A stochastic frontier model with correction for sample selection

A double-copula stochastic frontier model with dependent error components and correction for sample selection

The traditional Stochastic Frontier Model (SFM) suffers from a very restrictive assumption of independence of its error components and also limited ability to address heterogeneity (inefficiency effects) satisfactorily, thereby leading to potential biases in the estimation of model parameters, identification of inefficiency effect variables influencing efficiency and, ultimately, efficiency scores. This paper aims to investigate the consequences of ignoring any dependency in error components and heterogeneity in the stochastic frontier model, and proposes a copula-based SFM with heterogeneity to resolve such weaknesses based on a simulation study to prove its superiority over the traditional SFM, followed by an empirical application on a sample of rice producers from northern Thailand. We demonstrate that the proposed model, i.e., copula-based SFM with dependent error components and heterogeneity, is unbiased and robust. The simulation experiments show that the traditional SFM can cause biases in parameter estimation and severe overestimation of technical efficiency. The traditional SFM with heterogeneity also has similar consequences. However, just ignoring heterogeneity does not have a great impact on parameter estimation and technical efficiency compared to the consequence of ignoring dependency in error components. The empirical application of the proposed model results show that land, labor and material inputs are all significant drivers of rice production in our copula-based SFM with dependent error components and heterogeneity, whereas in the traditional SFM model only the land variable seems to be a significant driver of rice production. The mean technical efficiency (MTE) score was also overestimated by two points in the traditional SFM, i.e., MTE = 0.88 versus 0.86. Finally, results of the copula-based SFM with dependent error components and heterogeneity reveals that both subsistence pressure and the use of hired labor are significantly associated with technical inefficiency, whereas the traditional SFM could identify the effect of hired labor use only. Therefore, caution is necessary when interpreting results from the conventional SFM as the results may be biased, incomplete and/or inadequate.

Group-specific stochastic production frontier models with parametric specifications

Most stochastic frontier models have focused on estimating average productive efficiency across all firms. The failure to estimate firm-specific effiicency has been regarded as a major limitation of previous stochastic frontier models. In this paper, we measure firm-level efficiency using panel data, and examine its finite sample distribution over a wide range of the parameter and model space. We also investigate the performance of the stochastic frontier approach using three estimators: maximum likelihood, generalized least squares and dummy variables (or the within estimator). Our results indicate that the performance of the stochastic frontier approach is sensitive to the form of the underlying technology and its complexity. The results appear to be quite stable across estimators. The within estimatoris preferred, however, because of weak assumptions and relative computational ease.

Recently, a skew-normal based stochastic frontier model has emerged as a promising tool for efficiency analysis. This paper introduces a Bayesian framework for statistical inference, integrating both informative and non-informative prior knowledge to estimate parameters of skew-normal distributions in stochastic frontier models. Through comprehensive evaluation using both simulation data and real data from a manufacturing productivity study, we demonstrate that the Bayesian approach provides more stable and accurate parameter estimates compared to the conventional maximum likelihood method. The results from both simulated and empirical analyses clearly highlight the superior performance of the Bayesian methodology, offering enhanced robustness and precision in estimating efficiency scores, thus contributing significantly to the advancement of stochastic frontier modeling.

Analysis of the behavior of technical inefficiency with respect to parameters and variables of a stochastic frontier model is a neglected area of research in frontier literature. An attempt in this direction, however, has recently been made. It has been shown that in a “standard” stochastic frontier model that both the firm level technical inefficiency and the production uncertainty are monotonically decreasing with observational error. In this paper we show, considering a stochastic frontier model whose error components are jointly distributed as truncated bivariate normal, that this property holds if and only if the distribution of observational error is negatively skewed. We also derive a necessary and sufficient condition under which both firm level technical inefficiency and production uncertainty are monotonically increasing with noise-inefficiency correlation. We next propose a new measure of the industry level production uncertainty and establish the necessary and sufficient condition for firm level technical inefficiency and production uncertainty to be monotonically increasing with industry level production uncertainty. We also study the limiting probabilistic behavior of these conditions under different parametric configuration of our model. Finally we carry out Monte Carlo simulations to study the sample behavior of the population monotonic property of the firm level technical inefficiency and production uncertainty in our model.

Estimation of Sample Selection Models with Spatial Dependence

This study investigated productive and profitability capacities of contour farming technologies in rice production in Barangwaje, Ikara Local Government Area and Dutsen Abba in Zaria Local Government Area of Kaduna State. In Barangwaje, 36 and 28 farmers from Dutsen Abba were selected based on interest for the trials. To compare the profitability, seeds, land preparation, fertilizer application and use of family labour, among others were used. Stochastic frontier model was employed to determine the efficiencies of contour rice farmers. Data were analysed using descriptive statistics, gross margin analysis and stochastic frontier model. The results showed that almost all (96%) of the respondents had annual income between ₦ 100, 000 and ₦150,000. High proportion (76%) of the respondents had extension contact and all the farmer had access to agricultural credit. In Barangwaje, the gross margin for one hectare of land cultivated was ₦420,253.75 for contour, ₦88,508.75 for contour + ridge-tie, N1,791.25 for flat land and ₦45,357.50 for farmer’s practice (up-down slope). In Dutsen Abba, gross margin obtained shows that contour + ridge tie had ₦34,978.56, flat land had ₦26,132.06, contour had ₦2,313.00 and farmer’s practice (up-down slope) had ₦114.31. Investment in rice cultivation was profitable as indicated by return per Naira invested. Stochastic frontier model shows that contour rice farmers were highly efficient as indicated by the value of gama (0.99), which implies that 99% of the variation of output from frontier was due to technical efficiency of the farmers. It concluded that rice production was highly profitable. Measures should be in place to reduce importation of rice in order to encourage local production. Constraints faced by farmers were not indicated in the abstract. Keywords: Rice, contour, contour + tie, profitability, allocative, efficiency

