(1995) and Blundell and Bond (1997), who propose a system estimator combining the regressions in differences and levels. To compute the system estimator, predetermined and endogenous variables in first differences are instrumented with suitable lags of their own levels, while variables in levels are instrumented with suitable lags of their own first differences.<sup>15</sup> Consistency of the GMM estimator obviously depends on the validity of the instrument set constructed in this way, and this in turn is determined by the autocorrelation structure of the error term. For example, if υ _it_ is serially uncorrelated then _yit-2_ , _xit-2_ , _pit-2_ and _git-2_ and their earlier lags would be valid instruments for the variables in differences, but if υ _it_ displays first order serial correlation the instrument set would have to be restricted to _yit3_<sup>,</sup><sup>_x_</sup> _it-3_<sup>,</sup><sup>_p_</sup> _it-3_<sup>,</sup><sup>_g_</sup> _it-3_<sup>and earlier lags. To assess the validity of the proposed instrument sets, we</sup> report two standard specification tests. The first is Hansen’s _J_ -test of over identifying restrictions, which examines the correlation between the instruments and the regression residuals. The second test examines the autocorrelation structure of the regression residuals themselves.

# _III.2 Control variables_

We turn to the specification of the set of control variables included in _x_ . The empirical growth literature has experimented with a vast number of alternative sets of explanatory variables.<sup>16</sup> Rather than adding to the already huge variety of growth models contributing yet another idiosyncratic set of regressors, we opt for considering three alternative growth specifications, in order to explore the sensitivity of our results to the specific choice of variables.

The first set of control variables is that used by Perotti (1996), Forbes (2000), Banerjee and Duflo (2003), and Knowles (2005). It includes the average years of secondary education of the male population, the average years of secondary education of the female population, and a measure of market distortions, given by the price of investment goods. All these variables are measured in levels at the beginning of the period.

The second specification we consider is more focused on standard policy indicators. It includes the inflation rate as an indicator of macroeconomic stability; the adjusted volume of trade as an indicator of the degree of openness of the economy;<sup>17</sup> and the ratio of public consumption to GDP as an indicator of the burden imposed by the government on the

> 15 A well-known shortcoming of panel GMM estimators in small samples is their tendency to result in over fitting and downward-biased standard errors – a consequence of the large number of instruments available for estimation (see, e.g., Ziliak 1997).  To reduce this bias,  in the estimations below we limit the number of over identifying restrictions by building only one instrument from each variable and lag distance, rather than building one separate instrument from each variable, and lag distance in each time period.

> 16 As noted by Durlauf and Quah (1999), by 1998 the number of individual regressors that had been considered as potential explanatory variables in growth regressions exceeded the number of countries in the standard growth dataset.

> 17 We use the residuals of a regression of openness on country size and two dummies indicating whether the country is landlocked and whether it is an oil exporter.

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