Learning from Incredible Commitments: Evolution and Impact of Bilateral Investment Treaties

Ostensibly, BITs are the ideal international treaty. First, until just recently, they almost uniformly came with explicit dispute resolution mechanisms through which countries could face real costs for violation (Montt 2009). Second, the signing, ratification, and violation of them are easily accessible public knowledge. Thus countries presumably would face reputational costs for violating these agreements. Yet, these compliance devices have not dissuaded states from violating these agreements. Even more interestingly, in recent years, both developed and developing countries have moved towards modifying the investor-friendly provisions of these agreements. These deviations from the expectations of the credible commitment argument raise important questions about the field's assumptions regarding the ability of international treaties with commitment devices to effectively constrain state behavior.

Prenegotiation public commitment in domestic and international bargaining

We use a formal bargaining model to examine why, in many domestic and international bargaining situations, one or both negotiators make public statements in front of their constituents committing themselves to obtaining certain benefits in the negotiations. We find that making public commitments provides bargaining leverage, when backing down from such commitments carries domestic political costs. However, when the two negotiators face fairly similar costs for violating a public commitment, a prisoner's dilemma is created in which both sides make high public demands which cannot be satisfied, and both negotiators would be better off if they could commit to not making public demands. However, making a public demand is a dominant strategy for each negotiator, and this leads to a suboptimal outcome. Escaping this prisoner's dilemma provides a rationale for secret negotiations. Testable hypotheses are derived from the nature of the commitments and agreements made in equilibrium.

Association between DNA damage response and repair genes and risk of invasive serous ovarian cancer.

BACKGROUND: We analyzed the association between 53 genes related to DNA repair and p53-mediated damage response and serous ovarian cancer risk using case-control data from the North Carolina Ovarian Cancer Study (NCOCS), a population-based, case-control study. METHODS/PRINCIPAL FINDINGS: The analysis was restricted to 364 invasive serous ovarian cancer cases and 761 controls of white, non-Hispanic race. Statistical analysis was two staged: a screen using marginal Bayes factors (BFs) for 484 SNPs and a modeling stage in which we calculated multivariate adjusted posterior probabilities of association for 77 SNPs that passed the screen. These probabilities were conditional on subject age at diagnosis/interview, batch, a DNA quality metric and genotypes of other SNPs and allowed for uncertainty in the genetic parameterizations of the SNPs and number of associated SNPs. Six SNPs had Bayes factors greater than 10 in favor of an association with invasive serous ovarian cancer. These included rs5762746 (median OR(odds ratio)(per allele) = 0.66; 95% credible interval (CI) = 0.44-1.00) and rs6005835 (median OR(per allele) = 0.69; 95% CI = 0.53-0.91) in CHEK2, rs2078486 (median OR(per allele) = 1.65; 95% CI = 1.21-2.25) and rs12951053 (median OR(per allele) = 1.65; 95% CI = 1.20-2.26) in TP53, rs411697 (median OR (rare homozygote) = 0.53; 95% CI = 0.35 - 0.79) in BACH1 and rs10131 (median OR( rare homozygote) = not estimable) in LIG4. The six most highly associated SNPs are either predicted to be functionally significant or are in LD with such a variant. The variants in TP53 were confirmed to be associated in a large follow-up study. CONCLUSIONS/SIGNIFICANCE: Based on our findings, further follow-up of the DNA repair and response pathways in a larger dataset is warranted to confirm these results.

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.

Three Essays on the Effects of Donor Supplied Contraceptives on Fertility, Usage, and Attitudes

After the 2012 London Summit on Family Planning, there have been major strides in advancing the family planning agenda for low and middle-income countries worldwide. Much of the existing infrastructure and funding for family planning access is in the form of supplying free contraceptives to countries. While the average yearly value of donations since 2000 was over 170 million dollars for contraceptives procured for developing countries, an ongoing debate in the empirical literature is whether increases in contraceptive access and supply drive declines in fertility (UNFPA 2014).

This dissertation explores the fertility and behavioral effects of an increase in contraceptive supply donated to Zambia. Zambia, a high-fertility developing country, receives over 80 percent of its contraceptives from multilateral donors and aid agencies. Most contraceptives are donated and provided to women for free at government clinics (DELIVER 2015). I chose Zambia as a case study to measure the relationship between contraceptive supply and fertility because of two donor-driven events that led to an increase in both the quantity and frequency of contraceptives starting in 2008 (UNFPA 2014). Donations increased because donors and the Zambian government started a systematic method of forecasting contraceptive need on December 2007, and the Mexico City Policy was lifted in January 2009.

In Chapter 1, I investigate whether a large change in quantity and frequency of donated contraceptives affected fertility, using available data on contraceptive donations to Zambia, and birth records from the 2007 and 2013 Demographic and Health Surveys. I use a difference-in-difference framework to estimate the fertility effects of a supply chain improvement program that started in 2011, and was designed to ensure more regularity of contraceptive supply. The increase in total contraceptive supply after the Mexico City Policy was rescinded is associated with a 12 percent reduction in fertility relative to the before period, after controlling for demographic characteristics and time controls. There is evidence that a supply chain improvement program led to significant fertility declines for regions that received the program after the Mexico City Policy was rescinded.

In Chapter 2, I explore the effects of the large increase in donated contraceptives on modern contraceptive uptake. According to the 2007 and 2013 Demographic and Health Surveys, there was a dramatic increase in current use of injectables, implants, and IUDs. Simultaneously, declines occurred in usage of condoms, lactational amenorrhea method (LAM), and traditional methods. In this chapter, I estimate the effect of the increase in donations on uptake, composition of contraceptive usage, and usage of methods based on distance to contraceptive access points. The results show the post-2007 period is associated with an increase in usage of injectables and the pill among women living further away from access points.

In Chapter 3, I explore attitudes towards the contraceptive supply system, and identify areas for improvement, based on qualitative interviews with 14 experts and 61 Zambian users and non-users of contraceptives. The interviews uncover systemic barriers that prevent women from consistently accessing methods, and individual barriers that exacerbate the deficiencies in supply chain procedures. I find that 39 out of 61 women interviewed, both users and non-users, had personal experiences with stock out. The qualitative results suggest that the increase in contraceptives brought to the country after 2007 may have not contributed to as large of a decline in fertility because of bottlenecks in the supply chain, and problems in maintaining stock levels at clinics. I end the chapter with a series of four recommendations for improvements in the supply chain going forward, in light of recent commitments by the Zambian government during the 2012 London Summit on Family Planning.

The Effect of Reputation Shocks to Rating Agencies on Corporate Disclosures

This paper explores the effect of credit rating agency’s (CRA) reputation on the discretionary disclosures of corporate bond issuers. Academics, practitioners, and regulators disagree on the informational role played by major CRAs and the usefulness of credit ratings in influencing investors’ perception of the credit risk of bond issuers. Using management earnings forecasts as a measure of discretionary disclosure, I find that investors demand more (less) disclosure from bond issuers when the ratings become less (more) credible. In addition, using content analytics, I find that bond issuers disclose more qualitative information during periods of low CRA reputation to aid investors better assess credit risk. That the corporate managers alter their voluntary disclosure in response to CRA reputation shocks is consistent with credit ratings providing incremental information to investors and reducing adverse selection in lending markets. Overall, my findings suggest that managers rely on voluntary disclosure as a credible mechanism to reduce information asymmetry in bond markets.