- Chapter 2 - LINKING CGE AND MICROSIMULATION MODELS: A COMPARISON OF DIFFERENT APPROACHES

Transcription

1 - Chapter 2 - LINKING CGE AND MICROSIMULATION MODELS: A COMPARISON OF DIFFERENT APPROACHES

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3 . INTRODUCTION In the literature that studies incoe ineuality and poverty, we can observe a recent developent of odels that link together a acroeconoic odel (usually a CGE odel) and a icrosiulation odel. The reason for this lays in the fact that poverty and ineuality are typically icroeconoic issues, while the policy refors or the shocks that are siulated have often a strong acroeconoic ipact on the econoy under study. Thus, an approach that takes into account both aspects of the econoy through the use of soe icro-acro linkages sees to be the right answer to the proble. The ain ai for which CGE and icrosiulation (MS) odels are linked is indeed to try to take into account full agents heterogeneity and the coplexity of incoe distribution on one side, while being able at the sae tie to consider the acroeconoic effects of the policy refors or of the shocks under study. As we have already seen in the introduction to the previous chapter, indeed, CGE odels following the representative household approach fail in capturing agents heterogeneity and especially the changes in the distribution within the representative households groups. On the other side, if we conduct the analysis only in the context of a icrosiulation fraework, we will just be able to perfor a partial euilibriu analysis, thus disregarding all the possible general euilibriu effects of the refor under study on the entire econoy. 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 they 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 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. 73

4 welfare, incoe distribution and poverty. The literature that follows this approach is uite flourishing in recent years: there are, aong others, the iportant contributions by Decaluwé et al. (999a) and (999b), Cogneau and Robilliard (200 and 2004), Cockburn (200), Cogneau (200), Bourguignon, Robilliard and Robinson (2003b), Boccanfuso et al. (2003) and Savard (2003). The ai of this chapter is to give an assessent of recent developents in this field, with a special concern for the different types of linking that are currently used in the literature. In particular, we will link the icro-data fro a survey to a CGE odel in three different ways: through a full integration of the survey data into a CGE fraework, as it is done for instance in Cockburn (200); by linking a behavioural icrosiulation odel to a CGE through a set of specific euations, which is the so called Top-Down ethod, as it is developed in Bourguignon et al. (2003b), and finally through a ethod which was developed by Savard (2003), also known as Top-Down/Botto-Up odel. We will build all the three types of odels using the sae data fro a fictitious econoy. After this, by running an identical policy refor in the three odels, we will analyse the different outcoes deriving fro different types of linking. We will see that, even with the sae econoy and under the sae policy siulation, we can obtain uite different results, especially in ters of incoe distribution and poverty change. The choice for the use of fictitious data describing a siple econoy is ade with the ai of being able to understand better the differences that are observed in the results of the odels, and to try to go behind these differences and look for the causes that generate the. Of course, this is of ore difficult realization when using true data of a real and thus ore coplex econoy, which naturally shows ore a coplex structure in its econoic relationships. The ain difference that distinguishes the icrosiulation odel we are going to use in this chapter fro the one described in the previous one is that we will now allow for individual behavioural responses by the agents, with a special concern for labour supply responses. In particular, we will analyse in ore detail the TD/BU approach as developed by Savard (2003) and propose an alternative way of taking into account feedback effects fro the icro level of analysis into the CGE odel (see paragraph 5.). 74

