Essays on Job Search and Labor Market Dynamics

This dissertation consists of three separate essays on job search and labor market dynamics. In the first essay, “The Impact of Labor Market Conditions on Job Creation: Evidence from Firm Level Data”, I study how much changes in labor market conditions reduce employment fluctuations over the business cycle. Changes in labor market conditions make hiring more expensive during expansions and cheaper during recessions, creating counter-cyclical incentives for job creation. I estimate firm level elasticities of labor demand with respect to changes in labor market conditions, considering two margins: changes in labor market tightness and changes in wages. Using employer-employee matched data from Brazil, I find that all firms are more sensitive to changes in wages rather than labor market tightness, and there is substantial heterogeneity in labor demand elasticity across regions. Based on these results, I demonstrate that changes in labor market conditions reduce the variance of employment growth over the business cycle by 20% in a median region, and this effect is equally driven by changes along each margin. Moreover, I show that the magnitude of the effect of labor market conditions on employment growth can be significantly affected by economic policy. In particular, I document that the rapid growth of the national minimum wages in Brazil in 1997-2010 amplified the impact of the change in labor market conditions during local expansions and diminished this impact during local recessions.

In the second essay, “A Framework for Estimating Persistence of Local Labor

Demand Shocks”, I propose a decomposition which allows me to study the persistence of local labor demand shocks. Persistence of labor demand shocks varies across industries, and the incidence of shocks in a region depends on the regional industrial composition. As a result, less diverse regions are more likely to experience deeper shocks, but not necessarily more long lasting shocks. Building on this idea, I propose a decomposition of local labor demand shocks into idiosyncratic location shocks and nationwide industry shocks and estimate the variance and the persistence of these shocks using the Quarterly Census of Employment and Wages (QCEW) in 1990-2013.

In the third essay, “Conditional Choice Probability Estimation of Continuous- Time Job Search Models”, co-authored with Peter Arcidiacono and Arnaud Maurel, we propose a novel, computationally feasible method of estimating non-stationary job search models. Non-stationary job search models arise in many applications, where policy change can be anticipated by the workers. The most prominent example of such policy is the expiration of unemployment benefits. However, estimating these models still poses a considerable computational challenge, because of the need to solve a differential equation numerically at each step of the optimization routine. We overcome this challenge by adopting conditional choice probability methods, widely used in dynamic discrete choice literature, to job search models and show how the hazard rate out of unemployment and the distribution of the accepted wages, which can be estimated in many datasets, can be used to infer the value of unemployment. We demonstrate how to apply our method by analyzing the effect of the unemployment benefit expiration on duration of unemployment using the data from the Survey of Income and Program Participation (SIPP) in 1996-2007.

Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Relative growth of the limbs and trunk in sifakas: heterochronic, ecological, and functional considerations.

Limb, trunk, and body weight measurements were obtained for growth series of Milne-Edwards's diademed sifaka, Propithecus diadema edwardsi, and the golden-crowned sifaka, Propithecus tattersalli. Similar measures were obtained also for primarily adults of two subspecies of the western sifaka: Propithecus verreauxi coquereli, Coquerel's sifaka, and Propithecus verreauxi verreauxi, Verreaux's sifaka. Ontogenetic series for the larger-bodied P. d. edwardsi and the smaller-bodied P. tattersalli were compared to evaluate whether species-level differences in body proportions result from the differential extension of common patterns of relative growth. In bivariate plots, both subspecies of P. verreauxi were included to examine whether these taxa also lie along a growth trajectory common to all sifakas. Analyses of the data indicate that postcranial proportions for sifakas are ontogenetically scaled, much as demonstrated previously with cranial dimensions for all three species (Ravosa, 1992). As such, P. d. edwardsi apparently develops larger overall size primarily by growing at a faster rate, but not for a longer duration of time, than P. tattersalli and P. verreauxi; this is similar to results based on cranial data. A consideration of Malagasy lemur ecology suggests that regional differences in forage quality and resource availability have strongly influenced the evolutionary development of body-size variation in sifakas. On one hand, the rainforest environment of P. d. edwardsi imposes greater selective pressures for larger body size than the dry-forest environment of P. tattersalli and P. v. coquereli, or the semi-arid climate of P. v. verreauxi. On the other hand, as progressively smaller-bodied adult sifakas are located in the east, west, and northwest, this apparently supports suggestions that adult body size is set by dry-season constraints on food quality and distribution (i.e., smaller taxa are located in more seasonal habitats such as the west and northeast). Moreover, the fact that body-size differentiation occurs primarily via differences in growth rate is also due apparently to differences in resource seasonality (and juvenile mortality risk in turn) between the eastern rainforest and the more temperate northeast and west. Most scaling coefficients for both arm and leg growth range from slight negative allometry to slight positive allometry. Given the low intermembral index for sifakas, which is also an adaptation for propulsive hindlimb-dominated jumping, this suggests that differences in adult limb proportions are largely set prenatally rather than being achieved via higher rates of postnatal hindlimb growth.(ABSTRACT TRUNCATED AT 400 WORDS)

Mid-term results and factors affecting outcome of a metal-backed unicompartmental knee design: a case series.

BACKGROUND: Controversies exist regarding the indications for unicompartmental knee arthroplasty. The objective of this study is to report the mid-term results and examine predictors of failure in a metal-backed unicompartmental knee arthroplasty design. METHODS: At a mean follow-up of 60 months, 80 medial unicompartmental knee arthroplasties (68 patients) were evaluated. Implant survivorship was analyzed using Kaplan-Meier method. The Knee Society objective and functional scores and radiographic characteristics were compared before surgery and at final follow-up. A Cox proportional hazard model was used to examine the association of patient's age, gender, obesity (body mass index > 30 kg/m2), diagnosis, Knee Society scores and patella arthrosis with failure. RESULTS: There were 9 failures during the follow up. The mean Knee Society objective and functional scores were respectively 49 and 48 points preoperatively and 95 and 92 points postoperatively. The survival rate was 92% at 5 years and 84% at 10 years. The mean age was younger in the failure group than the non-failure group (p < 0.01). However, none of the factors assessed was independently associated with failure based on the results from the Cox proportional hazard model. CONCLUSION: Gender, pre-operative diagnosis, preoperative objective and functional scores and patellar osteophytes were not independent predictors of failure of unicompartmental knee implants, although high body mass index trended toward significance. The findings suggest that the standard criteria for UKA may be expanded without compromising the outcomes, although caution may be warranted in patients with very high body mass index pending additional data to confirm our results. LEVEL OF EVIDENCE: IV.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

High-speed label-free functional photoacoustic microscopy of mouse brain in action.

We present fast functional photoacoustic microscopy (PAM) for three-dimensional high-resolution, high-speed imaging of the mouse brain, complementary to other imaging modalities. We implemented a single-wavelength pulse-width-based method with a one-dimensional imaging rate of 100 kHz to image blood oxygenation with capillary-level resolution. We applied PAM to image the vascular morphology, blood oxygenation, blood flow and oxygen metabolism in both resting and stimulated states in the mouse brain.