# **_5. Estimation methodology_**

This study uses the empirical methodology used in previous studies by Piancastelli (2001), Davoodi and Grigorian (2007), Gupta (2007), and Le et al (2008). As in previous studies, in this paper too, revenue potential is based on a regression analysis and the revenue potential of a given country is estimated from a comparison with the average performance of a sample of countries. Naturally, the larger the sample, the larger is the difference in the economic, institutional, tax policy and tax administration frameworks across the group, making it difficult to draw policy implications from such an exercise. Hence, in the context of studying the tax revenue potentials in the ECA region, as we do in this paper, we handle the "worldwide average" bias by cutting down the sample of countries to only those countries that share similar characteristics in terms of their tax structure to the ECA countries. This limits the countries to those that have both social security taxes and value added taxes. Hence, the sample set in this paper is smaller than most cross-country panel data studies that use over 110 countries in their analysis.

In this paper, the sample size is 61 countries, that covers 23 ECA countries (including 2 that have graduated from the World Bank recently, but for the purpose of this paper are grouped with ECA), 5 ECA countries that have graduated from the World Bank earlier and are (for the purposes of this paper) classified together with OECD countries, and 33 other countries in the OECD, LAC, EAP and AFR regions.

# **_Fixed effects and random effects_**

The fixed effect model specification is: yit = ɤi + βXit + _Υ_ Yit + δZit + εitwhere, yit is the total tax revenue as a percent of GDP in country _i_ at time _t_ , ɤi is the country fixed effect, Xit is the set of structural variables, Yit is the set of institutional variables, and Zitis the set of policy variables. The random effects specification is: yit = ɤ + βXit + _Υ_ Yit + δZit + ui + εit; where ui is the country-specific error term. The Hausman specification test is generally used to decide between the fixed effects and random effects model.

The crucial distinction between fixed and random effects is whether the unobserved country effects are correlated with the regressors in the model. A major motivation for using the fixed effects models is to control for this unobserved heterogeneity. Clark and Linzer (2013), note that while the main objection to using random effects is that the covariates may be correlated with the unit effects, it does not imply that any correlation between the covariates and the unit effects implies that the fixed effects should be favored since, except in exceptional circumstances, there would always be some level of correlation between the covariates and the unit effects.

The choice should, hence, depend on how much bias is created by this correlation, and how much variance is introduced by using the fixed effects instead of the random effects. Running Monte Carlo simulation exercises, Clark and Linzer (2013) find that when the variation of the covariates is primarily within the units, “there is rarely any divergence between the random effects estimator and the fixed effects estimator...and the conventional understanding that correlation between regressors and unit effects results in unwarranted bias in the estimate of the model parameters is unfounded”. The authors also find any bias in the slope parameter estimate is more than compensated for by the increase in estimate efficiency.

Clark and Linzer (2013) further suggest that when units are relatively similar to one another on average, and with larger amounts of data (typically more than five observations per unit), there is no discernible difference in estimates of β between the two estimators, even when the regressor and the unit effects are very highly correlated. Thus, the authors suggest, the appropriate model should be guided by the researcher's goals. For example, if one seeks to make predictions, then the random effects estimator should be preferred.

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