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• W2044005979 abstract "Abstract Granger and Sims noncausality (GSNC), a concept frequently applied in time series econometrics, is compared to noncausality based on concepts popular in microeconometrics, program evaluation, and epidemiology literature (potential outcome noncausality or PONC). GSNC is defined as a set of restrictions on joint distributions of random variables with observable sample counterparts, whereas PONC combines restrictions on partially unobservable variables (potential outcomes) with different identifying assumptions that relate potential outcome variables to their observable counterparts. Based on the Robins’ dynamic model of potential outcomes, we find that in general neither of the concepts implies each other without further (untestable) assumptions. However, the identifying assumptions associated with the sequential selection of the observables link these concepts such that GSNC implies PONC, and vice versa. Keywords: Dynamic treatmentsGranger causalityPotential outcome modelRubin causalityRobins causalitySims causalityJEL Classification: C21C22C23 ACKNOWLEDGMENT I am affiliated with ZEW, Mannheim, CEPR and PSI, London, IAB, Nuremberg, and IZA, Bonn. I am thankful to Jim Heckman for convincing me to write down some of the issues that appear in this article. Furthermore, I am grateful to James Robins, the editor of this Journal, Esfandiar Maasoumi, and an anonymous referee for very helpful comments on earlier versions of this article. I thank Stefan Wiehler for careful proofreading. Of course, the usual disclaimer applies. I very much appreciate the previous joint work on dynamic potential outcome models with Ruth Miquel, in which we touched on a couple of issues that reappear here. The first version of the article has been written while I was visiting the Economics Department of the University of Michigan. The hospitality is appreciated. Notes For an overview of the work by the Cowles commission, see for example Christ (Citation1994). Note that we do not attempt to analyze the relation of the approach of the Cowles commission concerning causality (see, for example, Haavelmo, Citation1943, or Simon, Citation1953, Citation1954) to the subsequent developments in econometrics, as this has already been done, for example, by Cooley and LeRoy (Citation1985), for macroeconometrics, and by Heckman (Citation2000), for microeconometrics. Heckman (Citation2000) contains also an excellent account of the relation of causality to ceteris paribus intervention as was seen by the very early economic theorists. Faithfulness analysis uses directed acyclical graphs to formalize its assumptions and causal relations. Details on directed acyclical graphs in causal analysis can be found, for example, in Pearl (Citation2000). White (Citation2006) calls these interventions natural experiments. He uses a technically highly sophisticated framework that is appropriate for his discussion but neither necessary nor helpful to support the ideas of this article. As already mentioned, the literature based on comparing the ceteris paribus approach to causality (based on untestable structural assumptions in simultaneous linear models) used by the Cowles commission to the Sims–Granger approach (e.g., Cooley and LeRoy, Citation1985) is related, as it is to some extent similar to the potential outcome approach. One of the major differences is that the latter is nonparametric and allows arbitrary effect heterogeneity and avoids explicit modelling of a large set of causal relations simultaneously. Therefore, the formal analysis of Cooley and LeRoy (Citation1985) does not carry over to this case. In those times, econometrics was almost entirely concerned with the estimation of linear relations of continuous variables. means that A and the elements of B are jointly independent conditional on C taking a value of c (i.e., Dawid, Citation1979). Denoting the cumulative distribution function (cdf) of D conditional on E evaluated at d and e as F D|E (d, e), this statement is equivalent to F A, B 1, B 2 | C (a, b 1, b 2, c) = F A|C (a, c)F B 1, B 2 | C (b 1, b 2, c), ∀ a, b 1, b 2. Engle et al. (Citation1983) discuss related, but not identical concepts of strict exogeneity. In that their discussion focuses on likelihood functions and the role of their parameters in efficient and consistent estimation, it does not lend itself directly to the desired comparison of different concepts of causality. Dufour and Renault (Citation1998) study the differences of long run causality from short run causality in a linear model by considering different lag lengths between the outcome variable and the causing and conditioning variables. See, for example, the classical works by Marshall (Citation1961), the Cowles Commission (e.g., Haavelmo, Citation1943; Simon, Citation1953, Citation1954), and others, as discussed in the historical account of causal analysis by Heckman (Citation2000), or the extensive discussion of ceteris paribus causality provided by Hicks (Citation1979). Heckman (Citation2005) provides an elaborate discussion of potential outcome models and how they are embedded in economic theory. Y(d′, u) and Y(d, u) are called potential outcomes, because “the world cannot be in the two different states at any given time.” Therefore, only Y(d′, u) or Y(d, u) is observed if one of those two states is realized at all. For a fierce attack from the statistical point of view on such a concept of causality, see for example Dawid (Citation2000). Despite that critique, this concept appears to be widely used in the sciences and economics, and particularly so in applied microeconometrics. For a further discussion, see the excellent exposition of the potential outcome approach by Holland (Citation1986). For attempts to bound effects that are based on the joint distribution, see Heckman et al. (Citation1997). However, their bounds turn out to be so large as to be only of very limited relevance in empirical applications. u t may contain past values of u, but this is suppressed for notational convenience. For an overview of all the different effects discussed in the applied microeconometric literature and an attempt to put them in a unified framework, see Heckman and Vytlacil (Citation2005). The emphasis on the effect heterogeneity in different populations that appear in many applied studies based on the potential outcome approach is not prominent in GSNC. This is probably due to their different origins and fields of application. The potential outcome approach is used frequently in fields in which cross-sectional effect heterogeneity is considered important and the data have a large cross-sectional dimension. Granger–Sims noncausality originates from the time series literature, which historically is much less concerned with heterogeneity of causal effects and frequently has to rely on only one draw from the population of interest. In order to simplify notation, the dependence of outcomes and treatments on u t is left implicit for most of this and the following sections. In such cases, u t is integrated out with respect to some distribution, which is obvious from the specific context. These articles are based on the so-called selection on observables assumption, which is the route followed below, although in a simplified way. Several articles by James Robins and co-authors are concerned with parametric and semiparametric estimations of this model, which thus far have been used little or not at all in econometric applications (e.g., Hernan et al., Citation2001; Robins, Citation1999; Robins et al., Citation1999a,b). Lechner (Citation2009) discusses weighting and matching estimators and points to some practical issues for evaluating labor market programs. Miquel (Citation2002) considers the case of selection on unobservables that requires more data than just the outcomes and treatments. Abbring and Heckman (Citation2008) provide a survey over dynamic causal models. Due its origins in experimental evaluations, it is common in this literature to call this randomization instead of exogeneity. In fact, depending on the exact formulation of these concepts they may be either very similar or even identical (see Imbens, Citation2004, for further considerations on this topic). Note that Assumption 1 differs from White's (Citation2006) DUNE assumption in that it conditions on observed past treatments and outcomes. To identify all usual treatment effects, Lechner and Miquel (Citation2005) suggest a more restrictive version of the W-DCIA by imposing additional conditions on the way in which past treatments can influence past observed outcomes (strong dynamic conditional independence assumption, S-DCIA). Furthermore, if the complete treatment path is randomized in the beginning of the first period, then this assumption is stronger than W-DCIA as well. “… and since the determination of the causal ordering implies identifiability, the test for spuriousness of the correlation requires additional assumptions to be made.” (Simon, Citation1954, p. 479). Most likely, such tests are most powerful when based on full distributions instead of quantile or moments and employ recent developments in this field (e.g., Li et al., Citation2009)." @default.
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• W2044005979 title "The Relation of Different Concepts of Causality Used in Time Series and Microeconometrics" @default.
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