Chapter 3: Analyzing repeated-game economics experiments: robust standard errors for panel data with serial correlation
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Many laboratory and field experiments in economics involve participants or groups of participants making a sequence of related decisions, usually with feedback, over many choice periods. For instance, this is typical of experimental work on auctions, bargaining, the private provision of public goods, tax compliance, and pollution control instruments. Through repeated-game play, researchers allow for developments such as learning, strategy refinement, establishment of equilibria, and observances of how decisions or outcomes change in response to experimental design variations. The widespread availability and improving functionality of computer software has made it increasingly common for experiments to be reasonably complex and involve many choice periods. Experimentalists traditionally have relied on fairly simple and computationally transparent parametric and nonparametric hypothesis tests to evaluate hypotheses (e.g. paired t-test, Wilcoxon test), such as those discussed in Davis and Holt (1993). It remains a somewhat common practice to address the time-series dimension superficially by using as the unit of observation the mean outcome across all periods for an individual or group. Time trends may be artificially accounted for by using the average outcome from the last decision period, last few periods, or by separately testing different period groupings. Such analyses rely on the variation in means across individuals or groups and insufficiently account for the variation in outcomes across decision periods. These approaches are particularly troublesome for experimental designs that expose the participant to multiple parameter changes.

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