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Suppose I have 4 years worth of monthly panel data on:

  1. exports of widgets $y$ from home country to 12 different nations (in US dollars)
  2. nominal exchange rates $x$ for those 12 countries (in US dollars per unit of local currency)
  3. domestic consumption of widgets $z$ (in US dollars)
  4. nominal exchange rate $r$ of home country (in US dollars per unit of home currency)

I am primarily interested in the effect of exchange rate volatility on exports. I estimated the following seasonally-differenced equation using OLS with standard errors clustered on country and time:

$$ \ln y_{i,t} - \ln y_{i,t-52} = \alpha + \beta \cdot(\ln x_{i,t}-\ln x_{i,t-52})+\gamma \cdot(\ln z_{i,t}-\ln z_{i,t-52}) +\eta \cdot(\ln r_{i,t}-\ln r_{i,t-52}) + (\varepsilon_{i,t}-\varepsilon_{i,t-52})$$

The subscript $i$ indexes countries and $t$ indexes months. Exports are all strictly positive, so taking logs is not a problem.

Two Questions:

  • My estimates are somewhat sensitive to whether I control for own exchange rate $r$, and $\hat \beta \approx -\hat \eta$. Does $r$ belong in the equation?

  • Are the any robustness checks that I should consider? Are there any problems that jump out? I am not familiar with this literature, so any references would be most welcome.

dimitriy
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  • Your description implies `x` and `r` are the same variable. `r` is usually interest rate. Please clarify. It may be better to calculate exchange rate volatility as the variance in exchange rate, rather than differencing. Or square your differenced term. References: Kennedy, A Guide to Econometrics (a very chatty explanation of applied econometrics. It is mathematically basic, but it may give you some initial leads on the robustness checks you are after.) Wooldridge, Econometric Analysis of Cross Section and Panel Data (follow up the above reference with this one for more detailed explanations) – Sav-econ Mar 10 '14 at 18:17
  • I think I now understand that `r` is a the exchange rate of a single "home" country versus vs each other country e.g. EUR/GBP, JPY/GBP (adjusted to USD), whereas `x` is combinations of all countries exchange rates e.g. JPY/EUR, EUR/CNY (adjusted to USD). In which case drop `r`, since you are controlling for information that is already included in another regressor (`x`). This will cause multicollinearity. – Sav-econ Mar 10 '14 at 18:24
  • I need both since they are capturing different information. One is the destination country and one is the home country. It's possible for the destination country's currency to be worth less and for the home currency to depreciate as well, which would have offsetting effects. In theory, $\beta>0$ and $\eta<0$ Alternatively, I can use the ratio of the two, which should be roughly equivalent. – dimitriy Mar 10 '14 at 20:35

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