k. For representative indicators, our choice of units for governance normalizes ~~g~~ k = 0 , and so the sample mean delivers a consistent estimate of αk. However, for a nonrepresentative indicator where the average level of governance is different from the world as a whole, ~~g~~ k ≠ 0 and the sample mean does not provide a consistent estimate of αk.

We can nevertheless obtain consistent estimates of the unknown parameters of the non-representative indicators by using the following simple argument. If gj were observable, we could estimate αk, βk and σk for any indicator by regressing the observed scores yjk on gj. Although gj is itself not observable, we do have an estimate of gj based on the representative indicators. In particular, let g*j denote this preliminary estimate of gj based on only on the data from the representative indicators. We can decompose this conditional mean into observed governance plus its deviation from the mean, i.e. g*j=gj+uj. Since uj is independent of gj, we can view g*j as measuring gj with classical measurement error. It is well-known that OLS estimates of βk from a regression of yjk on g*j will produce downward-biased estimates due to the usual attenuation bias. In particular, the probability limit of the OLS slope coefficient is βk ⋅ ⎛1− V[u*j ] ⎞ . Since ⎜<sup>⎜</sup> ⎝ V[g j ] ⎟<sup>⎟</sup> ⎠ the variance of uj is simply the variance of the conditional mean of gj given in Equation (3), and since V[g*j] is observable, we can correct the OLS coefficients for this attenuation bias to arrive at consistent estimates of the parameters of the nonrepresentative indicators.

Finally, we collect all of the parameter estimates from the representative and non-representative surveys, and insert them into the expressions in Equations (2) and (3) to arrive at estimates of governance and standard errors for each country. As discussed in the next section, there are two further rescaling steps before we arrive at the final estimates that we report.

# **D2.  Rescaling the Aggregate Governance Indicators**

We next perform two rescalings of the aggregate indicators obtained using the procedure described above. We first rescale the data to set the mean of the governance estimates to zero, and their standard deviation to one. The estimates of governance obtained from the UCM theoretically have a mean of zero, and a standard deviation slighly less than one. In any particular sample, however, the mean could be different. To avoid confusion in interpreting the data, we begin by setting the mean of the governance estimates for each indicator and year to zero, and the standard deviation to one. In particular, for each indicator and year, we subtract the sample mean (across countries) from each country, and divide by the sample standard deviation (across countries). We then also divide the standard errors of the governance estimates for each country by the sample standard deviation of the governance estimates.

This first rescaling is just a renormalization of the scores, and of course has no impact on countries' relative positions on the governance indicators. It is also consistent with our choice of units for governance noted above, and notably that it has a mean of zero and a standard deviation of one in each period. If there were trends in global averages of governance over time, this choice of units would not be appropriate.

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