A Comparison of Lag Structure Specification Methods in VAR Models
Ozcicek, Omer, Atlantic Economic Journal
This paper is concerned with selection of lag lengths for VAR models. Specifying the correct lag length is important because estimated VAR models with lag lengths different from the true model are misspecified.
Typically, the same lag length is used for all variables in all equations (symmetric VAR), even though there is no theoretical or statistical reason for doing so. The first method proposed to estimate asymmetric lag structures was by Hsiao [JME, 1981]. This approach treats each equation separately, i.e., the lag structure of an equation is determined independently from other equations. In his working paper, Keating  criticized Hsiao's method, arguing that the lag structure selected by Hsiao's method is likely to be biased. Keating proposed another approach to determine the lag structure of asymmetric VARs.
Consider a bivariate VAR as shown below:
[z.sub.t] = [[Beta].sub.10] + [[Beta].sub.11](L)[z.sub.t-1] + [[Beta].sub.12](L)[x.sub.t-1] + [u.sub.t] [x.sub.t] = [[Beta].sub.20] + [[Beta].sub.21](L)[z.sub.t-1] + [[Beta].sub.22](L)[x.sub.t-1] + [v.sub.t],
where [[Beta].sub.ij](L) are lag polynomials. In Hsiao's method, all lag polynomials are allowed to have different lags. In Keating's method, the lag polynomials of a variable (for instance, for the first variable [[Beta].sub.11](L) and [[Beta].sub.21](L)) have the same lag. However, the polynomials of different variables (for instance [[Beta].sub.11](L) and [[Beta].sub.12](L)) can have different lags. Keating estimates all possible lag structures and picks the one which yields the lowest criterion value. …