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Time Spent Exercising and Obesity: An Application of Lewbel’s Instrumental Variables Method

Charles Courtemanche, Joshua C. Pinkston, and Jay Stewart


This paper examines the role physical activity plays in determining body mass using data from the American Time Use Survey. Our work is the first to address the measurement error that arises when time use during a single day—rather than average daily time use over an extended period—is used as an explanatory variable. We show that failing to account for day-to-day variation in activities results in the effects of time use on a typical day being understated. Furthermore, we account for the possibility that physical activity and body mass are jointly determined by implementing Lewbel’s instrumental variables estimator that exploits first-stage heteroskedasticity rather than traditional exclusion restrictions. Our results suggest that, on average, physical activity reduces body mass by less than would be predicted by simple calorie expenditure-to-weight formulas, implying compensatory behavior such as increased caloric intake.