Alan D. Woodland

Estimation of consumer demand systems with binding non-negativity constraints☆

Although the economic and statistical theory underlying the estimation of systems of demand functions is well developed, very little attention has been paid to the problems which arise when the sample contains a significant proportion of observations in which expenditure on one or more goods is zero. For such a sample the econometric model should allow for zero expenditures to occur with positive probability. However, the econometric model used in most studies assumes that expenditures (or shares) follow a joint normal distribution and this does not allow for a positive probability of zero expenditures.’ Standard estimation methods for this model, such as Zellner’s two-stage estimator for seemingly unrelated regressions and the maximum likelihood estimator, do not take special account of zero expenditures, and consequently yield inconsistent estimates of the parameters. Indeed even if every observation containing zero expenditures on one or more goods was excluded for purposes of estimation, these standard estimators would be biased and inconsistent.’ Moreover, excluding these observations might significantly reduce the sample size. Regardless of whether or not the complete sample is used, the bias and inconsistency occur because the random disturbances have expectations which are not zero and which depend upon the exogenous variables.

Estimation of the Allocation of Time for Work, Leisure, and Housework

Previous attempts to estimate labor supply functions based upon the constrained maximization of a utility function with leisure and income as arguments have assumed that all time not spent at work on the job is leisure time. In this paper we formulate a model of a household in which time is allocated between work on the job, leisure, and housework, where leisure is defined to be net of time spent on housework. The model is estimated under two alternative stochastic specifications and the results compared to those obtained (i) assuming that housework time is exogenous and (ii) assuming that housework time is part of leisure time.

Stochastic specification and the estimation of share equations

Abstract The standard stochastic specification for a system of share equations is obtained by assuming that the shares have a joint normal distribution with means depending upon exogenous variables and a constant covariance matrix. This specification ignores the requirement that shares be between zero and unity by giving positive probability to shares outside this range. An alternative stochastic specification involving the Dirichlet distribution, which automatically limits shares to the unit simplex, is suggested. A comparison of results obtained from the two specifications is made using sampling experiments and data from three different empirical studies. The sampling experiments and empirical applications show that the results are generally quite close, thus providing some justification for the continued use of the normal distribution specification in the estimation of share equations.

Productivity- and Pareto-Improving Changes in Taxes and Tariffs

The paper investigates the problem of tariff reform in a small open multi-household economy that only has tariffs and domestic commodity taxes as policy instruments. The concept of a productivity improvement in tariffs and taxes is introduced and conditions for its existence are established. We prove that a Pareto-improving change in tariffs and domestic taxes exists if a productivity-improving change in tariffs exists and if the Weymark condition on the matrix of household demands holds. Conditions are established for particular tariff reforms, such as proportional reductions and reductions of extreme rates, to yield Pareto improvements in welfare.

Substitution of Structures, Equipment and Labor in Canadian Production

THE PURPOSE OF THIS PAPER is to present maximum-likelihood estimates for systems of factor demand functions for each of tenl major industries in Canada, and to test formally whether factor demiands are responsive to changes in the service prices of factors of production. The factors of production are defined to be Structures, Equipment, and Labor and the estimation is based upon annual data for the period 1946-1969. The industries correspond to the industrial divisions in the 1960 Standard Industrial Classification and comprise Agriculture, Forestry, Fishing and Trapping, Mining, Manufacturing, Constructioll, Transportation Communication and Utilities, Trade, Finance, and Services. It is important that economists have knowledge of the structure of the produLction sector since this structure determines in a significant way the effects throughout the economy of changes in policy and other parameters. An example of this dependence is provided by the effect of a change in the tariff structure uponl resource allocation and the distributioll of nationial iIncomlle. As anotlher example we note that the effect upon the employment of labor of a change in the taxation of capital earninigs depends upon the ability of producers to suLbstitute olle factor for another. Furthermore, if changes in the taxation laws differelntiate between Structures and Equipment then an analysis of the effects of such taxation changes must be based uponl appropriately disaggregated production functions if the differential effects are to be satisfactorily identified. Leontief [11] initiated studies on the structuLre of production based upon the idea of fixed coefficients of production. Since our primary interest is in the possibility of factor substitution we postulate a production function due to Diewert [5] which permits factor substitution but which reduces to the Leontief production function as a special case. We formally test whether the Leontief production function involving fixed coefficients is a valid representation of the technology or whether factor substitution is possible. In addition, we present point estimates of the Hicks-Allen elasticities of substitution between the various factors as measures of the degree of substitution. The present study differs from previous Canadian studies of productionl and factor demand functions in three respects. First, the present study is extensive in scope in that it involves all the major industrial divisions whereas pCevious

On the multilateral transfer problem: Existence of Pareto improving international transfers

Abstract This paper investigates the question of whether it is possible to create a strict Pareto improvement in welfare by a multilateral transfer of income between nations. We show that a strict Pareto improving multilateral transfer exist if and only if a generalized normality condition is violated. For a violation of this condition it is necessary that tariff distortions exist. Conditions for the non-existence of a Pareto improving transfer are also established. For example, a Pareto improving transfer does not exist if all commodities are normal and are net substitutes from a world point of view.

