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Given the fixed-effects framework, what I am estimating is the "within" effect of undervaluation, namely, the impact of changes in under- or overvaluation on changes in growth rates within countries.
The results in column 1-4 confirm further that the growth impact of undervaluation depends heavily on a country's level of development.
Interestingly, the estimated impact of undervaluation seems to be independent of the time period under consideration.
(13) However, the evidence strongly suggests that the relationship I have estimated does not rely on outliers: it is driven at least as much by the positive growth effect of undervaluation as by the negative effect of overvaluation.
Even though estimates from regressions that use such alternative measures are in turn likely to be biased downward (in the presence of Balassa-Samuelson effects that operate over time within countries), such estimates are still useful insofar as they provide a lower bound on the growth effects of undervaluation.
Even if the "correct" estimate is the lower one of 0.016, it still establishes a strong enough relationship between real undervaluation and economic growth to command attention: a 50 percent undervaluation would boost annual growth of income per capita by 0.8 percentage point.
The specifications reported thus far are rather sparse, including only a convergence factor, fixed effects, and the undervaluation measure itself.
Indeed, given the range of controls considered and the significant changes in sample size (from a low of 191 to a high of 790), the robustness of the central finding on undervaluation is quite striking.
As a final robustness check, I ran cross-sectional regressions using the full sample in an attempt to identify the growth effects of undervaluation solely through differences across countries.
To the extent that such policies are designed to move the real exchange rate in the first place, they are part of what I have in mind when I talk of "a policy of undervaluation." But to the extent they are not, the results in tables 4 and 5 indicate that undervaluation is associated with faster economic growth even when those policies are controlled for.
Many of the plausible sources of bias that one can think of would induce a negative relationship between undervaluation and growth, not the positive relationship I have documented.
There is a much more distinct trend in UNDERVAL for this subsample: the growth spurt takes place after a decade of steady increase in UNDERVAL and immediately after the index reaches its peak value (at an undervaluation of 10 percent).