علیت گرنجر، درونگرایی، هم انباشتگی، و تجزیه و تحلیل سیاست اقتصادی

Policy analysis had long been a main interest of Clive Granger’s. Here, we present a framework for economic policy analysis that provides a novel integration of several fundamental concepts at the heart of Granger’s contributions to time-series analysis. We work with a dynamic structural system analyzed by White and Lu (2010) with well defined causal meaning; under suitable conditional exogeneity restrictions, Granger causality coincides with this structural notion. The system contains target and control subsystems, with possibly integrated or cointegrated behavior. We ensure the invariance of the target subsystem to policy interventions using an explicitly causal partial equilibrium recursivity condition. Policy effectiveness is ensured by another explicit causality condition. These properties only involve the data generating process; models play a subsidiary role. Our framework thus complements that of Ericsson et al. (1998) (EHM) by providing conditions for policy analysis alternative to weak, strong, and superexogeneity. This makes possible policy analysis for systems that may fail EHM’s conditions. It also facilitates analysis of the cointegrating properties of systems subject to policymaker control. We discuss a variety of practical procedures useful for analyzing such systems and illustrate with an application to a simple model of the US macroeconomy.

Although just three of Clive Granger’s many papers explicitly focus on aspects of policy analysis (Granger, 1973, Granger, 1988 and Granger and Deutsch, 1992), a central and long-standing concern evident throughout his work is that econometric theory and practice should be informative and useful to policymakers. In this paper, we further this objective by providing a novel framework for economic policy analysis that blends together a number of concepts at the heart of Granger’s contributions to time-series econometrics: causality, exogeneity, cointegration, and model specification. We study a dynamic structural system with potentially cointegrated variables analyzed by White and Lu (2010) (WL) within which causal meanings are well defined. This system contains target and control subsystems, with possibly integrated or cointegrated behavior. We ensure the invariance of the target subsystem to policy interventions, obviating the Lucas critique, using an explicitly causal partial equilibrium recursivity condition. Another causality requirement ensures policy effectiveness. Causal effects are identified by a conditional form of exogeneity. These effects can be consistently estimated with a correctly specified model. Following WL, we show that, given conditional exogeneity, Granger causality is equivalent to structural causality. On the other hand, given structural non-causality, Granger causality is equivalent to failure of conditional exogeneity. In this sense, Granger causality is not a fundamental system property requisite for reliable policy analysis, but an important consequence of necessary underlying structural properties. By relying only on correct model specification and not weak exogeneity or its extensions (strong and superexogeneity), our framework complements the policy analytic framework of Ericsson et al. (1998) (EHM). Although giving up weak exogeneity may lead to loss of estimator efficiency, it also makes possible policy analysis for systems that may fail EHM’s conditions (see Fisher, 1993). As we also show, our approach readily lends itself to analysis of the structural consequences of a variety of control rules that the policymaker may employ. Among other things, we find that proportional (P) control cannot modify the cointegrating properties of a target system, whereas proportional–integral (PI) control can. In fact, PI control can introduce, eliminate, or broadly modify the cointegrating properties of the uncontrolled target system. Whereas cointegration between target variables and policy instruments is possible but unusual with P control, PI control can easily induce causal cointegration between the target variables (YtYt) and the policy instruments (ΔZtΔZt). The control mode also has interesting implications for estimation, inference, and specification testing in controlled systems. P control or a certain mode of PI control yields ΔZt∼I(0)ΔZt∼I(0), resulting in standard inference. Other modes of PI control yield ΔZt∼I(1)ΔZt∼I(1); the theory of Park and Phillips, 1988 and Park and Phillips, 1989 may be applied to these cases. The plan of the paper is as follows. In Section 2, we introduce the data generating process (DGP) for the controlled system we study here, together with notions of structural causality and policy interventions natural in these systems. These enable us to formulate causal restrictions, essential for reliable policy analysis, obviating the Lucas critique and ensuring policy effectiveness. Section 3 discusses a conditional form of exogeneity that identifies causal effects of interest and forges links between structural and Granger causality. Section 4 reviews properties of relevant cointegrated systems, with particular attention to their structural content. In Section 5, we give an explicit comparison of our framework with that of EHM, summarizing their similarities and differences and commenting on their relative merits. Section 6 analyzes the structural consequences of various rules that may be employed by policymakers to control potentially cointegrated systems. We pay particular attention there to how the policy rules may introduce, modify, or eliminate cointegration within the target system and to the possible cointegrating relations that may hold between policy instruments and target variables, or among the policy instruments. Section 7 illustrates these methods with an application to a simple model of the US macroeconomy, and Section 8 contains a summary and concluding remarks. In what follows, we often refer to processes “integrated of order dd”, I(d)I(d) processes for short. By this we mean a stochastic process that becomes I(0)I(0) when differenced dd times, where an I(0)I(0) process is one that obeys the functional central limit theorem.