5 2. THE INTEGRATED APPROACH The ain intuition behind this approach is to siply substitute the Representative Household Groups inside a standard CGE odel with the real households that are found in the survey 2. This way, 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 it tries to incorporate the data fro the household survey into the CGE odel. The first step to build such a odel is to pass fro the representative households data of the survey to population values; to do this, one should weight each variable at the household level with the weights usually given in the survey, thus obtaining population values for each variable. After this, we need a procedure to reconcile these population data coing fro the survey (incoes and expenditures) with the accounts contained in the social accounting atrix (SAM). 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 otherwise to adjust the SAM in order to eet the totals of the household survey. Another alternative would be that of using an interediate approach. 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. Our choice was for the alternative of keeping 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, we used an appropriate progra that iniizes least suares 3. 2 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 (200) for Nepal, by Boccanfuso et al. (2003) for Senegal, and by Cororaton and Cockburn (2005), who studied the case of Philippine econoy. 3 There exist different principles on which SAM-balancing progras can be based, such as the Row and Su or RAS ethod (see Bacharach, 97), least suares iniization principles, known also as Stone- 75

6 The CGE odel is the one described in section 3.2, except for the fact that we have added an index which refers to households 4. A thing should be noted at this point: certain types of euations that are coonly included in a behavioural odel, such as switching regie euations, like occupational choice euations, are not easily odelled within the standard CGE odelling softwares 5. Instead, icro-econoetric behavioural odelling provides uch ore flexibility in ters of the odelling structure used, and it 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. For instance, with a CGE odel like the one used for the integrated approach here, we are not able to predict which particular individual will enjoy the reduction (or will suffer fro the rise) of the uneployent level on the basis of soe characteristics of the individual or of the household that can be observed; this instead can be done with the use of 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 that show the highest probability of changing their labour arket status, on the basis of their personal or faily characteristics. This fact could bring above significant differences in the results between the two types of odels, even after the sae policy siulation, as we will see below. To this extent it is iportant to underline a fact about the treatent of involuntary uneployent. In a coon CGE odel it is possible to introduce involuntary Byron ethods (see Stone (977) and Byron (978)), or the ore recent cross-entropy approach proposed by Robinson et al. (200) and Robilliard and Robinson (2003). 4 For instance, the consuption deand function in Table 6 becoes: P C = α H CBUD, where is now the index for households. 5 For instance, a discrete labour supply choice odel in which individuals change their labour arket status is not of easy ipleentation in a syste of siultaneous euations like a CGE odel. To this regard, see Savard s (2003) discussion about the liits and advantages of the various approaches of linking. 76

7 uneployent due to structural characteristics of the labour arket. If we have representative household groups, we can odel the uneployent at the acro level (for instance with a Phillips curve) and then distribute the after-refor change in the uneployent level to the various groups, according to soe proportional law, for instance. But if we have, like in the integrated approach, thousands of individual households, which are not even grouped according to any socio-econoic characteristic, it is not clear how we can distribute the change in uneployent at the acro level to the single households. To do it in a proportional way would be inaccurate, because this is not what we observe in reality (we usually observe a person that loses her job, and not a proportional decrease in the worked hours of all the households, especially if the effect we are treating coes fro involuntary uneployent and not fro labour supply). 3. THE TOP-DOWN APPROACH We apply now the seuential or Top-Down approach as described in Bourguignon et al. (2003b). The basic idea is to develop separately a MS odel and then to run the siulation on the basis of changes in consuer/producer prices, wages, and sectoral eployent levels as predicted by the CGE odel. This approach thus uses the two fraeworks in a seuential way: first, the policy refor is siulated with the CGE odel, and the second step consists of passing the siulated changes in soe variables such as prices, wage rates, and eployent levels 6 down to the MS odule, as illustrated in Figure 4 (Chapter, page 53). 6 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 the siulation section. 77

8 3.. The Microsiulation Module The ain role of the icrosiulation odule in the linked 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 the 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. In this section we 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 we will use fictitious data describing a very siple econoy. In the household survey we 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, we have stated that each individual at working age (6-64) can be allocated according to two alternatives: being a full-tie wage worker, or being inactive. There are other variables in the survey that are referred to households rather than to individuals, for exaple the area of residence, the nuber of household coponents, the nuber of adults (over 8 years old) and children (under 8), and so on. All consuption goods of the econoy are grouped in two ain categories 7. We derive incoe variables referring to households fro initial individual data by suing up individual values for each household eber; this way, we obtain 7 The focus of our distribution and poverty analysis will be on disposable incoe, even if an ineuality and poverty analysis could also be conducted on expenditure rather than on incoe levels. 78

