The theory of mixed demand functions

The properties of Samuelson's mixed demand functions, which express demand as a function of a mixed set of prices and quantities, are derived. By analyzing compensated (or substitution) effects and uncompensated effects, the relationships between mixed demand functions and conditional (or rationed) demands are examined. This provides insights on the behavioral implications of consumer theory for alternative demand specifications.     

Optimal research for cournot oligopolists

An oligopolistic industry faces uncertain demand. Firms can conduct research prior to production, obtaining private data that is informative of the unknown parameters of demand. Firm strategies thus consist of a level of research and a subsequent production strategy based on their research findings. We characterize the Bayes equilibrium of such a model when demand is linear, with unknown intercept, and the information structure has linear conditional expectations. We compare the solution to an efficiency standard, finding inefficiencies even in the competitive limit.     

Equilibrium prices in the Bertrand and Cournot oligopolies

The equilibrium prices for the Bertrand and Cournot oligopolies with product differentiation are compared. If all firms have linear demand and cost functions, and if, in addition, the Jacobian matrix of the demand functions has a dominant negative diagonal, the Cournot equilibrium prices are not lower than the Bertrand ones. The general condition for the comparison of the Bertrand and Cournot equilibrium prices can be derived even if the nonlinearity is involved in the cost and/or demand functions.     

Semiparametric Estimation of Simultaneous-Equation Microeconometric Models with Index Restrictions

This article introduces semiparametric methods for the estimation of simultaneous-equation microeconometric models with index restrictions. The methods are motivated by a semiparametric minimum-distance procedure, which unifies the estimation of both regression-type and linear or nonlinear simultaneous-equation models without emphasis on the construction of instrumental variables. Single-equation and systematic estimation methods and optimal weighting procedures are considered. The estimators are √ n -consistent and asymptotically normal. For the estimation of nonparametric regression and some sample selection models where the variances of disturbances are functions of the same indices, the optimal weighted estimator attains Chamberlain's efficient bound for models with conditional moment restrictions. The weighted estimator is shown to be optimal within a class of semiparametric instrumental variables estimators.
JEL classification numbers: C14, C24, C34.     

Conditional and unconditional food demand elasticities in a dynamic multistage demand system

This paper estimates conditional and unconditional demand elasticities in a three stage analysis of consumer demand for food and non-food items in Greece. A dynamic version of the AIDS model is specified and estimated, and full system misspecification tests applied. Correction formulas for price and expenditure elasticities are used to calculate unconditional elasticities from conditional demand sub-systems. All food items rank as price inelastic. Deviations between the calculated conditional and unconditional price and expenditure elasticities are found to be significant, demonstrating the importance of correcting conditional elasticities before they can be used for policy purposes or welfare analyses.     

Outline of forecast theory using generalized cost functions

The cost functions used to form forecasts in practice may be quite different than the squared costs that is often assumed in forecast theory. The impact on evaluation procedures is determined and simple properties for the derivate of the cost function of the errors are found to provide simple tests of optimality. For a very limited class of situations are forecasts based on conditional means optimal, generally, the econometricians needs to provide the whole conditional predicted distribution. Implications for multi-step forecasts and the combination of forecasts are briefly considered.     

The existence of fully rational expectations approximate equilibria with noisy price observations

Nonrevealing fully rational expectations approximate equilibria exist in microeconomic pure exchange economies in which uninformed agents have suitably dispersed noisy price observations. Such traders maximize a state-dependent expected utility conditional on the price vector they observe, the distributions of noisy price observations, and the correct equilibrium relationship between states of the world and prices. In equilibrium, aggregate excess demand is small with high probability in every state of the world (and its expectation is also small); this magnitude diminishes as the noisy price observations become more accurate. Equilibria are obtained by applying a fixed point argument to state-dependent excess demand functions which are smooth because of the noisy price observations.     

Conditional price volatility,speculation, and excessive speculation in commodity markets: sheep or shepherd behaviour?

The present study aims to investigate the dynamics of primary commodity spot prices and the role of speculation for the period 1995–2012. Using a linear and nonlinear Granger causality analysis, the relationship between speculation and GARCH conditional price volatility on the one side, and the linkage between excessive speculation and GARCH conditional price volatility on the other side, is carefully examined with the scope to establish whether volatility drives speculation or speculation drives price volatility, or whether there are no linkages between the two variables. The results show that excessive speculation leads conditional price volatility, and that bilateral relationships often exist between price volatility and speculation. In addition, the lead-lag relationships are not found for the entire sample period, but rather when small sub-periods are taken into account. It turns out, in fact, that excessive speculation has driven price volatility for maize, rice, soybeans, and wheat in particular time frames, but the relationships are not always overlapping for all considered commodities. Generally, the results under linear causality tests are in agreement with those obtained under nonlinear counterparts.     

