7 Calibration, Solution and Validation of the CGE Model

189

Sánchez C., M.V. (2004), Rising inequality and falling poverty in Costa Rica’s agriculture during trade reform. A macro-micro general equilibrium analysis, Maastricht: Shaker. Chapter 7, pp. 189-226, and related appendices.

7 Calibration, Solution and Validation of the CGE Model

7.1 Introduction

Having made the choice of the functional form of the CGE model and constructed a data set in the form of a SAM, this study now explains the procedure that was followed to solve the model. This was a crucial step prior to moving to the implementation of the policy simulation analysis that was required to shed light on the remaining unanswered questions of the study. The solution of a CGE model entails finding parameter and elasticity values to feed the model equations. This commonly involves rigorous data gathering to ensure that the real structure of the economy being modelled is approximated as much as possible. Since in our case the data gathering already started with the compilation of the SAM, this chapter elaborates on the way in which the appropriate handling of the matrix transactions allowed computation of the model parameters using the calibration procedure. The chapter also explains the way in which the calibration procedure was completed by including own estimates of elasticity values and an exogenous update of parameters and variables using actual trends. Having indicated that the calibration procedure enabled solution of the CGE model, the chapter also shows that the model yielded a base-line whose trends quite well approximate the actual trends of the Costa Rican economy.

The calibration method and the steps followed to generate the static and dynamic general equilibrium model solutions are explained in detail in Section 7.2. The limitations and advantages of the calibration method are also highlighted in this section. A thorough presentation on the computation of SAM-based parameters and model elasticity values is included in Section 7.3, where some space is also devoted to explaining that the calibration is completed by including factor quantity and other exogenous information. Section 7.4 validates the model solution that is yielded by the calibration procedure, where the main purpose is to show the extent to which the model’s trends replicate actual trends during 1997-2002. Some remarks are also made in this section regarding the

190 Chapter 7

sensitivity of the model to elasticity values. Section 7.5 summarizes the main conclusions of the chapter and indicates the way forward.

7.2 Calibration method

7.2.1 Calibration and bench-mark equilibrium

The parameter and elasticity values that feed the equations of the CGE model are crucial to assess the impact of trade policy shifts. The parameter values are calculated using a calibration method that enables the static module equations to generate a base-year equilibrium observation or short-run solution. The calibration method relies on the assumption that the economy is in equilibrium. This is established by a bench-mark data set that represents an equilibrium for the economy so that the model is actually solved from equilibrium data for its parameter values rather than vice versa (Shoven and Whalley, 1992:103). In our particular case, the bench-mark data set is systematically represented in the compiled SAM. Equilibrium exists because the SAM is square and row and column sums for a given account are equal because all income must be accounted for by an outlay of one type or another (Pyatt and Round, 1979:854).

The calibration process is outlined in Figure 7.1. The first stage is the choice of functional form for the static module, which was already made in Chapter 5. The static module equations are fed with data in the second stage. All parameter and variable values are obtained from the SAM, although elasticity values and factor stocks data are found elsewhere. Since the SAM is estimated in value terms, units must be chosen for goods so that separate price and quantity observations are obtained (Shoven and Whalley, 1992:105). Following Harberger (1962), the ‘units convention’ is used, whereby units for goods are chosen so that they have a price of unity in the base year. This also involves setting the value of exogenous prices at unity in the base year. In this way, the bench-mark solution is expected to represent the state of the economy in real terms. A computer-based replication check is applied in the third stage using an accuracy test of computer code, which fails if a programming error arises when the model, via an iterative process, seeks the set of equilibrium prices. If such were the case, the functional form of the model would prove inconsistent with the data set, possibly due to unfeasible elasticity values or inappropriate sectoral breakdown.1 The replication check does not fail if a bench-mark equilibrium is reached, which is basically the case when, after the model has been fed with data, each quantity value generated in the model reproduces its corresponding value in the SAM. After this stage, any change in exogenous variables or parameters must generate a new data set from a new static equilibrium condition. If that were not the case, elasticity values would necessarily have to be investigated further.

Calibration, Solution and Validation of the CGE model 191

Figure 7.1 Flow chart outlining the calibration method

Choice of functional form for static module

Feeding of the stat ic module equations

SAM-based parameter and variable values

Exogenous elast icity values and factor-stock data

Computer-based replicat ion

Benchmark within-period equilibrium solution

Exogenous change check Dynamic calibrat ion

New stat ic equilibrium solut ion

Exogenous variable value update

New exogenous parameter and variable values

Second within-period equilibrium solution for dynamic solution

Exogenous variable values update

New within-period equilibrium solution for dynamic solution

Choice of functional form for dynamic module

Computer-based iterat ive process

Computer-based iterat ive process

7.2.2 From bench-mark to dynamic equilibrium solution

The bench-mark equilibrium solution provides not only the static model solution but also the equilibrium data set for a second within-period equilibrium solution (see Figure 7.1). The choice of functional form for the dynamic module is made at the same time, which in our case has already been presented in Chapter 5. While the bench-mark parameters and elasticities are kept constant, the dynamic calibration also entails updating some exogenous variable values set at unity in the bench-mark solution and including new exogenous variable and parameter values.2 A new computer-based iterative process generates the second within-period equilibrium solution. Keeping elasticity values constant, the second

192 Chapter 7

solution provides the equilibrium data set for a new within-period equilibrium solution that is obtained after updating exogenous variable values, again via a computer-based iterative process. This procedure is carried out recursively until the complete dynamic solution is obtained (see Figure 7.1). Each within-period equilibrium solution also provides variable values that are used as lagged values for the next within-period equilibrium solution.

7.2.3 Some caveats on method

The calibration method is a deterministic approach to calculating parameter values from a bench-mark equilibrium data set. Consequently, no statistical test of the model specification is used, except for the computation of elasticity values where, in a partial equilibrium framework, part of the structure of the model is simplified to allow for statistically feasible specification. Econometric work simplifies the structure of the model to allow substantial richness in statistical specification, while the richness of the economic structure alone provides only a much cruder statistical model that, in the case of calibration to a single year’s data, becomes deterministic (Shoven and Whalley, 1992:106). As a result, econometricians view the calibration method with scepticism (see, for example, McKitrick, 1998). The method, however, remains widely used for various reasons. Accounting for the model sector-factor-institution breakdown implies that many hundreds and sometimes thousands of parameter values are needed to solve the model. The simultaneous stochastic estimation of all these parameters would be unrealistic due to the scarcity of data in developing countries, the required sophistication of techniques, and the need for severe identification restrictions (Gunning and Keyzer, 1995; Lau, 1984). The major advantage of the calibration method is that only a few data are needed because the parameter estimation requires only one observation (which may, however, involve gathering a great deal of data when a SAM is estimated). In spite of these reasons, it may still be arguable that calibrated parameters may be unreliable due to the arbitrary choice of the bench-mark year (see Thissen, 2000, for a similar critique).

The bench-mark year of the Costa Rican CGE model is 1997 for various reasons. First, as explained in Chapter 3, the most profound structural shifts took place in the late 1980s and early 1990s; therefore, significant changes in the economy’s structure are not observed in 1997. Profound structural changes may affect the general equilibrium linkages in the economy, particularly from one period to another (Taylor, 1990). Second, the data for 1997 reproduce the relatively stable macro-economic performance observed during 1991-2002. Third, the trade policy reform in 1997 was a continuation of a process that initiated in the mid-1980s as part of the structural adjustment reforms. Fourth, from a practical point of view, the amount of data required for the compilation


of the SAM was entirely available for 1997. Fifth, using 1997 as the bench-mark year allowed us to include actual trends for the 1998-2002 period in the updating of exogenous variable and parameter values. This enhanced the dynamic calibration since no assumption had to be made regarding future socio-economic trends.

In order to account for all the equilibrium restrictions that are emphasized in calibration, stochastic estimation was only used for estimating elasticity values. As will be explained below, partial-equilibrium model specifications were estimated, which are, as much as possible, in line with the CGE model specification. The standard calibration problem solved was the following:

F(Ys, X; β, ε) = 0; subject to: Ys = Ya and ε = 0

where Ys and Ya are, respectively, vectors of the simulated and actual i endogenous variables in the model, X is a vector of exogenous variables in the model, β is a vector of unknown parameters (including elasticities), and ε is a vector of i stochastic disturbances.

Unlike the stochastic approach, which assumes a distribution for the vector ε, the calibration method assumes that the stochastic disturbances are zero. Given this assumption and using only one observation for the base year, the calibration method allows a solution of the resulting system of equations whereby the vector of parameters β includes the unknown values.3 The determination of some unknown parameter values depends on elasticity values that are estimated stochastically. As will be shown below, knowing the vector Ys from the SAM, including stochastically estimated elasticity values, and turning X into a vector of ones for all exogenous prices, except for a few exogenous variables which are also known from the SAM, enables the estimation of the vector β. Some refinements to the calibration method have been proposed, which entail adjusting the calibrated parameters to improve the model’s achievements over time and give tests about the performance of the model (see, for example, Thissen, 2000; Charemza, 1998). As will be demonstrated below, there was no need to refine the method which, given the SAM-based parameters, the elasticity estimates, and the exogenous parameter and value update, enabled the author to compute socio-economic trends from the CGE model that reproduce the corresponding actual trends quite reasonably.

194 Chapter 7

7.3 Parameters, elasticities and exogenous variable update

7.3.1 Computation of SAM-based parameters

As explained in Chapter 6, the SAM is a transaction matrix T, where tij is a payment from column-account j to row-account i. A SAM coefficient matrix A can be derived by dividing the cells in each column of T by the corresponding column sum. By using these conventions, the transaction values represented in the SAM provide initial values for the model endogenous variables (except for factor quantities), which are in turn the main input data required to estimate the model parameter values. Such a connection between the SAM and the model is possible because the SAM transactions values are calculated from algebraic expressions that are underlined by theory (Pyatt, 1988:328). According to the transactions value (TV) approach, the SAM can be filled with equations that describe in conceptual terms how the corresponding transaction values might be determined (ibid.:337). It is possible to demonstrate that, in line with the TV approach, the determination of transaction values in the Costa Rican SAM is consistent with the algebraic accounting identities that form the CGE model. Accordingly, a block of equations was used to estimate base-year values for the model endogenous variables using the transaction values of the SAM (see Appendix H, Table H.1). The base-year endogenous variable values were subsequently used to estimate the model parameters using another block of equations (see Appendix H, Table H.2).

The estimation of model parameters for the CES, CET and LES functions still required some additional work. The value of the function exponent parameter (ρ) in CES and CET functions is respectively calculated as follows:

ρ = (1 - σ)/σ (7.1) ρ = (-1 +σ)/σ (7.2)

where, σ is the elasticity of substitution in CES functions (eq. 7.1) or elasticity of transformation in CET functions (eq. 7.2) the values of which are estimated econometrically, as will be explained in the next subsection. The higher the value of σ, the smaller the value of ρ and the larger the optimal change in the quantity ratios in both types of functions in response to a change in relative prices. Therefore, both the degree of substitutability and transformability in CES and CET functions respectively will depend on the value of ρ and hence on the value of σ.4

Values for the marginal budget share of consumption spending (βch) and the subsistence consumption parameter (γch) which are required to calibrate LES functions are, respectively, calculated as follows:


αξβ chchch⋅= (7.3)

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+⋅

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

ℑh

chch

c

h

ch PQEH β

αγ (7.4)

where, αch represents the average budget shares; ξch is the income elasticity of demand (that is, Engel elasticity), ℑh is a parameter measuring the elasticity of the marginal utility of income with respect to income, often labelled as the Frisch parameter (Brown and Deaton, 1972; Frisch, 1959); EHh stands for consumption expenditure by household type; and PQc is the commodity consumer price.5

The value of αch and the base-year values of EHh and PQc are determined from the SAM (see Appendix H). The estimates of ℑh are based on cross-country studies in Lluch, Powell, and Williams (1977) according to which this parameter rises from -7.5 to -2.0 as per capita income rises from $100 to $3,000 (in 1970 US dollars). In the base year, Costa Rica’s GDP per capita was about $3,922 (in 1997 US dollars). Also, according to household survey data, mean incomes in 1997 were about $4,494 and $2,359 per person for urban and rural households, respectively. Given these mean incomes (in 1970 US dollars), the Frisch parameters were found to be approximately -1.8 and -3 for urban and rural households, respectively. The calibration of the LES functions was completed using own estimates of the income elasticity of demand, as will be explained below.

7.3.2 Role of elasticities in the model and elasticity value estimation

The elasticity values that feed the CGE model equations play a crucial role in the functioning of the model and consequently affect the results of policy and external shock simulations. As explained in Chapter 5, CES and CET functions entail optimization problems. The producer minimizes costs by finding the optimal quantity mix between value-added and intermediate consumption and production factors. The producer also maximizes profits by finding the optimal combined use of domestic output for domestic sales and exports. The consumer, on the other hand, faces the cost minimization problem of finding the optimal consumption mix between domestically produced goods and services and imported goods and services. The variation in relative prices is the adjustment mechanism through which an optimal ratio for the mix of all the quantities involved in the producer and consumer problems is found, given the function constraints. In turn, the degree of response of quantity ratios to relative price shifts depends on the values of elasticities of substitution and transformation. Furthermore, resource reallocation via changes in quantity ratios is also affected by elasticity values in the endogenous productivity growth function in

196 Chapter 7

agriculture, whereas the response from workers to a new resource allocation leading to changes in wages is affected by elasticity values in the labour supply function of agricultural and formal sector workers. The change in labour incomes affects household income, leading to final demand shifts that are simultaneously affected by income elasticities of demand in the LES functions.

In the absence of elasticity data or sufficient information to estimate them, it is common practice in the calibration of CGE models to borrow elasticity values from published data for countries whose level of development is similar to that of the country whose economy is being modelled. This practice is frequently complemented with educated guesses after observing production and consumption structures and the flexibility of sectors relative to trade shifts. Furthermore, the elasticities of substitution in both CES (Armington) and CET functions are very often given equal values for the same commodity regardless of the different underlying assumptions in the two functions. Also, in both functions the elasticity values are, almost as a general rule, assigned in descending magnitude from the primary to tertiary sector’s commodities. Although at times they are the last remaining resource to use, these practices do not increase the reliability of the parameters of the CGE model. These practices have commonly been used to calibrate CES, CET and LES functions in CGE models constructed for Costa Rica (see, for example, Cattaneo et al., 1999; Dessus and Bussolo, 1996). Other studies have used upper and lower bounds for all the model elasticities based on separate pieces of general econometric evidence for Costa Rica and developing countries and own intuition regarding plausible values from a medium-run perspective (see, for example, Sauma and Sánchez, 2003; Abler et al., 1999ab). The standard approach to elasticity value assignation is avoided in this study and, instead, an effort is made to estimate the model’s elasticities as allowed by the data availability. The remainder of this section is devoted to explaining the estimation of elasticity values.

Elasticities of substitution As explained in detail in Appendix I, a demand equation system was derived as a first order approximation of a CES function, yielding the following estimable equation:

log ζ = a + b log p + ct + d1cri + d2ref (7.5)

where, ζ is the quantity ratio in the CES function,6 p is a relative price index that measures the ratio of the implicit price deflators of the quantities in ζ, t is a time trend term, cri and ref are dummy variables that account for the debt-crisis and structural-adjustment reform episodes, respectively. The estimate of b plus one yields the estimated value of the elasticity of substitution σ (that is, σ = b + 1), whereas the estimate of a captures the combined effect of the elasticity of


substitution, the function shift parameter, the function share parameter and relative prices.

