Adaptive partial policy innovation: coping with ambiguity through diversification

This paper develops a broad theme about policy choice under ambiguity through study of a particular decision criterion. The broad theme is that, where feasible, choice between a status quo policy and an innovation is better framed as selection of a treatment allocation than as a binary decision. Study of the static minimax-regret criterion and its adaptive extension substantiate the theme. When the optimal policy is ambiguous, the static minimax-regret allocation always is fractional absent large fixed costs or deontological considerations. In dynamic choice problems, the adaptive minimax-regret criterion treats each cohort as well as possible, given the knowledge available at the time, and maximizes intertemporal learning about treatment response.

Interpreting the Predictions of Prediction Markets

Participants in prediction markets such as the Iowa Electronic Markets trade all-or-nothing contracts that pay a dollar if and only if specified future events occur. Researchers engaged in empirical study of prediction markets have argued broadly that equilibrium prices of the contracts traded are market probabilities' that the specified events will occur. This paper shows that if traders are risk-neutral price takers with heterogenous beliefs, the price of a contract in a prediction market reveals nothing about the dispersion of traders' beliefs and partially identifies the central tendency of beliefs. Most persons have beliefs higher than price when price is above 0.5, and most have beliefs lower than price when price is below 0.5. The mean belief of traders lies in an interval whose midpoint is the equilibrium price. These findings persist even if traders use price data to revise their beliefs in plausible ways.

Adaptive Minimax-Regret Treatment Choice, With Application To Drug Approval

Suppose that there are two treatments for a condition. One is the status quo, whose properties are known from experience and the other is an innovation, whose properties are not known initially. A new cohort of persons presents itself each period and a planner must choose how to treat this cohort. When facing situations of this kind, it has become common to commission randomized trials of limited duration to learn about the innovation. Rather than wait for the outcomes of interest to unfold over time, surrogate outcomes that can be observed early on are used to judge the success of the innovation. A close approximation to this process is institutionalized in the drug approval protocol of the U. S. Food and Drug Administration. This paper brings welfare-economic and decision-theoretic thinking to bear on the problem of treatment choice, with application to drug approval. I introduce the adaptive minimax-regret (AMR) rule, which applies to each cohort the minimax-regret criterion using the knowledge of treatment response available at the time of treatment. The result is a fractional treatment allocation whenever the available knowledge does not suffice to determine which treatment is better. The rule is adaptive because, as knowledge of treatment response accumulates, successive cohorts are allocated differently across the two treatments. I use the AMR idea to suggest an adaptive drug approval process that permits partial marketing of new drugs while scientifically appropriate long-term clinical trials are underway. The stronger the evidence on health outcomes of interest, the more treatment would be permitted, with a definitive approval decision eventually made when sufficient evidence has accumulated.

Statistical Treatment Rules for Heterogeneous Populations: With Application to Randomized Experiments

This paper uses Wald's concept of the risk of a statistical decision function to address the question: How should sample data on treatment response be used to guide treatment choices in a heterogeneous population? Statistical treatment rules (STRs) are statistical decision functions that map observed covariates of population members and sample data on treatment response into treatment choices. I propose evaluation of STRs by their expected welfare (negative risk in Wald's terms), and I apply this criterion to compare two STRs when the sample data are generated by a classical randomized experiment. The rules compared both embody the reasonable idea that persons should be assigned the treatment with the best empirical success rate, but they differ in their use of covariate information. The conditional success (CS) rule selects treatments with the best empirical success rates conditional on specified covariates and the unconditional success (US) rule selects a treatment with the best unconditional empirical success rate. The main finding is a proposition giving finite-sample bounds on expected welfare under the two rules. The bounds, which rest on a large-deviations theorem of Hoeffding, yield explicit sample-size and distributional conditions under which the CS Rule is superior to the US rule.

Academic Ability, Earnings, and the Decision to Become a Teacher: Evidence From the National Longitudinal Study of the High School Class of 1972

Perceived shortcomings in the quality of American education at the elementary and secondary school levels have drawn much public attention recently. In particular, concern with the composition of the teacher force has been prominent. Informed assessment of the various proposals for increasing the quality of the teaching force is possible only if we can forecast the extent to which these proposals, if enacted, would influence the occupational choice decisions of high ability young adults. Until now,there has been no basis for making such forecasts.The research reported here examines the relationships between academic ability, earnings, and the decision to become a teacher through analysis of data from a national sample of college graduates. Inspection of the data reveals that the frequency of choice of teaching as an occupation is inversely- related to academic ability. Conditioning on sex and academic ability, the earnings of teachers are much lower, on average, than those of other working college graduates. Conditioning on sex, the earnings of teachers tend to rise only slightly, if at all, with academic ability. An econometric analysis suggests that in the absence of a minimum ability standard, increases in teacher earnings would yield substantial growth in the size of the teaching force but minimal improvement in the average academic ability of teachers. If teacher salaries are not increased, institution of a minimum ability standard would improve the average ability of the teaching force but reduce its size. The average ability of the teaching force can be improved and the size of the teaching force maintained if minimum ability standards are combined with sufficient salary increases. It appears that the average academic ability of teachers can be raised to the average of all college graduates if a minimum SAT score (verbal +math) of 800 is required for teacher certification and teacher salaries are raised by about ten percent over their present levels.

Fractional Treatment Rules for Social Diversification of Indivisible Private Risks

Should a social planner treat observationally identical persons identically? This paper shows that uniform treatment is not necessarily desirable when a planner has only partial knowledge of treatment response. Then there may be reason to implement a fractional treatment rule, with positive fractions of the observationally identical persons receiving different treatments. The planning problems studied here share some important features: treatment is individualistic, social welfare is a strictly increasing function of a population mean outcome, and outcomes depend on an unknown state of nature. They differ in the information that the planner has about the state of nature and in how he uses this information to make treatment choices. In particular, I compare treatment choice using Bayes rules and the minimax-regret criterion. Following the analysis, I put aside the literal notion of a planner who makes decisions on behalf of society and consider the feasibility of implementing fractional treatment rules in functioning democracies.

Search Profiling with Partial Knowledge of Deterrence

Economists studying public policy have generally assumed that the relevant social planner knows how policy affects population behavior. Planners typically do not possess all of this knowledge, so there is reason to consider policy formation with partial knowledge of policy impacts. Here I consider the choice of a profiling policy where decisions to search for evidence of crime may vary with observable covariates of the persons at risk of being searched. To begin I pose a planning problem whose objective is to minimize the utilitarian social cost of crime and search. The consequences of candidate search rules depends on the extent to which search deters crime. Deterrence is expressed through the offense function, which describes how the offense rate of persons with given covariates varies with the search rate applied to these persons. I study the planning problem when the planner has partial knowledge of the offense function. To demonstrate general ideas, I suppose that the planner observes the offense rates of a study population whose search rule has previously been chosen. He knows that the offense rate weakly decreases as the search rate increases, but he does not know the magnitude of the deterrent effect of search. In this setting, I first show how the planner can eliminate dominated search rules and then how he can use the minimax or minimax-regret criterion to choose an undominated search rule.

Economic Analysis of Social Interactions

Economists have long been ambivalent about whether the discipline should focus on the analysis of markets or should be concerned with social interactions more generally. Recently the discipline has sought to broaden its scope while maintaining the rigor of modern economic analysis. Major theoretical developments in game theory, the economics of the family, and endogenous growth theory have taken place. Economists have also performed new empirical research on social interactions, but the empirical literature does not show progress comparable to that achieved in economic theory. This paper examines why and discusses how economists might make sustained contributions to the empirical analysis of social interactions.