Linking CGE and Microsimulation Models: A Comparison of Different Approaches

Transcription

1 INTERNATIONAL JOURNAL OF MICROSIMULATION (2010) 3) Linking CGE and Microsiulation Models: A Coparison of Different Approaches Giulia Colobo Departent of Econoic and Social Science - Catholic University of Milan and SiNSYS NV/SA; e-ail: giulia.colobo@sinsys.net ABSTRACT: In the literature that studies incoe ineuality and poverty, a recent developent has been the developent of odels that link together a acroeconoic odel (usually a Coputable General Euilibriu (CGE) odel) and a icrosiulation odel. Linking the two types of odel allows the odeller to take into account full agents heterogeneity, whilst at the sae tie considering the general euilibriu effects of a proposed policy refor. In this paper, I first review in detail three approaches to building linked CGE-icrosiulation odels: one in accordance with the fully integrated approach, and two following the layered approach (the so-called Top-Down and Top-Down/Botto-Up approaches). The principal goal of the paper is to present a considered evaluation of the erits and deerits of these alternative ethods currently used to link CGE and icrosiulation odels. To do so I use all three approaches to odel the acro- and icro-econoic ipacts of a policy shock to an archetypical econoy (constructed using fictitious data), and copare the results. This analysis highlights the iportance of (i) consistency between the underlying acro- and icro-data; and (ii) the precise echaniss by which feedback effects are passed between the acro and icro odels. I develop this latter point further by detailed analysis of the TD/BU approach outlined by Savard (2003), leading to a proposed refineent in the way that feedback effects fro the icro level of analysis are incorporated back into the CGE odel. 1. INTRODUCTION The study of poverty and ineuality in developing countries usually reuires two ain focuses: on one side a icroeconoic focus is reuired to have a detailed and precise picture of incoes and/or expenditures at the individual and household level, and to odel individual and household behavioural responses to soe refors/shocks, with a special concern for those whose incoe is around the poverty line; on the other side, a acroeconoic focus is often needed, as ost of the econoic policies (structural adjustent progras or trade liberalizations, for exaple) and of the exogenous shocks coonly analyzed for developing countries (such as fluctuations in the world price of raw aterials and agricultural exports) are often acroeconoic phenoena (or ay have, at least, soe structural effects on the econoy). Since the pioneering work by Adelan and Robinson 978) for South Korea and Lysy and Taylor 980) for Brazil, any Coputable General Euilibriu (CGE) odels for developing countries cobine a highly disaggregated representation of the econoy within a consistent acroeconoic fraework and a description of the distribution of incoe through a sall nuber of representative households (RHs). In order to account for heterogeneity aong the ain sources of the changes in household incoe, several representative households are necessary. Despite this need for variety, the nuber of RHs is generally sall in these odels (usually less than 10). The CGE/RH fraework soeties explicitly considers that households within a RH group are heterogeneous in a constant way. That is, in order to capture within-group ineuality, it is assued that the distribution of relative incoe within each RH follows an exogenous statistical law 1. But the assuption that relative incoes are constant within household groups is not reflected in reality. Indeed, epirical analyses conducted on household surveys show that the within-group coponent of observed changes in incoe distribution is generally at least as iportant as the between-group coponent of these changes 2. Thus, the RH approach based on this assuption ay be isleading in several circustances, and this is especially true when studying poverty. This arguent ay be better understood by presenting an exaple: consider a shock on the world arket of a certain good, which leads to a decrease in the exports and to a doestic contraction of this sector in the specific exporting country under study. After the siulation of the shock with a CGE/RH odel, suppose that I find a little change in the ean incoe of a particular RH group, say workers in the agricultural sector. In this case, poverty ight be increasing by uch ore than suggested by this drop in incoe: indeed, in soe households there ay be individuals that lose their job after the shock, or that encounter ore difficulties in diversifying their activity or consuption than others. For these individuals or failies, the relative fall in incoe is necessarily larger than for the whole group, and this fall in their incoe is not represented by the slight fall in the ean incoe of the whole group. Suppose, oreover, that the initial incoe of these individual was low. Then poverty ay be increasing by uch ore than what predicted by a siple RH odel, which is based on the assuption of distribution neutral shocks. So, the RH approach does not capture the effects that a shock or a policy change ay have on single individuals or households within a RH group. In contrast, icrosiulation odels can be very precise and detailed in their representation of icroeconoic individual behaviour, but