The time trend term and the two dummy variables are not part of the CGE model. Their inclusion in equation (7.5) is not trivial, though, since it improves the estimation of the elasticities of substitution. The time trend term may be important to take into account for changing tastes over time, such that misspecification is avoided (Hickman and Lau, 1973:349). In general, it is possible to say that adding up a time trend term somehow allows for omitted variables that are correlated with time and should also tend to reduce the misspecification bias in estimates of the elasticity of substitution. In fact, as will be explained below, in the estimation of 17 different elasticities of substitution, there was only one case in which the time trend term was found to be not statistically different from zero. As explained in Chapter 3, the Costa Rican economy hit bottom in 1980-83 as a result of the debt crisis, whereas the structural reforms began to be implemented right after the economy was stabilized in 1983-85. Given the use of relatively long time series for the estimation of equation (7.5) (that is, for the 1966-2000 period), ignoring the periods of debt crisis and structural-adjustment reform may have created a bias in the estimation of elasticities. This is the main reason why the two dummy variables were included in equation (7.5), activating for the periods 1980-83 and 1984-2000, respectively. As will be shown below, the inclusion of the dummy variables improved the estimation of elasticities in various cases.

Equation (7.5) was estimated separately for nine commodity groups as a derivation of the composite-supply (Armington) function, using time series analysis for the 1966-2000 period. The most satisfactory results after estimating different specifications of equation (7.5) are summarized in Table 7.1, according to which the use of the composite-supply function turned out to be feasible from the statistical point of view. The estimates of the relative-price index coefficients were found to be statistically different from zero at standard significance levels.7 The hypothesis that imports and domestic output sold domestically are imperfect substitutes could not be rejected for all commodity groups. Overall, the degree of substitution between imports and domestic output was found to be low, presumably for three plausible reasons. First, import shares of output in agriculture are not high in a country that is a net exporter of agricultural commodities and which, in most cases, does not produce the same agricultural commodities it buys from abroad. Second, even though import shares of output in manufacturing are much higher compared with agriculture, increased openness may have allowed consumers to purchase newly available manufactured goods from abroad that do not compete with domestic output very much. The fact that manufacturing has grown remarkably during the opening of trade, as indicated in Chapter 3, may actually be an indication that domestic producers in that sector have not been affected seriously by more import

198 Chapter 7

competition. Third, services have historically been of a non-tradable nature, for which the share of imports in the service sector has typically been very low.

Table 7.1 Estimation results for the import demand function by commodity group, 1966-2000 (t-values in parentheses)

Commodity group 0>a>0 0>b>0 0>c>0 0>d1 0>d2>0 R2 DW* σ = b + 1

-11.7417 -0.0460 0.0064 -0.0797 -0.1948 (-1.6119) (-9.5402) (1.6208) (-1.7178) (-2.0885)

Domestic-consumption agriculture2/ b/ a/ b/ b/ a/

0.96 1.98 0.9540

-85.9972 0.4155 0.0432 -1.3613 -0.9366 (-1.9300) (1.8173) (1.9253) (-2.4269) (-2.4918)

Traditional export agriculture 1/ a/ a/ a/ a/ a/

0.24 1.93 1.4155

-24.1522 0.8382 0.1086 -0.2166 (-4.5511) (1.7687) (4.5618) (-1.7040)

Non-traditional export agriculture2/ a/ a/ a/ b/

(-) 0.98 1.84 1.8382

-12.9477 -0.1841 0.0065 -0.0428 0.0922 (-1.9314) (-2.4647) (1.9298) (-1.7010) (1.8941) Food

industries2/ a/ a/ a/ b/ a/ 0.32 1.80 0.8159

-10.4864 0.0282 0.0053 -0.0589 0.2047 (-1.7029) (1.3221) (1.7027) (-1.9769) (2.6089) Oil and

chemicals2/ a/ b/ a/ b/ a/ 0.44 1.90 1.0282

-17.9709 0.1966 0.0091 0.0114 (-2.4826) (1.7977) (2.4891) (1.6993) Manufacturing

(other) 2/ a/ a/ a/

(-) a/

0.49 1.87 1.1966

9.3524 -0.0498 -0.0047 (4.8013) (-1.3488) (-4.8707)Transport2/

a/ b/ a/

(-) (-) 0.46 1.69 0.9502

22.8217 -0.5246 -0.0115 (6.6606) (-2.7171) (-6.6868)Financial

services2/ a/ a/ a/

(-) (-) 0.62 1.91 0.4754

-47.2174 -0.5117 0.0239 (-2.7834) (-1.3146) (2.9223) Other

services1/ a/ b/ a/

(-) (-) 0.46 1.94 0.4883

Notes: * The range of acceptance of the hypothesis of no autocorrelation for 35 observations at the 5

per cent significance level is: 1.653 – 2.347 for three coefficients, 1.726 – 2.274 for four coefficients, and 1.803 – 2.197 for five coefficients.

1/ The regression results for this commodity group are from an OLS equation. 2/ The regression results for this commodity group are from a generalized difference equation. (-) The coefficient was dropped from the initial equation due to lack of statistical significance. a/ Coefficient statistically significant at the 5 per cent or lower significance level. b/ Coefficient statistically significant at the 10 per cent significance level.


The debt-crisis was found to have reduced the share of imports in agriculture, food industries, and oil and chemicals. The reform seems to have affected import shares negatively in the traditional agricultural sectors but positively in manufacturing. The reform dummy variable was not found to be statistically significant for non-traditional export agriculture, probably because the effects of rises in the share of imports encouraged by the import liberalization in some sub-periods were undermined by previous or subsequent drops.8 Despite the fact that the reforms encouraged the development of tertiary sectors, as pointed out in Chapter 3, economic activity in these sectors did not entail important shifts in imports and was instead driven by a growing domestic supply of services coupled with a positive domestic demand response.

The elasticity value estimates for the nine commodity groups were assigned to the 12 importable commodities in the CGE model (see Statistical Appendix, Table A7.1). The estimate for manufacturing (other) was retained for the manufacturing commodity groups in the model, excluding food industries and oil and chemicals, the elasticity values of which were directly estimated. The estimate for transport was assumed to be the same for transport, storage and communication. Once all importable commodities in the model had been given a value for the elasticities of substitution, the Armington function exponent (ρc

m) was calculated from equation (7.1).9 The relatively low degree of substitution between imports and domestic output implies that changes in the domestic import price triggered by the manipulation of import tariffs would only result in a modest change in the domestic sales price, as will be observed Chapter 8.

Data availability only permitted the estimation of equation (7.5) for, on the one hand, two aggregate activities in the case of the value-added quantity share of total activity level and, on the other hand, six activity groups in the case of the labour share of total value-added quantity. The results turned out to be statistically robust for the specifications presented in Tables 7.2 and 7.3, respectively.10 The specifications chosen yielded statistically different from zero estimates for all the relative price coefficients. Hence, value-added and intermediate consumption on the one hand, and labour and capital on the other hand, were found to be imperfect substitutes in the aggregate activity groups. The low degree of substitution between value-added and intermediate consumption suggests that there is a great deal of complementarity between both components of gross domestic output. Given the relatively higher industrialization in manufacturing, the estimated elasticity of substitution between value-added and intermediate consumption in that sector was found to be higher than in agriculture (see Table 7.2). The fact that for the two aggregate activities the reform dummy variable was found to be statistically significant and negative is an indication that the reforms increased the share of intermediate consumption in gross domestic output relative to that of value-added. This change in the technology composition is consistent with the observed increase in

200 Chapter 7

imports during the trade policy reform, with imported intermediate goods being more freely available.

Low estimates of elasticities of substitution between labour and capital were also found for all the activity groups, in particular agriculture. This result suggests that skill and training requirements are to some extent high in the economy and supports the argument that the scope for substitution between labour and capital is low. Scarcity of data impeded to perform the estimation of the elasticity of substitution between skilled labour and capital and between different types of labour. The evidence presented in previous chapters suggests that capital and skilled labour became more complementary. It is likely that, as a result, the elasticity of substitution between skilled labour and capital is lower than that between unskilled labour and capital, which is possibly the explanation for the very low elasticities of substitution between aggregate labour and capital found after estimation. The reform dummy variable was found to affect labour shares of value-added positively in all activities, except in trade and services (see Table 7.3). This is another indication that the structural adjustment reforms affected the labour market, somehow pushing up the share of labour in value-added.

The estimated elasticity values for the aggregate activity groups in Tables 7.2 and 7.3 were retained for the corresponding sub-sectors in the CGE model (see Statistical Appendix, Table A7.1). Given the scarcity of data, no elasticity of substitution could be estimated for the activity-production function in the services sectors. The lower bound value for these sectors’ elasticity in the CGE model feasible solution range was therefore used (see Statistical Appendix, Table A7.1). Once all the elasticities of substitution had been assigned to all the activities in the model, the activity function exponents were computed from equation (7.1).11

Table 7.2 OLS estimation results for the value-added demand function by activity group, 1966-2000 (t-values in parentheses)

Activity group 0>a>0 0>b>0 0>c>0 0>d1 0>d2>0 R2 DW* σ = b + 1

21.0360 -0.4899 -0.0102 -0.3847 -0.2701 (1.9077) (-6.2722) (-1.8686) (-2.2428) (-1.3832)Agriculture

a/ a/ a/ a/ b/ 0.66 1.92 0.5101

-17.9976 -0.1993 0.0091 -0.0905 -0.0921 (-5.2661) (-3.4431) (5.2722) (-3.1525) (-2.5171)Manufacturing

a/ a/ a/ a/ a/ 0.76 1.84 0.8007

Notes: * The range of acceptance of the hypothesis of no autocorrelation for 35 observations and five

coefficients at the 5 per cent significance level is 1.803 – 2.197. a/ Coefficient statistically significant at the 5 per cent or lower significance level. b/ Coefficient statistically significant at the 10 per cent significance level.


Table 7.3 Estimation results for the labour demand function by activity group, 1976-2000 (t-values in parentheses)

Activity group 0>a>0 0>b>0 0>c>0 0>d1 0>d2>0 R2 DW* σ = b + 1

19.5930 -0.5780 -0.0093 0.0673 (5.9944) (-11.6791) (-5.8090) (3.7788)Agriculture1/

a/ a/ a/

(-) a/

0.92 1.78 0.4220

0.9557 -0.4959 0.0164 (7.4575) (-10.8559) (1.7480)Manufacturing2/

a/ a/

(-) (-) a/

0.84 1.80 0.5041

-17.1997 -0.5051 0.0095 0.0498 (-3.7349) (-12.7371) (4.0402) (1.7802)Construction2/

a/ a/ a/

(-) a/

0.91 1.77 0.4949

30.2910 -0.4695 -0.0148 0.0511 (13.7542) (-18.3524) (-12.9880) (3.3149)Basic

services1/, 3/ a/ a/ a/

(-) a/

0.99 1.88 0.5305

-6.3211 -0.5995 0.0034 (-2.1018) (-6.6087) (2.2947) Trade and

services2/, 4/ a/ a/ a/

(-) (-) 0.77 1.80 0.4776

40.0637 -0.5920 -0.0198 0.0659 0.1957 (5.6398) (-13.6558) (-5.4984) (1.7635) (3.0414)Other

services2/ a/ a/ a/ b/ a/ 0.95 1.98 0.4080


per cent significance level is: 1.654 – 2.346 for three coefficients, 1.767 – 2.233 for four coefficients, and 1.886 – 2.114 for five coefficients.

1/ The regression results for this activity group are from an OLS equation. 2/ The regression results for this activity group are from a generalized difference equation. 3/ Electricity, gas and water & transport, storage and communication. 4/ Wholesale and retail trade; restaurants, hotels and lodgings; and, financial services and

insurance. (-) The coefficient was dropped from the initial equation due to lack of statistical significance. a/ Coefficient statistically significant at the 1 per cent or lower significance level. b/ Coefficient statistically significant at the 5 per cent significance level.

Elasticities of transformation Export quantity shares of output level respond to relative price shifts in the CGE model, as indicated above. This relationship was imposed a priori using a restricted form of a complete export supply function, as explained in detail in Appendix I. Based on the form of the CET transformation function, whereby producers maximize per unit revenue from domestic and export sales, the restricted form for the export supply is set as in equation (7.6) (omitting superscript e and subscript c in the parameters for explanatory ease):

log(QEc/QXc) = a log δ0 + b log(PDc/PEc) +cε t + d1 cri + d2 ref (7.6)

202 Chapter 7

where the relative price coefficient (expected to be negative) is the elasticity of transformation, the intercept coefficient captures the effect of the function share parameter over time, the time trend term t accounts for the exogenous change in time and reduces the misspecification bias in the estimation, and d1 and d2 are the coefficients of two dummy variables that capture, respectively, the effect of the debt crisis and structural-adjustment reform episodes.

Various specifications of equation (7.6) were estimated for eight commodity groups. The most satisfactory results are summarized in Table 7.4 which in general indicate that the CET function is feasible from a statistical point of view.12 As expected, the relative price coefficient was found to be statistically different from zero and negative. The estimation results consequently suggest that the imperfect transformability assumption holds for the Costa Rican economy. The degree of transformability is relatively low, though, particularly in agriculture, food industries and services. This result is unsurprising for agriculture, which historically is a net export sector and whose output is not commonly constrained to satisfy the demand for exports first and then the domestic market. The more export-oriented the sector, the less the output constraint, and this is confirmed by the estimated elasticity values, which were found to decrease from domestic-consumption agriculture to non-traditional export agriculture (see Table 7.4).13 The values of the elasticities are expected to be low for services due to their non-tradable nature. In the case of the manufacturing commodity groups, a very low estimate of the elasticity of transformation was found for food industries, whereas relatively much higher estimates were found for the other commodity groups. For food industries, the explanation for such a finding relies on a similar argument to that given for agriculture. Since the country is a net importer of manufactured goods, transformation capacity for these goods is expected to be higher, especially for petroleum, which is not produced in the country.

The debt-crisis dummy variable was found to be statistically significant and negatively associated with export shares in all the commodity groups, except in non-traditional export agriculture which was an infant sector during the debt crisis. The reform dummy variable was found to be statistically significant, except for the manufacturing commodity groups, and it also turned out to be negatively associated with export shares in all cases except non-traditional export agricultural commodities. This evidently reflects the effect of deliberate export promotion and the reallocation of resources into non-traditional export activities. As pointed out in Chapter 3, the export promotion policies also targeted the drawback industry (maquila) and micro-processor production, especially under the perfeccionamiento activo y zonas francas regime. Yet, this was not confirmed by the regression results due to the limited disaggregation of the available data. The negative sign of the coefficient estimated for the services


groups is not surprising, given the steadily declining trend of export shares observed in services during the trade policy reform.

Table 7.4 Estimation results for the export-supply function by commodity group, 1966-2000 (t-values in parentheses)

Commodity group 0>a>0 0>b 0>c>0 0>d1 0>d2>0 R2 DW*

88.8301 -1.9199 -0.0447 -0.4164 -0.9109 (6.2939) (-12.5401) (-6.2388) (-3.5143) (-5.7686)

Domestic-consumption agriculture1/ a/ a/ a/ a/ a/

0.99 1.83

99.3825 -1.6825 -0.0497 -0.3441 -0.5142 (7.8291) (-3.4903) (-7.8929) (-6.3942) (-5.1631)

Traditional export agriculture2/ a/ a/ a/ a/ a/

0.97 1.81

74.7054 -1.5075 -0.0389 0.2463 (3.9404) (-1.7544) (-4.1751) (1.7653)

Non-traditional export agriculture2/ a/ b/ a/

(-) a/

0.78 1.98

95.9466 -0.8075 -0.0485 -0.0790 (32.1503) (-1.7886) (-32.7979) (-1.8640)Food

industries2/ a/ b/ a/ b/

(-) 0.97 1.99

73.5254 -4.0300 -0.0355 -0.0918 (6.9427) (-7.8313) (-6.7443) (-1.7503)Oil and

chemicals2/ a/ a/ a/ b/

(-) 0.75 1.85

73.0299 -1.7856 -0.0354 -0.2447 (9.5055) (-1.7151) (-8.6787) (-1.8638)Manufacturing

(other) 2/ a/ b/ a/ b/

(-) 0.76 1.87

83.6617 -0.4099 -0.0424 -0.1418 -0.2173 (14.5071) (-3.3881) (-14.7123) (-3.3851) (-3.8675)Transport2/

a/ a/ a/ a/ a/ 0.99 1.86

-96.9942 -0.7987 0.4856 -2.0114 -9.4855 (-3.5512) (-1.7617) (3.5514) (-1.9816) (-3.2608)Financial

services2/ a/ b/ a/ b/ a/ 0.34 2.06

40.0692 -0.4231 -0.0203 -0.1052 -0.0848 (8.7285) (-6.4205) (-8.7778) (-2.7455) (-1.7863)Other services2/

a/ a/ a/ a/ a/ 0.95 1.84


per cent significance level is: 1.726 – 2.274 for four coefficients and 1.803 – 2.197 for five coefficients.

