Estimating Intertemporal Preferences for Natural Resource Allocation Richard E. Howitta, Siwa Msangia, Arnaud Reynaudb, and Keith C. Knappc Abstract In this paper we show how the degree of risk aversion, discounting, and preference for intertemporal substitution for a natural resource manager can be structurally estimated within a recursive utility framework. We focus on the management of Oroville Reservoir, in Northern California, and test the data to see if they are more consistent with a recursive utility model specification than one with standard time-additive separability, and estimate the implied degree of risk aversion. The results show that the data on dam storage and releases are consistent with a risk-averse manager with recursive preferences, and that preferences are stationary over the observed period. The data also rejects time-additive separability, whether specified with or without risk-aversion, such as the standard CRRA utility model. The improvement in model fit when recursive preferences are used is notable. Contact author Richard Howitt Department of Agricultural and Resource Economics, University of California Davis, Ca 95616 Phone 530 752 1521 fax 530 752 5614 Email [email protected] a Department of Agricultural and Resource Economics, University of California at Davis. b LERNA-INRA, University of Social Sciences Toulouse. c Department of Environmental Sciences, University of California at Riverside. The authors gratefull acknowledge support from a risk management grant from USDA-ERS that made this study possible.2 Introduction Natural resource management problems are typically stochastic and dynamic in nature, by virtue of the characteristics of the underlying physical or biological processes that govern the evolution of the resource. This has been the reason for a number of empirical applications of Dynamic Programming within the natural resource literature, as chronicled by Williams (1989). However, the tendency of researchers to use risk-neutral expected net present value objective functions when modeling natural resource problems has caused policy-makers to be somewhat skeptical of the real-world relevance of resource economics analysis1. Given the uncertainty facing the decision-maker in each period of the planning horizon, due to the realization of stochastic shocks, we would expect risk-aversion and intertemporal substitution to feature prominently in the characterization of intertemporal preferences. While a number of authors have incorporated risk-aversion into analytical and numerical models in the economic literature (Knapp and Olson, 1996; Krautkramer et al., 1992), few have actually tried to estimate the degree to which it enters into the decision-makers objective criterion, and none of those papers consider natural resource management problems. Most of the resource literature has imposed severe restrictions on the preferences for intertemporal substitution by adopting a time-additive separable formulation of the objective function. We avoid this problem by using a recursive utility specification that is more general and allows preferences towards risk and intertemporal substitution to be decoupled (Epstein and Zin, 1989). The estimation of dynamic preferences has been implemented in a number of settings to elicit the underlying parameters of the decision-maker’s problem. Where adequate time-series data exists, it can be used to calculate empirical moments (Hansen and Singleton, 1982, 1983). Rust (1987) has applied alternative dynamic estimation techniques to analyze the actions of a single decision-maker. This approach has laid the foundation for several analyses of this type (Provencher and Bishop, 1997; Provencher, 1995; Miranda and Schnitkey, 1995). However in the few papers that apply dynamic 1 This paper was motivated by a comment made at an agency workshop in response to the presentation of results from a conventional risk-neutral SDP solution. The commentator was Dr. Francis Cheung of the California Department of Water Resources. He pointed out that optimization models tend to be discounted by decision-makers because they ignore the presence of risk in the objective function. We gratefully acknowledge support from USDA ERS grant “Measuring, Costing and Mitigating Institutional Risk in Californian Irrigation Water Supplies”3estimation to natural resource problems none specifically estimate intertemporal preference parameters, or quantify risk aversion (Provencher, 1995, Fulton and Karp, 1989). We seek to address this gap in the environmental and natural resource literature by applying dynamic estimation techniques to elicit the recursive intertemporal preferences with continuous state and control variables. We use the example of reservoir management, but take a different approach from authors in the water resources engineering literature who have only discussed the comparative dynamics of increasing risk-aversion in reservoir management (Kerr and Read, 1998; Craddock et al., 1998). We identify the degree of risk-aversion that is exhibited by the decision-maker’s actions, and employ likelihood ratios to test whether the data is consistent with a risk-averse decision-maker, and whether the preferences of the decision-maker can be better characterized by a recursive utility function. The outline of the paper is as follows. In the next section, we describe the general resource allocation problem and the recursive utility specification that we use. In the following section we discuss the specific empirical application of our problem to Oroville Reservoir and describe the dynamic estimation methodology. The succeeding section presents the estimation results, followed by a section of concluding remarks. Resource Allocation and Recursive Utility This section develops the specification for an intertemporal natural resource management problem for a stochastic flow resource with storage. The model is defined with continuous state and control variables, and uses reservoir management as an example. Three preference characteristics that are important for resource management are the discount rate that defines the relative weight of current period benefits to those accrued in the future; resistance to intertemporal substitution which embodies the decision-maker’s preferences for consumption smoothing; and risk aversion which represents the agent’s degree of dislike for variability in future