7

## 3.3 Econometric Issues

The estimation procedure needs to tackle three issues. First, rather than distort the available information by phase averaging using an arbitrary phase length (e.g., computing 5 or 10-year averages), we choose to work with the original annual data in order to retain all the information. This in turn means that we need to use a dynamic specification in order to allow for inertia, very likely to be present in the annual information. Inertia in saving rates can arise from lagged effects of the explanatory variables on saving. Thus, considering a dynamic specification allows us to discriminate between short- and long-run effects on saving.’? Second, some of the explanatory variables in the core specification above (e.g., the real interest rate, real income growth, etc.) are likely to be jointly determined with the saving rate; therefore, we must allow and control for the joint endogeneity of the explanatory variables. Third, we must also allow for the possible presence of unobserved country-specific effects correlated with the regressors.

_ To address these issues, our empirical analysis is based on Generalized-Method-ofMoments estimators applied to dynamic models using panel data. These estimators allow us to control for unobserved country-specific effects and potential endogeneity of the explanatory variables.° Before we proceed, we must clarify the extent to which we control for joint endogeneity. Our panel estimator controls for endogeneity by using “internal instruments,” that is, instruments based on lagged values of the explanatory variables. Through this method we can relax the assumption that the explanatory variables are strictly exogenous; however, we cannot allow for full endogeneity of the explanatory variables. To be precise, we must assume that the explanatory variables are “weakly exogenous,” which means that they can be affected by current and past realizations of the saving rate but must be uncorrelated with future realizations of the error term. Conceptually, weak exogeneity does not mean that future saving rates cannot be correlated with current realizations of variables such as income growth or the interest rate (as would be predicted by most forward-looking models). Rather, weak exogeneity means that future innovations (or unforeseen changes) to the saving rate do not influence previous realizations of the saving determinants. We believe that conceptually this assumption is not particularly restrictive; furthermore, we can examine its validity statistically through several specification tests, as explained below.

The following is a brief presentation of our preferred methodology. Consider the following dynamic reduced-form saving regression equation,

# S,,=OS;,,+O'X,, +N, +€;,

## (1)

where s is the saving rate, X represents a set of variables that potentially affect the saving rate, 7 represents a set of unobserved time-invariant country-specific effects, ¢ is the error term, and the subscripts i and f represent country and time period, respectively. M4 The usual method for dealing with the country-specific effect in the context of panel data has been to first-difference the regression equation (Anderson and Hsiao 1982). In this