1/ The regression results for this commodity group are from an OLS equation. 2/ The regression results for this commodity group are from a generalized difference equation. (-) The coefficient was dropped from the initial equation due to lack of statistical significance. a/ Coefficient statistically significant at the 5 per cent or lower significance level. b/ Coefficient statistically significant at the 10 per cent significance level.

204 Chapter 7

The estimated values for the elasticities of transformation of the nine commodity groups were assigned to the exportable commodities in the model (see Statistical Appendix, Table A7.1). The estimate for manufacturing (other) was retained for all manufacturing commodity groups in the model, including export regimes but excluding food industries and oil and chemicals, the elasticity values of which were also directly estimated (see Table 7.4). The estimate for transport was assumed to be the same for transport, storage and communication, and restaurants, hotels and lodgings. Having assigned values to the elasticities of transformation in the model, the CET-function exponents by activity (ρc

e) were calculated from equation (7.2).14 The use of relatively low elasticities of transformation will imply that changes in the domestic export price triggered by export promotion policies will only result in a modest change in the domestic sales price, as will be observed in Chapter 8.

Income elasticities of demand The household surveys are the main source of employment and income data used in this study. However, these surveys cannot be used to estimate income elasticities of demand because they do not contain any information on household expenditures. The national accounts are only suitable to estimate a single income elasticity of demand for the economy, the use of which would certainly bias the demand response of households for different goods and services, given a change in their total incomes. To avoid such a bias, income elasticities of demand were estimated using data from the National Survey of Income and Expenditure 1987-88, about which more information is provided in Appendix A. The following logarithmic commodity-wise expenditure demand function was estimated using the OLS method:

logCch = b0 + b1 logYh + ε (7.7)

where Cch, or total consumption of commodity c in household h, is expected to change by a proportion b1 (that is, the Engel elasticity, ξch, in equation 7.3) as a result of a variation in Yh, or total income of household type h excluding tax payments and savings.

The LES functions in the CGE model assume that total household consumption spending takes place within an income (budget) constraint. In every period in which the CGE model is solved, total household consumption expenditure is equal to total household income after taxes and savings (recall Appendix F, eq. F.35). This adding-up restriction was not imposed by means of estimating equation (7.7) simultaneously for 14 consumption commodity groups in the model. Instead, the household income data were corrected to remove total household income excess over total household consumption expenditure on the one hand, and to impute incomes for an important share of households whose


total consumption expenditure exceeded total income on the other.15 In other words, total household consumption expenditure and total household income were equalized and the latter was assumed to be equal to total household income after tax payments and savings in equation (7.7). After correcting the data, equation (7.7) was estimated for the 14 consumption commodities in the CGE model, using a sample of 1,568 urban households and 2,335 rural households separately.16 The estimation results are summarized in Table 7.5, where all the income elasticities of demand are statistically different from zero at 5 per cent or lower significance levels.

The estimated elasticity values have important implications for the model. As explained in Chapter 5, trade policy reform will induce changes in domestic relative prices. This will result in reallocation of resources, which in turn will affect the returns to production factors and the amount of factor earnings, mostly labour income, transferred to households. This income effect will enhance or constrain the capability of households to afford their basic consumption. According to the estimates of income elasticities of demand, households would be worse off if, as a result of the income effect from a trade policy shock, they could not afford to purchase necessary goods and services such as food (including agricultural products); wood products and furniture; and, electricity, gas and water (see Table 7.5). Household demand for such necessary goods and services would be expected to increase considerably if the income effect triggered by the trade policy shock was positive. However, household demand for luxury goods and services (that is, goods and services whose income elasticity of demand is larger than one in Table 7.5) would not vary very much should trade policy lead to an increase in household income.

It is worth noting from Table 7.5 that some elasticity values turned out to be very close to unity, in particular for the following commodity groups: textiles, clothing and leather fabrics, and paper, non-metallic minerals and basic services. This is an unsurprising result because the number of commodity groups for which the elasticities were estimated is relatively large. The particular implication is that the larger the number of commodity groups distinguished in the LES, the more the values of the marginal and average budget shares tend to be almost the same. Consequently, the income elasticities of demand are more likely to be around unity, with the implication that, if all the elasticity values tend to equal one, then the LES is basically reduced to a system of Cobb-Douglas consumption demand functions. This is not so in our case according to the estimated elasticity values presented in Table 7.5.

206 Chapter 7

Table 7.5 OLS estimation results for the commodity-wise expenditure demand function (t-values in parenthesis)

Urban households Rural households Consumption commodity group 0>b0>0 b1>0 R2 0>b0>0 b1>0 R2

0.6669 0.6348 0.3194 0.7363 Domestic-consumption agriculture (5.7628) (23.5373) 0.27 (4.0249) (37.8477) 0.39

1.4344 0.5403 1.1778 0.5504 Traditional export agriculture (8.3296) (6.0211) 0.30 (10.9529) (13.3439) 0.29

-0.4802 0.7557 -0.2150 0.6784 Non-traditional export agriculture (-3.1739) (21.5733) 0.26 (-1.8184) (23.6903) 0.24

0.2067 0.7529 0.0123 0.7963 Food industries (2.1243) (33.1814) 0.42 (2.1561) (41.3753) 0.43

-1.2055 1.0225 -1.2161 1.0271 Textiles, clothing and leather fabrics (-6.7165) (24.6085) 0.30 (-9.6669) (33.5733) 0.36

-0.4735 0.6962 0.7050 0.6861 Wood products and furniture (-1.7796) (8.1113) 0.21 (4.9909) (13.1110) 0.29

-0.2933 0.9673 -0.0459 0.9642 Oil, chemicals, and rubber and plastic products (-3.3298) (39.6761) 0.50 (-1.7318) (49.5076) 0.51

-1.8212 1.0322 -1.4174 1.1266 Paper, non-metallic minerals and basic metals (-11.5448) (27.6028) 0.34 (-10.8551) (28.1588) 0.28

-2.8593 1.4896 -2.6238 1.4327 Other manufacturing (-10.7168) (20.7281) 0.25 (-13.1137) (24.8964) 0.25

-1.4492 1.4399 -0.9407 1.6598 Restaurants, hotels and lodgings (-5.9441) (18.8066) 0.28 (-4.4243) (18.3899) 0.22

-1.4254 1.2400 -0.5084 1.5477 Transport, storage and communication (-6.8514) (20.9668) 0.27 (-2.7506) (18.0555) 0.21

1.1967 0.7594 0.4040 0.6979 Electricity, gas and water (10.7240) (17.3146) 0.16 (3.7814) (19.9541) 0.18

0.7385 0.9912 1.0306 1.5866 Financial services and insurance (1.6670) (3.5808) 0.09 (2.8709) (5.8605) 0.11

-2.7216 1.4141 -3.2157 1.5344 Other services (-14.5330) (32.1439) 0.42 (-14.0750) (26.4526) 0.32

Average budget shares (αch) and income elasticities of demand (ξch)

estimated from the National Survey of Income and Expenditure data proved consistent for the calculation of marginal budget shares (βch). After estimating βch from equation (7.3), the total sum of marginal budget shares was equal to one (Σcβch = 1) for both urban and rural households. This was a clear indication of the adding-up restriction that the total sum of household expenditures was equal to total household income after taxes and savings (see Statistical


Appendix, Table A7.2). Yet, as explained in Chapter 6 (sub-section 6.4.1), the estimation of the SAM indicated that some changes in the consumption patterns of households took place between 1987/88 and 1997. A comparison of average budget shares from the National Survey of Income and Expenditure and the compiled SAM revealed that households’ preferences presumably changed for six commodity groups. Since the CGE model is calibrated using average budget shares from the SAM, the marginal budget shares of the six commodity groups were re-estimated using equation (7.3). This implied assuming that the income elasticity of demand is to a large extent a permanent characteristic of all commodities, such that the income elasticities of demand of each of the six commodity groups remained unchanged between 1987/88 and 1997. The implication of this assumption is that the marginal budget share of each of the six commodity groups changed more or less in tandem with changes in the respective average budget share. In this way, drastic changes in the elasticities of income demand were avoided, which is reasonable for a ten-year period.17 The results of this re-estimation step for the particular case of the six commodity groups are presented in the Statistical Appendix (Table A7.3).

The estimation of average and marginal budget shares and income elasticities of demand for the 14 consumption commodity groups enabled the calculation of the subsistence consumption parameter (γch) using equation (7.4). The information obtained led to the conclusion that the ratio of ‘fixed or committed’ consumption to total consumption expenditure was 42.4 and 63.4 per cent for urban and rural households, respectively.18 This result is consistent with the fact that, since mean household incomes in the urban areas are higher than in the rural areas, ‘supernumerary expenditures’ are expected to be relatively higher for urban households. In line with this result also, the estimated SAM-based average propensity to save for urban households was found to be higher than that of rural households.19

Elasticities for the TFP growth function In line with the endogenous productivity growth model sketched out in Chapter 5 (sub-section 5.5.2), the growth rate of TFP is positively related with the stock of human capital and the degree of trade openness. This association was tested by estimating the following semi-logarithmic function at the sectoral level:

ϕ = b0 + ς log hk + τ log to + d1cri + d2ref + ε (7.8)

where, ϕ is a TFP growth rate, hk is the stock of human capital, to is a measure of trade openness, and cri and ref are the dummy variables that take into account the debt crisis and structural adjustment reform periods.

The sectoral TFP growth rate is expected to be positively associated with hk and to. The semi-logarithmic form in equation (7.8) is in line with the fact that

208 Chapter 7

ϕ is an annual (actual) TFP growth rate estimated for the 1977-97 period, as explained in Appendix C. Different variants of equation (7.8) were estimated for agriculture and manufacturing, using time series for the 1977-97 period. As indicated in Appendix C, these are the two sectors where economic reforms have somewhat affected the rate of TFP growth. The stock of human capital was initially proxied by the observed level and year-to-year change in the total labour force by sector, but these variables turned out to be not statistically different from zero in the specifications in which they were included. In contrast, the year-to-year change in the sectoral skilled-labour force (active population at working age with secondary or higher level of education) was found to be a much more satisfactory predictor of TFP growth from the statistical point of view. Also, the following indicators of trade openness were used - individually and in combined form - in the various estimated versions of equation (7.8): average import tariffs (annual rate and year-to-year change), import volumes lagged one period, trade volumes lagged one period, and average export taxes (annual rate and year-to-year change). The year-to-year change in the average import tariff turned out to be the most satisfactory predictor of TFP growth among the trade openness indicators. Thus, the final estimations of equation (7.8) included two explanatory variables (in addition to the dummy variables), namely the year-to-year change in the sectoral skilled-labour supply (with expected positive sign) and the year-to-year change in the import tariff at the commodity level (with expected negative sign). OLS regressions were initially estimated, although the final estimates resulted from a generalized difference equation because of the need to correct autocorrelation.

The endogenous productivity growth model underlying equation (7.8) was only found to be statistically robust for agriculture, as the estimation results indicate in Table 7.6. In the case of manufacturing, the estimated coefficient on the year-to-year change in the average import tariff was even found to be positive, yet statistically not different from zero. The estimated coefficient on the reform variable for the two sectors is not reported since it turned out to be negatively correlated with the year-to-year change in the average import tariff (and not statistically different from zero). In contrast, the estimated coefficient on the debt-crisis dummy was found to be statistically different from zero and negative, indicating the harmful effect of such a crisis on TFP growth. Overall, the estimation results support the hypothesis that productivity growth is endogenously determined only in agriculture. The results for manufacturing would presumably have become more significant had disaggregated data allowed the estimation of equation (7.8) for the manufacturing export sub-sectors that emerged during the trade policy reform. It is, however, not possible to identify the potential bias in the estimation of manufacturing growth resulting from TFP growth in the CGE model.


Table 7.6 Estimation results for the semi-logarithmic TFP growth equation by activity group, 1977-1997 (t-values in parentheses)

Activity group 0>b0>0 ς>0 0>τ 0>d1 R2 DW* -0.1519 0.0133 -0.2065 -0.0700

Agriculture

(-1.8735) (2.8157) (-2.8302) (-2.3799) a/ a/ a/ a/

0.55 1.92

-0.0986 0.0109 0.0144 -0.0700 Manufacturing (-0.6012) (0.9200) (0.6842) (-2.1642) b/ b/ b/ a/

0.43 2.13

Notes: * The range of acceptance of the hypothesis of no autocorrelation for 21 observations and

four coefficients at the 5 per cent significance level is 1.812 - 2.188. a/ Coefficient statistically significant at the 5 per cent or lower significance level. b/ Coefficient not statistically different from zero.

As explained in Chapter 5, the value of the TFP parameter in the CGE model (αa

va) is a function of its immediate past value and an endogenous TFP growth rate. The TFP growth rate is a function of an activity-productivity growth factor and will increase (decrease) as a result of a positive (negative) between-period change in the agricultural skilled-labour supply and a negative (positive) between-period change in the average agricultural import tariff rates. This formulation was, in fact, included in the CGE model on the basis of the empirical results that have been discussed in this sub-section. The estimated elasticity values in Table 7.6 were used to determine the response of TFP growth in agricultural activities given a between-period change in, respectively, agricultural import tariffs and the agricultural skilled-labour supply. These elasticity values were retained for the three agricultural activities in the CGE model. The value of the exogenous activity-productivity growth factor corresponds to the average TFP growth rate estimated for agriculture in line with the procedure spelled out in Appendix C. Given the use of the estimated elasticity values, the effect of between-period changes in agricultural import tariffs and the skilled labour supply in agriculture is expected to be only modest.20

Nominal wage indexation and labour supply elasticities Values for the elasticity of the activity-specific wage with respect to the consumer price index were required for the dynamic calibration, in order to take into account the minimum-wage indexation mechanism in the covered segments of the labour market. In line with the instantaneous adjustment of wages to consumer prices in the covered segments of the labour market introduced in

210 Chapter 7

Chapter 5, elasticity values were estimated using the following equation whose complete derivation explained in Appendix I:

εϖϖϖ ttiiiiiti wcpiw +++=−1,210, logloglog (7.9)

where, wi,t is the nominal wage rate in covered segment i, and ϖ0i, ϖ1i and ϖ2i are, respectively, the constant, the elasticity of the nominal wage with respect to the cpi, and the elasticity of the nominal wage with respect to its one-period lagged value. The lower-case subscripts t and t-1 indicate current period and immediate past period, respectively.

Equation (7.9) was estimated separately for seven aggregate sectors, using OLS regressions. The main estimation results are reported in Table 7.7, according to which minimum wages do adjust positively to the variation in consumer prices. The similarity of estimated values across sectors (with the exception of services) reflects the fact that the wage reaction to consumer price changes differs very little across the covered segments of the labour market. Since the data availability only allowed the estimation of elasticity values for seven aggregate sectors, the estimate of a whole aggregate sector was retained for each of its sub-sectors (see Statistical Appendix, Table A7.4).

Elasticity values for the labour supply function were also needed for the dynamic calibration. The following logarithmic function was accordingly estimated:

( ) ε ttltltltl DRECbwwblfbblf ++++=−− 31,,21,10, logloglog (7.10)

where lfl is the labour force of labour type l, wl,t/wl,t-1 is a between-period wage ratio of labour type l, and DREC is a dummy variable that captures the effect of sudden increases in the labour force as a result of economic recovery.

