Estimates of Armington parameters for a landlocked economy

Transcription

1 MPRA Munih Personal RePE Arhive Estimates of Armington parameters for a landloked eonomy Jean-Pasal Nganou World Bank 9. August 2005 Online at MPRA Paper No , posted 12. June :49 UTC

2 Estimates of Armington Parameters for a Landloked Eonomy Jean-Pasal N. Nganou 1 World Bank Abstrat: One of the most debated issues in the Computable General Euilibrium (CGE) literature onerns the validity of the key behavioral parameters used in the alibration proess. CGE modelers seldom estimate those parameters, preferring to borrow from the handful of estimates available in the literature. The lak of data is often ited as a reason for this type of modus operandi (tehniue). Estimating key parameters is very ruial sine CGE results are uite sensitive to parameter speifiation. This paper proposes a new and robust eonometri tehniue, the Generalized Maximum Entropy (GME), to estimate Armington elastiities for seleted ommodities. All the parameters estimated are intended for use in a Lesotho CGE model. Keywords: CGE; Maximum Entropy (GME); Armington; Afria; Lesotho 1 Jean-Pasal N. NGANOU: World Bank, 1818 H Street, NW, Room J7-114, Washington, DC 20433, USA. Tel: +1(202) ; Fax: + 1(202) ; jnganou@worldbank.org. This paper is based on the author's dissertation at Amerian University, Washington, DC (Nganou, 2005), written under the supervision of Amos Golan whose thoughtful advie and ritiism have been invaluable. The author is also grateful for omments and enouragement from the other members of his dissertation ommittee, inluding Vandana Chandra (World Bank), Hans Lofgren (World Bank), and Mieke Meurs (Amerian University). The author is also indebted to Sherman Robinson (University of Sussex) for his omments on a previous version of this paper. An earlier version of the paper was presented at the International Conferene Input-Output and General Euilibrium: Data, Modeling, and Poliy Analysis, Brussels (Belgium), September 2-4, Eletroni omments addressed to jnganou@worldbank.org. The usual dislaimer applies.

3 1. Introdution One of the most debated issues in the omputable general euilibrium (CGE) literature onerns the validity of the key behavioral parameters used in the alibration proess. CGE modelers seldom estimate these parameters empirially, preferring to borrow from the handful of estimates available in the literature. These estimates usually are more appropriate for ountries other than the ones the CGE model is trying to represent. Moreover, ritis argue that the partial euilibrium framework in whih these parameters are mostly estimated is inonsistent with CGE analysis. The pauity of data is often ited by CGE modelers as the major reason for onsidering ompromises to the empirial basis for the parameters used in CGE models. The literature on the estimation of Armington elastiities of substitution has been limited for the ontext of developing ountries. 2 Table 1 below, presents a summary of seleted studies on the estimation of Armington elastiities. In several studies, Shiells and his assoiates applied three eonometri methods (generalized least suare (GLS), maximum likelihood (ML), and simultaneous euations system) to a large multisetoral U.S. data set (Shiells, Stern, and Deardoff, 1986; Shiells and Reinert, 1993). While their studies suggested that the estimation method does not matter, their results were struturally inonsistent with the general euilibrium analysis, sine the formal analysis of the model largely ignored the supply side of the market. Galloway, MDaniel, and Rivera (2000) used time series regressions to estimate long-run Armington elastiities for the U.S, and their findings indiated higher Armington estimates ompared to those found by Shiells and assoiates. Arndt, Robinson, and Tarp (2002) employed a system of simultaneous euations-based generalized maximum entropy (SSE-GME) to estimate Armington parameters for Mozambiue. Their methodology is onsistent with the general euilibrium framework sine they exploit the flexibility of maximum entropy to add a general problem. 2 MDaniel and Balistreri (2002) provides a omprehensive literature review on Armington elastiities. 2

