This paper presents a maximum likelihood approach to estimation of cross sectional distributions of heterogeneous autoregressive (AR) parameters with short panel data. We construct a panel likelihood by integrating the unknown cross sectional density of heterogeneous AR parameters with respect to a known time-series data generating kernel. The solution to this extremal criterion recovers the unknown density of heterogeneous AR parameters. Applying our method to a model of employment dynamics with the firm-level data of Arellano and Bond (1991), we find that adjustment rates of employment are significantly heterogeneous across firms.
Mavroeidis, S., Sasaki, Y. and Welch, I. (2015). `Estimation of heterogeneous autoregressive parameters with short panel data’. Journal of Econometrics, 188(1), 219-235.