9 households labour and capital incoes, households public transfers and households total incoe: Household s labour incoe: Household s capital incoe: Public transfers to household : Household s total incoe: NC = YL YL i i= NC = YK YK i i= NC = TF TF i i= 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, we assue all initial prices noralized at one. The Model The core of the behavioural odel is represented by the following two euations: Regression odel for log-wage earnings: ( YLi ) a + b xi + c i vi Log = λ + (B.) Choice of labour arket status: W Ind[ + β z + γ rw + ε > 0] i = i i i α (B.2) The rest of the MS odule is ade up by 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. 79

10 Household s incoe generation odel: Y YD NC = YL i= i W Household disposable (after tax) incoe: ( ) i + YK + TF (B.3) = γ Y (B.4) Household specific consuer price index: Real disposable incoe: Savings: Household consuption budget: Consuption expenditure for coodity : Consuption level of coodity : 2 CPI = η P (B.5) = YDR = YD / CPI (B.6) S = ps YD (B.7) CEBUD CE = YD S (B.8) = η CEBUD (B.9) CE C = (B.0) P Household s capital incoe: YK = PK KS (B.) Description of the subscripts: Households =, 2,, 24 i Individuals belonging to household i =,, NC NC : nuber of coponents of household Goods =,2 The first euation of the odel, (B.), coputes the logarith of labour incoe (wage) of eber i of household as a linear function of his/her personal characteristics (vector of x i includes the logarith of age, sex, skill level and educational attainent) and λ i, which represents the inverse Mills ratio estiated for the selection odel (for ore details on the estiation process see below in the section Estiation of the Model ). The residual ter earnings. v i describes the effects of unobserved coponents on wage The second euation represents the choice of the labour status ade by household ebers 8. Each individual at working age has to choose between two alternatives: 8 In the literature this kind of euation is known as occupational choice odel, or selection odel (and also discrete choice odel of labour supply). However, it ust be specified that in our odelling context this euation is not really intended to explain the individual choice between being occupied and uneployed, but rather it tries to find out which characteristics strengthen the probability of being in one condition 80

11 being a wage worker, or being inactive. The variable W i is a dichotoic variable taking value one if individual i of household is a wage worker, and zero otherwise. The allocation of each individual is ade 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 is assigned to the alternative with the highest associated utility. Indeed, we will estiate the selection odel using a binoial logit specification, which assigns each individual to the alternative with the highest associated probability 9. In our odel we 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 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 rwi is the logarith of real labour incoe. The euation is defined only for individuals at working age. The third euation 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. The fourth euation coputes household disposable (after tax) incoe by applying incoe tax rates according to the rule reported in Table. In order to siplify coputations, we have assued that in this econoy direct incoe taxes are iposed on households total incoe Y, and not on individual incoes. Euation (B.5) coputes an household specific consuer price index through the consuption shares η. Real disposable incoe is then obtained by dividing households disposable incoe by this index (euation (B.6)). z i rather than in the other one for each individual, as it is described in ore detail in the estiation section below. This is the reason why in the rest of the chapter we will use the word choice in uotation arks. 9 See the next sub-section for ore details on econoic interpretation of logit odels. 8

12 Table Direct Incoe Tax Rates Incoe brackets: Tax rate Up to 0,000 0% Up to 5,000 5% Up to 26,000 24% Up to 70,000 32% Over 70,000 39% Then, to find out household s savings level, euation (B.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 for consuption ( euation (B.8)), which is spent on the two goods of the odel according to the budget shares η by euation (B.9). Again, the assuption in 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 budget shares η ), we use the initial data fro the survey in the following way: ps and Household s arginal propensity to save: Household s consuption budget shares: S ps = YD η CE = CEBUD Euation (B.0) derives then 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 (B.)). The initial values of the variables C and KS (consuption levels and capital endowents, respectively) are derived fro the initial data of the survey by aking use of the assuption that in the benchark situation all prices and returns are eual to one: 82

