the size distribution of per capita income / expenditure as summarized by the quintile shares. Figures 1.(b)-1.(f) present similar plots for the various subsamples.<sup>17</sup> Table 2 presents the results of OLS-based lognormality tests for the full sample and the various subsamples described above. The standard errors of the estimates are computed using a clustering procedure to allow for residual dependence; they also allow for heteroskedasticity.<sup>18</sup> The first thing that stands out in the table is the excellent fit of the regressions in all the samples considered, with R<sup>2</sup> ranging from 0.95 to 0.98. For a cross-country sample of this magnitude, such fit is remarkable. In turn, the regression slopes and intercepts are very close to their expected values under the null of one and zero, respectively. It is worth noting that in the samples including expenditure observations (the first, third and fifth columns) the estimated slopes are slightly below one, while the opposite happens in the regressions including only income-based observations. Formally, we can reject the null of unit slope in the Expenditure and Net subsamples (third and fifth columns). In turn, the estimated intercepts are positive in the samples including expenditure-based observations and negative in those including only income-based observations. Like with the slopes, in the Expenditure and Net subsamples we can also reject the null of zero intercept.

The bottom of Table 2 reports Wald tests of the null hypothesis of lognormality (6). Under the null, the test statistic follows a chi-square distribution with two degrees of freedom. As would be expected in the light of the point estimates, the null can be rejected at the 5 percent level in the two samples in which expenditure-based observations represent a sizeable share of the total number of data points. In contrast, the samples containing only income-based observations show little evidence against the null -- the p- values range from 0.62 to 0.93. In the full sample, in which expenditure-based observations represent only about 20 percent of the total, we also fail to reject the null, with a p-value of 0.35.

On the whole, the lognormality tests based on the OLS estimates suggest that the size distribution of income and expenditure follow significantly different patterns. In contrast, the distinction between gross and net income seems to be of little consequence. Table 3 repeats the same tests of Table 2 now based on ML estimation of the nested error-component model given by (4) and (9)-(10). In addition to the information contained in the preceding table, Table 3 also reports the estimated standard deviations of the error components in (9), and the results of tests of their individual and joint significance.

Inspection of Table 3 reveals a picture very similar to the one emerging from Table 2, in terms of both point estimates and standard errors. The pattern of signs and magnitudes of the point estimates across samples is the same as before. The middle block of the table reports the estimated standard deviations of the error components. The

> 17 Figures 1(e) and 1(f) show an apparent outlying observation (corresponding to Q2 in Norway 1989), which might be viewed as a candidate for removal from the sample. This, however, would be of no consequence for any of the empirical results in the paper.

> 18 The clustering is done by country. Doing it instead by survey yields slightly larger standard errors but does not cause any qualitative changes on the results of the hypothesis tests.

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