Distributional and Poverty Impact Analysis within a General Equilibrium
Framework
B. Essama-Nssah
The World BankDEC Course on Poverty and Inequality AnalysisModule 7: Evaluating the Distributional and Poverty Impacts of Economy-Wide PoliciesApril 28, 2009
2
Introduction Impact Analysis
An assessment of variations in individual and social welfare attributable to an exogenous shock or implementation of a policy.
Attribution based on a comparison of the policy state and the counterfactual, ceteris paribus.
3
Introduction Economy-Wide Shocks and Policies
Affect potentially the whole population Are bound to have both macroeconomic,
structural and distributional effects that work through a number of flow-of-fund variables and individual good or factor markets.
Need for an analytical framework that accounts for interdependence between stabilization, structural and distributional issues.
General equilibrium analysis offers such a framework.
4
Introduction Approaches
Standard Representative Household (RH) Impact on functional distribution of income, mean
welfare within a few representative socioeconomic groups, and between-group inequality, but not on poverty.
Extended Representative Household Extends the RH approach by modeling the size
distribution within group, hence allowing poverty analysis in addition to what RH allows. e.g. Lognormal (Dervis, de Melo and Robinson 1982) or
Beta (Decaluwé, Savard and Thorbecke 2005) or Parameterized Lorenz (Essama-Nssah 2005)
5
Introduction Approaches, continued
CGE-Micro-Simulation Use unit record data from household survey to
build a household model of expenditure, or income generation to allow a rich analysis of poverty and inequality.
Focus of Presentation A Stylized ERH Framework
Positive component: a two-sector model of an open economy
Structure Specification
6
Introduction
Stylized ERH, continued Normative component: the Lorenz model of
income distribution Structure Parameterization Recovering Inequality and Poverty Measures
Numerical Implementation Impact of Budgetary Policy
Policy Options Outcomes
7
A Two-Sector Model of an Open Economy
Structure A logical representation of a
socioeconomic system wherein the behavior of all participants is compatible.
Organized around the standard Walrasian template.
8
Structure, continued Two categories of agents: producers and
consumers, or firms and households. Supply and demand behavior: an observable
consequence of the optimization assumption. Market interaction: method of social
coordination by mutual adjustment among participants based on “quid pro quo” (Lindblom 2001).
Behavioral compatibility entails equilibrium on all markets.
9
Structure, continued
Comparative statics entails comparison of equilibrium states associated with changes in the socioeconomic environment.
Social desirability depends on chosen criterion Pareto efficiency focuses on how well the system
promotes individual objectives: efficiency implies no other situation is unanimously preferred by all participants.
Poverty-focused criterion: less poverty is preferred to more.
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Structure, continued Incentives configuration such that
amount of effective demand equals amount supplied.
Alternatively: No feasible change in individual behavior is
worthwhile. No desirable change in individual behavior is
feasible.
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Producers
Factor markets
Intermediate goods
ImportsExports
Factor services
Final goods
Circular Flow Chart for an Open Economy
Rest ofthe world
Households
Factor markets
Product markets
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Structure of a SAM for a Basic Model of an Open Economy
Activity Commodity Househol d Rest of
Wor l d Total
Activity Domest ic Sal es
Expor t s Tot al Sal es
Commodity Int er mediat e Consumpt ion
Househol d Consumpt ion
Tot al Absor pt ion
Househol d Payment s t o Fact or s of P r oduct ion
Bal ance of Tr ade
Tot al Househol d
Income
Rest of Wor l d
Impor t s Tot al Ear nings of Rest of t he
Wor l d Total Tot al
Fact or Payment s
Tot al Suppl y of
Consumpt ion Goods
Tot al Househol d
Expendit ur e
Tot al Expendit ur e by Rest of
Wor l d
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Structure, continued Social Accounting Matrix (SAM)
An accounting framework that reflects the circular flow of economic activity.
A square matrix: dimension based on the number of sectors and agents considered.
