Figures and tables in Linking CGE and microsimulation models: A comparison of different approaches

Abstract

In the literature that studies income inequality and poverty, a recent development has been the development of models that link together a macroeconomic model (usually a Computable General Equilibrium (CGE) model) and a microsimulation model. Linking the two types of model allows the modeller to take into account full agents’ heterogeneity, whilst at the same time considering the general equilibrium effects of a proposed policy reform. In this paper, I first review in detail three approaches to building linked CGE-microsimulation models: one in accordance with the fully integrated approach, and two following the layered approach (the so-called Top-Down and Top-Down/Bottom-Up approaches). The principal goal of the paper is to present a considered evaluation of the merits and demerits of these alternative methods currently used to link CGE and microsimulation models. To do so I use all three approaches to model the macro- and micro-economic impacts of a policy shock to an archetypical economy (constructed using fictitious data), and compare the results. This analysis highlights the importance of (i) consistency between the underlying macro- and micro-data; and (ii) the precise mechanisms by which feedback effects are passed between the macro and micro models. I develop this latter point further by detailed analysis of the TD/BU approach outlined by Savard (2003), leading to a proposed refinement in the way that feedback effects from the micro level of analysis are incorporated back into the CGE model.

This article contains 2 figures and 21 tables.

Figures

**Figure 2.** The Top-Down/Bottom-Up approach.

Tables

Table 1. Description of the subscripts for the microsimulation model.

m	Households	m = 1, 2, …, 24
i	Individuals belonging to household m	i = 1, …, NC_m	(NC_m: number of components of household m)
q	Goods	q = 1,2

Table 2. Direct income tax rates.

Household Income	Tax rate
Up to 10,000	0%
Up to 15,000	15%
Up to 26,000	24%
Up to 70,000	32%
Over 70,000	39%

Table 3. Heckman selection model, two-step estimates.

	Coefficient	Std. Error	z	P>\|z\|
constant	7.0321	0.3145	22.36	0.000
ln(age)	0.6978	0.0833	8.38	0.000
sex	−0.4662	0.1018	−4.58	0.000
qualification	0.3966	0.0772	5.14	0.000
education	0.5250	0.0872	6.02	0.000
Mills ratio	0.2160	0.1473	1.47	0.143
Selection
ln(age)	0.3386	0.0807	4.19	0.000
sex	−1.5492	0.2803	−5.53	0.000
qualification	1.0204	0.2729	3.74	0.000
children under 6	0.1682	0.2368	0.71	0.478
region	−0.7515	0.2980	−2.52	0.012
rho	0.7628
sigma	0.2832

Notes: Dependent variable: logarithm of wage.

Table 4. Binary logit model of labour status choice.

	Coefficient	Std. Error	z	P>\|z\|
ln(real wage)	0.1972	0.0465	4.25	0.000
sex	−1.8948	0.4078	−4.65	0.000
qualification	1.4408	0.4257	3.38	0.001
region	−0.7185	0.3295	−2.18	0.029
children under 6	0.2691	0.2973	0.91	0.365
education	−0.7633	0.6717	−1.14	0.256
Mean dependent var	0.6647	S.D. dependent var		0.4735
S.E. of regression	0.3767	Akaike info criterion		0.9015
Sum squared resid	23.2688	Schwarz criterion		1.0122
Log likelihood	−70.6305	Hannan-Quinn criter.		0.9464
Avg. log likelihood	−0.4155

Notes: Dependent Variable: Activity Status.

Table 5. SAM of the economy.

	C₁	C₂	S₁	S₂	K	L	H	G	SI	RoW	Total
C₁			57.5	15.5			95.2	61.2	30.3	23.5	283.3
C₂			17.1	23.5			312.8	48.5	14.2	76.5	492.5
S₁	283.3										283.3
S₂		492.5									492.5
K			72.2	23.0				13.1			108.3
L			83.2	353.8				116.4			553.4
H					108.3	553.4		39.8			701.5
G			12.3	17.7			249.0				279.0
SI							44.5				44.5
*RoW*			41.0	59.0							100.0
*Total*	283.3	492.5	283.3	492.5	108.3	553.4	701.5	269.9	44.5	100.0

Notes: C_q: consumption of good q; S_q: production sector q; K: capital account; L: labour account; H: representative household account; G: public sector; SI: savings-investments account, RoW: Rest of the World account.

Table 6. Values of some parameters for the CGE model.

