On dynamic stochastic approximation

The behaviour of the dynamic stochastic approximation algorithm suggested by DUPA[Cbreve] [4, 5] is examined under various conditions. Essentially, convergence in q.m. is proved and the rate of convergence is obtained for three classes of regression functions. Necessary and sufficient conditions are established for the convergence in q.m. of the algorithm in terms of the algorithm parameters for the stationary (nondynamic) case.     

Controlling type 1 error rate for sequential,bioequivalence studies with crossover designs

Sample size reestimation in a crossover, bioequivalence study can be a useful adaptive design tool, particularly when the intrasubject variability of the drug formulation under investigation is not well understood. When sample size reestimation is done based on an interim estimate of the intrasubject variability and bioequivalence is tested using the pooled estimate of intrasubject variability, type 1 error inflation will occur. Type 1 error inflation is caused by the pooled estimate being a biased estimator of the intrasubject variability. The type 1 error inflation and bias of the pooled estimator of variability are well characterized in the setting of a two‐arm, parallel study. The purpose of this work is to extend this characterization to the setting of a crossover, bioequivalence study with sample size reestimation and to propose an estimator of the intrasubject variability that will prevent type 1 error inflation.     

EARLY EVIDENCE ON RECREATIONAL MARIJUANA LEGALIZATION AND TRAFFIC FATALITIES

Over the last few years, marijuana has become legally available for recreational use to roughly a quarter of Americans. Policy makers have long expressed concerns about the substantial external costs of alcohol, and similar costs could come with the liberalization of marijuana policy. Indeed, the fraction of fatal accidents in which at least one driver tested positive for tetrahydrocannabinol has increased nationwide by an average of 10% from 2013 to 2016. For Colorado and Washington, both of which legalized marijuana in 2014, these increases were 92% and 28%, respectively. However, identifying a causal effect is difficult due to the presence of significant confounding factors. We test for a causal effect of marijuana legalization on traffic fatalities in Colorado and Washington with a synthetic control approach using records on fatal traffic accidents from 2000 to 2016. We find the synthetic control groups saw similar changes in marijuana-related, alcohol-related, and overall traffic fatality rates despite not legalizing recreational marijuana. (JEL K42, I12, I18)     

ADHD and Brain Anatomy: What Do Academic Textbooks Used in the Netherlands Tell Students?

Studies of brain size of children classified with ADHD appear to reveal smaller brains when compared to ‘normal’ children. Yet, what does this mean? Even with the use of rigorously screened case and control groups, these studies show only small, average group differences between children with and without an ADHD classification. However, academic textbooks used in the Netherlands often portray individual children with an ADHD classification as having a different, malfunctioning brain that necessitates medical intervention. This conceptualisation of ADHD might serve professional interests, but not necessarily the interests of children.     

Bounds to Memory Loss

If we express our knowledge in sentences, we will find that these sentences are linked in complex patterns governed by our observations and our inferences from these observations. These inferences are to a large extent driven by logical rules. We ask whether the structure logic imposes on our knowledge restricts what we forget and what we remember. The model is a two period S5 logic. In this logic, we propose a memory loss operator: the agent forgets a sentence pif and only if he knows pat time 1 and he does not know pat time 2. Equipped with the operator, we prove theorems on the relation between knowledge and memory loss. The main results point to classes of formulas that an agent cannot forget, and classes of formulas he must forget. A desirable feature is that most results hold in the S4 logic. The results illustrate bounds to memory loss, and thus to bounded rationality. We apply the model to single-agent conventions: conventions made between an agent and himself.     

Sample Splitting and Threshold Estimation

Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously‐distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are super‐consistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either cross‐section or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates (the threshold and the regression slopes) is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of Durlauf and Johnson (1995).     

Seeking Closure: Competition in Complementary Markets*

When offering a product that has a complementary product in a different market, a firm must consider the interdependence between the complementary products as well as the competition within markets. If the firm participates in both markets, the balancing act becomes even more challenging. This article provides insights about strategies in this latter setting: when should the firm seek to keep its products closed to competing complementary products, and when would the firm be better off by accepting a common standard? To address these questions, we employ standard game theoretic analysis to a simple spatial model that captures aspects of both intermarket externalities and intramarket competition. We find that if a firm participates in both markets and chooses a closed standard, it achieves lower profits compared to an open standard, but gains greater market share. Surprisingly, we find that customers are better off when standards are kept closed.     

Rate of Foot-and-Mouth Disease Virus Transmission by Carriers Quantified from Experimental Data

Upon infection with foot-and-mouth disease virus (FMDV) a considerable number of animals become carriers of the virus. These carriers are considered to be a risk for new outbreaks, but the rate at which these animals can transmit the infection has not been quantified. An analysis was carried out using data from previously published experiments in order to quantify the transmission rate parameter β of FMDV infection from carriers to susceptible animals. The parameter β was estimated at 0.0256 (likelihood-based confidence interval: 0.008–0.059) infections per carrier per month. Moreover, analysis of published experimental data indicates that the proportion of FMDV carriers decreases at a rate of 0.115 per month. Both parameters obtained from this study are useful for quantitative risk analyses of the trade of animals from FMDV-infected areas or the lifting of vaccination programs.