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31
A structural model of salesforce compensation dynamics: Estimation and field implementation
 Quant. Marketing Econom
, 2011
"... We present an empirical framework to analyze realworld salesforce compensation schemes, and report on a multimillion dollar, multiyear project involving a large contact lens manufacturer at the US, where the model was used to improve salesforce contracts. The model is built on agency theory, ..."
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We present an empirical framework to analyze realworld salesforce compensation schemes, and report on a multimillion dollar, multiyear project involving a large contact lens manufacturer at the US, where the model was used to improve salesforce contracts. The model is built on agency theory, and solved using numerical dynamic programming techniques. The model is exible enough to handle quotas and bonuses, outputbased 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
rms US salesforce. We use the model to evaluate pro
timproving, theoreticallypreferred changes to the extant compensation scheme. These recommendations were then implemented at the focal
rm. Agent behavior and output under the new compensation plan is found to change as predicted. The
Nonparametric Identification in Nonseparable Panel Data Models with Generalized Fixed Effects
, 2009
"... This paper is concerned with extending the familiar notion of fixed effects to nonlinear setups with infinite dimensional unobservables like preferences. The main result is that a generalized version of differencing identifies local average structural derivatives (LASDs) in very general nonseparable ..."
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Cited by 13 (3 self)
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This paper is concerned with extending the familiar notion of fixed effects to nonlinear setups with infinite dimensional unobservables like preferences. The main result is that a generalized version of differencing identifies local average structural derivatives (LASDs) in very general nonseparable models, while allowing for arbitrary dependence between the persistent unobservables and the regressors of interest even if there are only two time periods. These quantities specialize to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects. We extend the basic framework to include dynamics in the regressors and time trends, and show how distributional effects as well as average effects are identified. In addition, we show how to handle endogeneity in the transitory component. Finally, we adapt our results to the semiparametric binary choice model with correlated coefficients, and establish that average structural marginal probabilities are identified. We conclude this paper by applying the last result to a real world data example. Using the PSID, we analyze the way in which the lending restrictions for mortgages eased between 2000 and 2004.
2011): “Nonlinear Panel Data Analysis
 Annual Review of Economics
"... Nonlinear panel data models arise naturally in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of randomeffects likelihood approaches. We emphasize a link with Bayesian computation ..."
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Cited by 9 (0 self)
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Nonlinear panel data models arise naturally in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of randomeffects likelihood approaches. We emphasize a link with Bayesian computation and Markov Chain Monte Carlo, which provides a convenient approach to estimation and inference. Relaxing parametric assumptions on the distribution of individual effects raises serious identification problems. In discrete choice models, common parameters and average marginal effects are generally setidentified. The availability of continuous outcomes, however, provides opportunities for pointidentification. We end the paper by reviewing recent progress on non fixedT approaches. In panel applications where the time dimension is not negligible relative to the size of the crosssection, it makes sense to view the estimation problem as a timeseries finite sample bias. Several perspectives to bias reduction are now available. We review their properties, with a special emphasis on randomeffects methods. JEL codes: C23.
Identification and Estimation of Nonparametric Panel Data Regressions with Measurement Error
, 2012
"... This paper provides a constructive argument for identification of nonparametric panel data models with measurement error in a continuous explanatory variable. The approach point identifies all structural elements of the model using only observations of the outcome and the mismeasured explanatory var ..."
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Cited by 4 (0 self)
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This paper provides a constructive argument for identification of nonparametric panel data models with measurement error in a continuous explanatory variable. The approach point identifies all structural elements of the model using only observations of the outcome and the mismeasured explanatory variable; no further external variables such as instruments are required. Restricting either the structural or the measurement error to be independent over time allows past covariates or outcomes to serve as instruments. Time periods have to be linked through serial dependence in the latent explanatory variable, but the transition process is left nonparametric. The paper discusses the general identification result in the context of a nonlinear panel data regression model with additively separable fixed effects. It provides a nonparametric plugin estimator, derives its uniform rate of convergence, and presents simulation evidence for good performance in finite samples.
Identification and Estimation of Nonlinear Dynamic Panel Data Models with Unobserved Covariates
, 2010
"... This paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved voariates. Including such unobserved covariates may control for both the individualspecific unobserved heterogeneity and the endogeneity of the explanatory variables. Without specifying the ..."
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Cited by 4 (2 self)
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This paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved voariates. Including such unobserved covariates may control for both the individualspecific unobserved heterogeneity and the endogeneity of the explanatory variables. Without specifying the distribution of the initial condition with the unobserved variables, we show that the models are nonparametrically identified from three periods of data. The main identifying assumption requires the evolution of the observed covariates depends on the unoberved covariates but not on the lagged dependent variable. We also propose a sieve maximum likelihood estimator (MLE) and focus on two classes of nonlinear dynamic panel data models, i.e., dynamic discrete choice models and dynamic censored models. We present the asymptotic property of the sieve MLE and investigate the finite sample properties of these sievebased estimator through a Monte Carlo study. An intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the Panel Study of Income Dynamics (PSID).
Welfare Gains from Optimal Pollution Regulation
, 2012
"... Successful implementation of pollution regulation often requires redistributing a portion of the benefits back to firms who incur abatement costs. When firms have private information on their costs, they have an incentive to overstate these costs and demand higher compensation. Optimal pollution reg ..."