2 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 73 necessarily iss an iportant part of the story since they involve only a partial euilibriu analysis. In short, they iss a very iportant aspect represented by general euilibriu odels which is the structural effects of the refor/shock under study. In order to overcoe these probles, the recent literature has tried to develop new odelling tools which should be able at the sae tie to account for heterogeneity and for the possible general euilibriu effects of the policy refor (or the exogenous shock) under study. In view of the fact that ost of the available econoic odels have either a icroeconoic or a acroeconoic focus, and hence do not address the uestion adeuately, the recent literature has focused on the possibility of cobining two different types of odels. In particular, soe authors have tried to link icrosiulation odels to CGE odels, in order to account siultaneously for structural changes, for general euilibriu effects of the econoic policies, and for their ipacts on households welfare, incoe distribution and poverty. (More generally, this current of the literature develops the use of icro-data drawn fro household surveys in the context of a general euilibriu setting, which is usually but not necessarily a CGE odel.) The literature that follows this approach has flourished in recent years: there are, aong others, the iportant contributions by Decaluwé et al. 999a) and 999b), Cogneau and Robilliard (2001, 2004 and 2006), Cockburn (2001), Cogneau (2001), Bourguignon et al. (2003b), Boccanfuso et al. (2003), Savard (2003) and Davies (2009). In this paper I have two ain ais. First, to suarise recent developents in this field by detailing the three ain ethods developed to link the icro-data fro a survey into a CGE odel: the full integration of survey data into a CGE fraework, as is done for instance in Cockburn (2001); the linking of a behavioural icrosiulation odel to a CGE through a set of specific euations as developed in Bourguignon et al. (2003b) the so called Top-Down ethod; and the iterative coupling of CGE and icrosiulation outputs as developed by Savard (2003) the Top- Down/Botto-Up odel. Second, to present an assessent of the relative strengths and weaknesses of each of these three approaches. To fulfil these ais, in this paper I first outline each approach to linking CGE and icrosiulation odels in detail (Sections 2 to 4). I then use all three approaches to siulate the ipact of an identical policy refor, using as inputs for each the sae data fro a fictitious econoy. The use of fictitious data describing a siple econoy perits better understanding of the differences that are observed in the results of the odels, and of the causes that generate the. Having constructed and run the odels, in Section 5 I copare and contrast the acro- and icroeconoic outcoes derived fro each type of odel linking, drawing lessons regarding the iportance of data consistency and feedback echanis. This leads on to a ore detailed analysis of the TD/BU approach as developed by Savard (2003), and the proposal of an alternative way of taking into account feedback effects fro the icro level of analysis into the CGE odel. 2. THE INTEGRATED APPROACH The first approach to linking CGE and icrosiulation odels that I will consider is the integrated approach. The ain intuition behind this approach is to substitute the Representative Household Groups inside a standard CGE odel with the real households that are found in the survey. The first attept in this direction was ade by Decaluwé et al. 999b). Aong the odels following this approach there are the works by Cockburn (2001) for Nepal, by Boccanfuso et al. (2003) for Senegal, and by Cororaton and Cockburn (2005), who studied the case of the Philippine econoy. In practice, under this approach, one passes fro a odel with, for instance, ten representative agents to a odel with thousands of agents, thus increasing the coputational effort, but leaving substantially unchanged the odelling hypothesis of a standard CGE odel. Basically this approach does not include a true icrosiulation odule in the odelling fraework, but tries to incorporate the data fro the household survey into the CGE odel. The first step in building such a odel is to pass fro the representative households data to population values; to do this, one should weight each variable at the household level with the weights given in the survey, thus obtaining population values for each variable. After this, a procedure is reuired to reconcile these population data coing fro the survey (incoes and expenditures) with the accounts contained in the social accounting atrix (SAM). (For a fuller account of the SAM, see Section 3.2.) The literature on data reconciliation offers different alternatives. One ay choose to keep fixed the structure of the SAM and adjust the household survey, or to adjust the SAM in order to eet the totals of the household survey. Interediate approaches are also possible. Whatever the ethod used, however, one necessarily loses the structure of the original data, which is one of the ain drawbacks of the integrated approach. For this paper I have chosen the first alternative, and kept the original coposition of households incoes and expenditures unchanged. After these changes in the SAM, one encounters the proble of re-balancing it (row totals ust be eual to colun totals). To do this, I used an appropriate progra that iniizes least suares 3. The CGE odel I use for application of the integrated approach is the one described in

3 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 74 Section 3.2, except for the addition of an index which refers to households. This way, for instance, the consuption deand function in Table 8 becoes: P C H CBUD, where is now the index for households. One thing should be noted at this point: certain types of euations that are coonly included in a behavioural odel, such as occupational choice euations, are not easily odelled within standard CGE odelling software (see Savard, 2003), so that CGE-MS odels that follow the fully integrated approach are not always able to capture the behavioural responses of the agents to the policy refors that are ipleented. Instead, icro-econoetric behavioural odelling provides uch ore flexibility in ters of the odelling structure used, and is ore suitable to describe the coplexity of household and individual behaviour, and the way this ay be affected by the changes in the acroeconoic fraework that are subseuent to a policy refor or an external shock. The ain point here is that with a CGE odel like the one used for the integrated approach I a not able to predict which particular individual will enjoy the reduction (or will suffer fro the rise) in the eployent level on the basis of soe characteristics of the individual or of the household that can be observed; this instead can be done through a behavioural icrosiulation odel. Indeed, the ain feature that differentiates a icrosiulation odel fro a standard CGE fraework (not only one with representative agents, but even one with thousands of households fro a survey, as we have seen) is that it works at the individual level, selecting those individuals, on the basis of their personal or faily characteristics, that show the highest probability of changing their labour arket status. This fact could bring about significant differences in the results between the two types of odels, even after the sae policy siulation, as we will see below. 