Conditional density forecast of China’s energy demand via QRNN model

We propose a new method for conditional density forecast of China’s energy demand through quantile regression neural network (QRNN). This method has at least two advantages. First, it is flexible to explore the true nonlinearity in the energy demand system via neural network structure. Second, it is able to describe the whole conditional distribution of energy demand via quantile regression. In the empirical study on China’s energy demand, QRNN outperforms several classical methods in terms of forecast accuracy both in-sample and out-of-sample. Considering China’s economic and social environment, we set a scenario for predictors and forecast the conditional density of China’s energy demand from 2015 to 2020. The empirical results show that the conditional density curve moves to right and its dispersion increases over time, which indicates that the energy demand in China will keep growing with an average annual rate of 9.672% and its uncertainty is enlarged with 42.210%.     

Habit formation and long-run utility functions

This paper extends the work on habit formation of Pollak [Habit formation and dynamic demand functions. J. Polit. Econ. (1970)] and provides a critical counterexample to a conjecture of von Weizsäcker [Notes on endogenous changes of tastes, J. Econ. Theory (1971)] concerning the existence of a “long-run utility function.“ A linear specification of habit formation is applied to a general system of demand functions with linear Engel curves. It is shown that there exists a utility function which rationalizes the long-run demand functions if and only if they are the steady-state solution to a system of short-run demand functions generated by an additive utility function.     

Currency demand,new technology,and the adoption of electronic money: Micro evidence from Japan

We estimate currency demand functions conditional on electronic money adoption with household-level survey data from Japan under an Instrumental Quantile Regression framework. Contrary to theoretical predictions, our results suggest that users of electronic money hold more currency than non-users.     

A linear demand system within a seemingly unrelated time series equations framework

A seemingly unrelated time series equations framework for the linear almost ideal (AID) demand system is considered. The framework is applied to a consumer demand system covering nine non-durable commodities. Within a specification where the static linear AID system is augmented by latent variables representing stochastic trends and seasonality, demand homogeneity is tested; both in each equation and in the system as a whole. Income and own-price elasticities are calculated under homogeneity restrictions. Although the homogeneous model is formally rejected by statistical tests, it performs well with respect to interpretability, parameter stability and forecasting.     

A unified approach to incorporating demographic or other effects into demand systems

"A general method of introducing demographic effects into any demand system, using modifying functions, is described which permits complicated interactions of demographic variables with prices and expeditures. Theorems give properties the modifying functions must have to ensure integrability of the resulting system. Demand equations of the new system are given explicitly as functions of the original demand equations and the modifying functions. The procedure is interpreted as altering a household's technology, and is shown to encompass adult equivalent scales and related methods. Examples of modifying functions are derived and applications of the technique to uses other than demographic variation are considered."     

Limited knowledge of demand and oligopoly equilibria

In a standard model of oligopoly with differentiated products, the existence of an equilibrium at which the first-order conditions for profit maximisation are simultaneously satisfied for all firms is proved and this is done without imposing any restrictions on the demand functions. This is an equilibrium in the following sense: although some firms may not necessarily be maximising their profits, nevertheless if each firm's knowledge of demand is limited to the linear approximation of its own demand curve, then it will believe that it is indeed maximising its profits.     

Oligopoly Information Exchange when Non-negative Price and Output Constraints may Bind

The oligopoly information exchange literature has consistently employed linear demand functions. This paper explores whether earlier results are sensitive to the assumption of linear demand. Non-linearity arises naturally from the condition that prices and outputs be non-negative. We show standard results on information sharing can be reversed when there is the chance that non-negativity constraints bind: in a homogeneous-goods Cournot duopoly with constant marginal costs, information sharing can be profitable and it can reduce social welfare.     

The pricing of time-varying beta

We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.     

The allocative efficiency of government expenditure: Some comparative tests

This paper examines whether observed government expenditures are consistent with optimising behaviour in Australia, Portugal, Sweden and the U.K. Expenditures are treated as intermediate goods producing desired outputs (e.g. health, education, security) conditional on demographic variables. These outputs are arguments in an objective function, optimised subject to a budget constraint. Optimisation then implies testable homogeneity, symmetry and negativity restrictions on the derived demand functions. These were estimated, using the Deaton-Muellbauer AIDS system, on time series data for four categories of expenditure in each country and the restrictions tested, with both homogeneity and symmetry being accepted for Sweden.     

On the rate of convergence of oligopoly equilibria in large markets: An example

In this note we explore the rate of convergence of Cournot-Nash equilibria with free entry and those with an entry deterring monopolist in a replicated market where the market demand functions is linear and firms face linear cost curves.     

Estimation of demand and supply functions from univariate sample with known separation

It is shown that the joint unconditional density function of demand and supply is a computable function of parameters of the conditional density function of the observed quantity. Propositions of formulating unconditional and conditional disequilibrium measures are suggested.