4 Table 1: Seleted Empirial literature on Armington Parameters Estimation Studies Country Methodology Remarks Shiells, Stern, USA Based on: Methodology does not and Deardoff (1986); * generalized least matter. Shiells and Reinert suare(gls),maximum Struturally inonsistent (1993 likelihood (ML), system of with general euilibrium simultaneous euations. analysis: supply side of the market ignored. * Large multisetoral data. Gallaway, M- USA Time series regression *Found higher estimates. Daniel and (long-run analysis). Reinert (2000) Arndt, Tarp and Mozambiue Simultaneous euations Speifiation onsistent Robinson (2002) Generalized with general euilibrium Maximum Entropy. analysis. Soure: Nganou (2005) The purpose of this paper is to address some of the ritiisms leveled against the use of parameters taken from the literature in CGE models. In this paper, we provide an alternative estimation tehniue to the use of parameters taken from the literature in CGE models. Our methodology on the estimation of the Armington parameter is a variant of the methodology used in Arndt, Robinson, and Tarp (2002), to the extent that it relies on a single euation generalized maximum entropy (GME). However, unlike Arndt, Robinson, and Tarp (2002), we did not inlude a onstraint to aount for general euilibrium analysis. More speifially, our estimates of Armington elastiites depend on data availability, intended for use in a Lesotho CGE model. This is primarily to address some of the oneptual problems that would arise in estimating CGE models, as some of earlier studies have shown that results from CGE models are often sensitive to the value of those behavioral parameters (e.g., Arndt, Robinson, and Tarp 2002). 3

5 2. The Data Lak of data is the most ommon prediament in developing ountries for the estimation of Armington elastiities. Available data suggest that onsumers in Lesotho hoose between the following imported and domestially produed goods: Agriulture, Food, Beverages and Tobao, Textiles, Mining and uarrying, and Transport. Disaggregated annual data on imports were obtained from the Lesotho Bureau of Statistis overing Given that these series were in nominal loal urreny units, appropriate average annual import prie indies (or import pries, base year 1997=100), also from the Bureau of Statistis, were used to evaluate the transation import pries. Subseuently, real import series were taken to be the physial uantity of imported ommodities. Data on the prie of domesti output was obtained from the onsumer prie index (CPI) of the Bureau of Statistis, while real GDP data were used as the physial uantity of domestially produed goods and servies. Summary of desriptive statistis for real imports, real domesti outputs, import pries and domesti output pries are presented in Table 2. Table 2.Desriptive Statistis (means) for Key variables in the Armington Regression Commodities Imports a Domesti Prodution value a Import Prie Index b Domesti Prie Index b Agriulture Food & Bev. & Tobao Textiles Mining Transport Soure: Author s Calulations. Note. a=imports and domesti prodution are evaluated at onstant pries and measured in million of Maloti. b=for both prie indies, 1997 is the base year. 3. Estimation of Armington Parameters Given the dearth of data for the variables reuired for estimating Armington elastiities, GME tehniue was employed in this analysis. Earlier studies (see for example, Golan, Judge, and Miller 1996) have shown that GME method is more appropriate for ill-posed and limited data problems, as it provides more robust results. 4

6 A. A Brief Theoretial Bakground 3 The Armington elastiity, whih measures the degree of substitution between domesti and imported goods, is a key behavioral parameter that drives the results of interest to poliymakers. For instane, trade poliy an affet the prie of traded goods relative to domestially produed goods. Suh prie hanges will affet a ountry s trade opportunities, level of inome, and employment. The magnitude of these impats will largely depend on the magnitude of the elastiities, inluding Armington parameters. Partial and general euilibrium models that rely on the Armington elastiities are usually sensitive to these parameters (MDaniel and Balistreri 2002). Thus, it is important to use the right Armington parameters for the ountries of study. Therefore, despite the dearth of data for Lesotho, we used GME tehniue to estimate Armington parameters. The Armington assumption states that imported and domesti goods are imperfet substitutes for any traded good. 4 Conseuently, the model departs from the neolassial assumption of perfet substitutability of tradables and the law of one prie. Domesti final demand is oneptually omprised of household onsumption demand (QH), government onsumption demand (QG), investment demand (QINV), and the demand for intermediate inputs (QINT) generated by domesti produers. The reuired demand ould be met through either domesti prodution or imported ommodities. It is assumed that, for eah ommodity, supply from domesti and foreign soures is ombined to form a omposite ommodity (QQ) whih will be available to domesti onsumers. This is ahieved through the use of aggregated CES funtion with a given elastiity of substitution, and it is speified as follows: 1. (1 ). QQ QM QD (1) where α is an Armington funtion shift parameter; is an Armington funtion share parameter, and ρ is an Armington funtion exponent. In the above CES aggregation funtion, it is analogous to onsidering QM and QD to be the inputs generating domestially supplied omposite ommodity. Euation (1) implies that onsumer demand for imports and domestially produed ommodities are derived demand, 3 The theoretial foundations of the Armington demand are also presented in Nganou (2005; hapter 7). 4 This was named after its author (Armington,1969) who ame up with the idea of using a CES funtion for suh a purpose. 5

