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In this paper, a quantile function is suggested as an alternative description of a production technology. Since the quantile function may not share the same functional properties as the frontier function, it is argued that the quantile-based production function serves as a better benchmark for a firm’s production structure analysis. This argument is extended to the metafrontier analysis. The quantile metafrontier is defined as the envelopment of all groups’ quantile frontier at the same quantile level. The quantile technology gap serves as a more relevant indicator of efficiency in the adopted technology than the traditional measure of the metafrontier technology gap. The quantile approach is illustrated using survey data to estimate the earning profiles for men, and the impact of human capital on the industrial wage distributions in the service industry, the manufacturing industry, and all other industries in Taiwan.

In this paper, quantile regression models are suggested as an alternative description of a production technology. The quantile of continuous order defines the production profile and the quantile-based individual technical efficiency relative to the quantile order. Quantile-based production frontier and efficiency are easy to derive and estimate and do not envelop all sample observation points. A quantile-based production frontier is more robust to extreme observations than DEA or FDH. Furthermore, quantile regression does not make a distribution assumption. It is more robust to the misspecification of error structure than DFA or SFA. In this paper, the quantile regression methods are extended to semiparametric smooth coefficient models. A local linear fitting scheme to estimate the smooth coefficients is proposed in the quantile framework. An empirical application of the model to the Taiwan manufacturing industry demonstrates the potential for the estimation of production technology and efficiency measures.

This paper proposes a new two-step stochastic frontier approach to estimate technical efficiency (TE) scores for firms in different groups adopting distinct technologies. Analogous to Battese et al. (J Prod Anal 21:91–103, 2004), the metafrontier production function allows for calculating comparable TE measures, which can be decomposed into group specific TE measures and technology gap ratios. The proposed approach differs from Battese et al. (J Prod Anal 21:91–103, 2004) and O’Donnell et al. (Empir Econ 34:231–255, 2008) mainly in the second step, where a stochastic frontier analysis model is formulated and applied to obtain the estimates of the metafrontier, instead of relying on programming techniques. The so-derived estimators have the desirable statistical properties and enable the statistical inferences to be drawn. While the within-group variation in firms’ technical efficiencies is frequently assumed to be associated with firm-specific exogenous variables, the between-group variation in technology gaps can be specified as a function of some exogenous variables to take account of group-specific environmental differences. Two empirical applications are illustrated and the results appear to support the use of our model.

In this paper, we propose the copula-based maximum likelihood (ML) approach to estimate the multiple stochastic frontier (SF) models with correlated composite errors. The motivation behind the extension to system of SF regressions is analogous to the classical generalization to system of seemingly unrelated regressions (Zellner in J Am Statist Assoc 57:348–368, 1962). A demonstration of the copula approach is provided via the analysis of a system of two SF regressions. The consequences of ignoring the correlation between the composite errors are examined by a Monte Carlo experiment. Our findings suggest that the stronger the correlation between the two SF regressions, the more estimation efficiency is lost in separate estimations. Estimation without considering the correlated composite errors may cause significantly efficiency loss in terms of mean squared errors in estimation of the SF technical efficiency. Finally, we also conduct an empirical study based on Taiwan hotel industry data, focusing on the SF regressions for the accommodation and restaurant divisions. Our results, which are consistent with the findings in simulation, show that joint estimation is significantly different from separate estimation without considering the correlated composite errors in the two divisions.

This paper derives an analytic closed-form formula for the cumulative distribution function (cdf) of the composite error of the stochastic frontier analysis (SFA) model. Since the presence of a cdf is frequently encountered in the likelihood-based analysis with limited-dependent and qualitative variables as elegantly shown in the classic book of Maddala (Limited-dependent and qualitative variables in econometrics. Cambridge University Press, Cambridge, 1983), the proposed methodology is useful in the framework of the stochastic frontier analysis. We apply the formula to the maximum likelihood estimation of the SFA models with a censored dependent variable. The simulations show that the finite sample performance of the maximum likelihood estimator of the censored SFA model is very promising. A simple empirical example on the modeling of reservation wage in Taiwan is illustrated as a potential application of the censored SFA.