	Sector 1	Sector 2
Elasticity of substitution (EOS) in production function (aggregation of capital and labour)	0.7	0.5
Elasticity of substitution for Armington composite good	0.7	1.2
Elasticity of transformation for exports and domestic production delivered to the domestic market	−2.0	−3.0
Initial tariff rates on imports	0.3	0.3
Initial time endowment	656.7
Wage elasticity of labour supply (estimated from the household survey)	−0.18665

Table 7. Variables and parameters of the CGE model

Variables		Parameters
PK	Return to capital	ty	Income tax rate
PL	Wage rate	tm_q	Tariff rates on imports
P_q	Price of Armington composite good	ε_LS	Wage elasticity of labour supply
PD_q	Price of output	mps	Marginal propensity to save
PDD_q	Price of domestically produced good delivered to domestic market	αH_q	Cobb-Douglas power of commodity q in RH’s utility function
PWE_q	World price of exports (foreign currency)	αH_l	Cobb-Douglas power of leisure in RH’s utility function
PWM_q	World price of imports (foreign currency)	αCG_q	Cobb-Douglas power of commodity q in government utility function
PM_q	Price of imports (local currency)	αKG	Cobb-Douglas power of capital in government utility function
PE_q	Price of exports (local currency)	αLG	Cobb-Douglas power of labour in government utility function
ER	Exchange rate	io_qs	Technical coefficients
PC	Consumer price index	aF_q	Efficiency parameter production function
KS	Capital endowment (exogenous)	γF_q	Share parameter in production function
LS	Labour supply (endogenous)	σF_q	EOS in firm q’s production function
TS	Time endowment (exogenous)	aA_q	Efficiency parameter in Armington function
X_q	Domestic sales (Armington composite)	γA_q	Share parameter in Armington function
XD_q	Domestic production	σA_q	EOS in firm q’s Armington function
XDD_q	Domestically produced good delivered to domestic market	αI_q	Cobb-Douglas power of commodity q in Bank’s utility function
M_q	Imports	aT_q	Efficiency parameter in CET function
E_q	Exports	γT_q	Share parameter in CET function
K_q	Capital demand by firms	σT_q	Elasticity of transformation in CET function
L_q	Labour demand by firms
I_q	Investment good
C_q	Consumption demand by household
C_l	Demand for leisure
Y	Household’s income
S	Household’s savings
CBUD	Household’s consumption expenditure
TF	Public transfers to household
TAXREV	Tax revenues
CG_q	Consumption demand by government
KG	Capital demand by government
LG	Labour demand by government