Equation (7.10) was estimated for the labour categories in the CGE model, using household survey data for the 1980-2000 period. Details on data and variables used are provided in Appendix A. The estimation by labour categories implicitly assumes that the labour market is segmented and with no mobility across sectors, despite the fact that, as indicated in previous chapters, there is labour mobility in the labour market. But, the type of estimation only really aims at determining the response to wage changes from different type of workers, something that would not be possible if estimates for the total labour supply were used. The between-period wage ratio was constructed using average real wages data by labour type. The estimates of the coefficient on this wage ratio provided the elasticity values for the labour supply function of the CGE model. The reason for including the dummy variable is that year-to-year movements in the labour force participation reflect the state of the business cycle as well as underlying trends (Pencavel, 1986:10). This variable was activated in the years in which, for each labour type, the sectoral labour force


grew substantially as sectoral output recovered from recession and hence capacity utilization also increased.

Table 7.7 OLS estimation results for the nominal wage indexation function by sector, 1995-2000 (t-values in parenthesis)

Sector (activity group) 0>ϖ0i>0 ϖ1i>0 ϖ2i>0 R2 DW h

-0.2261 0.6744 0.4403 Agriculture

(-4.4914) (5.6202) (4.5001) 0.9923 1.9417 0.4009

-0.1984 0.6648 0.4362 Manufacturing (-4.3659) (5.6703) (4.4619) 0.9923 1.9440 0.6707

-0.1927 0.6488 0.4494 Construction (-4.2919) (5.6019) (4.6500) 0.9923 1.9529 0.6939

-0.1927 0.6488 0.4494 Electricity (-4.2916) (5.6018) (4.6501) 0.9923 1.9529 0.4926

-0.2093 0.6927 0.4145 Trade (-4.4915) (5.7885) (4.1676) 0.9920 1.9363 0.5829

-0.2183 0.6745 0.4361 Transport (-4.4317) (5.6138) (4.4211) 0.9920 1.9353 0.7422

-0.2525 0.7424 0.3853 Services (-4.7798) (5.9551) (3.8020) 0.9918 1.9357 0.5567

Note: Given the computed values of the Durbin’s h statistic, the null hypothesis that there is no first-order (positive or negative) autocorrelation was not rejected at the 5 per cent level.

The OLS method was initially used to estimate equation (7.10) but a generalized difference equation was finally estimated for some labour categories for which the OLS Durbin’s h statistic indicated autocorrelation problems. The most satisfactory regression results are summarized in Table 7.8. The wage-ratio elasticity estimates reflect clear patterns of the Costa Rican labour market. First, they are unambiguously higher for skilled labour relative to unskilled labour in the agricultural and formal sectors and, while they do not differ a great deal between self-employed and wage earners for skilled labour, relatively more important differences are observed in the unskilled segments. Clearly, unskilled workers in the agricultural and formal sectors do not change their labour supply as strongly as skilled workers do in response to wage changes. Second, the evidence unambiguously indicates that the wage-ratio elasticity is not statistically different from zero in the informal sector at standard significance levels. As shown in Table 7.8, the elasticity value even turned out to be negative for self-employed labour, but still not different from zero in statistical terms. The lack of evidence that labour responds positively to between-period wage changes in the informal sector is, in fact, an indication of the informal nature of the sector, which in reality plays a ‘residual role’ in the labour market.

212 Chapter 7

Table 7.8 Estimation results for the labour supply function by labour category, 1980-20001/ (t-values in parenthesis)

Labour category 0>b0>0 b1>0 b2>0 0>b3>0 R2 h*

4.8560 0.4901 0.3130 (-) 0.84 0.59 Skilled wage labour in the agricultural sector2/ (5.1243)

a/ (4.8740)

a/ (7.9619)

a/

3.4569 0.6283 0.3159 -0.1184 0.70 -0.14 Skilled self-employed in the agricultural sector2/ (2.9647)

a/ (4.8780)

a/ (2.9513)

a/ (-2.1925)

a/

0.8737 1.0942 0.2375 0.0823 0.99 -0.65 Unskilled wage labour in the agricultural sector3/ (2.3420)

a/ (2.3883)

a/ (7.6715)

a/ (2.9185)

a/

4.0054 0.6511 0.2812 (-) 0.57 -1.02 Unskilled self-employed in the agricultural sector2/ (2.0698)

a/ (3.8316)

a/ (3.2282)

a/

0.2735 0.9891 0.4563 (-) 0.99 0.98 Skilled wage labour in the formal sector3/ (1.7804)

a/ (6.0946)

a/ (2.4698)

a/

1.0796 0.9052 0.4572 (-) 0.97 1.27 Skilled self-employed in the formal sector2/ (2.5743)

a/ (2.9514)

a/ (2.3754)

a/

0.8650 0.9336 0.3383 (-) 0.91 -1.06 Unskilled wage labour in the formal sector2/ (1.7698)

a/ (2.4067)

a/ (3.8702)

a/

1.8437 0.8890 0.3870 (-) 0.88 0.87 Unskilled self-employed in the formal sector2/ 2.2890

a/ (2.3153)

a/ (2.7406)

a/

0.4652 0.9270 0.2685 (-) 0.81 0.19 Skilled wage labour in the informal sector3/ (0.5858)

c/ (7.8557)

a/ (1.0951)

c/

3.1633 0.6991 -0.0412 (-) 0.96 -0.64 Skilled self-employed in the informal sector2/ (1.6205)

b/ (3.7236)

a/ (-1.0291)

c/

0.4318 0.9526 0.0827 -0.2364 0.95 0.15 Unskilled wage labour in the informal sector2/ (0.8228)

c/ (4.2434)

a/ (0.5510)

c/ (-2.3477)

a/

5.7735 0.5066 -0.0528 (-) 0.35 -0.26 Unskilled self-employed in the informal sector2/ (2.1325)

a/ (2.1685)

a/ (-0.1448)

c/

Notes: 1/ The number of observations is equal to 18 because data were not available for 1981 and 1984 (for

more details on the data see Appendix A, Section A.2). 2/ The regression results for this labour category are from an OLS equation. 3/ The regression results for this labour category are from a generalized difference equation. * Given the computed values of the Durbin’s h statistic, the null hypothesis that there is no first-order

(positive or negative) autocorrelation was not rejected at the 5 per cent level. (-) The coefficient was dropped from the initial equation due to lack of statistical significance. a/ Coefficient statistically significant at the 5 per cent or lower significance level. b/ Coefficient statistically significant at the 10 per cent significance level. c/ Coefficient not statistically different from zero.


7.3.3 Factor quantity and exogenous data

The employment data needed for the bench-mark solution were extracted from the 1997 INEC Household Survey of Employment and Unemployment (see Statistical Appendix, Table A7.5).21 Labour force growth was periodically updated using an annual growth rate calculated from the observed number of active persons at working age in the 1997-2002 period (see Statistical Appendix, Table A7.6). The capital stock data used for the bench-mark solution were borrowed from the capital stock database of the Central Bank, from which the average annual economy-wide depreciation rate for 1997-2000 was also found to be equal to 0.0920. The mobility of the investable funds parameter (κ) was assumed to be equal to 0.25 after performing a sensitivity analysis, as will be explained in more detail in the next sub-section. Both the depreciation rate and the mobility of the investable funds parameter are assumed to be constant in the model. Other variable and parameter values were updated exogenously using observed annual growth rates (see Statistical Appendix, Table A7.6), while keeping the other exogenous values at unity. Given the vulnerability of the economy to changes in world prices, the world price of traditional exports (coffee, bananas, meat and sugar cane) and oil was updated using observed data for the 1998-2002 period.22 The world interest rate used in the model corresponds to the London InterBank Offered Rate (LIBOR) on deposits denominated in US dollars, using annual averages for the 1997-2002 period from IMF (2002b). Trade tax and export subsidy rates in 1997 were updated using the observed annual change in average rates during the 1997-2002 period.

7.4 Solution, parameter value sensitivity and validation of model results

7.4.1 Model solution

After all the CGE model equations had been fed with data, the simultaneous solution of the complete functional system was implemented. Given the large number of equations, the solution of the model implied a difficult computational problem. The model was solved with GAMS, a powerful computer package that allows model implementation while also paying attention to the syntax rules.23 This implied writing the equation blocks presented in Appendix F in standard algebraic notation using a GAMS code.24 The solution of the equation system for each within-period equilibrium solution was carried out using an algorithm that makes use of the constrained non-linear programme solvers known as MINOS and PATH.25

In brief, the solution of the system of non-linear equations was carried out considering a series of local linearizations of the non-linear equation system in

214 Chapter 7

the CGE model, for which a zero was sought for an equilibrium solution. The linear equation system was solved, with the linearization revised as the solution proceeded. Since market demands are the sum of individual agent demands, each linearization step involved the calculation of a Jacobian matrix containing the own- and cross-price derivatives of the model’s market demand functions of which the initial values are given by the bench-mark equilibrium. This entailed repeated calculation of point estimates of derivatives of the market excess demand functions via an iterative process, whereby each iteration performed an evaluation and factorization of a Jacobian matrix. The point estimates of derivatives were used to estimate successive adjustments to the initial guess about equilibrium prices.26 In our case, the iterative process was successfully terminated after seven iterations indicated that the residual of the iteration procedure was zero and the Jacobian matrix’s factorization succeeded in each iteration.27 As a result, convergence to an equilibrium solution was achieved, whereby, given the model’s equation constraints, the set of equilibrium prices that was found allowed the determination of 1,290 single variables using the same number of single equations.

The model was expected to be stable from a theoretical point of view given its functional form.28 In applied trade policy models, a set of equilibrium prices is commonly expected to be found via relative price adjustments, and given only the recursive update of stock variables and other parameter values. In our particular case, this adjustment was always conducive to stable areas in the equilibrium path, given the estimated elasticity values used (see next sub-section). This was further confirmed after a number of experiments in which various parameters and exogenous variables were manipulated, since the model continued to move into stable areas in the equilibrium path. The results of most of these experiments are reported in the next chapter. In a more general context, the experience of applied modellers who have used solution methods in which the Jacobian is calculated suggests that non-convergence difficulties have not been encountered frequently (Shoven and Whalley, 1992:67).

7.4.2 Parameter sensitivity

A sensitivity analysis helped to identify the feasible ranges within which the model elasticity values must have fallen in order to generate a stable dynamic equilibrium solution. This approach is not widely used in CGE modelling because of the large number of simulations involved. A one-by-one change in elasticity values was simulated for those model functions whose solution depended on elasticities (for a activities, c commodities or f factors). The estimated elasticity values were found to fall within the feasible ranges, and high sensitivity to elasticity values was only found in two instances, with no important repercussions for our purposes. First, the feasible range for CES and


CET elasticities narrowed moving from the bench-mark solution to the dynamic solution. The model became unstable after having been solved for 12 years, which suggested that a separate definition of short- and long-run elasticities was required for a few commodity groups, to allow a longer period solution. In addition to the possibility that short- and long-run elasticities may differ in reality, this result was in part due to the fact that the update of exogenous values was only carried out for six years. Ultimately, it was possible to maintain the estimated elasticity values constant since the model was built to provide a six-year solution. In general, the elasticities in the study are lower than those used in other studies of Costa Rica, where no econometric estimation is reported. The policy simulation results that will be presented in Chapter 8 may, therefore, not be strictly comparable with those in the existing literature on Costa Rica. Second, the model became unstable when elasticity values larger than one were used in the labour supply function for the particular case of waged workers in the informal sector. This caused no problem because, as explained earlier, the response of these workers to changes in the between-period wage ratio was found to be statistically not different from zero and, consequently, the labour supply of wage-labour in the informal sector was not associated with between-period wage changes.

The model’s results after imposing a trade policy shock were found to be highly sensitive to the value of the mobility of investable funds parameter, κ. As explained in Chapter 5, κ measures the inter-activity mobility of investable funds. When κ is larger than zero, the response of the sectoral reallocation of investment to rental-rate differentials is positive such that high-rental-rate sectors attract funds from low-rental-rate sectors. Sensitivity analysis indicated that, after making κ large, for example larger than 1, a small increase in some sectors’ relative profitability resulting from a trade policy shock implies exaggerated attraction of capital into these sectors. Given the default savings-driven investment closure, there is massive generation of savings, particularly from abroad, and changes in aggregate investment become unrealistic over time. The model does not become explosively unstable, though; for that reason, it stays within feasible areas of the equilibrium path. For example, when the effect of the actual export promotion policy for the 1997-2002 period is removed, the price shock makes sectors producing for the domestic market more profitable relative to export sectors. This scenario was conducted under the assumption that κ is either equal to 2.50 or equal to 0.25. When κ is equal to 2.50, relative sectoral rental rates oscillate considerably, and more profitable sectors massively attract funds from low-rental rate sectors. This would lead to an unrealistic aggregate investment of 67.77 per cent of GDP in 2002, compared with 28.33 per cent in the base-line. In contrast, when κ is set equal to 0.25, aggregate investment increases to 35.24 per cent of GDP in 2002. Without econometric

216 Chapter 7

analysis it is difficult to test the reasonable range of the value that should ultimately be used for κ. Sectoral data required for such purposes were not available for Costa Rica. Therefore, any option beyond the sensitivity analysis to determine whether changes in investment were relatively reasonable could not be seen. The calibration of the model was ultimately implemented assuming that κ is equal to 0.25.

7.4.3 Model trends vis-à-vis actual trends

The solution of the CGE model yielded a base-line that captures the combined effect of all economic policy reforms during 1997-2002. This sub-section seeks to show how closely the base-line permits approximation of the actual aggregate behaviour of the economy, based on a kind of backward validation. The economic trends included in the base-line were not expected to reproduce the actual economic trends with no error, obviously because many restrictive theoretical and empirical assumptions were implied in the model, which were nonetheless necessary for calibration and solution. A realistic calibration of the model was of course expected to provide a base-line capturing modelled economic trends which would not disperse very much from actual economic trends. A large number of trends were produced from the CGE model but, given the space limitation, the model’s representation of the overall economic performance is validated in this sub-section by including only selected economic trends. We are focusing on the main macro-economic aggregates, accounting in some cases for the shares of agriculture. Also, some labour market indicators are included, in addition to inequality and poverty results derived from the combination of the CGE model and the micro-simulation methodology.

Figure 7.2 includes actual trends and modelled trends. On the whole, the model enabled satisfactory approximation of the actual overall economic performance in the 1997-2002 period. As can be seen in panel (a), the trend of GDP at factor cost in the model almost exactly matches the reality. Also, agriculture’s share of GDP in the model is quite similar to the actual share, which is certainly a good validation of the workings of the endogenous productivity growth function, among other things. The CES and CET functions and the elasticity values used proved plausible for yielding trends in export and import value that closely follow the actual trends (see panels (b) and (c)). The relatively low dispersion in the case of the export value trend in 1998-2001 is explained by the fact that the model does not explicitly capture the direct investment effect of the multinational INTEL on the microprocessors export sub-sector. As pointed out in Chapter 3, INTEL established its facilities in Costa Rica and achieved booming exports in 1998-99. However, INTEL’s exports fell in 2000-2001 due to the decline in the world market for microprocessors. Also, while INTEL has evidently no direct link to agriculture, which is the sector of


concern in this study, the employment effect of its operation has only been modest.29 Still, the model export value trend reflects the similar fluctuating pattern of the actual trend (panel (b)). Agriculture’s shares of export and import values produced in the model also show a similar trend as in reality (panels (b) and (c)). Likewise, final consumption and gross nominal investment (panels (d)-(f)) grow in the model as they actually did during 1997-2002. The dispersions in the trends in panels (d) and (f) are respectively explained by, on the one hand, the fact that the quantity of government consumption is assumed to be fixed in the model; and, on the other hand, the specific way gross nominal investment is determined in line with the savings-investment closure.