7 analogous to demand for fator inputs in a onventional prodution funtion. Households hoose a mix of QM and QD aording to their relative pries. So given speified pries for domesti and imported goods, the onsumer s problem is to find a ommodity bundle (aggregate omposite ommodity) to minimize ost subjet to the onstraint stated in Euation (1), and this is mathematially presented as follows: min PQ.QQ = (PM.QM + PD.QD ); = 1,,6, (2) subjet to euation (1). The Lagrangian with respet to the onsumer hoie variables is therefore: L PM QM PD QD QQ QM QD 1... (1 ). Min Differentiating the above euation with respet to QM and QD and rearranging terms yields the following tangeny ondition: QM QD PD PM , = 1,,6 (4) The elastiity of substitution between ommodities from these two soures is given by 1, whih is a transformation of. Euation (4) defines the optimal mix between 1 imports and domestially produed goods. It suggests that an inrease in the domestiimport prie ratio generates an inrease in the import-domesti demand ratio. In this ase, the demand shifts away from more expensive soures. From euation (4), an be derived as follows: QM ln QD, = 1,,6; t = 1,,7 (5) PD ln PM where the numerator is the partial derivative of the logarithm of the ratio of uantity of imports and domesti output, the denominator is the ratio of pries of domesti output and imports, and t represents the time subsript (i.e., 7 years). Intuitively, is the proportionate hange in the ratio of uantities divided by the proportionate hange in the marginal rate of tehnial substitution in the demand between (3) 6

8 the two soures (i.e., domesti prodution and imports). The marginal rate of tehnial substitution is given by their pries ratio. For the purpose of estimation, the following parsimonious model speifiation, also ommon in the empirial literature on Armington elastiity of substitution, was used: QM 0 ln QD PD.ln PM, =1,,6; t=1,,7 (6) where is the onstant term, and (t) is the disturbanes term assoiated to eah 0 euation. B. Maximum Entropy: A Brief Review As disussed in Golan, Judge, and Miller (1996), the traditional maximum entropy (ME) is based on the entropy-information measure of Shannon (1948). Shannon used entropy to measure the state of knowledge (unertainty) that we have about the ourrene of a olletion of events. ME is a speial ase of the generalized maximum entropy (GME) where the data are represented in terms of exat moments. The GME proposed by Golan et al. (1996) uses a flexible, dual-loss objetive funtion - a weighted average of the entropy of the deterministi part of the model and the entropy from the disturbane or stohasti part. A detailed disussion on the properties of GME is provided in Golan, Judge, and Miller (1996), and here we briefly overview these properties. The GME approah uses all the data points and does not reuire any restritive moment or distributional error assumptions. Thus, the GME is robust for a general lass of error distributions. Additionally, the GME estimator may be used in several irumstanes namely, when the sample is small, there are many ovariates, and the ovariates are highly orrelated. Moreover, the GME method is very flexible as it an allow the user to easily impose nonlinear and ineuality onstraints (Golan, Perloff,and Shen, 2001). C. A GME Estimation of Armington Elastiities In order to estimate euation (6) above with GME 5, we need to express all the oeffiients and errors in the euation in terms of probabilities. For instane, to re-parameterize, we start by hoosing a set of disrete points, alled the support spae, z σ = (z σ 1; z σ 2,,z σ D) of dimension D>=2, that are at uniform intervals, symmetri around zero, and span the 5 To perform the estimation GAMS was employed. Alternatively SAS an be used. Version 9 of SAS inludes a speifi routine to implement GME. 7

