The Importance of Global Shocks for National Policymakers: Rising Challenges for Central Banks

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The dynamic factor model in VAR form (FAVAR) can be obtained by combining
factor analysis (equation 1) with a VAR model (equation 2):

(1)    X_t = AFt + D ( L ) X_t _1 + v_t

(2)    F_t = Φ( L ) F_t _i + Gη_t

where q ≤ r ≤ qp with r static factors F_t and q dynamic factors. A is a n × r
matrix, D(L) is a n × n matrix lag polynomial of order p , Φ(L) is a r × r matrix lag
polynomial of order p , G is r× q , η_t is a r -variate vector of global shocks driving the
common factors, v_t equals a n -variate vector of idiosyncratic shocks. Substituting the
factor evolution equation (2) into equation (1) and collecting terms yields the complete
FAVAR form:

The FAVAR contains the exclusion restriction implied by factor analysis, i.e. X_t
does not predict F_t given Φ(L)F_t-1 . Restrictions of this form closely resemble the
assumption of exogenous world variables which are used to identify global shocks in
open economy VARs. The FAVAR can be estimated via a two-step principal component
approach. In the first step, the common components F_t are estimated using the first r
principal components of X_t . In the second step, a VAR is estimated on these common
components. Bernanke, Boivin and Eliasz (2005) point out that this two-step approach
implies the presence of “generated regressors” in the second step. However, the
uncertainty in the factor estimates should be negligible when N is large relative to T.

In the first step, estimates of the common factors are obtained by dividing the data
set X_t into categories of variables. These categories are capturing different dimensions of
the economy across countries (X_t¹, X_t²,..., X_t^I) : economic activity as reflected by real
GDP; inflation which include consumer prices, producer prices, import prices and the
GDP deflator; commodity prices which include the HWWI and the CRB commodity
price index in domestic currency; house prices; monetary liquidity which include broad

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