Each entry represents a payment to a row-account by a column-account.
Consistency implies that row total must equal corresponding column total.
Also, if all but one accounts balance, the last one must balance as well (Walras’ law).
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Specification Based on Devarajan, Lewis and
Robinson (1990) Two sectors of production:
Export good not sold domestically. Home good used for both intermediate and final
consumption Imported and domestic intermediate goods
enter the production process. Production process in each sector
represented by a Cobb-Douglas function
.,;1; deiLKAX likiiiiiliki
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Specification, continued The demand for labor is derived from first
order conditions for profit maximization
Similarly for capital [capital is mobile in the long run]
.,;)(
deiw
XPVAL iilii
.,;)(
deir
XPVAK iiki
i
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Specification, continued The net price in sector i is given by
a2i is the amount of aggregate intermediate good (Q2) per unit of output in sector i.
.,,22 deiPQaPXPVA iii
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Specification, continued Producer price of exports
Two aggregate commodities for final (j=1) and intermediate consumption (j=2)
eee tRPX )1(
2,1;)1(1
jDMBQ j
jj
jjjjjj
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Specification, continued Import demand functions derived from cost
minimization.
Demand for domestic components of aggregate goods (implication of cost minimization).
2,1;)1( )1(
1)1()1(1 jQPMPDPMBM s
jjjjjjjjjjj
jjjjj
2,1;)1( )1(
1)1()1(1 jQPDPDPMBD s
jjjjjjjjjjj
jjjjj
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Specification, continued
Domestic price of imports inclusive of tariffs
Price of domestic sales includes a sales tax
2,1;)1( jtmRPM mjjj
2,1);1( jtxPXPD ddj
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Specification, continued Producer price of the domestic good
Price of composite goods
2,1;)1(2
2
1
jtxX
DPD
PXd
jjj
e
2,1);( jMPMDPDPQ jjjjj
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Specification, continued Rural household represents 60
percent of the population, and owns a fraction RL of labor and a fraction RK of capital (to be determined by data in SAM).
Urban household represents 40 percent of the population, and owns a fraction (1- RK ) of capital and a fraction (1- RL) of labor.
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Specification, continued Household income
Household demand for final good (no savings)
Government fiscal revenue
2
1
)(j
ddjmjjG XtxMRtmY
urhRSYrKSwLSY fhfGhghkhlh ,;)()(
h
dh
dhdh QQurh
PQ
YQ 11
11 ;,;
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Specification, continued
Total demand for intermediate good
Equilibrium in the home good market
Material balance for composite goods
.,;22 deiXaQi
iid
2
1
2,1;j
jd jDX
2,1; jQQ dj
sj
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Specification, continued Equilibrium condition for each factor market
under full employment of given amounts of capital and labor.
i i
ii deiKKSLLS .,;;
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Specification, continued Government budget balance
Trade balance
urhYY Gh
Ghg ,;
jj
mjfee MSX
2
1
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The Lorenz Model of Income Distribution
Structure A flexible statistical model of the
distribution of some welfare indicator, x, among the population.
The Lorenz curve maps the cumulative proportion of the population (horizontal axis) against the cumulative share of welfare (vertical axis), where individuals have been ranked in ascending order of x.
x dtttf
pLxFp0
)()()(
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Structure, continued
Alternative Expression based on : dp=f(x)dx
First-order derivative
dq
qxpL
p
0
)()(
)(
)(px
pL
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Structure, continued
Second-order derivative
Parameterization Based on General Quadratic (Datt 1992,
1998) Lorenz
)(
111)(
xfdx
dpdp
dxpL
2
122
2 )(2
1)( enpmpeppL
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Quadratic model, continued
First Derivative
Second derivative
)(4
2
2)(
22
2
enpmp
nmppL
8
)()(
2
3222
enpmprpL
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Recovering Inequality and Poverty Measures From a parameterized Lorenz model and the
mean of x, we can recover the following: X: based on the mean and the first order derivative
of the Lorenz function. Density function of x, f(x): based on the mean and
the second order derivative of the Lorenz function.
