We study estimation of the average partial effect (APE) in an irregular correlated random coefficients panel data model in which the time dimension equals the number of random coefficients, $T=p$, and the density function is degenerate. We extend Graham and Powell (2012) in two directions. First, we allow the density of $d_i=\det(X_i)$ to vanish or diverge at the origin at the polynomial rate $|d|^{a}$ with $a>-1$, and show that the aggregate time effects and the APE remain identified for every such $a$, extending earlier work studying the case $a = 0$. Second, we propose a three-step estimator: an $m$th-order local polynomial regression over the stayers for the time effects; a local polynomial fit of the conditional mean coefficient just outside the trimming threshold; and an imputation step that extrapolates the latter into the stayer region rather than discarding stayers. We establish joint asymptotic normality in three regimes determined by the sign of $a$, and obtain a convergence rate approaching $n^{-(m+1)/(2m+3)}$ when $a=0$, against $n^{-1/3}$ for Graham and Powell (2012), whose estimator is the special case $m=0$, $a=0$. The results show that smoothness of the underlying conditional expectations can be traded for a faster convergence rate in irregularly identified models. Simulations confirm lower bias and root mean squared error across designs. We redo the overidentification analysis of a markup model in Raval (2023), allowing for correlated random elasticities.
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