Durable Goods Adoption and the Consumer Discount Factor: A Case Study of the Norwegian Book Market

We exploit a change in Norway’s fixed book pricing policies to construct exclusion restrictions with which to identify consumers’ discount factor. We assume that the policy change generated an unanticipated, exogenous shock to consumers’ expectations about future price cuts. Our findings suggest that consumers are much more impatient than would be implied by the real rate of interest, challenging the standard assumed rate of discounting in the extant literature on dynamic demand estimation. The high rate of consumer impatience is consistent with laboratory studies in the behavioral economics and decision-making literatures. This paper was accepted by Matthew Shum, marketing.

kinkyreg: Instrument-free inference for linear regression models with endogenous regressors

In models with endogenous regressors, a standard regression approach is to exploit just-identifying or overidentifying orthogonality conditions by using instrumental variables. In just-identified models, the identifying orthogonality assumptions cannot be tested without the imposition of other nontestable assumptions. While formal testing of overidentifying restrictions is possible, its interpretation still hinges on the validity of an initial set of untestable just-identifying orthogonality conditions. We present the kinkyreg command for kinky least-squares inference, which adopts an alternative approach to identification. By exploiting nonorthogonality conditions in the form of bounds on the admissible degree of endogeneity, feasible test procedures can be constructed that do not require instrumental variables. The kinky least-squares confidence bands can be more informative than confidence intervals obtained from instrumental-variables estimation, especially when the instruments are weak. Moreover, the approach facilitates a sensitivity analysis for standard instrumental-variables inference. In particular, it allows the user to assess the validity of previously untestable just-identifying exclusion restrictions. Further instrument-free tests include linear hypotheses, functional form, heteroskedasticity, and serial correlation tests.

Regularization and variable selection in Heckman selection model

Sample selection arises when the outcome of interest is partially observed in a study. A common challenge is the requirement for exclusion restrictions. That is, some of the covariates affecting missingness mechanism do not affect the outcome. The drive to establish this requirement often leads to the inclusion of irrelevant variables in the model. A suboptimal solution is the use of classical variable selection criteria such as AIC and BIC, and traditional variable selection procedures such as stepwise selection. These methods are unstable when there is limited expert knowledge about the variables to include in the model. To address this, we propose the use of adaptive Lasso for variable selection and parameter estimation in both the selection and outcome submodels simultaneously in the absence of exclusion restrictions. By using the maximum likelihood estimator of the sample selection model, we constructed a loss function similar to the least squares regression problem up to a constant, and minimized its penalized version using an efficient algorithm. We show that the estimator, with proper choice of regularization parameter, is consistent and possesses the oracle properties. The method is compared to Lasso and adaptively weighted $$L_{1}$$ L 1 penalized Two-step method. We applied the methods to the well-known Ambulatory Expenditure Data.

The Comprehensive Effects of Sales Force Management: A Dynamic Structural Analysis of Selection, Compensation, and Training

This study provides a comprehensive model of an agent’s behavior in response to multiple sales management instruments, including compensation, recruiting/termination, and training. The model takes into account many of the key elements that constitute a realistic sales force setting: allocation of effort, forward-looking behavior, present bias, training effectiveness, and employee selection and attrition. By understanding how these elements jointly affect agents’ behavior, the study provides guidance on the optimal design of sales management policies. A field validation, by comparing counterfactual and actual outcomes under a new policy, attests to the accuracy of the model. The results demonstrate a tradeoff between adjusting fixed and variable pay; how sales training serves as an alternative to compensation; a potential drawback of hiring high-performing, experienced salespeople; and how utilizing a leave package leads to sales force restructuring. In addition, the study offers a key methodological contribution by providing formal identification conditions for hyperbolic time preference. The key to identification is that under a multiperiod nonlinear incentive system, an agent’s proximity to a goal affects only future payoffs in nonpecuniary benefit periods, providing exclusion restrictions on the current payoff. This paper was accepted by Matthew Shum, marketing.

Informal payments in Romanian health care system. A sample selection correction

This paper draws on economic theory, sociology and political science approaches to explain informal payments in the Romanian health care system. It estimates the likelihood of paying a bribe (informal payment) using a reduced health care demand equation in a probit model with sample selection correction. Social capital, as having a relationship with doctors, and the perception of the health care system, as corrupt, are found to influence the probability of making an informal payment. The likelihood of making an informal payment in the Romanian health care system is modelled using a maximum-likelihood probit estimation with sample selection correction. In the selection equation, reduced health care demand, self-perceived health status and being afraid of diseases are used as exclusion restrictions for identifying the parameters of the econometric model.

Identification and Estimation of Forward-Looking Behavior: The Case of Consumer Stockpiling

Understanding how forward-looking consumers respond to price promotions in storable goods markets is an important area of research in empirical marketing and industrial organization. In prior work, researchers have assumed that consumers in these markets are very forward-looking, and calibrated their weekly discount factors to levels around 0.9995. This calibration has been used because earlier research has assumed that a consumer’s storage cost is a continuous function of inventory, which rules out exclusion restrictions that can be used to identify the discount factor. We show that by properly modeling storage cost as a step function of inventory (because storage cost depends on the number of packages stored, instead of the actual amount of inventory), natural exclusion restrictions arise that allow for the discount factor to be point identified. In an application to a storable good category, we find that weekly discount factors are very heterogeneous across consumers, and are on average 0.71. We show through a counterfactual exercise that if one used a model that fixed the discount factor to be consistent with the standard calibrated value, one would overpredict the effect of increased promotional depth for a product on its quantity sold by 18% in the short term, and 15% in the long term.

Two-way exclusion restrictions in models with heterogeneous treatment effects

Summary In this paper, we propose a novel method to identify the conditional average treatment effect partial derivative (CATE-PD) in an environment in which the treatment is endogenous, the treatment effect is heterogeneous, the candidate 'instrumental variables' can be correlated with latent errors, and the treatment selection does not need to be (weakly) monotone. We show that CATE-PD is point-identified under mild conditions if two-way exclusion restrictions exist: (a) an outcome-exclusive variable, which affects the treatment but is excluded from the potential outcome equation, and (b) a treatment-exclusive variable, which affects the potential outcome but is excluded from the selection equation. We also propose an asymptotically normal two-step estimator and illustrate our method by investigating how the return to education varies across regions at different levels of development in China.

Microfinance and Moneylenders: Long-run Effects of MFIs on Informal Credit Market in Bangladesh

This paper provides evidence on the effects of microfinance competition on moneylender interest rates and households' dependence on informal credit. The views among practitioners diverge sharply: proponents claim that the MFI competition reduces both the moneylender interest rate and households' reliance on informal credit, while critics argue the opposite. Taking advantage of recent econometric approaches to address selection on unobservables without imposing standard exclusion restrictions, we find that the MFI competition does not reduce moneylender interest rates, partially repudiating the proponents. There is no perceptible effect at low levels of the MFI coverage, but when the MFI coverage is high enough, the moneylender interest rate increases significantly. In contrast, a household's dependence on informal credit goes down after becoming an MFI member, which contradicts part of the critic's argument. The evidence is consistent with models where either the MFIs or the moneylenders engage in cream skimming, and fixed costs are important in informal lending.