The evidence in Chapter 4 with regard to the agricultural labour market indicated that agricultural employment grew on average by 2.1 per cent per annum during 1996-2000. The CGE model generates a fairly good approximation of such a growing pattern. In fact, as panel (g) in Figure 7.2 indicates, the model closely reproduces the actual pattern in agricultural employment for the whole of the 1997-2002 period. Recalling Chapter 4 (sub-section 4.2.1), the actual employment trends were derived from a cross-tabulation analysis using household survey data, whereby each worker was associated with a labour market sector according to specific criteria. Such an association was impossible for a number of workers with unknown characteristics in the sample, who were, as a result, not taken into account. Given that the sectoral breakdown in the CGE model is not as large as that used in Chapter 4, in particular for agriculture, the identification of labour by sector during the calibration was easier and allowed inclusion of more workers in the sample. Therefore, the employment trend produced in the model was expected to overestimate the actual trend in Chapter 4 slightly, but this did not impede a close reproduction of the actual trend. Chapter 4 also showed that real incomes increased in tandem with employment in agriculture. In particular, real average agricultural labour income was found to have increased in 1996-2000 on the whole, despite a steep reduction in 1999-2000 (recall Figure 4.2). As depicted in Figure 7.2 (panel (h)), the model reproduces such a trend fairly reasonably and also reflects well what happened in the 1999-2000 sub-period. As explained in Chapter 5, consumer prices are determined endogenously in the CGE model. The resulting modelled CPI turned out to be slightly lower than the actual CPI. Hence, since the CPI was used to estimate real average labour income in this instance, the model was found to overestimate the actual trend of that income very moderately.

Figure 7.2 Trends of main macro-economic aggregates and agriculture’s shares, and agricultural employment and real average labour earnings, 1997-2002 (modelled trends vis-à-vis actual trends)

Panel (a): GDP at factor cost (Index 1997=100) and agriculture's share of GDP (%)

0%2%4%6%8%

10%12%14%

1997 1998 1999 2000 2001 2002

Agric

ultu

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Modelled trend of agriculture's share of GDPObserved trend of agriculture's share of GDPModelled trend of GDP at factor costObserved trend of GDP at factor cost

Panel (b): Total export value (Index 1997=100) and agriculture's share of total export value (%)

0%

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Modelled trend of agriculture's share of total export valueObserved trend of agriculture's share of total export valueModelled trend of total export valueObserved trend of total export value

Panel (c): Total import value (Index 1997=100) and agriculture's share of total import value

0%

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1997 1998 1999 2000 2001 2002

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Modelled trend of agriculture's share of total import valueObserved trend of agriculture's share of total import valueModelled trend of total import valueObserved trend of total import value

Panel (d): Government final consumption (Index 1997=100)

0

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250

1997 1998 1999 2000 2001 2002

Observed trend Modelled trend

Figure 7.2 (Continued)

Sources: Observed trends in macro-economic aggregates and agriculture’s shares are based on data from the Central Bank of Costa Rica. The actual trends in employment and real average labour earnings in agriculture are based on data from INEC Household Surveys of Employment and Unemployment.

Panel (e): Private consumption (Index 1997=100)

0

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1997 1998 1999 2000 2001 2002


Panel (f): Gross nominal investment (Index 1997 = 100)

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Panel (h): Real average agricultural labour income(Index 1997=100)

90

95100105110115120125

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Panel (g): Agricultural employment (Index 1997=100)

90

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1997 1998 1999 2000 2001 2002


220 Chapter 7

The CGE model, in conjunction with the micro-simulation methodology, also

proved consistent for generating plausible inequality and poverty trends. Recalling Chapter 4, the actual trends in the Theil and Gini coefficients suggest that the distribution of per capita agricultural household income deteriorated in 1996-2000 (Figures 4.3 and A4.3). In addition, the pace of the observed falling incidence of agricultural poverty in 1987-95 slowed down considerably in 1996-98 and the trend reverted in 1999 (Figure A4.5). As can be seen in Figure 7.3, the model base-line of inequality and poverty reproduces the trends presented in Chapter 4 very well, except for the actual reduction in the Theil index between 1999 and 2000 (see panel (a)). The divergence in the trends of incidence of agricultural household poverty in 2000-2002 in panel (b) is explained by a strong adjustment in the model as a result of the (actual) removal of export subsidies. As will be explained in Chapter 8, the exogenous manipulation of the export subsidy triggers very important price shifts and quantity allocations, with considerable implications for the incidence of agricultural poverty. The model results also suggest that the incidence of agricultural household poverty is underestimated when the official poverty lines are used (see panel (b)). This finding, in addition to the reasons given in Chapter 5 (sub-section 5.6.2), supports the use of an endogenous poverty line produced in the CGE model, in order to capture the impact of trade policy reform on the incidence of agricultural poverty more realistically.

Figure 7.3 Inequality and poverty indices for agricultural households, 1997-2002 (macro-micro modelled trends vis-à-vis actual trends)

Panel (a): Gini and Theil coefficients (Per capita household income)

90

95

100105

110

115

120

1997 1998 1999 2000 2001 2002

Inde

x 19

97=1

00

Modelled Gini trend Modelled Theil trend

Observed Gini trend Observed Theil trend

Statistical Appendix 221

Figure 7.3 (Continued)

Source: The actual inequality and poverty indices in agriculture are based on data from INEC Household Surveys of Employment and Unemployment.

7.5 Concluding remarks

In order to use the macro-micro model sketched out in Chapter 5 for simulating the effects of trade policy reform on inequality and poverty in agriculture, the author first faced the problem of feasibly solving the CGE model’s equation system. This implied calibrating all the equations to a consistent data set that plausibly approximated the structure and behaviour of the Costa Rican economy. This chapter has showed how, following the calibration method and using data systematically presented in the form of a SAM and own elasticity estimates, the author was able to feasibly solve the CGE model for the 1997-2002 period. Also, the consistency of the estimated SAM was demonstrated again, since, by solving the CGE model, the author also showed that a simultaneous connection of consistent SAM transactions through a system of equations existed. In addition, solving the model with the estimated elasticity values helped the author to conclude that the most crucial model assumptions were plausible for approximating the functioning of the Costa Rican economy. Among these assumptions are: endogenous agricultural productivity growth triggered by human capital levels and trade openness, low substitution levels at the production and commodity levels, minimum wage adjustments in selected segments of the labour market, and a positive response to nominal wage adjustments from agricultural and formal sector workers, among others.

Panel (b): Incidence of household poverty per capita

0

50

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1997 1998 1999 2000 2001 2002

Inde

x 19

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00

Modelled trend (off icial poverty line)Modelled trend (endogenous poverty line)Observed trend (official poverty line)

222 Chapter 7

A kind of backward validation showed that, although the model included many

restrictive assumptions, the calibration yielded a solution that permitted to reproduce quite closely the actual trends of the Costa Rican economy, in particular for macro-economic aggregates, agriculture’s shares, and labour market outcomes in agriculture. In addition, the micro-simulation methodology proved a reliable complement to the CGE model for producing inequality and poverty trends that quite reasonably reflect what has happened in reality. Evidence was also provided to suggest that the use of endogenous poverty lines produced by the CGE model reduces the estimation bias in the cost of basic consumption that arises from using official poverty lines when poverty is estimated from the macro-micro modelling framework. On the whole, this chapter has suggested that the macro-micro model, once calibrated to the comprehensive Costa Rican data set, is complete and consistent for developing a set of policy simulation experiments. The next chapter deals with reporting and analyzing selected results from a group of simulation experiments aimed at determining the impact of trade policy reform on inequality and poverty in Costa Rica’s agriculture.

Notes 1. When both export and import trade shares are high in one sector or CES and CET

elasticities are high, the model could display behaviour similar to that in a neo-classical model where all goods are perfect substitutes and two-way trade (both exports and imports) in a sector is not observed. In such a situation, and not having defined perfect substitutability functions but having defined CES and CET functions whereby substitution is allowed, a small price change could generate a big swing in both exports and imports, as the model really is only aimed at changing sectoral net trade. The result may be a wildly unstable model. The way to tackle this problem may be to disaggregate sectors so that they have either a large export share or a large import share, but not both.

2. Maintaining the bench-mark parameter and elasticity values constant for the dynamic solution is not a general rule in the calibration of dynamic CGE models. In fact, for the solution of some models, in particular those that are solved for very long periods of time, it might be necessary to differentiate between short- and long-run elasticities, provided that the short-run elasticities would not permit the whole dynamic solution. As explained in sub-section 7.4.2, we did not face this limitation given the relatively short dynamic solution of our CGE model.

3. Econometric models introduce stochastic disturbances to capture the effect of variables that are omitted from the model and error in the measurement of exogenous and endogenous variables. By assuming all disturbances equal to zero, the calibration


method entails that no factors other than those included in the model will affect the endogenous variables. Therefore, the calibrated parameters absorb all random errors in the data for the bench-mark year.

4. The value of σ varies from zero to infinity. In CES functions, the value of ρ varies from infinity to minus one. This restriction ensures that the corresponding isoquant is convex to the origin. In CET functions, on the other hand, the value of ρ varies from infinity to one. This restriction ensures that the isoquant corresponding to the output transformation function is concave to the origin.

5. The parameters αch, ξch, and ℑh, are not listed in Appendix F (Table F.2) because they are inputs for the estimation of βch and γch, which do form part of the list of CGE model parameters.

6. As outlined in Chapter 5, the quantity ratios in the CGE model are the following: the value-added quantity share of total activity level (QVAa/QAa) in the activity production function (eq. F.16), the employment share of total value-added quantity (ΣlQFla/QVAa) in the value-added function (eq. F.18), and the import quantity share of total quantity of demand (QMc/QQc) in the composite supply function (eq. F.29).

7. It was also confirmed that the intercept term played a role in explaining import quantity shares of total quantity of demand (QMc/QQc) in the composite supply function. The role of the trend term was also found to be statistically significant.

8. Imports of non-traditional export agricultural commodities were very low in 1966-80. They fell after the debt crisis and from 1988 began to show significant fluctuations, increasing in 1988-92, 1995-96 and 1998-99, and falling in 1992-95, 1996-98 and 1999-2000. The increases were basically due to higher temporary imports of apples, barley, brans, grapes, oil crops, and natural pulps.

9. The function exponent (ρcm) that was calculated for each importable commodity

group held the condition that ρcm > -1, given that all the estimated elasticity values

were found to be positive. 10. The intercept term was found to be statistically different from zero. The robustness

of the estimated specifications was also confirmed by the trend term, which turned out to be statistically different from zero in all cases, except for manufacturing in the estimation of the labour shares of total value-added quantity at the activity level.

11. All the estimated function exponents held the condition that ρ > -1, given that all the estimated elasticity values were found to be positive.

12. The intercept coefficient was found to be statistically significant in all the specifications, suggesting an important role of the function share parameter.

224 Chapter 7

13. The higher elasticity of transformation in domestic-consumption agriculture indicates

that, as import tariffs were reduced faster, the degree of transformation increased because of the larger import competition.

14. The estimated elasticity values allowed for the condition that ρce > 1 for all the

commodity groups. 15. Initially, due to underreporting of incomes and errors in the survey data, total

household consumption expenditure exceeded total household income for approximately 30.6 per cent of the urban households and 29.6 per cent of the rural households. Removing these households from the sample was not considered an option because this would have entailed losing considerable information on the consumption preferences of households. Therefore, total income was equalized to total consumption for all households.

16. Prior to the estimation of equation (7.7), all household expenditures on commodities at the six-digit disaggregation level were grouped into expenditures corresponding to the 14 consumption commodity groups in the CGE model.

17. An alternative method of re-estimation would have entailed recalculating the elasticity values of the six commodity groups for which the estimation of the SAM indicated a significant change in the average shares of total consumption between 1988/89 and 1997. Accordingly, given two SAM vectors of average budget shares α*

ch for urban and rural households respectively (where c = 6), and having estimated the initial two vectors of marginal budget shares βch from the survey data, it follows that the two new elasticity vectors ξ*

ch are given by:

αβξ **

chchch=

where only six elements in each of the two vectors ξ*ch are to differ from the original

vectors ξch, respectively. This approach has the limitation that the re-estimated elasticities may become unrealistic. For example, the rural income elasticity of demand for financial services (a ‘luxury good’) was estimated to be 1.5866 for 1987/88. Following the equation above, this elasticity was calibrated downwards to only 0.5210 for 1997, which indicated that the ‘luxury good’ turned into a ‘necessary good’ in a period of ten years. It was also possible to observe that the income elasticities of demand were more than halved and doubled for wood products and the textiles commodity group, respectively. This unrealistically indicated that textiles turned into the most luxurious consumption item, which provided obvious reasons for avoiding this re-estimation procedure.

18. The Frisch parameter (ℑh) in equation (7.4) corresponds to the ratio of total consumption expenditure by household type h and “supernumerary expenditure” (total expenditure minus ‘fixed or committed’ expenditure) and it is defined as:


)/( ∑ ⋅−=ℑc

chchhh PQEHEH γ

It follows that the ratio of ‘fixed or committed’ consumption to total consumption expenditure is determined from the following equation:

hc

chch EHPQ /)()/1(1 ∑ ⋅=ℑ− γ

19. The average propensity to save was found to be equal to 0.062, 0.051 and 0.427 for urban households, rural households and enterprises, respectively.

20. For example, base-year data for domestic-consumption agriculture indicate that the TFP parameter (αa

va) is 0.28, the exogenous activity-productivity growth factor is 0.24, the import tariff rate is 6.4 per cent, and the skilled-labour force is equal to 4,880 workers. Suppose that the tariff is reduced by 5 per cent, hence levelling off at 6.08 per cent, keeping the skilled-labour supply constant. Since the between-period tariff change is equal to 0.32, and given the estimated elasticity value, the endogenous TFP growth rate will be 0.22 and the TFP parameter will go up to 0.34. Suppose now that the tariff does not change and, instead, the skilled labour supply is increased by 5 per cent. This implies that 244 new skilled workers will be added to the labour force, so the endogenous TFP growth rate will be 1.02 and the TFP parameter will go up to 0.57. These changes in the TFP productivity parameter will only slightly affect agricultural output as will be demonstrated in Chapter 8 in different scenarios.

21. The exogenous commodity basket for urban and rural households and the total number of households by area are all also from INEC.

22. Notice that this exogenous price update affected the world export price of the traditional export agriculture commodity group and the world import price of the oil and chemicals commodity group.

23. GAMS is a package designed to solve fully determined non-linear CGE models, where the number of equations equals the number of variables, a condition which held in the Costa Rican CGE model.

24. The GAMS code included various sections following the procedure spelled out in Robinson et al. (1999). A SETS section identified all the indices used in the model and the subsets in these indices. The PARAMETER and INPUT DATA sections incorporated all the parameters and elasticities, as well as the SAM information used for calibration. These two sections also included the initial data for most of the variables, which were estimated as explained in section 7.3 and which were entered into dummy scalars, vectors and matrices to be used subsequently to initialize the GAMS variables. The CALIBRATION section calculated any parameters not already provided in the model, and given that the initial data had been already provided in the previous sections, it is in this section that subsets dependent on

226 Chapter 7

characteristics of the data (such as trade or non-trade classifications) were defined. The VARIABLES and EQUATION NAMES sections listed respectively the variables and equations of the model and their associated indexes. The INITIAL VALUES section transferred the initial data to the variables from the parameters and figures where they had been entered earlier. The CLOSURE section set the equilibrium constraint equations. Finally, the SOLVE AND DISPLAY section defined the model by giving it a name, specifying the list of equations to be used, providing the solver option, telling GAMS to solve the model, and displaying the results in one or more figures.

25. A detailed presentation on MINOS and PATH can be found in Brooke et al. (1998) and Ferris and Munson (2000), respectively. A formal presentation of the algorithm that was used is available in Adelman and Robinson (1978:233-43).