3. THE TOP-DOWN APPROACH I now turn to the seuential or Top-Down approach described in Bourguignon et al. (2003b). The basic idea here is to develop a stand-alone icrosiulation (MS) odel, and then to run it taking account of changes in consuer/producer prices, wages, and sectoral eployent levels predicted by a CGE odel. This approach thus uses the two fraeworks in a seuential way: first, the policy refor is siulated with the CGE odel, then siulated changes in selected variables, such as prices, wage rates, and eployent levels, are passed down to the MS odel, as illustrated in Figure 1. When the assuption of iperfect labour arket is adopted, or when the presence of a foral and an inforal sector is predicted, the rationing in the labour arket is usually carried out in the acro or CGE odel, while the ain use of the MS odule is to select those households or individuals who will actually be barred out of, or let in, eployent, or the foral sector. We will see this in ore detail in Section 5, when the siulation results are presented. 3.1 The icrosiulation odule The ain role of the icrosiulation odule in the linked CGE-MS fraework is to provide a detailed coputation of net incoes at the household level, through a detailed description of the tax-benefit syste of the econoy, and to estiate individual behavioural responses to a policy change. For instance, through the use of icroeconoetric euations, we can odel behaviours such as labour supply or consuption. Behavioural Microsiulation (MS) odels are developed to capture the possible reactions of the agents to the siulated policies, so that what happens after a refor can be very different fro what is predicted by the siple arithetical coputations included in an accounting odel. CGE odel Output A vector of changes in: - Prices, wage rates and interest rates - Quantities (for ex. occupational levels) Input MS odel Output New incoe levels after siulation Figure 1 The Top-Down approach

4 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 75 In this section I will describe in detail a siple behavioural odel, following uite closely the discrete labour supply choice odel used in Bourguignon et al. (2003b). Another description of a siilar MS odel for labour supply can be found in Bussolo and Lay (2003) with their odel for Colobia, and in Hérault (2005), who built a odel for the South African econoy. For the building of the odel I will use fictitious data describing a very siple econoy. In the household survey I have inforation about soe individual characteristics, such as age, sex, level of ualification, education, labour and capital incoe, the eventual receipt of public transfers, and the activity status. For the sake of siplicity, I have stated that each individual at working age 6-64) can choose between only two alternatives: being a full-tie wage worker, or being unoccupied. There are other variables in the survey that refer to households rather than to individuals, for exaple the area of residence, the nuber of adults (over 18 years old) and children (under 18), and so on. Also for the sake of siplification, I have grouped all consuption goods within the econoy into two ain categories. The focus of y distribution and poverty analysis will be on disposable incoe, even if in principle an ineuality and poverty analysis could also be conducted on expenditure rather than on incoe levels. I derive incoe variables referring to households fro initial individual data by suing up individual values for each household eber; this way, I obtain households labour and capital incoes, households public transfers and households total incoe, respectively: NC YL YL i i 1 NC YK YK i i 1 NC TF TF i i 1 Y YL YK TF, where YL i is labour incoe of individual i eber of household, YK i his/her capital incoe, and TF i are the public transfers he/she receives fro governent. All these uantities are sued up for each faily over all the individuals belonging to the faily (NC is the nuber of coponents of household ); then, household s total incoe, Y, is the su of all incoes received by the faily: labour incoe, capital incoe, and public transfers. For the benchark situation, I assue all initial prices noralized at one The odel The core of the behavioural odel is represented by the following two euations: Log ) ( YLi a b Xi c i vi ) W Ind Z RW 0] (2) i [ i i i The first euation is a regression odel for logwage earnings, while the second one represents individuals choice for labour arket status (see below for further explanations). The rest of the MS odule coprises siple arithetical coputations of price indices, incoes, savings and consuption levels. As the paraeters entering the following euations (arginal propensity to save ps, incoe tax rates γ, and budget shares η ) are constant, this part of the odel ay be regarded as purely accounting, as it does not contain any possible behavioural response to policy siulations. Household s incoe generation odel: Y NC i 1 YL i W i YK TF Household disposable (after tax) incoe: YD ) (3) ( 1 Y (4) Household specific consuer price index: 2 CPI P (5) 1 Real disposable incoe: YDR YD / CPI (6) Savings: S ps YD (7) Household consuption budget: CEBUD YD S (8) Consuption expenditure for coodity : CE CEBUD (9) Consuption level of coodity : CE C 0) P Household s capital incoe: YK PK KS 1) See Table 1 for a description of the subscripts.

