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A structural model of sales-force compensation dynamics: Estimation and field implementation

Abstract

We present an empirical framework to analyze real-world sales-force compensation schemes, and report on a multi-million dollar, multi-year project involving a large contact lens manufacturer at the US, where the model was used to improve sales-force contracts. The model is built on agency theory, and solved using numerical dynamic programming techniques. The model is flexible enough to handle quotas and bonuses, output-based commission schemes, as well as “ratcheting” of compensation based on past performance, all of which are ubiquitous in actual contracts. The model explicitly incorporates the dynamics induced by these aspects in agent behavior. We apply the model to a rich dataset that comprises the complete details of sales and compensation plans for the firm’s US sales-force. We use the model to evaluate profit-improving, theoretically-preferred changes to the extant compensation scheme. These recommendations were then implemented at the focal firm. Agent behavior and output under the new compensation plan is found to change as predicted. The new plan resulted in a 9% improvement in overall revenues, which translates to about $12 million incremental revenues annually, indicating the success of the field-implementation. The results bear out the face validity of dynamic agency theory for real-world compensation design. More generally, our results fit into a growing literature that illustrates that dynamic programming-based solutions, when combined with structural empirical specifications of behavior, can help significantly improve marketing decision-making, and firms’ profitability.

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Notes

  1. 1.

    These numbers may be viewed conservatively as a lower bound on the effect of the new plan due to the recession in 2009–2010.

  2. 2.

    Solving for the optimal plan is outside of the scope of the current analysis, and is an important, but methodologically challenging, direction for future research.

  3. 3.

    An alternative motivation of output-based contracts is that it may help attract and retain the best sales-people (Lazear 1986; Godes 2003; Zenger and Lazzarini 2004). This paper abstracts away from these issues since our data does not exhibit any significant turnover in the sales-force.

  4. 4.

    In other industries, agents may have control over prices (e.g. Bhardwaj 2001). In such situations, the compensation scheme may also provide incentives to agents to distort prices to “make quota”. See Larkin (2010), for empirical evidence from the enterprise resource software category.

  5. 5.

    The firm does not believe that sales-visits are the right measure of effort. Even though sales-calls are observed, the firm specifies compensation based on sales, not calls.

  6. 6.

    One alternative explanation for these patterns is that the spikes reflect promotions or price changes offered by the firm. Our extensive interactions with the management at the firm revealed that prices were held fixed during the time-period of the data (in fact, prices are rarely changed), and no additonal promotions were offered during this period.

  7. 7.

    We assume that once the agent leaves the firm, he cannot be hired back (i.e. χ t  = 0 is an absorbing state).

  8. 8.

    In case of the standard linear compensation plan, exponential CARA utilities and normal errors this specification corresponds to an exact representation of the agent’s certainty equivalent utility.

  9. 9.

    We also reject correlation of v t + 1 across agents, as well as correlation of v t + 1 with the demand shocks (ε t ) across agents. This rules out a story where subjective quota updating is used as a mechanism to filter out common shocks.

  10. 10.

    Implilcity, Ψ can be a function of the agent’s characteristics, \(\Psi\equiv\Psi\left( \mu,r,d,\mathcal{G}_{\varepsilon }\left( .\right) \right) \). For example, a counterfactual scheme could be characterized by a fixed salary and a commission specific to each agent. In this contract, the optimal salary and commision rate would be a function of the agent’s preferences. We suppress the dependence of Ψ on these features for notational simplicity.

  11. 11.

    Implicity, in Eq. 10, we assume that the distribution of demand shocks, \(\mathcal{G}_{\varepsilon }\left( .\right) \) stays the same under the counterfactual. In Eq. 10, we do not intergate against the ratcheting shocks \(\mathcal{G}_{v}\left( .\right) \), because all the counterfactual contracts we consider involve no ratcheting. Consideration of counterfactual contracts that involve ratchting would require a model for agents’ belief formation about quota updating under the new compensation profile, which is outside of the scope of the current analysis. Future research could consider solving for the optimal quota updating policy, under the assumption that agents’ beliefs regarding ratcheting are formed rationally. See Nair (2007) for one possible approach to solving for beliefs in this fashion applied to durable good pricing.

