**Appendix C : Estimates of the Dixit-Stiglitz Elasticities of Substitution for Goods**

It was necessary for us to obtain estimates of the Dixit-Stiglitz product variety elasticities of substitution for the imperfectly competitive sectors in our model. Christian Broda, Joshua Greenfield and David Weinstein (2006) estimated Dixit-Stiglitz product variety elasticities of substitution at the 3 digit level in 73 countries. Among the 73 countries, there were four in sub-Saharan Africa: the Central African Republic, Madagascar, Malawi and Mauritius. We judged that Madagascar was the country closest in characteristics to Tanzania, so we took the values of the elasticities estimated for Madagascar as a proxy for the elasticities for Tanzania.

Broda et al., estimate 3 digit elasticities for 130 goods sectors, but there are 34 goods sectors in our model, It was necessary to map the sectors estimated by Broda et al. into the sectors of our model. In table C1 of this appendix, we show the mapping for the imperfectly competitive sectors. (These elasticities are not relevant in our model for perfectly competitive sectors.) Next, since there are often multiple sectors from Broda et al. mapped into a single sector in our model, it was necessary to determine a method of weighting the Broda et al. elasticities. There are reasons to use both export shares as well as import shares. A larger share of a subcategory in imports reflects more imports, and more likely there are more varieties of imports. So weighting by the import share of a subcategory is better than an unweighted measure. Domestic varieties are also important. Since we do not have production data for the subcategories, we use export shares as a proxy for domestic production by subcategory. Analogously, weighting subcategories by export shares is better than unweighted categories. Since both import shares and export shares are useful in the weighting, we take one half the shares of both exports and imports as the weights. We obtained the data for the import and export shares from the COMTRADE database. The resulting elasticities are reported in table C1.

For the sensitivity analysis, we must take upper and lower bounds of the elasticities. Unfortunately, Broda et al. only report point estimates in their on-line Excel file. In the paper itself, however, Broda et al. (2006, table 4, p. 36) list the standard error of the median Dixit-Stiglitz estimate for the country. The standard errors are rather small for most countries. In the case of Madagascar, the median Dixit-Stiglitz elasticity is 3.6 with a standard error (of the median estimate) of 0.27.

Although we don’t have standard errors at the product line level, we use the overall estimate of the standard error to guide our choice of upper and lower values of the estimates. The low standard error suggests that we do not need to take very large ranges to check for robustness. For central values of 3.6 or less, we took plus or minus three times the average standard error of 0.27. CGE modelers have often doubled and halved the central estimate in the sensitivity. For central values greater than 3.6, we took plus or minus 50% of the value of the parameter, which gives a wider band than plus or minus three times the standard error. For these elasticities, this presents a tougher test of the robustness of our model.

Broda, Christian , Joshua Greenfield and David Weinstein (2006), “From Groundnuts to Globalization: A Structural Estimate of Trade and Growth,” National Bureau of Economic Research Working Paper 12512. Available at: http://faculty.chicagobooth.edu/christian.broda/website/research/unrestricted/TradeElasticities/T radeElasticities.html.

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