coefficients are no longer statistically significant when we estimate the model over 1994-2013, 1996-2015, and 1998-2017 (columns 6, 8, and 10). The point estimates indicate that the association between FDI and growth is about four times larger in the IV estimations than in the OLS estimations (compare columns 1 and 3 with columns 2 and 4). This is also the case when the OLS estimates are statistically significant (columns 5 and 7) and the IV estimates are not significant (compare columns 5 and 7 with columns 6 and 8).

These results could be driven by the presence of measurement error which leads to attenuation bias in the OLS estimates. However, it is unlikely that correcting attenuation bias would lead to such a large difference. This is especially so because endogeneity bias should lead to OLS estimates that amplify the positive correlation between FDI and growth. Hence, correcting for endogeneity should lead to lower point estimates. One possible explanation for our result has to do with the fact that our instrument is not very strong. To explore this possibility, we start by describing the first stage estimations associated with Table 4 to then discuss possible sources of bias.

Table C.1 in the Appendix shows first stage results. The instrument is strongly correlated with FDI for the 1990-2009 and 1992-2011 samples. However, the correlation becomes weaker for the 1994-2013 and 1996-2015 samples and it is not statistically significant for the 1998-2017 sample. Standard methods for assessing underidentification and the presence of weak instruments are the Cragg-Donald Wald F-Statistics on the excluded instrument and the Kleibergen-Paap rk LM statistics for underidentification. For the models estimated over 1990-2009 and 1992-2011, we find that the F statistics place our model in what Stock and Yogo (2002) call “the range of ambiguity.” There is no clear evidence that the instrument is very strong or very weak (the statistics are consistent with a 5% test that the worst-case relative bias is 20% or less). The Kleibergen-Paap rk LM statistics indicate that we can reject the null hypothesis that the equation is underidentified, with a 5% confidence level (the p-values are 0.026 and 0.029, respectively). The weak instrument and underindentification statistics, suggest that our instrument does not work well when we estimate the model over the 1994-2013, 1996-2015, and 1998-2017 periods.

There are two sources of bias related to the presence of a weak instrument. First, even if the exclusion restrictions are valid, the presence of weak instruments leads IV estimates to be biased towards the OLS estimates. Second, the presence of a weak instrument amplifies the bias of even small violations of the exclusion restriction.

One way to assess how serious the weak instrument problem is, is to estimate the reduced form model. Given that the reduced form is estimated with OLS, it does not suffer from IV bias. Finding that the instrument is strongly correlated with the dependent variable does not guarantee that the instrument is valid, but at least it tells us that it has some strength. It is thus comforting that the reduced form regressions always show a strong correlation between our instrument and GDP growth (Table C.2 in the Appendix).

If more than one instrument is available, it is also possible to estimate the overidentified model with both two-stage least squares (TSLS) and limited information maximum likelihood (LIML) and compare these two sets of estimates. Finding LIML estimates which are very different from TSLS is an indication that the instruments are problematic. We are thus reassured that, in our 20