Table 8. Equations of the CGE model

Description	Equations
Demand for consumption goods	$P_{q} \cdot C_{q} = α H_{q} \cdot C B U D, where q = 1, 2$
Leisure	$C_{I} = {[(1 - t y) \cdot P L]}^{- 1} \cdot \frac{α H_{I}}{(1 - α H_{I})} \cdot C B U D$
Labour supply	$L S = T S - C_{I}$
Savings	$S = m p s \cdot (1 - t y) \cdot Y$
Consumer price index	$P C = \prod_{q = 1}^{2} P_{q}^{α H_{q}}$
CES production function	$X D_{q} = a F_{q} \cdot {[γ F_{q} \cdot K_{q}^{\frac{(σ F_{q} - 1)}{σ F_{q}}} + (1 - γ F_{q}) \cdot L_{q}^{\frac{(σ F_{q} - 1)}{σ F_{q}}}]}^{\frac{σ F_{q}}{(σ F_{q} - 1)}}$
CES FOC for capital	$K_{q} = \frac{X D_{q}}{a F_{q}} \cdot {(\frac{γ F_{q}}{P K})}^{σ F_{q}} \cdot {[γ F_{q}^{σ F_{q}} \cdot P K^{(1 - σ F_{q})} + {(1 - γ F_{q})}^{σ F_{q}} \cdot P L^{(1 - σ F_{q})}]}^{\frac{σ F_{q}}{(1 - σ F_{q})}}$
Demand for investment goods	$P_{q} \cdot I_{q} = α I_{q} \cdot S$
Price of imports in local currency	$P M_{q} = (1 + t m_{q}) \cdot P W M_{q} \cdot E R$
Price of exports in local currency	$P E_{q} = P W E_{q} \cdot E R$
Armington function	$X_{q} = a A_{q} \cdot {[γ A_{q} \cdot M_{q}^{\frac{(σ A_{q} - 1)}{σ A_{q}}} + (1 - γ A_{q}) \cdot X D D_{q}^{\frac{(σ A_{q} - 1)}{σ A_{q}}}]}^{\frac{σ A_{q}}{(σ A_{q} - 1)}}$
Armington FOC for imports	$M_{q} = \frac{X_{q}}{a A_{q}} \cdot {(\frac{γ A_{q}}{P M_{q}})}^{σ A_{q}} \cdot {[γ A_{q}^{σ A_{q}} \cdot P M_{q}^{(1 - σ A_{q})} + {(1 - γ A_{q})}^{σ A_{q}} \cdot P D D_{q}^{(1 - σ A_{q})}]}^{\frac{σ A_{q}}{(1 - σ A_{q})}}$
CET function	$X D_{q} = a T_{q} \cdot {[γ T_{q} \cdot E_{q}^{\frac{(σ T_{q} - 1)}{σ T_{q}}} + (1 - γ T_{q}) \cdot X D D_{q}^{\frac{(σ T_{q} - 1)}{σ T_{q}}}]}^{\frac{σ T_{q}}{(σ T_{q} - 1)}}$
CET FOC for exports	$E_{q} = \frac{X D_{q}}{a T_{q}} \cdot {(\frac{γ T_{q}}{P E_{q}})}^{σ T_{q}} \cdot {[γ T_{q}^{σ T_{q}} \cdot P E_{q}^{(1 - σ T_{q})} + {(1 - γ T_{q})}^{σ T_{q}} \cdot P D D_{q}^{(1 - σ T_{q})}]}^{\frac{σ T_{q}}{(1 - σ T_{q})}}$
Market clearing condition for labour	$\sum_{q = 1}^{2} L_{q} + L G = L S$
Market clearing condition for capital	$\sum_{q = 1}^{2} K_{q} + K G = K S$
Market clearing condition for commodity q	$X D_{q} + M_{q} \cdot (1 + t m_{q}) = \sum_{s = 1}^{2} i o_{q s} \cdot X D_{q} + C G_{q} + C_{q} + I_{q} + E_{q}$
Income definition	$Y = P K \cdot K S + P L \cdot L S + T F \cdot P C$
Disposable income minus savings	$C B U D = (1 - t y) \cdot Y - S$
Zero profit condition in production function	$P D_{q} \cdot X D_{q} = P K \cdot K_{q} + P L \cdot L_{q} + \sum_{s = 1}^{2} i o_{s q} \cdot X D_{q} \cdot P D_{s}$
Zero profit condition in Armington function	$P_{q} \cdot X_{q} = P M_{q} \cdot M_{q} + P D D_{q} \cdot X D D_{q}$
Zero profit condition in CET function	$P D_{q} \cdot X D_{q} = P E_{q} \cdot E_{q} + P D D_{q} \cdot X D D_{q}$
Demand of commodity q by government	$P_{q} \cdot C G_{q} = α C G_{q} \cdot (T A X R E V - T F \cdot P C)$
Demand of capital by government	$P K \cdot K G = α K G \cdot (T A X R E V - T F \cdot P C)$
Demand of labour by government	$P L \cdot L G = α L G \cdot (T A X R E V - T F \cdot P C)$
Tax revenues	$T A X R E V = t y \cdot Y + \sum_{q = 1}^{2} (t m_{q} \cdot P W M_{q} \cdot E R)$

Table 9. Simulation results: percentage changes (CGE model).

	Integrated Approach	Top-Down Approach	TD/BU Approach (C&LS)	TD/BU Approach (LS)
Government Surplus	0.00	0.00	0.00	0.00
Wage Rate	−14.87	−14.67	−14.42	−14.64
Capital Return	19.70	19.30	17.91	19.13
Consumer Price Index	0.00	0.00	0.00	0.00
Exchange Rate	53.83	53.76	53.83	53.70
Labour Supply	−1.00	−1.18	−1.32	−1.32
Government Use of Labour	4.82	4.23	3.72	4.06
Government Use of Capital	−25.45	−25.45	−24.72	−25.43
Income*	−9.50	−9.39	−9.50	−9.48
Disposable Income*	−9.50	−9.39	−9.50	−9.48
Consumption Expenditure*	−9.50	−9.39	−7.90	−9.48
Marginal Propensity to Save	0.00	0.00	−16.22	0.00
Savings*	−9.28	−9.39	−24.18	−9.48
Tax Revenues	−9.28	−9.48	−9.63	−9.58

For the integrated model, these changes are computed as average percentage changes across households.

Table 10. Simulation results: percentage changes (CGE model).

