On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992 ), is a simulation-based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.     

Kenya's tourist industry and global production networks: gender,race and inequality

In this article, I consider the position of gender and race in the tourism global production network in Kenya. To address a gap in scholarship on global production networks, I explore the racial and gender characteristics evident in functionally upgraded national tour operators and socially upgraded workers and community members around the Maasai Mara National Reserve. The main findings address the relation of race and gender to disarticulation practices identified in ‘societal’, ‘network’ and ‘territorial’ forms of embeddedness supported by racial and gender representations of skill capabilities and tourist desires. These practices and representations support a production network symbolized by whites, Kenyan‐Asians and expatriates in the highest value segments and jobs, and indigenous African, Maasai and female workers in the lowest value positions. The findings highlight how disarticulation in economic and social upgrading is a gendered and racial process that perpetuates social difference and hierarchy.     

INCIDENCE AND CONSEQUENCES OF RISK‐TAKING BEHAVIOR IN TOURNAMENTS—EVIDENCE FROM THE NBA

We empirically explore the relevance and efficiency of risk‐taking behavior in tournaments. We use data from the National Basketball Association (NBA) and measure risk‐taking by the fraction of three‐point shots in basketball games. We examine how point differences between teams during games affect their subsequent risk‐taking behavior. It is found that teams that are trailing are more likely to increase their use of three‐point shots. We additionally analyze the consequences of this change in behavior. Enhanced risk‐taking is inefficient in the vast majority of cases and is only beneficial if a team is trailing by a rather large margin. We discuss possible explanations for these decision errors. (JEL M5, D81, J30)     

The Fletcher Report 1930: A Historical Case Study of Contested Black Mixed Heritage Britishness

Abstract  This article examines a controversial report that focused negatively on mixed heritage children born and raised in the city of Liverpool. The official title was: Report on an Investigation into the Colour Problem in Liverpool and other ports . The social researcher was Muriel E. Fletcher, who had been trained in the Liverpool School of Social Science at The University of Liverpool in the early 1920s. The report was published in 1930 amid controversy for its openly stigmatizing content of children and mixed heritage families of African and European origin. It could be deemed the official outset in defining Liverpool's 'half castes' as a problem and blight to the "British way of life" in the city.     

Using a Markov Chain to Construct a Tractable Approximation of an Intractable Probability Distribution

Abstract.  Let π denote an intractable probability distribution that we would like to explore. Suppose that we have a positive recurrent, irreducible Markov chain that satisfies a minorization condition and has π as its invariant measure. We provide a method of using simulations from the Markov chain to construct a statistical estimate of π from which it is straightforward to sample. We show that this estimate is 'strongly consistent' in the sense that the total variation distance between the estimate and π converges to 0 almost surely as the number of simulations grows. Moreover, we use some recently developed asymptotic results to provide guidance as to how much simulation is necessary. Draws from the estimate can be used to approximate features of π or as intelligent starting values for the original Markov chain. We illustrate our methods with two examples.     

Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation

Abstract.  Wang & Wells [ J. Amer. Statist. Assoc. 95 (2000) 62] describe a non-parametric approach for checking whether the dependence structure of a random sample of censored bivariate data is appropriately modelled by a given family of Archimedean copulas. Their procedure is based on a truncated version of the Kendall process introduced by Genest & Rivest [ J. Amer. Statist. Assoc. 88 (1993) 1034] and later studied by Barbe et al . [ J. Multivariate Anal. 58 (1996) 197]. Although Wang & Wells (2000) determine the asymptotic behaviour of their truncated process, their model selection method is based exclusively on the observed value of its L ²-norm. This paper shows how to compute asymptotic p -values for various goodness-of-fit test statistics based on a non-truncated version of Kendall's process. Conditions for weak convergence are met in the most common copula models, whether Archimedean or not. The empirical behaviour of the proposed goodness-of-fit tests is studied by simulation, and power comparisons are made with a test proposed by Shih [ Biometrika 85 (1998) 189] for the gamma frailty family.     

PRODUCT DIFFERENTIATION UNDER CONGESTION: HOTELLING WAS RIGHT

We introduce negative network externalities—“congestion costs”—into H. Hotelling's (1929) model of spatial competition with linear transportation costs. For any firm locations on opposite sides of the midpoint, a pure strategy price equilibrium exists and is unique if congestion costs are strong enough relative to transportation costs. We analyze product differentiation and find that Hotelling's Principle of Minimum Differentiation comes closer to holding in the presence of congestion costs. The greater are congestion costs, the less differentiated products can be in (locationally symmetric) equilibrium. In fact, minimum differentiation comes arbitrarily close to holding depending on the magnitude of these costs relative to transportation costs. Intuitively, greater congestion effects stabilize competition at closer quarters, eliminating aggressive pricing equilibria. Thus, negative network externalities can play a significant role in product differentiation. (JEL D21, L15, R12)     

ANDREAS HEINRICH VOIGT AND THE HICKS‐ALLEN REVOLUTION IN CONSUMER THEORY

In 1893, Andreas Heinrich Voigt argued that utility admits only an ordinal characterization. We discuss the apparent impact of Voigt's now forgotten early argument for an ordinal approach to utility on later economists. Edgeworth cited Voigt's ordinal‐cardinal distinction several times in the Economic Journal, bringing both the concept and the terminology into Anglophone economics. In 1927, Rosenstein‐Rodan, too, cited Voigt's argument for ordinal utility. Since Hicks apparently learned the cardinal‐ordinal terminology from Edgeworth, and discussed utility theory and complementarity with Rosenstein‐Rodan, it appears that Voigt's 1893 article is the original source of ordinal utility in economics. (JEL B13, B21)     

AN ANALYTIC HISTORY OF DELIVERED PRICE LITIGATION: DO COURTS PROPERLY DISTINGUISH RIVALROUS FROM COLLUSIVE INSTANCES?

The federal judiciary's present, cautious approach to delivered pricing is appropriate. Using court records and recent contributions to the economic literature, this article evaluates the antitrust history of those practices. Delivered pricing can replace mill pricing naturally in some rivalrous settings, but under special circumstances could be collusive. Thus, delivered pricing has sometimes been adjudged a Sherman Act violation, but only given other evidence of collusion. For a time, however, the legal system threatened to treat delivered pricing as a per se violation of the Clayton and Federal Trade Commission Acts. That reflected poor economic understanding.