Academic journal article Federal Reserve Bank of St. Louis Review

The Efficient Market Hypothesis and Identification in Structural VARs

Academic journal article Federal Reserve Bank of St. Louis Review

The Efficient Market Hypothesis and Identification in Structural VARs

Article excerpt

For a variety of reasons economists have long been interested in measuring the economy's response to exogenous shocks. The shocks are thought to result, for example, from specific unexpected policy actions, sources that are exogenous to the domestic economy (such as an oil price shock), or sudden changes in technology. The economic structure (or data-generating process) that determines any economic outcome must be inferred from the observed data, and a structural interpretation of the data is obtained from economic theory. However, there are alternative economic theories and, consequently, alternative structural interpretations of the same observations. Hence, economists are faced with the very difficult problem of discriminating among these interpretations and, consequently, identifying the specific source of the shock or the economy's response to it.

Before a structural model can be evaluated, it must be identified. A structural model is identified when one can obtain the structural parameters from the estimates of the reduced-form parameters. A model is "just identified" when there is a one-to-one correspondence between the structural parameters and the reduced-form parameters. On the other hand, a model is over-identified if there is more than one set of structural parameters that is consistent with a given set of reduced-form parameters, whereas it is unidentified when there is no way to obtain the structural parameters from the estimated reduced-form parameters. (1)

Generally speaking, there have been two broad approaches to identification, the Cowles Commission (CC) methodology and the so-called structural vector autoregression (SVAR) methodology. (2) As a consequence of Sims's (1980) critique of the CC methodology, the SVAR methodology has become arguably the most widely used method of structural analysis. Both methodologies assume that the structural economy can be approximated by a linear, dynamic system of structural equations with an additive stochastic structure. In applications of the CC methodology, identification was typically achieved by placing restrictions (typically homogenous, i.e., zero, restrictions) on some of the coefficients of a dynamic structural model of the economy. While it was well understood that identification could be achieved by placing restrictions on the stochastic structure of the model, this was seldom done in practice. (3)

In contrast, in the SVAR methodology (which is attributed to Bernanke, 1986; Blanchard and Watson, 1986; and Sims, 1986) identification is achieved by imposing contemporaneous restrictions on both the structure of the economy and the stochastic structure of the model. (4) Exclusion restrictions on the structural dynamics--which were frequently imposed in applications of the CC methodology--are never imposed.

The restrictions that the SVAR methodology imposes on the structural shocks have often been criticized (e.g., Bernanke, 1986; Stock and Watson, 2001 ), and Cooley and LeRoy (1985) have noted that, in the absence of these restrictions, the estimated shocks from the SVAR would be linear combinations of all the structural shocks in the reduced-form VAR. This paper extends and refines Cooley and LeRoy's observation by noting that if the VAR includes one or more efficient market variables (EMVs)--variables that reflect all information relevant for their determination--the covariance restrictions that are typically employed in a SVAR identification are inappropriate and may have to be replaced with alternative restrictions. Our paper is close in spirit to those of Wall is (1980) and Pesaran (1981) in the rational-expectations literature; however, we focus on SVARs rather than on more general structural rational-expectations models.

Strictly speaking, our analysis applies only to VARs that include variables that are efficient in the strong form of the efficient market hypothesis (EMH). We argue, however, that our analysis is likely to have implications for VARs that include variables that meet the less stringent requirements of semistrong market efficiency. …

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