This is all we need to compute all inequality and poverty measures.
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Numerical Implementation Data
Base Year SAM
Export Domestic Final Intermediate Labor Capital Rural Urban World Total
Export 30.00 30.00 Domestic 73.00 2.00 75.00 Final 40.00 60.00 100.00 Intermediate 5.00 5.00 Labor 20.00 30.00 50.00 Capital 5.00 45.00 50.00 Rural Household 35.00 5.00 40.00 Urban Household 15.00 45.00 60.00 World 27.00 3.00 30.00 Total 30.00 75.00 100.00 5.00 50.00 50.00 40.00 60.00 30.00
Source: Adapted from Devarajan, Lewis and Robinson (1990)
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Data, continued
Calibrated Parameters
Calibrated Parameters for the Two-Sector Model L K A M D B Export 0.80 0.20 1.98 Domestic 0.40 0.60 1.98 Final 0.38 0.62 1.89 Intermediate 0.69 0.31 1.92
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Data, continued A is tfp (total factor productivity) parameter in
the Cobb-Douglas production function ’s are factor shares (exponents in the
production function). ’s are shares in the Armington aggregation
function and B is a scale factor. Distribution of factor income in base year
SAM: RL=0.70, UL=0.30, RK=0.10, and UK=0.90
Distribution of government transfers: RG=0.60 and UG=0.40
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Data, continued Distribution of foreign transfers: RF=0.20 and
UF=0.80 Base Year Income Distribution
Size Distribution of Income within the Two Socioeconomic Groups
Group Mean Poorest
Decile
2nd 3rd 4th 5th 6th 7th 8th 9th 10th
National 1.00 0.01 0.03 0.04 0.06 0.07 0.09 0.11 0.14 0.18 0.28
Rural 0.66 0.02 0.03 0.05 0.07 0.08 0.10 0.12 0.14 0.17 0.21
Urban 1.50 0.00 0.04 0.06 0.07 0.09 0.10 0.12 0.14 0.16 0.23
Source: Author’s calculations
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Data, continued
Baseline Inequality (Extended Gini)
Focus National Rural Urban 1 0.00 0.00 0.00 2 0.41 0.32 0.32 3 0.57 0.47 0.47 4 0.65 0.56 0.57 5 0.71 0.62 0.64 6 0.74 0.66 0.69
Source: Author’s Calculations
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Data, continued Parameters underlying the General Quadratic
Lorenz ModelParameterization of the Lorenz Model
Parameter National Rural Urban
1 1.52 2.16 1.46
2 -0.89 -1.42 -1.83
3 0.02 0.08 -0.15
e -1.65 -1.82 -0.48
m -5.29 -6.60 -2.51
n 2.86 4.84 2.37
r 8.11 10.50 2.82
Source: Author’s calculations
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Policy Options Case 1: Reference
Tax on domestic sales: 15.4 percent Tariff on imports of final and intermediate
goods: 12.5 percent Case 2: Reform Option A
Increase domestic sales tax by 5% (from reference)
Lower tariff on final import by 17.6% Increase tariff on intermediate by 46.4 %
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Policy Options, continued
Case 3: Reform Option B Lower sales tax by 5% Increase tariff on final goods by
18.4% Lower tariff on intermediate by 44%
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Policy Options, continued
Tax Rates (percentage)
Case Domestic Good Final Imports Intermediate Imports
1 15.4 12.50 12.50
2 16.17 10.3 18.30
3 14.63 14.80 7.00
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Social Impact of Budgetary Policy Base Case 1 Case 2 Case 3
Exports 30.0 100.0 102.2 97.7 Domestic Good 75.0 100.0 99.3 100.8 Final Imports 27.0 100.0 102.3 97.6 Intermediate Imports 3.0 100.0 101.1 98.8 Total Consumption 100.0 100.0 100.0 100.0 Rural Consumption 40.0 106.7 107.1 106.3 Urban consumption 60.0 95.6 95.3 95.8 Total Poverty Incidence 59.2 97.5 97.3 97.6 Rural Poverty Incidence 78.3 95.2 94.9 95.5 Urban Poverty Incidence 30.5 106.4 106.8 106.0 Overall Poverty Gap 29.7 95.8 95.6 96.1 Rural Poverty Gap 38.7 93.5 93.1 93.9 Urban Poverty Gap 16.3 104.1 104.4 103.9
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Outcomes, continued
Case 1: Pattern of production and imports unchanged from
the base case where there is no government intervention.