In this paper, we focused on the new stochastic frontier model with the nonlinear autoregressive structure in panel data. In classic finance models, uncorrelated errors are considered, which are frequently not met in empirical situations. In our stochastic frontier model, the composite error consists of two components, the statistical error and technical inefficiency, whereas the technical inefficiency is assumed to be autocorrelated. A semiparametric method is suggested to estimate nonlinear autoregressive function by two steps procedure as parametric Taylor series expansion and nonparametric adjustment factor. For the model parameters estimation, the Expectation-Maximization approach is applied and the performance of the estimation is checked by Monte Carlo simulation. Finally, we investigate the applicability of new model using a real data set.

This letter considers the following two questions: How much are the estimates of the parameters of stochastic cost frontier and cost inefficiency of Japanese hospitals affected (1) by the utilization of the panel structure of data in estimation; and (2) by considering a hospital-specific intercept in the cost frontier? Three models are estimated: a stochastic cost frontier model with a hospital-specific intercept treated as a random variable for panel data; a stochastic cost frontier model without a hospital-specific intercept for panel data; and the conventional stochastic frontier model that treats the data as if they were cross-sectional. The main findings are: (1) the introduction of panel structure into the frontier estimation changes the cost inefficiency estimate significantly compared with the estimate based on cross-sectionally treated data; (2) the intercept of the cost frontier is significantly different among hospitals.

Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper distributional specification of the error components of a stochastic frontier model is, generally, still open along with which variables influence inefficiency. Given the concern over the impact that model uncertainty is likely to have on the stochastic frontier model in practice, the present research proposes two distinct model averaging estimators, one which averages over nested classes of inefficiency distributions and another that has the ability to average over distinct distributions of inefficiency. Both of these estimators are shown to produce optimal weights when the aim is to uncover conditional inefficiency at the firm level. We study the finite-sample performance of the model average estimator via Monte Carlo experiments and compare with traditional model averaging estimators based on weights constructed from model selection criteria and present a short empirical application.

Banks are designed to be efficient as they play a vital role in the economic development; otherwise, banks may create obstacles in the development process of any country. This chapter employs an appropriate stochastic frontier model to investigate the performance of banks, traded in Kuala Lumpur Stock Exchange (KLSE) market. Based on the likelihood ratio test, the Cobb-Douglas stochastic frontier model is found to be more preferable than Translog stochastic frontier model for this study. The market data are used as the input and output variables. Banks traded in KLSE exhibited a commendable overall efficiency level of 99.52% during 2005-2009 hence suggesting minimal input waste of 0.48%. Among the banks, the Rashid Hussain bank is found to be highly efficient with a score of 0.9973 and BIMB (BIMB Holdings) bank is noted to have the lowest efficiency with a score of 0.9917. The results also show that the technical efficiency effect is increased over time.

In this paper, we propose an estimator for models in which an endogenous dichotomous treatment affects a count outcome in the presence of either sample selection or endogenous participation using maximum simulated likelihood. We allow for the treatment to have an effect on the participation or the sample selection rule and on the main outcome. Applications of this model are frequent in-but no limited to-health economics. We show an application of the model using data from Kenkel and Terza (2001), who investigate the effect of physician advice on the amount of alcohol consumption. Our estimates suggest that in these data (i) neglecting treatment endogeneity leads to a wrongly signed effect of physician advice on drinking intensity, (ii) accounting for treatment endogeneity but neglecting endogenous participation leads to an upward biased estimate of the treatment effect and (iii) advice affects only the drinking intensive margin but not drinking prevalence.

Specification tests for normal/gamma and stable/gamma stochastic frontier models based on empirical transforms

Summary The problem of non-random sample selectivity often occurs in practice in many fields. The classical estimators introduced by Heckman are the backbone of the standard statistical analysis of these models. However, these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. We develop a general framework to study the robustness properties of estimators and tests in sample selection models. We derive the influence function and the change-of-variance function of Heckman's two-stage estimator, and we demonstrate the non-robustness of this estimator and its estimated variance to small deviations from the model assumed. We propose a procedure for robustifying the estimator, prove its asymptotic normality and give its asymptotic variance. Both cases with and without an exclusion restriction are covered. This allows us to construct a simple robust alternative to the sample selection bias test. We illustrate the use of our new methodology in an analysis of ambulatory expenditures and we compare the performance of the classical and robust methods in a Monte Carlo simulation study.