U:S: 1989 is the average total household income in the U.S. in 1989, and y model is the average total household income observed in the model economy. This method produces 88 an average tax rate on a household with average income in the model that is equal to the average tax rate on a household with average income in the U.S. in 1989. Following [9], y US 1989 is fixed at 50 which corresponds to an income of $50; 000. The government taxes the income not only progressively but also constantly. The constant tax rate on income, t 3 , is set within the model in order for the government budget to be balanced after the the revenues from progressive taxation of income and consumption tax are taken into account. The constant consumption tax rate is set to 5:5% that is the average tax rate on consumption estimated by [22]. Another parameter, f o b , the fraction of pension payments that is conditionally subject to income taxation is taken to be 0:5. The limit of income, y o b , below which the old do not pay tax on pension transfer he receives is set to $32; 000 which is taken from the SSA. Finally, the government purchases are assumed to be equal to 21:5% of the aggregate output as in [13]. 89 Table 3.2: Calibrated Parameters in OG Model Parameter Value Explanation Household i m 80 Maximum age (100 years) p d 45 Retirement age (65 years) 1:500 Relative risk aversion 0:976 Time discount factor n 1:012 Population growth factor Intermediation 0:370 Leverage ratio 0:050 Extra cost of borrowing Corporate Technology g 1:0165 Technological growth rate 0:360 Share of capital 0:039 Depreciation rate Non-Corporate Technology 0:880 Share of profit [u 1 u 2 ] [0:317; 0:563] Shares of capital and labor [ 1 2 3 4 ] [0; 1:27; 1:50; 2:66] Vector of efficiency grids P in text Transition probabilities Labor Efficiency h 1.000 Time endowment [l 1 l 2 l 3 l 4 l 5 ] [0:25; 0:45; 0:77; 1:31; 2:36] Vector of efficiency grids P l in text Transition probabilities Taxation c 0:055 Consumption tax rate [ 0 1 2 3 ]] [0:26; 0:37; 0:77; 0:05] Income taxation constants y o b y l 0:842 SSA 90 3.5 Quantitative Results This section presents the numerical results concerning the removal of the unfunded social security in the benchmark model. The results of the same experiment in the absence of entrepreneurs are also reported for comparison motives. The policy change is assumed to be revenue neutral regarding the government purchases. In other words, the level of government purchases in the initial steady state (with social security) is unchanged in the final steady state (without it). The degree of progressiveness of the income taxation is preserved in the new steady state by allowing the parameters of the income tax formula to adjust. Figure 3.1: Cross-Section Consumption The cross section levels of consumption across ages are drawn on Figure 3.1 for the benchmark model in the both steady states. This figure shows that the average level of steady state consumption at early ages is considerably climbing up in the absence of the social security taxes while it is lowered for later ages- more specifically after the age of 29. Similarly, Figure 3.2 shows a graph of the average wealth transferred to the next 91 period for each age group in the both steady states. According to this figure, the average wealth transferred to the next period is notably higher without the social security. Figure 3.2: Profile of Intertemporal Wealth Transfers 3.5.1 Macroeconomic Aggregates The unfunded social security system partly insures households against risks associated with mortality, old-age income, and lifespan by providing them with a certain income throughout their retirement. The households raise their savings in the absence of this partial insurance after the removal of the unfunded social security. This is the only channel through which households can react to the policy reform in this economy since they are deprived of the other channel, labor supply, by the assumption of inelastic labor supply. Hence, the reform has significant effects on the key macroeconomic aggregates through the changes in the savings of the households. This section provides some find- ings of the quantitative analysis with and without entrepreneurs. The upper half of Table 3.3 gives the values of the selected aggregates with and without the social security as well as the percentage change after the policy shift in the 92 Table 3.3: The Long-run Aggregate Effects of the Policy Change, OG With Entrepreneurs t s r w K Y C K Y SSS* 9% 3:45% 1:57 5:70 2:14 1:27 2:66 No SSS 0% 2:43% 1:70 7:89 2:30 1:28 3:43 % 29% 9% 39% 8% 1% 29% Without Entrepreneurs t s r w K Y C K Y SSS 9% 9:63% 1:11 3:66 1:37 0:83 2:66 No SSS 0% 7:22% 1:24 4:97 1:54 0:90 3:24 % 25% 12% 36% 12% 9% 22% * SSS stands for Social Security System benchmark economy, while the lower half documents the same findings for the standard economy. The social security tax rate is roughly 9% in both economies prior to the reform. In general, the effects on the aggregate variables in both economies are in the same direction but level differences are observed in terms of percentage changes. More specifically, the interest rate falls while the wage rate, aggregate capital, output, and consumption increase in both economies. Even if the two economies do not differ from each other in terms of the percentage rise in physical capital, the percentage increase in aggregate output without entrepreneurs is 50% higher than that with entrepreneurs. More interestingly, this difference becomes nine times in case of the aggregate consump- tion. What accounts for this difference can be understood by taking a closer look at the non-corporate sector. A model that ignores the presence of entrepreneurial incentives for saving may significantly overestimate the rise in the aggregate consumption. 