26. The solution of a CGE model involves solving for a zero of excess demand equations. Shoven and Whalley (1992:67-8) represent this problem as a special case of the more general problem of finding a zero for a system of N excess demand functions: Gi = Gi(P1,…,PN) (i = 1,…, N) The Jacobian matrix J contains the derivatives of the excess demand functions with respect to the prices: J = [∂Gi/ ∂Pj] (i = 1,…, N, j = 1,…, N) At any trial set of prices, P, the excess demand functions Gi(P) can be evaluated. Using the elements of the Jacobian matrix, the changes in each price, ∆Pi

*, required to eliminate excess demand Gi(P) can be calculated:

∆Pi* = ∑

=

N

j 1

[∂Pi/ ∂Gj]⋅Gi(P) (i = 1,…, N)

Some multiple k∆Pi* is added to the price Pi to give a further trial solution Pi’=Pi+

k∆Pi* for each commodity, with the Pi’ normalized to sum to unity. This leads to a

new evaluation of the excess demand functions, a further application of derivatives appearing in the Jacobian matrix, and a continuation of the procedure. The procedure ends when all Gi(P) are within a desired criterion of closeness to zero. The adjustment factor k is typically determined on a trial-and-error basis. In our particular case, the choice of the initial starting values corresponded to the bench-mark equilibrium.

27. A large deviation of elements in the Jacobian matrix may cause an unbalanced solution process which significantly slows down the solution time (Thissen, 2000:256). Moreover, very small partial derivatives may cause the solver to stop searching for a better solution because the progress between iterations becomes too


small. Therefore, the relative size of the partial derivatives in addition to the size of the initial variables in the model may cause scaling problems that hinder an optimal solution. To prevent scaling problems from occurring, the value of the variables and the elements of the Jacobian matrix should be of the same magnitude. The Costa Rican CGE model was, for that reason, scaled by altering the formulation of all its variables in thousands of units instead of units.

28. The structure of the Jacobian is given by the functions in the model, which actually means that it is possible to know a priori whether the model is expected to be stable from a theoretical point of view. Ginsburgh and Waelbroeck (1981:Ch. 7) provide formal examples of how knowledge of the structure of the Jacobian matrix suggests easy ways of solving ‘hard’ problems. They argue that such an evaluation often reveals that lack of convergence is due to a coding or specification error rather than the intrinsic weaknesses of tâtonnement procedures.

29. According to INTEL’s corporate relations director, the multinational’s number of employees was only 1,800 in October 2002 (La Nación, 2002). That only represented approximately 0.8 per cent of manufacturing employment.

228 Chapter 7

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McKitrick, R. (1998) ‘The Econometric Critique of Computable General Equilibrium Modeling: The Role of Functional Forms’, Economic Modelling 15(4): 543-74.

Mukherjee, C., H. White and M. Wuyts (1998) Econometrics and Data Analysis for Developing Countries. London and New York: Routledge.

Nerlove, M. (1958) The Dynamics of Supply. Estimation of Farmer’s Response to Price. Baltimore: The Johns Hopkings University Press.

Pencavel, J. (1986) ‘Labor Supply of Men: A Survey’, in O. Ashenfelter and R. Layard (eds) Handbook of Labor Economics, vol. 1, pp. 3-102. Amsterdam: North-Holland.

Pyatt, G. (1988) ‘A SAM Approach to Modeling’, Journal of Policy Modeling 10(3): 327-52.

Pyatt, G. and J.I. Round (1979) ‘Accounting and Fixed Price Multipliers in a Social Accounting Matrix Framework’, The Economic Journal 89(356): 850-73.

Sauma, P. and M.V. Sánchez C. (2003) Exportaciones, Crecimiento Económico, Desigualdad y Pobreza: El Caso de Costa Rica. San José: Editorial ISIS.

Shoven, J.B. and J. Whalley (1992) Applying General Equilibrium. Cambridge: Cambridge University Press.

Storm, S. (1992) Macro-economic Considerations in the Choice of an Agricultural Policy: A study into Sectoral Interdependence with Reference to India. Amsterdam: Thesis Publishers.

Taylor, L. (1990) ‘Structuralist CGE Models’, in L. Taylor (ed) Socially Relevant Policy Analysis. Structuralist Computable General Equilibrium Models for the Developing World, pp. 1-70. Cambridge, Massachusetts: The MIT Press.

Thissen, M. (2000) Building Financial CGE Models: Data, Parameters, and the Role of Expectations. A Financial CGE Model for Egypt. PhD dissertation, University of Groningen.

300 Technical Appendices

Statistical Appendix: Figures and Tables Table A7.1 Elasticity values used for the calibration of CES and CET functions

σ cm σ c

a σ cva σ c

e Aggregate sector/commodity group (a) (b) (c) (d)

Domestic-consumption agriculture (AGDC) 0.9540 0.5101 0.4220 1.9199 Traditional export agriculture (AGTE) 1.4155 0.5101 0.4220 1.6825 Non-traditional export agriculture (AGNE) 1.8392 0.5101 0.4220 1.5075 Food manufactures (FOOD) 0.8159 0.8007 0.5041 0.8075 Textiles, clothing and leather fabrics (TEXT) 1.1966 0.8007 0.5041 1.7856 Wood products and furniture (WOOD) 1.1966 0.8007 0.5041 1.7856 Oil, chemicals, and rubber and plastic products (CHEM) 1.0282 0.8007 0.5041 4.0300 Paper, non-metallic minerals and basic metals (PMBM) 1.1966 0.8007 0.5041 1.7856 Other manufacturing (OMAN) 1.1966 0.8007 0.5041 1.7856 Perfeccionamiento activo y zonas francas (PAZF) - 0.8007 0.5041 1.7856 Construction (CONS) - 0.8007 0.4949 - Trade (TRAD) - 0.9180 0.4776 - Restaurants, hotels and lodging (RHLP) - 0.9180 0.4776 0.4099 Transport, storage and communication (TRAN) 0.9502 0.9180 0.5305 0.4099 Electricity, gas and water (ELWA) - 0.9180 0.5305 - Financial services and insurance (FSIN) 0.4754 0.7000 0.4776 0.7987 Other services (OSER) 0.4883 0.1900 0.4080 0.4231

Notes: (a) Elasticities of substitution for the calibration of the composite-supply function. Values are not

assigned to non-importable commodity groups. (b) Elasticities of substitution for the calibration of the activity-production function. (c) Elasticities of substitution for the calibration of the value-added production function. (d) Elasticities of transformation for the calibration of the CET function. Values are not assigned to

non-exportable commodity groups.


Table A7.2 Estimates of LES parameters from the INEC 1987/88 National Survey of

Income and Expenditure

Average budget shares (αch)

(a)

Income elasticities of demand (ξch)

(b)

Marginal budget shares (βch)

(a) * (b) = (c) Consumption commodity group

Urban Rural Urban Rural Urban Rural

Domestic-consumption agriculture 0.1284 0.1795 0.6348 0.7363 0.0815 0.1322 Traditional export agriculture 0.0137 0.0277 0.5403 0.5504 0.0074 0.0152 Non-traditional export agriculture 0.0325 0.0297 0.7557 0.6784 0.0245 0.0201 Food industries 0.1466 0.1598 0.7529 0.7963 0.1103 0.1272 Textiles, clothing and leather fabrics 0.1054 0.1056 1.0225 1.0271 0.1078 0.1084

Wood products and furniture 0.0712 0.0874 0.6962 0.6861 0.0496 0.0600 Oil, chemicals, and rubber and plastic products 0.0931 0.1039 0.9673 0.9642 0.0901 0.1002

Paper, non-metallic minerals and basic metals 0.0303 0.0264 1.0322 1.1266 0.0312 0.0298

Other manufacturing 0.0611 0.0529 1.4896 1.4327 0.0911 0.0758 Restaurants, hotels and lodgings 0.0141 0.0149 1.4399 1.6598 0.0203 0.0248 Transport, storage and communication 0.0754 0.0690 1.2400 1.5477 0.0935 0.1068

Electricity, gas and water 0.0395 0.0260 0.7594 0.6979 0.0300 0.0181 Financial services and insurance 0.0099 0.0286 0.9912 1.5836 0.0098 0.0453 Other services 0.1788 0.0886 1.4141 1.5344 0.2528 0.1360 Total sum 1.0000 1.0000 -- -- 1.0000 1.0000

Table A7.3 Re-estimated LES parameters for selected commodity groups

Average budget shares

(αch) (a)

Income elasticities of demand (ξch)

(b)

Marginal budget shares (βch)

(a) * (b) = (c) Commodity group

Urban Rural Urban Rural Urban Rural

Domestic-consumption agriculture 0.0920 0.1298 0.6348 0.7363 0.0584 0.0956 Non-traditional export agriculture 0.0704 0.0606 0.7557 0.6784 0.0532 0.0411 Textiles, clothing and leather fabrics 0.0499 0.0518 1.0225 1.0271 0.0510 0.0532

Wood products and furniture 0.0100 0.0203 0.6962 0.6861 0.0070 0.0140 Transport, storage and communication 0.1642 0.1416 1.2400 1.5477 0.2036 0.2192

Financial services and insurance 0.0363 0.0956 0.9912 1.5836 0.0360 0.1514

Note: the average budget shares are re-estimated from the SAM estimation (in Chapter 6), whereas the marginal budget shares are re-estimated using equation (7.3), maintaining fixed income elasticities of demand.


Table A7.4 Elasticity of the nominal wage rate with respect to the CPI in the covered segments of the labour market

Labour category Sector of the labour

market Activity Skilled

wage labour

Skilled self-employed

labour

Unskilled wage labour

Unskilled self-

employed labour

Domestic-consumption agriculture 0.6744 - - -

Agricultural sector Non-traditional export

agriculture 0.6744 - - -

Food industries 0.6648 0.6648 0.6648 0.6648 Textiles, clothing and leather fabrics 0.6648 0.6648 0.6648 0.6648

Wood products and furniture 0.6648 0.6648 0.6648 0.6648 Oil, chemicals, and rubber and plastic products 0.6648 0.6648 0.6648 -

Paper, non-metallic minerals and basic metals 0.6648 0.6648 0.6648 0.6648

Other manufacturing 0.6648 0.6648 0.6648 - Perfeccionamiento activo y zonas francas 0.6648 - 0.6648 -

Construction 0.6488 0.6488 0.6488 0.6488 Trade 0.6927 0.6927 0.6927 0.6927 Restaurants, hotels and lodgings 0.6927 0.6927 0.6927 0.6927

Transport, storage and communication 0.6745 0.6745 0.6745 0.6745

Electricity, gas and water 0.6488 0.6488 0.6488 0.6488 Financial services and insurance 0.7424 0.7424 0.7424 0.7424

Formal sector

Other services 0.7424 0.7424 0.7424 0.7424


Table A7.5 Factor quantity data, 1997 (number of units)

QFla1/

AGDC-A AGTE-A AGNE-A FOOD-A TEXT-A WOOD-A CHEM-A PMBM-A OMAN-A SWAAG 2098 6261 6674 SNWAG 2782 4756 2060 UWAAG 12799 66457 40748 UNWAG 24972 34805 24421 SWAFO 15075 9575 1964 11495 9317 12918 SNWFO 805 336 572 206 658 3552 UWAFO 24296 22297 6467 8803 11681 13592 UNWFO 180 93 243 95 SWAIN 873 621 1049 355 2205 1440 SNWIN 1948 4364 799 415 643 3644 UWAIN 5526 3131 4459 1500 1287 4607 UNWIN 6987 15609 5289 244 1274 7372

QFla1/

QFSl1/

PAZF-A CONS-A WSRT-A RHLP-A TMCS-A ELWA-A FSIN-A OSER-A SWAAG 15794 SNWAG 9657 UWAAG 128359 UNWAG 84910 SWAFO 28108 7216 58553 12749 21743 10857 32703 195643 449584 SNWFO 4057 10229 2681 2711 416 25628 59963 UWAFO 19218 24267 37432 14030 19113 4544 1649 59462 292797 UNWFO 895 830 269 812 568 11716 SWAIN 2178 14450 2717 4573 152 472 20148 55937 SNWIN 5984 25035 5538 4465 19321 73063 UWAIN 22919 25849 13122 8989 355 69848 176634 UNWIN 26931 53935 14332 17193 46554 199299

QFka2/

AGDC-A AGTE-A AGNE-A FOOD-A TEXT-A WOOD-A CHEM-A PMBM-A OMAN-A Capital 297044 564830 402110 884387 38409 20951 298953 220761 126074

QFka2/

QFSk2/

PAZF-A CONS-A WSRT-A RHLP-A TMCS-A ELWA-A FSIN-A OSER-A Capital 121362 118074 1307878 464480 998853 284087 369874 1652936 8171063

Notes: 1/ The quantity demanded of labour type l in activity a (QFla) is the observed number of workers

employed in 1997. The quantity supplied of labour type l (QFSl) is the observed number of individuals of type l in the labour force or active population at working age (that is, aged 12 or older). The unemployment level of labour type l is determined as: UNEMPl = QFSl - ΣaQFla. The base-year level of migration is not reported since it is derived from a report equation that is solved once the CGE model generated the bench-mark solution.

2/ The sum of the quantity demanded of capital in all activities (QFka) is equal to the economy-wide supply of capital (QFSk) or capital stock. Capital stock data are gross and in millions of colones at constant prices of 1997. The level or excess capacity in the base year is determined by the CGE model solution.

Sources: Employment data are from the INEC Household Survey of Employment and Unemployment, whereas the capital stock data are from the Central Bank’s capital stock data base (for more details on data, see Appendix A).


Table A7.6 Observed percentage annual change in parameter and variable values, 1997-2002

1997-1998 1998-1999 1999-2000 2000-2001 2001-2002

Average import tariff rate 1/

Agricultural commodities -6.29 -18.94 -2.83 -1.60 -0.90 Manufactured commodities -10.17 -31.00 -3.13 -0.60 -0.12 Services -9.13 -27.54 -4.36 -0.98 -0.22

Average export tax rate (economy-wide) 2/ -5.88 -40.00 -66.67 -0.62 -1.06

Average export subsidy rate (economy-wide) 2/ 5.68 -75.27 -34.78 100.00 0.00

Labour force 3/ 5.85 0.52 0.52 3.26 2.60

Nominal exchange rate 4/ 10.97 11.13 9.87 6.64 7.45

World price of traditional exports 5/ 7.91 -3.87 -9.40 2.49 1.95

World interest rate (%) 6/ 5.53 5.71 6.83 3.86 2.17

World oil price 7/ 73.54 -46.55 60.28 -20.55 -6.31

Notes and sources: 1/ Nominal weighted-average tariff (1997=100) from the Ministry of International Trade of

Costa Rica. 2/ The calculation of this rate is explained in Appendix A. 3/ The labour force is the EAP at working age (that is, aged 12 to 64) from INEC

Household Surveys of Employment and Unemployment. 4/ The nominal exchange rate is the price of one US dollar in terms of local currency

(1997=100) from the Central Bank of Costa Rica. 5/ The world price of traditional exports is a composite weighted average price constructed

by the author using data from the Central Bank of Costa Rica. It includes the world price of coffee (US$ per sack), bananas (US$ per ton), meat (US$ per kilogram) and sugar-cane (US$ per sack). The weights were constructed using the commodity shares of total traditional export value.

6/ The London Inter-bank Offer Rate on US Dollar Deposits is used as a proxy for the world interest rate. Percent annual averages from IMF (2002b) were used.

7/ The world oil price is the average annual price in the international market valued as US dollars per barrel, from EIA (2003).

Technical Appendices 325

Technical Appendices Appendix C: Estimations of productivity

C.1 Labour productivity decomposition with sectoral labour reallocation

This first sub-section of Appendix C explains the way in which labour productivity is decomposed while sectoral labour reallocation is also determined, using the method spelled out in Taylor and Vos (2002). Accordingly, aggregate labour productivity ρ is defined as follows:

ρ = Y/L = Σ(Yi/Li) (C.1)

where Y and L are, respectively, output and level of employment, and subscript i represents the sector.