Direct and Indirect Trade Utility Functions

In this paper the concept of an indirect trade utility function is introduced, its properties are developed, and its application to the theory of international trade and to the econometric estimation of export supply and import demand functions are discussed. The indirect trade utility function expresses the maximum level of utility a trading nation can attain, assuming the existence of a direct community utility function, as a function of a vector of prices for commodities, a vector of factor endowments and the balance of trade. As such it provides a summary of all the consumption and production decisions within a competitive economy. In Section 2 the indirect trade utility function is defined in terms of the ordinary indirect utility function and the gross national product (or variable profit) function. An extension of Roys Identity is developed, allowing the easy generation of net export functions by differentiation. The fact that the derivatives of the indirect trade utility function with respect to the prices of commodities are proportional to the excess supply or net export functions implies that indirect utility is stationary at a closed equilibrium. It is then proved that the set of price vectors which minimize the indirect trade utility function coincides with the set of closed equilibrium price vectors. Section 3 specifies the properties of the indirect trade utility function implied by the model and then illustrates various applications in the theory of international trade. These include the welfare effects of divergence of prices from autarky levels and the characterization of optimal tariff structures. Section 4 briefly considers the extent to which the results of Section 2 can be extended to the case where there are many consumers. In Section 5 the relationship between the indirect trade utility function and the direct trade utility function of Meade, and between the latter and the direct utility function and the production possibility set are outlined. Section 6 is devoted to establishing rigorously the formal relationships between all these functions under quite general conditions. The results of this section serve to widen the application of duality theory, as surveyed by Diewert (1974), (1978b) for example, to the area of international trade theory. Some of the results on the direct trade utility function have previously been developed by Chipman (1970) in unpublished notes, but he did not consider the indirect trade utility function. In Section 7 the usefulness of the indirect trade utility function in generating functional forms for export and import demand functions and factor price functions suitable for the purposes of econometric estimation using data on prices, net exports and factor endowments is discussed. Section 8 concludes the paper with an indication of how the model may be reinterpreted to accommodate nontraded goods and variable factor supplies. While the discussion is focussed on a national economy trading with other nations in the world market, it should be clear that the model applies equally well to the individual consumer who undertakes marketable production. Examples include the self-employed businessman or farmer. The indirect trade utility function then indicates the maximum utility attainable given the prices of the commodities (marketable products and purchasable

On testing weak separability

Abstract A new framework for testing for the existence of a consistent aggregator for a subset of inputs in a production function is developed in terms of the variable profit function. In contrast to the Berndt–Christensen framework, in which the parametric restrictions required to attain weak separability also impose unwanted restrictions on the form of the aggregator, the aggregator function has a flexible functional form. Consequently this procedure should permit a less restrictive test of separability or aggregation. Application of the procedure to the data for U.S. manufacturing assuming a production function involving two labour inputs (blue- and white-collar workers) and two capital inputs (structures and equipment) leads to the conclusion that there does not exist a consistent aggregator for labor whereas there is some mild support for the existence of a consistent aggregator for capital.

The relationship between factor endowments and commodity trade

Abstract The paper establishes general propositions concerning the relationship between a nations factor endowments and its pattern of commodity trade in a multi-factor, multi-product context. Inequality relationships between endowments and autarky prices, autarky and free trade prices, and between autarky prices and free trade net exports are established using a general model of trade. Attention is then restricted to a multi-product, multi-factor version of the Heckscher-Ohlin-Samuelson model of trade. From an initial autarky equilibrium a comparative statics analysis yields the effect on net exports of a change in one nations endowment. A bilinear inequality between the changes in endowments and net exports is established. It is also shown that if a good were to be exported (imported) when endowments changed and world prices were held fixed, then it will continue to be exported (imported) when world prices have adjusted to re-establish free trade equilibrium.

Estimation of Australian Wool and Lamb Production Technologies under Uncertainty: An Error-Components Approach

A model of producer behavior, which explicitly accounts for both output price and production uncertainty, is formulated and estimated. If the production technology is multiplicatively separable in its deterministic and stochastic components, then the expected utility maximization problem implies cost minimization for planned or expected output. Consequently, our empirical model of three lamb- and wool-producing sectors in Australia involves the estimation of a system of input cost share and cost equations whose disturbances have an error-components structure. The empirical results are evaluated in terms of input demand elasticities, and estimates of the stochastic components of production are presented.