Sums and Products of Indirect Utility Functions

There are relatively few known demand systems that are theoretically satisfactory and practically implementable. This paper considers the possibility of deriving more complex demand systems from simpler known ones by considering sums and products of the component indirect utility functions, an approach that does not seem to have been exploited previously in the literature. While not all sums and products of valid utility functions need yield new valid utility functions, it is possible to usefully extend the range of available utility functions. Some of the demand systems that result are interesting and potentially useful - the simpler (in a parameter parsimony sense) for applied general equilibrium studies and for theoretical explication, while more complex systems have potential for the analysis of real world consumption data.

The Generalised Extreme Value Distribution as Utility Function

The idea that probability distribution functions could provide appropriate mathematical forms for utility functions representing risk aversion is of respectable antiquity. But the relatively few examples that have appeared in the economics literature have displayed quite restrictive risk aversion properties. This paper examines the potential of the generalised extreme value (GEV) distribution as utility function, showing it possesses considerable flexibility as regards risk aversion properties, even in its single parameter form. The paper concludes that the GEV utility function is worth considering for applications in cases where parametric parsimony matters.

The Generalised Extreme Value Distribution as Utility Function

The idea that probability distribution functions could provide appropriate mathematical forms for utility functions representing risk aversion is of respectable antiquity. But the relatively few examples that have appeared in the economics literature have displayed quite restrictive risk aversion properties. This paper examines the potential of the generalised extreme value (GEV) distribution as utility function, showing it possesses considerable flexibility as regards risk aversion properties, even in its single parameter form. The paper concludes that the GEV utility function is worth considering for applications in cases where parametric parsimony matters.

Generalised Translation of Indirect Utility Functions

This paper considers the derivation of new demand systems from existing ones through replacing an indirect utility function ) , ( y U p by } ) / ( , { j y p y y U j j â ã Ó . p , where p is a vector of prices and y is income. This is a generalisation of Gorman translation ) , ( j j p y U ã Ó . p and will be shown to be effective in terms of producing new demand systems with both good regularity and flexibility properties.Translation,indirect utility functions,demand equations

When Do Probit Residuals Sum to Zero?

Probit residuals need not sum to zero in general. However, if explanatory variables are qualitative the sum can be shown to be zero for many models. Indeed this remains true for binary dependent variable models other than Probit and Logit. Even if some explanatory variables are quantitative, residuals can sum to almost zero more often than might at first seem plausible.

A New System of Consumer Demand Equations

This paper commences from a new indirect utility function and derives the corresponding system of equations, relating commodity demands to prices and income, that satisfies the constraints imposed by utility maximisation (aggregation, homogeneity, Slutsky symmetry and negativity). As the famous linear expenditure system (LES) is a special case of this new system, it is named the generalised Stone-Geary system (GSGS) and it incorporates a generalisation of the ‘subsistance’ income concept to one of ‘committed’ income. However, the GSGS is not subject to the well known limitations of the LES and it can model a reasonably representative range of consumer behaviour. It is also relatively parsimonious in parameters involving just 3n - 1, where n is the number of commodities. The new system has greater ranges of theoretical validity than various systems derived from ‘flexible’ functional forms. As with the LES, simple conditions on the parameters guarantee the validity of the system for all variable values except, perhaps, at low incomes.

Generalised Means of Simple Utility Functions with Risk Aversion

The paper examines the properties of a generalised mean of simple utilities each displaying risk aversion, that is, with first derivative positive and second derivative negative. It proves the mean is itself a valid utility function with the appropriate signs for derivatives and investigates risk aversion properties. It shows that simple component utilities, each of which may have quite restricted risk aversion properties, can be parsimoniously combined through the generalised mean formula to give a much more versatile utility function.

Efficient Probit Estimation with Partially Missing Covariates

A common approach to dealing with missing data is to estimate the model on the common subset of data, by necessity throwing away potentially useful data. We derive a new probit type estimator for models with missing covariate data where the dependent variable is binary. For the benchmark case of conditional multinormality we show that our estimator is efficient and provide exact formulae for its asymptotic variance. Simulation results show that our estimator outperforms popular alternatives and is robust to departures from the benchmark case. We illustrate our estimator by examining the portfolio allocation decision of Italian households.missing data, probit model, portfolio allocation, risk aversion

GENERATING GLOBALLY REGULAR INDIRECT UTILITY FUNCTIONS

Despite their scarcity in the literature, an abundance of globally regular indirect utility functions, involving as many parameters as desired, exists. They are easily constructed as a function of simple homothetic component utilities.Global regularity,indirect utility functions,

An Efficient Estimator for Dealing with Missing Data on Explanatory Variables in a Probit Choice Model

A common approach to dealing with missing data in econometrics is to estimate the model on the common subset of data, by necessity throwing away potentially useful data. In this paper we consider a particular pattern of missing data on explanatory variables that often occurs in practice and develop a new efficient estimator for models where the dependent variable is binary. We derive exact formulae for the estimator and its asymptotic variance. Simulation results show that our estimator performs well when compared to popular alternatives, such as complete case analysis and multiple imputation. We then use our estimator to examine the portfolio allocation decision of Italian households using the Survey of Household Income and Wealth carried out by the Bank of ItalyMissing Data, Probit Model, Portfolio Allocation, Risk Aversion