Maximum Simulated Likelihood Estimation Research Articles

Modelling Interest Rate Dynamics in a Corridor with Jump Processes

A simulated maximum likelihood (SML) estimator is derived in order to estimate a jump-diffusion model of interest rates, which takes explicitly into account the monetary system by forcing a corridor on the short term interest rates. In order to obtain the SML estimator, we develop a method to simulate a diffusion process through certain values at future time points. The method is based on Monte Carlo simulations where we make use of a discretization scheme for the dynamics. A finite difference approach is used to obtain the entire term structure of interest rates. The method is applied on interest rate data from the German money market, and the results show that the authorities only have direct impact on the short end of the term structure, given that they try to change the level of the corridor.

Statistical inference in the multinomial multiperiod probit model

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.

Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results

This article reports Monte Carlo results on the simulated maximum likelihood estimation of discrete dynamic panel models introduced by James Heckman (1981a). The simulated maximum likelihood method is numerically stable even for long panels. Regression models and Polya and Renewal models can be better estimated than Markov models. With a moderate number of simulation draws, most of these complex models can be adequately estimated for panels with length up to 30. Polya and Renewal models can be accurately estimated for panels up to 50 periods. Estimates of Markov models can be sensitive to misspecified initial states but Polya, Renewal, and Habit Persistence models may not.

Estimation of the Stochastic Volatility Models by Simulated Maximum Likelihood: C++ Code

This is documentation for a C++ implementation of the simulated maximum likelihood (SML) estimation method, where the SML algorithm is applied to the stochastic volatility (SV) model. The algorithm and code can easily be adapted to a richer class of SV models, as well as to more general dynamic latent-variable models.

Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models

In this article, we investigate a bias in an asymptotic expansion of the simulated maximum likelihood estimator introduced by Lerman and Manski (pp. 305–319 in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, Cambridge: MIT Press, 1981) for the estimation of discrete choice models. This bias occurs due to the nonlinearity of the derivatives of the log likelihood function and the statistically independent simulation errors of the choice probabilities across observations. This bias can be the dominating bias in an asymptotic expansion of the simulated maximum likelihood estimator when the number of simulated random variables per observation does not increase at least as fast as the sample size. The properly normalized simulated maximum likelihood estimator even has an asymptotic bias in its limiting distribution if the number of simulated random variables increases only as fast as the square root of the sample size. A bias-adjustment is introduced that can reduce the bias. Some Monte Carlo experiments have demonstrated the usefulness of the bias-adjustment procedure.

Alternative Computational Approaches to Inference in the Multinomial Probit Model

This research compares several approaches to inference in the multinominal profit model, based on two Monte Carlo experiments for a seven choice model. The methods compared are the simulated maximum likelihood estimator using the GHK recursive probability simulator, the method of simulated moments estimator using the GHK recursive simulator and kernel-smoothed frequency simulators, and posterior means using a Gibbs sampling-data augmentation algorithm. Overall, the Gibbs sampling algorithm has a slight edge, with the relative performance of MSM and SML based on the GHK simulator being difficult to evaluate. The MSM estimator with the kernel-smoothed frequency simulator is clearly inferior. Copyright 1994 by MIT Press.

Testing the differences between the determinants of moody's and standard & poor's ratings an application of smooth simulated maximum likelihood estimation

AbstractThis paper extends previous studies on bond ratings by modeling as a system of equations the determinants of a municipality's decision to obtain a bond rating and the determinants of the municipality's rating for the two major rating agencies. Our model provides a framework to examine formally the differences between the two agencies in the determinants of the ratings. We estimate the four‐equation system by smooth simulated maximum likelihood estimation and then construct minimum χ2 tests on cross‐equation restrictions based on optimal minimum distance estimation. Self‐selection is found to be important in Moody's ratings while not in those of S&P. Split ratings appear to reflect differences in both the weight attached to specific determinants of the ratings and differences in the way the bonds are classified.

On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models

This article considers methods of simulated moments for estimation of discrete response models. It is possible to use the same set of random numbers to simulate the choice probabilities for each individual in the sample. In addition to the method of simulated moments of McFadden, we have considered also maximum simulated likelihood estimation methods. An asymptotic theory for such procedures is provided. The estimators are shown to be consistent and asymptotically normal by the theory of generalizedU-statistics. Asymptotic efficiency is discussed. Monte Carlo experiments on the finite sample performance of the estimators are reported.