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A social accounting matrix multiplier analysis of a water supply shortage in the Los Angeles County water service area SEZ 386

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A social accounting matrix multiplier analysis of a water supply shortage in the Los Angeles County water service area SEZ 386

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A Social Accounting Matrix Multiplier Analysis of a Water Supply Shortage in the
Los Angeles County Water Service Area SEZ 386
By: Lillian Anderson

Faculty of the USC Graduate School
Masters of Arts in Economic Development Programming
University of Southern California
May 2018

2

Table of Contents

I. Introduction ………………………………………………………………………………………………………………… 2
II. Review of the Literature …………………………………………………………………………………………………… 3
III. Multiplier Analysis ………………………………………………………………………………………………………… 8
A. Multiplier Decomposition ……………………………………………………………………………………………… 8
B. Constrained SAM Multiplier Linear Programming Model …………………………………………………………... 11
1. The LP Approach ………………………………………………………………………………………………..... 11
2. Specification of the Model …………………………………………………………………………………........... 12
IV. The Economy of SEZ 386 and the Role of Water ……………………………………………………………………….... 16
V. Model Construction ……………………………………………………………………………………………………….. 20
A. Constructing the SAM ………………………………………………………………………………………………... 20
B. The Water Sector and Water Coefficients ……………………………………………………………………………. 22
VI. Multiplier Decomposition Analysis ………………………………………………………………………………………. 23
VII. Analysis of a Water Supply Disruption …………………………………………………………………………………... 31
A. Simulation Scenario – Across-the-Board Rationing ………………………………………………………………….. 32
B. CSMLP Optimum Employment Scenario (cut total water supply by 25%) ………………………………………….. 36
VIII. Conclusion ……………………………………………………………………………………………………………….... 40
References ………………………………………………………………………………………………………………… 42
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I. Introduction

Economics is both a descriptive and an analytical science, and each aspect can be aided by building models of decisions,
activities, and systems. Such models do not correspond to all of reality. As the prominent economic historian Max Weber argued in
his concept of ideal types, reality is continuous where models are discontinuous; as researchers we isolate the parts or systems of
reality that interest us. The rest are ‘residuals’ – things and actions that might affect or be affected by economic decisions, activities or
systems, but not part of the models as such (Galbács, 2015). Incorporating such effects external to a model, or beyond its margins, and
variously incorporating additional variables is met in economic analysis by enhancing connections between macro and micro levels of
analysis, or bringing an analytical model closer to incorporating more finely-grained data of an empirical problem.
This thesis is about such a problem – specifically, “down-scaling” input-output (I-O) and social accounting matrices (SAMs)
models from higher level national or county level data to the closely approximate zones of specific economic (and other) activities that
we want to unite in a model accounting for the impacts of ordinary economic activity, external shocks or policy in one or more of its
components. The reason for this model refinement is to incorporate more of those impacts for planning by bringing them within the
economic model as part of its specification. In other words, we would be creating additional economic objects, or, ‘objectifications’ in
Weber’s terms, that can be brought within the I-O balances or SAMs used in economic analysis.
In economic terms, this is a problem of decisions, activities and systems at a macro level, such as captured in national or even
county data, do not include data of lower level aggregations, which are left over as residuals or analytically invisible to analysis. The
reverse is also true; so the problem is how to extend analysis from the former (macro) to meso or micro without the use of too many
simplifying assumptions. Development generally and planning in particular can be rife with such problems, where local level models
do not attend to or have to hold constant macro level features, such as GDP or other features of capital and labor flows, while macro
level data do not capture any but their own range of inputs, dismissing all other data or relegating them analytically to externalities.
4

Weber’s point was that no such data are in any sense natural, not at any level. Just as nation, county, census tract, zip code or
planning zone are culturally – or in his terms ‘historically’ – defined, so are the data describing choices, activities and systems in them
(Galbács, 2015). It is the latter that interests us here and specifically incorporating into I-O or SAM-based model data of choices,
activities and systems at lower levels to capture and analyze more of their impacts in development and for planning development. My
objective is to identify and render such margins more accessible to quantitative analysis short of having to develop a model as
complex as historical realities, which would be the case in simply disaggregating macro data of large systems into micro data about
small ones. These are different data.
This thesis will be part of a larger project undertaken by USC’s Center of Risk and Economic Analysis of Terrorism Events
(CREATE), on behalf of the Los Angeles Department of Water and Power (LADWP), that will analyze the economic benefits of
upgrading the LADWP water system to mitigate losses from a major earthquake. Under the direction of Dr. Adam Rose, the team will
analyze mitigation strategies emanating from the Seismic Resilient Pipeline Network (SRPN) concept, which is designed to withstand
earthquake damage to continue providing water or reduce service outage times, even while meeting community needs and recovery
efforts. The project will focus on Downtown Los Angeles and a single earthquake scenario on the Hollywood Fault, and two
mitigation strategies. Previous work on similar scenarios includes a study on the impacts of an earthquake on the LADWP (Rose et al.,
2011), and this thesis and the larger project will refine and adapt the models and methodology used.
The model that will be used in the larger study is a computable general equilibrium (CGE) model that was developed for the
United States (at a national level) and Los Angeles (at a county level) by Adam Rose and Gbadebo Oladosu (Rose and Oladosu, 2002;
Rose and Liao, 2005; Rose et al., 2007a,b) and refined by the research team at USC (Rose et al. 2009; Rose et al., 2011; Prager, 2013;
Prager et al., 2016). This thesis will create a SAM for Los Angeles County from IMPLAN 2015 data, and perform a SAM analysis of
the economic impact of water service disruptions due to an earthquake using the updated social accounts.
The social accounting matrix (SAM) forms the backbone of CGE models. The SAM is the record of the flow of funds
associated with all transactions within an economy and forms the key data set on which any CGE model is built (Pyatt, 1988). CGE
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models are multi-market models of the behavioral responses of producers and consumers to changes in prices, technology, and
external shocks within the limits of capital, labor and natural resources available (Rose, 1995). Though they are complex, CGE models
are extremely useful in resilience and disaster mitigation analysis for several reasons (see, e.g., Rose et al., 2011a). CGE models are
general, in that they capture not only the direct effects of an economic change or shock, but also the indirect effects that arise from
linkages in an economy through price an quantity interactions, i.e., the interindustry relationships, as well as the induced effects of
household-industry relationships and the total economic impacts. CGE models are computable, which allows researchers to run
simulations when historical data are insufficient or unavailable. Finally, CGE models typically have equilibrating assumptions –
demand and supply decisions and their influence on commodity and factor prices are represented.
This thesis is an application of SAM analysis techniques to a local/regional set of accounts in order to estimate the economic
impacts of a disaster on a small area economy. First I will describe the current state of the literature in Section II. Then, I will discuss
the analysis techniques I used – Pyatt and Round’s (1979) multiplier decomposition and the constrained SAM multiplier scenario – in
Section III. Section IV discusses the structure of the sub-county economy, and the role of water in it. Next, in Section V I will utilize
county- and zip- code-level data from Impact Analysis for Planning (IMPLAN) to construct a SAM for a sub-region of Los Angeles
County, using several techniques in previous related literature (Cole, 1998; Seung, 2014) developed for similar regional impact
analyses. Then I will use the SAM analysis techniques from Section IV to estimate the economic impact of a water service disruption
to Los Angeles County due to an earthquake in Section VI. Finally, in Section VII I will present the results, policy implications, and
concluding remarks.