9 interval [z σ 1,,z σ D]. The vetor of orresponding unknown weights is also introdued as follows: p σ = (p σ 1, p σ 2,,p σ D) suh that D p d 1 and d 1 D z d pd for all, d=1,2,...,d is the d 1 index used for the number of disrete points (dimension) in the support spae for eah unknown oeffiient. Similarly, the onstant term same approah. 0 an be re-parameterized using the In order to re-parameterize the errors (t), the definition of a transformation matrix V that onverts the possible outomes from the dimensions of disrete points u (t) to the interval [0,1] is reuired. Suh a transformation is done by speifying a vetor of M>=2 disrete points v = (v 1, v 2,, v M ), distributed uniformly about zero, and an assoiated vetor of proper unknown weights w = (w 1 (t), w 2 (t),, w M (t)) suh that v. w u m m ( t ). With GME, there m is no need to assume any subjetive information on the distribution of the probabilities (Golan, Perloff, and Shen 2001). Inorporating the above re-parameterized terms into our euation of interest (E. 6), we obtain: QM ln QD D d 1 z 0 d p 0 d D d 1 z d p d PD.ln PM M m1 m w The GME estimator maximizes the entropy of all the probabilities representing the signal and the noise ( (t) ), subjet to the data (Euation (7) above) and the adding up 0 (, ) onstraints of the probabilities. Letting p = (p α, p σ ), the GME estimator is given by the following optimization problem: max R p, w p '.ln( p ) w '.ln( w ) subjet to the data (i.e., E. (7)) and the GME adding-up onditions, D D M 0 d d d d 1 d 1 m1 p p w 1 (8) The solution to this maximization problem is uniue. Forming the Lagrangian and solving for the first-order onditions yields the optimal solution, from whih the following point estimates for our eonometri model are derived: m (7) 8

10 D ˆ zd pd d 1 ˆ (9) D ˆ z d pd d 1 ˆ (10) M uˆ v wm (11) m1 m The Choie of Support Spaes An extensive disussion on the hoie and dimension of the support spae on parameters and error term is provided in Golan, Judge, and Miller (1996) (Chap. 8). With respet to the dimension or the number of points in the support spae for the parameters we will onsider 5 (i.e., D = 5). In fat, based on some experiments, Golan, Judge, and Miller (1996) argue that the greatest improvement in preision ould be obtained when the support spae on the parameters has 5 elements (see page 140). Sine there is no theoretial justifiation that illuminates the true Armington parameters, the value of elastiities remains entirely an empirial issue. While some strutural eonomists have argued that most often the trade elastiities used in CGE models are too large and do not suffiiently reflet institutional rigidities in trade (e.g. import uotas, or other protetionist trade poliies), while other market-leaning eonomists have argued to the ontrary (Liu, Arndt, and Hertel 2001). In suh onditions, it is always reommended to hoose a wider support spae for the parameters. Also, in so doing, the impat of the support spae on the parameters is redued while that of the data is inreased (Golan, Judge, and Miller 1996). Moreover, entertaining a variety of plausible bounds onstitutes a hek for the robustness of the estimated parameters to the support spae. As for the support spae on the error term, for eah euation we used the three-sigma rule symmetri around zero, as reommended in Golan, Judge, and Miller (1996). The dimension of the support spae on the disturbane terms is 3 (i.e., 3 elements). The support spae for the errors is therefore: [-3.stdev, 0, 3.stdev], where stdev is the empirial (data) standard deviation of the dependent variable. Estimation Evaluation and Inferene Issues A simple way to evaluate the estimated oeffiients ould be based upon the a priori (from theory) expetations in terms of their signs and magnitude. However, the omputation of 9