13 Household s consuption level of coodity : Household s capital endowent: C = CE (B.2) KS = YK (B.3) Moreover, we 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 (B.3), for capital endowent, respectively. Econoic Interpretation of a Binoial Logit Model This odel can be interpreted as follows. Suppose an individual i assigns utility U Wi to the alternative of being a wage worker (in order to siplify the analysis, we drop subscript referred to the household), on the basis of his/her personal characteristics, z i and that he/she assigns utility U Bi to the alternative of being unoccupied. Furtherore, suppose that these utilities are linear functions of z i, that is: U U Wi Bi = α + β z + ε (B.4) W B W B i i Bi Wi = α + β z + ε. (B.5) One ay now define that an individual i selects the alternative of being a wage worker if the utility of being a wage worker exceeds that of being uneployed, that is: Pr [ OCSi = Z i ] = Pr[ UWi > U Bi Z i ] = Pr[ α + ( β β ) z > ε ε Z ] α W B W B i Bi Wi i (B.6) = Pr[ ε < α + β z Z ], i i i where OCS i is the occupational status of individual i of household, which takes value one if individual i is a wage worker, and zero otherwise, while i β euals ( βw β B ), and α is ( W α B ) ε is eual to ( ) ε, Bi ε Wi α. This shows that one cannot identify the individual paraeters in (B.6); one can only identify the difference between the paraeters. Hence, one way to look at the paraeters α and β is to see these as easuring the effect of being inactive 0. z i on the choice for being wage worker relative to that of 0 For ore details on this interpretation of a binoial odel, see Franses and Paap (200). 83

14 In this sense, euation (B.2) can be seen as expressing in an iplicit way the utility associated with each of the two labour arket alternatives. In our odel we have arbitrarily set to zero the utility of being uneployed, which eans setting to zero the coefficients α B and β B of euation (B.5). Thanks to this, the error ter ε i in (B.6) corresponds now to the error ter of euation (B.4), ε Wi, the coefficient β of euation (B.6) euals This way, euation (B.6) becoes: Pr [ OCSi = Z i ] = Pr[ UWi > 0 Z i ] = Pr[ + β z β W, and the intercept paraeter α is now α W. α W W i > ε Wi Z i ] (B.7) = Pr[ α + β z + ε > 0 Z ], i i i which is substantially what we have in the euation of the odel, (B.2), except for the issing household subscript, which has been dropped before, for siplicity. Estiation of the Model The only two euations in the MS odule that need to be estiated are euations (B.) and (B.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 two-step odel (see Heckan (976) and (979)). We follow this approach to correct for the selection bias which is iplicit in a wage regression, that is, the fact that we observe a positive wage only for those individuals that are actually eployed at the oent of the survey. As we cannot assue that the decision of participating in the labour arket is ade randoly, but rather it is based, aong others, on the level of wage that is offered in the arket, the estiate ade only on the sub-saple of individuals who have a positive wage will be biased. Indeed, individuals who have low wages are ore unlikely to choose to work (as they have a reservation wage that is greater than the wage offered by eployers), and thus the saple of observed wages would probably be biased upward. 84

