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?