II. Review of the Literature

Impact analysis is a prominent topic for economic research and development studies. Initially, such analysis was restricted mainly
to the national level for a variety of reasons, including lack of the kind of extensive regional data that the models used for such
analysis need, as well as the problems that arise from the greater openness of regional economies in comparison with national ones
6

(Partridge and Rickman, 1998). However, with new methodologies and increased availability and extent of regional data, researchers
can now more readily perform impact analyses at the regional level.
Among the first regional impact analysis studies of disasters to use inter-industry models such as input-output (I-O) or computable
general equilibrium (CGE) was Cochrane’s (1974) work that used a linear programming formulation of I-O for the economy as a
whole, which characterizes the economy as a set of interdependent linear equations. I-O and CGE models soon came to be applied to
lifeline utility (e.g. water and electricity) disruptions in the event of a natural or man-made disaster or hazard event, earthquakes in
particular. Rose (1981) outlined a similar framework that incorporated resource reallocation across sectors that minimized losses from
a disaster. Rose et al. (1997) incorporated, for the first time, the engineering aspects of electricity lifelines into the previously
examined I-O model, clarified neglected features of impact analysis such as indirect effects (ripples up and down the supply chains)
caused by bottlenecks, and developed an algorithm that enabled examination of optimal mitigation and resilience strategies. Other
applications included Gordon and Richardson (1996), Santos and Haimes (2004), and Rose and Wei (2013).
I-O models dominated the field of regional impact analysis, but, lately, increased attention has been given to CGE models, which
are much more flexible and comprehensive than I-O models. As CGE models are non-linear, they are less rigid, and they also
incorporate behavioral responses into their frameworks (Rose, 2004), and so are better for detailed assessments of the impacts a
disaster has on an economy – be it regional or national (Koks et al., 2016). Several studies have implemented regional CGE models
for their analysis. For example, Rose and Liao (2005) extend CGE modeling for analyzing post-disaster disruptions of a water utility
lifeline in a regional economy, explicitly incorporating a disequilibrium by the constraint on water supplies and in the presence of
resilience. Many studies of utility lifeline disruptions resulting from earthquakes have focused on the electric power grid or the water
system of a region or city, Los Angeles in particular (see, e.g., Rose and Guha, 2004; Rose and Oladosu, 2008; Rose et al., 2011a;
Rose et al., 2011b). Rose et al. (2009) used a CGE model that incorporates features of inherent (what already exists under normal
circumstances) and adaptive (responses to crisis situations) resilience at the individual level and market level, and gauged quantity and
price interaction effects across sectors to assess the national and regional impacts of the 9/11 terrorist attacks. Rose et al. (2011a)
7

incorporated the spatial aspects of the water service system in addition to the engineering aspects, disaggregating a regional/county
level model from national and state level data. Rose et al. (2012) incorporated resilience tactics used by both producers and
consumers.
In regards to SAM analysis, Pyatt (1999) presents a formal demonstration of the similarities and differences between I-O tables
and SAM accounts. Pyatt and Round (1979) defined a generalized method for multiplier analysis, using a national SAM for Sri Lanka
as an example. Pyatt (2001) compared different multiplier analysis methods for SAMS, showing that Miyazawa and Masegi’s (1963)
and Pyatt et al.’s (1973) multipliers are both overlapping subsets of the more generalized Pyatt and Round (1979) method. Defourney
and Thorbecke (1984) developed an alternative to Pyatt and Round’s (1979) multiplier decomposition method, called structural path
analysis, which analyzed all the paths through which an exogenous injection of income into one account transmits through the
economy on its way to a destination account. Cole (1998) laid out a county-level multi-region SAM for the New Madrid Area to
examine the impacts of lifeline utility disruptions as a result of an earthquake on a small region of Tennessee. Seung (2014) used an
interregional SAM for Alaska to show spillover effects from one region that relies on imports from another and examined in much
greater detail the linkages between one regional economy and another, revealing how total impacts from exogenous changes to
industries and households can be disentangled into intra-regional and spillover effects.
Earlier studies scaled down national data, with estimation methodologies designed for the assumptions of closed systems at that
level. More recent studies (e.g., Rose et al., 2011a) use regional data and shift the methodological focus instead to refining estimation
methodologies and by incorporating other necessarily local/regional aspects of lifeline utilities, such as the physical layout of the
power grid or water pipelines of a city or region, that are not present in national level data. These studies extend economic and
mathematical modeling of impacts of disasters and resilience not only through the inclusion of more data, but also by extending the
models to include indirect effects and behavioral responses to disasters – in other words, linking the macro-level features of systems to
the decisions and actions of individual agents at the micro-level. They internalize what had previously been external to the system and
thus the modeling of it by showing how macro- and micro-level responses to disasters converge in adaptive resilience (responses after
8

shocks to the system) of individuals and markets, distinguishable from inherent resilience (typically equilibrium-restoring measures
within the system). This methodology identifies linkages between the macro- and micro- levels.

III. Multiplier Analysis

A. Multiplier Decomposition

A SAM by itself is not a model. It is a set of accounts that describe the transaction flows within an economy, with three key
features. A SAM is a square matrix, with rows corresponding to receipts of income and columns corresponding to payments. It is
comprehensive, meaning it represents all the transactions within an economy, and it is detailed, able to be disaggregated to varying
degrees as well as emphasizing different aspects of an economy (Round, 2003). To turn a SAM into a model requires the specification
of functional relationships between inputs and outputs. Furthermore, multiplier analysis, where the industry and institutional
interdependencies are shown explicitly, similar to I-O modeling, provide a way of decomposing the interdependencies.
This thesis follows Pyatt and Round’s (1979) decomposition method, and applies it to the constructed SAM for a major portion
of the Los Angeles County economy. To start, each account must be designated as endogenous or exogenous, with convention holding
that transactions in the government account, the capital account, and the rest of the world account be exogenous. This convention
arises because government expenditures are taken to be policy-determined and thus outside the domestic sectors, and the rest of the
world accounts are taken as given. The endogenous accounts are therefore production, factors, and households (Round, 2003). Pyatt
and Round perform multiplier decomposition for two different types – accounting multipliers and fixed-price multipliers. Though they
only demonstrate the derivation for accounting multipliers, the process is the same for both.
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This thesis will focus on accounting multipliers, as fixed-price multipliers are for analyzing the endogenous effects of an
exogenous injection of income into or an external shock on the economy. The first equation comes directly out of the structure of a
SAM. Equation (1) is the starting point for multiplier analysis, where y
n
is endogenous income, A
n
1
is a square matrix of average
propensities to consume in relation to spending of the income, and x is exogenous expenditures.

𝒚
!
= 𝑨
!
𝒚
!
+𝒙 (1)

Using matrix algebra, Equation (1) can be solved as Equation (2), where (I – A
n
)
-1
is the accounting multiplier matrix M
a
.

𝒚
!
= (𝑰− 𝑨
!
)
!!
𝒙 = 𝑴
!
𝒙 (2)

Pyatt and Round (1979) proceed to demonstrate how the accounting multiplier matrix, M
a
, can be decomposed into three separate
matrices, M
a1
, M
a2
, and M
a3
. Equations (3), (4), and (5) show the decomposition.

𝒚
!
= 𝑨
!
𝒚
!
+𝒙= 𝑨
!
−𝑨
!
𝒚
!
+ 𝑨
!
𝒚
!
+𝒙
𝒚
!
= 𝑰−𝑨
!
!!
𝑨
!
−𝑨
!
𝒚
!
+ 𝑰−𝑨
!
!!
𝒙
𝒚
!
= 𝑨
∗
𝒚
!
+ 𝑰−𝑨
!
!!
𝒙 (3)

1
The A matrix (technical coefficient matrix) can be partitioned into four parts, A
11
, A
12
, A
21
, and A
22
, where the subscripts 1 and 2 refer to endogenous and
exogenous accounts, respectively. This notation will be used throughout this thesis.

10

Where 𝑨
!
is a square matrix of the same rank (size) as 𝑨
!
such that 𝑰−𝑨
!
!!
exists.

𝒚
!
= 𝑨
∗𝟐
𝒚
!
+ (𝑰+𝑨
∗
) 𝑰−𝑨
!
!!
𝒙 (4)

Multiplying through Equation (4) by 𝑨
∗𝟐
and then substituting 𝑨
∗𝟐
𝒚
!
gives Equation (5).

𝒚
!
= 𝑨
∗𝟑
𝒚
!
+ (𝑰+𝑨
∗
+𝑨
∗𝟐
) 𝑰−𝑨
!
!!
𝒙 (5)

Rearranging Equation (5) results in the decomposition of the accounting multiplier matrix into the three multiplier matrices M
a1
, M
a2
,
and M
a3
, provided that (𝑰−𝑨
∗𝟑
)
!!
exists.

𝒚
!
= (𝑰−𝑨
∗𝟑
)
!!
(𝑰+𝑨
∗
+𝑨
∗𝟐
) 𝑰−𝑨
!
!!
𝒙 (6)

Equation (7) defines the three matrices.