Taking first differences of equation (C.1) yields the following three equations for the aggregate labour productivity growth rate ρ*:

ρ* = Σ[(Yi/Y)⋅ yi - (Li/L)⋅ li] (C.2.a) ρ* = Σ[(Li/L)⋅ ρ*

i ]+ Σ[(Yi/Y)- (Li/L)]⋅ yi (C.2.b) ρ* = Σ[(Yi/Y)⋅ ρ*

i ]+ Σ[(Yi/Y)- (Li/L)]⋅ li (C.2.c)

where yi is the output growth rate in sector i, li is the employment growth rate in sector i, ρ*

i stands for productivity growth rate in sector i, Yi/Y is the sector share of total output, and Li/L is the sector share of total employment.

Equation (C.2.a) decomposes productivity growth into the difference between output change and employment growth. Equations (C.2.b) and (C.2.c) define productivity growth as the weighted average of sectoral productivity growth plus a ‘correction term’ that accounts for sectoral reallocations of, respectively, output and employment. The reallocation weights [(Yi/Y)-(Li/L)] reflect productivity differences across sectors.

This methodology was used to estimate productivity growth rates for the aggregate and sectors, weighted sectoral productivity growth [(Yi/Y)⋅ρ*

i], and sectoral labour reallocation [(Yi/Y)-(Li/L)]⋅li, using Costa Rican data on output and employment for the 1987-2000 period (details on data sources are presented in Appendix A). The purpose of estimating the total sectoral labour reallocation


component of labour productivity was to determine the extent to which structural employment changes during the trade policy reform contributed to labour productivity growth. The estimation results are summarized in Chapter 3 (see Table 3.4).

C.2 Total factor productivity (TFP) growth This second sub-section of Appendix C elaborates on the method used to estimate TFP growth for five aggregate sectors of the Costa Rican economy. The methodological approach was to perform a growth accounting decomposition based on the assumption that each sector’s production function was of the standard Cobb-Douglas type:

Yt = AtKtαLt

1-α (C.3)

where Yt is the sector’s gross domestic product, At is a technological constant (whose value is between 0 and 1), Kt is the stock of capital input, Lt is the amount of labour used as input, and t is a time subscript. Equation (C.3) represents the amount of sectoral output, as a function of inputs, in any specific period t. The underlying assumption is that returns to scale between capital and labour are constant and the economy fully employs all factors under perfect competition. Following Solow (1957), the rate at which Yt grows is decomposed as follows:

y = θ + α k + (1-α)l (C.4)

where y, k and l are respectively growth rates of output, capital and labour inputs, α is the share of capital, (1- α) is the share of labour, and θ is a constant that accounts for the rate at which TFP grows (that is,, the Solow residual).

TFP growth was obtained residually after feeding equation (C.4) with historical growth rates of capital and labour inputs and technological factor shares. The latter are commonly estimated using two alternative methods. The first uses national accounts data to measure the share of income that is distributed to each factor of production (that is, income shares). This method has three limitations from a practical point of view. First, the national accounts are not 100 per cent consistent. Second, small changes in the accounting can generate important changes in the participation of a factor, which may lead to important variations in TFP (De Gregorio et al., 2002). Third, the problems related to the classification of workers who are not employees are ignored, implying that the compensation to employers, self-employed workers and unpaid family workers is not taken into account (Sarel, 1997). Imputations of income may certainly be done, yet under very restrictive assumptions about the distribution of earnings and workers by type. The second traditional method consists of estimating equation (C.4) econometrically, which is the procedure followed in this study. An alternative method is proposed in Sarel (1997) for the


particular case of cross-country studies, which assumes that technological factor shares are also determined by the industrial structure of the economy and by its level of development.

Technological factor shares were estimated by first dividing both sizes of equation (C.3) by the size of the labour force, taking logs, and first-differencing:

ln(yt / yt-1) = ln(At / At-1) + α ln(kt / kt-1) (C.5)

where the rate of change in output per worker is related to the rates of change of TFP and capital per worker. The rate of growth of TFP was assumed to be a constant (θ) plus a random term (ε) which yielded the following estimable equation:

ln(yt / yt-1) = θ + α ln(kt / kt-1) + εt (C.6)

One criticism of this estimation approach is that it assumes that the growth rate of each input is exogenous, although in reality it may change over time because of changes in the production composition among sectors. In principle, this limitation should not affect our estimations since they are for sectors and not for the country as a whole. The estimation by sector does take into account the fact that different activities may use different production technologies, although the degree of sectoral aggregation will always remain an issue of controversy. The estimation by sector also reduces the potential bias of not taking into account quality change in factor inputs. Cross-country studies show that taking the effect of quality change into account (by reflecting changes in the composition of factors) improves the estimates of TFP (see Jorgenson and Griliches, 1967, for a theoretical note; Young, 1995, for cross-country evidence; and, Roldos, 1997 and De Gregorio et al., 2002, for country-case results).

Two important aspects were taken into consideration for the estimation of equation (C.6). First, it is possible that θ had suffered a break in some sectors after the reform period (say, 1985 onwards), when a noticeable recovery fuelled by an important reduction in unemployment was observed. In that case there should be some control for such a break so that it does not affect the TFP growth estimates. Second, short-run fluctuations (that is, business cycle) may disguise changes in capacity utilization as changes in TFP. This is important in the Costa Rican context, where, during severe recessions such as the debt crisis (1980-83) and less severe recessions in 1991 and 1996, firms may have been forced to reduce capacity utilization. Overlooking such an effect may imply important biases in the measurement of TFP growth, hence important adjustments have to be made for it (Griliches, 1992:111-12). In the light of these two important aspects, and adopting an approach that has been used for other Latin American countries (Fajnzylber and Lederman, 1999, Lefort and Solimano, 1994), the following equation was estimated for the 1976-97 period:

ln(yt / yt-1) = θ + α ln(kt / kt-1) + DREF + DREC1 + DREC2 + εt (C.6.a)


where DREF is a dummy variable activated in the years in which the economy is considered to be reformed, DREC1 is a dummy variable activated in the years of recession, and DREC2 is a dummy variable activated in the years in which an index of TFP growth turned negative (following Fajnzylber and Lederman, 1999). The dummies in equation (C.6.a) are only a ‘crude’ way of capturing the impact of changes in capacity utilization on TFP. Some more complex models may also be estimated. For example, De Gregorio et al. (2002) use continuous macro-economic indicators against the production function residuals and IV tests to take the influence of the business cycle into account.

Equation (C.6.a) was estimated for the 1977-97 period using data on physical capital stocks and gross domestic output (GDP) from the Central Bank of Costa Rica (at 1966 prices). The labour force data are from INEC. More details on the data, especially some remarks on the labour force data, are presented in Appendix A. The variable DREF was activated in 1985-97, whereas DREC1 was activated when sectoral GDP growth became negative, which was, in most cases, observed for the debt-crisis period and economic recessions in 1991 and 1996. The inclusion of DREC2 relies on an assumption made in Griliches and Lichtenberg (1994:472) that “true” productivity can only improve, so that measured reductions in TFP can only reflect short-term fluctuations. Given this assumption, the TFP series are only allowed to increase or stay constant. Griliches and Lichtenberg also estimate an equation like (C.6) after averaging the variables over five-year periods, which is not done in this study to avoid an important loss of degrees of freedom. The index of TFP growth is calculated on the basis of equation (C.5) assuming a value for α. A 0.4 average capital share of output has been used in Fisher (1993), Marfan and Bosworth (1994), Nehru and Dareshwar (1995) and Fajnzylber and Lederman (1999). Collins and Bosworth (1996) have used a value of 0.3 for α in a study that compares the growth experience of East Asian economies with that of other regions. The conclusion from all this literature is that a plausible range for the capital share is 0.3 to 0.4. In our particular case, the rate of TFP growth was found to be negative in various years and this result did not vary much under the assumption that the capital share was either 0.3 or 0.4. As can be seen in Table C.1, a common pattern is that TFP growth declined at the onset and during the debt-crisis period and also as the economy approached or fell into recession in 1991 and 1996. DREC2 was activated under the assumption that α was equal to 0.4.


Table C.1. Years in which sectoral TFP growth (θ) was negative in Costa Rica, assuming two different values for the average capital share of output (α)

Sector θ < 0 (if, α = 0.3) θ < 0 (if, α = 0.4)

Agriculture 1979-80, 1982, 1985, 1987-88, 1990, 1996-97

1979-80, 1982, 1985, 1987-88, 1990, 1993, 1996-97

Manufacturing 1/ 1979-83, 1987, 1989, 1991, 1996 1977, 1979-83, 1987, 1989, 1991, 1996

Construction 1978, 1980-82, 1987, 1990-91, 1995 1978, 1980-82, 1987, 1990-92, 1995

Basic services 2/ 1980, 1982, 1984-85, 1995 1980, 1982, 1984-85, 1995

Trade and services 3/ 1978, 1980-82, 1991, 1995, 1996-97 1978, 1980-82, 1991, 1995, 1996-97

Other services 1978-82, 1988, 1995-97 1978-82, 1988, 1995-97

Notes: 1/ This sector includes mining and quarrying. 2/ Electricity, gas, water, transport, storage, and communications. 3/ Trade, restaurants, hotels and lodgings, financial services, insurance, and real estate.

The main estimation results are summarized in Table C.2, where it can be

seen that all coefficients are statistically different from zero at standard significance levels. The average TFP growth rate for the 1977-97 period turned out to be positive in all sectors. Cross-country evidence for Latin America confirms this result for the country as a whole (see, for example, Fajnzylber and Lederman, 1999; De Gregorio, 1992). Given the use of transformed data, there was no generalized problem of non-stationarity, so the OLS method was used. It is, however, worth noting that the chosen specifications for agriculture, manufacturing and construction differ slightly from that implied by equation (C.6.a). A problem of positive first-order serial correlation was detected in the estimation of the first two sectors. This problem was only corrected after estimating a generalized difference equation, which suggested that DREC1 and DREC2 were highly correlated in the particular case of those two sectors. The serial correlation was due to a problem of model specification, which was removed by estimating the specifications presented in Table C.2. In the case of construction, DREF was not found statistically different from zero. The coefficient on DREF only turned positive for agriculture and manufacturing. This indicates that, according to the method followed, TFP growth increased in agriculture and manufacturing during the reform period, although this effect was only modest.

The estimation method provided robust estimates of actual TFP growth. The estimates of factor shares in Table C.2 were used to perform a growth


accounting decomposition following equation (C.4). The results are summarized in Table 3.5 in Chapter 3. Under the assumption of constant factor shares, the growth accounting decomposition enabled the author to construct time series for actual annual growth rates of TFP for the 1977-97 period, which were used to estimate elasticity values for the endogenous productivity growth function of the CGE model. Complementary estimations were performed using an equation like (C.6) and only including the debt-crisis dummy variable (DCRI). By comparing the results of these complementary estimations with the initial ones, the author found that the inclusion of DREC1 and DREC2 was indeed necessary to purge the measured change of TFP from the effect of recessions. The estimation results for agriculture confirm that ignoring the effect of recessions would have led to an important overestimation of TFP growth. Consider the estimates for 1984-95 in Table C.3, for example. TFP growth in agriculture was found to be relatively high in 1987-95 when the effect of recessions was ignored, whereas it even turned negative when such an effect was included. Similar estimation biases were encountered for the other sectors of the economy.


Table C.2 OLS estimation results for the transformed growth accounting

decomposition function, 1977-97 (t-values in parentheses)

Sector θ α DREF D

REC1 DREC2 R2 DW* 1 - α

0.2384 0.7531 0.0103 0.0115 0.81 1.94 0.2469 Agriculture

(1.9538) b/

(3.6456) a/

(2.2031) a/

(2.4630)a/

(-)

0.3348 0.6594 0.0012 0.0168 0.61 2.11 0.3406 Manufacturing (1.9877)

b/ (1.9273)

b/ (1.7828)

b/ (-) (2.8279)

a/

0.2948 0.6905 0.0136 0.0289 0.70 1.87 0.3095 Construction (1.8181)

b/ (4.3031)

a/ (-) (1.9142)

b/ (3.5268)

a/

0.3896 0.6107 -0.0068 0.0115 0.0082 0.89 1.97 0.3893 Basic services (6.6117)

a/ (10.1914)

a/ (-2.1673)

a/ (1.7483)

b/ (2.0681)

b/

Trade and services 0.5385 0.4623 -0.0034 0.0092 0.0075 0.66 1.99 0.5377 (3.9541)

a/ (3.3984)

a/ (-1.8291)

b/ (2.1281)

a/ (2.3900)

a/

Other services 0.2994 0.7052 -0.0070 0.0012 0.0025 0.92 1.98 0.2948 (4.6736)

a/ (10.9688)

a/ (-4.9276)

a/ (1.8575)

b/ (1.8855)

b/


per cent significance level is: 1.964 - 2.036 for five coefficients and 1.812 - 2.188 for four coefficients.

(-) Dummy variable dropped out of the initial equation given problems of misspecification. a/ Coefficient statistically significant at the 5 per cent or lower significance level. b/ Coefficient statistically significant at the 10 per cent significance level.

Table C.3 Period-averages of TFP growth in agriculture under two alternative specifications, 1984-95 (percentages)

Period averages Econometric specification

1984-86 1987-90 1991-95

ln(yt / yt-1) = θ + α ln(kt / kt-1) + DREF + DREC1 + εt 0.8 -5.6 -1.3

ln(yt / yt-1) = θ + α ln(kt / kt-1) + DREF + DCRI + εt 2.1 3.2 3.1


Appendix H: Equation blocks for SAM-based calibration

Table H.1 SAM-based equation blocks for base-year variable value estimation

Equation Domain Equation Domain

∑∈

⋅=Cc

cc cwtsPQCPI PQtQINT ccaca

= c∈ C a∈ A

tTEG GOVISGOV ,−−= PQtQINV cIScc −

= , c∈ C

∑∈

=Cc

chh tEH h∈ H ttQM cIMPTcROWc ,, += c∈ C

tFSAV ROWIS ,−= QMQDQQ ccc

+= c∈ C

tGSAV GOVIS ,−= ∑

∈

=Ff

faa tQVA a∈ A

∑∈

⋅=Cc

cc QINVPQI

∑∈

=Aa

acc tQX c∈ C

∑∈

⋅=Cc

ccaa PQicaPINTA a∈ A tQXAC acac

= a∈ A c∈ C

∑∈

⋅=Cc cc qinvshPQPK

)( QFtWF faAa

faf ∑∈

=

f∈ F

∑∈

⋅=Cc

cc dwtsPDPPI WFtWFDIST ffafa =

a∈ A f∈ F

QQtTPQ cCc

ROWccc⎟⎠

⎞⎜⎝

⎛−= ∑

=,

c∈ C WFKAV

WFDISTWFWFDISTKk

kakka

⋅=

a∈ A f∈ F

TQA aa= a∈ A ∑

∈

⋅⋅

=

Aa kakak

k

capshWFDISTWFWFKAV

k ∈ K

QEQXQD ccc−= c∈ C CPIWFWFREAL ll =

l∈ L

tttQE EXPSccEXPTROWcc ,,,+−= c∈ C ∑

∈

=Aa

faf tYF

f∈ F

tQG GOVcc ,= c∈ C TYG GOV=

)( PQtQH cCc

chh ∑∈

= h∈ H tYFI finsdfinsd ,, =

insd∈ INSD f∈ F

)( PQtQINTA cCc

caa ∑∈

= a∈ A TYI insdnginsdng =

insdng∈ INSDNG

Notes: lower-case subscripts stand for model sets (see Appendix F, Table F.1) and upper-case subscripts refer to SAM accounts (see Chapter 6, Table A6.4). An upper-case letter T stands for SAM account sums, whereas a lower-case letter t represents SAM transactions. Most prices associated with quantities and the CPI are not included because they are set at unity, and factor quantities (QFfa) are exogenous information. The investment adjustment factor (IADJ in eq. F.38 in Appendix F) is equal to one in the base year. No differentiation is made between fixed and unfixed variables.


