Application of the Information Matrix Test on the National Productivity Analysis as the Cause of International Trade

Abstract

Purpose In order to analyze the national competitiveness of the Korean economy, it is necessary to estimate the total factor productivity correctly, because incorrect assumptions in the model can lead to serious estimation errors. Therefore, in order to estimate the suitability of the model, an information matrix test was proposed as an applicable method to the actual stochastic frontier production function. Design/Methodology/Approach We first examine the large sample distribution properties of maximum likelihood estimation (MLE) and quasi-maximum likelihood estimation (QMLE), and introduce several versions of the stochastic frontier product function models proposed by different scholars. Finally, we derive the Information Matrix Test (Battese and Coelli, 1992) for the stochastic frontier production function model. Also, a Monte Carlo simulation was applied to verify the correctness of the model. Findings From the results, we derive an analytical form of the Information Matrix Test (Battese and Coelli, 1992) on the stochastic frontier production function model using the simplified form proposed by Lancaster (1984). and as a result of empirical analysis by applying this process to each of the seven countries (Korea, China, Japan, the United States, United Kingdom, Germany, France), each  value was below the 95% significance level in all countries, indicating that the translog production function model was specified correctly. Research Implications The Information Matrix Test by White (1982) is an important solution for misspecified regression models. To solve this issue, Lancaster (1984) suggested the simpler form of the Information Matrix Test of White (1982). However, this method is also complex to apply in a real model. Therefore, until now, the Information Matrix Test has not been properly implemented in a regression model. This study presents an analytical form of the Information Matrix Test for the stochastic frontier production function, which is very important for analyzing national, industrial, and corporate competitiveness.