𝑴
!!
= 𝑰−𝑨
!
!!
; 𝑴
!!
= 𝑰+𝑨
∗
+𝑨
∗𝟐
; 𝑴
!!
= (𝑰−𝑨
∗𝟑
)
!!
(7)

Furthermore, Equations (1) and (6) imply the relationship shown in Equation (8).

𝑴
!
=𝑴
!!
𝑴
!!
𝑴
!!
(8)

11

Alternatively, Equation (8) can be expressed in Stone’s (1978) additive formulation shown in Equation (9).

𝑴
!
= 𝑰+ 𝑴
!!
− 𝑰 + 𝑴
!!
− 𝑰 ∗𝑴
!!
+ 𝑴
!!
− 𝑰 ∗𝑴
!!
∗𝑴
!!
(9)

Each of these three multiplier matrices represents a different type of effect on the economy. 𝑴
!!
represents the within-account
effects, or the effects that an exogenous injection of income into one set of accounts (such as households) has on that same set of
accounts. 𝑴
!!
represents the cross effects (or “spillover” effects), and is alternatively called the open-loop effects multiplier matrix.
This means that this matrix represents the effects that an injection of income into one set of accounts has on another with no reverse
effects. 𝑴
!!
represents the between-account effects (and thus is called the closed-loop multiplier matrix), or the full circular effects of
an exogenous injection of income into one set of accounts as it ripples through the economy and back into the original set of accounts
(Round, 2003). In the Stone additive decomposition formulation, the identity matrix I is the initial injection, the second term, 𝑀
!!
−
𝐼 , is the net transfer multiplier effects, the third term, 𝑀
!!
− 𝐼 ∗𝑀
!!
, is the net cross-multiplier or open-loop effects, and the fourth
term, 𝑀
!!
− 𝐼 ∗𝑀
!!
∗𝑀
!!
, are the net circular or closed-loop multiplier effects.

B. Constrained SAM Multiplier Linear Programming Model

1. The LP Approach

One of the realities of modeling the economic impacts of a water service disruption is that the indirect effects are likely to be
stronger downstream than upstream -– the customers of the water sector are impacted more than the water sector’s suppliers. This is
because, when the pipelines are damaged, those industries that require water as an input are severely limited in their production
capabilities, as are the subsequent industries in the downstream supply chain. Linear programming offers a way to model these
12

downstream linkages, because one can limit one or more natural resource, other factors of production, or any intermediate good and
find the resulting allocation of water across industries that results in the optimal distribution of production output.

2. Specification of the Model

The CSMLP model, an early version of which can be seen in Cesal et al., 1989, is specified below.

min (𝑄𝐹𝑆
!
− 𝐴
!"
∗𝑌
!! !
) (10)

The objective function minimizes employment loss.
2
𝑄𝐹𝑆
!
is the total size of the labor force. Subtracted from it is the sum, over
activities (industries), of the amount of labor required for each activity’s output level (see additional variable and parameter definitions
below). The vector A
la
is the employment coefficients for each industry – in other words, the amount of labor, l, required for each
sector, a’s, output, Y
1a
. These coefficients are taken from the technical coefficients matrix calculated in the early steps of the multiplier
model. This difference is then minimized subject to the following constraints:

𝐴
!"!!
!"#
= 𝑋
!
∗𝐴
!"!!
(11)

This constraint adjusts the commodities, c, by household, h, accounts, A
12ch
, in the A
12
matrix of the SAM by the exogenous demand
X
1
.

2
This formulation of minimizing employment loss would yield the same results as a formulation that maximizes total employment in the economy, both subject
to the water availability constraint.
13

𝐴
!"!"
!"#
=𝐴
!"!"
(12)

This constraint sets the commodities, c, by rest of world accounts, r, in the adjusted A
12
matrix of the SAM equal to the unadjusted
values.

𝑀= 𝐼−𝐴
!!
!!
∗𝐴
!"
!"#
!
(13)

This equation defines the adjusted multiplier matrix, M, summing over all activities, commodities, and institutions. A
11
is the
endogenous accounts by endogenous accounts structural matrix and A
12
is the endogenous by exogenous structural matrix. This is one
of the standard multiplier analysis equations, along with the adjusted exogenous demand equation (below),

𝑋
!"
=𝐴
!"
!"#
∗𝑌
!
(14)

This equation specifies the level of adjusted exogenous demand, X
12
, for the endogenous by exogenous accounts, by multiplying the
exogenous by endogenous structural matrix A
12
by exogenous demand, Y
2
.

𝑌
!!
= 𝑀 ∗𝑌
! !
(15)

This equation defines endogenous output, 𝑌
!!
, as the sum over all activities, commodities, and institutions of the multiplier matrix
times the vector of exogenous output, Y
2
. This equation is an alternative to 𝑌
!
= (𝐼−𝐴
!!
)
!!
∗𝑋
!
, which defines endogenous output
as the multiplication of the Leontief inverse of the endogenous accounts in the SAM and the endogenous final demand.

14

𝑌
!!
= 𝐼−𝐴
!!
!!
∗ 𝐴
!"
∗𝑌
!! ! !
(16)

This equation solves for exogenous output, 𝑌
!!
, by summing, over exogenous accounts, the multiplication of the Leontief inverse of
the exogenous by exogenous accounts, 𝐼−𝐴
!!
!!
, and the sum over the endogenous accounts of the exogenous by endogenous final
demand, given by the multiplication of the exogenous by endogenous structural matrix A
21
and endogenous output, Y
1d
. This equation
is, in essence, the same as 𝑌
!
= (𝐼−𝐴
!!
)
!!
∗𝑋
!
, but solves for exogenous output rather than endogenous output.

𝐺𝐷𝑃𝐹𝐶= 𝑌
!! !
(17)

This equation defines GDP at factor costs, 𝐺𝐷𝑃𝐹𝐶, by summing total endogenous output, Y
1f
, over the factors of production, f.

𝑄𝐹𝑆
!
= 𝐴
!"
∗𝑌
!! !
(18)

This equation defines the quantity of each factor available,𝑄𝐹𝑆
!
, for each endogenous activity, summing over all activities, a, the
factors of production coefficients for each activity, A
fa
, multiplied by the endogenous output Y
1a
, for each activity. This equation
determines the amount of each factor of production that the economy needs.

𝐻2𝑂
!
= 𝐴
!"
∗𝑌
!! !
(19)

This constraint defines the total amount of water, H2O
w
, demanded by summing over activities the multiplication of the water
coefficients (the amount of water each activity requires to produce one unit of that good/service), A
wa
, by the endogenous output for
each activity, Y
1a
.
15

𝐴
!"
∗𝑌
!!
=𝑄𝑀
!"
(20)

This equation is the import constraint. The left-hand side represents leakages from endogenous accounts to exogenous accounts, given
by the multiplication of the exogenous by endogenous structural matrix A
21
and the endogenous output of each commodity Y
1c
, which
must be equal to the quantity of imports to commodities from the rest of the world and rest of the United States, 𝑄𝑀
!"
.

𝑄𝐹𝑆
! !
≤𝑄𝐹𝑆
!
(21)

This equation limits the quantity of labor services, 𝑄𝐹𝑆
!
, available. It states that the sum of labor services demanded must be less than
a pre-defined upper limit, given as 𝑄𝐹𝑆
!
, such as the total size of the labor force.

𝑄𝐹𝑆
!
≤𝑄𝐹𝑆
!
(22)

This equation constrains all factors of production. QFS
f
is the quantity of factor services demanded, and 𝑄𝐹𝑆
!
is the upper limit of
factor services available. In other words, the economy cannot use more of a factor of production than is available.

𝐺𝐷𝑃𝐹𝐶≤𝐺𝐷𝑃𝐹𝐶 (23)

This equation constrains GDP at factor cost by some predefined upper limit, 𝐺𝐷𝑃𝐹𝐶.

𝐻2𝑂
!
≤𝐻2𝑂
!
(24)
16

This is the water supply constraint, limiting the total water available to the economy to 𝐻2𝑂
!
. When the water supply is shocked, I
simulate the total water available to be reduced by 10, 25, and 50% of the sector’s base-level output in the simulations below.

