Interpretation of coefficients for PPMLHDFE with Instrumental Variable

[Andrew Bernal]

Hello all,

My project involves estimating the impact of exchange rate volatility(EV)(taken as the standard deviation of daily percentage changes of bilateral exchange rates) on export-volume for bilateral country-pairs. From the relevant literature, a PPML gravity-type model is the best fit for this topic. I am running the below regression, essentially (shown in a linear fashion):

Exports = (B1)EV + relevant control variables

Using PPML, with exporter-importer and year fixed effects, the result for B1 = 0.003, and is statistically insignificant, which is expected from the literature. However, I am unsure of the interpretation of this coefficient. Based on my knowledge, I believe the elasticity measure is calculated by taking the B1 value and multiplying by the mean value of EV (0.003 * 0.67 = 0.002) which would represent a less than 0.5% increase in trade as exchange_volatility is increased by one standard deviation.

Now, when I run the estimation using Wooldridge's (2008, 2019) IV methods for non-linear models, I run the following code:

* First Stage
xtreg EV IV rta comcur log_gdp_o log_gdp_d i.year, fe
predict double v2h_fe, e
* Second Stage
ppmlhdfe exports EV v2h_fe rta comcur log_gdp_o log_gdp_d, a(imp#exp year)

B1 = -0.609 and is statistically significant. This drastic increase in the value of the coefficient and its significance leads me to believe something may be wrong with my model, or I am interpreting the coefficients incorrectly. If anyone could correct me and/or point me to the relevant literature regarding this interpretation, it would be very much appreciated.

[Andrew Bernal]

Clarifying information: I have been attempting to interpret the coefficients as in Tenreyro (2006), but it isn't clear to me how to interpret such a large coefficient. Additionally, Lin and Wooldridge (2019) outlines the proposed methodology for using an IV in a non-linear model.

More generally perhaps, what I need clarity on is how to interpret the coefficient in front of a standard deviation variable. It is not clear to me, nor does it seem possible, that a one-standard deviation increase in exchange rate fluctuation leads to such a large percentage decrease in exports.