Bayesian robustness of credible regions in the presence of nuisance parameters

The problem of finding the most robust γ-level credible region for the parameter of interest in the presence of a nuisance parameter, with respect to a class of ε-contaminated priors, is studied. The case of arbitrary con-taminations is first analyzed; it is proved that the most robust region for the parameter of interest is theγ-level highest marginal likelihood region (forγ ≥ 0.5). Then, the result is extended to any measurable (not necessarily one-to-one) function of the parameter. Finally, the case of contaminations assigning fixed probabilities to the sets of a partition of the parameter space is analyzed and a partial result is given.     

Random-Time Aggregation in Partial Adjustment Models

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortaçsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.     

Identification and Inference With Many Invalid Instruments

We study estimation and inference in settings where the interest is in the effect of a potentially endogenous regressor on some outcome. To address the endogeneity, we exploit the presence of additional variables. Like conventional instrumental variables, these variables are correlated with the endogenous regressor. However, unlike conventional instrumental variables, they also have direct effects on the outcome, and thus are “invalid” instruments. Our novel identifying assumption is that the direct effects of these invalid instruments are uncorrelated with the effects of the instruments on the endogenous regressor. We show that in this case the limited-information-maximum-likelihood (liml) estimator is no longer consistent, but that a modification of the bias-corrected two-stage-least-square (tsls) estimator is consistent. We also show that conventional tests for over-identifying restrictions, adapted to the many instruments setting, can be used to test for the presence of these direct effects. We recommend that empirical researchers carry out such tests and compare estimates based on liml and the modified version of bias-corrected tsls. We illustrate in the context of two applications that such practice can be illuminating, and that our novel identifying assumption has substantive empirical content.     

Bayesian semi-parametric analysis of Poisson change-point regression models: application to policy-making in Cali,Colombia

A Poisson regression model with an offset assumes a constant baseline rate after accounting for measured covariates, which may lead to biased estimates of coefficients in an inhomogeneous Poisson process. To correctly estimate the effect of time-dependent covariates, we propose a Poisson change-point regression model with an offset that allows a time-varying baseline rate. When the non-constant pattern of a log baseline rate is modeled with a non-parametric step function, the resulting semi-parametric model involves a model component of varying dimensions and thus requires a sophisticated varying-dimensional inference to obtain the correct estimates of model parameters of a fixed dimension. To fit the proposed varying-dimensional model, we devise a state-of-the-art Markov chain Monte Carlo-type algorithm based on partial collapse. The proposed model and methods are used to investigate the association between the daily homicide rates in Cali, Colombia, and the policies that restrict the hours during which the legal sale of alcoholic beverages is permitted. While simultaneously identifying the latent changes in the baseline homicide rate which correspond to the incidence of sociopolitical events, we explore the effect of policies governing the sale of alcohol on homicide rates and seek a policy that balances the economic and cultural dependencies on alcohol sales to the health of the public.     

Sample size for estimating a binomial proportion: comparison of different methods

The poor performance of the Wald method for constructing confidence intervals (CIs) for a binomial proportion has been demonstrated in a vast literature. The related problem of sample size determination needs to be updated and comparative studies are essential to understanding the performance of alternative methods. In this paper, the sample size is obtained for the Clopper–Pearson, Bayesian (Uniform and Jeffreys priors), Wilson, Agresti–Coull, Anscombe, and Wald methods. Two two-step procedures are used: one based on the expected length (EL) of the CI and another one on its first-order approximation. In the first step, all possible solutions that satisfy the optimal criterion are obtained. In the second step, a single solution is proposed according to a new criterion (e.g. highest coverage probability (CP)). In practice, it is expected a sample size reduction, therefore, we explore the behavior of the methods admitting 30% and 50% of losses. For all the methods, the ELs are inflated, as expected, but the coverage probabilities remain close to the original target (with few exceptions). It is not easy to suggest a method that is optimal throughout the range (0, 1) for p. Depending on whether the goal is to achieve CP approximately or above the nominal level different recommendations are made.     

