A note on the correctness of the causal ordering algorithm

Vector autoregressions (VARs) are economically interpretable only when identified by being transformed into a structural form the (SVAR) in which the contemporaneous variables stand in a well-defined causal order. These identifying transformations are not unique. It is widely believed that practitioners must choose between them using a priori theory or other criteria not rooted in the data under analysis. We show how to apply graph-theoretical approach of searching for causal structure based on relations of conditional independence to select the possible causal orders – or at least to reduce the admissible them to a narrow equivalence class. This study investigates the dynamic structure of four major stock markets using an error correction model and directed acyclic graphs (DAG). The DAG representation provides a structure of causality among these markets in a contemporaneous time. Building this contemporaneous structure and the estimated error correction model, innovation accounting techniques are applied.

Econometrics demands that economists be familiar both with mathematical statistics and with different branches of higher mathematics. Economists – Lombardini argues in his essay – believe this scientific discipline has some utility, insofar as it paves the way to new perspectives and new paths in economic research. The A. offers a systematic description of the origins and the most recent developments of econometrics and introduce the reader to the most debated methodological issues arising in the building up of econometric models, such as the identification problem, the aggregation of individual demand or supply functions and the stochastic character of economic relations, citing what he deem essential for the critical evaluation of the new econometric methods. The A. highlights the potential as well as the limitations of econometric research, focusing especially on the need to develop a truly dynamic analysis and to bring the influence of institutions at the centre of economic inquiry.

Boosting the Hodrick-Prescott Filter

This paper focuses on two communication modes, namely Logically Instantaneity (li) and Causal Order (co). These communica- tion modes address two different levels of quality of service in message delivery. li means that it is possible to timestamp communication events with integers in such a way that (1) timestamps increase within each process and (2) the sending and the delivery events associated with each message have the same timestamp. So, there is a logical time frame in which for each message, the send event and the corresponding delivery events occur simultaneously. co means that when a process delivers a message m, its delivery occurs in a context where the receiving process knows all the causal past of m. Actually, Li is a property strictly stronger than co.The paper explores these noteworthy communication modes. Their main interest lies in the fact that they deeply simplify the design of message- passing programs that are intended to run on distributed memory parallel machines or cluster of workstations.KeywordsCausal OrderCluster of WorkstationsCommunication ProtocolDistributed MemoryDistributed SystemsLogical TimeLogical InstantaneityRendezvous

Modern economic theory, both at the micro and macro levels, and ever-increasing complexity of economic processes have led to the need to create and improve the use of mathematical modeling and quantitative analysis. On the basis of the latter, one of the areas of economic research emerged and was formed - econometrics. Econometric models and methods are now not only powerful tools for obtaining new knowledge in economics, but also a widely used apparatus for making practical decisions in forecasting, banking, and business. The development of information technologies and special ap-plication programs, the improvement of analysis methods have made econ-ometrics a powerful tool for economic research. The paper presents the prob-lem of numerical calculation of turbulent flow in a channel with a minor ob-stacle based on the COMSOL MULTIPHYSICS® software package. The SA and SST models were used for the numerical calculation of turbulent flow in the channel. The results obtained using the COMSOL MULTIPHYSICS® package were compared with experimental data and also analyzed in term of computational load. The results are obtained for Reynolds number Re = 20,000.

In four experiments, the predictions made by causal model theory and the Rescorla-Wagner model were tested by using a cue interaction paradigm that measures the relative response to a given event based on the influence or salience of an alternative event. Experiments 1 and 2 uncorrelated two variables that have typically been confounded in the literature (causal order and the number of cues and outcomes) and demonstrated that overall contingency judgments are influenced by the causal structure of the events. Experiment 3 showed that trial-by-trial prediction responses, a second measure of causal assessment, were not influenced by the causal structure of the described events. Experiment 4 revealed that participants became less sensitive to the influence of the causal structure in both their ratings and their predictions as trials progressed. Thus, two experiments provided evidence for high-level (causal reasoning) processes, and two experiments provided evidence for low-level (associative) processes. We argue that both factors influence causal assessment, depending on what is being asked about the events and participants' experience with those events.

A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression

Reconstructions of quantum theory usually implicitly assume that experimental events are ordered within a global causal structure. The process matrix framework accommodates quantum correlations that violate an inequality verified by all causally ordered correlations. Using a generalized probabilistic framework, we propose three principles constraining bipartite correlations to the quantum bound. Our approach highlights the role of a measure of dependence other than mutual information for an information-theoretic reconstruction of causal structures in quantum theory.