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Successful implementation of pollution regulation often requires redistributing a portion of the benefits back to firms who incur abatement costs. When firms have private information on their costs, they have an incentive to overstate these costs and demand higher compensation. Optimal pollution regulation in this environment sacrifices allocative efficiency to reduce information rents. I measure the gains from optimal pollution regulation by empirically examining the effect of sulfur dioxide emissions regulation on electric utilities. These electric utilities also face economic regulation, and I exploit this institutional detail. I derive estimates of marginal abatement costs from the cost of jointly producing electricity and emissions, allowing for timevarying unobserved heterogeneity to capture cost efficiency. Cost efficiency consists of exogenous (intrinsic type) and endogenous (managerial effort) components which are private information of the firm. To separately identify these components, I model economic regulation as a signaling game of auditing. I show that a particular equilibrium exists where the firm does not exert effort during the “rate case”, but it exerts a positive level of effort afterwards. I provide empirical evidence for the plausibility of this equilibrium using cost and rate case data. This equilibrium generates exclusion restrictions that are used to estimate parameters of the cost function and disutility of effort. I show that the type distribution can be nonparametrically identified
2014): “Nonparametric Identification in Panels using Quantiles,” Cemmap Working Paper
"... This paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity. The effects of interest are derivatives of the average and quantile structural functions of the model. We find that these derivatives are identi ..."
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This paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity. The effects of interest are derivatives of the average and quantile structural functions of the model. We find that these derivatives are identified with two time periods for “stayers”, i.e. for individuals with the same regressor values in two time periods. We show that the identification results carry over to models that allow location and scale time effects. We propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects. The bootstrap proposed allows uniform inference for functionvalued parameters such as quantile effects uniformly over a region of quantile indices and/or regressor values. An empirical application to Engel curve estimation with panel data illustrates the results.
Identification of Panel Data Models with Endogenous Censoring ∗
"... Thispaperanalyzestheidentificationquestionincensoredpaneldatamodels,where the censoring can depend on both observable and unobservable variables in arbitrary ways. Under some general conditions, we derive the tightest sets on the parameter of interest. These sets (which can be singletons) represent ..."
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Thispaperanalyzestheidentificationquestionincensoredpaneldatamodels,where the censoring can depend on both observable and unobservable variables in arbitrary ways. Under some general conditions, we derive the tightest sets on the parameter of interest. These sets (which can be singletons) represent the limit of what one can learn about these parameters given the model and the data in that, every parameter that belongs to these sets is observationally equivalent to the true parameter. We consider two separate sets of assumptions, motivated by the previous literature, each controlling for unobserved heterogeneity with an individual specific (fixed) effect. The first imposes a stationarity assumption on the unobserved disturbance terms, along the lines of Manski (1987), and Honoré (1993). The second is a nonstationary model that imposesaconditionalindependenceassumption. Forbothmodels, weprovidesufficient conditions for these models to point identify the parameters. Since our identified sets are defined through parameters that obey first order dominance, we outline easily implementable approaches to build confidence regions based on recent advances in Linton et.al.(2010) on bootstrapping tests of stochastic dominance. We also extend our results to dynamic versions of the model.
2011), "A Triangular Treatment Effect Model with Random Coeffi cients in the Selection Equation," unpublished manuscript
"... Abstract. In this paper we study nonparametric estimation in a binary treatment model where the outcome equation is of unrestricted form, and the selection equation contains multiple unobservables that enter through a nonparametric random coefficients specification. This specification is flexible be ..."
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Abstract. In this paper we study nonparametric estimation in a binary treatment model where the outcome equation is of unrestricted form, and the selection equation contains multiple unobservables that enter through a nonparametric random coefficients specification. This specification is flexible because it allows for complex unobserved heterogeneity of economic agents and nonmonotone selection into treatment. We obtain conditions under which both the conditional distributions of Y0 and Y1, the outcome for the untreated, respectively treated, given first stage unobserved random coefficients, are identified. We can thus identify an average treatment effect, conditional on first stage unobservables called UCATE, which yields most treatment effects parameters that depend on averages, like ATE and TT. We provide sharp bounds on the variance, the joint distribution of (Y0,Y1) and the distribution of treatment effects. In the particular case where the outcomes are continuously distributed, we provide novel and weak conditions that allow to point identify the joint conditional distribution of Y0,Y1, given the unobservables. This allows to derive every treatment effect parameter, e.g. the distribution of treatment effects and the proportion of individuals who benefit from treatment. We present estimators for the marginals, average and distribution of treatment effects, both conditional on unobservables and unconditional, as well as total population effects. The estimators use all the data and discard
Nonparametric Identification of a Nonlinear Panel Model with Application to Duration Analysis with Multiple Spells,”mimeo
, 2010
"... This paper develops a nonparametric generalization of the quasidifferencing method of linear panel data models. A nonparametric panel data model is shown to be identified using three time periods of data. The fixed effects and idiosyncratic errors are not additively separable from the covariates, a ..."
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This paper develops a nonparametric generalization of the quasidifferencing method of linear panel data models. A nonparametric panel data model is shown to be identified using three time periods of data. The fixed effects and idiosyncratic errors are not additively separable from the covariates, and hence affect the marginal effects. In contrast to the existing literature the structural function is allowed to vary over time in an arbitrary fashion. The paper also obtains nonparametric identification results for a nonparametric panel transformation and a multiple spell duration models. The later result substantially extends Honore’s (1993, Review of Economic Studies) result by relaxing the assumption of multiplicative separability of the unobserved heterogeneity in the specification of the duration function.