Optimal configuration of taxes to the extent that they do not distort private production decisions.
The redistributive policy associated transfers to households causes an increase in rural consumption and a decrease in urban consumption.
As a consequence overall poverty incidence decline by about 2.5 percent.
Rural poverty decreases by 5 percent while urban poverty increase by more than 6 percent.
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Outcomes, continued Case 2:
Production of exports increases, that of the domestic good declines. Both categories of imports increase.
Pattern of change in poverty incidence is similar to the reference case, but reduction in rural poverty and increase in rural poverty are a bit higher than in the reference case.
Case 3: Production of exports and all imports fall while
production of domestic good increases. Change in poverty similar to previous cases.
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Conclusion Evaluating the social impact of economy-wide policies
requires a social policy model framed within the logic of general equilibrium analysis.
Such a model has two basic components A structural representation of individual behavior and social
interaction based on the principles of optimization and quid pro quo.
A social evaluation function reflecting a chosen set of value judgments (e.g. efficiency and fairness).
A stylized analysis of the social impact of budgetary policy revealed the following:
The outcome hinges crucially on the underlying mechanisms allocating burdens and advantages among individuals.
Aggregate welfare effects may be negligible while structural and distributional impacts are significant.
the latter drive the political economy of policy-making.
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References
Datt, Gaurav. 1998. Computational Tools for Poverty Measurement and Analysis. Washington D.C.: International Food Policy Research Institute (IFPRI) Discussion Paper No.50 (Food Consumption and Nutrition Division).
Datt, Gaurav. 1992. Computational Tools for Poverty Measurement and Analysis. Washington D.C.: The World Bank (mimeo)
De Melo Jaime and Robinson Sherman. 1989. Product Differentiation and the Treatment of Foreign Trade in Computable General Equilibrium Models of Small Economies. Journal of International Economics, Vol. 27:47-67.
Devarajan, Shantayanan, Jeffrey D. Lewis, and Sherman Robinson. 1990. Policy Lessons From Two-sector Models. Journal of Policy Modeling 12 (4): 625-657.
Dervis, Kemal, de Melo, Jaime, and Robinson, Sherman. 1982. General Equilkibrium Models for Development Policy. Washington, D.C.: the World Bank.
Decaluwé, B., Savard. L. and Thorbecke, E. 2005. General Equilibrium Approach for Poverty Analysis: With an Application to Cameroon. African Development Review, Vol. 17, No.2: 213-243.
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Dinwiddy, C.L. and F.J. Teal. 1988. The Two-Sector General Equilibrium Model: A new Approach. Oxford: Philip Allan.
Essama-Nssah, B. 2006. Macroeconomic Shocks and Policies. In Aline Couduel and Stefano Paternostro (eds) Analyzing the Distributional Impact of Reforms. Washington, D.C.: The World Bank.
Essama-Nssah, B. 2005. Simulating the Poverty Impact of Macroeconomic Shocks and Policies. World Bank Research Working Paper No. 3788. Washington, D.C.: The World Bank.
Lindblom Charles E. 2001. The Market System: What Is It, How It Works and What to Make of It. New Haven: Yale University Press.
Varian Hal R. 1984. Microeconomic Analysis (Second Edition) New York: Norton & Company.
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