Keane (1994) A Computationally Practical Simulation Estimator for Panel Data

Summary

This paper makes McFadden's method-of-simulated-moments (MSM) estimator practical for panel limited-dependent-variable models with serially correlated errors — the case where maximum likelihood requires a choice-probability integral whose dimension grows with the number of time periods. Keane factorizes the MSM first-order condition into a product of one-period-ahead transition probabilities and introduces a highly accurate recursive method — the GHK (Geweke-Hajivassiliou-Keane) simulator — for simulating those transition probabilities smoothly. The upshot is that rich error structures (random effects plus ARMA serial correlation) become estimable at roughly the cost of a simple random-effects ML-quadrature model, and Monte Carlo experiments show the estimator competitive with quadrature-ML and simulated-ML even when those use many quadrature points / accurate probability simulators.

Key Claims

• The panel LDV problem. ML for a panel probit/multinomial-probit requires evaluating choice probabilities that are multivariate normal integrals of order proportional to $T$ (the panel length); tractable ML usually forces an i.i.d. or equicorrelated (random-effects) error covariance (Butler-Moffitt Gaussian quadrature), which rules out genuine serial correlation.
• MSM avoids the high-dimensional integral. Extending McFadden (1989), the estimator matches simulated moments rather than maximizing a simulated likelihood, so it needs only unbiased simulators of the moments — and MSM is consistent for a fixed number of simulation draws (unlike simulated ML, whose bias needs the draws to grow).
• Factorization into transition probabilities. Keane rewrites the MSM first-order condition as a product/sequence of transition probabilities $P(\text{choice}_t\mid\text{choices}_{1:t-1})$, reducing the panel problem to a recursion over time.
• The GHK recursive simulator. Those transition probabilities are simulated by the recursive-truncation, importance-sampling method now known as the GHK simulator — sequential draws from univariate truncated normals with the interval probabilities accumulated — which is smooth in the parameters, strictly in $(0,1)$, and highly accurate.
• Rich error structures, low cost. Models combining random effects with ARMA serial correlation estimate in time comparable to simple random-effects ML-quadrature; Monte Carlo shows small bias and good performance versus both quadrature-ML and simulated-ML.

Concepts Introduced or Extended

• GHK Simulator
• Simulation-Based Estimation
• Multinomial Probit

Entities Mentioned

• Michael P. Keane

Quotes

"I develop a practical extension of McFadden's method of simulated moments estimator for limited dependent variable models to the panel data case. The method is based on a factorization of the MSM first order condition into transition probabilities, along with the development of a new highly accurate method for simulating these transition probabilities."

My Take

This is one of the papers that put the "K" in GHK: the recursive-truncation importance sampler for multivariate-normal rectangle probabilities is developed here for exactly the panel-LDV problem that motivated it, and paired with MSM rather than simulated likelihood so that consistency does not require an ever-growing number of draws. The practical selling point — that you can finally let panel discrete-choice errors be serially correlated (ARMA) instead of imposing equicorrelation for computational convenience — is what made it matter for applied panel econometrics. For the wiki it is a founding source of the GHK simulator page (alongside Geweke and Hajivassiliou) and a concrete instance of the MSM branch of simulation estimation. The lasting caveat is the usual MSM tension: robustness to a fixed simulation size buys consistency but at some efficiency loss relative to a well-simulated likelihood, and the moment/instrument choice still matters.