Wage differentials within retail chains, even at the lowest levels, can be quite large: for example, full-time sales staff at a major clothing retail chain are paid roughly $16,000 per annum on average, but store managers earn around $33,600, over twice that amount. Further up the hierarchy, district managers make on average over $60,800 (in 1986 dollars). Why do these differentials arise? One explanation is that employees at higher levels of a firm are paid more, because they work harder, or are more productive. Alternatively, the tournament literature proposes that wages at the top of a hierarchy must be kept high in order to provide incentives for workers, even in low levels of the hierarchy, to exert effort.
Despite the sizable theoretical literature on tournament models (see McLaughlin (1989) and Bolton and Dewatripont (2005, chap. 8) for surveys), empirical work related to these models is limited. Previous empirical work on tournament models have mainly focused on testing the predictions of these models. This includes papers on executive compensation (cf. Main, O’Reilly, and Wade (1993), Eriksson (1999)), professional sports (eg. Ehrenberg and Bognanno (1990a), (1990b), Bronars and Oettinger (2001)), and agricultural (poultry) production (Knoeber and Thurman (1994)). One common feature of these papers is their focus on industries for which productivity measures at the individual worker level are observable.
However, for many industries, these worker productivity measures are difficult to obtain (or unavailable). In this paper, we consider the structural estimation of tournament models when we observe only aggregate firm-level information on employment and wages at each hierarchical level within the firm. Importantly, our empirical strategies do not require observation of workers’ productivity levels. By exploiting the equilibrium restrictions of the elimination tournament model, we derive estimates of model unobservables including workers’ equilibrium effort levels — which are consistent with the observed wage data. Hence, the aim of this paper is not to test the tournament theory (as in the previous empirical work), but to use it as a guide to obtain values for the structural elements of the tournament model.
Recently, several papers have estimated structural models of tournament models, as is done in this paper. Ferrall (1996), (1997), estimates structural models of internal labor markets within, respectively, law firms and engineering firms. Zheng and Vukina (2007) estimate a rank-order tournament model using the Knoeber and Thurman (1994) data, and use the estimated structural parameters to simulate outcomes under an alternative cardinal compensation scheme. The empirical approaches taken in those papers and the present paper are quite different, due to both differences in the underlying theoretical tournament model being considered, as well as differences in the datasets used for estimation.
We illustrate our methodologies by estimating tournament models using a dataset of wages and employment levels within a number of large American retail chains (including many retailers found in typical shopping malls). Our empirical analysis focuses on the lower hierarchical levels (i.e., the sales staff, assistant store manager, and store manager positions) of these firms. We are able to estimate the equilibrium effort levels in these positions, consistent with the observed data and the theoretical tournament model.
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