93 3.5.2 Non-Corporate Sector A more detailed study of non-corporate sector may shed some light on how the entrepreneurs react to the policy change and through which channels it leads to the previous observation about the aggregate output and consumption. Since the amount up to which an entrepreneur can borrow depends on his wealth and the highly productive entrepreneurs can extremely raise their profits by employing large amounts of capital, entrepreneurship somewhat creates an additional saving motive for households regard- less of the current occupation except for the retired. The removal of the unfunded social security system has effects on the non-corporate sector via the factor prices and the increase in the savings of for insurance purposes. Table 3.4: The Long-run Effects of the Policy Change on the Non-corporate Firm Size, OG SSS No SSS % Maximum Firm Size 2 = 1:27 12:5 14:5 16% 3 = 1:50 48:9 57:8 16% 4 = 2:66 711:9 591:2 17% Average Firm Size 2 = 1:27 6:8 9:8 44% 3 = 1:50 17:2 21:5 25% 4 = 2:66 60:0 58:9 2% Overall 29:8 33:1 2% * SSS stands for Social Security System The effects of the privatization on the average and maximum firm sizes for every efficiency point are exhibited on Table 3.4. Theoretically speaking, the maximum size of a firm is the profit maximizing level of capital without borrowing. This level is expected to be higher for every level of entrepreneurial productivity after the privati- zation. However, the maximum firm size is observed to increase for only the second 94 and third efficiency levels and to fall for the highest efficiency. Only 10% and 14% of the entrepreneurs have enough wealth to employ the profit maximizing level of capital without borrowing in the first and second steady states, respectively. None of the most efficient households reaches the profit maximizing levels. Since they operate below the profit maximizing levels, they lose a notable amount of profit after the reform. There- fore, the maximum wealth that those entrepreneurs can accumulate is significantly low- ered in the final steady state, so is the maximum firm size. Similar results are obtained for the average size of the entrepreneurial firms. The average size of the firms with productivity levels of 2 and 3 goes up by 44% and 25%, respectively, while it falls by 2%, a relatively very small percentage, when the entrepreneur realizes 4 . The overall average is observed to rise by only 2% due to the strong effect of the most productive firms. There is a couple of factors contributing to the increase in the firm size with 2 and 3 . First of all, the firms that produce at the profit maximizing level optimally employ more capital after the privatization. Second, overall average wealth in the final steady state is considerably higher than that in the initial steady state. Finally, the minimum firm sizes increase at each value of. Table 3.5: The Long-run Effects of the Policy Change on Non-corporate Sector, OG SSS* No SSS % Ratio of Entrepreneurs 7:60% 7:90% 4% Wealth held by Entrepreneurs 2:30 2:41 5% Share of Entrepreneurs’ Wealth in Total 40:85% 30:92% 24% Share of Entrepreneurs’ Income in Total 31:17% 29:34% 6% Median Wealth Entrep.-to-Non-entrep. ratio 7:36 4:97 33% Non-Corporate Capital (K e ) 2:47 2:61 6% Non-Corporate Labor (H e ) 0:53 0:46 15% Non-Corporate Output (Y e ) 1:48 1:37 7% Corporate Capital (K c ) 3:23 5:29 64% Corporate Labor (H c ) 0:27 0:35 30% Corporate Output (Y c ) 0:66 0:93 41% * SSS stands for Social Security System 95 Additionally, the quantitative results of the policy change on some selected moments in the non-corporate sector are listed in Table 3.5. The table reports an increase of 4% in the fraction of entrepreneurs after policy change. The fraction of old entrepreneurs do not vary after the privatization, because the old always choose to be entrepreneur as long as they realize positive efficiency shocks. Hence, their ratio only depends on the parameters of the stochastic process that governs the entrepreneurial productivity. For a better understanding of the change in the fraction of entrepreneurs, Figure 3.3 graphs the fraction of the young entrepreneurs across cohorts in the two steady states. The number of young entrepreneurs is higher with the social security for the cohorts younger than 24. Above this age, the opposite is observed. In the end, the ratio of entrepreneurs increases by 4% because the increase in the later years outweighs the fall in the early years. Figure 3.3: Fraction of Young Entrepreneurs The level of wealth held by entrepreneurs climbs up by 5% in accordance with the increase in the ratio of entrepreneurs. Since this number is much lower than the increase in the aggregate wealth, 39%, the share of entrepreneurs in total wealth is dras- tically lowered; to be more specific, by 24%. Likewise, the ratio of median wealth of 96 entrepreneurs to that of the rest also falls by 33%. The median wealth of entrepreneurs falls after the removal of the unfunded social security due to the lower profit rates of the most productive entrepreneurs while the median wealth of non-entrepreneurs goes up as households accumulate more wealth on average in the absence of the partial insurance provided by the unfunded social security. Even though their number slightly increases, the income share of entrepreneurs in total falls by 6% because of the losses in entrepreneurial profit. In line with the increase in the total wealth of entrepreneurs and the minimum level of capital for entrepreneurship, the capital employed in the non-corporate sec- tor increases by 6%. The entrepreneurs who can afford to reach the profit maximizing output without borrowing switch from labor to capital in order to take advantage of relatively cheaper labor. On the other hand, the lower profit levels prevent highly pro- ductive entrepreneurs from accumulating huge amounts of capital. As a result of the increasing wages, the labor demand in the non-corporate sector considerably decreases; numerically, by 15%. The adverse effect of the policy reform through the wage rate reduces the the total output of the non-corporate firms by 7%. This clearly explains the lower percentage increase in aggregate output and aggregate consumption in the bench- mark model than those obtained by a model without entrepreneurs. On the other hand, corporate capital, labor and output are all observed to rise significantly. 