5 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 76 Table 1 Description of the subscripts for the icrosiulation odel Households = 1, 2,, 24 i Individuals belonging to household i = 1,, NC (NC : nuber of coponents of household ) Goods = 1,2 The first euation of the odel, ), coputes the logarith of labour incoe (wage) of eber i of household as a linear function of his/her personal characteristics (vector X i includes the logarith of age, sex, skill level and educational attainent) and of Λ i, which represents the inverse Mills ratio estiated for the selection odel (for ore details on the estiation process see below). The residual ter v i describes the effects of unobserved coponents on wage earnings. The second euation (2) represents the choice of the labour status ade by household ebers. In the literature this kind of euation is known as an occupational choice odel, or selection odel (and also discrete choice odel of labour supply). However, it ust be specified that in our case this euation is not really intended to explain the individual choice between being occupied or uneployed, but rather it tries to find out which characteristics strengthen the probability of being in one condition rather than in the other one for each individual, as described in ore detail in the estiation section below. Each individual at working age has to choose between two alternatives: being a wage worker, or being inactive. The variable W i is a dichotoous variable taking value one if individual i of household is a wage worker, and zero otherwise. The choice is ade by each individual according to soe criterion, the value of which is specific to the alternative, and the alternative with the highest criterion value is selected. A natural econoic interpretation of this criterion value is utility: each individual chooses the alternative with the highest associated utility. I will estiate this selection odel using a binoial logit specification, which assigns each individual to the alternative with the highest associated probability. In the odel I have arbitrarily set to zero the utility of being inactive. Function Ind is an indicator function taking value one if the condition is verified, and zero otherwise. Vector Z i of explanatory variables includes soe personal characteristics of individual i of household, that is: age, sex, skill and educational level, the area of residence and the nuber of children under 6 living in the household. Variable RW i is the logarith of real labour incoe. The euation is defined only for individuals at working age. Euation (3) is an accounting identity that defines total household incoe, Y, as the su of the wage incoe of its ebers YL i, of the exogenous household capital incoe YK, and of the total aount of public transfers received by household, TF. In this euation, variable W i stands for a duy variable that takes value one if eber i is a wage worker and zero otherwise. Euation (4) coputes household disposable (after tax) incoe by applying incoe tax rates according to the rule reported in Table 2. In order to siplify coputations, I have assued that in this econoy direct incoe taxes are iposed on households total incoe Y, and not on individual incoes. Table 2 Direct incoe tax rates Household Incoe 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% The fifth euation coputes a household-specific consuer price index through the consuption shares η. Real disposable incoe is then obtained by dividing each household s disposable incoe by this index (euation (6)). To find a household s savings level, euation (7) ultiplies this disposable incoe by the arginal propensity to save of each household, ps. The assuption underlying this euation is that household savings behaviour is unvarying, as the savings level is a fixed fraction of household disposable incoe. Then, subtracting savings fro disposable incoe one obtains the budget that each household spends on consuption (euation (8)), which is spent on of the two goods in the odel according to the budget shares η, using euation (9). Again, the assuption underpinning this euation is that consuption behaviour is not flexible: that is, households spend a constant fraction of their consuption budget for each of the two goods. To get the values of these exogenous paraeters (arginal propensity to save ps and budget shares η ), I use the initial data fro the survey in the following way: ps S YD CE CEBUD. Euation 0) then derives the consuption levels for each household by dividing the expenditure for each good by its price. Finally, incoe fro capital is obtained by ultiplying capital endowent of each faily, KS, by the return to capital, PK (euation 1)).

6 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 77 The initial values of the variables C and KS (consuption levels and capital endowents, respectively) are derived fro the survey data aking use of the assuption that in the benchark situation all prices and returns are eual to one: C CE 2) KS YK 3) Moreover, I assue that public transfers paid to households and household capital endowents are exogenously given. They are fixed at the level reported in the survey, for public transfers, and at the level as coputed in euation 3), for capital endowent, respectively Estiation of the odel The only two euations in the MS odule that need to be estiated are euations ) and (2). The forer, which expresses the logarith of wage earnings as a linear function of soe individual characteristics and of Λ i, the inverse Mills ratio, was estiated using a Heckan twostep odel (see Heckan 976) and 979)). I followed this approach to correct for the selection bias which is iplicit in a wage regression, that is, the fact that I observe a positive wage only for those individuals that are actually eployed at the oent of the survey. The results of the estiation are reported in Table 3. The estiation was conducted on the subsaple of individuals at working age 6-64). The ai of the wage euation in the odel is to assign an estiated wage to the individuals that are inactive in the survey, and change their labour arket status after the siulation run. Paraeters of euation (2) were obtained through the Maxiu Likelihood estiation using a binoial logit odel and assuing that the residual ters ε i are distributed according to the Extree Value Distribution Type I 4. The estiation was conducted on the sub-saple of individuals at working age 6-64). Explanatory variables include individual characteristics such as the logarith of predicted real wage, sex, skill and education level, as well as the region of residence and a variable accounting for the presence or