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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.

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.

I. INTRODUCTION Institutions of higher education comprise knowledge creation (research) and knowledge dissemination (teaching). Thus, the university's mission is to deliver quality undergraduate and graduate education and to expand the frontier of academic research. Numerous studies (Verry and Layard 1975; Cohn, Rhine, and Santos 1989; deGroot McMahon, and Volkin 1991; Nelson and Hevert 1992; Lloyd, Morgan, and Williams 1993; Dundar and Lewis 1995; Koshal and Koshal 1995, 1999) have investigated, as in the case of firms, the multiple-product cost function of producing the vector of outputs on undergraduate and graduate education and research. The cost structure of higher education is studied via the scale economies and the scope economies of the cost function. However, these measures of scale and scope economies may be elusive if the quality dimension of colleges and universities is not considered. Without taking into account the quality variation, in the short-run, a university can reduce the average cost of operation by lowering the quality. Universities with more congested educational facilities are substituting facility utilization for capital; universities with a higher student/faculty ratio and less research engagement are substituting quality of education for quantity of undergraduate and graduate enrollment. The consequence is an upward bias in estimating the economies of scale and scope. This conclusion is consistent with the early studies of Nelson and Hevert (1992) which showed that failure to control for class size in cost function may result in specification bias, and an economy of scale is evident if class size is allowed to expand. Quality of higher education is multidimensional. Quality in instruction, faculty research, and the quality of educational environment are all significant factors determining the long-run university cost structure and the crucial determinants of the scale and scope economies of higher education. How and to what extent quality affects a university's operating cost depends on the goal and orientation of the institutions. Higher quality increases the university's cost of operation. But, in a large research-oriented university, a disproportional share of the budget often benefits the graduate, not the undergraduate program. It is unrealistic to assume that quality affects only the average cost and that the marginal costs of various educational programs are independent of quality. Quality is unlikely to be simply a neutral cost-shifting factor. The purpose of this paper is to propose a university cost function and a semiparametric-estimating technique that treats quality as a nonneutral cost-shifting factor, which directly affects the marginal cost of outputs in undergraduate and graduate education. More precisely, the marginal costs of outputs are specified as a nonparametric smooth function of quality. A semiparametric specification of university cost is applied to 56 comprehensive and science/technology universities in Taiwan over the period 2000-2003. II. SEMIPARAMETRIC COST FUNCTION AND ESTIMATION TECHNIQUE Following the conventional multiproduct cost specification for higher education (Cohn, Rhine, and Santos 1989; deGroot, McMahon, and Volkin 1991; Lloyd, Morgan, and Williams 1993; Dundar and Lewis 1995; Koshal and Koshal 1995, 1999), the total cost (C) is specified as a quadratic function of outputs, undergraduate and graduate enrollments. However, the quadratic cost function is modified by allowing for the coefficients to be functions of quality in the following form: (1) C = [[beta].sub.0](Q) + [k.summation over i=1] [[beta].sub.i](Q)[Y.sub.i] + (1/2) X [k.summation over i=1], [k.summation over j=1], [[beta].sub.ij](Q)[Y.sub.i][Y.sub.j] + [m.summation over i=1], [[alpha].sub.i][Z.sub.i] + [epsilon] where C is the total cost of producing k educational outputs (Y), and [Z.sub.i] is the ith institutional characteristics. …

This study adopts a semiparametric smooth coefficient model to evaluate the export–wage premiums, firm size–wage premiums, and the wage gap between skilled and unskilled labor. Particular focus is placed upon widespread evidence indicating that pay levels in ‘large’ and ‘export-oriented’ firms are higher than in their ‘small’ and ‘domestic-oriented’ counterparts. Applying the firm-level data for Taiwanese manufacturing firms, we find a positive export–wage premium for skilled workers and a negative export–wage premium for unskilled workers. The hypothesis of a constant export premium across firm size is rejected. While most of the export–wage premiums for skilled labor can be attributed to the small and medium firms, the large exporting firms have a significant adverse effect on wages for unskilled labor. Moreover, our results suggest that the firm size–wage premiums for skilled workers are larger than those for unskilled workers. The wage gap between the two skill groups is also sensitive to size categories.

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 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.

The financial sector of the Taiwan economy has experienced major structural changes in the past decade. The banking system has been liberalized, a regulated money market has developed, and the foreign exchange market has been deregulated. Nevertheless, Taiwan's financial sector is still characterized by dualism, with the coexistence of both regulated and unregulated (curb) markets. The ratio of financial loans from the unregulated market to those from the regulated market for the total private enterprise has been consistently large, averaging 27.5% for the period 197188.' Interest rates in the unregulated markets of Taiwan are generally much higher than those in the regulated markets. Figure 1 shows the disparity in interest rates between these two markets. The difference in interest rates grew during the 1970s, reaching an annual rate of 23 percent in the second quarter of 1979. Since then, the differential has declined steadily to about 17 percent in 1988.

A model of expected utility maximization is used to study the optimal allocation of a professor's time between research and teaching in a situation where both production activities are subject to uncertainty. It was shown that, in general, a professor's optimal allocation of time under uncertain production departs from the certainty strategy. An explicit model was developed to evaluate the effects of time effort in research and teaching with respect to changes in the degree of uncertainty, the Pratt-Arrow index of risk aversion, and the unit output rewards of research and teaching (for example, “merit pay”).

OLS and BLUS residuals in the classical linear regression model are compared with respect to testing the normality of regression disturbances. It is shown that in theory both types of residuals suffer from the common problem of lack of independence under the alternative hypothesis of nonnormal disturbances. Further, Monte Carlo experiments appear to show the superiority of OLS over BLUS residuals, as well as the superiority of the Shapiro-Wilk test over other tests studied, when one is testing for normality.

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.

The existing analyses of the general problem of estimating economic relations between a dependent variable Y and a set of independent variables X, e.g., Y = Y(G(X), u), where u is a stochastic error, usually focus on the formulation of the "deterministic part," G(X), of the relationship while little attention is paid to the specification and interpretation of the stochastic distrubance term, u, Two commonly employed specifications, Y = G(X) + u and Y = G(X)eu, appear when G(X) is linear in the parameters. Since nothing a priori is known in practice about the form of the disturbance, a more general specification of the error term based on a family of power transformations, including both additive and multiplicative forms as special cases, has been proposed [2; 4; 6; 9; 10; 11]. However, economic theory is often concerned with the mathematical properties of the deterministic part G (X) and it is natural to ask whether the conditional mean function, E(Y X), preserves these properties. It is well known that if u is normallly distributed the conditional mean function does not equal G (X) when the disturbance is multiplicative. Suppose, for example, that the deterministic part G(X) represents the market demand schedule derived from consumer utility maximization in a non-stochastic world. The actual individual demand schedule Y(G(X), u), however, is a sto

where Y is an N X 1 observation vector of the dependent variable, X is an N X K observation matrix with rank K of regressors, and e is the N X 1 vector of random disturbances. The disturbances are assumed to be temporally independent with constant covariance matrix a2IN. It has been shown that the distribution of the least-square residual vector e is singular normal with zero mean vector and covariance matrix