One of Clive Granger’s long-standing and central concerns was that econometric theory and practice should have direct value to policymakers. Here, we present a framework for economic policy analysis that provides a novel integration of several fundamental concepts at the heart of Granger’s contributions to time-series analysis. We work with a dynamic structural system analyzed by WL with well defined causal meaning. The system contains target and control subsystems, with possibly integrated or cointegrated behavior. We ensure the invariance of the target subsystem to policy interventions and thus obviate the Lucas critique using an explicitly causal partial equilibrium recursivity condition, plausible on informational, behavioral, and empirical grounds. Policy effectiveness corresponds to another explicit causality condition. Identification of system coefficients holds given conditional exogeneity, an extension of strict exogeneity distinct from weak exogeneity or its extensions. As we discuss, given conditional exogeneity, Granger causality and structural causality are equivalent. Given structural non-causality, Granger causality and the failure of conditional exogeneity are equivalent. In this sense, Granger causality is not a fundamental system property requisite for reliable policy analysis, but an important consequence of necessary underlying structural properties. By relying only on correct model specification and not weak exogeneity, our framework complements the policy analytic framework of Ericsson et al. (1998). As we show, our approach readily lends itself to analysis of the structural consequences of a variety of control rules that the policymaker may employ. Among other things, we find that proportional (P) control cannot modify the cointegrating properties of a target system, whereas proportional–integral (PI) control can. In fact, PI control can introduce, eliminate, or broadly modify the cointegrating properties of the uncontrolled target system. Whereas cointegration between target variables and policy instruments is possible but unusual with P control, PI control can easily induce causal cointegration between the target (YtYt) and the policy instruments (ΔZtΔZt). These properties are preserved under PID control. The control mode also has interesting implications for estimation, inference, and specification testing in controlled systems. P, PI33, or PI33D control yield ΔZt∼I(0)ΔZt∼I(0), which results in standard inference. Other modes of PI or PID control yield ΔZt∼I(1)ΔZt∼I(1); the theory of Park and Phillips, 1988 and Park and Phillips, 1989 applies to these cases. One of the hallmarks of Clive Granger’s work is that it has vigorously stimulated research, often in an astonishing number of different productive directions. Putting a positive spin on the fact that the analysis here leaves a potentially embarrassing number of questions asked but not answered, we are hopeful that, like Clive’s work, these unanswered questions will stimulate interest in resolving them. In addition to suggesting the relevance of new theory for inference in partially nonstationary systems with covariates and conditional heteroskedasticity, the analysis here suggests, among other things, opportunities for developing specification tests distinguishing structural shifts and neglected nonlinearities, for studying control of nonlinear systems with cointegration using a misspecified model, for studying covariates in control, for developing methods useful for real-time monitoring of structural change in cointegrated systems, and for analyzing recursive methods of adaptive policy control, robustly able to operate in cointegrated systems subject to exogenous structural shifts. We hope, also, that the practical methods described and illustrated here will, as Clive would have desired, have direct value to policymakers.