15 A solution can be found if there are soe variables that strongly affect the chances for observing the reservation wage but not the outcoe under study (the offer wage), such as the nuber of children living in the household, for exaple. In this case, one has to estiate two euations: one, the wage regression euation, which expresses the wage as a function of individual characteristics such as age or education (in our case, the logarith of wage is a function of the logarith of age, of the skill level and of the educational attainent), and the other one, the selection euation, which easures the likelihood of observing the wage (i.e. the likelihood of working) as a function of soe individual characteristics. In the estiation of our selection euation, we used as explanatory variables sex and the logarith of age, which is in turn supposed to deterine the wage too. With the two-step procedure, the selection euation is estiated through a probit odel, and then the estiated paraeters are used to calculate the Inverse Mills Ratio. The value of the latter is included as an additional explanatory variable in the wage euation, which is then estiated with a siple OLS procedure. The results are reported in Table 2 below. The estiation was conducted on the sub-saple of individuals at working age (6-64). Table 2 Heckan Selection Model, Two-Step Estiates Dependent variable: logarith of wage Coefficient Std. Error z P> z constant ln(age) sex ualification education Mills ratio Selection ln(age) sex ualification children under region rho siga

16 The interpretation of the coefficients for the wage euation thus follows that of a siple linear regression. As we can observe in Table 2, age, schooling and skill level have a positive effect on the wage, while being a woan shows a negative effect. It is iportant to say that the ai of the wage euation within the odel is that of obtaining an efficient estiate for an eventual wage incoe only for those individuals that are observed to be inactive in the survey, in the case that, after a policy refor, one or ore of the will change their labour arket status and becoe wage workers. In this case, through these estiates, we will be able to assign an estiated wage to the individual that has changed his/her labour arket status after the siulation run. For all the other individuals that are observed to receive a wage in the survey, we use instead the observed wage level and not the estiated one. Paraeters of euation (B.2) were obtained through the estiation of a binoial logit odel, assuing that the residual ters ε i are distributed according to the Extree Value Distribution Type I. The estiation was conducted on the sub-saple of individuals at working age (6-64). Our explanatory variables include individual characteristics such as the logarith of predicted real wage, sex, skill and education level, the region of residence and a variable accounting for the presence or not of children under 6 years old in the household. The odel is estiated by Maxiu Likelihood. Results are presented in Table 3. A binoial odel states that the probability of observing the dependent variable assuing value one, given the explanatory variables (OCS i = Z i ), is eual to the cuulative distribution function of ε i (the Extree Value Type I distribution in our case), evaluated at β Z i, that is: β Z [ OCS = Z ] = F( β Z ) = exp( e i ) Pr. (B.8) i i i The Extree Value distribution (Type I) is also known as Gubel (fro the nae of the statistician who first studied it) or double exponential distribution, and it is a special case of the Fisher-Tippett distribution. It can take two fors: one is based on the sallest extree and the other on the largest. We will focus on the latter, which is the one of interest for us. The standard Gubel distribution function (axiu) has the following probability and cuulative density functions, respectively: x pdf: f ( x) = exp( x e ) x CDF: F( x) = exp( e ). 86

17 Table 3 Binary Logit Model for Labour Status Condition Dependent Variable: Activity Status Coefficient Std. Error z-statistic Prob. 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.0220 Log likelihood Hannan-Quinn criter Avg. log likelihood The effects that the explanatory variables have on the dependent binoial variable are not linear, because they get channelled through a cuulative distribution function. Thus, by observing the values and signs of the estiated coefficients, we can say soething about the effect that explanatory variables have on the probability that the dependent binoial variable takes value one (wage worker), relatively to the probability that it takes value zero, but not in a linear way. For instance, expected real wage and ualification see to influence in a positive way the probability that the dependent variable takes value one (the ore ualified the individual is, the higher is the probability for hi/her to be eployed), as well as the presence of children under 6 does, which is the opposite of what was expected, but anyway this result is not significant. Moreover, for en the probability of being eployed is higher than for woen, as the variable SEX, which takes value zero for en and one for woen, shows a negative coefficient. The sae can be said about the region of residence: people living in the first region have a higher probability of being eployed than people living in the second one. The variable referring to education, instead, sees to have a negative influence on the probability of being eployed, which is the opposite of what we expected, and anyway it is not highly significant. However, with the estiated coefficients we cannot perfectly predict the true labour arket statuses that are actually observed in the survey. Thus, following the procedure 87

