Maximum entropy estimation of seemingly unrelated regression and its application to Chinese household expenditure survey data.

摘要

Since the introduction of the maximum entropy principle to the econometrics literature by Golan, Judge and Miller, the properties of the GME estimators in the context of a series of econometric models have been studied and developed. In particular, the performance of the maximum entropy-based estimator in Seemingly Unrelated Regression (SUR) context is a very important research topic. The challenge in extending the maximum entropy principle to SUR is to handle the contemporaneous correlation inherent in this type of model specification.; In this dissertation, the generalized maximum entropy estimator is extended to the linear equations system model. By directly applying the maximum entropy principle within the SUR context, the standard generalized maximum entropy estimator for SUR models is obtained. This standard GME estimator, which is an analogue to the application of equation-by-equation OLS to the equations in a SUR model, is consistent and asymptotically normal, and can achieve efficiency gains over OLS from the prior information that is incorporated into the approach. However, the GME estimator is invariant to any linear transformation of the data constraint. Thus, two GME-based estimators, which only transform the data points, are proposed to achieve efficiency gain. The two-step GME estimator, which is inspired by the Aitken two-step estimator in the usual Least Squared metric, uses the estimated covariance structure obtained from the standard GME estimates to transform the data points only. The variance-parameterized GME, estimates the elements of the variance structure directly by Cholesky decomposition.; The Monte Carlo simulations verified a priori expectation that the performance of GME estimations depend on the type of prior knowledge available about the unknown parameters. Given accurate prior knowledge, the GME estimators are much more efficient that both the OLS and GLS estimators, especially in the case of small sample size. With vague prior knowledge, the bias of the GME estimates decrease as the sample size increases. Among the three GME-based estimators, the standard GME estimator appears quite promising. It is superior to it counterpart, OLS, for the most part, due to its incorporation of prior knowledge about the unknowns. The performance of the other two contemporaneous correlation-adjusted GME estimators, two-step GME and variance-parameterized GME depends even more on the accuracy of the prior knowledge about the unknown parameters.; An Almost Ideal Demand System was estimated utilizing GME on Chinese household survey data. It suggests that GME is a viable alternative to the estimation of the SUR model. With a priori knowledge about the parameters incorporated into the support points, the final estimation results are more reasonable and easier to interpret.; Empirically, the analysis of Chinese household survey data revealed significant provincial difference in Coastal China. The results indicate that the socio-demographic structure as well as food consumption patterns are different across provinces. With economic and social reform deepening, this significant provincial gap is an important factor to any Chinese social and economic research, as well as a major concern for the Chinese government.