Empirical studies on the influence of sunk costs in high stakes decisions have come to mixed conclusions. As observational studies have primarily used professional sports labor markets, we analyze the effect of sunk costs, player compensation, on the labor utilization of defensive players in the National Football League (NFL). Our analysis has several advantages. First, we measure the direct impact of increased financial commitment. Second, we analyze the effect of sunk costs when firms have accurate and abundant performance feedback; therefore, our conclusions are not driven by uncertainty. Finally, we control for possible endogeneity by using the exogenous variation in compensation generated when players become eligible for free agency or change teams. Our results indicate sunk costs are significant determinants of player utilization. A 15 % increase in compensation has an equivalent effect on playing time as an increase of five to eleven solo tackles, one to two interceptions and two to five and a half sacks in the previous season for linebackers, defensive backs and defensive linemen respectively. Furthermore, the sunk-cost fallacy is persistent throughout the entire career of an average NFL player.
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See Ho et al. (2015) for an empirical investigation of the sunk-cost fallacy using the driving behavior of people purchasing vehicles in Singapore.
Our data exhibit another common count-data problem, excess zeros. Therefore, we estimate our empirical strategy using zero-inflated NB (ZINB) regression. However, ZINB results are nearly identical to NB results. As a result, we focus on NB regression as the results are more easily interpreted. ZINB results are available from the author.
Conditional FE NB regression allows for individual heterogeneity in the distribution of the overdispersion parameter. However, it does not control for individual time invariant factors. Conditional FE Poisson regression controls for time invariant factors, but requires equidispersion.
The CBA originated in 1993. The 1993 CBA granted veteran players unrestricted free agency in exchange for a hard salary cap on players’ salaries. The CBA was extended in 1998, 2002 and 2006. However, 2009 was the final year and 2010 was played without a salary cap (Vrooman 2012).
The ZINB elasticity, calculated the means of the independent variables, is 0.336 and highly significant, to the 1 % level, with a delta-method standard error of 0.0203.
Since the natural logarithm difference is only a good approximation of percentage change when the difference is small, we use the formula % Δw = exp(β) − 1.
The effects of restricted and unrestricted free agency eligibility are very large throughout the distribution and similar to Berri and Simmons (2009). Using quantile regression, the effect of restricted free agency is 21.7, 16.4, 27.9, 31.8 and 47.8 % for the 0.10, 0.25, 0.50, 0.75 and 0.90 quantiles respectively. The effect of unrestricted free agency compared to restricted free agency is 23.2, 28.5, 41.1, 45.5 and 48.9 % for the 0.10, 0.25, 0.50, 0.75 and 0.90 quantiles respectively.
The results are also robust to the use of untransformed salary cap value as the measure of compensation and the exclusion of previous season games played and previous season percentage of games played that were started. Furthermore, the results remain significant when estimating standard errors clustered on players.
The increase in compensation as a result of becoming eligible for unrestricted free agency is estimated to increase the number of games started by 10 % when using IV conditional FE Poisson regression.
The effect of solo tackles for linebackers is 0.00602 with a standard error of 0.00263. The effect of interceptions for defensive backs is 0.0303 with a standard error of 0.0122. The effect of sacks for defensive linemen is 0.116 with a standard error of 0.00956.
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The authors declare that they have no conflict of interest.
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Keefer, Q.A.W. Performance Feedback Does Not Eliminate the Sunk-Cost Fallacy: Evidence From Professional Football. J Labor Res 36, 409–426 (2015). https://doi.org/10.1007/s12122-015-9215-y
- Sunk-cost fallacy
- Performance feedback
- Labor utilization