11 asymptoti standard errors for estimated oeffiients (and therefore t-tests) is also possible, and may failitate a more onventional inferene approah (Mittelhammer and Cardell 1997). Mittelhammer, Judge, and Miller (2000) show that under some regularity onditions (e.g., the true error values and parameters should be ontained in their respetive support bounds) defined by Mittelhammer and Cardell (1997) the GME estimator is onsistent and asymptotially normal (also see Golan, Judge, and Miller (1996)). Fraser (2000) provides an appliation of Mittelhammer et al s inferene approah. Another evaluation tool is the normalized entropy on the GME oeffiients, obtained by dividing the Shannon objetive funtion by the natural log of M, the number of points in the parameter support. The normalized entropy rule proposed in Golan et al (1996) an be used in the seletion of variables in a regression model. A variable is extraneous in a regression model if its normalized entropy statisti is lower than 0.99 (Golan, Judge, and Miller 1996). Additionally, it is possible to use the overall degree of fit (R 2 ) in estimated euations as a diagnosti tool. This overall goodness of fit measure remains a useful summary statisti, although it is said to be biased downward in GME ases 6 as it uses out of sample information (Fraser 2000). This is also supported by our findings (see Tables 3-8). In our analysis, the above-mentioned diagnosti tools were omputed and reported for eah regression. They also served as a guide in the seletion of the best model speifiation (i.e., the support speifiation that would produe the final estimated elastiities to be inluded in the CGE model). D. GME Estimation Results Given the lak of preise knowledge about the bounds of Armington elastiities from eonomi theory as mentioned before, it was useful, as reommended in Golan, Judge, and Miller (1996), to speify various support spaes on the parameters (interept and elastiity estimates) and to measure the sensitivity of results aross support spae speifiations. Estimation results of oeffiients along with assoiated standard errors are presented in Tables The R-suare derived in the GME ase will tend to be lower than that derived by the OLS estimator. 10

12 A sensitivity analysis of the GME estimates: While the sign of all estimated elastiities seems onsistent aross various support spaes, their magnitude is sensitive to the hoie of support values, exept for ommodities for whih estimated elastiities were statistially signifiant (i.e., Agriulture, and Food). Table 3. Sensitivity Tests of GME Estimates of Armington Elastiity for Agriulture Normalized Parameters Support Estimated Elastiity Entropy value Entropy Ratio S(p k ) R 2 [-150, -75, 0, 75, 150] a (0.135) [-100, -50, 0, 50, 100] a (0.135) [-50, -25, 0, 25, 50] a (0.135) [-20, -10, 0, 10, 20] a (0.135) [-10, -5, 0, 5, 10] a (0.135) Soure: Author s Calulations. Note. a = signifiant at 1 perent level, b= signifiant at 5 perent level, = signifiant at 10 perent level. The support on errors is based on a 3-sigma rule symmetri around 0. Sigma is the empirial standard deviation on the dependent variable. Here we used [-1.721, 0, as error support. The parameter s asymptoti standard errors are provided in the parentheses. S(P k ) is the normalized entropy statisti on the estimated parameter (here the Armington elastiities). It measures the informational ontent of the estimates with 1 refleting uniformity (omplete ignorane) of the estimates and 0 refleting perfet knowledge. More preisely, the Armington elastiity estimates for Agriulture and Food are statistially signifiant at 5 perent and 10 perent, respetively, and have the orret sign. They are also very robust in the sense that they do not vary with the support spae speified (Tables 3 and 4). The elastiity estimate for Textiles was marginally signifiant (at 11 perent) in the first and seond support spae speifiations. However, in terms of robustness, it an be notied that with a tight support spae (support speifiations 3 and 4) the estimated oeffiient for Textiles is shrinking signifiantly (Table 5). 11

13 Table 4. Sensitivity Tests of GME Estimates of Armington Elastiity for Food Normalized Parameters Support Estimated Elastiity Entropy value Entropy Ratio S(p k ) R 2 [-150, -75, 0, 75, 150] b (0.596) [-100, -50, 0, 50, 100] 1.37 b (0.596) [-50, -25, 0, 25, 50] b (0.596) [-20, -10, 0, 10, 20] b (0.596) [-10, -5, 0, 5, 10] b (0.597) Soure: Author s Calulations. Note. a = signifiant at 1 perent level, b= signifiant at 5 perent level, = signifiant at 10 perent level. The support on errors is based on a 3-sigma rule symmetri around 0. Sigma is the empirial standard deviation on the dependent variable. Here we used [-1.82, 0, 1.82] as error support. The parameters asymptoti standard errors are provided in the parentheses; See Table 7 for the definition of S(P k ). It is worth mentioning that the estimated Armington elastiity for Other Manufaturing was statistially signifiant, insensitive aross support spae speifiations, but with a negative sign (ontrary to the theory preditions). This ould be due to a model inaurate (Table 6). Estimated Armington elastiities with wrong signs are also ommon in the literature. Further efforts, suh as, using several speifiations with (unweighted as well as weighted priors) generalized ross entropy (GCE) were undertaken in order to see whether we an get robust estimates on Other Manufaturing with the orret sign. The estimated oeffiients were very small in size (lose to 0) and statistially insignifiant. 7 7 Results are not reported here but are available from the author. 12

