EM Algorithm Estimation of Simultaneous Equation Model with Limited Variables: An Example of Cigarette Consumption

Abstract

The two-part model and Heckman's sample selection model are often used in economic studies which involve analyzing the demand for limited variables. This study proposed a simultaneous equation model (SEM) and used the expectation-maximization algorithm to obtain the maximum likelihood estimate. We then constructed a simulation to compare the performance of estimates of price elasticity using SEM with those estimates from the two-part model and the sample selection model. The simulation shows that the estimates of price elasticity by SEM are more precise than those by the sample selection model and the two-part model when the model includes limited independent variables. Finally, we analyzed a real example of cigarette consumption as an application. We found an increase in cigarette price associated with a decrease in both the propensity to consume cigarettes and the amount actually consumed.

Keywords:

• EM algorithm
• Missing values
• Price elasticity
• Simultaneous equation model

Mathematics Subject Classification:

• 62F10
• 62P20

Acknowledgments

This research was supported by the Bureau of Health Promotion (Grant Number: BHP-92-Anti-Tobacco-2H02).

Notes

Notes: Upper number in each cell is lower number in each cell is MSE.

SS1: Sample selection model without imputation for missing or unobserved price; SS2: Sample selection model with unconditional mean imputation for missing or unobserved price; SS3: Sample selection model with conditional mean imputation for missing or unobserved price; SS4: Sample selection model with stochastic regression imputation for missing or unobserved price; TP1: Two-part model without imputation for missing or unobserved price; TP2: Two-part model with unconditional mean imputation for missing or unobserved price; TP3: Two-part model with conditional mean imputation for missing or unobserved price; TP4: Two-part model with stochastic regression imputation for missing or unobserved price; EM-SEM: EM algorithm.

∗p-value ≤0.05