not of children under 6 years old in the household. Results are presented in Table 4. With the estiated coefficients I cannot perfectly predict the true labour arket statuses that are actually observed in the survey. Thus, following the procedure described in Duncan and Weeks 998), I drew a set of error ters ε i for each individual fro the extree value distribution, in order to obtain an estiate that is consistent with the observed activity or inactivity choices. Fro these drawn values, I select 100 error ters for each individual, in such a way that, when adding it to the deterinistic part of the odel, it perfectly predicts the activity status that is observed in the survey. In other words, the residual ter for an Table 3 Heckan selection odel, two-step estiates Coefficient Std. Error z P> z constant ln(age) sex ualification education Mills ratio Selection ln(age) sex ualification children under region rho siga Dependent variable: logarith of wage Table 4 Binary logit odel of labour status choice Coefficient Std. Error z P> z ln(real wage) sex ualification region children under education Mean dependent var S.D. dependent var S.E. of regression Akaike info criterion Su suared resid Schwarz criterion Log likelihood Hannan-Quinn criter Avg. log likelihood Dependent Variable: Activity Status

7 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 78 individual that is observed to be a wage earner in the survey should be such that: ˆ ˆ 4 ˆ 1 Log( RW AREA i ˆ 5 ) ˆ 2 CH6 i SEX ˆ i 6 ˆ 3 SCH while, for an individual that is observed to be inactive in the survey, the sae ineuality should be of opposite sign ( ). After a policy change, only the deterinistic part of the odel is recoputed. Then, by adding the rando error ters previously drawn to the recoputed deterinistic coponent, a probability distribution over the two alternatives (being a wage worker or being inactive) is generated for each individual. This iplies that the odel does not assign every individual fro the saple to one particular choice, but it gives the individual probabilities of being in one condition rather than in the other. This way, the odel does not identify a particular choice for each individual after the policy change, but generates a probability distribution over the different alternatives. This procedure is also described in Creedy and Kalb (2005); see also Creedy et al. (2002b) The CGE odel CGE odels are a class of econoic odels that use econoic data to estiate how an econoy ight react to changes in policy, technology or other external factors. A CGE odel consists of a syste of euations describing odel variables and a database consistent with the odel euations. General Euilibriu odels are used to estiate what is the effect of a change in one part of the econoy upon the rest. CGE odels have been used widely to analyse trade policy. More recently, CGE has becoe a popular way to estiate the econoic effects of easures to reduce greenhouse gas eissions. CGE odels always contain ore variables than euations, so that soe variables ust be set outside the odel. These variables are usually called exogenous variables. The choice of which variables are to be exogenous is called the odel closure. Variables defining technology, consuer tastes, and governent instruents (such as tax rates) are usually exogenous. For a ore detailed introduction to a basic CGE odel, please refer to the standard odel described in Löfgren et al. (2002). The CGE odel for our econoy (all euations are presented in Table 8) is characterized by a representative household who axiizes a Cobb- Douglas utility function with three arguents: leisure and two consuption goods. These coodities are also used as inputs, together with capital and labour, in the production process, which is operated by two firs following a Leontief technology in the aggregation of value added and Q i i i 0, the interediate coposite good, a Constant Elasticity of Substitution (CES) function for assebling capital and labour into value added, and a Leontief function in the aggregation of interediate goods. Both factors of production, capital and labour, are obile aong sectors. The capital endowent is exogenously fixed, while labour supply is endogenously deterined through household utility axiization (subject to fixed tie endowent). The wage elasticity of labour supply is estiated fro the household survey, in order to have consistency in labour supply behaviour between the two odels. Investents are savings-driven, while governent axiizes a Cobb-Douglas utility function to buy consuption goods and uses labour and capital. The public sector also raises taxes on household incoe, places tariffs on iported goodsand pays transfers to households. For the foreign sector I have adopted the Arington assuption (Arington, 1969) of constant elasticity of substitution for the foration of the coposite good (doestic production delivered to doestic arket plus iports) which is sold on the doestic arket. Doestic production is partially delivered to the doestic arket and partially exported, according to a Constant Elasticity of Transforation (CET) function. The sall country hypothesis is assued (the econoy is price taker in the world arket). In total the odel coprises 49 variables and 41 euations, which, with the 8 exogenous variables (capital endowent, KS, tie endowent, TS, public transfers, TF, the four world prices PWE and PWM, and the nueraire, PC), fully deterine the odel and allow for satisfaction of Walras law (we have a redundant euation). The calibration of the paraeters of the CGE odel is done on the basis of a Social Accounting Matrix (SAM) for the econoy. A SAM represents the flows of all econoic transactions that take place within an econoy. SAMs usually refer to a single year, thus providing a static picture of the econoy. The coluns of a SAM represent buyers (expenditures) and the rows represent sellers (receipts). Coluns and rows are added up to ensure accounting consistency, and each colun is added up to eual each corresponding row. The SAM for the econoy under study and the initial values of soe other variables are consistent with the benchark situation of the icro-data (for instance, in the benchark of the two odels I have the sae average incoe tax rate, the sae average arginal propensity to save, the sae budget shares for consuption of the two goods, and so on). The SAM is reported in Table 5. Values of other initial paraeters for the CGE odule are shown in Table 6, while the variables and euations used in the odel can be found in Tables 7 and 8 below. The data in the SAM are in illions of the onetary unit used in the survey.