𝑋
!
≥ 0 (25)

This is a non-negativity condition for the multiplier for exogenous demand, X
1
.

I apply both the decomposition process outlined above and the constrained multiplier analysis to the SAM for the sub-region of
Los Angeles County in Section VI.

IV. The Economy of SEZ 386 and the Role of Water

The SEZ 386 study region covers a land area of 81 square miles, bounded in red in Figure 1, and has a total population of 1.2
million people. Of this population, a little under half (545 thousand) are employed. Gross regional product (GRP) is $55.7 billion, with
about half coming from labor income ($27.55 billion). The average household income is $161 thousand, and household final demand
is $34.24 billion. As for the government, indirect taxes sum to $4.4 billion, income and other taxes on factors of production total $3.8
billion in federal taxes and $1.775 billion in state/local taxes. Taxes on households sum to $2.05 billion in federal taxes and $1.83
billion in state/local taxes. Government final demand is $922.8 million from the Federal Government and $7.2 billion from the
State/Local Government. State/Local transfers to households sums to $4.53 billion, while Federal transfers to households sums to
17

$9.69 billion. The economy’s domestic and foreign exports total $33.9 billion and $4.95 billion respectively, while intermediate and
institutional imports total $13.3 billion and $15.65 billion respectively. The region’s ten largest sectors, by employment, are
Professional and Technical Services (at 90,008 employees), Entertainment and Recreation (64,282 employees), Personal and Repair
Services (60,369 employees), Real Estate (44,348 employees), Retail Trade (44,345 employees), Schools and Libraries (43,256
employees), Wholesale Trade (33,940 employees), Light Industry (28,476 employees), Government Industry (22,852 employees), and
Medical (17,493 employees).

18

Figure 1. Map of SEZ 386
Red outlines the boundary of SEZ 396. Blue outlines the boundary of Los Angeles City

In regards to water, all water used in the region is imported, with intermediate imports (in other words, the water that is used as
an intermediate input in production) at $57.1 million and institutional imports (the water that is used as final demand by households,
19

government, and other institutions) at $136.3 million. Household water demand totals $108.8 million, Federal Government water
demand $851 thousand, and State/Local Government water demand $26.6 million. As for water use as an intermediate input, the top
ten industries that use the most water, from most to least, are Real Estate, Entertainment and Recreation, Retail Trade, Personal and
Repair Services, Religious Activities, Schools and Libraries, Professional and Technical Services, Government Industry,
Food/Drugs/Chemicals, and Universities and Colleges.
A comparison of the major economic indicators of the economy of the sub-county region of SEZ 386 and the economy of Los
Angeles County as a whole is presented in Table 4. First, the GRP of Los Angeles County is about 11.5 times greater than the GRP of
SEZ 386. Second, the population of Los Angeles County is ten times greater than the population of SEZ 386, and a greater proportion
of the population is employed, although average household income is very similar in the full county as in the smaller sub-region. The
largest sectors, by employment, in the county are Professional and Technical Services, Entertainment and Recreation, Retail Trade,
Personal and Repair Services, Real Estate, Schools and Libraries, Banking and Finance, Government Industry, Wholesale Trade, and
Medical. Note that these industries are very similar to the sub-county region, which indicate that the economy of the sub-county region
of SEZ 386 is very similar to the full-county economy. In regards to the water sector, the net commodity supply of water is $1.6
billion and the total gross commodity demand is $2.05 billion. Household demand is $671 million, Federal Government demand is
$23.7 million, and State/Local demand is $929 million. The county’s economy exports a total of $301 million of water (the vast
majority of which is domestic exports), and imports a total of $751 million, two-thirds of which goes to institutions and the remaining
one-third of which is used as intermediate inputs in production. Overall, the SEZ 386 economy is very similar to the Los Angeles
County economy.

Table 2. SEZ 386 and Los Angeles County Economic Indicators
a

Economic Indicator SEZ 386 Los Angeles County
Gross Regional Product $55.7 billion $633.23 billion
20

Population 1.2 million 10.2 million
Total Employment 545,000 6.2 million
Unemployment Rate 5.5% 3.9%
Average Household Income $161,000 $161,000
a
Data taken from IMPLAN (2015)

V. Model Construction

A. Constructing the SAM

The first step in this model is to construct the social accounting matrix for the sub-county region of water service area SEZ
386. To do this, I first determined which zip codes are within the WSA using a previously created map with the boundaries of the
water service area and a city map that has zip code boundaries. Then, after constructing a model in IMPLAN (2015) for those zip
codes, I exported the Industry by Commodity (IxC) Social Accounting Matrix IMPLAN produced to an Excel worksheet. To
aggregate the 536-Sector SAM to a 29-Sector SAM, I used GAMS software and the sector-bridging scheme presented in Table 1.

Table 1. Aggregation Scheme
Aggregated Sector Names
Sector Names
Abbreviation
IMPLAN Sector Codes
(536 Sector Scheme)
Agriculture - Annual AAG 1-3, 7-10
Agriculture - Perennial PAG 4-6
Agriculture - Other OAG 11-19
Metals, Minerals, and Processing MMP 20-40, 199-230
Electric Power ELE 41-49, 519, 522, 525
21

Water WAT 51
Construction CON 52-64
Food, Drugs, and Chemicals FDC 65-110, 156-187
Light Industry LIN 111-155, 188-198, 277, 323-342, 368-278,
383-394, 417-421
Heavy Industry HIN 231-258, 260-267, 269-271, 273-276,
278-300, 343-356, 362-367
High Tech Industry HTI 259, 268, 272, 301-322, 357-361, 379-
382, 422, 430-432
Wholesale Trade WST 395
Retail Trade RET 396-407, 442-444
Professional and Technical
Services
PTS 50, 408-416, 445-471
Motion Picture and Video MPV 423
Entertainment and Recreation ENR 424-426, 488-498, 501-503
Telecommunications TCO 427-429
Banking and Finance BFI 433-439
Real Estate RES 440-441, 499-500, 517
Schools and Libraries SCL 472, 474, 532, 534
Colleges and Universities UNI 473
Medical MED 475-481
Hospitals HSP 482
Nursing Homes NRS 483-484
Personal and Repair Services PRS 485, 487, 506-512
Parking Services PKS 504-505
Religious Activities RNP 513-516
Government Industry GVT 518, 520-521, 523-524, 526-531, 535, 536
22

Community Food, Housing, and
Relief Services
CRS 486

Because IMPLAN exports and imports industries/activities rather than commodities, like in a traditional SAM, I had to adjust
the resulting SAM to be exporting and importing commodities in order to run simulations. Industries produce commodities, and it is
these commodities that are sold to other industries (as intermediate inputs), to institutions (as final demand), or exported to the rest of
the world (and the rest of the United States in this case). So in a traditional SAM, it is the commodities, or the products and services
produced by the industries, that are bought and sold and not the industries themselves. The adjustment needed is simple. First I moved
the exports to the rest of the world and the rest of the United States from the industries accounts to the commodity accounts. Then, to
balance the SAM, I added each industry’s exports to its entries in the make matrix portion of the SAM (the industry by commodity
accounts). To move the imports, I created two new commodities, Commodities for Rest of World (C-MROW) and Commodities for
Rest of the United States (C-MROUS). I then moved all entries for imports into these new commodities, essentially treating them as
non-comparable imports. Finally, I assumed all column entries for ROW and ROUS to be financial flows to the institutions in the
SAM.

