Browsing by Author "Khan, Shakeeb"

This dissertation consists of three chapters relating to

identification and inference in dynamic microeconometric models

including dynamic discrete games with many players, dynamic games with

discrete and continuous choices, and semiparametric binary choice and

duration panel data models.

The first chapter provides a framework for estimating large-scale

dynamic discrete choice models (both single- and multi-agent models)

in continuous time. The advantage of working in continuous time is

that state changes occur sequentially, rather than simultaneously,

avoiding a substantial curse of dimensionality that arises in

multi-agent settings. Eliminating this computational bottleneck is

the key to providing a seamless link between estimating the model and

performing post-estimation counterfactuals. While recently developed

two-step estimation techniques have made it possible to estimate

large-scale problems, solving for equilibria remains computationally

challenging. In many cases, the models that applied researchers

estimate do not match the models that are then used to perform

counterfactuals. By modeling decisions in continuous time, we are able

to take advantage of the recent advances in estimation while

preserving a tight link between estimation and policy experiments. We

also consider estimation in situations with imperfectly sampled data,

such as when we do not observe the decision not to move, or when data

is aggregated over time, such as when only discrete-time data are

available at regularly spaced intervals. We illustrate the power of

our framework using several large-scale Monte Carlo experiments.

The second chapter considers semiparametric panel data binary choice

and duration models with fixed effects. Such models are point

identified when at least one regressor has full support on the real

line. It is common in practice, however, to have only discrete or

continuous, but possibly bounded, regressors. We focus on

identification, estimation, and inference for the identified set in

such cases, when the parameters of interest may only be partially

identified. We develop a set of general results for

criterion-function-based estimation and inference in partially

identified models which can be applied to both regular and irregular

models. We apply our general results first to a fixed effects binary

choice panel data model where we obtain a sharp characterization of

the identified set and propose a consistent set estimator,

establishing its rate of convergence under different conditions.

Rates arbitrarily close to n-1/3 are

possible when a continuous, but possibly bounded, regressor is

present. When all regressors are discrete the estimates converge

arbitrarily fast to the identified set. We also propose a

subsampling-based procedure for constructing confidence regions in the

models we consider. Finally, we carry out a series of Monte Carlo

experiments to illustrate and evaluate the proposed procedures. We

also consider extensions to other fixed effects panel data models such

as binary choice models with lagged dependent variables and duration

models.

The third chapter considers nonparametric identification of dynamic

games of incomplete information in which players make both discrete

and continuous choices. Such models are commonly used in applied work

in industrial organization where, for example, firms make discrete

entry and exit decisions followed by continuous investment decisions.

We first review existing identification results for single agent

dynamic discrete choice models before turning to single-agent models

with an additional continuous choice variable and finally to

multi-agent models with both discrete and continuous choices. We

provide conditions for nonparametric identification of the utility

function in both cases.

Social networks affect a broad class of economic activities. The three chapters of my dissertation study social networks from two different lines of research. The first line of research examines the formation process of a social network. In Chapter 2, I introduce a new identification strategy and a semiparametric estimator for the formation process of an undirected network with additive agent-specific fixed effects. In Chapter 3, I analyze the formation process of a directed network with a broader type of unobserved heterogeneity. This heterogeneity is modeled as interactive fixed effects. The second line of my research complements the first approach by exploring the influence that network structures have on different economic activities. In Chapter 4, I recover the endogenous and exogenous social effects in a high-dimensional panel data model with an unobserved network structure.

The dissertation consists of three essays. The first essay describes and estimates the model of bidding on eBay. Internet auctions (such as eBay) differ from the traditional auction format in that participants 1) typically face a choice over several simultaneous auctions and 2) often have limited information about rival bidders. Since existing economic models do not account for these features of the bidding environment, it should not be surprising that even casual empiricism reveals a sharp discrepancy between the predictions of existing theory and the actual behavior of bidders. In this paper, I show that the presence of multiple, contemporaneous auctions for similar items coupled with uncertainty regarding rival entry can explain both features. I analyze these features in a continuous-time stochastic auction model with endogenous entry, in which bidder types are differentiated by their initial information regarding the entry process. Empirical estimates using eBay auctions of pop-music CDs confirm my theoretical prediction that the rate of entry depends on price. I then test my model against alternative explanations of observed bidding behavior using a detailed field experiment.