18 described in Duncan and Weeks (998), we 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 conditions. Fro these drawn values, we select 00 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 individual that is observed to be a wage earner in the survey should be such that: α ˆ β Log( RW ) + ˆ β SEX + ˆ β Q + ˆ β AREA + ˆ β CH 6 + ˆ β SCH + ε 0, ˆ + i 2 i 3 i 4 5 i 6 i i > 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 alternative, 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 The CGE Model The CGE odel for the fictitious econoy 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 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 2 This procedure is also described in Creedy and Kalb (2005). See also Creedy et al. (2002b). 88

19 factors of production, capital and labour, are obile aong sectors. The capital endowent is exogenously fixed, while labour supply is endogenously deterined through household s 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 s incoe and tariffs on iported goods, while it pays transfers to the representative household. For the foreign sector we have adopted the Arington assuption 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). Table 4 SAM of the Econoy C C 2 S 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 : sector ; K: capital account; L: labour account; H: representative household account; G: public sector; SI: savings-investents account, RoW: Rest of the World account. 89

20 In the odel there are in total 49 variables and 4 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 allows 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, in such a way that the benchark situation is consistent with that of the icrosiulation odule (for instance, in the benchark of the two odels we 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 for the econoy under study and the initial values of soe other variables are reported in Tables 4 and 5, while the euations of the odel can be found in Table 6 below. The data in the SAM are in illions of the onetary unit we have used for the survey. Table 5 Values of Paraeters for CGE Model Sector Sector 2 Elasticity of substitution 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)

21 Table 6 Euations for the CGE Model Deand for consuption goods CBUD H C P = α =,2 C. Leisure ( ) [ ] ( ) CBUD H H PL ty C l l l = α α C.2 Labour supply l C TS LS = C.3 Savings ( ) Y ty ps S = C.4 Consuer price index = = 2 H P PC α C.5 CES production function ( ) ( ) ( ) ( ) + = F F F F F F L F K F af XD γ γ C.6 CES FOC for capital ( ) ( ) ( ) [ ] ( ) F F F F F F F PL F PK F PK F af XD K γ γ γ + = C.7 Deand for investent goods S I I P = α C.8 Price of iports in local currency ( ) ER PWM t PM + = C.9 Price of exports in local currency ER PWE PE = C.0 Arington function ( ) ( ) ( ) ( ) + = A A A A A A XDD A M A aa X γ γ C. Arington FOC for iports ( ) ( ) ( ) [ ] ( ) A A A A A A A PDD A PM A PM A aa X M γ γ γ + = C.2 9

22 XD = at CET function ( T ) T γt E + γt ( ) T ( T ) ( T ) T XDD C.3 CET FOC for exports Market clearing condition for labour E XD = at γt PE T ( ) ( ) [ ( ) ] ( T T ) T T T γt T PE + γt PDD 2 = L + LG = LS C.4 C.5 Market clearing condition for capital 2 = K + KG = KS C.6 Market clearing condition for coodity XD + C ( + t ) 2 + M = s= + I + E io s XD + CG + C.7 Incoe definition Disposable incoe inus savings CBUD ( ty) Y S Y = PK KS + PL LS + PC TF C.8 = C.9 Zero profit condition in production function PD + 2 s= XD io s = PK K XD PD s + PL L + C.20 Zero profit condition in Arington function Zero profit condition in CET function Deand of coodity by governent P X = PM M + PDD XDD C.2 PD XD = PE E + PDD XDD C.22 ( TAXREV PC TF ) P CG = α CG C.23 Deand of capital by governent PK KG = KG ( TAXREV PC TF ) Deand of labour by governent PL LG = LG ( TAXREV PC TF ) α C.24 α C.25 2 Tax revenues = ty Y + ( t PWM ER) TAXREV C.26 = Nuber of variables: 49 Nuber of euations: 4 Nuber of exogenous variables: 8 Walras law satisfied Model hoogeneous of degree one Exogenous variables: - capital endowent (KS) - tie endowent (TS) - public transfers (TF) - world prices (PWE and PWM ) - nueraire: consuer price index (PC) 92