3.5.3 Wealth and Income Distributions The introduction of entrepreneurs into the standard OG model incredibly increases the ability of the model to match the U.S. wealth distribution. At this point, this paper deviates from the previous literature on the social security reform by successfully repli- cating the wealth distribution observed in the U.S. data. Though it is not intended, the 97 model also does a very good job in matching the U.S. income distribution. Therefore, the effects of the social security reform on the income inequality are also reported in this section. Table 3.6: The Long-run Effects of the Policy Change on Wealth Distribution, OG % of the wealth owned by the top % with Wealth 1% 5% 10% 20% 40% 60% a 0 Gini Data 34:70 57:80 69:10 81:70 93:90 98:90 6:9 12:9 0:803 Entrep. and SSS 27:33 51:94 62:72 77:36 93:01 98:76 12:45 0:765 Entrep. and no SSS 17:63 37:58 50:35 68:39 89:14 97:84 10:72 0:684 No Entrep. but SSS 4:84 19:66 34:22 56:20 83:50 96:13 8:31 0:572 No Entrep. and no SSS 4:77 19:57 34:24 56:56 84:06 96:56 9:42 0:577 * The wealth shares and wealth Gini are taken from [24]. The results regarding the wealth distribution in the economy are presented in Table 3.6 for the benchmark and standard economies. In a standard pure life-cycle OG model, the elimination of the unfunded social security vaguely increases the wealth Gini, a com- monly used measure of wealth inequality. More interestingly, the fraction of households with zero wealth in the standard model increases by 13% after the policy shift. Most of those households are very young; for instance, almost 55% of them in both steady states are younger than the age of 6. The fall in the rate of return on saving is capable of deter- ring the very young households from saving even in the presence of future uncertainties when combined with expectation of higher future labor income due to the shape of the age dependent efficiencies. On the contrary, the benchmark findings show an apparent and substantial fall in the wealth Gini of the benchmark economy after privatization. More specifically, the wealth Gini falls from 0:765 to 0:684 in the final steady state of the benchmark economy gener- ating a more equal wealth distribution. There two sources for the fall in the wealth Gini- the reduction in the wealth share of the wealthiest and the expansion in the share of the poorest. More precisely, the share of the wealthiest 1% falls by 36% in the benchmark 98 model because of the lower profits of entrepreneurs. Unlike the wealthiest, the share of the bottom 40% increases from 1:24% to 2:16% as households save more for insurance purposes in the absence of the unfunded social security. Table 3.7: The Long-run Effects of the Policy Change on Income Distribution, OG % of the income of the top Income 1% 5% 10% 20% 40% 60% Gini Data 17:50 32:80 43:10 58:00 78:00 90:50 0:553 Entrep. and SSS 16:57 31:24 41:76 57:93 77:58 88:83 0:533 Entrep. and no SSS 14:51 29:28 40:85 58:32 79:90 91:90 0:563 No Entrep. but SSS 3:26 14:57 26:66 44:93 69:53 85:24 0:398 No Entrep. and no SSS 3:39 15:32 28:19 47:29 72:20 87:12 0:432 * Income distribution data is taken from [24]. Table 3.7 reports the results concerning the income distribution. The definition of income encompasses labor earnings, interest income, profits, and social security trans- fers to the retired before any taxes are applied. The benchmark model successfully generates an income distribution that is very close to the one observed in the U.S. data. The income Gini in the benchmark model jumps up by 6%, from 0:533 to 0:563. The removal of pension income lowers the share of the lowest 40% from 11% to 8%, and this is mainly responsible for the higher income Gini even if the shares of the top 1%, 5% and 10% are reduced after the elimination of the unfunded social security. Accommodat- ingly, the income Gini in the standard model also increases but by a greater percentage, 9%. 3.5.4 Welfare Comparisons The welfare analysis in this section compares the steady states before and after the elim- ination of the unfunded social security. In doing so, an answer to the question that 99 into which economy an unborn household would like to be born is searched. This type of study does not provide any evidence for the desirability of the privatization by the current residents of the model economy. The main point is how the presence of entrepreneurs affect the welfare gains associated with the policy change when the two long-run equilibria of the same economy are compared. Considering the big differ- ence between the two economies in terms of aggregate consumption, it is important to analyze its welfare implications. Table 3.8: Welfare Effects of the Policy Change in the Long Run, OG SSS No SSS CC (%) Expected Utility at Birth with Entrepreneurs 55:41 52:80 10:14% Expected Utility at Birth Without Entrepreneurs 51:51 46:77 21:31% * CC is the consumption compensation. The expected utility of an unborn household is