1% ============================================================================2\section{Robustness Checks}3\label{sec:robustness}4% ============================================================================56We conduct several robustness tests to assess the sensitivity of our baseline results.78\subsection{Alternative Variable Definitions}9\label{subsec:alt_definitions}1011We first verify that our results are not driven by the specific construction of the dependent variable. Table~\ref{tab:app_robustness} in Appendix~\ref{app:tables} reports estimates using \ldots{} as alternative measures. The coefficient on $X_{i,t}$ remains statistically significant and economically meaningful across all specifications.1213\subsection{Alternative Estimation Methods}14\label{subsec:alt_estimation}1516We re-estimate the model using \ldots{} to address potential concerns about \ldots{} The results are qualitatively unchanged.1718\subsection{Placebo Tests}19\label{subsec:placebo}2021As a falsification exercise, we replace the main explanatory variable with \ldots{} If our baseline results reflect a genuine economic relationship rather than spurious correlation, we expect the placebo coefficients to be statistically insignificant. Consistent with this expectation, none of the placebo estimates are significant at conventional levels.2223\subsection{Sensitivity to Sample Period}24\label{subsec:sample_period}2526We examine whether our results are sensitive to the sample period by \ldots{} The estimates remain stable across sub-periods, suggesting that our findings are not driven by a specific time window.27