Macro variables	Integrated Approach		Top-Down Approach		TD/BU Approach (C&LS)		TD/BU Approach (LS)
Macro variables	Sector 1	Sector 2	Sector 1	Sector 2	Sector 1	Sector 2	Sector 1	Sector 2
Commodity Prices	−0.99	0.30	−1.23	0.38	−1.70	0.52	−1.27	0.39
Domestic Sales	−8.69	−12.52	−8.81	−12.54	−10.21	−12.05	−8.88	−12.64
Domestic Production	27.81	−14.20	27.91	−14.31	26.77	−13.86	27.84	−14.43
Labour Demand	43.52	−13.22	43.05	−13.36	41.08	−12.94	42.88	−13.48
Capital Demand	13.07	−26.82	13.14	−26.72	12.72	−25.84	13.15	−26.76
Consumption*	−8.60	−9.78	−8.26	−9.73	−6.58	−8.30	−8.32	−9.84
Investment	−7.65	−8.84	−8.26	−9.73	−22.87	−24.57	−8.32	−9.84
Imports	−32.92	−47.63	−33.11	−47.57	−34.37	−47.21	−33.16	−47.60
Exports	207.36	−78.38	209.23	−78.53	209.10	−78.48	209.11	−78.59

For the integrated model, these changes are computed as average percentage changes across households.

Table 11. Simulation results: Inequality indices on disposable per capita real income (MS model).

	Benchmark Values	Integrated Approach*	Top-Down Approach*	TD/BU Approach (C & LS)*	TD/BU Approach (LS)*
Gini Index	31.85	3.02%	1.68%	1.52%	1.66%
Atkinson’s Index, ε = 0.5	8.46	4.94%	3.01%	2.72%	2.97%
Coefficient of Variation	65.86	3.78%	2.84%	2.64%	2.81%
Generalized Entropy Measures:
I(c), c = 2	21.69	7.69%	5.75%	5.35%	5.70%
Mean Logarithmic Deviation, I(0)	17.72	3.99%	2.10%	1.83%	2.07%
Theil Coefficient, I(1)	17.82	5.89%	3.89%	3.58%	3.85%

Percentage deviations from benchmark values.

Table 12. Simulation results: Poverty indices on disposable per capita real income (MS model).

	Benchmark Values	Integrated Approach*	Top-Down Approach*	TD/BU Approach (C & LS)*	TD/BU Approach (LS)*
General Poverty Line
Headcount Index, P₀	40.98	56.00%	8.00%	8.00%	8.00%
Poverty Gap Index, P₁	9.84	119.46%	27.25%	27.01%	27.21%
Poverty Severity Index, P₂	0.00	143.04%	28.95%	28.51%	28.88%
Extreme Poverty Line
Headcount Index, P₀	4.92	166.67%	33.33%	33.33%	33.33%
Poverty Gap Index, P₁	1.00	71.09%	4.77%	4.64%	4.75%
Poverty Severity Index, P₂	0.00	45.33%	−0.03%	0.03%	−0.03%

Percentage deviations from benchmark values.

Table 13. SAM of the economy made consistent with the Household Survey.

	C₁	C₂	S₁	S₂	K	L	H	G	SI	RoW	Total
C₁			57.8	15.6			95.4	62.6	28.1	23.6	283.0
C₂			17.1	23.5			313.2	48.8	13.6	76.6	492.8
S₁	283.3										283.0
S₂		492.5									492.8
K			73.4	23.2				13.2			109.8
L			81.7	353.8				117.5			552.6
H					109.8	552.6		38.7			701.2
G			12.3	17.7			250.8				280.8
SI							41.7				41.7
*RoW*			40.8	59.4							100.2
*Total*	283.0	492.8	283.0	492.8	109.8	552.6	701.2	280.8	41.7	100.2

Notes: C_q: consumption of good q; S_q: production sector q; K: capital account; L: labour account; H: representative household account; G: public sector; SI: savings-investments account, RoW: Rest of the World account.

Table 14. Simulation results with consistent data: Percentage changes (CGE model).

	TD/BU Approach (C & LS)	TD/BU Approach (LS)
Government Surplus	0.00	0.00
Wage Rate	−14.63	−14.81
Capital Return	18.36	19.37
Consumer Price Index (num.)	0.00	0.00
Exchange Rate	53.90	53.80
Labour Supply	−1.18	−1.18
Government Use of Labour	4.13	4.42
Government Use of Capital	−24.89	−25.48
Income	−9.45	−9.43
Disposable Income	−9.45	−9.43
Consumption Expenditure	−8.14	−9.43
Marginal Propensity to Save	−14.13	0.00
Savings	−22.24	−9.43
Tax Revenues	−9.57	−9.52

Table 15. Simulation results with consistent data: Percentage changes (CGE model).

