Statistical inference in the multinomial multiperiod probit model

By John Geweke, Michael P. Keane, D. Runkle. 1997

Abstract Statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions, posterior distributions, or moment conditions in these models. We describe three alternative estimators, implemented using simulation-based approaches to inference, that circumvent the integration problem: posterior means computed using Gibbs sampling and data augmentation (GIBBS), simulated maximum likelihood (SML) estimation using the GHK probability simulator, and method of simulated moment (MSM) estimation using GHK. We perform a set of Monte-Carlo experiments to compare the sampling distributions of these estimators. Although all three estimators perform reasonably well, some important differences emerge. Our most important finding is that, holding simulation size fixed, the relative and absolute performance of the classical methods, especially SML, gets worse when serial correlation in disturbances is strong. In data sets with an AR(1) parameter of 0.50, the RMSEs for SML and MSM based on GHK with 20 draws exceed those of GIBBS by 9% and 0%, respectively. But when the AR(1) parameter is 0.80, the RMSEs for SML and MSM based on 20 draws exceed those of GIBBS by 79% and 37%, respectively, and the number of draws needed to reduce the RMSEs to within 10% of GIBBS are 160 and 80 respectively. Also, the SML estimates of serial correlation parameters exhibit significant downward bias. Thus, while conventional wisdom suggests that 20 draws of GHK is ‘enough’ to render the bias and noise induced by simulation negligible, our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strong.

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Citations in the corpus

MCMC Estimation of Restricted Covariance Matrices (2009, background): “Prior informativeness is very important given the small dataset (N = 522), the potential for poor likelihood identification (e.g., Geweke, Keane, and Runkle 1997), and the fact that the dataset is not well balanced (the first and last categories in this example involve only 2.5% and 1.5% of the…”
Tradeoffs and Complementarities in the Adoption of Improved Seeds, Fertilizer, and Natural Resource Management Technologies in Kenya (2016, background): “The Geweke–Hajivassiliou–Keane (GHK) simulator is a particularly popular choice in empirical research (Geweke et al., 1997; Hajivassiliou et al., 1996).”
Heterogeneity in R&D cooperation strategies (2004, background): “The GHK simulator (Geweke et al. 1997; Hajivassiliou et al. 1996) has been a particularly popular choice.”
Comparing Dynamic Equilibrium Models to Data (2001, unknown): “7 = ψ4 2 ( 16 ) 2f1f2 =1 , 2f3f4 = gγ1, 2f5f6 = gγ0, 2f7f8 =1 (17)”
Does the Use of Imported Intermediates Increase Productivity? Plant-Level Evidence (2008, methodology): “(15) To identify βx, βk, and βd, we use the following three moment conditions:”
Federal Reserve Bank of Minneapolis Research Department Staff Report 237 Mixture of Normals Probit Models (unknown): “The generalization of the mixture of normals model to the multivariate case is straightforward as is its incorporation into Markov chain Monte Carlo methods for the multinomial probit model that we have described elsewhere (Geweke, Keane, and Runkle 1994, 1997).”
Comparing dynamic equilibrium models to data: a Bayesian approach (2004, background): “Fourth, also as shown in the paper, the small sample performance of Bayesian estimates tends to outperform classical ones even when evaluated by frequentist criteria (for similar findings, see Jacquier, Polson, and Rossi (1994) or Geweke, Keane and Runkle (1997)).”
Smoking Habits: Like Father, Like Son, Like Mother, Like Daughter (2010, unknown): “In contrast, Gruber (2000) nds that prices have a signicant negative e¤ect on smoking participation and that this e¤ect is more remarkable for older teens.”
A model of health plan choice:: Inferring preferences and perceptions from a combination of revealed preference and attitudinal data (1998, background): “Despite this, the published Monte-Carlo work on small sample performance of simulation-based estimators has dealt exclusively with probit models (see Keane, 1994; Geweke et al., 1994, 1997; Lee, 1997).”