A New Example of a Closed Form Mean-Variance Representation

In most finance papers and textbooks mean-variance preferences are usually introduced and motivated as a special case of expected utility theory. In general, the two sufficient conditions to allow this are either quadratic preferences with an arbitrary distribution of stochastic assets, or arbitrary preferences with Normally distributed assets. In the first case, the specific functional form of mean-variance preferences follows naturally. In the second case, the only specific functional form usually provided is the case of negative exponential preferences. In this note, the specific functional form for mean-variance preferences is derived for the much more realistic example of lognormally distributed assets, and constant relative risk aversion (CRRA) preferences.Mean-variance preferences; expected utility; lognormal assets; risk aversion

The Econometric Specification of Input Demand Systems Implied by Cost Function Representations

In the case of input demand systems based on specification of technology by a Translog cost function, it is common to estimate either a system of share equations alone, or to supplement them by the cost function. By adding up, one of the share equations is excluded. In this paper it is argued that a system of n-1 share equations is essentially incomplete, whereas if the n-1 share equations are supplemented by the cost function the implied error structure is inadmissible. Similarly, if the technology is specified by a normalized quadratic cost function, it is common to estimate either a system of n-1 demand equations alone, or to supplement them by the cost function. In both cases, the implied error structure is again inadmissible.Cost Function; Input demands; Share equations; Translog; Normalized Quadratic; Error specification.

Regular and Estimable Inverse Demand Systems: A Distance Function Approach

To be useful for realistic policy simulation in an environment of rapid structural change, inverse demand systems must remain regular over substantial variations in quantities. The distance function is a convenient vehicle for generating such systems. While it directly yields Hicksian inverse demand functions, those functions will not usually have an explicit representation in terms of the observable variables. Note however that this problem need not hinder estimation and could be solved by using the numerical inversion estimation approach. This paper develops the formal theory for using distance functions in this context, and demonstrates the operational feasibility of the method.Inverse Demands; Distance Functions; Numerical Inversion Estimation Method; Separability.

The Benefit Function Approach to Modeling Price-Dependent Demand Systems: An Application of Duality Theory

In this article we advocate more extensive use of the benefit function in specifying price-dependent or inverse demand models. In particular, we demonstrate how duality theory may be used to establish the inter-relationships between the Marshallian (or Hicksian) inverse demands and Luenberger's adjusted price functions, allowing estimable inverse demands to be derived directly from a benefit function. We also make use of a numerical inversion estimation method to rectify the "unobservability of utility problem" encountered in the empirical analysis of these inverse demands. To illustrate the usefulness of the proposed methods, we estimate two systems of inverse demands for Japanese quarterly fish consumption. Results generally indicate that the proposed methods are promising and operationally feasible so that we have opened up a wider range of empirical inverse demand specifications that can be subjected to tight theoretical restrictions.Benefit Functions; Duality Theory; Numerical Inversion Estimation Method

A Regular Demand System with Commodity-Specific Demographic Effects

Regular consumer demand systems almost invariably employ specifications that involve common functional forms in all equations. When applications involve crosssectional data it is often the case that demographic effects are important. However it is plausible that demographic effects are commodity-specific. In this case, there may be a loss of efficiency if a common functional form across commodities is imposed artificially by entering redundant explanators in demand equations for which specific demographic influences are unwarranted. This paper explores an approach to specifying a complete system of demand equations which is fully regular but which nevertheless allows for commodity-specific variation in the functional form of the demand equations.Consumer Economics: Theory, Consumer Economics: Empirical Analysis, Demographic Economics

Multi-Output Broadacre Agricultural Production: Estimating A Cost Function Using Quasi-Micro Farm Level Data From Australia

Existing econometric models for Australian broadacre agricultural production are few and have become dated. This paper estimates a multi-product restricted cost function using a unique quasi-micro farm level dataset from the Australian Agricultural and Grazing Industries Survey. Both the transcendental logarithmic and normalized quadratic functional forms are employed. Heteroskedasticity caused by the particular nature of the quasi-micro data is also assessed and accommodated. Allen partial elasticities of input substitution and own-and cross-price input demand elasticities are computed. The estimated demands for most production factors are inelastic to prices. Hired labour is responsive to own price and cropping input prices.Production Economics, Research Methods/ Statistical Methods,

Nonsimultaneity and Futures Option Pricing: Simulation and Empirical Evidence

Empirical tests of option pricing models are joint tests of the 'correctness' of the model, the efficiency of the market and the simultaneity of price observations. Some degree of nonsimultaeity can be expected in all but the most liquid markets and is therefore evident in many non-US markets. Simulation results indicate that nonsimultaneity is potentially a significant problem in empirical tests of futures option pricing models. Empirical results using Australian data show that a five-minute window for matching transactions does not remove the nonsimultaneity bias for near-the-money and out-of-the money options. A more accurate matching may therefore be required. The nonsimultaneity bias is effectively removed if a five-minute window is employed for in-the-money options.Nonsimultaneity; Futures option; Mispricing

ON THE ESTIMATION OF DEMAND SYSTEMS WITH LARGE NUMBER OF GOODS: AN APPLICATION TO SOUTH AFRICA HOUSEHOLD FOOD DEMAND

The estimation of large demand systems to investigate the patterns of consumption of households is notoriously difficult. This study develops a modified Almost Ideal Demand System model based on a flexible two-stage budgeting demand modelling framework to examine the effect of estimation procedures (Bottom-up and Top-down) on South African household food consumption parameters. Household food consumption was divided into seven broad food groups: meat and fish; grains; dairy products; fruits; vegetables; other foods. The demand systems were estimated using data from the 1993 South Africa Integrated Household Survey (SIHS) conducted by the South African Labour and Development Research Unit (SALDRU). Empirical results indicate that the Top-down approach is more suited for estimation of South African household food demand. Results indicate that own-price do play an important role in influencing household food consumption. Results also indicate no presence of gross substitution between and within food groups. Expenditure elasticity estimates indicate that meat and fish, dairy products and fruits are luxury products, while grains, vegetables and other foods are necessities in South African household diet.Consumer/Household Economics, Research Methods/ Statistical Methods,

Cobb-Douglas Utility - Eventually!

Consider the following two opinions, both of which can be found in the literature of consumer demand systems: (a) As the real income of a consumer becomes indefinitely large, re-mixing the consumption bundle becomes irrelevant: having chosen the ultimately satisfying budget shares at any given set of relative prices, the superlatively wealthy continue to allocate additional income in the same proportions. With very large and increasing per capita income, ultimately the utility function becomes indistinguishable from Cobb-Douglas. (b) Consumer demand systems in which the income elasticities monotonically approach one (from above, in the case of luxuries; from below, in the case of necessities) are unsatisfactory both theoretically and empirically. For instance, a necessity with a low (consumer demand system; applied general equilibrium; separability; implicitly directly additive preferences; effectively global regularity; Cobb-Douglas, calibration; AIDADS.