This paper develops the stochastic frontier model with multiple endogenous regimes to solve biased and inconsistent estimates due to sample selection bias. If we encompass heterogeneous observations into one regression equation, then the estimated parameters may be invalid. Moreover, if heterogeneous observations did not randomly fall into regression equations with reasonable coefficients, this statistically implies that sample selection bias exists. This paper extends the stochastic frontier model with two endogenous regimes to include multiple regimes and expand the empirical application. Based on the sample selection/regime-switching information, I derived the closed form of the likelihood function and the estimator of the technical efficiency index for the proposed model. Additionally, I rendered an estimate using the maximum likelihood estimation. In this empirical study, I analyzed the cost efficiency of doctoral-granting universities in the United States and applied this to the proposed model with three regimes. Evidence suggests that considering sample selection and the multiple-regime model is necessary when observations are heterogeneous. 

This study developed the Heckman selection model with endogeneity and includes the stochastic frontier (SF) model as its main equation, which allowed us to solve the problems of selectivity and endogeneity bias simultaneously in the SF model, otherwise the estimated parameters are biased and inconsistent. The proposed model can be applied to three cases of endogeneity, including the endogeneity that exists only in the SF model (main equation), in the selection equation, or in both. For the proposed model, I derived the closed form of the likelihood function and the estimator of the technical efficiency index using information on selectivity and endogeneity. By using the two-step estimation, I was able to easily estimate the proposed model without having to undertake the complicated estimation procedure. In the empirical study, I analyzed the operating efficiency of air carriers in the United States. The results suggest that considering both selectivity and endogeneity is necessary, otherwise the predicted technical efficiency indices are invalid.

This paper combines the double hurdle model and stochastic frontier model with ordered multiple choices, allowing for the two choices in the second selection stage to be expanded to multiple possible choices. By doing so, we can correct for the sample selection bias that may arise from a two-stage selection instead of a one-stage selection, and also take into account heterogeneous observations. For the proposed model, I derived the closed form of the likelihood function and the estimator of the technical efficiency index based on the sample selection information. In the empirical study, I studied the production efficiency of the labor market in the United States. Evidence suggests that considering a multiple-regime model in the second selection stage is necessary when observations are heterogeneous. Otherwise, the estimated production structure and technical efficiency indices are invalid.

The traditional stochastic frontier model assumes that all observations are inefficient. The inefficiency term is continuously distributed in this model, implying zero probability (i.e., impossibility) of an observation with full efficiency. However, fully efficient observations may exist under a competitive market. Estimation of the production technologies and technical efficiencies or inefficiencies of these observations through the traditional stochastic frontier model is thus invalid. Moreover, when a single stochastic frontier model is used to estimate parameters for heterogeneous observations with different production technologies, bias emerges. This paper presents an econometric model developed to solve these problems. In the empirical study, I

analyze the operating cost efficiency of universities in the United States by the proposed model. The results suggest that considering the multiple-regime model and fully efficient observations are necessary when observations are heterogeneous and market conditions are competitive; otherwise, the estimated technical efficiency indices for each observation would be biased and inconsistent.

This study employs a panel data and an inefficiency stochastic frontier model to analyze the operational efficiency of Taiwan’s banking industry from 2014 to 2023. The analysis covers private banks, public banks, and foreign banks, with financial data obtained from the Central Bank and financial supervisory authorities. Compared to the traditional panel data stochastic frontier model, the inefficiency model further incorporates environmental variables to account for their direct influence on inefficiency. The empirical findings indicate that the efficiency of banks in Taiwan is influenced by internal asset allocation, government policies, and macroeconomic conditions. Notably, significant fluctuations in operational strategies and outcomes were observed during periods of external shocks, such as the U.S.-China trade war and the COVID-19 pandemic. Furthermore, statistical tests confirm that incorporating the direct effects of environmental variables on inefficiency is essential for reliable efficiency estimation; otherwise, the resulting efficiency indices may be biased. Overall, the empirical results shed light on the operational performance of Taiwan’s banking sector in a highly competitive market environment and offer valuable insights for policymakers and industry stakeholders.