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I have a problem in interpreting a coefficient in my regression below:

I am estimating the following regression in the spirit of an event study analysis with daily data:

$\Delta ER_t = \beta_1 MPS_t +\beta_2 MPS_t \Delta Res_{t'} +\epsilon_t$

in which $\Delta ER_t$ is the exchange rate between day $t$ and day $t-1$, $MPS_t$ is a monetary policy shock at time $t$ and $\Delta Res_{t'}$ is the change in foreign exchange reserve between the $\textbf{month}$ following the monetary policy shock and the $\textbf{month}$ previous to the monetary policy shock (I do not have daily data on international reserves but only monthly data).

How should I interpret $\beta_2$, the interaction term between the monetary policy shock and the change in international reserves? It is clearly not uncovering causation since $\Delta Res_{t'}$ includes a lead variable (the level of reserves one month after the shock), but then can I still argue for an inverse causation effect? For example if I find that the $\beta_2$ is positive and significant, can I claim that larger future international reserves (which increase $\Delta Res$) arise as a consequence of monetary policy shocks that have a larger impact on the exchange rate today?

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  • $\begingroup$ I would try to understand its meaning pretending that $\Delta Res_t$ was available and then worry about $t'$. Why not the level of $Res$ given at $t$ especially if you have a panel data set. $\endgroup$ – chan1142 Oct 26 '16 at 23:29
  • $\begingroup$ If you want to model the relationship between monetary policy shocks and reserves, why don't you use reserves as dependent variable? In any case, I would not be convinced by a causal interpretation unless you can clearly articulate your exclusion restriction and plausibly argue that it holds. Typically this is quite difficult in a macro setting. $\endgroup$ – Tobias Jan 25 '17 at 2:39
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No, it's a regression model. You can't infer any causality from it.

At best, you can infer that there is correlation between the terms.

But note that even that inference can be hazardous. Without knowing how you got the model terms, what your priors are, and what the data is, it's not possible to say whether or not the correlation is spurious

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  • $\begingroup$ well, the whole point of an event study is to determine causality, by using intraday/daily data; for instance, I can say that a $1\%$ monetary policy shock causes a reaction equal to $\beta_1$ on the exchange rate on that same date, a few hours later the FOMC announcement. What bothers me is that $\Delta Res$ is a monthly data, but still, I am interacting it with a monetary policy shock which is daily, so, if I find a significant coefficient, can't I establish any relationship which goes farther than simple correlation between the two (that is reserves changes and exchange rate) . $\endgroup$ – night_owl89 Jun 29 '16 at 16:48
  • $\begingroup$ also I am using a large panel data model (with 20+ countries) $\endgroup$ – night_owl89 Jun 29 '16 at 16:48

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