In most empirical studies, once the best model has been selected according to a certain criterion, subsequent analysis is conducted conditionally on the chosen model. In other words, the uncertainty of model selection is ignored once the best model has been chosen. However, the true data-generating process is in general unknown and may not be consistent with the chosen model. In the analysis of productivity and technical efficiencies in the stochastic frontier settings, if the estimated parameters or the predicted efficiencies differ across competing models, then it is risky to base the prediction on the selected model. Buckland et al. (Biometrics 53:603–618, 1997) have shown that if model selection uncertainty is ignored, the precision of the estimate is likely to be overestimated, the estimated confidence intervals of the parameters are often below the nominal level, and consequently, the prediction may be less accurate than expected. In this paper, we suggest using the model-averaged estimator based on the multimodel inference to estimate stochastic frontier models. The potential advantages of the proposed approach are twofold: incorporating the model selection uncertainty into statistical inference; reducing the model selection bias and variance of the frontier and technical efficiency estimators. The approach is demonstrated empirically via the estimation of an Indian farm data set.

An important issue when conducting stochastic frontier analysis is how to choose a proper parametric model, which includes choices of the functional form of the frontier function, distributions of the composite errors, and also the exogenous variables. In this paper, we extend the likelihood ratio test of Vuong, Econometrica 57(2):307–333, (1989) and Takeuchi’s, Suri-Kagaku (Math Sci) 153:12–18, (1976) model selection criterion to the stochastic frontier models. The most attractive feature of this test is that it can not only be used for testing a non-nested model, but also still be applicable even when the general model is misspecified. Finally, we also demonstrate how to apply this test to the Indian farm data used by Battese and Coelli, J Prod Anal 3:153–169, (1992), Empir Econ 20(2):325–332, (1995) and Alvarez et al., J Prod Anal 25:201–212, (2006).

Individuals save for future uncertain health care expenses. This is less efficient than pooling health risk through insurance. The provision of comprehensive health insurance may raise welfare by providing the missing market to smooth out consumption through the life cycle. We employ a semiparametric smooth coefficient model to examine the effects of the introduction of the National Health Insurance in Taiwan in 1995 on savings and consumption over the life cycle. The idea is to estimate the coefficients of health insurance which vary with age. Our results suggest that younger households are more sensitive to the risk reductions, and that they demonstrate a greater response in the reduction of their precautionary saving. Copyright © 2004 John Wiley & Sons, Ltd.

In this article, we propose a semiparametric smooth coefficient model as a useful yet flexible specification for studying a general regression relationship with varying coefficients. The article proposes a local least squares method with a kernel weight function to estimate the smooth coefficient function. The consistency of the estimator and its asymptotic normality are established. A simple statistic for testing a parametric model versus the semiparametric smooth coefficient model is proposed. An empirical application of the proposed method is presented with an estimation of the production function of the nonmetal mineral industry in China. The empirical findings show that the intermediate production and management expense has played a vital role and is an unbalanced determinant of the labor and capital elasticities of output in production.

In this paper, a switching regression model is developed to analyze farmers' choice behavior and cost efficiency in field plowing arrangement in Taiwan. We find that the decision on the choice of plowing arrangement is determined by a cost comparison between self-plowing and hired-service, and other non-cost considerations, such as the availability of family labor and machinery, education level, non-farm income, age, and regional effects. Across a spectrum of farmer characteristics, empirical results indicate a potentially substantial cost-savings by hiring service for field plowing than by self-plowing. Self-plowing farmers also subject to a significant level of cost inefficiency.

This paper utilizes the average derivative estimation of Stoker (1986) and the pesudo-likelihood estimation of Fan, Li, and Weersink (1996) to estimate a semiparametric stochastic frontier regression, y = g(x) + e, where the function g(.)is unknown and e is a composite error in a standard setting. The proposed semiparametric method of estimation is applied to data on farmers' credit unions in Taiwan. Empirical results show that the banking services of the farmers' credit unions is subject to economies of scale, but high degree of cost inefficiency in operation.

An expectation-maximum (EM) likelihood algorithm is used to estimate two seemingly unrelated Tobit regressions in which the dependent variables are truncated normal. An illustrative example on the determination of the life-health insurance and pension benefits is also given.

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