When the causal ordering, functional form, and lag structure are believed known, all that needs to be done is to estimate the model. Nonetheless, any assumptions underlying a model should be tested. In what follows, our discussion is primarily on a conceptual level. Technical details can be found in most leading econometric texts; Judge et al. (1985) is especially helpful in providing guidance for applied work.1

Applying a probabilistic causal approach, we define a class of time series causal models (TSCM) based on stationary Bayesian networks. A TSCM can be seen as a structural VAR identified by the causal relations among the variables. We classify TSCMs into observationally equivalent classes by providing a necessary and sufficient condition for the observational equivalence. Applying an automated learning algorithm, we are able to consistently identify the data-generating causal structure up to the class of observational equivalence. In this way we can characterize the empirical testable causal orders among variables based on their observed time series data. It is shown that while an unconstrained VAR model does not imply any causal orders in the variables, a TSCM that contains some empirically testable causal orders implies a restricted SVAR model. We also discuss the relation between the probabilistic causal concept presented in TSCMs and the concept of Granger causality. It is demonstrated in an application example that this methodology can be used to construct structural equations with causal interpretations.

Analysts associated with the Cowles Commission attached great importance to the distinction between structural and reduced-form models: in their view structural models, but not reduced-form models, allow the analysis of causal relations. They did not present clear justification for this view. Here we show that this insight is correct, and make the demonstration of it precise. Causal relations are shown to depend on parameter restrictions that are explicit in the structural form, but not in the reduced form when the coefficients are interpreted as unrestricted constants. The requisite parameter restrictions are those associated with implementation-neutral causation. A graphical procedure is outlined that identifies causal orderings and also the ordering based on implementation-neutral causation. The same procedure applied to reduced form models produces the implementation-neutral causal ordering only if the parameter restrictions are explicitly incorporated in the reduced form. The analysis is applied in investigating the validity of the causal Markov condition.

T.C. Koopmans was born in 1910 at ‘s Graveland, The Netherlands, and died in 1985 at New Haven, USA. His MA was from Utrecht in 1933 in mathematics and theoretical physics, and his Ph.D. was from Leiden in 1936 in mathematical statistics with applications to economics. His career was rather peripatetic for eight years: the Netherlands School of Economics, the League of Nations in Geneva, Princeton University, New York University, the Penn Mutual Life Insurance Company, and the Combined Shipping Adjustment Board in Washington (where he worked on the problem of optimizing the allocation of ships during the Second World War). Then in 1944 he joined the Cowles Commission for Research in Economics at the University of Chicago, where he remained until 1955 when the entire Cowles group moved to Yale. He retired from Yale in 1981. He was Research Director of the Cowles Commission at Chicago from 1948 to 1954, and of the Cowles Foundation at Yale from 1961 to 1967. He was a member of the economics faculty at Chicago from 1946 to 1955, and at Yale from 1955 to 1981.KeywordsActivity analysisAdditivityAmerican Economic AssociationBusiness cyclesCowles CommissionDantzig, G.Econometric SocietyEconometricsEfficient allocationEstimationExhaustible resourcesFelicity functionFisher, R. A.Frisch, R. A. K.IdentificationImpatienceInfinite horizonsKoopmans, T. C.Limited information maximum likelihood estimatorLinear programmingLinear regressionMaximum likelihoodOptimal economic growthRenewable resourcesShadow pricingSimplex method for solving linear programsSimultaneous equations modelsTwo-stage least squares estimatorUtility representation of preferencesJEL ClassificationsB31

Mediation analysis empirically investigates the process underlying the effect of an experimental manipulation on a dependent variable of interest. In the simplest mediation setting, the experimental treatment can affect the dependent variable through the mediator (indirect effect) and/or directly (direct effect). However, what appears to be an indirect effect in standard mediation analysis may reflect a data-generating process without mediation, including the possibility of a reversed causal ordering of measured variables, regardless of the statistical properties of the estimate. To overcome this indeterminacy where possible, the authors develop the insight that a statistically reliable total effect, combined with strong evidence for conditional independence of the treatment and the outcome given the mediator, is unequivocal evidence for mediation as the underlying causal model into an operational procedure. This is particularly helpful when theory is insufficient to definitely causally order measured variables, or when the dependent variable is measured before what is believed to be the mediator. The procedure combines Bayes factors as principled measures of the degree of support for conditional independence, with latent variable modeling to account for measurement error and discretization in a fully Bayesian framework. The authors reanalyze a set of published mediation studies to illustrate how their approach facilitates stronger conclusions.