8 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 79 Table 5 SAM of the econoy C 1 C 2 S 1 S 2 K L H G SI RoW Total C C S S K L H G SI RoW Total C : consuption of good ; S : production sector ; K: capital account; L: labour account; H: representative household account; G: public sector; SI: savings-investents account, RoW: Rest of the World account. Table 6 Values of soe paraeters for the CGE odel Sector 1 Sector 2 Elasticity of substitution (EOS) in production function (aggregation of capital and labour) Elasticity of substitution for Arington coposite good Elasticity of transforation for exports and doestic production delivered to the doestic arket Initial tariff rates on iports Initial tie endowent Wage elasticity of labour supply (estiated fro the household survey) Table 7 Variables and paraeters of the CGE odel Variables Paraeters PK Return to capital ty Incoe tax rate PL Wage rate t Tariff rates on iports P Price of Arington coposite good ε_ls Wage elasticity of labour supply PD Price of output ps Marginal propensity to save PDD Price of doestically produced good Cobb-Douglas power of coodity in RH s αh delivered to doestic arket utility function PWE World price of exports (foreign currency) αh l Cobb-Douglas power of leisure in RH s utility function PWM World price of iports (foreign currency) αcg Cobb-Douglas power of coodity in governent utility function PM Price of iports (local currency) αkg Cobb-Douglas power of capital in governent utility function PE Price of exports (local currency) αlg Cobb-Douglas power of labour in governent utility function ER Exchange rate io s Technical coefficients PC Consuer price index af Efficiency paraeter production function KS Capital endowent (exogenous) γf Share paraeter in production function LS Labour supply (endogenous) σf EOS in fir s production function TS Tie endowent (exogenous) aa Efficiency paraeter in Arington function X Doestic sales (Arington coposite) γa Share paraeter in Arington function XD Doestic production σa EOS in fir s Arington function XDD Doestically produced good delivered to Cobb-Douglas power of coodity in Bank s αi doestic arket utility function M Iports at Efficiency paraeter in CET function E Exports γt Share paraeter in CET function K Capital deand by firs σt Elasticity of transforation in CET function L Labour deand by firs I Investent good C Consuption deand by household C l Deand for leisure Y Household s incoe S Household s savings CBUD Household s consuption expenditure TF Public transfers to household TAXREV Tax revenues CG Consuption deand by governent KG Capital deand by governent LG Labour deand by governent

9 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 80 Table 8 Euations of the CGE odel Description Deand for consuption goods Leisure Labour supply Savings Euations P C l LS C [ TS H ty) Cl CBUD, where = 1,2 PL] S ps ( 1 ty) Y 1 Hl CBUD H ) l Consuer price index PC 2 H P 1 CES production function XD af F K ( F 1) F F ) ( F 1) F L F ( F 1) CES FOC for capital K XD af F PK F [ F F PK F ) F ) F PL F F ) F ) ] Deand for investent goods P I I S Price of iports in local currency PM ( 1 t ) PWM ER Price of exports in local currency PE PWE ER Arington function X aa A M ( A 1) A A ) XDD ( A 1) A A ( A 1) Arington FOC for iports M X aa A PM A [ A A PM A ) A ) A PDD A A ) A ) ] CET function XD at T E ( T 1) T T ) XDD ( T 1) T T ( T 1) CET FOC for exports E XD at T PE T [ T T PE T ) T ) T PDD T T ) T ) ] Market clearing condition for labour 2 L 1 LG LS Market clearing condition for capital 2 1 K KG KS Market clearing condition for coodity Incoe definition Disposable incoe inus savings Zero profit condition in production function Zero profit condition in Arington function Zero profit condition in CET function XD Y PK M KS ( 1 t ) PL CBUD ( 1 ty) Y PD P PD X XD XD PM PK PE M LS K E S 2 io s s 1 TF PL PDD PC L PDD XD 2 io s s 1 XDD XDD Deand of coodity by governent P CG CG ( TAXREV TF PC) Deand of capital by governent PK KG KG ( TAXREV TF PC) Deand of labour by governent PL LG LG ( TAXREV TF PC) Tax revenues TAXREV ty Y 2 1 ( t PWM CG ER) XD C PD s I E

10 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches Linking the odels The basic difficulty of the top-down approach is ensuring consistency between the icro and acro levels of analysis. For this reason, one ay introduce a syste of euations to ensure the achieveent of consistency between the two odels. This way, what happens in the MS odule can be ade consistent with the CGE odelling by adjusting paraeters in the MS odel. In practice, this consists in iposing the acro results obtained with the CGE odel onto the icroeconoic level of analysis. In particular: 1) changes in the coodity prices, P, ust be eual to those resulting fro the CGE odel (euation 5)); 2) changes in average earnings with respect to the benchark in the icrosiulation odule ust be eual to changes in the wage rate obtained with the CGE odel (euation 6)); 3) changes in the return to capital of the icrosiulation odule ust be eual to the sae changes observed after the siulation run in the CGE odel (euation 7)); 4) changes in the nuber of wage workers in the icrosiulation odel ust atch those observed in the CGE odel (euation 8)) For our odel, these consistency conditions translate into the following set of constraints, which could be called linking euations: CE C 5) CGE P ) ˆ CGE Log ( YL ) Log[ YL PL )] 6) i i CGE YK KS PK ) 7) 24 NC 1 i 1 24 NC 1 i 1 Wˆ i WA i 100 EMP CGE 8) The variables with no superscripts are those coing fro the icrosiulation odule; those with the ^ notation correspond to the ones that have been estiated: in particular, Log(ŶL i ) is the wage level resulting