Recovering Risky Technologies Using the Almost Ideal Demand System: An Application to U.S. Banking Mutual Funds

Abstract

Using modern duality theory to recover technologies from data can be complicated by the risk characteristics of production. In many industries, risk influences cost and revenue and can create the potential for costly episodes of financial distress. When risk is an important consideration in production, the standard cost and profit functions may not adequately describe the firm's technology and choice of production plan. In general, standard models fail to account for risk and its endogeneity. We distinguish between exogenous risk, which varies over the firm's choice sets, and endogenous risk, which is chosen by the firm in conjunction with its production decision. We show that, when risk matters in production decisions, it is important to account for risk's endogeneity.

For example, better risk diversification that results, e.g., from an increase in scale, improves the reward to risk-taking and may under certain conditions induce the firm to take on more risk to increase the firm's value. A choice of higher risk at a larger scale could add to costs and mask scale economies that may result from better diversification.

This paper introduces risk into the dual model of production by constructing a utility-maximizing model in which managers choose their most preferred production plan. We show that the utility function that ranks production plans is equivalent to a ranking of subjective probability distributions of profit that are conditional on the production plan. The most preferred production plan results from the firm's choice of an optimal profit distribution. The model is sufficiently general to incorporate risk aversion as well as risk neutrality. Hence, it can account for the case where the potential for costly financial distress makes trading profit for reduced risk a value-maximizing strategy. We implement the model using the Almost Ideal Demand System to derive utility-maximizing share equations for profit and inputs, given the output vector and given sources of risk to control for choices that would affect endogenous risk. The most preferred cost function is obtained from the profit share equation, and we show that, if risk neutrality is imposed, this system is identical to the standard translog cost system except that it controls for sources of risk.

We apply the model to the U.S. banking industry using the 1989-90 data on banks with over $1 billion in assets. Consistent with the significant regulatory and financial costs of bank distress, we find evidence that managers trade return for reduced risk. In addition, we find evidence of significant scale economies that help explain the recent wave of large bank mergers. Using these same data, we also estimate the standard cost function, which does not explicitly account for risk, and we obtain the usual results of essentially constant returns to scale, which contradicts the often stated rationale for bank mergers.

JEL Classification: G21, L23