14 Table 5. Sensitivity Tests of GME Estimates of Armington Elastiity for Textiles Normalized Parameters Support Estimated Elastiity Entropy value Entropy Ratio S(p k ) R 2 [-150, -75, 0, 75, 150] (4.73) [-100, -50, 0, 50, 100] (4.735) [-50, -25, 0, 25, 50] (4.754) [-20, -10, 0, 10, 20] (5.01) [-10, -5, 0, 5, 10] (5.45) Soure: Author s Calulations. Note. a = signifiant at 1 perent level, b= signifiant at 5 perent level, = signifiant at 10 perent level, d = signifiant at 11 perent level. The support on errors is based on a 3-sigma rule symmetri around 0. Sigma is the empirial standard deviation on the dependent variable. Here we used [-1.65, 0, 1.65] as error support. The parameters asymptoti standard errors are provided in the parentheses; See Table 7 for the definition of S(P k ). The estimated oeffiients for the remaining ommodities (Mining and Transport), although with the orret sign, were both not statistially signifiant (see Tables 7 and 8). Additionally, the Armington elastiities for Mining and Transport are sensitive to tighter support spae of the parameters (espeially in the [-20,...,20] and [-10,,10+ support speifiations). Table 6. Sensitivity Tests of GME Estimates of Armington Elastiity for Other Manufaturing Normalized Parameters Support Estimated Elastiity Entropy value Entropy Ratio S(p k ) R 2 [-150, -75, 0, 75, 150] (0.686) [-100, -50, 0, 50, 100] (0.686) [-50, -25, 0, 25, 50]

15 (0.686) [-20, -10, 0, 10, 20] (0.686) [-10, -5, 0, 5, 10] (0.686) Soure: Author s Calulations. Note. a = signifiant at 1 perent level, b= signifiant at 5 perent level, = signifiant at 10 perent level. For the 3 last regressions, only the support spae on the estimated elastiity was further restrited to be positive. The onstant s support was maintained at *-150, -75, 0, 75, 150]. The support on errors is based on a 3-sigma rule symmetri around 0. Sigma is the empirial standard deviation on the dependent variable. Here we used [-0.976, 0, as error support. The parameters s asymptoti standard errors are provided in the parentheses. See Table 7.7 for the definition of S(P k ). Table 7. Sensitivity Tests of GME Estimates of Armington Elastiity for Mining Normalized Parameters Support Estimated Elastiity Entropy value Entropy Ratio S(p k ) R 2 [-150, -75, 0, 75, 150] (16.52) [-100, -50, 0, 50, 100] (16.53) [-50, -25, 0, 25, 50] (16.62) [-20, -10, 0, 10, 20] (16.83) [-10, -5, 0, 5, 10] (17.04) Soure: Author s Calulations. Note. a = signifiant at 1 perent level, b= signifiant at 5 perent level, = signifiant at 10 perent level. The support on errors is based on a 3-sigma rule symmetri around 0. Sigma is the empirial standard deviation on the dependent variable. Here we used [-5.52, 0, as error support. The parameters s asymptoti standard errors are provided in the parentheses; See Table 7 for the definition of S(P k ). 14

16 Table 8. Sensitivity Tests of GME Estimates of Armington Elastiity for Transport Normalized Parameters Support Estimated Elastiity Entropy value Entropy Ratio S(p k ) R 2 [-150, -75, 0, 75, 150] (5.054) [-100, -50, 0, 50, 100] (5.076) [-50, -25, 0, 25, 50] (5.092) [-20, -10, 0, 10, 20] (5.093) [-10, -5, 0, 5, 10] (5.16) Soure: Author s Calulations. Note. a = signifiant at 1 perent level, b= signifiant at 5 perent level, = signifiant at 10 perent level. The support on errors is based on a 3-sigma rule symmetri around 0. Sigma is the empirial standard deviation on the dependent variable. Here we used [-2.27, 0, as error support. The parameters s asymptoti standard errors are provided in the parentheses; See Table 7 for the definition of S(P k ). The Choie of the final Armington elastiities: In order to hoose the Armington elastiity estimates that will be used in the CGE model, we make use of the diagnosti tools desribed earlier, as well as our knowledge of the ountry. Given that Lesotho is an import-dependent eonomy, one might expet the Armington elastiity to be relatively high. It is worth mentioning that in determining the final estimates, we will lean towards those with both wider support spae and lower assoiated normalized entropy statistis. In so doing, our lak of prior knowledge about the parameter bounds, as mentioned before, will be aounted for, as well as our efforts to let the data speak. As mentioned before, estimates for Agriulture and Food are robust aross support speifiations. Therefore, the hoie of a support speifiation does not make a differene. The speifiation hosen for both ommodities is the one with the widest support, given the lak of prior knowledge of the support bounds for the estimates. Thus, the Armington elastiity for Agriulture is while that for Food is For Mining and uarrying, 15

