Impact factors

Abstract

In this paper we discuss sensitivity of forecasts with respect to the information set considered in prediction; a sensitivity measure called impact factor, IF, is defined. This notion is specialized to the case of VAR processes integrated of order 0, 1 and 2. For stationary VARs this measure corresponds to the sum of the impulse response coefficients. For integrated VAR systems, the IF has a direct interpretation in terms of long-run forecasts. Various applications of this concept are reviewed; they include questions of policy effectiveness and of forecast uncertainty due to data revisions. A unified approach to inference on the IF is given, showing under what circumstances standard asymptotic inference can be conducted also in systems integrated of order 1 and 2. It is shown how the results reported here can be used to calculate similar sensitivity measures for models with a simultaneity structure. r

A general inversion theorem for cointegration

“…Counterfactual thought experiments on the long-run behavior of cointegrated systems also lead to long-run impact multipliers that are functions of the MA impact matrix C 0 , see Johansen (2005). Omtzigt and Paruolo (2005) derived maximum likelihood estimation and inference on related long-run impact multipliers in cointegrated systems. The MA impact matrix plays also a central role in the estimation of the long-run variance matrix, see Paruolo (1997b) and Phillips (1998).…”

Common trends and cycles in I(2) VAR systems

“…In this section we present an application to the Australian prices data set analyzed by Banerjee et al (2001) and Omtzigt and Paruolo (2005), inter alia. 7 We refer to the latter paper for the analysis of the initial specification and the cointegration analysis.…”

“…intervention dummies defined in Omtzigt and Paruolo (2005). Table 4 reports the result of the test statistics.…”

The Likelihood Ratio Test for the Rank of a Cointegration Submatrix*

“…For the VAR process in it can be shown (see, e.g. Bruneau and Jondeau, 1999; Johansen, 2005; Omtzigt and Paruolo, 2005), that when h →∞ one has where is the MA impact matrix (see, e.g. Johansen, 1996), where rk( C )= p − r .…”

“…2 2 The conditions (5) and (6) can be phrased as restrictions on the first block of rows in the impact factors defined in Omtzigt and Paruolo (2005) Proposition 1, p. 40. …”