used in the calculation of the con- sumption compensation which is the required percentage change in the consumption of the household in every period and contingencies of the initial steady state in order for this household to be indifferent between the two steady states of the same economy 3 . According to the calculations on Table 3.8, the policy reform increases the expected utility of an unborn household in both benchmark and standard economies. Neverthe- less, the compensation compensation in the standard model is 110% as much as the one in the benchmark model. This big difference is accounted for by the big loss in the over- all income of the entrepreneurs in the final steady state. If a standard OG model is used 3 CC = " V NS 0 V S 0 1 1 1 # where V S 0 and V NS 0 are the expected value functions of an unborn household with and without the social security, respectively. 100 to compare these two long-run equilibria, the removal of the unfunded social security would be highly overvalued compared to the benchmark model. 3.6 Sensitivity Analysis The robustness of the benchmark results is tested with respect to the changes in the two parameters of the model. The first parameter is the coefficient of relative risk aversion whose benchmark value is fixed at 1:5 and allowed to take two additional values, 1:0 and 2:0. The other parameter controls the share of capital in corporate and non-corporate production technology. First, the assumption that the non-corporate share is proportional to the corporate share is preserved but the corporate share is altered to take 0:34 and 0:42. Second, in a similar yet different way, the corporate share of capital remains constant but the non-corporate share takes two additional values; 0:30 and 0:42. 3.6.1 Coefficient of Relative Risk Aversion, The coefficient of relative risk aversion, , determines how a household reacts to the future uncertainties in the framework of this model. The higher the coefficient is, the less the household loves risk. Since there are different values of this parameter estimated and used in numerical exercises in the literature on the social security reform, a sensitivity analysis regarding the risk aversion coefficient is helpful to understand the degree of persistence of the benchmark results. Two values, 1:0 and 2:0, are considered for the sensitivity analysis because those are widely used in the existing literature. Moreover, the interest rate in the final steady state might fall below the growth rate of technology by creating the problem of dynamic inefficiency. 101 Table 3.9: The Long-run Effects on the Non-corporate Firm Size with OG, Percentage Change Following the Reform = 1:0 = 1:5 = 2:0 Average Firm Size 2 24% 44% 46% 3 21% 25% 27% 4 4% 2% 0% Overall 3% 2% 4% Maximum Firm Size 2 13% 16% 19% 3 13% 16% 19% 4 14% 17% 17% * Benchmark calibration. Table 3.9 lists percentage change in the average and maximum firm sizes for each specification of as the economy moves from the initial steady state with the unfunded social security to the final steady state without it. The benchmark results about the maximum firm size are robust to changes in and there is a monotone relationship between the value of and the percentage changes. The results for the average firm size do not differ much from the benchmark case strengthening the benchmark findings. However, the average firm size of the entrepreneurs with 4 seems unaffected by the privatization. This is not really surprising because the higher the risk averseness of a household, the more he saves in the presence of risks and at some point this dominates the effect of lower profits on the wealth accumulation and average firm size. Next, Table 3.10 presents further results of the sensitivity experiment on the non- corporate sector. According to these findings, the benchmark results concerning the non-corporate labor demand and output, the share of entrepreneurs in both total wealth and income, and median wealth ratio of entrepreneurs to non-entrepreneurs seem very robust to the given changes in. The percentage change in the non-corporate output and 102 Table 3.10: The Long-run Effects of the Policy Change on Non-corporate Sector with OG, Percentage Change after the Reform = 1:0 = 1:5 = 2:0 Ratio of Entrepreneurs 3% 4% 4% Wealth held by Entrepreneurs 2% 5% 8% Share of Entrepreneur’s Wealth in Total 24% 24% 26% Share of Entrepreneur’s Income in Total 7% 6% 7% Median Wealth Entrep.-to-Non-entrep. ratio 30% 33% 33% Non-Corporate Capital (K e ) 0% 6% 8% Non-Corporate Labor (H e ) 14% 15% 16% Non-Corporate Output (Y e ) 8% 7% 7% * Benchmark calibration. labor demand after privatization shows ignorable dependence on the value of the relative risk aversion coefficient. On the other hand, the effect of the privatization on the fraction of entrepreneurs, the level of their wealth, and their capital demand is reversed when is unity, the case of logarithmic period utility. The reversal of effect is significant for the ratio and wealth of entrepreneurs unlike capital demand. The decrease in the number of entrepreneurs when = 1:0 is around 3%, a fairly small percentage. After the removal of the unfunded social security, the minimum level of capital at which the household can at least compensate for his labor income loss significantly increases due to the changes in the factor prices. As a consequence, it becomes more difficult for a young household to begin his own business even if he has a highly productive entrepreneurial project. In this case, the increase in the wealth of the households stays low relative to the increase in the minimum wealth level for entrepreneurship generating a smaller number of entrepreneurs in the final steady state. In accordance