The second essay is on empirical analysis of executive compensation in the continuous-time environment. In this essay, I develop a methodology for the identification and non-parametric estimation of a continuous-time principal-agent model. My framework extends the existing literature on optimal dynamic contracts by allowing for the presence of unobserved state variables. To accommodate such heterogeneity, I develop an estimation method based on numerically solving for the optimal non-linear manager's response to the restrictions of the contract. To demonstrate this feature, I apply my methodology to executive contracts from the retail apparel industry.

The third essay provides a tractable methodology for the construction and structural estimation of continuous time dynamic models. The specific class of models covered by my framework includes competitive dynamic games where there are no direct spillovers between objective functions of players. I develop an estimation methodology based on the properties of the equilibrium of the model. The methodology that I design can be applied to welfare and revenue analysis of large dynamic models. As an example, I compute the revenue and welfare gains for a counter-factual exercise in which the eBay auction website changes the format of its auctions from second-price to a flexible ending.

My dissertation contains three chapters which develop new identification and estimation methods for multinomial choice models in both cross-sectional and panel

data settings. In the first chapter, I propose a new semiparametric identification and

estimation approach to multinomial choice models using cross-sectional data. The approach relies on the rank-order property proposed by Manski (1975) and employed

by recent studies such as Fox (2007) and Yan (2013), which is a distribution-free restriction

on the random utility framework underlying a multinomial choice model.

From the rank-order property, a novel reparameterization provides a multivariate

nonlinear least squares (population) criterion identifying the structural parameters.

This identification result then motivates a sieve-based estimation procedure, which

is the first in the semiparametric literature to allow joint estimation of regression

coefficients and reduced-form parameters such as choice probabilities and marginal

effects. Asymptotic properties of two functional estimators are developed. A Monte

Carlo study indicates that these functional estimators perform well in finite samples.

I illustrate the implementation of the estimation procedure via estimating a model

of college major choice using UCOP data of 1998-2003. As extensions, I also propose

estimators for the model using a choice-based sample and the model with ranking

information.

The estimation problem in the second chapter is motivated by the local nonlinear

least squares (LNLS) estimation of preference parameters (regression coefficients) in the multinomial choice model under uncertainty in which the decision rule is affected

by conditional expectations. I propose a two-stage LNLS estimation procedure for

the preference parameters. In the first stage, conditional expectations are estimated

nonparametrically. Then, in the second stage, the preference parameters are estimated

by the LNLS estimator of multinomial choice model, using the choice data

and first-stage estimates. The two-stage estimator has the advantage of being easily

implementable using standard software packages. In this chapter, I establish consistency

of the two-stage LNLS estimator. Monte Carlo simulation results illustrate

that the proposed two-stage LNLS estimator performs well in finite sample.

The third chapter is a part of a co-authored project with Shakeeb Khan and Elie

Tamer. In this work, we consider identification, estimation, and inference on regression

coefficients in semiparametric multinomial response models. Our identification result is constructive and estimation is based on a localized rank objective function,

loosely analogous to that used in Abrevaya et al. (2010). We show this achieves sharp

identification which is in contrast to existing procedures in the literature such as, for

example, Ahn et al. (2015). In that sense, our procedure is adaptive (Khan and

Tamer (2009)) in the sense that it provides an estimator of the sharp set when point identification does not hold, and a consistent point estimator when it does. Furthermore,

our rank procedure extends to panel data settings for inference in models

with fixed effects, including dynamic panel models with lagged dependent variables

as covariates. A simulation study establishes adequate nite sample properties of

our new procedures.

Extremal quantile index is a concept that the quantile index will drift to zero (or one)

as the sample size increases. The three chapters of my dissertation consists of three

applications of this concept in three distinct econometric problems. In Chapter 2, I

use the concept of extremal quantile index to derive new asymptotic properties and

inference method for quantile treatment effect estimators when the quantile index

of interest is close to zero. In Chapter 3, I rely on the concept of extremal quantile

index to achieve identification at infinity of the sample selection models and propose

a new inference method. Last, in Chapter 4, I use the concept of extremal quantile

index to define an asymptotic trimming scheme which can be used to control the

convergence rate of the estimator of the intercept of binary response models.