fro the regression odel for individual i, eber of household, while Ŵ i is the labour arket status of individual i of household deriving fro the estiation of the binoial choice odel. ΔP CGE, ΔPL CGE and ΔPK CGE indicate, respectively, the change in the prices of goods, the change in the wage rate and in the return to capital deriving fro the siulation run of the CGE odel, while paraeter ΔEMP CGE is the eployent level percentage change taken fro the CGE fraework. WA i is a duy variable taking value one if individual i of household is at working age 6-64), and zero otherwise. Fro euation 8), the nuber of eployed over the total nuber of individuals at working age resulting fro the MS odel ust be eual to the change in the eployent level observed after the CGE run. This iplies that the CGE odel deterines the eployent level of the econoy after the siulation, and that the MS odel selects which individuals aong the inactive persons have the highest probability of becoing eployed (if the eployent level is increased fro the CGE siulation result), or either who, aong the wage workers, has the lowest probability of being eployed after the policy change (if the eployent level is decreased), and, in this case, his/her new wage level will be deterined by the regression odel of wage earnings (euation )). One possible way of iposing euality between wages and eployent at the two levels is through a change in the paraeters of the selection and regression odels. Following Bourguignon et al. (2003b), this translates into changing the intercepts of function ) and (2) in the icrosiulation odule. In other words, changes in average earnings with respect to the benchark in the icrosiulation ust be eual to changes in the wage rate obtained with the CGE odel, and this is done by adapting intercept a of euation ). This just shifts proportionally the estiated wages of all individuals, without causing any change in the ranking between one individual and the other. Likewise, intercept α of the activity status choice function (euation (2)) is changed to atch changed results in the CGE odel. This will shift proportionally all the individual probabilities of being a wage worker, without changing their relative positions in the probability distribution, just letting soe ore individuals to becoe eployed (or soe less if the eployent rate of the CGE odel is decreased), irrespectively of their personal characteristics. This change in the intercept will be of the aount that is necessary to reach the nuber of wage workers resulting fro the CGE odel. Thus, this choice preserves the ranking of individuals according to their ex-ante probability of being eployed, which was previously deterined by the estiation of the binoial odel. For this reason the change in the intercept paraeter satisfies this neutrality property. 4. THE TOP-DOWN/BOTTOM-UP APPROACH A third approach to linking CGE and MSM was developed by Savard (2003). It attepts to overcoe the lack of consistency between the icro and acro levels of the Top-Down approach by introducing a bi-directional link between the two odels: for this reason it is also called the Top-Down/Botto-Up approach (TD/BU). According to this ethod, aggregate results fro the MS odel (such as consuption levels and/or labour supply) are incorporated into the CGE odel, and a loop is used to run both odels

11 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 82 iteratively until the two produce convergent results. The value added of this approach is that it takes into account the feedback effects that coe fro the icro level of analysis, which are copletely disregarded by the Top-Down odel. The basic assuption behind the TD/BU approach is that the icroeconoic effects provided by the MS odel run do not correspond to the aggregate behaviours of the representative households used in the CGE odel, and that it is thus necessary to take these effects back into the CGE odel to fully account for the effects of a siulated policy. A stylized schee of the way in which this approach works can be observed in Figure 2. The bilateral counication between the two levels of analysis is achieved through a set of vectors of changes, as in the Top-Down approach: fro the acro to the icro level of analysis counication is guaranteed by the changes in the price, wage and return vector and in the eployent levels, as before, while for counication fro the icro to the acro level I consider in this paper two different strategies: in one, I use as input for the CGE odel a vector of changes in the aggregate consuption and in the labour supply levels fro the MS odel; in the other, only the change in the labour supply level which results fro the MS odel will be used as input for the CGE odel. In either case the process is iterated as any ties as is necessary to coe to a convergent point, that is, when convergence (at a certain nuber of decials) is obtained in the aggregate variable levels of the two odels. The choice for consuption and labour supply as counicating variables is ade following Savard (2003). However, as both consuption and labour supply are not exogenous in the CGE odel, soe of the initial hypotheses of the odel ust be changed. First, I reove the euations deterining consuption deand by the representative household (the first euation in Table 8), substituting the with the following single euation: i 2 CBUD P i C i. 1 In the initial hypothesis (endogenous consuption) I had two endogenous variables (C i ) and two euations. Now I have two exogenous variables and one euation. As I need to insure the balancing of the household s budget constraint, a variable needs now to be endogenized in the following euation: CBUD ( PK KS ps) PL LS ty) TF). Following Savard, I choose to endogenize the arginal propensity to save, ps, which is now a variable that changes in order to satisfy the budget constraint. In addition, I introduce an exogenous level of labour supply into the CGE odel, and just leave out the euation that deterines the deand for leisure (the second euation in Table 8). This way, the third euation will now yield the deand for leisure as the tie reaining after having supplied an exogenous level of labour. In the second variant of the TDBU odel, I introduce an exogenous level of labour supply into the CGE odel, but oit the euation that deterines the deand for leisure (the second euation in Table 8). 