When designing data collection, crucial questions arise regarding how much data to collect and how much effort to expend to enhance the quality of the collected data. To make choice of sample design a coherent subject of study, it is desirable to specify an explicit decision problem. We use the Wald framework of statistical decision theory to study allocation of a budget between two or more sampling processes. These processes all draw random samples from a population of interest and aim to collect data that are informative about the sample realizations of an outcome. They differ in the cost of data collection and the quality of the data obtained. One may incur lower cost per sample member but yield lower data quality than another. Increasing the allocation of budget to a low-cost process yields more data, while increasing the allocation to a high-cost process yields better data. We initially view the concept of “better data” abstractly and then fix attention on two important cases. In both cases, a high-cost sampling process accurately measures the outcome of each sample member. The cases differ in the data yielded by a low-cost process. In one, the low-cost process has non-response and in the other it provides a low-resolution interval measure of each sample member’s outcome. In these settings, we study minimax-regret sample design for prediction of a real-valued outcome under square loss; that is, design which minimizes maximum mean square error. The analysis imposes no assumptions that restrict the unobserved outcomes. Hence, the decision maker must cope with both the statistical imprecision of finite samples and the partial identification of the true state of nature.

When designing data collection, crucial questions arise regarding how much data to collect and how much effort to expend to enhance the quality of the collected data. To make choice of sample design a coherent subject of study, it is desirable to specify an explicit decision problem. We use the Wald framework of statistical decision theory to study allocation of a budget between two or more sampling processes. These processes all draw random samples from a population of interest and aim to collect data that are informative about the sample realizations of an outcome. They differ in the cost of data collection and the quality of the data obtained. One may incur lower cost per sample member but yield lower data quality than another. Increasing the allocation of budget to a low-cost process yields more data, while increasing the allocation to a high-cost process yields better data. We initially view the concept of “better data” abstractly and then fix attention on two important cases. In both cases, a high-cost sampling process accurately measures the outcome of each sample member. The cases differ in the data yielded by a low-cost process. In one, the low-cost process has non-response and in the other it provides a low-resolution interval measure of each sample member’s outcome. In these settings, we study minimax-regret sample design for prediction of a real-valued outcome under square loss; that is, design which minimizes maximum mean square error. The analysis imposes no assumptions that restrict the unobserved outcomes. Hence, the decision maker must cope with both the statistical imprecision of finite samples and the partial identification of the true state of nature.

Incomplete observability of data generates an identification problem. What one can learn about a population parameter depends on the assumptions one finds credible. Rubin has promoted random multiple imputation (RMI) as a general way to deal with missing values. The recommendation has been influential to researchers who seek a simple fix to the nuisance of missing data. This paper provides a transparent assessment of the mix of Bayesian and frequentist thinking used by Rubin to argue for RMI. It evaluates random imputation to replace missing outcome or covariate data when the objective is to learn a conditional expectation.

Federal statistical agencies in the United States and analogous agencies elsewhere commonly report official economic statistics as point estimates, without accompanying measures of error. Users of the statistics may incorrectly view them as error free or may incorrectly conjecture error magnitudes. This paper discusses strategies to mitigate misinterpretation of official statistics by communicating uncertainty to the public. Sampling error can be measured using established statistical principles. The challenge is to satisfactorily measure the various forms of nonsampling error. I find it useful to distinguish transitory statistical uncertainty, permanent statistical uncertainty, and conceptual uncertainty. I illustrate how each arises as the Bureau of Economic Analysis periodically revises GDP estimates, the Census Bureau generates household income statistics from surveys with nonresponse, and the Bureau of Labor Statistics seasonally adjusts employment statistics. I anchor my discussion of communication of uncertainty in the contribution of Oskar Morgenstern (1963a), who argued forcefully for agency publication of error estimates for official economic statistics.

I analyse social interactions that stem from the successive endeavours of new cohorts of heterogeneous decision makers to learn from the experiences of past cohorts. A dynamic process of information accumulation and decision making occurs as the members of each cohort observe the experiences of earlier ones, and then make choices that yield experiences observable by future cohorts. Decision makers face the "selection problem" as they seek to learn from observation of past actions and outcomes, while not observing the counterfactual outcomes that would have occurred had other actions been chosen. Assuming that all cohorts face the same outcome distributions, I show that social learning is a process of sequential reduction in ambiguity. The specific nature of this process, and its terminal state, depend critically on how decision makers make choices under ambiguity. I use the problem of learning about innovations to illustrate. Copyright The Review of Economic Studies Limited, 2004.

This paper examines the reflection problem that arises when a researcher observing the distribution of behaviour in a population tries to infer whether the average behaviour in some group influences the behaviour of the individuals that comprise the group. It is found that inference is not possible unless the researcher has prior information specifying the compisition of reference groups. If this information is available, the prospects for inference depend critically on the population relationship between the variables defining reference groups and those directly affecting outcomes. Inference is difficult to implossible if these variables are functionally dependent or are statistically independent. The prospects are better if the variables defining reference groups and those directly affecting outcomes are moderately related in the population.

Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own seminal development of statistical decision theory. Haavelmo favorably cited Wald, but econometrics did not embrace statistical decision theory. Instead, it focused on study of identification, estimation, and statistical inference. This paper proposes use of statistical decision theory to evaluate the performance of models in decision making. I consider the common practice of as‐if optimization : specification of a model, point estimation of its parameters, and use of the point estimate to make a decision that would be optimal if the estimate were accurate. A central theme is that one should evaluate as‐if optimization or any other model‐based decision rule by its performance across the state space, listing all states of nature that one believes feasible, not across the model space. I apply the theme to prediction and treatment choice. Statistical decision theory is conceptually simple, but application is often challenging. Advancing computation is the primary task to complete the foundations sketched by Haavelmo and Wald.

This article discusses the history underlying the new literature, describes some of what has been learned thus far, and looks ahead towards making further progress