Geographical AnalysisVolume 13, Issue 2 p. 95-116 Free Access Maximum Entropy Spectra and the Spatial and Temporal Dimensions of Economic Fluctuations in an Urban System Claude Marchand, Claude Marchand The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. Claude Marchand is assistant professor of geography, University of Montreal.Search for more papers by this author Claude Marchand, Claude Marchand The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. Claude Marchand is assistant professor of geography, University of Montreal.Search for more papers by this author First published: April 1981 https://doi.org/10.1111/j.1538-4632.1981.tb00719.xCitations: 17 Claude Marchand is assistant professor of geography, University of Montreal. The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED Bartels, C. P. A. (1977). “The structure of Regional Unemployment in the Netherlands. Regional Science and Urban Economics, 7, 103– 5. Bartels, C. P. A., M. Booleman, and W. H. Peters (1978). “A Statistical Analysis of Regional-Unemployment Series. Environment and Planning A, 10, 937– 54. Bennett, R. J. (1979). Spatial Time Series: Analysis—Forecasting—Control. London: Pion. Brechling, F. (1967). “Trends and Cycles in British Regional Unemployment. 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EMPIRICAL research in economics has seen the development in recent years of large simultaneous equation econometric models -large both in terms of detail and degree of disaggregation but also in their demands upon a limited of data. In the main these models have been models of macro-economic activity estimated from annual or quarterly data in the postwar period. Statistical methods for estimating simultaneous equation models were first developed by the researchers at Cowles Commission [8]. In recent years, the sheer size of such empirical models has brought a new problem to the fore, as the estimation methods previously developed cannot be used without modification. Most of those estimators -those of the kclass and three-stage-least-squares involve a first of regression or estimation using the predetermined variables of the model as regressors.1 But frequently in large models the is smaller than the number of predetermined variables, so that a meaningful first-stage regression is not possible.2 This is a sample problem of a different sort instead of needing more observations in order that the distribution of the estimates will be satisfactorily approximated by their asymptotic distributions, the is small relative to the size of the large model, to the extent that the standard simultaneous equation estimators either do not exist or are identical to ordinary least squares.3 A variety of solutions have been proposed to cope with the large-model problem, two of which are examined in detail in this paper. Each can be viewed as a modification of twostage-least-squares: 1) 2SPC (Two Stage Principal Components), originally proposed by Kloek and Mennes [11], in which a limited number of principal components of the predetermined variables are used in the first stage. 2) SOIV (Structurally Ordered Instrumental Variables), proposed by Fisher [5, 6], in which a limited number of predetermined variables are selected for the first stage by detailed use of the structure of the model. A complete assessment of the properties of these estimators in a large econometric model requires the knowledge of their small-sample distributions. These are in general unknown, although some progress has recently been made for small models by Amemiya [1], Basmann [2], Kadane [9], Mariano [12], Sawa [15], and Takeuchi [17]. Some information might be obtained by Monte Carlo techniques, except that the computational cost of systematically exploring the parameter space of a large model would be prohibitive. Still, a feasible project would be to employ a miniature model with a very few equations, but having more predetermined variables than observations. It is not clear, however, that the distributions would * This work was supported in part by National Science Foundation Grant GS-2635 and by the Brookings Institution. The initial research was undertaken during the tenure of fellowships from the Danforth Foundation and the National Science Foundation. Computations were done at the Massachusetts Institute of Technology and Stanford University computation centers. I am happy to acknowledge the numerous helpful suggestions of T. Amemiya, T. W. Anderson, P. J. Dhrymes, E. Kuh, F. M. Fisher and a referee. Much of the data was made available by G. Fromm. 1 The limited-information-maximum-likelihood method requires extraction of a characteristic root from a matrix of moments of the predetermined variables; the method can be interpreted as a first-stage regression of a synthetic endogenous variable on the predetermined variables. 2 Full information maximum likelihood estimators fail to exist when the number of parameters to be estimated in the model exceeds the size, another problem which occurs in large models. Because of computational complexity, FIML has not been a feasible estimator for models of even moderate size. 'In other cases the problem may occur in a less acute form -there may be more observations than predetermined variables, but the excess may be small, and in some sense better estimates may be obtained by using fewer variables in the first stage.