Investment in information acquisition

This paper presents a simple model in which a community must decide on the amount of real investment and investment in information so as to maximise the expected utility of consumption over two periods. It is shown that under conditions involving the product of the elasticity of the marginal utility of consumption and the elasticity of the production function that optimal real investment is either a monotone function of the information or is independent of it. In the former case information is of value and it is optimal to invest a positive amount in information acquisition. In the latter case information has no value and society devotes no resources to information acquisition.     

An Empirical Model of Advertising Dynamics

This paper develops a model of dynamic advertising competition, and applies it to the problem of optimal advertising scheduling through time. In many industries we observe advertising “pulsing”, whereby firms systematically switch advertising on and off at a high-frequency. Hence, we observe periods of zero and non-zero advertising, as opposed to a steady level of positive advertising. Previous research has rationalized pulsing through two features of the sale response function: an S-shaped response to advertising, and long-run effects of current advertising on demand. Despite considerable evidence for advertising carry-over, existing evidence for non-convexities in the shape of the sales-response to advertising has been limited and, often, mixed. We show how both features can be included in a discrete choice based demand system and estimated using a simple partial maximum likelihood estimator. The demand estimates are then taken to the supply side, where we simulate the outcome of a dynamic game using the Markov perfect equilibrium (MPE) concept. Our objective is not to test for the specific game generating observed advertising levels. Rather, we wish to verify whether the use of pulsing (on and off) can be justified as an equilibrium advertising practice. We solve for the equilibrium using numerical dynamic programming methods. The flexibility provided by the numerical solution method allows us to improve on the existing literature, which typically considers only two competitors, and places strong restrictions on the demand models for which the supply side policies can be obtained. We estimate the demand model using data from the Frozen Entree product category. We find evidence for a threshold effect, which is qualitatively similar to the aforementioned S-shaped advertising response. We also show that the threshold is robust to functional form assumptions for the marginal impact of advertising on demand. Our estimates, which are obtained without imposing any supply side restrictions, imply that firms should indeed pulse in equilibrium. Predicted advertising in the MPE is higher, on average, than observed advertising. On average, the optimal advertising policies yield a moderate profit improvement over the profits under observed advertising.JEL Classification: L11, L66, M30 M37 R12     

Labor market dynamics when effort depends on wage growth comparisons

We present an efficiency wage model in which workers' disutility of effort depends on the level and on the growth rate of their wage relative to an alternative wage. Using data for four countries (US, UK, FR, GY), the implications of the model are examined and are found to be in accordance with the information in the non-stationary data. The restrictions implied by the model dynamics are not rejected by the data and the structural parameters are found to be constant through time. One interesting result is that the workers' disutility of effort depends less on relative wages growth and more on relative wage levels in the US than in the three European countries analyzed. First version received: September 1998 / Final version accepted: November 1999     

Optimal investment with correlated stochastic volatility factors

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the situation with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. Our proposed approximation requires to solve numerically two linear equations in lower dimension instead of a fully nonlinear HJB equation. A rigorous accuracy result is derived by constructing sub- and super-solutions so that their difference is at the desired order of accuracy. We illustrate our result with a particular model for which we have explicit formulas for the approximation. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.