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Essays in international economics

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Content ESSAYS IN INTERNATIONAL ECONOMICS by Jihad C. Dagher 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 Jihad C. Dagher Acknowledgments This dissertation would not have been possible without the help and encouragement of my advisor Vincenzo Quadrini to whom I am very indebted. I am also very grateful to the members of my committee: Caroline Betts, Yong Kim and Robert Dekle for their continuous support throughout the last five years. Finally, I benefited tremendously from the guidance I received from Andy Neumeyer while he was a visiting professor at the Marshall school of Business. ii Table of Contents Acknowledgments ii List of Tables v List of Figures vi Abstract vii Chapter 1: Introduction 1 Chapter 2: Sudden Stops, Output Drops and Credit Collapses 11 2.1 Introduction 11 2.2 From Sudden Stops to output recoveries: The Evidence 18 2.2.1 Sample selection and data 19 2.2.2 The Evidence 19 2.3 Model Economy 27 2.3.1 Quantitative properties with homogeneous firms 36 2.3.2 Heterogeneous firms and the size effect 42 2.4 Conclusion 49 Chapter 3: Inflation and the Maturity Structure of Nominal Debt 52 3.1 Introduction 52 3.2 Evidence 56 3.3 The model 61 3.3.1 Characteristics of the economy 61 3.3.2 Event tree 61 3.3.3 Implications of the stabilization risk 66 3.3.4 Example 76 3.4 Concluding Remarks 80 iii Bibliography 83 Appendix A: Appendix to Chapter 2 87 A.1 First order conditions 87 A.2 Numerical Procedure 88 A.3 Figures and Tables 89 Appendix B: Appendix to Chapter 3 101 iv List of Tables Table 3.1: Correlations from monthly data 60 Table 3.2: The impact of inflation on the trade in bonds. 80 Table A.1: Determinants of firms’ performance between 1997 and 2002. 92 Table A.2: Average growth rates before and after the crisis. 93 Table A.3: Determinants of firms’ performance between 1997 and 1999. 96 Table A.4: Determinants of firms’ performance between 1997 and 2002, by country. 97 Table A.5: Determinants of firms’ performance between 1997 and 2002, by sector. 98 Table A.6: The growth effect. 99 Table A.7: Benchmark Calibration 100 Table A.8: Calibration for the small and the large firms. 100 v List of Figures Figure 2.1: The ratio of credit to GDP. 17 Figure 2.2: A credit-less recovery. 20 Figure 2.3: Comparing the performance of large and small firms. 22 Figure 2.4: Small Businesses’ profits 26 Figure 2.5: The model’s dynamics after a shock 38 Figure 2.6: Leverage and amplification of the shocks 41 Figure 2.7: Output drops and financial frictions 42 Figure 2.8: The size effect 47 Figure 3.1: Average Maturity and nominal interest rates. 58 Figure 3.2: Effects of changes in the stabilization risk. 81 Figure A.1: The absence of the size effect under TFP shocks. 90 Figure A.2: Average of debt-to-sales and Tobin’s Q ratios in the data. 91 Figure A.3: Real GDP and its growth rate. 94 Figure A.4: The collapse in the market value 95 vi Abstract The Mexican crisis that took place in 1994 was followed by nearly a decade of frequent and severe financial crises in the emerging economies. These crises episodes that were characterized by dramatic reversals in capital flows and large losses in output are atypical to the more advanced economies. This dissertation explores the characteristics, and in particular the vulnerabilities, of the emerging markets that could explain this difference. In the first part of my dissertation, I study the impact of the Asian financial crisis on firms in Southeast Asia using firm-level data. I then develop a model that shows how shocks to the expectations of agents and foreign investors could explain well the patterns observed during and following the crisis. The chapter emphasizes the credit-less recovery pattern that is left unexplained by the earlier sudden stop models. It also emphasizes the role of financial frictions in these economies as one of the important factors that makes them more vulnerable than the advanced economies to both expectations and productivity shocks. The model can account for both the patterns in the aggregate data as well as the heterogeneity of performance of firms of different leverage, size and growth opportunities. The second part of my dissertation addresses another vulnerability of the emerging markets, which is their non-standard maturity structure of debt. It is a well-known fact that vii the excess reliance on foreign currency and short-term maturity debt in these economies tends to amplify the impact of negative shocks to these economies. One of the given explanations of this irregularity in the composition of debt points to the high and volatile inflation levels that characterized the emerging economies during the last two decades. In this chapter I show, in a general equilibrium model, a new mechanism through which high inflation levels can shorten the maturity of traded debt. In particular, the model suggests that the possibility of price stabilization by the central bank can significantly affect the ability of agents in the economy to borrow at long maturities. viii Chapter 1: Introduction In the recent decades many developing countries lifted barriers to international invest- ment and liberalized their capital account. This enhanced access to the international finan- cial market has been characterized by boom-bust cycles of foreign borrowing growth followed by abrupt financial crises. These crises were particularly common during the 1990’s among the emerging economies. Argentina, Mexico, Russia, South Korea and many other countries experienced sudden reversals of capital flows to their economies marking a painful end to episodes of credit boom. Typically, these sudden stops in capi- tal flows have been followed by major drops in output and investment. Although output recovered to its pre-crisis level relatively quickly investment and credit in these economies suffered for many years following the initial collapse. These events revived and polar- ized the debate about globalization and the merits of financial liberalization. Indeed, these crises would have been unconceivable in the 1960’s when capital controls were the rule in most of these countries. Hence it is all but surprising that financial liberalization came under attack from those who thought that the costs of globalization outweigh its benefits. However the empirical evidence suggests the contrary. It is now a documented fact that countries that opened their doors to international capital experienced higher growth on 1 average notwithstanding the crises episodes. Yet these crises and the evident increase in volatility following financial liberalization are puzzling for the standard economic theory on financial openness. Theoretically there are many benefits to financial liberalization. It first improves risk sharing among countries by allowing them to trade their imperfectly correlated income risks. This increased risk sharing should decrease volatility by allowing agents from dif- ferent countries to insure themselves against negative shocks that are specific to their economies. The theory also suggests that financial liberalization should improve inter- temporal trade by enhancing the development and the efficiency of local financial markets. It is also arguable that financial liberalization could give the right incentives to local gov- ernment to implement the right policies. Irresponsible fiscal and monetary policies could discourage foreign investors and make them to look for the nearest exit at times where their investments and money are most valuable. Given this bright outlook from the economic theory on the potential benefits of finan- cial liberalization one might wonder why it failed to predict the potential and observed risks of liberalization at least in the short run. For many, the answer lies simply in the governments’ actions. Indeed, one cannot expect for a country to reap the benefits of glob- alization when policy makers are corrupt and engaged in inefficient policies. This is one of the central ideas of the first-generation models of financial crises. These models were motivated by the earlier currency crises that some emerging markets experienced during the 1980’s when fixed exchange rate regimes were very common. First-generation models show how the collapse of fixed exchange rate regimes can be caused by an unsustainable 2 fiscal policy. Under a fixed exchange rate regime the government’s ability to raise seignor- age revenues is very limited. If the government monetizes some of its debt, it will likely end up increasing inflation in the economy and therefore putting pressure on the exchange rate to depreciate. Therefore persistent deficits force the government to deplete its assets in form of foreign reserves or to borrow at an increasing rate from abroad. However such strategy cannot go on indefinitely; foreign reserves will soon be depleted and foreigners unwilling to buy the government’s debt. This is when the currency crises will take place as the government will have to resort to debt monetization. This picture of a financial crisis induced by bad fiscal policy however, does not describe well what happened during the 1990’s. The evidence offers many examples of countries that were hit by a crisis due to a sudden stop in capital flows while being at the same time engaged in prudent policies. Recent economic research on financial crises suggest that what lacks in the standard economic theory on open economies are the financial market imperfections and other fric- tions. These frictions, as the recent research suggests, can offer an explanation to the observed post-liberalization trend in the emerging markets. In particular they are central in explaining the large drops in aggregate production that follow the reversals in capital flows. In fact, standard economic theory in a frictionless environment suggests that a posi- tive reversal in the current account should lead to an increase in GDP. The recent literature, sometimes referred to as the third generation models of financial crisis, adds frictions to the standard model in the form of endogenous borrowing constraints and costly adjust- ments in capital and debt. Endogenous borrowing constraints describe well the reality of borrowing in both the developed and the developing countries. Due to contract enforce- ability problems, lenders often place a borrowing ceiling on lenders that is proportional 3 to borrower’s wealth. Indeed such contract enforceability problems are more common in the developing world. This can lead to tighter constraints in these countries. However, as is shown in chapter 2, what is behind these sudden and severe crises is not the restricted borrowing by the companies at the steady state but instead is the high volatility of these borrowing ceiling. This volatility can indeed create these lending booms and busts. The literature on financial crises in emerging markets went a long way in improving our understanding of the relationship between the sudden reversal of capital flows and the observed drops in output and investment. It also can account for the heterogeneous performance of the tradable and non-tradable sector during these crises. However there are many facts that remain puzzling for the current models on financial crises. Recently, Calvo, Izquierdo and Talvi (2006) showed that one of the stylized facts of these sudden stop episodes is the credit-less recovery of output. They found that while generally output recovers relatively quickly following these crises, credit and investment take much longer to recover. Little work has been done on the literature to understand the recovery pattern from these crises. The first chapter in this dissertation, entitled “Sudden Stops, Output Drops and Credit Collapses”, starts from the premise that a better understanding of the crisis also involves learning and trying to understand the recovery path. Therefore, unlike earlier studies, it collects evidence from a sudden stop episode from collapse to recovery. Another inno- vative aspect of this chapter is that it used micro data in additional to macro data which allows one to take a closer look at the impact of crises on firms. In particular the chapter documents the main patterns in firm-level data in Southeast Asia during and following the 1997 crisis. This Asian crisis started in Thailand with the decision of the Thai government 4 to float the Thai Baht after major efforts trying to support the peg to the US dollar. The crisis quickly spread to most Southeast Asia and saw slumping currencies and a collapse in asset prices. The year of 1998 witnessed major drops in output, particularly in Thailand, Indonesia, Korea and Malaysia. While the year of 1999 brought some mild improvement in GDP it was not until the end of 2000 that GDP in the region started a quick recovery to its pre-crisis level. However the stock market in the region had a different story, as it did not see a major improvement after its collapse until many years later. The same was for credit and to some extent investment. In this first chapter I also compare the performance across firms and I find that there is a significant heterogeneity. Firms in the tradable sector and exporters performed consid- erably better than those in the non-tradable sector. This observation has a straightforward explanation: following the devaluations in this region exporters gained competitiveness on the foreign market and therefore this limited the impact of the crises on their sales. I also find a considerable size effect on the performance of publicly listed firms during and following the crisis. In particular I find that larger firms significantly outperformed smaller firms. Another significant effect on the performance of firms is the relative size of debt to total assets, i.e. the leverage of the firms. I find that firms with higher leverage performed relatively worse than other firms. These findings will be explained within a simple firm level model that incorporates the main elements to analyze the behavior of a firm during a crisis. In particular the model incorporates financial frictions, which as mentioned ear- lier, the recent literature suggest it is at the heart of the story. The model features firms that maximize the stream of dividends and face endogenous borrowing constraints. These constraints put a ceiling on the amount of debt that a firm can borrow, a ceiling that is 5 function of the market value of the company. Therefore fluctuations in asset prices will lead to fluctuations in the level of debt when these constraints are binding. Firms also face financial frictions in the form of costly substitution between debt and equity. This is an important feature of the model. During bad times, firms might need to decrease their debt level by increasing their internal financing. However such substitution is costly and can therefore affect the production of a firm that is trying to adjust to a new and lower debt level. Sudden stops take place in the model following a change in the expectations about future growth rates. I model this by assuming that the trend of growth in the economy is subject to shocks. This assumption is motivated by recent findings (e.g. see Aguiar and Gopinath, 2007) that suggest that business cycles in emerging markets are driven by trend shocks. Therefore my model departs from the standard business cycle model where total factor productivity shocks drive booms and recessions. In fact I show that earlier sudden stop models cannot generate a recovery like the one that is observed in the data due to their underlying assumption that these crises are driven by TFP shocks. Shocks to the trend instead, can account for most of the observation in the data. Furthermore, and unlike TFP shocks, they are in agreement with the many models that place agents’ expectations at the center stage of these crises. As I show in chapter 2, shocks to the trend create this observed dichotomy between output and asset prices. Following a shock to the trend, asset prices decrease due to the downward revision in future profits. The presence of borrowing constraints will lead to a drop in debt levels, which, due to financial frictions, will lead to a costly adjustment and a drop in output. However the drop in output is only temporary as it is due to the financing adjustment of the firms. Once this adjustment is over, firms can still operate at the same pre-crisis level and therefore output can recovery rather swiftly. 6 This recovery in output does not hinge upon a recovery in agent’s expectations or, in other words, a recovery in the trend. Therefore whenever these trends shocks are persistent the recovery of output will be relatively quick compared to the persistent collapse in debt levels and assets prices. The model presented in chapter 2 can also explain the difference in performance of large and small firms observed in the data. The explanation is based on the observation that small firms are on average growth firms. With much growth ahead of them, a larger share of the market value of these small firms is due to the market’s expectations about their future profit. In contrast the market value of larger firms reflects their current market size and capital. Therefore a change in future growth rates will tend to affect more the market value of the smaller firms. I find strong support in the data for this hypothesis. One of the conclusions of the first chapter is that the considerable financial frictions in the emerging markets are one of the main factors behind the volatility of output. These fric- tions make the real economy more vulnerable to changes in expectations about the future. Although quantitatively important, there are many other weaknesses that are known to have played an important role during these crises. One of these factors is the non-standard composition of debt in the emerging markets. In most developed economies foreign bor- rowing is done in local currency at long maturity. In most cases, such maturity and cur- rency composition offer the best insurance for borrowers. First, large devaluations tend to occur during deep recessions and periods of crises and therefore when debt is denomi- nated in local currency, the repayment that the borrower has to make is lower in real value during bad times. Second, when agents borrow at short maturities, they might be unable to roll-over their debt during bad times. In this respect, long-term debt is evidently a better 7 option whenever there is a risk of recession or a crisis. The second chapter in my disser- tation studies this issue and focuses on the maturity structure of nominal debt in emerging markets. The evidence points to an anomaly in the way the emerging markets borrow from the world. This anomaly was recently labeled the “Original Sin” of emerging markets (see Eichengreen and Hausmann, 1999). This label suggests that these markets cannot borrow abroad in local currency and that they also cannot borrow at long maturities. Most stud- ies suggest that this composition of debt is due to an inability instead of unwillingness. However they differ on the reasons behind this inability. Some suggest that the problem is due to an imperfection in the international capital market. They argue that, despite the gains from diversification, it becomes increasingly costly for foreign lenders to learn about the new and exotic currencies and therefore will refuse to hold debt denominated in these currencies. Others argue that this view is not plausible. The inability of these emerging markets to borrow in a way to best insure themselves against financial crises is due to fiscal and monetary problems. When foreigners and locals buy local currency debt they run the risk of seeing the real value of their debt being deflated by a government’s policy to mon- etize some of the debt. The higher the risk of debt monetization, the less attractive is local currency denominated debt in these countries. This argument offers a potential explanation to the two observed regularities: the reliance on foreign currency in the foreign markets and the reliance on short maturity bonds in the local markets. The evidence gives some support to the latter argument in particular for the relationship between the credibility of monetary policy and the maturity of local currency debt. Jeanne and Guscina (2006) and Mehl and Reaynaud (2005) have collected data on local currency debt in emerging markets from various sources. These recent data show a clear negative link between the maturity 8 length of fixed interest rate and inflation in these countries. That is, they show that coun- tries with high inflation risk tend to issue fixed interest rate bonds in shorter maturities. So far, this has been understood in terms of a relationship between the variance of inflation and the maturity of nominal debt. Indeed, the variance of inflation increases the risk profile of these nominal bonds, which may lead some risk-averse investors to shy away from the long maturity market. In the second chapter I argue that this is not the only link between inflation and maturity. I first provide evidence from time-series of correlation between the level of inflation in Turkey and the average maturity issues by the Turkish treasury. So far the empirical literature has examined this relationship in cross-sectional data. Therefore it was not able to provide any evidence about the relationship over time between inflation and average maturity. I show that there is a strong, negative and significant correlation between the level of inflation and nominal interest rates on one side and the average matu- rity on the other. This relationship cannot be explained by the usual risk argument. In other words, the increase in average maturity that accompanies short-lived decreases in inflation cannot be due to a change in the variance of inflation since this latter is theoretically con- stant in the short run. To explain this co-movement I develop a simple general equilibrium model with incomplete markets of agents trading nominal bonds under different inflation processes. The model incorporates a stabilization risk. That is, the risk that the central bank will suddenly and successfully stabilize prices. The reason why I incorporate the possibility of such event in my model is because emerging markets often sought to fight inflation by implementing stabilization policies that rarely worked. However the presence of such policies do have important consequences on the actions of agents in the economy. In fact those agents who borrow during high inflation run the risk of paying very high 9 real interest rates if the government installs a successful stabilization program before the repayment date. I show in my model that there exist a range of stabilization probabilities and inflation levels that will generate this negative correlation between inflation and aver- age maturity issued. Note that, unlike earlier studies, this relationship arises due to the unwillingness and not the inability of the issuer to borrow at long maturities. This result assumes that the issuer is also unwilling to default on its debt or that default is extremely costly. Such assumption is especially compelling for the case of the local debt issued by the government. History shows very few examples of government defaulting on their local debt. 10 Chapter 2: Sudden Stops, Output Drops and Credit Collapses 2.1 Introduction In recent decades, many emerging countries were hit by episodes of severe financial distress, characterized by dramatic current account reversals and large losses in output. These so-called “Sudden Stop” episodes prompted much theoretical research that attempts to understand the nature of these crises. This literature has so far been guided mainly by evidence from macro data and has focused on explaining the main features observed before and during the output drops. Recoveries from these episodes were viewed as sharp and quick. In fact the Sudden Stop phenomenon was sometimes referred to as a “Mexican wave”. However, these crises were far from being a quick wave. As recently documented by Calvo, Izquierdo and Talvi (2006), these episodes, unlike regular business cycle fluctu- ations, display a strong recovery of output in the space of three to four years after the crisis with virtually no improvement in credit or investment after their collapse. In our firm-level data taken from Southeast Asia we also find that debt levels and asset prices collapsed and 11 did not show any sign of recovery even after the recovery of sales to their pre-crisis levels. These so-called “credit-less” recoveries, as labeled by Calvo, Izquierdo and Talvi (2006), are left unexplained. They are also at odds with current models that study Sudden Stops in a framework of excess volatility and thereby generate a strong procyclicality in debt and asset prices. Another, albeit related, shortcoming of this literature is that it has not taken advantage of the available firm-level data. This is surprising given that in most Sud- den Stop models firm-level frictions and borrowing constraints are the main mechanisms behind the large output drops. To fill this gap, this paper gathers evidence from firm-level data during a Sudden Stop episode and explores how a simple model with optimizing firms can qualitatively and quantitatively explain the features in the data. We emphasize both the patterns displayed by the average firm throughout the episode, from the collapse in sales to their recovery to pre-crisis levels, as well as the cross-firm heterogeneity present in the data. In particular, we study the Sudden Stop episode in Southeast Asia by looking at the balance sheets and income statements of publicly listed firms in Indonesia, Malaysia and Thailand from 1996 to 2003. This episode display the typical patterns of Sudden Stops as documented by Calvo, Izquierdo and Talvi (2006), including the credit-less recovery (see Figure 1). We find that the market value of the companies in these countries collapsed at the beginning of the crisis and remained low throughout the episode. This drop in the market value was followed by a drop in total sales which recovered relatively quickly over the three years following the crisis. Total debt however, was on a decreasing trend and did not show any sign of recovery by the end of 2003. That is, firm-level data display a severe form of credit-less recovery: not only did net credit not recover to its pre-crisis level but 12 it also remained negative on average for six consecutive years following the crisis while the sales of these companies were recovering. We also find that investment, both gross and net, collapsed and did not recover by the end of 2003. Another striking pattern in the data is the fact that larger companies significantly outperformed the smaller ones. This size effect is significant even after controlling for other factors such as the export status of these firms and their degree of leverage which also were important determinants of firms’ performance during the crisis. The model contributes to the literature by (i) generating a Sudden Stop and output drop following a negative shock to expectations of future growth rates, (ii) explaining the “credit-less” nature of the recovery from these episodes, (iii) explaining the relationship between the size of a firm and its performance during a crisis and also by (iv) generating a strong leverage effect as observed in the data. The model features optimizing firms in a small open economy that choose capital and debt levels to maximize the expected future stream of dividends. The economy is subject to shocks to the growth rate of the aggregate technology level. Aguiar and Gopinath (2007) show that these shocks are the primary source of fluctuations in emerging markets. Firms face borrowing constraints which limit their borrowing to a linear function of their expected market value. The market value of a firm is itself endogenous to the firm’s financial decisions and to the state of the economy. Firms pay dividends and are allowed to issue equity, although deviating from a long run payout target can be costly for a firm. This introduces a friction at the firm level that limits the degree of substitutability between debt and equity. In this context, a sudden negative shock to the expected future growth rates in the economy decreases the market value of 13 the firms which will be followed by a decrease in their debt levels when the borrowing constraints are binding. Due to financial frictions, this adjustment is costly and therefore will drain resources that would otherwise be used for production and therefore results in a drop in output. However, this decrease in the level of output is only temporary as it is due to the costly transition from states of high debt to those of lower debt. That is, even a persistent negative shock that can cause a persistent decrease in both the market value and the debt level as seen in the data, will only cause a temporary decrease in output. After the adjustment process output recovers to the trend and hence to the pre-crisis level too. Our model is therefore able to generate a credit-less recovery since the recovery in output is not necessarily associated with that of the market value or the debt level. In that respect, trend shocks can produce patterns that are similar to the ones observed in the data during both the collapse of output and its subsequent recovery. Our model features two types of firms which differ in their level of technology. Firms with higher technology accumulate higher levels of capital and are therefore larger than firms with the low level of technology. Assuming that smaller firms have a possibility of becoming large, an assumption that is consistent with the empirical literature, will be suffi- cient in this context to generate a positive correlation between size and performance. This is because the market value of small firms becomes more volatile under this assumption due to the “growth option” that they possess. 1 The intuition behind this result is the fol- lowing: compared to large firms, a sizable share of the small firms’ market value is due to 1 We call the possibility of small firms becoming larger a “growth option” with a slight abuse of ter- minology. In fact every firm that receives a positive technology shock in our model will find it optimal to increase its capital and grow. 14 the expectations that the market place on future growth rates. Therefore changes in these expectations will have a larger impact on the market value of small firms. In our model where changes in the market value drive changes in output levels due to financial frictions, this will translate into a higher volatility in the sales of small firms. We show that the data display evidence that supports our theory behind the size effect. In particular we find that smaller firms have on average higher pre-crisis Tobin’s Q and that this ratio is negatively correlated with performance during the crisis, as predicted by the model. Note that the Tobin’s Q is a standard measure of the perceived growth opportunities of a firm. We also show that trend shocks in our model can generate a strong negative correlation between the pre-crisis leverage of a firm and its performance during the crisis. This leverage effect can provide an explanation to the fact that small household businesses, as observed in Paulson and Townsend (2005), were significantly less affected by the crisis than the publicly listed firms that are usually less financially constrained. The model is at the crossroads of several strands of literature. First and like most recent Sudden Stop models, it is related to the literature on the financial accelerator in macroeco- nomic models (see for example Bernanke and Gertler, 1989; Kiyotaki and Moore, 1997); Mendoza (2005) has shown how such a mechanism can explain the Sudden Stop phe- nomenon in the emerging countries. In Mendoza (2005), Sudden Stops are generated endogenously following negative TFP shocks of standard magnitudes. Through an ampli- fication mechanism, these shocks can generate output drops of a magnitude that is sim- ilar to what is observed in the data. However TFP shocks in Mendoza (2005) generate procyclical debt and asset prices. Instead our model relies on shocks to growth rates to generate both the macro and micro features observed in the data. In that respect the model 15 is related to the literature that emphasizes the importance of trend shocks in explaining the business cycle. Aguiar and Gopinath (2007) show that the emerging economies are sub- ject to substantial volatility in trend growth and that this volatility is the primary source of fluctuations in their business cycles. We borrow this feature for two other reasons: first, we observe that growth rates have significantly decreased in the post-crisis period in Indonesia, Malaysia and Thailand. This decrease in post-crisis growth rates has also been documented in earlier studies such as Barro (2001). This can be captured in our model by a persistent change in the slope of the trend. Second, it has been often argued in the litera- ture that changes in investors’ sentiment can be a driving force behind these crises. In that context, trend shocks can capture the sudden change in the confidence of investors about the future. However this model does not address the issue of whether crises can be a self- fulfilling mechanism; this mechanism is only one interpretation of the persistent growth shocks in our economy. Finally the model is related to the finance literature that studies financing decisions of firms in terms of their choice between equity versus debt financing and their dividend payout policy. In that respect our model is most related to the recent paper by Jermann and Quadrini (2007) which shows the negative relationship between the volatility of the business cycle and the degree of flexibility in firms’ financing. In partic- ular we borrow their quadratic adjustment cost in dividends. This cost function is meant to capture the cost of equity issuance 2 as well as the desire of managers to smooth divi- dends. 3 This function can also capture other costs that firms have to pay when re-adjusting their financing structure. We first show, in section 2, the empirical evidence from both 2 This cost is well documented in the data, see for example Kim, Palia and Saunders (2003). 3 See Lintner (1956), Fama and Babiak (1968) and Laub (1976) 16 the macro and the firm-level data from Indonesia, Malaysia and Thailand. We show the strong dichotomy in the patterns displayed by firms’ sales on one hand and their market value and debt levels on the other. Furthermore we stress the considerable size effect that we find in the data by showing regressions of firms’ performance during the crisis on the main determinants used in the literature. We also compare the performance of our publicly listed firms with that of a sample of small household businesses in Thailand to show that highly financially constrained firms were the least affected by the crisis. In section 3 we present a model that will be able to explain these patterns. We leave the final remarks to the conclusion in section 4. 1990 1995 2000 2005 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Credit over GDP Thailand Malaysia Indonesia Figure 2.1: The ratio of credit to GDP. Data source: International Financial Statistics, IMF. Credit is taken from the “Credit to the private sector” entry, line 22d. 17 2.2 From Sudden Stops to output recoveries: The Evi- dence Southeast Asian economies have enjoyed a long period of high and uninterrupted growth before the financial crisis which started in late 1997 with the devaluation of the Thai Baht. Following this devaluation, these economies experienced large losses in their output in 1998, and for some, these losses continued in 1999 before the economic activity started a strong recovery in 2000. In this paper we examine the balance sheets of the pub- licly listed companies from Indonesia, Malaysia and Thailand. We choose to study this financial crisis and in particular these three countries for two main reasons: First, due to a wealth of firm-level data from this episode, we can construct a larger and better quality data set compared to what we can obtain from the episodes in Latin America. Second, the macro data from these countries during this episode display the main patterns of the average Sudden Stop episode as documented by Calvo, Izquiero and Talvi (2006). That is, the three countries experienced a large reversal in capital flows, large drops in output and a credit-less recovery. Figure 2.1 shows how the ratio of credit to GDP collapsed in these countries following the crisis episode and did not recover by the year 2005, even though output has started to recover in these countries by the year 2000. Figure A.3 in the appendix shows an index of the real GDP in these countries. Among the three countries, Indonesia’s recovery was the slowest; its real GDP recovered to its pre-crisis level only by the end of 2003. On the right column in Figure A.3 we compare the growth rates in these countries before and after the crisis. It is clear that after the major drop in output growth rates did not return to their pre-crisis level. Table A.2 compares the average growth rates 18 during the period 1990-1996 with those observed during the period 2000-2006. We find that post-crisis growth rates are significantly smaller 4 . In the remainder of this section we look at the evidence from firm-level data. 2.2.1 Sample selection and data Our sample consists of 548 non financial firms listed on the stock market in Indonesia, Malaysia and Thailand. We focus on the period December 1996-2003, that is, we examine the balance sheets of these companies from the pre-crisis year till the year in which output has recovered in the three countries. So that the patterns in our data be independent of firm entry and exit we choose to have a balanced sample. The data we use are obtained from Worldscope (Thomson Financial) and they include firms’ balance sheets, income statements, flow of funds as well as other informations. We only choose companies for which the main balance sheet items are available. From the 548 firms that we have in our sample, 109 firms are from Indonesia, 267 are from Malaysia and 172 are Thai firms. 2.2.2 The Evidence Figure 2.2 shows the behavior of the main aggregate variables in our sample over the Sudden Stop episode. In box II.a we plot the natural logarithm of the average sales in our sample. The biggest drop in sales took place in 1998 which was followed by another decrease in 1999. Thereafter sales were increasing and recovered their level of 1997 by 4 A t-test rejects the equality of the means at the1% confidence level. 19 1996 1998 2000 2002 2004 12.1 12.15 12.2 12.25 12.3 12.35 II.a sales 1996 1998 2000 2002 2004 60 70 80 90 100 110 II.b sales debt 1996 1998 2000 2002 2004 20 40 60 80 100 120 II.c sales investment 1996 1998 2000 2002 2004 −50 0 50 100 150 II.d sales credit Figure 2.2: A credit-less recovery. Notes: Except box II.a which plots the logarithm of average sales in our sample, this figure shows indexes of sales, debt, investment and credit where the 1997 value is normalized to 100. Data source: Worldscope, Thomson Financial. the end of 2001. Box II.b plots an index of average debt against an index of sales. Average debt is computed as the average of total liabilities on firms’ balance sheet. Except for a slight increase in 2000, average debt was constantly decreasing after 1997 and was cut by 30% by the end of 2003. In other words, net credit, which is the first difference in total liabilities was still negative 6 years after the crisis as shown in box II.d. Our firm-level therefore shows a more severe of “credit-less” recovery than the macro data. This is because not only did the credit not recover to its pre-crisis level but it remained negative even after the recovery of output. That is firms were still repaying more debt than they are taking on new credit. As for investment defined here as the capital expenditure of 20 the firm, it decreases by more than60% during the crisis and remains low without showing a sign of recovery. A plot of investment is shown in box II.c. Although this credit-less recovery pattern is quite uniform across firms of different characteristics in our sample, some firms were more affected by the crisis than other. In fact we find that in our sample of publicly listed companies, larger firms outperform smaller firms during the crisis. In particular the drop in sales has been much more signifi- cant for smaller firms and their recovery has been also slower. In Figure 2.3, we compare two subsamples of our original sample. To do this, we first rank the companies based on the dollar amount of their fixed assets of these companies in year 1996. Then, we select the upper and lower 35% of the main sample. The drop in sales exceeded 20% for the smaller firms while it was below10% for the larger firms. The recovery of sales was also slower for the small firms. Smaller firms had also to decrease their stock of debt signifi- cantly more than the larger firms. Investment in this figure is computed as the difference in a company’s fixed assets as opposed to capital expenditure as in Figure 2. This is mainly to show the similarity between the change in total assets and the change in total liabilities. The difference between theese two subsets is striking. However this difference can be due to many other factors that are correlated with size which we need to control for. Therefore we run regressions where the dependent variable is the change in log of sales over the cri- sis period as a proxy for a firm’s performance. The explanatory variables that we include in the regression are the following: 1. Industry dummies to control for the main sectors in our sample. 2. A dummy that takes the value one if the firm is an exporter. 3. A measure of the firm’s leverage which we compute as the ratio of total liabilities to total assets. 4. A measure of the average interest rate paid by the firm which we compute as the ratio of 21 1996 1998 2000 2002 2004 60 80 100 120 Sales 1996 1998 2000 2002 2004 60 70 80 90 100 Debt 1996 1998 2000 2002 2004 −50 0 50 100 Investment 1996 1998 2000 2002 2004 −100 −50 0 50 100 Credit Large Small Figure 2.3: Comparing the performance of large and small firms. Notes: Figure 3 plots an index of average sales, debt, investment and credit where the 1997 value is normal- ized to 100. The dotted line shows the figure for the smaller companies while the solid line is for the largest firms. Firms are ranked by their size in 1996 based on the dollar value of their fixed assets. Data source: Worldscope, Thomson Financial. total interest payments to total liabilities. 5. A measure of the profitability of the firm for which we use the ratio net income divided by total assets. 6. We also include a dummy for Thailand and a dummy for Indonesia to control for country effect. That is, we use the standard explanatory variables found in the literature to look for the main determinants of firms’ performance during the crisis. We focus on two measures of performance during the crisis: The change in the log of sales between 1996 and 2002, that is the change from peak to recovery, and the change of log of sales between 1996 and 1999 that is the change between peak and trough. In Table A.1 we look at the performance of firms between 1996 22 and end of 2002. The dependent variable is the change in log of sales between end of 1996 and end of 2002, while the right hand side variables are end of year 1996 measures. In the first column we only include the measure of a firm’s starting size. With no other controls included the coefficient on the size is positive and significant at the1% level. In the second column we control for the export status of the firm. We include a dummy variable for the firms that are exporters as indicated by Worldscope. We find that the coefficient on this variable is positive and signficant at the 10% level. Note that this regression looks at the performance of the firms in terms of sales during the whole episode and therefore might not reflect how exporters might have outperformed non-exporters during the height of the crisis. In columns 3 and 4 we introduce the country and industry dummies respectively. We find that the publicly listed Thai firms in our sample fared better than the other firms from Indonesia and Malaysia. This is the case even though the GDP of Thailand decreased significantly more than the GDP of Malaysia during the crisis. This can be due to a host of possibilities that are beyond the scope of this paper. In the fifth column of Table A.1 we introduce three financial ratios: The leverage ratio which is the ratio of total debt to total assets of a company; The interest ratio which is given by the ratio of a company’s total interest payments to the total debt and the profitability ratio which we compute as the ratio of net income to total assets. We find that the coefficient on this latter is positive and significant at the 10%. The coefficient on the leverage ratio is negative however not significant. As we will see shortly, this is due to the fact that we are looking at the whole episode from the first drop in output till its recovery. We will find however that the leverage of firms in 1996 was strongly and significantly negatively correlated with their performance during the midst of the crisis. As for the size effect, it 23 remains positive and significant across these specifications 5 . Note furthermore that the coefficient changes only slightly when we introduce new controls. The effect of the size of the firm is also quantitatively important. The results suggest that an increase of 100% in the size of the firm improves its performance by 10%. This is significant especially that our sample is very heterogeneous in terms of firm size. The upper 35% sub-sample include firms that are at least three times as large as the lower 35% sub-sample. To make sure that the size effect is prelavent in the three countries, we run the same regression in column (5) of Table A.1 for each country and we show the results in Table A.4. The results point to a strong and significant size effect across the three countries. Note that this OLS regression regresses the changes in the log of sales between 1996 and end of 2002. It will be interesting to see what factors that explain the performance during the crisis. For this we run a regression where the dependent variable is the change in log of sales between end of 1996 and end of 1999. The results are shown in Table A.3. This table is similar to Table A.1 except that it only covers the crisis from peak to trough. We find that the size effect is strong and significant at the 1% level in all specifications. We also find a much stronger “export” effect than in Table A.1. This is because during the midst of the crisis large currency devaluations have taken place. However results from Table A.1 show that there is some catch up by non-exporters from the trough to the recovery. The leverage effect is also much stronger and significant at the 1% in this regression. The coefficient suggest that an increase in leverage by 0.1 is on average associated with lower growth in sales by 1.8% which is very significant. The profitability ratio is also stronger and more 5 We tried other specification by including more financial variables and the size effect remains positive and significant 24 significant. However there is no evidence that firms that were paying higher interest rates had a worse performance. One might argue that this size effect might be originating from the fact that larger firms export more often and also export possibly a larger share of their production. To make sure that this is not the case, we ran the regressions for both the tradable sector and the non-tradable sector and we find that the size effect is significant in both sectors. The results are shown in Table A.5. Note that in this table the dependent variable measures the performance of firms between peak and recovery just as in Table A.1. Small Businesses during the Crisis In the previous subsection we showed evidence from the publicly listed firms, which as we mentioned earlier, produce a relatively large share of GDP. Given their size, under- standing the behavior of these firms is important for a good understanding of the Sudden Stop episodes. However, it would also be interesting to know how their performance com- pare with that of other firms in the economy, in particular, the small businesses 6 . Unfor- tunately, data from small businesses in Southeast Asia is scarce. Since we cannot collect good data from these businesses from Southeast Asia, we compare the results we obtain from our Thai sample to the data in Paulson and Townsend (2005) which covers rural and semi-rural family businesses in Thailand. Paulson and Townsend (2005) found that these small businesses did not experience a major decrease in their income and profit levels. In fact this is clear in Figure 2.4 where we plot an index of these small businesses’ income 6 We divided our sample of publicly listed companies into small and large firms. However even the small firms in this sample are much larger and have different characteristics than what we call here the small businesses. 25 1997 1998 1999 2000 0 50 100 150 200 250 Retained Earnings Net Income Profit of Hous. Buis. Figure 2.4: Small Businesses’ profits Notes: Figure 4 compares the performance of firms in our sample with the performance of a sample of household businesses in Thailand. The solid line shows the median profits for the household businesses. We compare this with the median net income and median retained earnings in our sample. Data source: World- scope and Townsend Thailand Project, see Paulson and Townsend (2005) for a more detailed description of the sample. against both an index and the income of the publicly listed firms and an index of their retained earnings. Other than their considerable size difference, the small household busi- nesses are considerably much financially constrained (see Paulson and Townsend, 2005) than the firms in our stock market sample. In fact these household businesses carry lit- tle debt while the publicly listed firms in our sample have on average leverage ratio that neighbors 0.6. In section 3, we show that such difference in leverage can explain, in our model, the significant difference in their performance during the crisis. 26 2.3 Model Economy The model analyzes an emerging market represented by a small open economy. The economy is populated by a continuum of firms subject to both aggregate and individual shocks. Firms finance their projects by borrowing from both foreign and domestic lenders. We assume that they face borrowing constraints which impose an upper limit on their debt level such that it does not exceed a fraction of their expected market value. These endogenous borrowing constraints, common to the Sudden Stop literature, play a central role in our model. In particular, they transmit shocks from asset prices to the real side even when the production is not subject to TFP shocks. This transmission hinges on the existence of financial frictions. In our model these frictions take the form of adjustment costs in equity financing, in particular, it is costly for firms to issue and repurchase shares as well as to pay dividends. We first describe the environment in which a firm operates. After characterizing the problem solved by the firm, we show the response of the firm to changes in the state of the economy. We also show the impact of the firm’s size on its response to shocks. The general environment The economy is populated by a continuum of firms indexed by j, where j ∈ [0,1]. Firms decide on production and financing plans to maximize the lifetime value of dividends V j,t =E t ∞ X k=t β k−t d j,k . (2.1) Entrepreneurs discount time at rate β < 1. We assume that firms are heterogeneous in technology levela j and that at any point in timet,a j,t ∈{a S ,a L }. We denote by S⊂ [0,1] 27 the set of firms with a low technology, a j,t = a S and L⊂ [0,1] the set of firms with high technology. By assumption S∪ L = [0,1]. In this model the size of the firm will be determined by its individual technology level since we assume decreasing returns to scale. Therefore the steady state of capital will be higher for firms which possess a higher technology level. We allow for small firms to grow in size, i.e., to acquire a higher level of technology and we also allow for large firms to shrink following a negative technology shock. Therefore we assume thata j,t follows a first-order Markov process with a transition matrix Π. Let η t be the proportion of firms such that a j = a S , we impose assumptions so that η t = η,∀t. In particular, given Π, we choose η 0 such that our sample is stable. In this respect our model is similar to Simon (1960) where not only small firms can receive a positive technology shock but also large firms can with some probability decline in size. The parameters of Π will be calibrated to match the data. That is both, Π(S|L), i.e. the probability of a large firm becoming small, and Π(L|S) will be set to match the ratio of Tobin’s Q between the small firm sample and the large firm sample. Firms produce a single good with a capital inputk j,t , using a decreasing returns to scale technology, Y j,t = a j,t k α j,t Γ 1−α t (2.2) where α ∈ (0,1) represents capital’s share of output. 7 The parameter Γ t represents the stochastic trend in the economy which is the cumulative product of growth shocks. In par- ticular, Γ t = Q t j=1 g j . The growth factor g is stochastic and follows a first order Markov 7 For simplicity we do not model the TFP shock with no loss of generality. However we look at the effect of that shock later when we study the quantitative properties of the model. 28 process with transition probability Λ(g,g ′ ). We assume that this growth factor takes val- ues that are bigger than 1, making the economy experience an unbounded growth with fluctuations around a stochastic trend. Timing, financial frictions and the firms’ borrowing constraint At the beginning of each period t, firms start with a level k t of capital and b t of debt accumulated from last period. After observing the aggregate technology shock g t and after discovering its new technology levela j,t each firm decides on its investment, borrowing and its dividend payments. After dropping the index j for notational simplicity, the budget constraint of any firm is given by : f(k t ,a t ,Γ t )+(1−δ)k t −k t+1 +b t+1 −(1+r)b t =ϕ(d t ) (2.3) Whereϕ(d t ) is the cost of paying dividendsd t and we assume it is given by: ϕ(d t ) = d t + κ Γ t−1 (d t −Γ t−1 d) 2 (2.4) whered is a long-run dividend payout target. This function captures the frictions in equity financing as in Jermann and Quadrini (2007). There is a large empirical literature in finance that study the dividend payout strategies taken by managers and there is a grow- ing evidence that these managers prefer to smooth their dividend payments as first shown by Lintner (1956). Dividend smoothing is often explained in the theoretical literature as the result of a signaling mechanism (see for example: Miller and Rock, 1985; Allen, Bernardo and Welch, 2000 and Guttman, Kadan and Kandel, 2007). In our paper this function has two main additional objectives: First, it captures the cost of equity issuance, 29 as it is well documented in the data (see Kim, Palia and Saunders, 2003). In fact if equity was not costly then managers can substitute freely between debt and equity in our model and therefore a credit crunch will not have an effect on firms’ performance. Second, the costly deviation from a long run target captures many of the adjustment costs that a firm can face when it is subject to an external shock. For the sake of simplicity, we choose to have all the frictions on the equity financing function instead of having both: costly equity issuance and adjustments costs on capital or debt. Note that the stochastic trend enters ϕ(d t ) and over time the cost of a marginal deviation from the long run payout decrease because of increased financial flexibility over time. However this feature does not affect the results in our model but it simplifies the de-trended form of the firms’ problem. We assume that firms face state-contingent borrowing constraints. They can borrow from foreign and domestic lenders up to a limit which is a function of their expected market value. In particular, they face a borrowing constraint of the following form: βEV(k t+1 ,b t+1 ,a t+1 ,Γ t+1 )≥ φb t+1 (2.5) That is, we assume that lenders do not allow the companies’ debt to exceed a fraction 1 φ of their expected market value. We do not formally derive this as a feature of a bargaining problem between the firm and the lenders, although this could be one interpretation of this borrowing constraint. In such case, the parameterφ can express the degree of enforceabil- ity of the contract with the firm. That is the higher is φ the less a given firm can borrow, everything else constant. State-contingent borrowing constraints are common in Sudden Stop models and are borrowed from the literature on the financial accelerator in macroeco- nomic models (see for example Bernanke and Gertler, 1989; Kiyotaki and Moore, 1997). 30 The firms’ maximization problem The growth in the aggregate level of technology Γ t implies that the variables in the model are non-stationary and experience unbounded growth. To solve the model we de-trend all the variables by the factor Γ t−1 which is the compounded growth up to t−1. We denote by ˆ x the de-trended counterpart of x t . Note that we do not de-trend using the current aggregate technology level for practical reasons. This choice does not affect the solution of the problem (see e.g. Aguiar and Gopinath, 2007). However, when we look at the quantitative properties of the model we de-trend all the variables by the factor Γ t instead, without loss of generality. This allows a simpler interpretation of the results and makes it comparable to standard stationary business cycle models. We can now write the maximization problem of the firm recursively where all the variables are de-trended. The firm chooses at timet its new investment and new credit as well as its timet dividends to maximize: ˆ V( ˆ k t , ˆ b t ,a t ,g t ) = max ˆ k t+1 , ˆ b t+1 , ˆ dt { ˆ d t +βg t E ˆ V( ˆ k t+1 , ˆ b t+1 ,a t+1 ,g t+1 )} subject to: f( ˆ k t , ˆ b t ,a t ,g t )+(1−δ) ˆ k t − ˆ k t+1 g t + ˆ b t+1 g t −(1+r) ˆ b t = ˆ ϕ( ˆ d t ) βg t E ˆ V( ˆ k t+1 , ˆ b t+1 ,a t+1 ,g t+1 )≥ φg t ˆ b t+1 Note that after de-trending the variables, ˆ ϕ( ˆ d t ) is given by: ˆ ϕ( ˆ d t ) = ˆ d t +κ( ˆ d t −d) 2 . (2.6) 31 Taking the firm’s interest rate as exogenous, the first order conditions are: β 1 ϕ ˆ d ( ˆ d ′ ) (f ˆ k ( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ )+(1−δ))(1+μ) = 1 ϕ ˆ d ( ˆ d) (2.7) β −1 ϕ ˆ d ( ˆ d ′ ) (1+r)(1+μ) = μφ− 1 ϕ ˆ d ( ˆ d) (2.8) The detailed derivations are shown in the appendix. We denote byμ the Lagrange mul- tiplier on the borrowing constraint and use subscripts to denote derivatives. For notational simplicity we denote by ˆ k ′ , ˆ b ′ , ˆ d ′ next period’s capital, debt and dividends respectively. Since our use of the functionϕ(d) is partly motivated by the fact that managers prefer to smooth dividend payouts we set ¯ d to the steady state value of ˆ d. 8 Equation (8) links the borrowing constraint’s multiplier to the interest rate which we assume is exogenous in our model: μ = ϕ ˆ d ( ˆ d ′ )−β(1+r)ϕ ˆ d ( ˆ d) ϕ ˆ d ( ˆ d)(ϕ ˆ d ( ˆ d ′ )φ+β(1+r)) (2.9) Proposition 1 At the steady state the multiplier on the borrowing constraint is indepen- dent of the growth factorg and is positive forβ(1+r) < 1 implying that the constraint is binding under such assumption. Proof. This follows directly from equation (9). At the steady state ϕ ˆ d ( ˆ d ′ ) = ϕ ˆ d ( ˆ d) = 1 and therefore μ = 1−β(1+r) φ+β(1+r) which is independent of g and greater than zero as long as β(1+r) < 1. Note that the assumption that β(1 + r) < 1 is standard in our context. It implies that firms will prefer to borrow at the steady state. In the presence of endogenous borrowing 8 This can be easily implemented since there is a single value ford for which ˆ d SS = ¯ d. 32 constraints, however, we know that the path of debt is not explosive. If we were not to impose the assumption that the discount rate is smaller than the interest rate, we could study instead the dynamics of the model when the firms are below the steady state and hold a lower debt level than the optimal one. However this will only complicate the anal- ysis without adding much insight to the problem in hand. Proposition 1 has two central implications to our analysis: First it implies that debt levels will fluctuate with the market value since the borrowing constraint is binding at the steady state. Second, sinceμ deter- mines the marginal cost of capital, we know that this latter will be independent of changes ing. Proposition 2 The steady state detrended capital levels are independent of changes ing. Proof. This follows directly from Proposition 1 and equation (2.7). From equation (2.7) we have that: αθ( ˆ k g ) α−1 +1−δ = 1 1+μ (2.10) Therefore the detrended capital at time t, ˆ k g is independent ofg as long asμ is independent ofg which is shown to hold at the steady state in proposition 1. The intuition behind this result is simple. Assuming that the interest rate is exogenous in this small open economy and independent of the growth rate of this economy, the marginal cost of capital is unchanged for different levels of growth rates, as shown in proposition 1, and therefore the optimal amount of de-trended capital held by firms at the steady state will not change. Note however that changes in growth rates will indeed impact the growth rate of capital. An interesting feature of this model is therefore the dichotomy between capital, and therefore output, and the market value. It is clear from equation (1) that a change in the 33 growth rate will have an impact on the market value of the firm. In particular a permanent change from g to g will decrease permanently the market value of the firm even in de- trended terms, since it decreases the growth rates of the dividends. Furthermore, since firms’ debt is limited by their market value, and since the borrowing constraint is binding over any steady state, a drop ing will be followed by a decrease in both the market value and the firm’s debt. If the drop in g is permanent the decrease in the de-trended market value and debt will be too. However during the period in which the debt level is transiting to a new and lower level the firm needs to adjust either its capital or its dividends to be able to pay for its old debt. This can be clearly seen from the budget constraint of the firm. Therefore the firm will face a trade-off between a decrease in capital and a decrease in dividend payments. If a one dollar decrease in dividends will provide the company with a one dollar to pay its debt than the company would prefer to act on its dividends instead of decreasing the capital stock. This is because the marginal cost of decreasing the capital stock is higher, since it decreases next period’s output while changes to dividend payouts do not bare an effect on next period’s productivity. In other words if the company does not face frictions in its equity financing or dividend payment, capital and therefore output will not be responsive to changes in the growth rates. We showed earlier on that at the steady state the de-trended capital will not be affected by changes in the growth rates, in the following proposition we show that whenκ = 0 the firms’ output will not change even during the transition to the new steady state. 34 Proposition 3 Whenκ = 0 a firm’s output is non-responsive to changes ing. Proof. This follows directly from the first order conditions, which forκ = 0 become, β(f ˆ k ( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ )+(1−δ))(1+μ) = 1 (2.11) β−(1+r)(1+μ) = μφ−1 (2.12) since ϕ ˆ d ( ˆ d ′ ) = ϕ ˆ d ( ˆ d) = 1 in this case. Therefore changes in g will have no effect on μ and on the time-t de-trended capital for a similar argument to the one in proposition 2. Since the de-trended capital level does not change when κ = 0 this means that the cost of transition to a lower debt level will be absorbed by either a decrease in dividends or by issuance of new equity. This follows directly from the budget constraint of the firm. However this result does not hold anymore for κ > 0 since in this case the substitution between debt and equity becomes costly. In this case the trade-off between a decrease in capital and a decrease in dividends is not completely in the favor of the latter. In fact a decrease in dividends will be accompanied by a drop in capital as can be seen from equation (2.7). 9 Therefore following a negative and permanent shock to g the firm will be forced to reduce capital in the short-run, since as we showed, the capital will converge back to its steady state level which is unaffected by changes in g. Hence, our simple model is able to match an important feature in the data, not present in the previous models, which is the persistent collapse in debt that is coupled with a quick recovery in output. Note that we focus on the case where the drops in the growth rate are permanent or very persistent because only such shocks are consistent with the persistent drop in the market 9 Note thatϕ(d) is convex ind and thereforeϕ d (d) < ϕ d (d ′ ) ifd< d ′ . 35 value that is observed in the data. As we showed earlier in fact, the market value collapsed in 1997 in the countries that we study and did not show significant recovery even by the end of 2003. 2.3.1 Quantitative properties with homogeneous firms Calibration We parametrize the model on a quarterly basis. The steady state growth rate is set to 0.02 to match the average annual growth rate of 8% in these countries between 1990 and 1996. As shown in Table A.2, the average growth rates between 1990 and 1996 were around7.2%,9.5% and8.1% for Indonesia, Malaysia and Thailand respectively. Therefore the steady state quarterly growth factor ¯ g is set to1.02. The discount rate is set toβ = 0.97 and thereforeβ¯ g≈ 0.99. Note that in our model and similarly to models that incorporate a stochastic trend in the neo-classical framework, β¯ g is the equivalent to the discount factor in the stationary models. This is why we setβ¯ g to a standard quarterly value of the discount factor. The interest rater is taken from the firm level data. We measure it as the average of the ratio of interest payments to total liabilities in 1996. For the parametrization of the production function we set α, the income share of capital, to the standard value of 0.3. The borrowing constraint parameter is chosen to match the average of the leverage ratios of the companies in 1996 which was around0.51. Note that the leverage ratios of the companies increase significantly in 1997 and were on average close to 0.6. This is partly because of the devaluation that happened in Thailand in that year. It is very likely that a leverage ratio of 0.51, our benchmark value, does not reflect the liability dollarization of 36 these companies. This dollarization can justify the use of a higher value, since during the crisis the companies were more leveraged and had to adjust from an even higher level of debt. However since the higher is the leverage in our model, the stronger will be the impact of the shock on output, we choose to use a lower value for robustness. The parameter κ determines the degree of financial frictions in equity issuance. 10 We show how changes to κ will affect the impact of the shock on output. Finally, since in our benchmark case, firms are not subject to individual technology shocks we set the probability of retaining the same technology to be equal to one. The parameters are shown in Table 2. Response to shocks For simplicity, we disregarded so far the standard TFP shocks typical to business cycle models. However our aim is also to compare the effect of these shocks to the “growth” or trend shocks. For this reason we now add a stationary shock to the production function which is now written as: Y j,t =a j,t z t k α j,t Γ 1−α t (2.13) where z t represents the level of TFP. We are mainly interested in comparing the effect of a permanent shift in the TFP to a permanent change in the trend. This is because only a very persistent shock can generate the observed persistent in the market value of the firms. Independent of which framework one uses to model the economy, the market value of the firms is simply the sum of the discounted future dividends of the firms. Therefore, to generate a persistent decrease in this market value one needs an either large and persistent 10 The lowerκ the less costly it is for firms to substitute between equity and debt. 37 0 10 20 30 40 −4 −2 0 2 Output 0 10 20 30 40 −30 −20 −10 0 Debt 0 10 20 30 40 −30 −20 −10 0 10 Debt to Output 0 10 20 30 40 −30 −20 −10 0 10 Tobin Q Figure 2.5: The model’s dynamics after a shock Notes: The solid line plots the response to a−1% permanent shock to theg as% deviation from the steady state. The broken line shows the response to a−1% permanent TFP shock. drop in the de-trended dividends or a persistent drop in their growth rates. Furthermore regarding the growth shock, there is a significant evidence that the growth rates did not recover to their pre-crisis level as we discussed earlier in section 2. Therefore we compare the effect of a 1% permanent decrease in TFP level to a 1% permanent decrease in the growth factor. The numerical method is described in the appendix. We compare these two shocks qualitatively. The impulse responses are shown in Figure 2.5. The horizontal axis shows the number of quarters after the shock which takes places at time 0. Looking at the TFP shock first we find that both output and debt collapse by a similar magnitude and never recover. This figure serves to illustrate the fact that TFP shocks create the same persistence in output and in debt. That is whether they recover 38 swiftly or slowly over time, debt, output and asset prices will follow a similar pattern. In fact the ratio of debt to Output and the Tobin’s Q do not change significantly and recover quickly to their steady state values. Comparing these results with the trend shock, the picture is very different. Following a negative 1% permanent shock to g output drops in the following period by around3.8% and starts a relatively quick recovery in the following periods to recover to its pre-crisis de-trended level in 20 quarters. Debt however collapses by around 26% and remain low afterward. This is because the fall in debt in percentage terms is equal to the fall in the market value which is clear from the borrowing constraint of the firms. We do not show the response of the market value and debt as they are similar. We only plot the imuplse response function of the debt (see Figure 10). Debt to output ratio also collapses as in the data, although in the data this ratio decreases slowly over time. Note that our model does not generate a smooth transition between the two levels of debt to output because we do not incorporate the frictions on the adjustment of the debt level. Furthemore in our model we only consider one period debt for simplicity, however in reality companies hold debt of different maturities. One would expect that these firms will decrease their holdings of the shortest maturities first implying a smoother decrease in the debt levels. As for the Tobin’s Q, following a negative shock to the trend, the market value collapses at time 0, and therefore the Tobin’ Q will also decrease at the time of the shock. Note that the decrease in capital in the period following the shock will imply a further decrease in the market value. By the time capital and output have recovered to their pre-crisis de-trended levels, the Tobin’s Q will stabilize to a value below its pre-crisis level. Indeed the long term drop in the Tobin’s Q is by about 25% which is equal in percentage terms the drop in debt and in the market value. Qualitatevely our simple model matches 39 well the main findings from the data: The collapse in the market value, followed by a collapse in debt and a drop and a subsequent credit-less recovery of output. Quantitatively, the1% drop in the growth factorg is of a magnitude similar to the drop in the data. See for example the drop in the growth rates in Table A.2. In our model, this negative permanent shock to the trend generates a collapse in debt to output ratio and in Tobin’s Q of about 25%. In the data we observe a decline in these ratios neighbouring 40%. 11 Note that the drop in these ratios is solely driven in our model by the drop in the market value which responsiveness to the growth shock is determined by parameters such as the discount factor and the mean of the growth factor. The drop in the output however is also affected by the degree of leverage of these firms, as well as by the degree of the financial frictions present at the equity level. We observed in the data a significant effect of firms’ leverage on their performance. This is also true when we compare the performance of our publicly listed companies with the performance of the much smaller and much less leveraged household businesses. We conjecture that such difference stems mainly from the fact that household businesses, unlike the publicly listed companies, do not need to adjust signficantly their debt levels (since they are already low as observed by Paulson and Townsend, 2005). In Figure 2.6 we show the difference in the amplification of the shocks for different levels of leverage, as implied by a different parameter φ. The lower panel in Figure 2.6 shows the impact of 1% negative and permanent shock to the trend on output for a leverage of 0.1, 0.6, and 1. As you can see, the higher is the firm’s leverage the stronger is the impact of the shock on output. Furthermore, for low levels of leverage the effect of the shock is 11 We prefer comparing ratios from the model to these ratios in the data to avoid making assumptions about the level of the trend that drives the growth of sales in our sample of publicly listed companies 40 0 5 10 15 20 25 30 35 −1.5 −1 −0.5 0 TFP shock 0 5 10 15 20 25 30 35 −10 −5 0 5 Trend shock Leverage=1 Leverage=0.5 Leverage=0.1 Figure 2.6: Leverage and amplification of the shocks very mild. This property of the growth shock is concordant with the data. It offers one possible explanation for the contrast between the performance of small businesses and that of the publicly listed companies in our data. The impact of a 1% negative and permanent shock to the TFP level is shown in the top panel of Figure 2.6. In our model, a higher leverage is only slightly correlated with a worse performance when the shock is to the TFP. It is possible however that a larger amplification of the shock, and hence a different specification of the model, might lead to larger impact of leverage on performance even under a TFP shock. However by the nature of the TFP shock which affect production directly, it will be challenging to explain the large variety in firms’ performance and in particular the observation from the household businesses that we have shown earlier. The results that so far were obtained for a κ = 0.25. This value however is reasonably only 41 5 10 15 20 25 30 35 −4.5 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 Trend shock − Changing kappa (the cost of dividend payout) k=0 k=0.1 k=0.75 k=2 Figure 2.7: Output drops and financial frictions a lower bound to what the true κ is for Southeast Asia. This is because a κ of 0.25 is the value used by Jermann and Quadrini (2007) as a measure of the financial frictions in the U.S. 12 . For this reason, Figure 2.7 plots the impulse response function of output following a1% negative and permanent shock to the trend. We can clearly see that higher levels of κ increase the responsiveness of output to the growth shocks. Furthermore and as proposition 3 indicates, whenκ is null the de-trended output is not affected by changes in the trend. 2.3.2 Heterogeneous firms and the size effect Section 2 shows strong evidence that larger firms outperformed the smaller one during the crisis episode in Indonesia, Malaysia and Thailand. Table A.1 for example suggests 12 Although the model is Jermann and Quadrini is different than the one in this paper, we borrow the same cost function for equity issuance and dividend payout. Therefore the κ in the two models are comparable because they directly determine the marginal cost of equity issuance at the steady state 42 that on average a twice larger firm had a 10% higher growth rate in sales between 1997 and 2002. Table A.3 shows that most of this difference is accounted by the performance between the peak and the trough of the crisis which was reached in 1999. This difference is quite surprising. Furthermore smaller firms had not only worse performance in terms of sales but also their market value and their debt collapsed significantlty more than the larger firms. This section shows how the model can explain this significant heterogeneity. The argument relies on small firms having a higher potential of growth. There is a strong evidence from a large body of empirical research that, on average, small firms tend to grow faster than the larger ones (see for example Hall, 1988; Evans, 1987). While our pre-crisis data is too short to test a relationship between firm size and growth, in our data we find that in 1996 (the pre-crisis year) smaller firms had on average a higher Tobin’s Q. This in itself is an indication that the market expected the smaller firms to grow on average more than the large firms. The model has a continuum of firm on the [0,1] interval. A proportion η of these firms are small firms with a technology parameter a S . For simplicity we assume that the probability of small firms becoming large is equal to the probability that larger firms fall back and become small. The reason for which we make use of this assumption is simply because we need to calibrate the transition matrix of the technology parametera to match the ratio of the Tobin’s Q in the data. Therefore to match one moment from the data anything more than one parameter will lead to multiple solutions and one would have to choose among the possible options. Note however that this should not affect the results since they are mainly driven by the fact that small firms are growth firms. This is true even 43 if we do not set any restriction on the transition matrix; Since to match a higher Tobin’s Q for smaller firms, the transition matrix has to be such that the smaller firms display a higher average growth in the long run. For our sample to be stationary we therefore assume thatη = 1 2 with no loss of generality. Amplification due to a “growth option”: A simple example Before showing the quan- titative properties of the model with heterogeneous firms, we present a simple example that gives the main intuition behind the result. In our model a larger drop in the market value implies a larger drop in output, everything else equals. Therefore to explain the difference in the performance of large and small firms, we only need to give the intuition behind the larger volatility of the market value of small firms. We show that this follows directly from the assumption that these firms can grow to become large. To simplify the analysis let us assume that there are large firms and small firms in the economy, that distribute at time t dividends d L Γ t and d S Γ t respectively, where d L > d S . Γ t is the stochastic trend that drives growth in the economy and has the same properties described above. At the begin- ning of each period small firms can either remain small or become large with a probability p. Large firms remain large forever. That is we make few simplifications on the original problem. Under such assumptions the market value of large firms can be written as: V L = ∞ X j=0 (βg) j d L (2.14) 44 The market value of the small firms is a function ofV L : V S = d S +βg[pV S +(1−p)V L ] (2.15) Proposition 4 Let us assume that growth rates of Γ are known to be constant and equal to g. At time t the growth rate changes suddenly and permanently to g ′ 6= g. This shock to the growth rates will have a larger impact on the value of small firms, i.e., the absolute value of the percentage change in the market value of small firms is higher than the one for the large firms. Proof. It is straightforward to see that both V S and V L are both strictly increasing in g. Therefore it is enough to show that V S V L is strictly increasing in g to prove that the percentage change in V S is higher in absolute value than the percentage change in V L . Note thatV L = d L 1−βg and therefore: V S V L = d S d L [1−βg] 1−βg(1−p) + βgp 1−βg(1−p) Which can be re-written as: V S V L = d S d L 1−βg(1−p)[ d S d L −p d S d L (1−p) ] 1−βg(1−p) (2.16) From this equation it is clear that V S V L is strictly increasing ing as long as d S d L < 1 which is always true by assumption 13 . 13 This follows from the fact that 1−xα 1−x is increasing in x ifα <1 45 The intuition behind this result is simple. Compared to large firms, a sizable share of the small firms’ market value is due to the expectations that the market place on future growth rates. Therefore changes in these expectations will have a larger impact on the market value of the small firms. In other words, small firms have a “growth option” which itself is a function of the future growth rates. That is unlike large firms, a fraction of the market value of the small firms reflects their future opportunities which have not realized yet. However these opportunities are very sensitive to changes in the growth rates which makes the market value of the small firms relatively more affected by these changes. Note that we have assumed that the large firms do not become smaller for simplicity. If this was possible, then the main logic would still apply. This is because such possibility would only decrease the volatility of the large firms. Since in the original model the borrowing constraint binds at the steady state, a larger change in the market value would induce a larger change in the debt level of a company. This directly implies that the small firms’ production will also be more affected by changes in growth rate. In the following we compare the response of small firms and large firms to a trend shock in the original model. Calibration We choose parameters such that these firms are representative of our upper and lower subsamples respectively. We first normalize a l to one. Then we choose a s such that the larger firm has three times more capital than the smaller firm as observed in our subsam- ples. The other parameter that we need to choose is the probability of switching size, i.e., the probability of smaller firms becoming large and the probability of large firms becom- ing small. This parameter will determine the Tobin’s Q of both the large and the small 46 0 5 10 15 20 25 30 −5 −4 −3 −2 −1 0 1 Output 0 5 10 15 20 25 30 −30 −25 −20 −15 −10 −5 Tobin’s Q Large Small Figure 2.8: The size effect firms. For this we choose this probabilityp to match the ratio of the Tobin’s Q of the small firm to the Tobin’s Q of the large firm. This ratio is equal to 1.25 in the data. Note that given this heterogeneity, even when these firms are subject to the same degree of borrow- ing constraint they might accumulate different ratios of debt to capital. In particular, the fact that the small firm is a growth firm will allow it to accumulate relatively more debt given its higher ratio of market value to capital. However since in the data the leverage of both large firms and small firms are not significantly different we choose to impose a tighter constraint on the small firms to generate the same leverage ratio that is in the data which is around 0.51. The calibrated parameters are shown in Table A.8. 47 Quantitative properties Note that although a small firm can acquire a new technology overnight, due to the borrowing constraint it might not be able to accumulate the optimal capital in one period. That is, unlike the earlier simple example, in this case small firms have to follow a path to become large firms which starts at the period in which they acquire the new technology. The results are shown in Figure 2.8. The upper panel shows the reaction of the output of large (solid line) and small firms to a 1% permanent negative shock to g. We can see that the de-trended output of the small firm drops significantly more, before it recovers relatively quickly to the pre-crisis level. The lower panel in Figure 2.8 shows that both the Tobin’s Q of the large and the small firm decrease, but that the drop in the latter is significantly larger. The TFP shock does not induce a significant heterogeneity in the response of large and small firms as shown in Figure A.1. This is because unlike the growth shock a TFP shock affects directly the firm’s output and subsequent changes in the market value are due to this output change. In that respect, the growth shock outperforms the TFP shock in generating the observed heterogeneity. The story proposed by the model is however one based on the assumption that small firms are growth firms. As we discussed earlier such assumption is supported by evidence from our data and it is also motivated by the findings of the empirical empirical literature on firm size. The model however implies that it is the growth option that is responsible for this increased volatility of small firms, i.e., in other words it is the Tobin’s Q rather than the firms size in 1996 that should be negatively correlated with the firm’s performance during the crisis. Indeed such prediction is extreme, since in general a Tobin’s Q is correlated with higher subsequent growth rates. Furthermore in reality there are many reasons for which a firm might have a high Tobin’s 48 Q and still perform well during the crisis. Examples like this include exporters and other firms that received a positive shock before the crisis. Despite these obstacles we do find in the data evidence that supports the prediction of the model. Although the beginning period Tobin’s Q is not negatively correlated with the performance of the firms during the whole episode, it is significantly negatively correlated with their performance during the height of the crisis in 1998. That is what is shown in Table A.6. When we introduce the Tobin’s Q to the earlier regressions we find that its coefficient is negative and significant and that the positive coefficient on size loses significance. To make sure that this does not reflect the impact of a higher leverage ratio, even though we do control for this ratio, we replace the Tobin’s Q in column 3 and 4 by the ratio of the market value to capital and we find that it is strongly and significantly negatively correlated with the performance in 1998. Note that theR 2 obtained when using this ratio alone (see column 4) is higher than the one in column 1, i.e., theR 2 obtained from including the firm size. Therefore the data show strong evidence that supports the model’s hypothesis and predictions. 2.4 Conclusion In this paper, we first documented the main patterns displayed in firm-level data during the Sudden Stop episode in Southeast Asia and then we presented a model to explain theses features. The model contributes to the literature by (i) generating a Sudden Stop and output drop following a negative shock to the expectations of future growth rates (ii) explaining the “credit-less” nature of the recovery from these episodes and also (iii) by explaining the impact of the size as well as the leverage of a firm on its 49 performance during a crisis. Earlier Sudden Stop models, which rely on TFP shocks, generate pro-cyclical debt and asset prices and therefore cannot explain the nature of the credit-less recovery. In the firm level data we find that there is a strong dichotomy between sales on one side and credit, investment and market value on the other. For example, while firms’ sales recovered on average three years after the crisis, their average net credit not only did not recover, but also remained negative for six consecutive years following the output drop. Recently Calvo, Izquierdo and Talvi (2006) examined macro data from a sample of Sudden Stop episodes and found that this credit-less recovery is a main characteristic of these episodes. Furthermore, they found that regular business cycles, even in emerging markets, do not display these features. In our model, we find that growth shocks outperform regular TFP shocks in generating these stylized facts of Sudden Stops. We also show that the growth shocks can generate a significant size and leverage effect. That is, the model can explain why large firms outperform small firms during the crisis and why a high pre-crisis leverage is associated with a worst performance during the crisis. Small firms in our data are on average growth firms as reflected by their higher Tobin’s Q. We model this by allowing small firms to become large with some probability. The possibility of small firms growing will alone lead, in our model, to a higher volatility in their market value which also leads to a higher volatility in their output. We test our conjecture using the data and we find that much of the size effect is indeed due to the higher market value to capital ratio of these small firms as implied by the model. In our model, it is the costly adjustment in debt levels that is responsible for the drop in output. Therefore, as observed in the data, firms that carry little debt are not significantly affected by the crisis. This leverage effect can provide an explanation for the fact that highly 50 financially constrained firms, like the small household businesses, were significantly less affected by the crisis than the publicly listed companies in our sample. Our model carries the analysis at the firm level making it amenable to firm-level data. The model’s parameters can be estimated from the data to explore the implications of different policies during the crisis through counter-factual analysis; a topic that we are currently investigating. 51 Chapter 3: Inflation and the Maturity Structure of Nominal Debt 3.1 Introduction Episodes of high inflation are generally accompanied by a shortening of the maturity of nominal debt contracts. This paper (i) brings new evidence from time series on newly issued debt about the relationship between inflation and the maturity of nominal bonds and (ii) investigates the extent to which the risk of inflation stabilization during periods of high inflation can explain the observed facts. When compared to the developed economies, the emerging markets display puzzling fea- tures in their debt contracts. Typically, both the government and the private sector in these economies borrow too often in foreign currency and use nominal debt contracts virtually only at short maturities (see Eichengreen and Hausmann, 1999). These patterns in emerg- ing markets’ debt received much attention in recent decades from both the policy and the academic circles. This issue is still a concern today. For example, in 2007, the G7 finance ministers issued a brief note stating that: “Developing local bonds markets deserves a 52 higher priority to reduce emerging markets’ vulnerability to external shocks and financial crises and to promote growth”. The inability or unwillingness of these markets to borrow in local currency bonds at long maturities creates both a currency and maturity mismatch on their balance sheets. While their liabilities are often biased toward foreign currency their assets are often denominated in local currency. Furthermore, they typically possess more assets than liabilities for medium- and long-term obligations. Under such condi- tions, a currency devaluation can have devastating effects on the economy. It leads to a decrease in net worth of their assets and a increase in the real value of their liabilities. The vulnerability of these economies to exchange rate perturbations is documented in many recent empirical papers (e.g. see Hausmann, Panizza and Stein, 2001; Calvo, Izquierdo and Meja, 2004). This evidence raises the following question: Why do these economies borrow in such a way that makes them so vulnerable to crises? Much theoretical research has been dedicated to answer this question. This literature advanced a series of alternative explanations for this phenomenon. The most common of these explanations is the moral hazard argument. For example McKinnon and Pill (1998), Krugman (1998), Burnside et al., (2001) and Schneider and Tornell (2004) argue that government policies such as bailout guarantees can provide incentives for agents in the economy to borrow excessively in dollar. A similar argument is advanced by Dooley (2000), Velasco and Chang (2004) and Chamon and Hausmann (2005), who point the finger of blame on the government’s commitment to stabilize exchange rates. Calvo (2001) and Cowan and Do (2003) suggest that a government may issue a dollar debt as a commitment device just to reveal its pref- erence for a stable exchange rate. However many studies cast doubt on the ability of a moral hazard argument to explain this phenomenon (see e.g. Arteta, 2002; Eichengreen 53 and Hausmann ,1999). Other papers argue that the excessive dollar borrowing and the short term borrowing are simply due to fact that the domestic financial system in these countries is underdeveloped. Eichengreen and Hausmann (1999) on the other hand argue that the problem of the “original sin 14 ” can be due to the structure and operation of the international financial system. There is a growing evidence however that some countries with a recent good economic record are able to access the international market using their own local currency (see e.g. Burger and Warnock, 2006). In this paper I look at the role of the risk of stabilization common during periods of high inflation in explaining the inability of agents to issue long term debt in local currency. With the recent empirical findings it is becoming clear that inflation plays a central role in explaining the ”original sin” of the emerging markets. For example Jeanne and Gus- cina (2006) and Mehl and Reaynaud (2005) have collected data on local currency debt in emerging markets from various sources. This recent data show a clear negative link between the maturity length of fixed interest rate and the level of inflation in these coun- tries. That is, they find that countries with high levels of inflation tend to issue fixed interest rate bonds in shorter maturities. Most of the above-mentioned studies acknowl- edge the importance of inflation in explaining this phenomenon. However the link through which inflation generates a dollarization of liabilities and shortening of maturities relies often on asymmetric information arguments. Indeed, inflation per se, affects the nomi- nal interest rates on these bonds. However, in a standard general equilibrium model, it is not clear why the nominal market would vanish even under expectations of high inflation 14 This term was first used in Eichengreen and Hausmann (1999) to denote a predicament faced by most of the emerging markets, which is their inability to borrow in long term local currency bonds in the international market. 54 as I show in this paper. What I also show is that there are some stochastic properties of inflation rate that could generate this phenomenon. Such stochastic properties would arise when there is a small risk of stabilization. In that respect our paper is most related to Neumeyer (1999). In a two-period general equilibrium model with incomplete markets Neumeyer (1999) shows how hyperinflation coupled with a small risk of stabilization can cause the nominal bond market to vanish. Our paper extends this analysis to a T-period model. By doing so I am able to analyze the effect of inflation ( and not only hyperin- flation) on the nominal contracts and I can study the relationship between inflation and the maturity structure of the nominal bond market. That is while the results in Neumeyer (1999) explain the disappearance of the nominal bond market during hyperinflation peri- ods, with this model I am able to explain the negative correlation between the average maturity of the bonds and inflation. Indeed the result in Neumeyer (1999) is also obtained as a special case of our model. Another contribution of this paper is that it brings new evidence from time series about the relationship between inflation and expected inflation (as reflected by the nominal interest rate) on one side, and the maturity of new nominal bonds’ issues. Earlier studies show a negative relationship between inflation and average maturity using cross-sectional data from many emerging countries. A valid concern how- ever is that this relationship might arise due to other factors that are due to structural and institutional differences across these countries that are difficult to account for. By using time series data from the same country I minimize this concern. Our time series data is formed by averaging weekly observation from treasury auctions in Turkey between 1986 and 2003. Turkey is a particularly interesting country to study during that period, since a stabilization risk was present during the periods of high inflation as I discuss. I find that the 55 weighted average monthly maturity of the issued bonds and notes is negatively correlated with both inflation and the nominal interest rate. By doing so this paper shows strong and new evidence where the maturity of nominal bonds is not only affected by the variance of the inflation (i.e., by inflation risk) but also fluctuates with the levels of inflation and the nominal interest rates. We first review the evidence from the literature and present the findings from our data in section 2. We then present the model in section 3. In section 4 I show a numerical example of how high inflation coupled with a risk of stabilization can lead to the disappearance of longer term nominal bonds. In section 5 I conclude. 3.2 Evidence Most emerging markets have a debt structure that is at variance with that of developed countries. This is generally true for both sovereign as well as corporate debt 15 . Sovereign debt structure in particular has received much attention recently especially following the so-called Original Sin hypothesis which has been advanced by Eichengreen, Hausmann and Panizza (2003a, 2003b). These authors documented two major characteristics of emerging markets’ debt, that stand at odds with their OECD counterpart. First, the bulk of their international borrowing is issued in foreign currencies. Second, domestic borrowing, unlike in OECD countries, comprises only a small share of fixed interest domestic currency bonds of medium to long-term maturity (henceforth DLTF Debt 16 ). Recently Jeanne and Guscina (2006) and Mehl and Reynaud (2005) have compiled new 15 For the maturity of corporate debt in emerging markets see Demirguc-Kunt and Maksimovic (1996) and Bleakley and Kowan(2003) 16 DLTF stands for Domestic Long Term Fixed interest 56 data sets on domestic borrowing in emerging markets. These data sets show a significant heterogeneity across the emerging markets. Nevertheless, with the exception of some East Asian countries, the percentage of DLTF debt seldom reaches the levels observed in developed countries. In fact, the observed heterogeneity is mainly due to the different forms of substitutes for DLTF debt found in emerging markets. For example while Argentina has mainly relied on foreign currency (or foreign currency indexed debt), Israel and Chile have relied more on inflation indexed bonds. In light of this evidence one question arises: How much does inflation affect the way countries and corporations borrow ? Many of the available observations on the structure of domestic debt in emerging markets point to a link between inflation and the maturity structure of local currency debt. For example, during the 1980s and 1990s, decades of high inflation in Latin America, the share of DLTF in this area declined from40% (of total domestic debt) in 1980 to a around 20% in 1990, to be cut again in half and reach 10% in 2000 17 . Another prominent example is Turkey which has experienced many episodes of accelerating inflation between 1979 and 2000 period, during which the share of DLTF debt gradually declined from 66 to 29 percent 18 . Mehl and Reynaud (2005), using a measure of the share of DLTF in total debt, find that inflation variance significantly decreases this share. Note however that both studies, Mehl and Reynaud (2005) and Jeanne and Guscina (2006) rely on a measure of the outstanding debt, which means that they are not able to account clearly for the short term effect of the inflation level on new DLTF debt issues. To look at this effect, I use a treasury auction data from Turkey. This 17 Source: Jeanne and Guscina (2006) 18 Source: Jeanne and Guscina (2006) 57 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 0 100 200 300 400 500 600 700 800 Average Maturity 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 20 40 60 80 100 120 140 160 Interest Rate Interest Rate Figure 3.1: Average Maturity and nominal interest rates. Notes: This figure plots (in solid line) the monthly weighted average of the maturities (in days) of bonds and notes issued by the Turkish treasury (see left axis). It also shows the nominal interest rate during the same period (see right axis). See details in the text. Sources: central bank of Turkey and the State Planning Organization. offers two clear advantages. First, the data des not involve aggregations or estimations and it is provided by the central bank of Turkey. Second and most importantly it allows one to look at the fluctuations in bills and bonds issues over a relatively long period with high frequency observations. The data is constructed from the observations at each treasury auction in Turkey between May 1985 and December 2003. The data is compiled from the central bank of Turkey and the State Planning Organization. We include only Lira denominated bills and bonds. The variables that I use from this data set are, the date of issue, the date of maturity, the amount sold and the implied yearly interest rate. We also use monthly CPI data from Global Financial Data. The frequency of the auction varies a great deal. While during some months the treasury auctions at weekly intervals, during 58 some others, auctions will be held only once. Therefore it will be convenient to rearrange the data to monthly observations 19 . The way this is done is by weighting each maturity issued during a month by its weight in the total amount auctioned in that particular month. As for nominal interest rates at auctions, I compute the monthly weighted average 20 The weighted maturity is plotted in fig.1 against the nominal interest rates series. A quick look at Fig.1 reveals some interesting observations. First, the weighted matu- rity at the treasury auctions between 1986 and 2004 have reached its minimum at about 16.48 days of average maturity,(about 6% of the average maturity during the 86-04 period) in May 1994. This corresponds indeed to the highest nominal interest rate reached during the same period (167.9% interest rate in May 94). We observe similar peaks in interest rates that are accompanied with a significant maturity shortening in late 1995, late 1997 and early 2001. Second, the weighted maturity reached its peak in late 1999 (October 1999) while at the same time interest rates have been steadily decreasing to reach their lowest point in early 2000 (In February interest rates were at 27%). Third, between 2002 and 2004 interest rates have been on steady decrease while maturities were steadily length- ening. The correlation of the two series between 1986 and 2004 is equal to -0.44 as shown in table 1. It is no surprise that weighted maturity is more correlated with interest rates than it is with inflation. This is arguably because changes in inflation, will have a stronger 19 Out of 149 monthly observations, 7 are missing and this is due to no-issuance during these months 20 Note that variations in the term structure of interest rate should not have a strong effect on the average, given the high correlation between interest rates of different maturities. In other words, variations in the average interest rates are too big to be explained solely by changes in the term structure. 59 Table 3.1: Correlations from monthly data Notes: This table shows the correlations between average maturity, inflation and interest rates over the sample period 1986-2003. Sources: central bank of Turkey and the State Planning Organization. Correlations Maturity Inflation Interest Rate Maturity 1 −.32 −.44 Inflation −.32 1 .36 impact on long debt maturities when they are perceived to be persistent. This will be suggested as well in the model in section 3. Turkey is a prominent example of an economy where inflation never reached the hyper- inflation levels but the maturity structure of the nominal shortened significantly during inflation hikes. The episodes of inflation hikes started in the late 1970s in Turkey. In 1980, when inflation neighbored the 100% during some months, the government installed by the military regime put in place a stabilization plan that helped bring down inflation slowly to levels around 30% before it accelerated again after 1983. After the crisis in 1994, the dis- inflation measures taken in 1995, 1998 and 2000 were even less successful than the 1980 stabilization plan. Furthermore a stabilization program set in December 1999 was quickly abandonned. It is the uncertainty brought by such measures that represent the main focus of this paper. More than two decades of high inflation and failed stabilization programs accompanied by high nominal interest rates especially between 1994 and 1998 when they reached unprecedented levels, have been accompanied by a steady decrease in the long term nominal debt in the country. In this paper I show how this could be a direct effect of high inflation coupled with a risk of stabilization. Note that the data from the auction strongly suggests that even short term fluctuations in interest rates and inflation affect the 60 structure of debt issues , pointing that there is a level effect and not only a variance effect. One can see from the above that even short term decreases of interest rates have been accompanied by a lengthening maturity. This will be indeed explained in the model. 21 We argue that it is the high (nominal) borrowing cost together with the presence of a small probability of a successfull stabilization program that will make agents shy away from the medium and long-term nominal debt market. In section 3 and 4 I show this effect in the context of a general equilibrium model with incomplete markets. 3.3 The model I consider a multiperiod endowment economy with uncertainty, heterogeneous agents, one perishable good and incomplete markets. Time and uncertainty are represented by an event-tree with T periods and a set of n states of nature. The following section describes the characterstics of the economy. 3.3.1 Characteristics of the economy 3.3.2 Event tree I examine an economy overt = 0,...,T <∞ with uncertainty that is modeled as an event treeD. I denote a generic node of the event tree by ξ ∈ D. There is a unique root nodeξ 0 which does not have a predecessor, otherwise all nodes have a unique predecessor ξ − and finitely many direct successors each of which belong to a set that I label ξ + . For 21 A model that rely on the variance of inflation to explain the thinning of the nominal medium and long term bond market, will have difficulty explaining their comovements 61 a terminal node,ξ + ={∅}. The set of terminal nodes is denoted byD T and the set of all non-terminal nodes byD − . Furthermore, the set of strict successors of ξ is denoted by D + ( ¯ ξ) = {ξ ∈ D(ξ)|ξ ≥ ( ¯ ξ)}. The function ˜ t: D −→ T , whereT = {0,1,...,T} and ˜ t(ξ) indicates the position of ξ on the time axis. For example ˜ t(ξ 0 ) = 0. We would say that ξ ′ succeeds ξ (strictly) if ˜ t(ξ ′ ) ≥ ˜ t(ξ) (if ˜ t(ξ ′ ) > ˜ t(ξ)), and I would denote it ξ ′ ≥ ξ (ξ ′ >ξ) for simplicity. Letn be the total number of nodes in the event tree,n = #D. In each period t one shock s t ∈ S = {1,...,S} of S possible shocks is realized. Shocks inS follow a first-order Markov chain with transition probabilitiesπ(s,s ′ ) for all s,s ′ ∈ S. It is important to assume that the transition probability between the shocks is always positive in this economy and therefore π(s ′ ,s) 6= 0 for all s ′ ,s ∈ S. Each node in the event tree is associated with a history of shocks. For a typical node one can write ξ = s t = (s 0 ,s 1 ,...,s t ). It is also useful to define the function ˜ s :D−→S, where ˜ s(ξ) would denote the last shock s that led toξ regardless of its history, that is, ˜ s(ξ) =s t . The economy is populated by a finite number of T-period lived agents indexed by i ∈ I = {1,...,I}. To leave the analysis and the notation as simple as possible I assume that at each node of the event tree there is only one perishable good available for consumption. Agent’s i endowment of this good at any node ξ = (s t ) ∈ D is given by ω i (ξ) ∈ R. Therefore endowments are solely determined by the current shock. The following assumption characterizes the consumption sets, preferences and endowments of the agents. 62 Assumption 1 : 1. The consumption set is R n + with consumption bundles x i ∈ R n + , ∀i ∈ I, where n = #D. 2. ω i (ξ)∈R n ++ , ∀i∈I 3. Preferences are described by the utility function u i = v i 0 (x i (ξ 0 ))+ P ξ∈D + (ξ 0 ) β ˜ t(ξ) ℘(ξ|ξ 0 )v i (x i (ξ)) where β ∈ (0,1) is a discount factor and v i (ξ) : R + −→ R and in each function v i (ξ) is assumed to be continuous, strictly increasing, differentiable and strictly concave. Furthermorelim x i (ξ)−→0 ∂v i ∂x i (ξ) x i (ξ) =∞ Inflation In this model, money is completley exogenous and determined by the actions of the monetary authorities. However I do not assume that the monetary authorities have a complete control of the growth rate of money. Since the only function of money in this model is to determine the level of prices, I choose to cast our discussion in terms of prices and inflation instead of modeling explicitly the money supply. In particular, I assume that money supply is such that the inflation level at each node, τ(ξ), belongs to a finite set N of S inflation levels. The functione τ(.) : S −→ N maps of shocks into the set of inflation levels. Note that, for the sake of simplicity, what I call inflation in this model is the inflation factor which is simply the ratio of the current price level over the level of the previous price. Let p denote the vector of prices in this economy, 63 p = (p(ξ),ξ∈D)∈R n ++ , where I normalize p(ξ 0 ) = 1. Let the vector of states beS = (S L ,S M ,S H ) and letS L = (1,...,l),S M = (l +1,...,m) andS H = (m+1,...,S) be the low, medium and high inflation states. States are arranged such thate τ(s) <e τ(s ′ ) fors <s ′ and from now on I make the assumption thate τ(1) = 1. Assets In this economy, agents have access to a financial market where they can trade bonds in order to transfer wealth between time periods. Without loss of generality I abstract from equities in this model. There exist a real and a nominal discount bond for each maturity. That is, J, the number of securities available at time zero is equal 2T. The real bonds pay one unit of the good at the maturity while nominal bonds are a promise of one unit of currency. Note that in this economy the number of bonds are decreasing over time which is a common, yet unpleasant, feature of finite time period models with assets of different maturities. All bonds in this economy are issued at date zero, and agents re-trade the ones that did not expire at each period. Note that for simplicity I only consider zero-coupon bonds. Let z i (ξ) = (z i N (ξ),z i R (ξ)) denote the vector of agent i’s holding of bonds at ξ where z i N and z i R denote the vector of nominal and real bonds’ holdings respec- tively. z i N (ξ) = (z i N,1 (ξ),...,z i N,T (ξ)) where z i N,k (ξ) denotes the holding by agent i the nominal bond that matures at t = k. Similarily, the vector of real bonds’ holdings is z i R (ξ) = (z i R,1 (ξ),...,z i R,T (ξ)). V N,k (ξ),V R,k (ξ)∈R are the payements at node ξ of the k-maturity nominal and real bonds respectiveley, 64 V N,k (ξ) =      1 p(ξ) ift(ξ) = k ; 0 otherwise      andV N (ξ) = (V N,1 (ξ),...,V N,T (ξ)) whileV R,k (ξ) is given by: V R,k (ξ) =      1 ift(ξ) =k ; 0 otherwise      . Let V(ξ) = (V 1 (ξ),...,V J (ξ)) = (V N (ξ),V R (ξ)) and let J(ξ) be the set of actively traded financial contracts at nodeξ,J(ξ) ={j ∈ (1,2,...,J)|∃ξ ′ ∈D + (ξ)s.t. V j (ξ ′ )6= 0} whereD + (ξ) = {ξ ′ ∈ D| ˜ t(ξ ′ ) > ˜ t(ξ)}. The space of portfolios is defined over the non-terminal nodesD − , and is given by: Z =      z∈R (#D − )J z = (z N (ξ),z R (ξ), ξ∈D − ) andz j = 0 ifj / ∈ J(ξ), j = 1.....,J.      . Let ξ − denote the note that directly precedes ξ. Given ω i ∈ R n + , the choice of portfolio Z i ∈ Ξ induces a consumption vectorx i ∈R n + for agenti satisfying: x i (ξ 0 )−ω i (ξ 0 ) =−q(ξ 0 )z i (ξ 0 ) x i (ξ)−ω i (ξ) = (V(ξ)+q(ξ))z i (ξ − )−q(ξ)z i (ξ), ∀ξ∈D + (ξ 0 )∩D − x i (ξ)−ω i (ξ) = V(ξ)z i (D − ), ∀ξ∈D T Here q(ξ) = (q N,1 (ξ),...,q N,T (ξ),q R,1 (ξ),...,q R,T (ξ)) = (q 1 (ξ),...,q J (ξ)) denotes the 1×J the vector of prices for the J bonds at nodeξ. We can write the equations above in a useful matrix form, x i −ω i = Wz i (3.17) 65 where x i ,ω i are of n× 1 dimension and W is of n× (#D − ).K and takes the form. In section 4 I show a simple example that illustrates the structure of this matrix.                 −q(ξ 0 ) 0 0 0 0 V(ξ + 0 )+q(ξ + 0 ) −q(ξ + 0 ) .... 0 0 0 ... ... 0 0 0 0 V(ξ)+q(ξ) −q(ξ) ... 0 0 ... ... 0 0 0 0 0 V(ξ f )                 Therefore the budget set of agenti in this economy can be written as: B(p,q,ω i ,V) ={x i ∈R n + : x i −ω i =W(p,q,V)z i , z i ∈Z} (3.18) 3.3.3 Implications of the stabilization risk This section first introduces assumptions that are needed in this model to study infla- tion and the maturity of bonds in a high inflation economy with risk of stabilization. The objective is to study the relationship between inflation and the volume of trade in the long maturity bonds when a risk of price stabilization is present. For this, I focus on the T-period nominal bond for simplicity. I derive relationships between the stochastic proper- ties of inflation, the price and the demand for this bond. I show how for a class of inflation processes, agents’ trade in this nominal bond vanishes. These processes have on common feature: persistent high inflation states, persistent low inflation states and a small transition probability between these 2 categories of states of nature. Note that it is sufficient to have 66 on state of low inflation that is very persistent. I study these properties of the inflation rate motivated by the evidence from emerging markets. Many of these countries experi- enced episodes of high inflation (e.g., Latin American economies during the 1980’s) that were also characterized by attempts from the government to stabilize prices. Although the successful stabilization programmes were very few, this model shows that the existence of such possibility have a significant effect on the nominal contracts traded in the economy. LetF = S T be the number of final nodes, henceforth denoted byξ 1 ,ξ 2 ,....ξ F for simplic- ity. We divide the set of final nodesD T into three subsets such thatD L T = (ξ F ,...,ξ F ), D M T = (ξ L+1 ,...,ξ M ) andD H T = (ξ M+1 ,...,ξ F ). These subsets are chosen so that (i) ξ r ∈ D H T if and only if ξ r = s t = (s 0 ,s 1 ,...,s t ) where s t ∈ S H , ∀t ∈ T and (ii) ξ r ∈ D L T if and only if ξ r = s t = (s 0 ,s 1 ,...,s t ) where s t ∈ S H , ∀t ∈ T . We order the nodes inD H T andD H L so that p(ξ 1 ) < ... < p(ξ L ) and p(ξ M+1 ) < ... < p(ξ F ). Note however that prices in the middle states are not necessarily bounded by p(ξ L ) and p(ξ F ). Agents’ expectations about the price that will prevail at time T determine the nominal interest rate, at each period, of the nominal bond that matures at T. Note that when T is high, the time zero variance of the price level at time T will be high. However in this model, agents’ expectations are biased toward high prices prevailing at time T. Assumption 2 : The states of high inflation are persistent and the probability of switching to a lower inflation, i.e. the probability of stabilization, is low. In particular: 1. π(s ′ ,s)≤ ǫ for alls ′ ∈ (S L ,S M ) ands∈S H . 2. For alls,s ′ ∈S L ,π(s ′ ,s) is such that P L r=1 ℘(ξ r |ξ∈ ˜ D L )≥ 1−ǫ. 67 where ǫ > 0 is some small number inR and f D L = {ξ ∈D|ξ = (s 1 ,...,s t ) = s t where s t ∈S L for all t}. Note that here π(s ′ ,s) denote the probability of transition from s to s ′ . Assumption 2 is essential to the results in this paper. The main argument behind the model relies on the fact that during periods of persistent high inflation, there exist always a small porbability for which this inflation might decrease and that prices stabilize relatively. The objective of the model is prove how the existence of such stabilization risk makes borrowing at long maturities unfeasible for agents under no default. Definition 1 Let θ be the ratio of the lowest inflation in the high inflation states to the highest inflation in the states of high inflation, that is,θ = τ m+1 τ l . Assumption 3 K < l where l is the number of states with low inflation (l = #τ l ) and K is the number of available bonds atξ 0 . This assumption implies that markets are incomplete. Note that the above assumption guarantees market incompleteness. It however imposes stronger conditions then what is necessary to obtain market incompleteness. Therefore we say that assumption 3 implies that markets are “strongly incomplete”. Lemma 1 If ˜ s(ξ 0 )≥ m+1, and under the above assumptions, the price of the T-period nominal bond at time zeroq N,T (ξ 0 )−→ 0 asτ T m+1 −→∞ andǫ−→ 0. The proof of lemma 1 is shown in the appendix. Definition 2 Let ˜ q = min ξ∈ ˜ D L ,j∈J q j (ξ). In words ˜ q is the lowest price of a bond reached on f D L . 68 Lemma 2 z i T,N (ξ 0 ) is finite as long as the nominal interest rate in periods of low inflation remains finite, in other words, as long as ˜ q > c> 0. Proof. We know from the budget constraint of agenti in (#) that, x i (ξ + 0 )−ω i (ξ + 0 ) = W[ξ + 0 ,ξ 0 ]z(ξ 0 )−W[ξ + 0 ,ξ + 0 ]z(ξ + ) where, • x i (ξ + 0 ) is the column vector of copnsumption at nodes ξ ∈ ξ + 0 in other words x i (ξ + 0 ) = (x i (ξ),ξ∈ ξ + 0 ) ′ . • ω i (ξ + 0 ) is similarily defined asω i (ξ + 0 ) = (ω i (ξ),ξ∈ ξ + 0 ) ′ . • W[ξ + 0 ,ξ 0 ] is the matrix formed by the S rows in W corresponding to the nodes ξ + 0 and by the columns corresponding to the assets’ payements and prices atξ 0 . • z i (ξ + 0 ) = (z i (ξ),ξ∈ ξ + 0 ) ′ . Note that the value of last period’s borrowing (or lending) is given byW[ξ + 0 ,ξ 0 ]z(ξ 0 ) and is equal to the sum of the payements of the maturing assets plus the current value of longer term bonds. Unlike W[ξ + 0 ,ξ 0 ], W[ξ + 0 ,ξ + 0 ] is independant of the bonds’ payements and is formed only by the current prices of longer term bonds. The above equation gives us S equalities from which we take the firstJ, while assuming as stated above thatJ ≤ l. [x i (ξ + 0 )−ω i (ξ + 0 )] J = [W[ξ + 0 ,ξ 0 ]] J z i (ξ 0 )−[W[ξ + 0 ,ξ + 0 ]] J z i (ξ + 0 ) 69 which could equivalently be written as, z i (ξ 0 ) = [W[ξ + 0 ,ξ 0 ]] −1 J {[x i (ξ + 0 )−ω i (ξ + 0 )] J +[W[ξ + 0 ,ξ + 0 ]] J z i (ξ + 0 )}. We know that: • P i∈I ω i (ξ + 0 )> x i (ξ + 0 )−ω i (ξ + 0 ) >−ω i (ξ) , thereforex i (ξ + 0 )−ω i (ξ + 0 ) is finite and bounded. • Sinceq(ξ)<∞ ∀∈D − then[W[ξ + 0 ,ξ + 0 ]] J is finite. • Since I assume that ˜ q > c > 0 then q(ξ) > c > 0 for all ˜ s(ξ) < l, and therefore [W[ξ + 0 ,ξ 0 ]] −1 J is bounded. therefore, asz i (ξ 0 )−→∞ agenti can only satisfy his budget constraint by lettingz i (ξ + 0 ) go to infinity as z i (ξ + 0 ) −→ ∞. In particular z i (ξ) −→ ∞ for all ξ such that ˜ t(ξ) = 1 and ˜ s(ξ) ≤ J. The same logic applies to show that z i (ξ ′′ ) −→ ∞ as z i (ξ ′ ) −→ ∞ for ˜ t(ξ ′′ ) = 2 and ˜ s(ξ ′′ )≤ J−2. This follows from the following equation: [x i (ξ + s )−ω i (ξ + s )] J−2 = [W[ξ + s ,ξ s ]] J−2 Z i (ξ s )−[W[ξ + s ,ξ + s ]] J Z i (ξ + s )] Following this recursion and going down the tree along the lowest possible inflation state, we reach the nodeξ f prior to the final nodesξ 1 ,...,ξ S and we know that: [x i (ξ + f )−ω i (ξ + f )] 2 = [W[ξ + f ,ξ f ]] 2 z i (ξ f ). 70 Since [W[ξ + f ,ξ f ]] −1 2 [x i (ξ + f )−ω i (ξ + f )] 2 is clearly bounded and so z i (ξ f ) has to be, which contradictsz i (ξ 0 )−→∞. Therefore I proved by contradiction thatz(ξ 0 ) has to be finite. A direct implication of is the following lemma: Lemma 3 q N,T (ξ 0 )z N,T (ξ 0 )−→ 0 asq N,T (ξ 0 )−→ 0 as long as ˜ q > c> 0. Proof. Lemma 3 follows directly from lemma 2. Lemma 2 shows that if ˜ q T,N (ξ) >> 0 thenz T,N (ξ 0 ) is finite. Therefore ifq T,N (ξ 0 )−→ 0 thenq T,N (ξ 0 ).z T,N (ξ 0 )−→ 0 Lemma 2 showed that the demand for the nominal bonds at time 0 is bounded. What is interesting is that Lemma 2 shows that this is the case even when inflation is very high and the price of the T period nominal bond approaches 0 at time 0. In fact, when there is no risk of stabilization, agents will simply increase the demand for the nominal bond as its price decreases. That is, inflation should not affect the ability of agents to smooth their consumption. An agent i can receive a $1 payment at time T for n units of the T period nominal bond bought at time zero. As inflation increases, n increases too. Note however thatn remains feasible since the price of the bond decreases with inflation. However when markets are incomplete and under the presence of a low stabilization risk n cannot go to infinity even if the price of the bond goes to zero. This is what Lemma 2 shows. The intuition behind this result is simple. Bond prices at time zero reflect the payments at the maturity date under different states of nature. If the stabilization risk is significant then the price of the nominal bond will reflect this possibility and therefore cannot become arbitrary small as inflation increases. This is however not the case when the probability of stabilization is very small. In this case, even when agents can purchase large quantities of the bond, they will refrain from doing so since their budget constraint will not hold 71 under some states of nature, however unlikely these states are. It is important to stress that a high variance of inflation alone will not lead to this disruption of trade in nominal contracts. What is left is to show that the trade of nominal bonds is affected by inflation through the mechanism described above even when inflation levels do not go to infinity (i.e., when there is no hyperinflation). In what follows I show how the trade in the long maturity nominal bonds is negatively correlated with inflation. I also show that the number of maturity traded is also negatively correlated with the level of inflation. In the limit case, when inflation goes to infinity the nominal bond market vanishes even at the shortest maturities. Lemma 4 Let ˜ q T,N (ξ) = min ξ∈ ˆ D L q T,N (ξ). It follows directly from Lemma that ˜ q−→ 0 if and only ifT −→∞ and therefore if and only if ˜ q T,N −→ 0. The proof is shown in the appendix. The result in Lemma 4 is very useful as it it implies that we can focus on the case ˜ q T,N (ξ) −→ 0. This is because we know that as long as ˜ q T,N (ξ) > c > 0 there exists b such that ˜ q > b > 0. We ordered the final nodes ξ 1 ,...,ξ F , such thatp(ξ 1 ) <...< P(ξ L ) andP(ξ M+1 ) <...< P(ξ F ), wherep(ξ 1 ) = 1, p(ξ L ) = τ T l whilep(ξ M+1 ) =θ T τ T l andP(ξ F ) =τ T H . We know 22 that forξ∈ ˜ D L ˜ q N,T (ξ)≈ β T X r ξ∈D L T Λ i ( r ξ,ξ)℘( r ξ|ξ) 1 P( r ξ) . (3.19) where Λ i ( r ξ,ξ) = ∂v i (x i ( r ξ))/x i ∂v i (x i (ξ))/x i . As shown in Lemma 2, ˜ q N,T (ξ) −→ 0 if and only if T −→ ∞ for which β T −→ 0 and there exists r ξ ∈ ˜ D L such that P( r ξ) −→ ∞. As for 22 ˜ q N,T (ξ) = β T P ξ∈D L T Λ i (ξ)℘( r ξ|ξ) 1 P( r ξ) + β T P r ξ∈D M T Λ i (ξ)℘( r ξ|ξ) 1 P( r ξ) + β T P r ξ∈D H T Λ i (ξ)℘( r ξ|ξ) 1 P( r ξ) . But since assumption 5b imply that P r ξ∈D L T ℘( r ξ|ξ) −→ 1 then ((8)) follows directly 72 q N,T (ξ 0 ) 23 , we know from lemma 1 that it is given by q N,T (ξ 0 )≈ β T X r ξ∈D H T Λ i ( r ξ,ξ 0 )℘( r ξ|ξ 0 ) 1 P( r ξ) . (3.20) One can clearly see that prices in states D H T (and therefore the prices that determine q N,T (ξ 0 )) converge faster to infinity than P(ξ) for ξ ∈ D L T (prices in the ˜ q N,T (ξ) equa- tion). In fact, β T τ T l is the series with the smallest convergence rate in ˜ q N,T (ξ) (that is, it converges faster to zero) and its convergence rate is given by β τ l ; At the same time β T θ T τ T l is the series with the highest convergence rate inq N,T (ξ 0 ) (that is, its convergence to zero is slower) and it is given by β θτ T l . Therefore θ is an adequate measure of the speed of convergence of q N,T (ξ 0 ) relative to ˜ q N,T (ξ). Note that when θ −→ ∞, β T θ T τ T l converges super-linearly to zero. We will revisit this issue shortly. The following Lemma, states the properties of a simple yet useful function that defines the range of maturities over which β T θ T τ T l ≈ 0 while β T τ T l is bounded away from 0 by a positive number c. Lemma 5 Let Ψ(c,ǫ,θ) = {T ∈N + | β T (θτ l ) T ≤ ǫ and β T τ T l ≥ c} where ǫ ∈ R + , θ ≥ 1 and c≤ 1.Ψ(c,ǫ,θ) have the following properties : 1. θ ′ >θ =⇒Ψ(c,ǫ,θ)⊆Ψ(c,ǫ,θ ′ ) and∃θ ′′ >θ s.t. Ψ(c,ǫ,θ)⊂Ψ(c,ǫ, b θ) ∀ b θ≥θ ′′ . 2. ǫ ′ >ǫ=⇒Ψ(c,ǫ,θ)⊆Ψ(c,ǫ ′ ,θ) and∃ǫ ′′ >ǫ s.t. Ψ(c,ǫ,θ)⊂Ψ(c,b ǫ,θ) ∀b ǫ≥ǫ ′′ 3. c ′ >c=⇒Ψ(c ′ ,ǫ,θ)⊆Ψ(c,ǫ,θ) Furthermore ifc≤ β τ l ,∃θ such thatΨ(c,ǫ,θ)6={∅}. 23 Always assuming thatξ 0 is a high inflation state 73 The proof of Lemma 5 is shown in the appendix. Note that since c is constrained by c ≤ 1, we cannot increase it indefinitely and therefore we cannot always find c ′ > c =⇒ Ψ(c ′ ,ǫ,θ) ⊂ Ψ(c,ǫ,θ). Let χ = #Ψ(c,ǫ,θ), lemma 5 has shown that χ is increasing in θ and ǫ and decreasing in c. This mean that ∃ǫ ≈ 0, θ, 1 ≥ c >> 0 such that χ 6= 0. That is, there exists values for θ for which at some maturities (values of T) ( β T (θτ l ) T − 0) ≤ ǫ ≈ 0 while ( β T τ T l − 0) ≥ c >> 0. It is straightforward to see that for θ −→ ∞, this is true even for T=1, as long as β τ l >> 0. However, for reasonable values forβ andτ l , χ6= 0 for even finite values of theta. To take an example to show the intuition behind Lemma 4, let the monthly β = 0.998 and τ l = 1.02 and let ǫ = 0.001 while c = 0.2. For θ = 1.0784, Ψ(0.2,0.001,1.0784) = (72,73,...,105) (T in months), andχ = 34. While forθ = 1.2255,Ψ(0.2,0.001,1.2255)= (31,32,...,105). Note that we are comparing the highest convergence rate series from the low inflation states with the lowest convergence rate of the high inflation series. Since ˜ q N,T (ξ) is a weighted sum of series which have a slower convergence than β θτ T l , and since q N,T (ξ 0 ) is a weighted sum of series that converge to zero faster than β θτ T l , Lemma 6 follows directly from Lemma 5. Lemma 6 Let ¯ Ψ(c,ǫ,θ) ={T ∈N + |q N,T (ξ 0 )≤ ǫ and ˜ q N,T (ξ)≥ c} 1. ¯ Ψ(c,ǫ,θ) has the same properties ofΨ(c,ǫ,θ) shown in Lemma 4. 2. ∃θ ≥ 1 such that ¯ Ψ(c,ǫ,θ) ={T ∈N + |q N,T (ξ 0 )≤ ǫ and ˜ q N,T (ξ)≥ c}6={∅} for ǫ≈ 0 and somec>> 0 74 The proof of Lemma 6 is shown in the appendix. Lemma 6, shows that there exist values of θ and T for which lemma 2 holds. Again, this is clear for the case of θ −→∞ for which even the one period bond disappears 24 . This case is the one discussed in Neumeyer(1999) and is a special case of this T-period bond economy. However, as shown above, θ −→ ∞ is not the only case for which Lemma 2 holds. The above illustrations show that this is possible for reasonable values ofθ and T. Interpretation and remarks. The model presented above imposed assumptions on the inflation process to an otherwise standard T period general equilibrium model with incom- plete markets. The assumptions are added to emulate the properties of inflation in many emerging markets 25 . This paper is in particular interested in studying the episodes of high inflation that many of these markets knew. Section 2 showed evidence that these episodes were accompanied by a significant shortening of the maturity of the fixed interest nominal bonds. The objective of the model was to explain this fact. The evidence shown in section 2 from the treasury auctions’s data from Turkey is important in that respect. It showed how the level of inflation has a direct effect on the maturity of the new issues. A the- ory that is solely based on “inflation risk” cannot account for the observed co-movement between the level of inflation and the average maturity. The model shows that indeed, this co-movement can be generated in a standard model when inflation had the follow- ing properties (i) Inflation switches between states of high inflation and between states of 24 That isT =1∈ ¯ Ψ(c,ǫ,θ) as long as β τ l >>0 25 Note that for simplicity the model does not feature a supply of money. It is assumed that the movements in the inflation rate are directly implied by changes in the money supply. 75 high inflation and states if low inflation (ii) The probability of transition between states of high inflation and states of low inflation is very small (iii) There exist a state of low inflation that is very persistent. These assumptions can describe well the inflation rates in for example Turkey between 1986 until now. Inflation was relatively high during long episodes, even though it never reached the stage of a hyperinflation. The variance of infla- tion was indeed also high which can be interpreted as due to changes between states of high inflation. However a stabilization risk was always present due to many attempts by the governments and the military to stabilize prices. These stabilization programs were mostly unsuccessful until 2001 when inflation decreased and remained low. This state of successful stabilization, I argue, brings about a possibility of large changes in the price of bonds to which borrowers are very averse. Note however that if the probability of stabi- lization is high, then it will be significantly reflected in the bond prices which can at this moment serve as a hedge against inflation by borrowers; in this case, the trade in these bonds will not necessarily be reduced. Note that the higher is inflation the stronger is the impact and any T-period bond. When inflation reaches the hyperinflation states even the shortest maturities will be affected. In what follows a show a simple example with 2 peri- ods of the negative relationship between inflation and the quantity traded in the 2-period nominal bond. I contrast this with the trade in the one period bond. The exercise also shows the impact of the stabilization risk on the trade in these bonds. 3.3.4 Example We consider a simple example of the economy defined in section 3 withI = 2,T = 2 andJ = 2; that is I consider a two period economy. Z = (z 2,N ,z 2,R ) and therefore I do not 76 consider one-period bonds to simplify the the analysis. Let x i ∈R 13 + be the consumption vector for agent i, where x i (ξ) ∈ R + denote the consumption of agent i at node ξ. Let v i 0 (x i (ξ 0 )) = log(x i (ξ 0 )) andv i (x i (ξ)) = log(x i (ξ)) for all agents. Agenti maximization problem is given by Max x i v i 0 (x i (ξ 0 ))+ X f∈{1,2,3} β℘(ξ f |ξ 0 )    v i (x i (ξ f ))+β X h∈{1,2,3} ℘(ξ f h |ξ f )v i (x i (ξ f h ))    (3.21) under the following budget constraints: x i (ξ 0 )−ω i (ξ 0 )=−q 1 (ξ 0 )z i 2,N (ξ 0 )−q 2 (ξ 0 )z i 2,R (ξ 0 ) (3.22) x i (ξ f )−ω i (ξ f )=q 1 (ξ f )(z i 2,N (ξ 0 )−z i 2,N (ξ f ))+q 2 (ξ 0 )(z i 2,R (ξ 0 )−z i 2,R (ξ 0 )) (3.23) x i (ξ f h )−ω i (ξ f h )=z i 2,N (ξ f ) 1 P(ξ f h ) +z i 2,R (ξ f ) (3.24) ∀f,h∈{1,2,3}. Which can also be written as: x i −ω i = WZ i (3.25) In this economy s = {1,2,3}, s H = 1 and s L = 2,3 26 . The inflation is fixed for the low states, τ 2 = 1 (0% inflation) and τ 3 = 1.05 as for τ H I let it vary to study its effect on nominal bond holdings. The endowments at each node of the tree are exogeneous. We assume that agent 1 is endowed with one unit at node 0 and with nothing in the following 26 Clearly, I could have added more states of high inflation and medium inflation but there is no advantage from doing so, as I am trying to simplify the notation as much as possible. 77 periods. Agent 2 is assumed to be endowed with one unite at node 0, two units at nodes 1 and with three units at nodes 2. We have chosen endowments to be such that there will be significant borrowing and lending in this economy. Furthermore note that with this specification for inflation and endowments, nominal bonds offer some degree of insurance, which make them attractive for the borrower. Note thatW , in this simple example, is the following matrix:                                        −q 1 (ξ 0 ) −q 2 (ξ 0 ) . . . . . . q 1 (ξ 1 ) q 2 (ξ 1 ) −q 1 (ξ 1 ) −q 2 (ξ 1 ) . . . . q 1 (ξ 2 ) q 2 (ξ 2 ) . . −q 1 (ξ 2 ) −q 2 (ξ 2 ) . . q 1 (ξ 3 ) q 2 (ξ 3 ) . . . . −q 1 (ξ 3 ) −q 2 (ξ 3 ) . . 1 P(ξ 1 1 ) 1 . . . . . . 1 P(ξ 1 2 ) 1 . . . . . . 1 P(ξ 1 3 ) 1 . . . . . . . . 1 P(ξ 2 1 ) 1 . . . . . . 1 P(ξ 2 2 ) 1 . . . . . . 1 P(ξ 2 3 ) 1 . . . . . . . . 1 P(ξ 3 1 ) 1 . . . . . . 1 P(ξ 3 2 ) 1 . . . . . . 1 P(ξ 3 3 ) 1                                        The results from this exercise are shown in Table 2. The first column indicates the spec- ification number for which the transition matrix is displayed in the appendix while the level of inflation in the high inflation state is displayed in the the second column of table 2. The third and fourth columns show the equilibrium quantities of the nominal and the real bond (respectively) traded in equilibrium. Columns 5 and 6 show the value traded in these bonds. Note that based on the observations from section 2, what we are interested in 78 is clearly the nominal value of the trade in bonds and not the number of these bonds. In Specification 1 the persistence of the high state is moderate and it is equal to 0.4. Inflation in the high state is 10% and therefore θ = 1.0476. In this benchmark case that resembles an economy with volatile inflation but moderate inflation expectations the trade in nominal bonds is equal to−.31 and 31 times larger than the trade in real bonds which is equal to −.01. As I mentionned earlier endowments and inflation in this economy are such that nominal bonds partially insure the borrower since at the terminal node with the highest price level, endowments are relatively low compared to the endowments at the nodes with low realized inflation. Note that since the total endowment of the economy is equal to 2 at node ξ 0 , the trade in the nominal bond amounts to15.5% of that total income. Specification 2 differs from the previous one by having a higher persistence of the high inflation state. As you can see from the transition matrix π(H|H) = .9 while the transi- tions probabilities from the low states remain the same. However with this level of inflation the results do not change significantly. Specification 3 is the case where high inflation is equal to 50% while the transition matrix from now on is the same as specification 2. We see a drastic change in the holding of bonds, and nominal bonds, significantly less held than real bonds, amount to only 4.5% of total income. Increasing the high inflation state in specifications 4 and 5, decreases significantly the use of nominal bonds as the amount traded in these specifications become insignificant compared to the total income and the use of the real bond. As we increased inflation in high state in this example, not only the value traded in the bond has decreased but also the number of these contracts have sig- nificantly declined too. This is due to the change in the risk profile of the nominal bonds 79 Table 3.2: The impact of inflation on the trade in bonds. τ H N Z q N .N q Z .Z Spec.1 10% −.4 −.01 -.31 −.01 Spec.2 10% −.35 −.04 -.28 −.04 Spec.3 50% −.19 −.24 -.09 −.23 Spec.4 100% −.06 −.32 -.02 −.3 Spec.5 200% −.03 −.33 -.006 −.32 which made the real bond more attractive. The same exercise is repeated for the case where there is no real bond. This allows us to look at the stabilization risk effect when there are no substitutes for the nominal bond. The example is similar to the one above with the same values for the low inflation. Agents’endowments are the same. For a π(H|H) = .98 figure A.5 shows a relationship between the nominal bond holding and θ where θ determines the level of the high state inflation (see definition (1)). It is clear how the holdings decrease significantly with each increase ofθ. We allowθ to take relatively high values since there are only three periods. The lower panel in Figure A.5 shows how the more persistent is the high inflation state the smaller is the trade in the nominal bond for a fixed θ = 3. The stabilization risk effect is clear even when there are no substitutes for the nominal bond. 3.4 Concluding Remarks Most emerging markets have a debt structure that is at odds with that of the OECD countries. First, the bulk of the emerging markets’ international borrowing is placed in 80 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 Theta Trade 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0 0.1 0.2 0.3 0.4 Persistence Trade Figure 3.2: Effects of changes in the stabilization risk. Notes: The upper panel in this figure plots the trade in nominal bonds (when it is the only available bond) for different values ofθ. The lower panel plots the trade in nominal bonds for different persistence levels of the high inflation. foreign currencies, in the U.S. Dollar in particular. Second, their local currency bonds, generally issued in the domestic market, comprises a small share of fixed interest medium to long-term maturities. These findings summarized in Eichengreen and Hausmann (1999) prompted much theoretical research. This literature advanced series of alternative explana- tions for this phenomenon sometimes known as the “Original Sin”. Most of these expla- nations are based on asymmetric information. Note that the two characteristics of the emerging markets’ borrowing can possibly be very related. One might expect that it is the inability of these markets to issue bonds in local currency at long maturities that makes them dependent on international borrowing in a foreign currency. This paper looked at the role of inflation in explaining this phenomenon. Earlier studies 81 have discussed the effect of “inflation risk” on the maturities traded on the market. How- ever the predicted negative relationship between the variance of inflation and the average maturities is too small to explain what is observed in the data. Furthermore this paper shows evidence that the maturity of nominal bonds is affected by the level of inflation. It shows how the average maturity of new issues in Turkey between 1986 and 2003 was negatively correlated with both inflation and the nominal interest rates. Such relationship is left unexplained. This paper tries to fill this gap. It studies the impact of inflation on the maturity structure of nominal bonds in the context of a general equilibrium model with incomplete markets. A central assumption in the model is the existence of inflation sta- bilization risk during periods of high inflation. Such risk of a sudden drop in inflation is present during most episodes of high inflation since inflation is both economically and politically very costly. The model shows that in the presence of a low probability of infla- tion stabilization, the level of inflation can have a strong impact on the maturity of nominal bonds. In particular, the higher is the level of inflation the smaller will be the trade in the longer maturities. The model therefore generates a negative relationship between average maturity and inflation. There is no default in the model and therefore agents borrow when they are able to repay in all states of nature. 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(1960), “Some further notes on a class of skew distribution func- tions”, Information and Control V ol. 2, pp. 80-88. 86 Appendix A: Appendix to Chapter 2 A.1 First order conditions Let λ and μ be the Lagrange multipliers on the budget constraint and the borrowing constraint respectively. Taking the derivatives we get: ˆ d : 1−λϕ ˆ d ( ˆ d) = 0 ˆ k ′ :−λg +(1+μ)βgEV ˆ k ( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ ) = 0 ˆ b ′ : λg +(1+μ)βgEV ˆ b ( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ )−μφg = 0 The envelope conditions are: V ˆ k ( ˆ k, ˆ b,a,g) =λf ˆ k ( ˆ k, ˆ b,a,g)+λ(1−δ) V ˆ k ( ˆ k, ˆ b,a,g) =−λ(1+r) 87 Using the first order conditions and substituting the envelope condition we get the condi- tions 2.7 and 2.8. A.2 Numerical Procedure We used Malab 7.0 to find the approximate solution to the problem. The numerical problem consist of finding the solution to the program that maximizes the de-trended mar- ket value subject to the borrowing and budget constraints. To solve the problem recur- sively, we have the following equations: 1 ϕ( ˆ d) g+(1+μ)βgEV ˆ b ( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ )−μφg = 0 − 1 ϕ( ˆ d) g+(1+μ)βgEV ˆ k ( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ ) = 0 βgE ˆ V( ˆ k ′ , ˆ b ′ ,a ′ ,g ′ )≥ φg ˆ b ′ f( ˆ k, ˆ b,a,g)+(1−δ) ˆ k− ˆ k ′ g+ ˆ b ′ g−(1+r) ˆ b = ˆ ϕ( ˆ d) The computational procedure We first solve for the steady states for each shockg and set accordingly the space of the grids. We then make a guess about the value function and its derivatives with respect to the state variables. For these guesses one can solve for all the variables assuming the borrowing constraint binds. If μ is positive, this means the borrowing constraint is indeed binding. If μ is negative we solve the problem again settingμ = 0 since this means that the constraint does not bind. This is done at every grid. The grid points are joined with bilinear functions so that the approximate functions are 88 continuous. We update the initial guesses until convergence. Note that the problem with heterogeneous firms is solved in a similar way. A.3 Figures and Tables 89 Figure A.1: The absence of the size effect under TFP shocks. This figure shows the response of output to a 1% negative and permanent TFP shock. The response of the large firm (see calibration in Table 3) is plotted in solid line. The other two lines show the response of a small firm for different values of Tobin’s Q ratios: one with a Tobin’s Q that is 1.25 times larger than the Tobin’s Q of the large firm, and the other with 1.8 times larger Tobin’s Q. It is shown that in both cases the growth effect does not lead to a significant size effect under a TFP shock, contrary to the case with growth shocks. 0 5 10 15 20 25 30 35 40 −1.6 −1.5 −1.4 −1.3 −1.2 −1.1 −1 −0.9 TFP Shock Large Ratio = 1.25 Ratio = 1.8 90 Figure A.2: Average of debt-to-sales and Tobin’s Q ratios in the data. Notes: This figure shows the average debt-to-sales and Tobin’s Q ratios in our sample of Southeast Asian firms during and following the Sudden Stop episode. As the model would predict following a negative growth shock, the Tobin’s Q collapses at the time of the shock (1997) and the drop in debt follows in the next period. Both ratios do not recover by 2003. Source: Worldscope, Thomson Financial. 1996 1997 1998 1999 2000 2001 2002 2003 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Debt to Sales Tobin’s Q 91 Table A.1: Determinants of firms’ performance between 1997 and 2002. Notes: The sample is formed by merging the data from Indonesia, Malaysia and Thailand after converting all values to the U.S. dollar of 2000. The dependent variable is the change in the log of sales between end 1996 and end of 2002. The Table shows the output of OLS regressions for different specifications. The right hand variables are end of 1996 values measures in dollars of 2000. “Leverage” is the ratio of total liabilities to total assets in 1996. “Interest” is the ratio of the total interest payments to total liabilities in 1996. “Prof- itability” is the ratio of net income to total assets in 1996. Data source: Worldscope, Thomson Financial. Δ log(sales) Δ log(sales) Δ log(sales) Δ log(sales) Δ log(sales) Size 0.117*** 0.104*** 0.116*** 0.109*** 0.109*** (4.70) (3.42) (3.84) (3.22) (3.19) Export 0.160* 0.156 0.174* 0.180* (1.74) (1.62) (1.66) (1.73) Thailand 0.347*** 0.297** 0.320** (3.33) (2.44) (2.47) Indonesia 0.0533 0.0397 0.0454 (0.39) (0.26) (0.29) Leverage -0.203 (-0.81) Interest 0.284 (0.16) Profitability 0.879* (1.82) Industry Dummies NO NO NO YES YES Constant -1.314*** -1.258*** -1.499*** -1.431*** -1.428*** (-4.72) (-3.61) (-4.27) (-3.68) (-3.49) R2 0.0545 0.0493 0.0868 0.105 0.124 t statistics in parentheses. * p<0.10, ** p<0.05, *** p<0.01 92 Table A.2: Average growth rates before and after the crisis. Notes: The data is taken from the IFS. The table shows the simple average of growth rates before the crisis (1990-1996) and after the crisis (2000-2006). The standard errors are shown in italic. A t-test rejects the equality of the means between the two samples. Indonesia Malaysia Thailand Annual: 1990−1996 7.2% 9.5% 8.1% Standard errors 0.002 0.001 0.004 Annual: 2000−2006 4.4% 5.2% 4.9% Standard errors 0.002 0.009 0.006 93 Figure A.3: Real GDP and its growth rate. The left panels in this figure plot an index of the Real GDP in Indonesia, Malaysia and Thailand between 1991 and 2006. The right panels plot the growth rates in the Real GDP during this period. The three countries experienced their largest losses in output in the year 1998. Data source: IFS. 1991 1998 2006 80 100 120 140 Indonesia − RGDP 1991 1998 2006 −0.1 −0.05 0 0.05 0.1 Indonesia − growth rates 1991 1998 2006 60 80 100 120 140 Thailand − RGDP 1991 1998 2006 −0.1 −0.05 0 0.05 0.1 Thailand − growth rates 1991 1998 2006 50 100 150 Malaysia − RGDP 1991 1998 2006 −0.1 −0.05 0 0.05 0.1 Malaysia − growth rates 94 Figure A.4: The collapse in the market value The upper panel in this figure shows an index of the average market value in the subsample of large firms and the subsample of small firms. The market value of the small firms dropped significantly more (15 % more than large firms in 1997) on average. The lower panel compares the average Tobin’s Q of the two subsamples. Smaller firms had on average a higher Tobin’s Q before the crisis. However after the crisis the Tobin’s Q of small firms dropped significantly more than the Tobin’s Q of the larger firms. Data source: Wolrdscope, Thomson Financial. 1996 1997 1998 1999 2000 2001 2002 2003 20 40 60 80 100 Index of Market Value 1996 1997 1998 1999 2000 2001 2002 2003 1 1.5 2 2.5 Tobin’s Q Large Small 95 Table A.3: Determinants of firms’ performance between 1997 and 1999. Notes: The sample is formed by merging the data from Indonesia, Malaysia and Thailand after converting all values to the U.S. dollar of 2000. The dependent variable is the change in the log of sales between end 1996 and end of 1999. The table shows the output of OLS regressions for different specifications. The right hand variables are end of 1996 values measures in dollars of 2000. “Leverage” is the ratio of total liabilities to total assets in 1996. “Interest” is the ratio of the total interest payments to total liabilities in 1996. “Prof- itability” is the ratio of net income to total assets in 1996. Data source: Worldscope, Thomson Financial. (1) (2) (3) (4) (5) Δ log(sales) Δ log(sales) Δ log(sales) Δ log(sales) Δ log(sales) Size 0.0850*** 0.0729*** 0.0773*** 0.0647*** 0.0654*** (12.05) (8.63) (9.12) (6.87) (6.89) Export 0.123*** 0.120*** 0.135*** 0.140*** (4.81) (4.44) (4.60) (4.81) Thailand 0.128*** 0.0555 0.0695* (4.39) (1.63) (1.92) Indonesia 0.0269 -0.0240 -0.0211 (0.69) (-0.57) (-0.49) Leverage -0.187*** (-2.69) Interest 0.371 (0.73) Profitability 0.418*** (3.04) Industry Dummies NO NO NO YES YES Constant -0.949*** -0.861*** -0.951*** -0.814*** -0.790*** (-11.99) (-8.92) (-9.66) (-7.52) (-6.93) R2 0.0451 0.0410 0.0493 0.0610 0.0719 t statistics in parentheses * p<0.10, ** p<0.05, *** p<0.01 96 Table A.4: Determinants of firms’ performance between 1997 and 2002, by country. Notes: The dependent variable is the change in the log of sales between end of 1996 and end of 2002. Size is computed as the log of the dollar value of the total fixed assets in 1996. “Export” is a dummy that takes one if the firm is an exporter or carries its main operations outside Asia. Sector dummies reflect the most common industries in our sample. The financial and construction sector are excluded. Thailand Indonesia Malaysia Δ log(sales) Δ log(sales) Δ log(sales) Size 0.113** 0.247** 0.102** (2.07) (2.38) (2.13) Export 0.432** 0.580 0.0123 (2.64) (1.52) (0.09) Leverage -0.236 1.533* -0.561 (-0.65) (1.90) (-1.58) Interest -3.223 5.749 1.975 (-1.42) (1.36) (0.63) Profitability -0.993 -1.394 1.729*** (-1.35) (-0.78) (2.77) Industry Dummies YES YES YES Constant -0.935 -4.167*** -1.221** (-1.52) (-3.17) (-2.12) R2 0.242 0.351 0.140 t statistics in parentheses. * p<0.10, ** p<0.05, *** p<0.01 97 Table A.5: Determinants of firms’ performance between 1997 and 2002, by sector. Notes: The dependent variable is the change in the log of sales between end of 1996 and end of 2002. We divide the sample into tradable goods and non-tradable goods’ firms using the SIC code which is available in our data. “Employees” is the log of the number of a firm’s total employees in 2001. Since such data is not available for our firms before the year 2001 we focus in this paper on the log of total fixed assets as a measure of the size of the company. Non-Tradable Non-Tradable Tradable Tradable Δ log(sales) Δ log(sales) Δ log(sales) Δ log(sales) Size-96 0.126** 0.107*** (2.60) (2.87) Leverage-96 -0.506 -0.615 -0.163 -0.247 (-1.27) (-1.64) (-0.58) (-0.88) Interest-96 -0.964 -1.726 1.230 0.867 (-0.39) (-0.74) (0.56) (0.39) Profitability-96 0.249 -0.550 1.271*** 0.915* (0.25) (-0.57) (2.64) (1.91) Thailand 0.470** 0.329* 0.260* 0.204 (2.61) (1.91) (1.87) (1.47) Indonesia -0.0317 -0.169 -0.0627 -0.0848 (-0.15) (-0.86) (-0.41) (-0.55) Employees 0.171*** 0.167*** (3.60) (4.25) Export 0.180 0.118 (1.57) (1.02) Constant -1.350** -0.900** -1.477*** -1.402*** (-2.35) (-2.37) (-3.17) (-4.28) R2 0.111 0.145 0.141 0.193 t statistics in parentheses. * p<0.10, ** p<0.05, *** p<0.01 98 Table A.6: The growth effect. Notes: The dependent variable is the change in the log of sales during the year 1998, i.e. between end of 1997 and end of 1998. Tobin’s Q is the ratio of the sum of the market value and total liabilities to total assets at the end of 1996. Value-to-capital is the ratio of the mar- ket value to total fixed assets at the end of 1996. All regressors are end-of-1996 pre-crisis val- ues. This Table shows that a large part of the size effect that we document in the data, is due to a growth effect as predicted by the model. Data source: Worldscope, Thomson Financial. Δ log(sales) Δ log(sales) Δ log(sales) Δ log(sales) Size 0.032** 0.021 0.013 (2.13) (1.39) (0.66) Export 0.157*** 0.139** 0.140** 0.143** (2.89) (2.48) (2.51) (2.58) Leverage -0.321** -0.379*** -0.401*** -0.396*** (-2.46) (-2.79) (-2.96) (-2.93) Interest 0.103 0.195 -0.0979 -0.178 (0.11) (0.20) (-0.10) (-0.18) Profitability -0.012 0.063 0.115 0.138 (-0.05) (0.24) (0.43) (0.52) Thailand -0.060 -0.128* -0.159** -0.174** (-0.90) (-1.79) (-2.12) (-2.42) Indonesia 0.064 0.038 0.011 0.003 (0.80) (0.45) (0.13) (0.04) Tobin’s Q -0.030* (-1.94) Value-to-capital -0.070** -0.080*** (-2.20) (-2.80) Industry Dummy YES YES YES YES Constant -0.366* -0.218 -0.063 0.095 (-1.72) (-0.95) (-0.25) (1.05) R2 0.164 0.189 0.192 0.191 t statistics in parentheses. * p<0.10, ** p<0.05, *** p<0.01 99 Table A.7: Benchmark Calibration Description Parameter Values Discount factor β = 0.97 Growth factor ¯ g = 1.02 Interest rate r = 0.0123 Depreciation rate δ = 0.08 Share of capital α = 0.3 Borrowing constraint parameter φ = 13 Cost of equities parameter κ = 0.25 Table A.8: Calibration for the small and the large firms. Description Parameter Values Discount factor β = 0.97 Growth factor ¯ g = 1.02 Interest rate r = 0.0123 Depreciation rate δ = 0.08 Share of capital α = 0.3 Borrowing constraint parameter φ L = 12.8 φ S = 13.6 Probability of switching p = 0.017 Cost of equities parameter κ = 0.25 100 Appendix B: Appendix to Chapter 3 Proof of Lemma 1. The maximum problem of agent i in a financial market equilibrium is given by: max{u i (x i )|x i −ω i = W(q,p,V)Z i (x i ,z i )∈R n ×Ξ} (B.26) Where q is a no-arbitrage price process. The budget constraint at each node induces a Lagrange multiplier. The vector of Lagrange multipliers is denoted λ = (λ i (ξ)ξ∈D), and the Lagrangean function is given by: L i (x i ,z i ,λ i ) = u(x i )−λ i (x i −ω i −W(¯ q,V)Z i ) (B.27) The first order conditions are necessary and sufficient. The first order conditions with respect toZ i is given by ¯ λ i W(¯ q,P,V) = 0. This will directly imply that q k (ξ) = 1 λ i (ξ) X ξ ′ ∈ξ + λ(ξ ′ )(V J (ξ ′ )+q J (ξ ′ )), k∈ K(ξ) (B.28) 101 which when solved recursively gives q k (ξ) = 1 λ i (ξ) X ξ ′ ∈D + λ(ξ ′ )V k (ξ ′ ), k∈ K(ξ). (B.29) Given the form of the utility function this will imply that, q N,T (ξ 0 ) = X ξ∈D T β T ℘(ξ|ξ 0 ) ∂v i (x i (ξ))/x i ∂v i (x i (ξ 0 ))/x i 1 P(ξ) . (B.30) It follows from assumptions 2 that: P ξ∈D M T ℘(ξ|ξ 0 ) 1 P(ξ) −→ 0 and P ξ∈D L T ℘(ξ|ξ 0 ) 1 P(ξ) −→ 0. Therefore q N,T −→ β T P ξ∈D H T ∂v i (x i (ξ))/x i ∂v i (x i (ξ 0 ))/x i ℘(ξ|ξ 0 ) 1 P(ξ) . When ξ ∈ D H T we know that 1 P(ξ) = Q T i=1 1 τs i ≤ 1 τ T m+1 −→ 0 wheres i ∈ S H . Thereforeq N,T (ξ 0 )−→ 0. Proof of Lemma 4. We know that: q N,T (ξ) = β T { X ξ∈D H T ℘(ξ|ξ 0 )Λ i (ξ) 1 P(ξ) + X ξ∈D M T ℘(ξ|ξ 0 )Λ i (ξ) 1 P(ξ) + X ξ∈D L T ℘(ξ|ξ 0 )Λ i (ξ) 1 P(ξ) } (B.31) where Λ i (ξ) is the marginal rate of substitution (see (8)) which we know is finite and bounded from zero by assumption 1. If T is finite, q N,T (ξ) > 0 since P ξ∈D L T ℘(ξ|ξ 0 )Λ i (ξ) 1 P(ξ) > 0 given assumption 5, and the fact that when ξ ∈ D L T P(ξ) ≤ τ T l << ∞ when T << ∞. If T −→ ∞ then β T −→ 0 and since Λ i (ξ)<<∞∀ξ∈D thenq N,T (ξ)−→ 0∀ξ∈D. 102 Proof of Lemma 5. In the following we prove the three properties ofΨ(c,ǫ,θ). 1. IfT ∗ ∈ Ψ(c,ǫ,θ) =⇒ β T ∗ (θτ l ) T ∗ ≤ ǫ =⇒ β T ∗ (θ ′ τ l ) T ∗ ≤ ǫ ifθ ′ > θ. Therefore Ψ(c,ǫ,θ)⊆ Ψ(c,ǫ,θ ′ ). Furthermore let T be such that T ∈ Ψ(c,ǫ,θ) and T − 1 / ∈ Ψ(c,ǫ,θ) there existsθ ′′ such that β T (θ ′′ τ l ) T ≤ ǫ and since β T τ T l ≥ c =⇒ β T−1 τ T−1 l ≥ c thenT −1 ∈ Ψ(c,ǫ,θ ′′ ) =⇒Ψ(c,ǫ,θ)⊂ Ψ(c,ǫ, b θ) ∀ b θ≥ θ ′′ . 2. If T ∗ ∈ Ψ(c,ǫ,θ) =⇒ β T ∗ (θτ l ) T ∗ ≤ ǫ =⇒ β T ∗ (θτ l ) T ∗ ≤ ǫ ′ if ǫ ′ > ǫ.Therefore Ψ(c,ǫ,θ)⊆ Ψ(c,ǫ ′ ,θ). Furthermore let T be such that T ∈ Ψ(c,ǫ,θ) and T − 1 / ∈ Ψ(c,ǫ,θ) there existsǫ ′′ such that β T (θτ l ) T ≤ ǫ ′′ and since β T τ T l ≥ c =⇒ β T−1 τ T−1 l ≥ c then T −1 ∈ Ψ(c,ǫ ′′ ,θ) =⇒Ψ(c,ǫ,θ)⊂ Ψ(c,b ǫ,θ) ∀b ǫ≥ ǫ ′′ . 3. If T ∗ ∈ Ψ(c ′ ,ǫ,θ) =⇒ β T ∗ (τ l ) T ∗ ≥ c ′ =⇒ β T ∗ (τ l ) T ∗ ≥ c if c ′ > c. Therefore Ψ(c ′ ,ǫ,θ)⊆ Ψ(c,ǫ,θ). Proof of Lemma 6. Since by assumption 0 << Λ i << ∞, let Λ i and Λ i be such that Λ i < Λ i (ξ)< Λ i ∀ξ∈D. step 1: Let e Ψ(c,ǫ,θ) = {T ∈ N + |Λ i β T (θτ l ) T ≤ ǫ and Λ iβ T τ T l ≥ c}, if e Ψ(c,ǫ,θ) 6= {∅} for someǫ≈ 0 and somec >> 0 andθ then ¯ Ψ(c,ǫ,θ)6={∅}. From equations (8) and (9) it is clear that q N,T (ξ 0 )≤ Λ i β T (θτ l ) T and ˜ q N,T (ξ)≥ Λ iβ T τ T l ≥ c}. Hence it follows directly that e Ψ(c,ǫ,θ) ⊆ ¯ Ψ(c,ǫ,θ) and if e Ψ(c,ǫ,θ) 6= {∅} =⇒ ¯ Ψ(c,ǫ,θ)6={∅} step 2:∃θ,c >> 0 for which e Ψ(c,ǫ,θ)6=∅ for someǫ≈ 0 let c ′ = c Λ i since 0 << Λ i < ∞∃c such that 0 << c Λ i ≤ β τ l ≤ 1. And let ǫ ′ = ǫ Λ i since 0 << Λ i <∞∃ǫ≈ 0 such that ǫ ′ ≈ 0. Therefore e Ψ(c,ǫ,θ) = Ψ(c ′ ,ǫ ′ ,θ) and we know 103 from lemma 4 that∃θ such thatΨ(c ′ ,ǫ ′ ,θ)6={∅}. Step (1) and (2) prove (2). Since Ψ(c ′ ,ǫ ′ ,θ) = e Ψ(c,ǫ,θ) ⊆ ¯ Ψ(c,ǫ,θ) =⇒ ¯ Ψ(c,ǫ,θ) is increasing in θ and ǫ, furthermore it is clear from the definition of ¯ Ψ(c,ǫ,θ) that it is decreasing in c. 104

Abstract (if available)

Abstract The Mexican crisis that took place in 1994 was followed by nearly a decade of frequent and severe financial crises in the emerging economies. These crises episodes that were characterized by dramatic reversals in capital flows and large losses in output are atypical to the more advanced economies. This dissertation explores the characteristics, and in particular the vulnerabilities, of the emerging markets that could explain this difference.

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Creator Dagher, Jihad C. (author)

Core Title Essays in international economics

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 08/08/2008

Defense Date 04/15/2008

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

Tag capital inflows,Debt,emerging markets,financial frictions,OAI-PMH Harvest,sudden stops

Place Name Asia (continents)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Quadrini, Vincenzo (committee chair), Betts, Caroline M. (committee member), Dekle, Robert (committee member), Protopapadakis, Aris (committee member)

Creator Email dagher@usc.edu,jihad.dagher@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1549

Unique identifier UC1236090

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Dmrecord 105748

Document Type Dissertation

Rights Dagher, Jihad C.

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

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