Table H.2 SAM-based equation blocks for parameter estimation

Equation Domain

( ) ρρρ δδαva

a

a

a

a

a QINTAQVAQA a

a

aa

a

aa

a

a

1

1−

−

⎥⎦

⎤⎢⎣

⎡⋅+

−⋅= −

a∈ A

ρρρ δδαe

c

e

c

e

c QDQEQX c

e

cc

e

cc

e

c

1

)(1 ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−+⋅= c∈ C

ρρρ δδαm

c

m

c

m

c QDQMQQ c

m

cc

m

cc

m

c

1

)(1−

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅−+

−⋅= c∈ C

( ) ρρδαva

a

va

a

Fffa

va

aa

va

a QFQVA1

−

∈

−

⎥⎦

⎤⎢⎣

⎡⋅= ∑

a∈ A

∑∈

=Cc

chchch ttα a∈ A

( ) ( )( ) ( )

a

a

a

a

QINTAQVAPINTAPVA

QINTAQVAPINTAPVA

aaaa

aaaaa

a ρ

ρ

δ +⋅+

+⋅=

1

1

1

c∈ C

( ) ( ) 111

−⋅+

=ρδ e

cQDQEPEPD cccc

e

c

c∈ C

( ) ( )( ) ( ) ρ

ρ

δ +⋅+

+⋅

=1

1

1m

c

m

c

QDQMPDPM

QDQMPDPM

cccc

ccccm

c

a∈ A

( )ρ

ρ

δ va

a

va

a

Fffaffa

faffava

a

QFWFWFDIST

QFWFWFDIST+

∈

+

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⋅⋅=

∑1

1

a∈ A, c∈ C

Tt aacac=θ c∈ C, h∈ H

tTtaps insdngYTAXinsdnginsdngISinsdng ,,−=

− insdng∈ INSDNG

∑∈

=Aa kakaka QFQFcapsh

a∈ A, k∈ K

∑∑∑∈ ∈∈

=Cc Hh

chHh

chc ttcwts c∈ C

∑ ∑∑∈ ∈∈

⎟⎠

⎞⎜⎝

⎛−⎟

⎠

⎞⎜⎝

⎛−=

CcROWc

AaacROWc

Aaacc ttttdwts ,,

c∈ C

QINTAtica acaca = a∈ A, c∈ C

in QAQINTAta aaa=


Table H.2 (Continued) Equation Domain

∑∈

=Cc

ccc QDQDpdwt c∈ C

∑∈

=CEc

ccc QEQEpwewt c∈ C

∑∈

=CMc

ccc QMQMpwmwt c∈ C

⎟⎠

⎞⎜⎝

⎛+

=

∑ ∑∈ ∈CEc CMc

cc

cc

QMQEQEpwexwt

c∈ C

⎟⎠

⎞⎜⎝

⎛+

=

∑ ∑∈ ∈CEc CMc

cc

cc

QMQEQMpwimwt

c∈ C

( ) PQttqstch cDSTKcIScc ,, +=−

c∈ C

PQtqg cGOVcc ,= c∈ C

QINVqinv cc= c∈ C

∑∈

=Cc

cccQINVQINVqinvsh

c∈ C

Ttshif ffinsdfinsd ,,= insd∈ INSD

Ttta aaATAXa ,= a∈ A

ttte ROWccETAXc ,,= c∈ C

Tttins insdnginsdngYTAXinsdng ,= insdng∈ INSDNG

tttm cROWcIMPTc ,,= c∈ C

Tttq ccSTAXc ,= c∈ C

ttrnsfr fROWfROW ,,= f∈ F, I∈ I

ttrnsfr ROWfROWf ,,=

f∈ F, i∈ I

ttrnsfr ROWinsdROWinsd ,,= i∈ I

ttrnsfr GOVinsdGOVinsd ,,= i∈ I

ttts ROWcEXPScc ,,= c∈ C Notes: lower-case subscripts stand for model sets (see Appendix F, Table F.1) and upper-case subscripts refer to SAM accounts (see Chapter 6, Table A6.4). An upper-case letter T stands for SAM account sums, whereas a lower-case letter t represents SAM transactions. Most prices associated with quantities are not included because they are set at unity, and factor quantities (QFfa) are exogenous information. No differentiation is made between fixed and unfixed variables. Shift and share parameter equations are determined from the CES and CET equations.


Appendix I: Equations for estimation of elasticity values

I.1 Elasticities of substitution and transformation

A demand-side equation system can be derived as a first-order approximation of the composite-supply (Armington) function, in order to arrive at an equation that enables estimation of elasticities of substitution (σ). The estimated coefficients for the relative price term can be interpreted properly as elasticities of substitution. This procedure was first proposed in Hickman and Lau (1973) and was used later in Kouwenaar (1988). The derivation of the demand-side equation system begins by applying the Lagrange multiplier in the minimization problem given by the composite-supply function equations (Appendix G, eqs. (G.8) and (G.11)). Taking out the sales tax term (1-tqc), with no implication since the data used are net of taxes, and removing the superscript m in the parameters for explanatory ease, yields:

σ

δα σσc

cc

PMPQ

QQQM

c

ccc

c

c

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅⋅= −1 (I.1)

and the commodity import share of total composite commodity supply, ζc, is: 1

1

−

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⋅⋅=

⋅

⋅=

σ

δαζ σσc

cc

PMPQ

QQPQQMPM

c

ccc

cc

cc

c

(I.2)

The derivation of the demand-side equation system includes the usual restrictive assumptions of perfect competition among users of a commodity, such that importers are in equilibrium; that is, the desired cost-minimizing demand is equal to the actual realized demand (Kouwenaar, 1988:360). In such a setting, import shares are estimated as functions of relative (producer) prices. The CES function share parameters (δc) are subject to an exogenous change, that is (removing subscript c):

e t

t

εδδ 0= (I.3)

As Hickman and Lau (1973:349) explain, the inclusion of a term for the exogenous change in the share parameters is important for taking into account changing tastes over time, such that misspecification is avoided. In addition, the adding-up properties of the equation system are still preserved. The derivation of the estimable function carries on by defining implicit price deflators that are calculated as the ratio of imports in current prices (including tariffs) to imports at constant prices (including tariffs) as follows:

( )PMQMPMQM

PMPM

conscons ⋅⋅

= (I.4)


Also using an implicit price deflator for the domestic supply (PQ/PQcons), the following relative price index is constructed:

PMPMPQPQp

cons

cons

//

= (I.5)

which is equal to the ratio of import shares in constant and current prices. Applying logarithms to equation (I.2), substituting the relative price index

into it, and assuming that the share parameters are subject to an exogenous change yields:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+++= −−− PM

PQPMPMPQPQ

tcons

cons

cons

cons log)1(//log)1(loglog)1(log 0 σσεσδσασζ

or: logζ = a + b log p + ct (I.6)

where,

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛++= −− PM

PQa

cons

conslog)1(loglog)1( 0 σδσασ

b = (σ - 1) c =σε

Equation (I.6) is an import demand function which, after econometric estimation, provides elasticity values (σ) directly from the regression coefficients. This function implicitly assumes that, as seems reasonable in this case, the supply of imports to the country is completely elastic. Notice that no allowance is made for quantitative restrictions on imports in equation (I.6). This facilitates the estimation because, as argued in Kouwenaar (1988:361), including quantitative restrictions on imports would imply that importers are ‘kicked off’ their demand curves and elasticities cannot be estimated properly. Given the use of relatively long-time series, the inclusion of two dummy variables in equation (I.6) proved necessary in some cases to take into account debt crisis and structural adjustment reform periods, respectively (see Chapter 7).

An equation like (I.6) can also be used to estimate the elasticities of substitution in the activity-production and value-added functions; thus, for the former we have:

⎟⎟⎠

⎞⎜⎜⎝

⎛++= −− PVA

PAacons


⎟⎟⎠

⎞⎜⎜⎝

⎛=

PVAPVAPAPAp

cons

cons

//

and, for the value-added function we have:

⎟⎟⎠

⎞⎜⎜⎝

⎛++=

⋅−− WFDISTWF

PVAacons



⎟⎟⎠

⎞⎜⎜⎝

⎛=

⋅⋅ WFDISTWFWFDISTWFPVAPVAp

cons

cons

//

The export quantity share of domestic output level in the CGE model responds to changes in relative prices. This relationship can be imposed a priori as a restriction in an export-supply function, which assumes a restricted form of a complete export supply function (Kouwenaar, 1988). Accordingly, the model’s CET aggregation function is used, including a time trend term to account for an exogenous change in time. The restricted export-supply function is written in such a way that the relative price coefficient corresponds to the elasticity of transformation, as follows (omitting superscript e and subscript c in the parameters for explanatory ease):

log(QEc/QXc) = a log δ0 + b log(PDc/PEc) + cε t (I.7)

where δ is an exogenously changing distribution parameter defined as δ = δ0 exp{ε t}, and b is the elasticity of transformation. Again, the inclusion of two dummy variables to account respectively for the debt crisis and structural adjustment reform periods proved necessary for the estimation of some elasticities of transformation in the Costa Rican context (see Chapter 7).

The type of data used for the estimation of elasticities of substitution and transformation are outlined in Table I.1. The detail on data sources is presented in Appendix A. All estimations covered the 1966-2000 period, except for the value-added function because employment data were only available from 1976. Lack of sectoral breakdown in the data limited the estimation, particularly on gross output value for the estimation of elasticities in the activity-production function. Price deflators for 1997 were used for the estimation of relative price indexes and quantities (or values at 1997 prices) in line with the base year of the CGE model. The dummies for the debt crisis and reform periods were activated in 1980-83 and 1984-2000, respectively.

The unit roots method indicated that some of the logarithmic data were not stationary. Additionally, after initially applying OLS estimations, the Durbin-Watson statistic suggested that there were some problems of autocorrelation (positive serial correlation). Autocorrelation was corrected using the C-O two-step procedure. Therefore, the estimation of elasticities of substitution and transformation combines results from estimated OLS and generalized difference equations. The main results are reported in Tables 7.1-7.4 in Chapter 7.


Table I.1 Description of data used in the estimation of elasticities of substitution and transformation

Data 1/ Disaggregation 2/ Period Function

Aggregate employment 2 sectors 6 sectors

1966-2000 1976-2000

Activity-production function Value-added function

Export price index (1997=100) 9 sectors 1966-2000 CET function Export value (current and constant)

9 sectors 1966-2000 CET function

GDP at factor cost (current and constant)

2 sectors 6 sectors

1966-2000 1976-2000


Gross output value and implicit price

2 sectors 1966-2000 Activity-production function

Implicit price in GDP at factor cost (1997 = 100)

2 sectors 6 sectors

1966-2000 1976-2000


Import price index (1997 = 100) 9 sectors 1966-2000 Armington function Import value (including tariff revenue - current and constant)

9 sectors 1966-2000 Armington function

Labour income3/ 2 sectors 6 sectors

1966-2000 1976-2000


Producer price index (1997=100) 9 sectors 1966-2000 Armington function Total demand (supply) in current and constant prices

9 sectors 9 sectors

1966-2000 1966-2000

Armington function CET function

Wholesale price index (1997=100)4/

Total index 1966-2000 CET function

Notes: 1/ All value data are in millions of colones at current and constant (1997) prices. Quantity

variables are proxied by deflating current values using the corresponding 1997 price index. 2/ 2 sectors: agriculture and manufacturing.

6 sectors: agriculture; manufacturing; construction; basic services; trade & restaurants, hotels and lodging & financial services and insurance; and, other services. 9 sectors: domestic-consumption agriculture; traditional export agriculture; non-traditional export agriculture; food industries; chemicals, oil and petroleum; manufacturing (other); transport; financial services; and, other services.

3/ Labour income is the total average monthly income from all occupations. To construct the implicit price for labour, average wages in current prices were divided by average wages in 1997 prices.

4/ Following Goldstein and Khan (1985:1054-6), export volumes were estimated deflating the nominal value of exports using the wholesale price index (1997). This type of transformation of export value helps to reduce the risk of having to face the problem of non-stationary data.

I.2 Elasticities for the nominal wage indexation

The minimum wage adjustment in the CGE model is instantaneous, whereby the activity-specific wage in the covered segments of the labour market responds to changes in the CPI, as explained in Chapter 5 (sub-section 5.4.3).This adjustment is determined using the elasticity of the activity-specific wage with respect to the CPI, the estimation of which is carried out following the method outlined in Storm (1992). Accordingly, the nominal wage indexation is


expressed in a partial adjustment framework analogous to acreage response functions presented in Nerlove (1958), which can be reformulated in terms of a sector-specific bargaining process between employees (probably represented by labour unions) and employers. Employees in the covered segment i strive after some “desired” nominal wage in period t, w*

i,t, which they relate to the consumer price index cpie

t:

cpiwe

tiiti φφ 10

*

, += (I.8)

where φ1i reflects the degree of indexation desired by employees, given the restriction that 0< φ1i <1.

The employees form their consumer price expectation adaptively as follows:

⎥⎦⎤

⎢⎣⎡ −⋅=−

−−cpicpicpicpi e

tti

e

t

e

t 11 ι (I.9)

where ιi is the coefficient of price expectation under the restriction that 0< ιi ≤1. Nominal wage rates in each period t are formed on the basis of the past-

period wage rate (basic wage) and the wage rate desired by employees:

www tiitiiti 1,

*

,,)(1 −⋅+= −ψψ (I.10)

where ψi denotes the rate of adjustment reflecting the bargaining power of employees vis-à-vis employers, given the restriction that 0< ψi < 1.

Most of the analytical literature focuses on the role of ex ante wage indexation (Agénor, 1996). However, wage indexation is in practice ex post (as in the Costa Rican case), with current wages adjusting to past changes in prices. That is why we introduce an ex post adjustment from equation (I.9). The method proceeds by substituting equation (I.8) into (I.10):

wcpiw tii

e

tiiiiti 1,10, )(1 −⋅++= −ψφψφψ (I.11)

and then, combining equations (I.9) and (I.11) yields:

wcpicpiw tii

e

tiiitiiiiiti 1,1110,)()( 11 −−⋅⋅⋅⋅++= −− ψιφψιφψφψ (I.12)

Lagging equation (I.11) by one period, multiplying it by (1- ιi) and subtracting it from equation (I.12) results in the following equation:

[ ] [ ] wwcpiw

tiiitiii

tiiiiiiti

2,1,

10,

)()()()( 1111 −−⋅+−⋅+

++=

−−−− ψιψιιφψιφψ (I.13)

Assuming that ιi = 1, or that cpite = cpit, which is consistent with the

instantaneous minimum wage adjustment, yields the following estimable function:

wcpiw tiitiiti 1,210, −++= ϖϖϖ (I.14)

where, ϖ0i = ψiφ0i, ϖ1i = ψiφ1i, ϖ2i = (1-ψi) are, respectively, the constant, the elasticity of the nominal wage rate with respect to the CPI, and the elasticity of


the nominal wage rate with respect to its one-period lagged value. Both elasticities are between zero and one.

Equation (I.14) was estimated using OLS and monthly data for the 1995-2000 period. Data availability for the minimum wage index and the CPI from the Central Bank of Costa Rica enabled the estimation of seven aggregate-sector equations. Both the minimum wage and the CPI were indexed to the 1997 December price. Logarithms were used in order to estimate elasticities, and this in turn helped to correct autocorrelation (Mukherjee et al., 1998). The results of the estimation were statistically satisfactory. In particular, the elasticities were found to be statistically significant and falling within the expected range (see Chapter 7, Table 7.7).

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7 Calibration, Solution and Validation of the CGE Model