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UBC Theses and Dissertations

Essays in production theory : efficiency measurement and comparative statics Mendoza, Maria Nimfa F.


Nonparametric linear programming tests for consistency with the hypotheses of technical efficiency and allocative efficiency for the general case of multiple output-multiple input technologies are developed in Part I. The tests are formulated relative to three kinds of technologies — convex, constant returns to scale and quasiconcave technologies. Violation indices as summary indicators of the distance of an inefficient observation from an efficient allocation are proposed. The consistent development of the violation indices across the technical efficiency and allocative efficiency tests allows us to obtain comparative measures of the degrees of technical inefficiency and pure allocative inefficiency. Constrained optimization tests applicable to cases where the producer is restricted to optimizing with respect to a subset of goods are also proposed. The latter tests yield the revealed preference-type inequalities commonly used as tests for consistency of observed data with profit maximizing or cost minimizing behavior as limiting cases. Computer programs for implementing the different tests and sample results are listed in the appendix. In part II, an empirical comparison of nonparametric and parametric measures of technical progress for constant returns to scale technologies is performed using the Canadian input-output data for the period 1961-1980. The original data base was aggregated into four sectors and ten goods and the comparison was done for each sector. If we assume optimizing behavior on the part of the producers, we can reinterpret the violation indices yielded by the efficiency tests in part I as indicators of the shift in the production frontier. More precisely, the violation indices can be considered nonparametric chained indices of technical progress. The parametric measures of technical progress were obtained through econometric profit function estimation using the generalized McFadden flexible functional form with a quadratic spline model for technical progress proposed by Diewert and Wales (1989). Under the assumption of constant returns, the index of technical change is defined in terms of the unit scale profit function which gives the per unit return to the normalizing good. The empirical results show that the parametric estimates of technical change display a much smoother behavior which can be attributed to the incorporation of stochastic disturbance terms in the estimation procedure and, more interestingly, track the long term trend in the nonparametric estimates. Part III builds on the theory of minimum wages in international trade and is a theoretical essay in the tradition of analyzing the effects of factor market imperfections on resource allocation. The comparative static responses of the endogenous variables — output levels, employment levels of fixed-price factors with elastic supply and flexible prices of domestic resources — to marginal changes in the economy's exogenous variables — output prices, fixed factor prices and endowments of flexibly-priced domestic resources -— are examined. The effect of a change in a fixed factor price on other flexible factor prices can be decomposed Slutsky-like into substitution and scale effects. A symmetry condition between fixed factor prices and flexible factor prices is obtained which clarifies the concepts of "substitutability" and "complementarity" between these two kinds of factors. As an illustration, the model is applied to the case of a devaluation in a two-sector small open economy with rigid wages and capital as specific factors. The empirical implementation of the general model for the Canadian economy is left to more able econometricians but a starting point can be the sectoral analysis performed in Part II.

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