17 speifiation 3 (i.e., [-50,...,50]) is hosen sine it has the lowest normalized entropy statisti (0.996) on the estimated oeffiient. Also, its R 2, although low, is similar to that for the first two speifiations. Moreover, Lesotho does not impose any trade barriers on mining produts imported from South Afria. The Armington elastiity for Mining is therefore The Armington elastiity for Textiles is 4.232, sine it displays the lowest normalized entropy statisti. Based on the same riterion, Armington estimate for Transport is We ould have hosen but, instead, we leaned towards the estimated oeffiient with a wider support spae and for whih R 2 does not hange drastially, refleting the limited impat of non-sample information. Finally, sine Armington elastiity ould not be negative, our hoie of Armington elastiity for Other Manufaturing was not based on its eonometri estimation, rather we used its value (i.e., 0.5) proposed by de Janvry and Sadoulet (2001) in their arhetypal CGE model for Afria, whih also seems plausible for Lesotho where handirafts industry is proteted. Comparing Armington Elastiities from Seleted Soures: There is no onsensus on the value of the parameters used in CGE models. Although many approahes to eonometri estimation of these elastiities have been offered for the last 30 years, many trade eonomists view the estimates as fairly small 8. We believe that parameters should be ountry-speifi, but lak of data seldom allows their estimation for eah ountry. Nevertheless, we an ompare our Armington estimates to those of a seleted literature, although we annot provide any evidene of the statistial signifiane of the differene between the estimates 9. A omparison of the estimated Armington elastiities with those used in seleted studies is presented in Table 9. First, the table reveals that the majority of Lesotho s estimates are higher than the Armington elastiities used in de Janvry and Sadoulet (2001). However, exept for Mining and Textiles, the parameters are below those provided by GTAP (Global Trade Analysis Projet of Purdue University). For Textiles, the Armington parameter (2.69) is apparently not far from the 3.3 used in the GTAP studies. In omparison, only Mining and Transport have an elastiity of substitution between imports and domesti output that is 8 MDaniel and Balistreri (2002) provide a omprehensive review of literature on the estimation of Armington elastiities. 9 Obviously, suh a omparison is not a perfet one, given that the ommodity lassifiation used in seleted studies was not idential. 16

18 greater in magnitude than the South Afrian parameters. Interestingly, our estimates for Textiles and Food are very lose in size to those for South Afria. Table 9. A Comparison of Seleted Armington Elastiities South Afria Mozambiue Our Janvry et al. Lofgren (Thurlow et (Arndt et al estimates GTAP 2001 (Egypt's CGE) al) (2002)) Agriulture Food Textiles NA Mining NA Transport Soure: Compiled by the Author. Note. GTAP: Global Trade Analysis Projet of Purdue University Comparison also reveals that, exept for Food, Lesotho estimates for elastiities are higher than those of Egypt. Finally, beause Arndt et al. (2002) use a GME approah in their estimation of trade parameters for Mozambiue, a ountry with some similar features (e.g., very poor, small dependent eonomy) as Lesotho, we found it useful to ompare our estimates to theirs. In general, estimated oeffiients are not very distant aross the two studies (e.g., Transport servies and Agriulture). But the advantage of our approah ompared to that of Arndt et al. (2002) is that it is simpler sine it is based on the single regression euations. In sum, sine there is a divergene of parameter values aross studies, it might not be a good idea to use results of ross-ountry estimations in a ountry s CGE model. Using ountryspeifi elastiities should be the way to go. 4. Conlusion The objetive of this paper was to estimate some key parameters intended for use in the CGE model for Lesotho. Given the poor uality of data available, we employed GME tehniues to estimate Armington elastiities. Using only 7 years of data, we were able to obtain some interesting and sensible estimates. Although we found that many of the 17

