smoothing arguments one would expect less dispersion in the expenditure-based surveys.<sup>15</sup> One might wonder if in our sample the result is driven by the fact that the panel is unbalanced. But even if we give equal weight to each country’s average Gini coefficient we find a similar picture: the resulting overall means are 0.40 for incomebased and 0.42 for expenditure-based observations, respectively. The latter, however, are more concentrated around their mean. In other words, there is a lower frequency of countries with extreme (whether high or low) inequality in the expenditure-based subsample than in the income-based subsample.

On the other hand, there is a noticeable difference between the average Gini coefficients of the subsamples based on gross and net income. Gross income-based Gini coefficients average 0.40, whereas those based on net income average 0.33. Although one should be careful in attaching any particular economic interpretation to these figures, it is tempting to view them as reflecting the effect of government interventions that lead to income redistribution.

# **III Empirical results**

We turn to the empirical implementation of the lognormality tests. We perform them on the full sample as well as different sub-samples defined by type of data -- i.e., according to whether the observations are based on expenditure or income surveys and, in the latter case, whether income is measured on a net or gross basis. Apart from allowing some robustness checks, this differentiation is also of interest for two other reasons. First, if the distribution of income is lognormal, and households engage in consumption smoothing, the distribution of consumption will not be lognormal in general.<sup>16</sup> Hence the common practice of pooling together income- and expenditure-based observations in applied work could yield misleading test results in our case. Second, gross income could be lognormally distributed while net income is not -- for example if taxes and transfers are lump-sum rather than proportional to income.

To be specific, in addition to (i) the full sample we also consider sub-samples of (ii) income-based observations only (labeled “Income” for short); (iii) expenditure-based observations only (“Expenditure”); (iv) gross income-based observations only (“Gross Income”); (v) a combination of expenditure and net income-based observations (“Net”); and finally (vi) net income-based observations only (“Net Income”).

For the full sample, Figure 1.(a) shows a scatter plot of the observed quintile shares (vertical axis) against their theoretical counterparts, as computed under the null hypothesis of lognormality (horizontal axis). The data points cluster along the 45-degree line, suggesting that the lognormal distribution provides a fairly close approximation to

> 15 For this reason, Forbes (2000) and Deininger and Squire (1996) raise expenditure-based Gini coefficients by 0.066 to make them comparable with income-based ones.

16 Under consumption smoothing, current consumption will depend on some weighted sum of current and future anticipated income. In the textbook permanent-income model, the consumption level of household _h_ in period _t_ would take the form _Cth_ = θ _Ath_ + _s_ ∞∑= _t_ 1( + _r_ ) _s_ − _t Et_ [ _xsh_ ] , where _x_ is income, _A_ denotes

> financial wealth, _r_ is the real interest rate, θ is a parameter, and _E_ t denotes the conditional expectation. Even if _xs_ is lognormally distributed, the infinite sum in the square brackets will not be in general, a simple consequence of the fact that the sum of lognormally-distributed variables is not itself lognormally distributed.

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