B. The Water Sector and Water Coefficients

The water coefficients for each commodity and institution sector are assumed to be the same for the sub-county region of SEZ
386 as they are for the county as a whole. Under this assumption, I used a Los Angeles County I-O Table calculated for a previous
water service disruption study (Rose et al., 2012) to calculate the water input coefficients. The coefficients, which are the amount of
water services required per unit output, are simply the water commodity sector in the technical coefficients matrix (also called the A
matrix). These coefficients are for water services only, whereas in the extracted SAM the water services sector includes wastewater
services, which are performed by the government. As a result, the wastewater services must be separated from water services. Because
23

the government provides wastewater services, wastewater services are separated and subsumed into the Government Industry (C-
GVT) sector.
Taking the water coefficients, I multiplied each sector’s coefficient by its corresponding total output to obtain the amount of
water services alone required by each sector. I then subtracted these new values for the water sector from the values shown in Table 2
to obtain the wastewater services performed by the government, which were added into the Government Industry sector. Some
elements of the new government industry sector were negative, and so further adjustment was needed. I set those negative elements in
the Government Industry sector to zero, and adjusted the corresponding elements in the inventory row by those negative elements.
Since those also became negative, I set those elements equal to zero and adjusted foreign trade (C-MROW) by the same values.
Finally, I input these new adjusted values into the corresponding cells in the adjusted SAM. Then, I re-balanced the SAM using the
estimation methodology presented in Robinson et al. (2001)

VI. Multiplier Decomposition Analysis

The analysis began with establishing the baseline data and multiplier model. First, I calculated the accounting multipliers using
the General Algebraic Modeling Systems (GAMS) software. The accounting multiplier matrix, which includes the industries,
activities, factors of production, and households, shows the total effects on producers and consumers of a change in final demand (see
Equation (2) above). The multiplier matrix is then decomposed according to the Pyatt and Round (1979) method outlined above as
well. Table 3 presents both the accounting multipliers and the Stone additive decomposition multipliers for all industries, activities,
factors of production, and households. I chose to present the Stone additive format because the decomposition of the accounting
multipliers into the three effects was clearer than the Pyatt and Round multiplicative form. The Stone decomposition also provides the
net multiplier effects.
24

Focusing first on the industries that use the most water directly (Real Estate, Retail Trade, Personal and Repair Services,
Government Industry, Food/Drugs/Chemicals, Professional and Technical Services, and Religious Services and Activities), I found
that the output multipliers of those industries were fairly large, ranging from 3.7 in Real Estate to 4.5 in Government Industry. These
values are larger than the corresponding Type I output multiplier in an input-output model as more activities are taken as endogenous
to the system in a SAM. The output multipliers for each endogenous sector, as well as their decomposed elements using the Stone
additive formulation, are shown in Table 3.

Table 3. Output Multipliers for SEZ 386
Industry Stone Decomposition
Output Multipliers Closed-loop effects Cross Effects Transfer Effects
Industry - Agriculture - Annual 3.818 1.054877021 1.283 0.479731758
Industry - Agriculture - Perennial 3.881 1.16196316 1.196 0.524805554
Industry - Agriculture - Other 3.969 1.19598553 1.312 0.466610675
Industry - Metals, Minerals, Processing 3.53 0.671650308 0.769 1.090328927
Industry - Electric Power 4.445 0.98782084 1.436 1.021954742
Industry - Professional and Technical Services 4.185 1.131944041 1.286 0.758853681
Industry - Construction 3.847 0.845659822 1.012 0.990964732
Industry - Food, Drugs, Chemicals 3.378 0.542199318 0.685 1.150660993
Industry - Light Industry 3.809 0.840644436 0.945 1.020360036
Industry - Heavy Industry 3.488 0.691788252 0.808 0.993500826
Industry - High Tech Industry 3.966 0.834636463 0.989 1.141977904
Industry - Wholesale Trade 3.999 0.939781858 1.116 0.939297749
Industry - Retail Trade 4.037 1.047873314 1.222 0.762388134
Industry - Motion Picture and Video 4.031 1.019845941 1.588 0.427384647
25

Industry - Entertainment and Recreation 4.491 1.332101619 1.475 0.68448365
Industry - Tele-communications 4.013 0.772427577 1.135 1.099012064
Industry - Banking and Finance 4.19 0.990823674 1.25 0.943599143
Industry - Real Estate 3.715 0.757352839 1.372 0.585588717
Industry - Schools and Libraries 4.591 1.739447548 1.768 0.085392235
Industry - Universities and Colleges 4.369 1.317094099 1.417 0.636661164
Industry - Medical 4.491 1.339110329 1.424 0.732934138
Industry - Hospitals 4.404 1.278061901 1.36 0.764116189
Industry - Nursing Homes and Services 4.484 1.370140202 1.409 0.704877612
Industry - Personal and Repair Services 4.489 1.337105906 1.334 0.814999068
Industry - Community Food, Housing, Relief Services 4.176 1.106920552 1.347 0.721031515
Industry - Parking Services 3.962 1.096911836 1.116 0.748132465
Industry - Religious Services and Activities 4.32 1.003832514 1.165 1.155577047
Industry - Government Industry 4.483 1.628355865 1.741 0.111567471
Commodity - Agriculture - Annual 4.011 0.833634148 1.011 1.165401355
Commodity - Agriculture - Perennial 4.881 1.16196316 1.196 1.524805554
Commodity - Agriculture - Other 3.286 0.675686335 0.744 0.831548474
Commodity - Metals, Minerals, Processing 4.531 0.672654526 0.772 2.087339982
Commodity - Electric Power 5.445 0.98782084 1.436 2.021954742
Commodity - Professional and Technical Services 5.165 1.131943461 1.284 1.742052911
Commodity - Water 5.291 1.557297773 1.664 1.065243245
Commodity - Construction 4.847 0.845659822 1.012 1.991169373
Commodity - Food, Drugs, Chemicals 4.379 0.542197345 0.685 2.147700475
Commodity - Light Industry 4.81 0.838643416 0.945 2.020402897
26

Commodity - Heavy Industry 4.491 0.689776746 0.806 1.987497691
Commodity - High Tech Industry 4.961 0.834634407 0.987 2.140029664
Commodity - Wholesale Trade 4.999 0.939781858 1.116 1.939297749
Commodity - Retail Trade 5.041 1.04787225 1.223 1.769446502
Commodity - Motion Picture and Video 5.031 1.019845942 1.588 1.42738468
Commodity - Entertainment and Recreation 5.48 1.332100596 1.473 1.679456655
Commodity - Tele-communications 5.013 0.772427577 1.135 2.099012064
Commodity - Banking and Finance 5.19 0.990823674 1.25 1.943599143
Commodity - Real Estate 4.714 0.758359483 1.37 1.585586704
Commodity - Schools and Libraries 5.559 1.722437449 1.757 1.077479768
Commodity - Universities and Colleges 4.308 0.995828576 1.072 1.238080045
Commodity - Medical 5.246 1.264049601 1.344 1.631936427
Commodity - Hospitals 3.483 0.718038942 0.767 2.931763249
Commodity - Nursing Homes and Services 5.484 1.371138262 1.403 0.765246636
Commodity - Personal and Repair Services 5.482 1.334103842 1.332 1.814042967
Commodity - Community Food, Housing, Relief Services 5.143 1.093913272 1.335 0.714007546
Commodity - Parking Services 4.962 1.096911836 1.116 1.748409226
Commodity - Religious Services and Activities 5.32 1.003832514 1.165 2.155577047
Commodity - Government Industry 5.185 1.517265011 1.623 1.03914287
Commodity - Imports – Rest of World 1 – – –
Commodity - Imports – Rest of U.S. 1 – – –
Labor Income 3.702 0.76473109 1.929278062 –
Capital – Proprietary Income 3.859 0.778839919 2.076721848 –
Capital – Other Property Type Income 2.436 0.299603102 1.134081611 –
27

Taxes on Production and Imports 1 – – –
Households less than 15 K 4.515 0.988526631 2.526490514 0.001857393
Households 15-30K 4.043 0.865714912 2.174987299 0.003280795
Households 30-40K 3.724 0.767778122 1.953932079 0.005384993
Households 40-50K 3.464 0.688832045 1.76281911 0.007634271
Households 50-70K 3.534 0.713144483 1.806754452 0.009629694
Households 70-100K 3.641 0.747513276 1.883818294 0.010001312
Households 100-150K 3.417 0.682770953 1.716595177 0.016094743
Households 150-200K 3.24 0.642228032 1.579458859 0.017419841
Households greater than 200K 2.327 0.37931093 0.91881581 0.03577614
Private Capital Accounts 2.209 0.23003586 0.574784296 0.398
Destock / Inventory 4.795 1.000641831 2.796978105 –

Focusing on the individual elements of the water commodity output multiplier (the sum of the water commodity column of the
Leontief Inverse), which has a value of 5.291, and their Stone decomposition values, which are presented in Table 4, I found that a
unit expansion of the water commodity has a multiplier of 0.049 in the Professional and Technical Services Industry, the largest
industry in SEZ 386 in terms of both output and employment. In other words, a unit increase in the demand of the water commodity
results in an 4.9% expansion in the Professional and Technical Services industry directly as into the water service industry and
indirectly through various interdependencies The largest accounting multiplier among the industries for a unit increase in the water
commodity is Government Industry at 0.964. This is because water treatment and sewage services were subsumed into the
Government Industry sector, and so a unit increase in the water commodity would have a greater impact on this sector than might be
expected.

28

Table 4. Water Commodity Output Multiplier by Industry and Institution.

Accounting
Multipliers
Stone Decomposition
Closed Circular Effects Net Cross Effects Net Transfer Effects
Agriculture - Annual 0.00000012 0.00001195 – 0.00000006367
Agriculture - Perennial 0.00001370 0.00001351 – 0.0000001982
Agriculture - Other 0.00001928 0.00001904 – 0.0000002412
Metals, Minerals, Processing 0.001 0.00024139 – 0.001
Electric Power 0.005 0.005 – 0.000293814
Professional and Technical Services 0.049 0.037 – 0.011
Construction 0.009 0.003 – 0.006
Food, Drugs, Chemicals 0.011 0.01 – 0.000141458
Light Industry 0.004 0.003 – 0.000264109
Heavy Industry 0.000701 0.000359758 – 0.000340872
High Tech Industry 0002 0.002 – 0.000200726
Wholesale Trade 0.029 0.025 – 0.004
Retail Trade 0.045 0.045 – 0.000616798
Motion Picture and Video 0.002 0.002 – 0.00005467
Entertainment and Recreation 0.038 0.037 – 0.001
Tele-communications 0.011 0.011 – 0.000375736
Banking and Finance 0.043 0.037 – 0.006
Real Estate 0.093 0.091 – 0.002
Schools and Libraries 0.004 0.004 – 0.000006632
29

Universities and Colleges 0.006 0.006 – 0.000003271
Medical 0.028 0.028 – 0.00000021205
Hospitals 0.018 0.018 – 0
Nursing Homes and Services 0.006 0.006 – 0
Personal and Repair Services 0.014 0.013 – 0.000714185
Community Food, Housing, Relief Services 0.002 0.002 – 0
Parking Services 0.006 0.006 – 0.00008972
Religious Services and Activities 0.016 0.016 – 0.00008361
Government Industry 0.964 0.005 – 0.959
Labor Income 0.892 0.122 0.77 –
Capital – Proprietary Income 0.032 0.029 0.003 –
Capital – Other Property Type Income 0.240 0.091 0.149 –
Taxes on Production and Imports 0.019 0.024 – –
Households less than 15 K 0.011 0.002 0.009 –
Households 15-30K 0.044 0.008 0.036 –
Households 30-40K 0.051 0.009 0.042 –
Households 40-50K 0.0058 0.01 0.047 –
Households 50-70K 0.119 0.021 0.098 –
Households 70-100K 0.155 0.027 0.128 –
Households 100-150K 0.153 0.027 0.126 –
Households 150-200K 0.084 0.016 0.068 –
Households greater than 200K 0.173 0.04 0.133 –
30

Private Capital Accounts 0.088 0.033 0.055 –

Real Estate, Personal and Repair Services, and Retail Trade are the industries that use the most water per unit output. The
accounting multipliers for these industries are 0.093 for Real Estate, 0.014 for Personal and Repair Services, and 0.045 for Retail
Trade, respectively.
Next I focused on the largest industries by employment in SEZ 386. This adds the entertainment and recreation sector – which
also has a large technical coefficient for water – plus Schools and Libraries, Wholesale Trade, Light Industry, and Medical industries.
Of these industries, Schools and Libraries, and Light Industry have the smallest accounting multiplier at 0.004, and Wholesale Trade
and Medical have the largest accounting multipliers of 0.029 and 0.028, respectively.
In regards to the decomposed elements of the multipliers for the industries, the closed-loop effects amount to a 3.7% increase
in production in Professional and Technical Services through the feedback, as the impact of the unit expansion in the water
commodity on the Professional and Technical Services industry ripples through the economy. The net transfer effects – how an
injection into the activities/commodities accounts affects those same accounts – generate a 1.1% increase in production in Professional
and Technical Services. For the other industries, the closed-loop effects are substantial, and make up the majority of the accounting
multiplier. This implies that the extra income generated by an expansion of the water commodity is used in such a way that it results,
through the closed-loop, in extra demand on production activities. This is in contrast to Government Industry, where the net transfer
effects account for almost all its multiplier effects. This means that the extra income generated in the Government Industry sector does
not ripple through the entire economy, but remains within the production activities.
I next examined the accounting multipliers for the capital account, factors of production accounts, and household accounts.
Labor has one of the largest accounting multipliers overall at 0.892, second only to Government Industry. This implies that a unit
expansion of the water commodity generates an 89.2 percent increase in labor income from the water commodity. The two capital
31

sectors in the factors of production accounts have accounting multipliers of 0.032 and 0.240, implying that there is some increase in
income from capital when the water commodity sector expands.
In regards to households, the household income block of 40K-50K has the smallest output? multiplier of 0.0058, and the other
household income block multipliers range from a low of 0.044 for households with an annual income of 15K-30K to a high of 0.119
for households with an annual income of 50K-70K. In other words, household income increases by a slight amount for a unit
expansion in the water commodity, with the greatest impacts seen in the wealthier income blocks.
Lastly, I looked at the elements of the decomposition for the factors of production accounts and household accounts. Regarding
the factors of production, I found that the labor income element of the water commodity output multiplier was mostly due to open-
loop effects, or spillovers, whereas the capital (proprietary income) was mostly comprised of the closed-loop effects. The extra capital
income ripples through the economy and back, while the extra labor income generated affects the other accounts in such a way that
those effects do not loop back around and generate more demand for water, rather, they generate more demand for other commodities.
For the households, they all benefit from the open-loop effects; the spillovers, of a unit increase in the water commodity, though the
closed-loop effects, while small, are not negligible.

VII. Analysis of a Water supply Disruption

This study presents two types of scenarios regarding water supply disruption – an across-the-board rationing where all sectors’
water inputs are hit equally and the CSMLP model that cuts the overall water supply and then re-apportions it to producers and
institutions in order to minimize employment loss. For the first set of scenarios, I ran three simulations, with the water supply cut by
10%, 25%, and 50%. This was to determine if the impacts are linear with the level of impact. For the CSMLP model, I only ran one
scenario, where the overall water supply was cut by 25%.

32

A. Simulation Scenario – Across-the-Board Rationing

The results by industry sector for the first of the two scenarios – across-the-board rationing – for labor income and total final
demand, respectively, are presented in the second, third, and fourth columns of Tables 5 and 6. The impacts are smaller than expected.
However, upon further consideration and comparison of my results with other similar studies, I concluded that these results are small
because they represent the impacts in a single moment in time immediately after the water supply is cut rather than the effects felt a
period of time after the supply was cut (24 hours or more for example). This is equivalent to the first scenario examined in Rose et al.
(2011) that evaluated, using a CGE model, the 0-hour impact, with no resilience adjustments, of an equivalent 22% reduction in the
water supply to Los Angeles County as a whole.
The scenario results are similar in scale as well. The impacts to labor income, GDP, and industry production, in percentage
terms, are linear with the percent reduction in the water supply. Total labor income decreased by 0.035, 0.088, and 0.176 percent for
the 10, 25, and 50% reduction cases respectively. Total final demand decreased by 0.0161, 0.0402, and 0.0804 percent for the three
cases respectively. Concerning labor income, the Government Industry suffered the greatest losses at 0.364, 0.91, and 1.821 percent
for the three cases, respectively. After Government Industry, the Metals, Minerals, and Processing and Construction sectors suffered
the greatest losses in labor income. In regards to final demand, the Hospitals and Nursing Homes sectors suffered the greatest loss in
final demand, at 0.0132, 0.0330, and 0.660 for Hospitals and 0.0130, 0.0325, and 0.0651 for Nursing Homes. In absolute terms, the
losses of labor income are $9.68 million, $24.2 million, and $48.9 million for the three scenarios and total final demand lost $29.1
million, $72.75 million, and $145.5 million respectively. While these losses are, in absolute terms, large and significant, when
compared to the overall size of the economy of SEZ 386, they are much less so.

33

Table 5. Percent Change in Labor Income

Base Values
a
10% Reduction 25% Reduction 50% Reduction
Agriculture - Annual 0.863 -0.00003 -0.00008 -0.00017
Agriculture - Perennial 2.284 -0.00005 -0.00013 -0.00027
Agriculture - Other 1.197 -0.00009 -0.00022 -0.00044
Metals, Minerals, Processing 35.634 -0.00600 -0.01500 -0.02900
Electric Power 189.130 -0.00046 -0.00100 -0.00200
Professional and Technical
Services
4953.738 -0.00100 -0.00300 -0.00500
Construction 501.320 -0.00300 -0.00700 -0.01400
Food, Drugs, Chemicals 351.264 -0.00006 -0.00015 -0.00030
Light Industry 1233.945 -0.00008 -0.00019 -0.00038
Heavy Industry 112.633 -0.00086 -0.00200 -0.00400
High Tech Industry 231.119 -0.00026 -0.00065 -0.00100
Wholesale Trade 2449.714 -0.00060 -0.00100 -0.00300
Retail Trade 1450.154 -0.00018 -0.00046 -0.00091
Motion Picture and Video 1059.597 -0.00002 -0.00004 -0.00008
Entertainment and Recreation 2740.847 -0.00021 -0.00052 -0.00100
Tele-communications 210.125 -0.00032 -0.00081 -0.00200
Banking and Finance 1191.764 -0.00200 -0.00500 -0.00900
Real Estate 784.530 -0.00018 -0.00046 -0.00092
Schools and Libraries 3130.614 0.00000 -0.00001 -0.00001
Universities and Colleges 404.414 -0.00001 -0.00001 -0.00003
Medical 1009.220 0.00000 0.00000 0.00000
34

Hospitals 647.705 0.00000 0.00000 0.00000
Nursing Homes and Services 341.987 0.00000 0.00000 0.00000
Personal and Repair Services 840.171 -0.00041 -0.00100 -0.00200
Community Food, Housing, Relief
Services
84.707 0.00000 0.00000 0.00000
Parking Services 180.620 -0.00022 -0.00056 -0.00100
Religious Services and Activities 797.213 -0.00004 -0.00011 -0.00022
Government Industry 2623.999 -0.36400 -0.91000 -1.82100
Total 27560.506 -0.03500 -0.08800 -0.17600
a
Base values are in millions of dollars.

Table 6. Percent Change in Final Demand

Base Values
a
10% Reduction 25% Reduction 50% Reduction
Agriculture - Annual 4.29 -0.0051 -0.0127 -0.0255
Agriculture - Perennial 7.94 -0.0024 -0.0060 -0.0120
Agriculture - Other 8.01 -0.0046 -0.0116 -0.0232
Metals, Minerals, Processing 361.83 -0.0002 -0.0005 -0.0010
Electric Power 732.57 -0.0057 -0.0142 -0.0284
Professional and Technical
Services
16,293.38 -0.0013 -0.0033 -0.0067
Construction 4,181.66 -0.0003 -0.0007 -0.0014
Food, Drugs, Chemicals 5,377.54 -0.0028 -0.0070 -0.0140
Light Industry 7,973.79 -0.0004 -0.0010 -0.0021
Heavy Industry 820.28 -0.0003 -0.0007 -0.0013
35

High Tech Industry 1,566.79 -0.0010 -0.0025 -0.0050
Wholesale Trade 13,276.33 -0.0022 -0.0056 -0.0112
Retail Trade 6,991.10 -0.0091 -0.0227 -0.0453
Motion Picture and Video 7,299.02 -0.0002 -0.0005 -0.0009
Entertainment and Recreation 14,049.35 -0.0029 -0.0074 -0.0147
Tele-communications 1,871.72 -0.0073 -0.0182 -0.0364
Banking and Finance 3,404.63 -0.0088 -0.0221 -0.0441
Real Estate 19,659.57 -0.0054 -0.0135 -0.0270
Schools and Libraries 7,005.20 -0.0010 -0.0025 -0.0049
Universities and Colleges 1,654.95 -0.0072 -0.0180 -0.0359
Medical 3,827.18 -0.0104 -0.0261 -0.0522
Hospitals 3,825.25 -0.0132 -0.0330 -0.0660
Nursing Homes and Services 1,087.27 -0.0130 -0.0325 -0.0651
Personal and Repair Services 3,729.72 -0.0045 -0.0111 -0.0223
Community Food, Housing, Relief
Services
386.97 -0.0074 -0.0186 -0.0371
Parking Services 759.18 -0.0109 -0.0273 -0.0545
Religious Services and Activities 4,349.80 -0.0053 -0.0134 -0.0267
Government Industry 4,255.39 -0.0076 -0.0189 -0.0378
Total 180,917.88 -0.0161 -0.0402 -0.0804
a
Base values are in millions of dollars.

36

B. CSMLP Optimum Employment Scenario (cut total water supply by 25%)

The results of a second scenario, using the CSMLP model, were much more interesting. For this second scenario, I took
households as exogenous. The model reallocates inputs, such as water, factors, and production activities so as to minimize
employment loss, and so the results are quite different from the across-the-board rationing scenario presented in the previous section.
Labor income losses and total final demand losses are several degrees of magnitude larger in the CSMLP model than the previous
scenarios, and total a 31% loss for labor income and 40% for total final demand. These values translate to, in absolute terms, $6.04
billion in total labor income losses and $61.5 billion in total final demand losses. However, the model is fixed in its demand
composition. In other words, there is no substitution between sectors to shift production away from water-intensive sectors or towards
labor-intensive sectors. Thus, the economy is limited not by the number of commodities or resources, but by whichever resource is
exhausted first (Chenery and Clark, 1959). In this case, it is water that is exhausted, since I cut the supply by 25%, resulting in a near-
uniform 25% cut to all sectors’ labor income and final demand. The total final demand results of this second scenario are presented in
the second column of Table 8.
In third scenario, I remove the fixed proportions of final demand in order to allow substitution possibilities between sectors
when faced with a water supply cut. To do so, I first determined which sectors had the greatest direct and indirect effects from a unit
increase in the water commodity, in other words, determining the most water-intensive sectors. I determined these sectors to be
Schools and Libraries, Universities and Colleges, Professional and Technical Services, Medical, Hospitals, Personal and Repair
Services, and Real Estate. Next, I exogenously change the composition of final demand in each scenario by the amounts shown in
Table 7. As expected, the losses were lessened greatly when substituting away from water-intensive sectors is allowed.

37

Table 7. Simulation Set-Up for Changes in Demand Composition

Overall Water
Supply Cut
Exogenous Reduction in
Final Demand of Water-
Intensive Sectors
Base 0% 0%
Fixed Demand Proportions 25% 0%
Low 25% 5%
Medium 25% 10%
High 25% 25%

When the composition of final demand is changed, substituting away from water-intensive sectors, the sectors with the
greatest losses in total final demand are the Schools and Libraries, Motion Picture and Video, Heavy Industry, Light Industry, Metals,
Minerals, and Processing, and Construction sectors. Some sectors see an increase in final demand when water is shocked, such as
Hospitals, Medical, and Nursing Homes. Water demand also increases slightly, possibly because of the fact that water is now a scarce
resource and so will be in higher demand than before the cut. Overall, the economy is responding exactly as the theory would suggest
– the demand for water-intensive commodities decreases much more than the demand for less-water intensive commodities. For
example, Schools and Libraries see a drop in final demand of 33.6% in the low reduction simulation, whereas a less water-intensive
sector, such as Community Food, Housing, and Relief Services, sees a drop in final demand of 8.4% for the same case. This can be
seen in the demand shares in percentage terms. Furthermore, contrary to expectations, the greater the exogenous reduction in the final
demand for water-intensive commodities, the less of a hit final demand takes, both overall and by sector. This is because, as the water
is cut and the economy shifts away from water-intensive sectors, it frees up the water that would normally go into these sectors to be
used in the other sectors. This allows for more production and lessens the overall impact. Though the changes across simulations are
small, the demand shares of water-intensive sectors do go down, while shares in less water-intensive sectors, as well as imports,
increases. In absolute terms, final demand losses when demand composition is allowed to change are $30.4 billion, $24.7 billion, and
38

37.3 billion for the three simulations respectively. The total final demand shares for the water-intensive sectors aggregate, water
sector, non-water-intensive sectors aggregate, and total imports are presented in Table 8, and percent change in final demand for each
commodity is presented in Table 9.

Table 8. Final Demand Shares by Percent
Base Shares Fixed Proportions Low Medium High
Non-Water-Intensive Sectors 67.98396 65.38285 64.95017 65.21481 66.04139
Water Commodity 0.08392 0.11182 0.11151 0.10609 0.08947
Water-Intensive Sectors 12.46451 12.81025 12.76497 12.13537 10.20632
Imports - Total 23.86209 25.56262 25.79621 25.96478 26.47404
Total 100.000 100.000 100.000 100.000 100.000

Table 9. Percent Change in Final Demand

Base Values
a
Fixed Proportions Low Medium High
Agriculture - Annual 3.61 -39.12 -17.23 -12.84 3.35
Agriculture - Perennial 7.40 -43.55 -25.45 -21.44 -6.62
Agriculture - Other 6.84 -40.62 -18.51 -14.20 1.69
Metals, Minerals, Processing 359.68 -46.61 -30.27 -26.48 -12.42
Electric Power 601.75 -38.86 -15.37 -10.92 5.50
Professional and Technical Services 15,696.77 -44.58 -27.79 -23.90 -9.50
Water 130.91 -19.26 7.01 6.42 4.05
Construction 4,181.66 -44.24 -29.77 -25.95 -11.81
Food, Drugs, Chemicals 4,907.29 -43.17 -23.89 -19.81 -4.71
Light Industry 7,872.45 -46.33 -29.79 -25.96 -11.79
39

Heavy Industry 814.84 -46.08 -30.06 -26.26 -12.19
High Tech Industry 1,522.14 -45.27 -28.48 -24.62 -10.35
Wholesale Trade 12,354.72 -43.34 -25.15 -21.13 -6.27
Retail Trade 4,963.37 -31.67 -6.35 -6.71 -8.25
Motion Picture and Video 7,254.89 -46.36 -30.22 -26.41 -12.29
Entertainment and Recreation 12,730.65 -43.37 -23.35 -19.26 -4.11
Tele-communications 1,459.63 -35.15 -10.40 -5.73 11.47
Banking and Finance 2,442.28 -31.80 -2.36 2.68 21.23
Real Estate 16,268.67 -39.30 -15.76 -11.33 5.02
Schools and Libraries 6,854.83 -46.67 -33.60 -34.47 -37.56
Universities and Colleges 1,271.66 -35.29 -13.56 -13.86 -15.17
Medical 2,531.22 -27.93 0.79 0.34 -1.51
Hospitals 2,171.12 -18.30 23.54 29.78 52.70
Nursing Homes and Services 618.31 -15.38 16.74 16.21 14.02
Personal and Repair Services 3,203.61 -40.95 -23.05 -23.25 -24.19
Community Food, Housing, Relief Services 295.06 -35.39 -8.44 -3.67 13.89
Parking Services 496.55 -27.06 7.20 12.66 32.73
Religious Services and Activities 3,605.44 -39.51 -16.06 -11.62 4.75
Government Industry 4,137.75 -23.54 -24.92 -21.32 -8.20
Imports – Rest of World 3,193.27 -28.48 0.47 5.57 24.31
Imports – Rest of United States 34,028.45 -35.70 -14.19 -9.71 6.79
Total 155,986.85 -39.40 -19.46 -15.82 -2.39
a
Base values are in millions of dollars.

40

I next looked at the changes in economic aggregates, such as labor income, GDP at factor cost, and total production. The drop
in labor income reduces from 31% with fixed demand proportions to 23%, 21%, and 15% with a low, medium, and high exogenous
reduction in final demand for water-intensive commodities, respectively. GDP at factor cost and total production see similar
reductions in losses. The results are presented in Table 10.

Table 10. Percent Changes in Economic Aggregates

Base Value
a

Fixed
Proportions
Low Medium High
Labor Income 27,560.51 -31.343 -23.228 -21.329 -14.615
GDP at Factor Cost 51,315.35 -31.16 -22.92 -20.70 -12.82
Total Final Demand 155,986.85 -39.40 -19.46 -15.82 -2.39
Total Production 8,7294.48 -31.10 -22.82 -20.49 -12.25
a
Base values are in millions of dollars.

VIII. Conclusion

This thesis examines SAM multiplier analysis and decomposition, as well as a linear programming model and method to
analyze the economic impacts of varying levels of a water shortage, and applies it to a small region of Los Angeles County. The
accounting multipliers reveal the effects of a unit increase in income, and their decomposition provides insight into the structure of the
economy and how those effects propagate throughout the different economic accounts.
I first detailed the multiplier decomposition derivation of Pyatt and Round (1979). Then I specified the CSMLP model to
examine impacts of a water supply shortage. I then applied these methods to the SAM for SEZ 386 in the study year of 2015. Firstly,
the multiplier analysis shows that a single unit of extra income can increase any sector’s output by at least three-fold. Secondly, the
first set of simulations show that, while the losses due to a proportional water supply shortage across sectors to labor income and final
41

demand are significant in absolute terms, when compared to the economy as a whole the impacts are small. Thirdly, the CSMLP
simulation shows the effects on labor income and final demand both when demand proportions are fixed and when the economy is
allowed to substitute across sectors. The results show that demand matters. When substitution among final demand elements is
allowed, the results vary even more greatly from sector to sector, shifting even more away from water-intensive sectors, and the losses
in economic aggregates, such as labor income, GDP at factor cost, total final demand, and total production were reduced.
A couple of caveats to this analysis must be given, however. The first is that this is a SAM analysis based on a multiplier
model, and, as such, does not easily allow for the substitutability of inputs and imports. The model does not include income
elasticities, substitution elasticities or a price system, which could change the results. In the face of a resource scarcity, the prices of
that resource would be raised, which would enable an endogenous change in demand composition, rather than setting an exogenous
one – changing the demand composition by hand. Also, this analysis does not include any resilience measures, which would lessen the
impacts even further. Both of these can be addressed using a different SAM-based model. A CGE model, for instance, can include
different resilience measures, and has a price system that can endogenize changes in demand composition. In sum, this paper is a case
study applying SAM multiplier analysis and decomposition of the impacts of a utility lifeline disruption.

42

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Abstract (if available)

Abstract Utilities are the lifelines of modern cities such as Los Angeles. Recently, there has been much literature on modeling the impact to cities of a disruption in such services using various economic modeling and analysis methods. One such method to model and measure the flow of goods and services in the economy is the Social Accounting Matrix (SAM). This paper uses SAM multiplier decomposition to analyze the effects of a disruption to one such utility—water—to a sub‐region of Los Angeles County. First explaining the theory and methods behind multiplier decomposition, it then analyzes the effects of disrupting water service to an area within Los Angeles County, through two different methods—an across‐the‐board rationing scheme where all sectors are hit equally and a Constrained SAM Multiplier Linear Programming (CSMLP) approach that optimizes economic activity in the face of a disruption to water service. The thesis finds that it is demand that drives how severe the losses to production, labor income, and other factors are, with losses falling from 31% when demand is fixed, to 12% when demand can shift away from water‐intensive goods and services.

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Asset Metadata

Creator Anderson, Lillian (author)

Core Title A social accounting matrix multiplier analysis of a water supply shortage in the Los Angeles County water service area SEZ 386

School College of Letters, Arts and Sciences

Degree Master of Arts

Degree Program Economic Developmental Programming

Publication Date 04/27/2018

Defense Date 04/27/2018

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

Tag impact analysis,Los Angeles County,multiplier decomposition,OAI-PMH Harvest,social accounting matrix multipliers,water service

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Advisor Nugent, Jeffrey (committee chair), Dekle, Robert (committee member), Robinson, Sherman (committee member), Rose, Adam (committee member)

Creator Email lcanders@usc.edu,lcanders93@gmail.com

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