with the change in the number of entrepreneurs, the size of their wealth and non-corporate capital demand slightly shrinks. The fall in the non-corporate capital 103 demand is reduced by entrepreneur’s access to borrowing when compared to the change in the wealth of the entrepreneurs. Table 3.11: The Long-run Aggregate Effects with OG, Percentage Change after the Removal of the SSS = 1:0 = 1:5 = 2:0 Entrep No Entrep Entrep No Entrep Entrep No Entrep K 29% 24% 39% 36% 45% 47% Y 6% 8% 8% 12% 9% 15% C 1% 6% 1% 9% 1% 11% * Benchmark calibration. The percentage changes in the aggregate variables in both benchmark and standard models are given on Table 3.11 for each specification of. According to these numbers, the effects of the privatization on interest rate, wage rate, aggregate capital, output, and consumption are very robust to the choice of. Especially, the aggregate consumption increases by only 1% for all values of considered in the sensitivity analysis. The percentage change in aggregate consumption with entrepreneurs is very small compared to its equivalent in the standard model. Table 3.12: Wealth and Income Distribution with OG, = 1:0 = 1:5 = 2:0 SSS No SSS SSS No SSS SSS No SSS Wealth Gini 0:756 0:687 0:765 0:684 0:758 0:674 Share of top 1% 24:94% 17:30% 27:33% 17:63% 26:82% 16:64% Share of lowest 40% 01:25% 02:04% 01:24% 02:16% 01:40% 02:38% Income Gini 0:523 0:554 0:533 0:563 0:532 0:561 Share of top 1% 13:48% 11:24% 16:57% 14:51% 16:40% 14:11% Share of lowest 40% 11:30% 08:39% 11:17% 08:10% 11:18% 08:15% * Benchmark calibration. 104 The sensitivity of the benchmark conclusion regarding the wealth and income dis- tribution is also studied in the light of the findings listed on Table 3.12. These results exhibit that the effects of the elimination of the unfunded social security on the wealth and income distribution for the specified choices of are in line with the implications of the benchmark model except for small level differences. The wealth distribution becomes more equal in the final steady state after privatization while the income distri- bution becomes more unequal and this statement is robust to the changes in the value of . The wealth and income shares of the top 1% and the lowest 40% change in the same direction and similarly for the choices of shown on the table. Table 3.13: Consumption Compensation with OG, = 1:0 = 1:5 = 2:0 CC with Entrep 6:74% 10:14% 15:21% CC Without Entrep 16:32% 21:31% 26:71% * Benchmark calibration. The last table in this section, Table 3.13, exhibits the required consumption com- pensations that make unborn households indifferent between the two steady states of the same economy for each value of . The compensation in an economy without entrepreneurship is still significantly larger than what it would be with entrepreneurs. More specifically, the benchmark finding is 142% and 76% larger than that in the stan- dard model when is 1:0 and 2:0, respectively. There is an inverse relationship between the value of and the percentage change observed in this measure after the removal of the unfunded social security. 105 3.6.2 Share of Capital, First, is allowed to take 0:34 and 0:42 keeping e =. For the values of lower than 0:34, the interest rate goes below the growth rate of the technology,g, in which case the problem of dynamic inefficiency occurs. Therefore, smaller values of are ignored in order to avoid this problem. In the second strategy, the corporate share is fixed at its benchmark value, but the non-corporate share parameter, e , takes two different values- 0:30 and 0:42. Table 3.14: The Long-run Effects on the Non-corporate Firm Size with OG, Percentage Change Following the Reform e = 0:30 e = 0:36 e = 0:42 = 0:34 = 0:42 Average 2 27% 44% 47% 48% 32% 3 23% 25% 20% 25% 24% 4 2% 2% 1% 2% 2% Overall 2% 2% 4% 2% 3% Maximum 2 5% 16% 31% 17% 13% 3 5% 16% 31% 17% 13% 4 15% 17% 14% 15% 16% * Benchmark calibration. ** = 0:36 ande changes in the first three columns. ***e = holds in the last two columns. Table 3.14 exhibits the results for average and maximum firm sizes in the non- corporate sector. According to these numbers, the benchmark results about average and maximum firm sizes are very robust to the changes in the share parameters of the capital. Average and maximum firm sizes increase after the privatization if the entrepreneur has 2 and 3 . For the highest level of entrepreneurial efficiency, average and maximum size of the non-corporate firm falls because of the associated slump in the profit. The case in which e is set to 0:42 expresses a smaller percentage fall in the average firm size of the most productive entrepreneurs compared to the other cases. If the non-corporate share is 106 larger than the corporate share, the entrepreneurs whose wealth is above a certain level increases their profit even though they are producing below the profit maximizing lev- els. This enables those entrepreneurs to accumulate higher wealth and to employ more capital. Eventually, the average firm size of these entrepreneurs falls implying that most of of them are not able to increase their profit. Table 3.15: The Long-run Effects of the Policy Change on Non-corporate Sector with OG, Percentage Change after the Reform e = 0:30 e = 0:36 e = 0:42 = 0:34 = 0:42 Ratio of Entrepreneurs +0% 4% 2% 5% 1% Wealth held by Entrepreneurs 2% 5% 5% 6% 4% Wealth Share of Entrepreneurs 30% 24% 21% 25% 21% Income Share of Entrepreneurs 9% 6% 5% 5% 7% Median Wealth Ratio 37% 33% 27% 36% 24% Non-Corporate Capital (K e ) 2% 6% 7% 7% 4% Non-Corporate Labor (H e ) 17% 15% 14% 15% 15% Non-Corporate Output (Y e ) 11% 7% 6% 7% 7% * Benchmark calibration. Further changes in the non-corporate sector for each specification of share parame- ters