Jeremy T. Fox

IMPROVING THE NUMERICAL PERFORMANCE OF STATIC AND DYNAMIC AGGREGATE DISCRETE CHOICE RANDOM COEFFICIENTS DEMAND ESTIMATION

The widely used estimator of Berry, Levinsohn, and Pakes (1995 )p roduces estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks, and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLP’s estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward-looking demand models where the Bellman equation must also be solved repeatedly. Several Monte Carlo and real-data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization. For static BLP, the constrained optimization approach can be as much as ten to forty times faster for large-dimensional problems with many markets.

Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation

The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLPs estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward-looking demand models where Bellmans equation must also be solved repeatedly. Several Monte Carlo and real-data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization.

A Clinically Relevant Review of Hip Biomechanics

The hip is a complex anatomic structure composed of osseous, ligamentous, and muscular structures responsible for transferring the weight of the body from the axial skeleton into the lower extremities. This must be accomplished while allowing for dynamic loading during activities such as gait and balance. The evaluation of hip pain and periarticular pathology can be challenging because of the complex local anatomy and broad differential diagnosis. Recent advancements in the evaluation and surgical treatment of hip pathology have led to a renewed interest in the management of these disorders. An understanding of the basic biomechanical and kinematic function of the hip and the consequences of associated pathology can greatly assist the orthopaedic surgeon in appropriately diagnosing and treating these problems. In this review we discuss the basic biomechanical concepts of the native hip and surrounding structures and the changes experienced as a result of various pathologies including dysplasia, femoroacetabular impingement, labral injury, capsular laxity, hip instability, and articular cartilage injury. We will also discuss the clinical implications and surgical management of these pathologies and their role in restoring or preserving the native function of the hip joint.

Firm‐Size Wage Gaps, Job Responsibility, and Hierarchical Matching

I present the fact that wage gaps due to firm size increase with job responsibility. I use Swedish data to determine whether wage gaps increase with a direct measure of job responsibility, to compare the age patterns of the wage gaps for blue‐ and white‐collar workers, and to compare wages by job responsibility and spans of control. With U.S. data, I compare supervisory to nonsupervisory occupations and find that wage gaps increase with job responsibility for most occupational ladders. This fact is consistent with hierarchical matching models in which the larger number of subordinates amplifies managerial talent.

Identification in matching games

I study a many-to-many, two-sided, transferable-utility matching game. Consider data on matches or relationships between agents but not on the choice set of each agent. I investigate what economic parameters can be learned from data on equilibrium matches and agent characteristics. Features of a production function, which gives the surplus from a match, are nonparametrically identified. In particular, the ratios of complementarities from multiple pairs of inputs are identified. Also, the ordering of production levels is identified.

A simple estimator for the distribution of random coefficients

We propose a simple mixtures estimator for recovering the joint distribution of parameter heterogeneity in economic models, such as the random coefficients logit. The estimator is based on linear regression subject to linear inequality constraints, and is robust, easy to program, and computationally attractive compared to alternative estimators for random coefficient models. For complex structural models, one does not need to nest a solution to the economic model during optimization. We present a Monte Carlo study and an empirical application to dynamic programming discrete choice with a serially correlated unobserved state variable.

Reconfigurable Radios: A Possible Solution to Reduce Entry Costs in Wireless Phones

With advances in telecommunications, an increasing number of services rely on high data rate spectrum access. These critical services include banking, telemedicine, and exchange of technical information. As a result, spectrum resources are in ever-greater demand and the radio spectrum has become overly crowded. For efficient usage of spectrum, smart or cognitive radios are sought after. However, current wireless phones can only select a few specific bands. In this paper, we discuss the advantages of reconfigurable radios in not only increasing the efficiency of spectrum usage but also in potentially reducing the cost of wireless handsets and the barriers for new wireless service providers to enter the market. We review available technologies that make the implementation of reconfigurable radios possible and discuss technical challenges that need to be overcome before multistandard reconfigurable radios are put into practice. We also evaluate the ability of reconfigurable radios in reducing entry costs for new competitors in wireless service.

Unobserved Heterogeneity in Matching Games

Agents in two-sided matching games vary in characteristics that are unobservable in typical data on matching markets. We investigate the identification of the distribution of unobserved characteristics using data on who matches with whom. In full generality, we consider many-to-many matching and matching with trades. The distribution of match-specific unobservables cannot be fully recovered without information on unmatched agents, but the distribution of a combination of unobservables, which we call unobserved complementarities, can be identified. Using data on unmatched agents restores identification.

Reliability of measurements of clavicle shaft fracture shortening in adolescents.

Background: A relative indication for surgical treatment of midshaft clavicle fractures is shortening ≥2.0 cm. A standard method for determining shortening with routine clavicle radiographs has not been established. This study evaluated the interobserver and intraobserver reliability when measuring shortening of midshaft clavicle fractures in adolescents. Methods: We identified all clavicle radiographs of simple midshaft clavicle fractures in adolescents from 2006 to 2010. Thirty-two radiographs were chosen following a power analysis for 7 observers. Each film was measured twice by each evaluator using 2 separate methods. Method 1 was the evaluator’s method of choice to determine shortening on the digital radiographs. Method 2 was standardized. Intraclass correlation coefficient and confidence intervals (CI) were calculated to determine interrater reliability, and average differences between the 2 time points with 95% CI were calculated to determine intrarater reliability. Results: Interrater reliability for method 1 was 0.771 (95% CI, 0.655-0.865) and 0.743 (95% CI, 0.604-0.851) at the 2 time points for fair agreement. Interrater reliability for method 2 was 0.741 (95% CI, 0.629-0.842) and 0.685 (95% CI, 0.554-0.805) at the 2 time points, for fair and poor agreement, respectively. Neither method was statistically superior to the other. For method 1, the SD for the measurements averaged 3.1 mm. For method 2, the average SD was 3.0 mm. Intrarater reliability for method 1 was 2.62 mm average difference between the 2 time points (95% CI, 2.24-3.00), and for method 2 it was 3.34 mm average (95% CI, 2.88-3.80). Method 2 had a significantly greater difference at the 2 time points than method 1 (P=0.027). Conclusions: There is only fair agreement among observers when measuring the shortening of clavicle fractures in adolescents on digital clavicle radiographs by either method described. However, as the average difference among measurers was only 3 mm, this is unlikely to influence clinical decision making. A lack of standardization of measurement in previous studies on clavicle fracture treatment may not represent a significant problem. Level of Evidence: Level III diagnostic study.

Consolidation in the Wireless Phone Industry

The initial wireless phone industry in the United States had many competitors, but due to mergers and acquisitions the industry has become highly consolidated. This paper documents the history of the consolidation. More importantly, I use the geographic path of consolidation to distinguish whether consolidation has been motived by retail market power or efficiency explanations. One efficiency explanation is that consumers prefer national coverage areas. I use data on roaming agreements in the early cellular industry to analyze whether contracts can substitute for roaming agreements. Finally, in joint work with Patrick Bajari and Stephen Ryan we estimate the consumer valuation for national coverage areas using plan demand data.