Can We Still Learn Something From the Relationship Between Fertility and Mother’s Employment? Evidence From Developing Countries

In this work, I study the impact of fertility on mothers’ employment for a sample of developing countries. Using the event of multiple births as an instrumental variable (IV) for fertility, I find that having children has a negative impact on female employment. In addition, three types of heterogeneity are found. First, the magnitude of the impact depends on the birth at which the increase in fertility takes place. Second, the types of jobs affected by a fertility shock (multiple births) are jobs identified with a higher degree of informality, such as self-employment or unpaid jobs. Finally, the heterogeneity analysis reveals that an unexpected change in fertility is stronger at a higher education level of the mother and in urban areas.     

Testing the Personal Wellbeing Index on 12–16?Year-Old Adolescents in 3 Different Countries with 2 New Items

The 7-item adult version of the Personal Wellbeing scale (Cummins et al. Social Indic Res 64:159?C190, 2003) was administered to two samples of adolescents aged 12?C16 in Brazil (N?=?1,588) and Spain (N?=?2,900), and to a sample of adolescents aged 14?C16 in Chile (N?=?843). The results obtained were analyzed to determine its psychometric characteristics when used with adolescents in the three different countries and to check whether two additional items would improve its qualities. Results reveal that the new PWI-9 version worked well with the adolescents in the three countries, improving some of the qualities of the PWI-7. One of the added items, satisfaction with oneself, appears to be a major contributor to unique explained variance when regressed on the single-item of overall life satisfaction (OLS). The model we present using structural equations shows good fit statistics for the factor structure, with both 7 and 9 items. Separate in-country analyses demonstrate that cultural context has a strong influence on correlations and saturations between the studied variables and also on the explained variance. Probably related to this fact, the Model fit structure is good in Brazil (with a low PWI variance accounted for by its predictors) and Spain (medium), but rather modest in Chile, where data show a high proportion of the PWI variance accounted for by its predictors. However, a multi-group factor analysis among the three countries restricting saturations to 1 in each country in order to make data comparable across countries still show a good fit of the proposed model for both PWI-7 and PWI-9.     

Income Inequality Indices Interpreted as Measures of Relative Deprivation/Satisfaction

This paper considers different ways of making comparisons between individuals in terms of deprivation and/or satisfaction. This allows the Gini index, the Bonferroni index and the De Vergottini index to be interpreted as social deprivation measures as well as social satisfaction measures. The inequality measures that belong to the ?? family, or linear combinations of them, are obtained when using different weighting schemes to average the deprivation and satisfaction associated with each income level. Particularly, the generalised Gini indices (Yitzhaki, Int Econ Rev 24:617?C628 in 1983), the indices proposed by Aaberge (J Econ Inequal 5(3):305?C322, 2007) or those proposed by Imedio-Olmedo et al. (J Public Econ Theory 13(1):97?C124, 2011) can be used to evaluate social deprivation or social satisfaction in an income distribution.     

Copper mining productivity: Lessons from Chile

Chile represents almost one third of the world’s copper production. Mining is one of the main industries that contributes to our country’s development with resources and is globally recognized. Due to the end of the commodity cycle, improving productivity will be a key variable in mining performance in incoming years. This paper studies mining productivity in Chile by relying on two indicators: measure of the total factor productivity (TFP) using the traditional Solow methodology, and labor productivity. Since 2000, we found a decrease in TFP, explained mainly by the participation of capital as well as diverse factor adjustments to labor and capital inputs. Average labor productivity also decreases 42% from 1999 to 2010, a decrease explained by four determinants: real mining wages, electricity prices, copper prices and mineral grade. Since 2010, average labor productivity has increased 30%, and there is also an opportunity for additional improvement by reducing energy costs as well as by aligning productivity and labor performances.     

A flexible cure rate model based on the polylogarithm distribution

Models for dealing with survival data in the presence of a cured fraction of individuals have attracted the attention of many researchers and practitioners in recent years. In this paper, we propose a cure rate model under the competing risks scenario. For the number of causes that can lead to the event of interest, we assume the polylogarithm distribution. The model is flexible in the sense it encompasses some well-known models, which can be tested using large sample test statistics applied to nested models. Maximum-likelihood estimation based on the EM algorithm and hypothesis testing are investigated. Results of simulation studies designed to gauge the performance of the estimation method and of two test statistics are reported. The methodology is applied in the analysis of a data set.