are listed on Table 3.15. The non-corporate capital demand increases for all values of and e shown on the table while the non-corporate labor and output notably fall. These observations strengthen the robustness of the corresponding benchmark findings. In case of the fraction of entrepreneurs, this value tends to zero for e = 0:30 still staying positive. This can still be explained by the increase in the minimum wealth requirement for entrepreneurship at every level of productivity. Especially, the number of young entrepreneurs jumps down after the privatization while the number of older entrepreneurs increases. The long-run aggregate effects are shown on Table 3.16 for all specifications of the relevant parameters. These findings justify the benchmark conclusions regarding 107 Table 3.16: The Long-run Aggregate Effects with OG, Percentage Change after the Removal of the SSS = 0:34 = 0:36 = 0:42 Entrep No Entrep Entrep No Entrep Entrep No Entrep K 41% 38% 39% 36% 32% 40% Y 7% 12% 8% 12% 8% 15% C 0% 8% 1% 9% 4% 19% e = 0:30 e = 0:42 K 45% 34% Y 8% 8% C 0% 3% * Benchmark calibration. the corresponding macroeconomic aggregates. Especially, the increase in the output is very robust to the changes in the non-corporate share of capital. The increase in the aggregate consumption still remains very low except for the cases e = 0:30 and = e = 0:34. For these cases aggregate consumption is even observed to fall slightly, even strengthening the benchmark conclusion that the increase in the aggregate consumption is very small with entrepreneurs. In this case, the fall in the total consumption of the entrepreneurs dominates the increase in the consumption of the rest of the households ultimately lowering the aggregate consumption. Table 3.17: Wealth and Income Distribution with OG, e = 0:30 e = 0:36 e = 0:42 SSS No SSS SSS No SSS SSS No SSS Wealth Gini 0:742 0:657 0:765 0:684 0:757 0:688 Wealth Share of the top 1% 22:49% 13:78% 27:33% 17:63% 27:13% 18:56% Income Gini 0:511 0:547 0:533 0:563 0:537 0:561 = 0:34 = 0:42 Wealth Gini 0:770 0:683 0:750 0:683 Wealth Share of the top 1% 27:55% 17:45% 26:52% 18:18% Income Gini 0:530 0:568 0:538 0:552 * Benchmark calibration. 108 The robustness of the benchmark results concerning wealth and income distribution is crucial for their reliability being the main point of the paper. Table 3.17 depicts how the effects of the policy reform on the wealth and income distribution change for the selected values of the share parameters. The measure of wealth inequality, wealth Gini coefficient, falls by at least 9% and the share of the wealthiest 1% in total wealth drops by at least 32% in each of the sensitivity experiments. In case of income distribution, the income Gini, a measure of income inequality, increases by at least 3% in the same experiments. Concisely, the benchmark results about the income and wealth distribution are robust to the changes in the capital share parameters according to the sensitivity experiments. Table 3.18: Consumption Compensation with OG, e = 0:30 e = 0:36 e = 0:42 = 0:34 = 0:42 CC with Entrep 7:16% 10:14% 13:84% 7:25% 16:31% CC Without Entrep 21:31% 21:31% 21:31% 19:85% 33:17% % 198% 110% 54% 174% 103% * Benchmark calibration. The last table in this section, Table 3.18, presents the changes in the consumption compensations for all different specifications of the share parameters. When share of capital in corporate technology is fixed at its benchmark value, the consumption com- pensation in an economy without entrepreneurs is at least 54% higher than what it would be with entrepreneurs. There is a monotone and proportional relationship between the value of e and consumption compensation with entrepreneurship. When the shares in both sectors are simultaneously altered, there is still a monotone relationship between and consumption compensations. Even though the percentage difference in compen- sation between two economies is inversely related to, the lowest it gets is still above 109 100%. The benchmark results from comparison of the two economies with respect to consumption compensation stay unchanged throughout the sensitivity experiments described in this section. 3.7 Conclusion In summary, this paper examines the effects of eliminating the unfunded social security in an economy that successfully replicates the wealth and income distributions observed in the U.S. data and is populated by occupationally heterogenous households. In such an economy, households save for either to insure themselves against income and lifes- pan uncertainties or to be able to achieve high profit income in case they possess a very productive entrepreneurial idea. The later incentive for saving opens new channels through which the removal of the unfunded social security can affect the behavior of the households as well as the aggregate economy. The quantitative results of the paper indicate a slight increase in the number of entrepreneurs after the privatization. However, this effect reverses when the coeffi- cient of relative risk aversion is set to unity in which case the increase in the savings of households are not enough to offset the adverse effect of the fall in the profit levels of entrepreneurs associated with the changes in the factor prices. The cross-section distri- bution of households is found to change in favor of the older entrepreneurs- more specif- ically those who are older than the model age of 24. Additionally, the non-corporate capital demand is observed to jump up in the final steady state while the non-corporate output and labor demand significantly decrease. Even though, the maximum firm size of the entrepreneurs considerably shrinks down in the aftermath of the reform, the average firm size slightly increases. 