# Monetary Policy and international reserves— interpretation of the estimated coefficient

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?

• 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. – chan1142 Oct 26 '16 at 23:29
• 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. – Tobias Jan 25 '17 at 2:39

• 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) . – night_owl89 Jun 29 '16 at 16:48