	TD/BU Approach (C & LS)		TD/BU Approach (LS)
	Sec 1	Sec 2	Sec 1	Sec 2
Commodity Prices	−1.44	0.44	−1.07	0.33
Domestic Sales	−9.86	−12.06	−8.89	−12.55
Domestic Production	26.77	−13.80	27.65	−14.27
Labour Demand	41.65	−12.85	43.17	−13.30
Capital Demand	12.70	−25.99	13.05	−26.76
Consumption	−7.13	−8.45	−8.45	−9.73
Investment	−21.11	−22.58	−8.45	−9.73
Imports	−34.12	−47.30	−33.10	−47.63
Exports	207.50	−78.34	207.46	−78.43

Table 16. TD/BU-C&LS approach with consistent data: RH shares from CGE model used in the MS model (percentage changes, CGE model).

	only ty	only ΔLS	only η_i & mps	ΔLS, ty, mps & η_i
Marginal propensity to save Savings	2.92	−14.82	−14.47	0.12
Savings	−6.78	−22.87	−22.55	−9.33

Table 17. Simulation results TD/BU approach: percentage changes (CGE model).

	ΔLS & ty (inconsistent data)	ΔLS, ty, mps & η_i (inconsistent data)	ΔLS, ty, mps & η_i (consistent data)
Government Surplus	0.00	0.00	0.00
Wage Rate	−14.70	−14. 62	−14.84
Capital Return	19.43	18.95	19.46
Consumer Price Index (num.)	0.00	0.00	0.00
Exchange Rate	53.90	53.95	54.02
Labour Supply	−1.18	−1.18	−1.18
Government Use of Labour	2.26	2.13	1.62
Government Use of Capital	−26.96	−26.69	−27.55
Income	−9.39	−9.40	−9.44
Disposable Income	−8.47	−8.48	−8.12
Consumption Expenditure	−8.47	−7.93	−8.14
Marginal Propensity to Save	0.00	−5.53	0.25
Savings	−8.47	−13.54	−7.89
Tax Revenues	−10.95	−10.97	−11.60

Table 18. Simulation results TD/BU approach: percentage changes (CGE model).

	ΔLS & ty (inconsistent data)		ΔLS, ty, mps & η_i (inconsistent data)		ΔLS, ty, mps & η_i (consistent data)
	Sec 1	Sec 2	Sec 1	Sec 2	Sec 1	Sec 2
Commodity Prices	−1.21	0.37	−1.38	0.42	−1.09	0.33
Domestic Sales	−8.75	−12.00	−9.27	−11.77	−8.92	−11.73
Domestic Production	28.13	−13.75	27.72	−13.53	27.87	−13.42
Labour Demand	43.37	−12.79	42.66	−12.58	43.46	−12.44
Capital Demand	13.28	−26.30	13.11	−25.93	13.20	−26.07
Consumption	−7.35	−8.81	−6.90	−8.24	−7.45	−8.35
Investment	−7.35	−8.81	−12.33	−13.91	−6.88	−8.19
Imports	−33.09	−47.31	−33.57	−47.16	−33.20	−47.23
Exports	210.17	−78.31	210.17	−78.27	208.79	−78.11

Table 19. Simulation results TD/BU approach: percentage changes (MS model).

	ΔLS & ty (inconsistent data)		ΔLS, ty, mps & η_i (inconsistent data)		TD Approach (inconsistent data)
	Sec 1	Sec 2	Sec 1	Sec 2	Sec 1	Sec 2
Consumption	−7.23	−8.28	−7.45	−8.35	−7.21	−8.28
Savings		−7.78		−7.88		−7.78

Table 20. Inequality indices on disposable per capita real income (MS model).

	Benchmark Values	ΔLS & ty (inconsistent data)*	ΔLS, ty, mps & η_i (consistent data)*
Gini Index	31.85	1.70%	1.66%
Atkinson’s Index, ε = 0.5	8.46	3.04%	2.97%
Coefficient of Variation	65.86	2.86%	2.81%
*Generalized Entropy Measures*:
I(c), c = 2	21.69	5.80%	5.70%
Mean Logarithmic Deviation, I(0)	17.72	2.13%	2.07%
Theil Coefficient, I(1)	17.82	3.93%	3.85%

Percentage deviations from benchmark values

Table 21. Poverty indices on disposable per capita real income (MS model).

	Benchmark Values	ΔLS & ty (inconsistent data)*	ΔLS, ty, mps & η_i (consistent data)*
*General Poverty Line*
Headcount Index, P₀	40.98	8.00%	8.00%
Poverty Gap Index, P₁	9.84	27.30%	27.21%
Poverty Severity Index, P₂	0.00	29.01%	28.88%
*Extreme Poverty Line*
Headcount Index, P₀	4.92	33.33%	33.33%
Poverty Gap Index, P₁	1.00	4.79%	4.75%
Poverty Severity Index, P₂	0.00	−0.03%	−0.03%

Percentage deviations from benchmark values