23 Variables: PK return to capital PL wage rate P Arington coposite good price PD output price PM iport prices in local currency PE export prices in local currency ER exchange rate (nueraire) PC consuer price index KS capital endowent (exogenous) LS labour supply (endogenous) TS tie endowent (exogenous) X doestic sales-arington coposite XD doestic output M iports E exports K capital deand by firs KG capital deand by governent L labour deand by firs LG labour deand by governent I deand for investent goods C deand for consuption goods C l deand for leisure CG governent coodity deand Y RH's incoe S RH's savings CBUD RH's disposable incoe TF public transfers to RH (exogenous) PDD price of doestic production delivered to doestic arket XDD doestic production delivered to doestic arkets PWE export prices in foreign currency (exogenous) PWM iport prices in foreign currency (exogenous) TAXREV tax revenue Paraeters: ty t ps io s af γf F αh αh l αi αcg αkg αlg aa γa A at γt T ε_ls direct incoe tax rate tariff rate on iports RH s arginal propensity to save technical coefficients efficiency paraeter of fir s production function share paraeter in CES production function elasticity of substitution in CES production function C-D power of coodity in RH s utility function C-D power of leisure in RH s utility function C-D power of good in Bank s utility function C-D power of coodity in gov. s utility function C-D power of capital in governent s utility function C-D power of labour in governent s utility function efficiency paraeter in Arington function share paraeter in Arington function elasticity of substitution in Arington function efficiency paraeter in CET function distribution paraeter in CET function elasticity of transforation in CET function wage elasticity of labour supply 3.3. Linking the Models The basic difficulty of this approach is to ensure 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 3. In practice, this consists in iposing the acro results obtained with the CGE odel onto the icroeconoic level of analysis. In particular: ) changes in the coodity prices, P, ust be eual to those resulting fro the CGE odel; 3 This way, what happens in the MS odule can be ade consistent with the CGE odelling by adjusting paraeters in the MS odel, but, fro a theoretical point of view, it would be ore satisfying to obtain consistency by odelling behaviour identically in the two odels. 93

24 2) 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; 3) changes in the return to capital of the icro-siulation odule ust be eual to the sae changes observed after the siulation run in the CGE odel; 4) changes in the nuber of wage workers in the icro-siulation odel ust atch those observed in the CGE odel. For our odel, these consistency conditions translate into the following set of constraints, which could be called linking euations: C CE = (M.) Consuption levels: CGE ( + ΔP ) Logarith of wage Log( YL ) ( CGE ) earnings: i = Log YLi + ΔPL CGE Capital incoe: YK KS ( + ΔPK ) Eployent level: 24 NC = i= 24 NC = i= [ ] ˆ (M.2) = (M.3) Wˆ i WA i 00 = ΔEMP CGE (M.4) 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 YLˆ ( i ) is the wage level resulting fro the regression odel for individual i, eber of household, while Wˆi is the labour arket status of individual i of household deriving fro the estiation of the binoial choice odel. CGE Δ, ΔPL and CGE P CGE Δ PK 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 change fro the CGE. CGE Δ EMP is the eployent level percentage 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 (M.4), the nuber of eployed over the total nuber of individuals at working age resulting fro the MS odel ust be eual to 94

25 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) 4. One possible way of iposing the euality between the two sets of paraeters of syste of euations (M) is through a change in the paraeters of the selection and regression odels. Following Bourguignon et al. (2003b), we restrict this change in the paraeters to a change in the intercept of the two functions (B.) and (B.2). The justification for this choice is that it iplies neutrality of the changes, that is, changing the intercepts a of euations (B.) just shifts proportionally the estiated wages of all individuals, without causing any change in the ranking between one individual and the other. The sae applies for the activity status choice euation: we choose to change the intercept α of euation (B.2), and this will shift proportionally all the individual probabilities of being a wage worker, without changing their relative positions in the probability distribution, only to let 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 And, in this case, his/her new wage level will be deterined by the regression odel of wage earnings. 95

