Does the Stochastic Specification Matter?

Konstantina Mari

Introduction

Underlying any statistical test of any hypothesis or any estimation of any model is some stochastic specification. It is fair to say that many economists generally pay scant attention to this, usually assuming normality somewhere. This chapter explores the implications of this, both for the hypothesis under study and the parameters being estimated.

The context in which we do this exploration is the estimation of the risk-aversion of decision-makers. This is crucial to most theories of decision-making under risk, and to many policy issues. There are several experimental methods of eliciting risk-aversion indices, the most prominent being Holt-Laury price lists (Holt and Laury 2002), pairwise choice questions (Hey and Orme 1994), the Becker-Degroot-Marschak mechanism (Becker et al 1964) and allocation problems (Loomes 1991). We concentrate here on the latter method. Wilcox (2009) has done a similar analysis using the method of pairwise choice (which can be considered to be a sort of unstructured Holt-Laury price list); he concludes that the stochastic specification may well be more important than the functional specifications. We do not have different functional specifications, so as to concentrate on the effect of the stochastic specification.

Like all methods of eliciting preferences, one can make a variety of stochastic assumptions, but these depend on the elicitation method. Here we use allocation problems. We describe these in Section 2. In Section 3 we describe what the DM ought to be doing. But in experiments there is noise in subjects’ behaviour. When we use experimental data to estimate their risk-aversion we need to take this noise into account. It is the description of this noise that is our stochastic specification. In Section 4 we discuss possible stochastic specifications. In order to compare between specifications we carry out extensive simulations – generating data under a variety of stochastic specifications and then estimating under them. We discuss our simulation and estimation methods in Section 5. Our results are in Section 6 and Section 7 concludes.

The paper

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