5. SIMULATION Having outlined three alternative approaches to integrating CGE with icrosiulation odels, in this section I copare the results fro each when used to siulate the sae policy. The siulation will be of an exogenous shock to the world price level of the good exported by sector 2, which is the labour intensive sector in our stylized econoy. In this shock the world price of good 2 is reduced by 64% fro its initial value. The siulation results for the ost relevant acroeconoic variables are reported in percentage changes in Tables 9 and 10. The acroeconoic results for the Top-Down odel (shown in the second coluns of the tables) represent the results that would eerge fro a stand-alone CGE odel, since they coe fro a siple run of the CGE odel. These acroeconoic changes are then iposed onto the icrosiulation odel, as explained in section 3.3, in order to obtain results at the icro level, which are shown in Tables 11 and 12. In all tables, the two different strategies adopted for the TD/BU approach are also taken into account, allowing coparison of the results arising fro two different ways of taking into account the feedback effects fro the icro level of analysis. This is done by introducing into the CGE odel, as inputs derived fro the icrosiulation odule, the consuption level and labour supply (C&LS), or the labour supply only (LS). In general, for ost of the acro variables, siilar results are produced by all four siulations. The shock has negative effects on the econoy. Indeed, as I can observe in Table 10, the fall in the price of the exported good for sector 2 causes a reduction of the production level for this sector, which reduces its deand for both factors of production. However, due to the depreciation of local currency, the reduction in the level of exports is lower than the 64% world price reduction. For the sae reason, exports for the other production sector becoe ore convenient, so that for this sector I observe an increase in the level of the exported good, an increase in the production level, and in the deand for capital and labour. The depreciation of local currency also has a negative effect on the level of iports, which contributes to a decrease in the aount of goods sold on the doestic arket.

12 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 83 CGE odel output A vector W 1 of changes in: - Prices, wage and interest rates - Quantities (for ex. eployent levels) 1 st run MS odel output Variable at the household level (ex. consuption or labour supply) Aggregate and weight Aggregated vector AV 1 of levels CGE odel output input 1 st iteration input MS odel output Variable at the household level A vector W 2 of changes in: - Prices, wage and interest rates - Quantities Aggregate and weight Aggregated vector AV 2 of levels CGE odel input 2 nd iteration input MS odel output and so on with as any iterations as are necessary to obtain convergence (to a given nuber of decials) of the aggregate variable level in the two odels output Figure 2 The Top-Down/Botto-Up approach

13 COLOMBO Linking CGE and icrosiulation odels: a coparison of different approaches 84 Table 9 Siulation results: percentage changes (CGE odel) Integrated Approach Top-Down Approach TD/BU Approach (C&LS) TD/BU Approach (LS) Governent Surplus Wage Rate Capital Return Consuer Price Index Exchange Rate Labour Supply Governent Use of Labour Governent Use of Capital Incoe * Disposable Incoe * Consuption Expenditure * Marginal Propensity to Save Savings * Tax Revenues * For the integrated odel, these changes are coputed as average percentage changes across households. Table 10 Siulation results: percentage changes (CGE odel) 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 Coodity Prices Doestic Sales Doestic Production Labour Deand Capital Deand Consuption * Investent Iports Exports * For the integrated odel, these changes are coputed as average percentage changes across households. Table 11 Siulation results: Ineuality indices on disposable per capita real incoe (MS odel) TD/BU TD/BU Benchark Integrated Top-Down Values Approach * Approach * Approach Approach (C & LS) * (LS) * Gini Index % 1.68% 1.52% 1.66% Atkinson s Index, ε = % 3.01% 2.72% 2.97% Coefficient of Variation % 2.84% 2.64% 2.81% Generalized Entropy Measures: I(c), c = % 5.75% 5.35% 5.70% Mean Logarithic Deviation, I(0) % 2.10% 1.83% 2.07% Theil Coefficient, I) % 3.89% 3.58% 3.85% * Percentage deviations fro benchark values. Table 12 Siulation results: Poverty indices on disposable per capita real incoe (MS odel) TD/BU TD/BU Benchark Integrated Top-Down Values Approach * Approach * Approach Approach (C & LS) * (LS) * General Poverty Line Headcount Index, P % 8.00% 8.00% 8.00% Poverty Gap Index, P % 27.25% 27.01% 27.21% Poverty Severity Index, P % 28.95% 28.51% 28.88% Extree Poverty Line Headcount Index, P % 33.33% 33.33% 33.33% Poverty Gap Index, P % 4.77% 4.64% 4.75% Poverty Severity Index, P % -0.03% 0.03% -0.03% * Percentage deviations fro benchark values.