  12. 12.

    Alternatively, one could assume a parameteric density for ε and use maximum likelihood methods. The advantage of our semiparametric approach is that we avoid the possibility of extreme draws inherent in parametric densities and the pitfalls that go along with such draws.

  13. 13.

    So as to avoid concerns about learning-on-the job, and its interactions with quotas, five sales-agents, who had been with the firm for less than 2 years were dropped from the data.

  14. 14.

    As a caveat, note this is true as long as the alternate compensation schemes do not change the structure of incentives from the current plan. For example, relative compensation schemes, which condition compensation of a given agent on the performance of others, would require consideration of new elements such as fairness and competition which are not present in the current structure.

  15. 15.

    To guard against the influence of outliers we integrate the profit function only over the interquartile range and renormalize the results.

  16. 16.

    We consider the valuation by agents of simplicity, and its manifestation as menu costs to the firm, an important direction for future research.

  17. 17.

    To assuage concerns about this period of change in the firm, the data from the last two quarters of 2008 are not used in the estimation of the model.

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Acknowledgements

We thank Dan Ackerberg, Lanier Benkard, Adam Copeland, Paul Ellickson, Liran Einav, Wes Hartmann, Gunter Hitsch, Phil Haile, Sunil Kumar, Ed Lazear, Philip Leslie, Kathryn Shaw, Seenu Srinivasan, John Van Reenan, and seminar participants at Berkeley, Chicago, Kellogg, NUS, NYU, Rochester, Stanford, UC Davis, Yale, as well as the Marketing Science, Marketing Dynamics, NBER-IO, SICS, SITE, and UTD FORMS conferences, for their helpful feedback. Finally, we thank the management of the anonymous, focal firm in the paper for providing data, for innumerable interviews, and for their support, without which this research would not have been possible. We remain, however, responsible for all errors, if any.

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Correspondence to Harikesh S. Nair.

Appendix: computational details

Appendix: computational details

This appendix provides computational details of solving for the optimal policy function in Eq. 9 and for implementing the BBL estimator in Eq. 28.

Solution of optimal policy function

The optimal effort policy was solved using modified policy iteration (see, for e.g., Rust 1996 for a discussion of the algorithm). The policy was approximated over the two continuous states using ten points in each state dimension, and separately computed for each of the discrete states. The expectation over the distribution of the demand shocks ε t and the ratcheting shocks v t + 1were implemented using Monte Carlo integration using 1000 draws from the empirical distribution of these variates for the agent. The maximization involved in computing the optimal policy was implemented using the highly efficient SNOPT solver, using a policy tolerance of 1E-5.

Estimation of agent parameters

We discuss numerical details of implementing the BBL estimator in Eq. 28. The estimation was implemented separately for each of the 87 agents. The main details relate to the sampling of the initial states, the generation of alternative feasible policies, and details related to forward simulation. For each, we sampled a set of 1002 initial state points uniformly between the minimum and maximum quota and cumulative sales observed for each agent, and across months of the quarter. At each of the sampled state points, we generated 500 alternative feasible policies by adding a normal variate with standard deviation of 0.35 to the estimated optimal effort policy from the first stage (effort is measured in 100,000-s of dollars). Alternative feasible policies generated by adding random variates with large variances (e.g. 5), or by adding noise terms to effort policies at only a small subset of state points, were found to be uninformative of the parameter vector. At each sampled state point, we simulated value functions for each of the 500 alternative feasible policies by forwards-simulating the model 36 periods ahead. The sample analog of the moment conditions are then obtained by averaging over the sampled states and alternative policies.

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Misra, S., Nair, H.S. A structural model of sales-force compensation dynamics: Estimation and field implementation. Quant Mark Econ 9, 211–257 (2011). https://doi.org/10.1007/s11129-011-9096-1

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Keywords

  • Compensation Scheme
  • Demand Shock
  • Policy Function
  • Effort Policy
  • Compensation Policy