A Unified Approach to the Characterization of Equivalence Classes of DAGs, Chain Graphs with no Flags and Chain Graphs

Abstract.  A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass of CGs with no flags . Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-called largest CGs , whereas a graphical characterization of equivalence classes of DAGs is provided by the essential graphs . In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible.     

GENDER, EARNINGS, AND THE ENGLISH SKILL ACQUISITION OF HISPANIC WORKERS IN THE UNITED STATES

Using the 1980 and 1990 Public Use Microdata Samples, we find that labor market outcomes associated with English proficiency vary with respect to gender. For example, a synthetic cohort analysis provides evidence of gender-related differences in Hispanic workers' English skill acquisition. Moreover, we observe that Hispanic women face a lower English deficiency earnings penalty that rises more sharply with education than the penalty obtained by their otherwise similar male peers. Finally, English fluency appears to serve as a stronger occupational sorting mechanism for women than men. ( JEL J3, J1)     

RENT SEEKING AND DEMOCRACY: EMPIRICAL EVIDENCE FOR URUGUAY

We provide evidence for Granger causality between rent-seeking behavior and democracy in Uruguay, where both rent-seeking behavior and political shifts have varied widely in the past 80 yr but ethnolinguistic heterogeneity and inequality have remained low. This helps identify "pure" interactions and their link with rent-seeking outcomes. The presence and duration of democracy appear to have been conducive to a decrease in rent seeking, although the reduction in rent seeking does not appear to have had a bearing on the quality of democratic regime. While the duration of democratic regime may impact rent-seeking behavior, rent seeking also displays a Granger causality to democratic duration. ( JEL O10, O1)     

THE EFFECT OF SELECTIVE INS MONITORING STRATEGIES ON THE INDUSTRIAL EMPLOYMENT CHOICE AND EARNINGS OF RECENT IMMIGRANTS

One effect of 1986's immigration reform was to make INS inspection of firms more costly relative to other industries. In response, we suggest, the INS refocused its enforcement efforts toward industries with a higher concentration of illegals per establishment, especially manufacturing. We test this hypotheses and model the effects of a selective monitoring strategy on the employment choice and wages of illegal workers. We find evidence of selective monitoring by the INS and that this policy has redistributed illegal workers from closely to weakly monitored industries. Specifically, we find a shift from the higher-paying manufacturing sector to the agricultural.     

On Block Ordering of Variables in Graphical Modelling

Abstract.  In graphical modelling, the existence of substantive background knowledge on block ordering of variables is used to perform structural learning within the family of chain graphs (CGs) in which every block corresponds to an undirected graph and edges joining vertices in different blocks are directed in accordance with the ordering. We show that this practice may lead to an inappropriate restriction of the search space and introduce the concept of labelled block ordering B corresponding to a family of B - consistent CGs in which every block may be either an undirected graph or a directed acyclic graph or, more generally, a CG. In this way we provide a flexible tool for specifying subsets of chain graphs, and we observe that the most relevant subsets of CGs considered in the literature are families of B -consistent CGs for the appropriate choice of B . Structural learning within a family of B -consistent CGs requires to deal with Markov equivalence. We provide a graphical characterization of equivalence classes of B -consistent CGs, namely the B - essential graphs , as well as a procedure to construct the B -essential graph for any given equivalence class of B -consistent chain graphs. Both largest CGs and essential graphs turn out to be special cases of B -essential graphs.     

Hyper Inverse Wishart Distribution for Non-decomposable Graphs and its Application to Bayesian Inference for Gaussian Graphical Models

While conjugate Bayesian inference in decomposable Gaussian graphical models is largely solved, the non-decomposable case still poses difficulties concerned with the specification of suitable priors and the evaluation of normalizing constants. In this paper we derive the DY-conjugate prior ( Diaconis & Ylvisaker, 1979 ) for non-decomposable models and show that it can be regarded as a generalization to an arbitrary graph G of the hyper inverse Wishart distribution ( Dawid & Lauritzen, 1993 ). In particular, if G is an incomplete prime graph it constitutes a non-trivial generalization of the inverse Wishart distribution. Inference based on marginal likelihood requires the evaluation of a normalizing constant and we propose an importance sampling algorithm for its computation. Examples of structural learning involving non-decomposable models are given. In order to deal efficiently with the set of all positive definite matrices with non-decomposable zero-pattern we introduce the operation of triangular completion of an incomplete triangular matrix. Such a device turns out to be extremely useful both in the proof of theoretical results and in the implementation of the Monte Carlo procedure.     

Statistical Analysis of the Hirsch Index

Abstract. The Hirsch index (commonly referred to as h‐index) is a bibliometric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes size and impact of the research output. In a formal setting, the h‐index is actually an empirical functional of the distribution of the citation counts received by the scholar. Under this approach, the asymptotic theory for the empirical h‐index has been recently exploited when the citation counts follow a continuous distribution and, in particular, variance estimation has been considered for the Pareto‐type and the Weibull‐type distribution families. However, in bibliometric applications, citation counts display a distribution supported by the integers. Thus, we provide general properties for the empirical h‐index under the small‐ and large‐sample settings. In addition, we also introduce consistent non‐parametric variance estimation, which allows for the implementation of large‐sample set estimation for the theoretical h‐index.     

RULES AND DISCRETION WITH NONCOORDINATED MONETARY AND FISCAL POLICIES

The time inconsistency of optimal monetary policy is due to the effects of tax distortions. Thus the issue of how to improve upon the time-consistent suboptimal monetary policy is related to that of the coordination of monetary and fiscal policy. We present a model with three players (the central bark, the fiscal authority, and wage setters) in which distortionary taxes are explicitly modelled. We show that binding commitments to monetary rules are not necessarily welfare improving if monetary and fiscal policy are not coordinated. We also examine the effects of different degrees of independence of the central bank.