26 4. THE TOP-DOWN/BOTTOM-UP APPROACH This approach was developed by Savard (2003). It allows overcoing the proble of 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: this is the reason why this approach is also called Top-Down/Botto-Up. According to this ethod, indeed, aggregate results fro the MS odel (such as consuption levels or labour supply) are incorporated into the CGE odel, and a loop is used to run both odels 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 instead copletely disregarded by the Top-Down odel. The basic assuption behind this 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 Figures 5 and 6 (Chapter, pages 59-60). 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 the counication is guaranteed by the changes in the price, wage and return vector and in the eployent levels, as before, while fro the icro to the acro level the counication we apply two different strategies: in one version, we will 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 5 ; in another version of the sae odel, only the 5 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, we have to change soe of the initial hypothesis of the odel. First, we reove the euations deterining consuption deand by the representative household (euation C. in Table 6), substituting the with the following single euation: CBUD = 2 i= P i C i. In the initial hypothesis (endogenous consuption) we had 2 endogenous variables (Ci) and 2 euations. Now we have 2 exogenous variables and one euation. As we need to insure the balancing of the household s budget constraint, a variable needs now to be endogenized 96

27 change in the labour supply level which results fro the MS odel will be used as input for the CGE odel 6. The process is iterated as any ties as it 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. 5. SIMULATION We will now run a policy siulation with each of the three odels. The siulation will be an exogenous shock on the world price level of the good exported by sector 2, which is the labour intensive sector in our stylized econoy. The world price of good 2 is reduced of 64% fro its initial value. The siulation results for the ost relevant acroeconoic variables are reported in percentage changes in Tables 7 and 8. In the tables, also the two different strategies adopted for the TD/BU approach are taken into account, so that we will copare the results coing fro the introduction into the CGE odel of, respectively, the consuption level and the labour supply coing fro the icrosiulation odule, and only the labour supply. In general, we can say that we have very siilar results for ost of the acro variables in all the four siulations. The shock has negative effects on the econoy. Indeed, as we can observe in Table 7, 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 ( ps) ( ty) ( PK KS PL LS PC TF) in the following euation: CBUD = + +. Following Savard, we 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, we introduce an exogenous level of labour supply into the CGE odel, and just leave out the euation that deterines the deand for leisure (euation C.2 in Table 6). This way, euation C.3 will now yield the deand for leisure as the tie reaining after having supplied an exogenous level of labour. 6 In this case, we only introduce an exogenous level of labour supply into the CGE odel, just leaving out the euation that deterines the deand for leisure (euation C.2 in Table 6). 97

28 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 convenient, so that for this sector we 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 has a negative effect on the level of iports, which contributes to a decrease of the aount of goods sold on the doestic arket. The lower level of labour deand as a whole (the second sector is labour-intensive, as can be observed in the SAM, Table 4) generates a reduction in the wage rate, which causes a decrease in labour supply. The opposite is observed for capital, as the first sector is ore capital-intensive. As a conseuence of the change in the price of the factors, governent increases its deand for labour input and decreases the deand for capital, as the latter has becoe relatively ore expensive. As the incoe of the representative household is based chiefly on the supply of labour, we observe a reduction in noinal incoe and, as a conseuence, of savings and consuption expenditure. The aount of consuption goods always decrease, but the percentage change varies according to the change in their relative price: the coodity produced by the second sector has becoe relatively ore expensive, due to the negative shock that hit the sector. As investents are savings-driven, we observe also a reduction in the deand for investent goods (again, the investent good produced by the second sector is now relatively ore expensive, so we observe a higher reduction for the deand of this good). 98