110 As the depressing effect of the social security on the savings of households is removed, the aggregate capital is observed to expand substantially in the benchmark model in line with the existing literature. On the other hand, the increase in the aggre- gate output in the benchmark model is notably lower than the one in a standard OG model. The difference becomes huge for the aggregate consumption. The aggregate consumption in the benchmark model increases by only 1%, even decreases when the non-corporate share of capital is set to 0:30, while the increase in a standard model is nine times higher. The increase in both aggregate output and consumption stay very low compared to the standard model because the entrepreneurs lose big amounts of profit income in total after the policy change. Finally and most importantly, wealth distribution in the benchmark model becomes more equal as indicated by the fall of wealth Gini from 0:765 to 0:684. There two main causes of the fall in wealth Gini. First, the wealthiest households lose a large part of their share in total. Second, the share of the poorest households in total wealth significantly increases. In contrast, the wealth Gini of the standard model is found to increase slightly after the privatization indicating a more unequal distribution of wealth. The benchmark model also generates an income distribution that is very similar to the U.S. income distribution. The income distribution is reported to become more unequal after the policy reform. 111 Bibliography [1] A. B. Abel, Precautionary saving and accidental bequests, American Economic Review 75 (1985), 777–791. [2] A. J. Auerbach and L. J. Kotlikoff, Dynamic fiscal policy, Cambridge University Press, New York, 1973. [3] R. J. Barro, Are government bonds net wealth?, Journal of Political Economy 82 (1974), 1095–1117. [4] Marco Cagetti and Mariacristina DeNardi, Entrepreneurship, frictions, and wealth, Journal of Political Economy 114(5) (2006), 835–870. [5] A. Casteneda, J. D´ ıaz-Gim´ enez, and Jos´ e-Victor R´ ıos-Rull, Earnings and wealth inequality and income taxation: Quantifying the trade-offs of switching to a pro- portional income tax in the u.s., Manuscript, University of Pennsylvania, 1999. [6] , Accounting for the u.s. earnings and wealth inequality, Journal of Politi- cal Economy 111(4) (2003), 818–857. [7] J. C. Conesa and D. Krueger, Social security reform with heterogenous agents, Review of Economic Dynamics 2(4) (1999), 757–795. [8] E. C. Diaz-Gimenez, E. C. Prescott, T. Fitzgerald, and F. Alvarez, Banking in computable general equilibrium economies, Journal of Economic Dynamics and Control 16(3-4) (1992), 533–559. [9] A. Erosa and T. Koreshkova, Progressive taxation in a dynastic model of human capital, 54(3) (2007), 667–685, Journal of Monetary Economics. [10] D. S. Evans and B. Jovanovic, An estimated model of entrepreneurial choice under liquidity constraints, National Tax Journal 47(2) (1994), 317–339. [11] Luisa Fuster, Is altruism important for understanding the long-run effects of social security?, Review of Economic Dynamics 2(3) (1999), 616–637. 112 [12] Luisa Fuster, Ayse Imrohoroglu, and Selahattin Imrohoroglu, A welfare analysis of social security in a dynastic framework, International Economic Review 44(4) (2003), 1247–1274. [13] , Elimination of social security in a dynastic framework, The Review of Economic Studies 73 (2006), 1–33. [14] M. Gouveia and R. P. Strauss, Effective federal individual income tax functions: an exploratory empirical analysis, Journal of Political Economy 34(3) (1994), 297– 323. [15] G. Hansen, The cyclical and secular behavior of the labor input: Comparing effi- ciency units and hours worked, Journal of Applied Econometrics 8 (1993), 71–80. [16] H. Huang, Selahattin Imrohoroglu, and T. Sargent, Two computations to fund social security, Macroeconomic Dynamics 1(1) (1997), 7–44. [17] R. G. Hubbard and K. L. Judd, Social security and individual welfare: Precau- tionary saving, liquidity constraints, and the payroll tax, The American Economic Review 77(4) (1987), 630–646. [18] R. G. Hubbard, J. Skinner, and S. P. Zeldes, The importance of precautionary motives in explaining individual and aggregate savings, Carneie-Rochester Con- ference Series on Public Policy 40 (1994), 59–125. [19] A. Imrohoroglu, S. Imrohoroglu, and D. Joines, A life cycle analysis of social security, Economic Theory 6 (1995), 83–114. [20] Sagiri Kitao, Entrepreneurship, taxation, and capital investment, 11(1) (2008), 44–69, Review of Economic Dynamics. [21] P. Krusell and A. A. Smith, Income and wealth heterogeneity in macroeconomy, 106(5) (1998), 867–896, Journal of Political Economy. [22] E. G. Mendoza, A. Razin, and L. L. Tesar, Effective tax rates in macroeconomics: Cross-country estimates of tax rates on factor incomes and consumption, Journal of Monetary Economics 97(4) (1989), 808–827. [23] Vincenzo Quadrini, Entrepreneurship, saving, and social mobility, Review of Eco- nomic Dynamics 3(1) (2000), 1–40. [24] Santiago Budria Rodriguez, Javier D´ ıaz-Gim´ enez, Vincenzo Quadrini, and Jos´ e- Victor R´ ıos-Rull, Dimesions of inequality: Facts on the u.s. distributions of earn- ings, income, and wealth, Federal Reserve Bank of Minneapolis Quarterly Review 26(3) (2002), 2–35. 113 [25] K. Storesletten, C. I. Telmer, and A. Yaron, Cyclical dynamics in idiosyncratic labor market risk, Journal of Political Economy 112(3) (2004), 695–717. [26] G. Tauchen and R. Hussey, Quadratue-based methods for obtaaining approximate solutions to nonlinear asset pricing models, Econometrica 59(2) (1991), 371–396. [27] H. P. Young, Progressive taxation and equal sacrifice, American Economic Review 80(1) (1990), 253–266. 114

