Estimation of Consumer Demand Functions When the Observed Prices Are the Same for All Sample Units

With the advent of the almost ideal demand system (AIDS) of Deaton and Muellbauer, the estimation of consumer demand functions revolves around specifications that use flexible functional forms of the indirect utility function. This dual approach has put on the backburner the traditional primal approach because the direct utility function exists only in a latent state. The lack of explicit, analytical invertibility of either system, however, is an indication that focusing exclusively on the dual side of the consumer problem is equivalent to disregard potentially important and independent information residing with the primal side. This paper suggests that efficient estimates (in the sense of using all the available information) of the demand functions require the joint estimation of all the primal and dual relations. The specification of this objective assumes that risk-neutral households maximize their expected utility subject to their expected budget constraint. This theoretical framework leads to a two-step procedure that produces consistent and efficient estimates of the model’s parameters. The generality of the approach proposed here can handle also the frequently encountered case when all the sample units face the same observed commodity prices. Finally, we present a general solution of the nonlinear errors-in-variables problem with a novel estimation procedure that avoids the pitfalls of the traditional approach.Consumer demand functions, primal, dual, nonlinear errors-in-variables, Demand and Price Analysis, Research Methods/ Statistical Methods, D0,

MELE: MAXIMUM ENTROPY LEUVEN ESTIMATORS

Multicollinearity hampers empirical econometrics. The remedies proposed to date suffer from pitfalls of their own. The ridge estimator is not generally accepted as a vital alternative to the ordinary least-squares (OLS) estimator because it depends upon unknown parameters. The generalized maximum entropy (GME) estimator of Golan, Judge and Miller depends upon subjective exogenous information that affects the estimated parameters in an unpredictable way. This paper presents novel maximum entropy estimators inspired by the theory of light that do not depend upon any additional information. Monte Carlo experiments show that they are not affected by any level of multicollinearity and dominate OLS uniformly. The Leuven estimators are consistent and asymptotically normal.multicollinearity, mean squared error, ordinary least squares, generalized maximum entropy, Research Methods/ Statistical Methods, C2,

DYNAMIC POSITIVE EQUILIBRIUM PROBLEM

The Dynamic Positive Equilibrium Problem (DPEP) is a methodology for dealing with time series about economic agents decisions, regardless of the amount of available information. The approach is articulated in three phases, as in the static counterpart Symmetric Positive Equilibrium Problem (SPEP), with the variant that it must be preceded by the estimation of the equation of motion which characterizes a dynamic model. Furthermore, the definition of marginal cost in the DPEP model is different from the same notion in the static SPEP. In this paper, the DPEP approach was applied to a panel data dealing with annual crops from California agriculture for a horizon of eight years. The dynamic character of the DPEP model is based upon then assumption of output price adaptive expectations that follows a Nerlove-type specification.Research Methods/ Statistical Methods,

MULTIPLE OPTIMAL SOLUTIONS IN QUADRATIC PROGRAMMING MODELS

The problem of determining whether quadratic programming models possess either unique or multiple optimal solutions is important for empirical analyses which use a mathematical programming framework. Policy recommendations which disregard multiple optimal solutions (where they exist) are potentially incorrect and less than efficient. This paper proposes a strategy and the associated algorithm for finding all optimal solutions to any positive semidefinite linear complementarity problem. One of the main results is that the set of complementary solutions is convex. Although not obvious, this proposition is analogous to the well-known result in linear programming which states that any convex combination of optimal solutions is itself optimal.Research Methods/ Statistical Methods,

AN ATEMPORAL MICROECONOMIC THEORY AND AN EMPIRICAL TEST OF PRICE-INDUCED TECHNICAL PROGRESS

An exhaustive comparative statics analysis of a general price taking cost-minimizing model of the firm operating under the influence of price-induced technical progress is carried out from a dual vista. The resulting refutable implications are observable and thus amenable to empirical verification, and take on the form of a symmetric and negative semidefinite matrix. Using data from individual cotton gins in Californias San Joaquin Valley, we empirically test the complete set of implications of the price-induced technical progress theory using both classical and Bayesian statistical procedures. We find that the data are fully consistent with the atemporal, costminimizing, price-induced microeconomic theory of technical progress.Research and Development/Tech Change/Emerging Technologies,

SENSITIVITY OF THE GME ESTIMATES TO SUPPORT BOUNDS

The claim has been made that the Generalized Maximum Entropy (GME) estimator of Golan, Judge and Miller is not sensitive to variations in the support bounds of either the parameters or the error terms. In this paper, we scrutinized this claim by means of Monte Carlo experiments and found that the parameter estimates are impacted in a substantial way by these changes. We also analyzed the famous data sample on the US manufacturing industry used by Cobb and Douglas in 1934 and found that the GME estimator is very sensitive to changes in support bounds. We conclude with a general result by Caputo and Paris according to which any support bound variation produces unexpected responses in the parameter estimates.Research Methods/ Statistical Methods,

Efficient Estimates of a Model of Production and Cost

In 1944, Marschak and Andrews published a seminal paper on how to obtain consistent estimates of a production technology. The original formulation of the econometric model regarded the joint estimation of the production function together with the first-order necessary conditions for profit-maximizing behavior. In the seventies, with the advent of duality theory, the preference seemed to have shifted to a dual approach. Recently, however, Mundlak resurrected the primal-versus-dual debate with a provocative paper titled “Production Function Estimation: Reviving the Primal.” In that paper, the author asserts that the dual estimator, unlike the primal approach, is not efficient because it fails to utilize all the available information. In this paper we argue that efficient estimates of the production technology can be obtained only by jointly estimating all the relevant primal and dual relations. Thus, the primal approach of Mundlak and the dual approach of McElroy become nested special cases of our general specification. The theory of the price-taking cost-minimizing, risk-neutral firm is based upon the expectation of prices and quantities as the relevant information used by the entrepreneur in making her decisions. The econometrician intervenes later on and collects information about those quantities and prices. In so doing, measurement errors creep into the econometric specification. A two-phase procedure is suggested to implement the primal-dual approach. A Monte Carlo analysis indicates that our primal-dual approach produces estimates that exhibit a smaller variance of the estimates than those obtained from either the traditional primal or the dual specification separately implemented. A bootstrapping approach is used to compute the standard errors of the model’s estimates.Primal, Dual, Cobb-Douglas, Nonlinear errors-in-variables, Productivity Analysis, Research Methods/ Statistical Methods, D0, C3,

EFFICIENT ESTIMATES OF A MODEL OF PRODUCTION AND COST

In 1944, Marschak and Andrews published a seminal paper on how to obtain consistent estimates of a production technology. The original formulation of the econometric model regarded the joint estimation of the production function together with the first-order necessary conditions for profit-maximizing behavior. In the seventies, with the advent of econometric duality, the preference seemed to have shifted to a dual approach. Recently, however, Mundlak resurrected the primal-versus-dual debate with a provocative paper titled "Production Function Estimation: Reviving the Primal." In that paper, the author asserts that the dual estimator, unlike the primal approach, is not efficient because it fails to utilize all the available information. In this paper we demonstrate that efficient estimates of the production technology can be obtained only by jointly estimating all the relevant primal and dual relations. Thus, the primal approach of Mundlak and the dual approach of McElroy become nested special cases of the general specification. In the process of putting to rest the primal-versus-dual debate, we solve also the nonlinear errors-in-variables problem when all the variables are measured with error.Research Methods/ Statistical Methods,

COMPARATIVE STATICS OF MONEY-GOODS SPECIFICATIONS OF THE UTILITY FUNCTION

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Satos (1984) treatment of this problem.Research Methods/ Statistical Methods,

A Dual Approach to Estimation With Constant Prices

In a recent paper, Mundlak assumes that the price-taking, risk-neutral and profit-maximizing entrepreneur makes his decisions on the basis of a planning model that maximizes expected profit using expected prices. In the same paper, the author asserts that when there is no sample price variation across competitive firms, it is impossible to estimate the supply and factor demand functions from cross-section data using a dual approach. In a famous paper, titled “To Dual or not to Dual,” Pope asserted a similar opinion. This paper shows that, using Mundlak’s assumption about planning decisions based upon expected profit, it is possible to use a dual estimator to estimate supply and factor demand functions. This objective is achieved by using Mundlak’s assumption about the individuality of the firm’s expectation process. A two-phase procedure is suggested to obtain consistent estimates of the expected quantities and prices which are then used, in phase II, in a nonlinear seemingly unrelated equations problem to obtain efficient estimates of the technological parameters.Constant prices, Dual approach, Cobb-Douglas, Nonlinear errors-in-variables, Demand and Price Analysis, Research Methods/ Statistical Methods, D0, C3,