Essays in Structural Estimation of Multidimensional Screening Models

Open Access
Aryal, Gaurab
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
June 16, 2010
Committee Members:
  • Isabelle Perrigne And Quang Vuong, Dissertation Advisor
  • Isabelle Perrigne, Committee Chair
  • Quang Vuong, Committee Chair
  • Vijay Krishna, Committee Member
  • Lisa Lipowski Posey, Committee Member
  • Multidimensional Screening
  • Nonlinear Pricing
  • Structural Estimation
Chapter 1: Nonparametric Identification of Insurance Models with Multidimensional Screening (with Isabelle Perrigne and Quang Vuong) This chapter studies the identification of an insurance model with multidimensional screening, where insurees are characterized by risk and risk aversion. The model is solved using the concept of certainty equivalence under constant absolute risk aversion and an unspecified joint distribution of risk and risk aversion. The paper then analyzes how data availability constraints identification under four data scenarios from the ideal situation to a more realistic one. The observed number of accidents for each insuree plays a key role to identify the model. In a first part, we consider the case of a continuum of coverages offered to each insuree whether the damage distribution is fully observed or truncated. Truncation arises from that an insuree files a claim only when the accident involves damage above the deductible. Despite bunching due to multidimensional screening, we show that the joint distribution of risk and risk aversion is identified. In a second part, we consider the case of a finite number of coverages offered to each insuree. When the full damage distribution is observed, we show that despite additional pooling due to the finite number of contracts, the joint distribution of risk and risk aversion is identified under a full support assumption and a conditional independence assumption involving the car characteristics. When the damage distribution is truncated, the joint distribution is identified up to the probability that the damage is above the deductible. In a third part, we derive the restrictions imposed by the model on observables for the fourth scenario. We also propose several identification strategies for the damage probability at the deductible. These identification results are further exploited in a companion paper developing an estimation method with an application to insurance data. Chapter 2: Nonidentification of Insurance Model with Probability of Accident (with Isabelle Perrigne and Quang Vuong) In contrast to Aryal, Perrigne and Vuong (2009), this note shows that in an insurance model with multidimensional screening when only information on whether the insuree has been involved in some accident is available, the joint distribution of risk and risk aversion is not identified. Chapter 3: Competition and Nonlinear Pricing in Yellow Pages (with Yao Huang) This chapter proposes a structural framework to analyze the nonlinear pricing strategies of two yellow page-advertising publishers. The data collected from the Yellow Page Association and the phone books suggest that the utility publisher is a leader in the market. Therefore, we consider a Stackelberg duopoly model of nonlinear pricing in which firms buying advertising are characterized by a bi-dimensional vector of tastes for the two directories. The model and the econometric specification incorporate the features observed in the data such as the quadratic price schedules and a basic free advertisement offered to all firms by both publishers. Empirical results show substantial heterogeneity among firms' willingness to pay. The estimated model is used to assess the welfare loss due to (i) asymmetric information, (ii) a merger between the two publishers and (iii) withdrawal of the non-utility publisher from the market.