Abstract (if available)

Abstract This study investigates the effects of eliminating the unfunded social security on an economy with entrepreneurs in the presence of individual income and lifespan uncertainties by using two different models, an infinite horizon and a pure life cycle overlapping generations (OG) model. Both models are very successful in replicating the dispersion of the wealth observed in the U.S. data. According to the quantitative results in both frameworks, the removal of the unfunded social security creates a significantly more equal distribution of wealth in the long run. More specifically, the wealth Gini, a commonly used measure of wealth inequality, falls from 0.807 to 0.521 and 0.765 to 0.684 in the infinite horizon and OG models, respectively. A mechanism, designed to guarantee a certain level of income for the households who fail to save adequately for their retirement years, generates a wealth distribution that is highly concentrated in the top tail. The first model, the infinite horizon model, reports a 39% increase in the fraction of entrepreneurs after privatization while the increase stays very low in the second model, around 4%. Unlike their fraction in the total population, their share in total net worth and income is considerably reduced after the policy change in both models. The stock of physical capital, aggregate output, and aggregate consumption are observed to increase after the privatization. However, the percentage increases in aggregate output and consumption in an economy with entrepreneurs are lower than those observed in an economy without them regardless of the choice of the model. The results also indicate a more unequal distribution of income, even if the share of the richest households is lowered after the removal of the unfunded social security.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Essays on interest rate determination in open economies

PDF

Identifying and mitigating the effects of urban heat islands in California

Asset Metadata

Creator Eren, Okan (author)

Core Title Effects of eliminating the unfunded social security system in an economy with entrepreneurs

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 06/20/2008

Defense Date 05/14/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag elimination of unfunded social security,entrepreneurship,OAI-PMH Harvest,Social Security,wealth distribution

Language English

Advisor Imrohoroglu, Selahattin (committee chair), Betts, Caroline M. (committee member), Quadrini, Vincenzo (committee member)

Creator Email oeren@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1280

Unique identifier UC1242318

Identifier etd-Eren-20080620 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-70991 (legacy record id),usctheses-m1280 (legacy record id)

Legacy Identifier etd-Eren-20080620.pdf

Dmrecord 70991

Document Type Dissertation

Rights Eren, Okan

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu