Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading by Joel Hasbrouck

Author:Joel Hasbrouck [Hasbrouck, Joel]
Language: eng
Format: azw3, pdf
Publisher: Oxford University Press
Published: 2007-01-03T16:00:00+00:00

For most of the VMA models considered up to this point, the VAR is an alternative representation that is particularly convenient for estimation. Here, though, if we attempt to determine the VAR coefficients, ϕ(L) in ϕ(L)Δpt = εt, by the usual method of series expansion of (I + θ1L)–1, we get an unpleasant surprise. The leading terms of the expansion are:

Apparently, the coefficients of the VAR representation do not converge. This difficulty is not specific to the present structural model. When variables are cointegrated, no convergent VAR representation exists for the first-differences.1

Fortunately, a modified version of the VAR does exist. This is the vector error correction model (VECM). The “error correction” attribute refers to a common early use of these specifications, the modeling of dynamic systems in disequilibrium. To build the VECM, note first that a VAR does in fact exist for the price levels. Because Δpt = (1 – L)pt, the VMA representation becomes (1 – L)pt = θ(L)εt. A VAR level representation, ϕ(L)pt = εt, would have the property that ϕ(L) = θ(L)–1(1 – L). Direct computation of this yields:

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