19 Armington estimates were not statistially signifiant (based on asymptoti standard errors), they were generally of the orret sign. However, as Mittelhammer and Cardell (1997) argued, asymptoti standard errors need to be interpreted autiously in the GME/GCE ontext. Sensitivity tests of parameters to the support spae undertaken in this paper were also proven to be an important hek for the robustness of GME estimates. In sum, the exuse of the lak of data usually advaned by CGE modelers for not using ountry-speifi parameters may not hold anymore. As was shown earlier in this paper, GME eonometris is possible for developing ountries (whose eonomi data are generally sare and onsidered poor in uality). It is worth noting that the partial euilibrium framework used for the estimation of parameters, although inonsistent with CGE analysis as argued by ritis, offers a omputational advantage for its simpliity. Overall, we found that estimates from Arndt et al (2002) were very lose to those provided in this paper using single euation GME regressions. 18

20 REFERENCES Arndt, Channing, Sherman Robinson, and Finn Tarp (2002) Parameter Estimation for a Computable General Euilibrium Model: A Maximum Entropy Approah, Eonomi Modelling 15, pp de Janvry, A. and Elisabeth Sadoulet (2001) World Poverty and the Role of Agriultural Tehnology: Diret and Indiret Effets, Journal of Development Studies, pp. Fraser, Iain (2000) An Appliation of Maximum Entropy Estimation: the Demand for Meat in the United Kingdom, Applied Eonomis 32, pp Galloway, MDaniel, and Rivera (2000) Estimating a Demand System with Nonnegativity Constraints: Mexian Meat Demand, The Review of Eonomis and Statistis 1(83), pp Golan, Amos, George Judge, and Douglas Miller (1996) Maximum Entropy Eonometris: Robust Estimation with Limited Data (Chihester, England). Golan, Amos, Jeffrey M. Perloff, and Zhihua Shen (2001) Estimating a Demand System with Nonnegativity Constraints: Mexian Meat Demand, The Review of Eonomis and Statistis 1(83), pp Judge, George G., R. Carter Hill, William E. Griffiths, Helmut Lutkepohl, and Tsoung-Chao Lee (1980) The Theory and Pratie of Eonometris (New York, USA). Liu, Jing, Channing Arndt, and Thomas Hertel (2001) Parameter Estimation and Measures of Fit in a Global, General Euilibrium Model, Conferene Proeedings Fourth Annual Conferene on Global Eonomi Analysis. Lofgren, H. (1994). A brief survey of elastiities for CGE models, Paper presented to the Ford Foundation. Amerian University in Cairo, Cairo. MDaniel, Christine A. and Edward J. Balistreri (2002) A Review of Armington Trade Substitution Elastiities, Mimeo, Researh Division, Eonomis Offie, U.S. International Trade Commission. Mittelhammer, R. and N. S. Cardell (1997) On the Consisteny and Asymptoti Normality of Dataonstrained GME Estimation in the GLM, Mimeo, Washington State University, Pullman, WA. Mittelhammer, R.C., George G. Judge, and Douglas J. Miller (2000). Eonometri Foundations (New York, USA). Nganou, Jean-Pasal Nguessa (2005) A Multisetoral Analysis of Growth Prospets for Lesotho: SAM-Multiplier Deomposition and Computable General Euilibrium Perspetives. Ph.D. Thesis, Amerian University, Washington, DC (US). Shiells, Clinton R., Robert M. Stern, and Alan V. Deardoff (1986) Estimates of the Elastiities of Substitution between Imports and Home Goods for the United States, Weltwirtshaftlihes- Arhiv 122(3), Shiells, Clinton R. and Kenneth A. Reinert (1993) Armington Models and Terms-of-Trade Effets: Some Eonometri Evidene for North Ameria, Canadian Journal of Eonomis 26(2), Thurlow, James and Dik Ernst van Seventer (2002) A Standard Computable General Euilibrium Model for South Afria, Disussion Papers of the Trade and Maroeonomis Division, International Food Poliy Researh Institute (100),