Abstract
This paper analyzes the relationship between commodity prices and consumer food prices in the euro area and in its largest countries (Germany, France and Italy) and tests whether the latter respond asymmetrically to shocks to the former. The issue is of particular interest for those monetary authorities that target headline consumer price inflation, which has been heavily influenced by pronounced swings in international commodity prices in the past decade. The empirical analysis is based on two distinct but complementary approaches. We first use a structural model, identify a shock to commodity prices and check through formal econometric tests whether the Impulse Response Functions of food consumer prices is invariant to the sign of the commodity price shock. Next, we employ predictive regressions and examine the relative forecasting ability of linear models with respect to that of models that allow for sign-dependent nonlinearities. Overall, the empirical analysis uncovers very little evidence of asymmetries.
Acknowledgments
We would like to thank seminar participants at the Banca d’ltalia and at the Fifth Italian Congress of Econometrics and Empirical Economics. We would also like to thank two anonymous referees for valuable comments that led to a substantial improvement of the paper. The usual disclaimer applies: the opinions expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of Italy.
Appendix
A Model selection in multistep predictive regressions
At each step in the forecast exercise we choose the number of lags p and q in the predictive regression (11) as the ones that minimize the following modified Akaike Criterion (AIC), see Pesaran, Pick, and Timmermann (2011):
where
where
B Forecast accuracy tests
In the case of nested models Clark and McCraken (2001, 2005) argue that both the DM and the HLN statistics have non standard distributions that depend on several nuisance parameters. In this case the critical values should be obtained through bootstrap simulations. The power and size of these tests has been more recently analyzed by Busetti and Marcucci (2013). On the basis of Monte Carlo simulations they confirm that for nested models and multistep forecasts the original DM test is undersized, but they also find that the original HLN test displays good size and power properties, especially as the prediction sample increases. In this case the Guassian distributed HLN statistics becomes relative more attractive than the computationally intensive procedure advocated by Clark and McCraken (2005). Also, Clark and McCraken (2012) find that the DM test has reasonable size provided that the long-run variance of the test statistics is estimated nonparametrically with a rectangular window rather than with a triangular one.
Considering the recommendations emerging from these literature we correct the DM test as in Clark and McCraken (2012) and use the HLN test in its standard formulation. We consider only one-sided encompassing tests, in the sense that the null hypothesis is that the nested (linear) model encompasses the nonlinear one, and the alternative is that the nesting (nonlinear) model yields better forecasts. If the test cannot reject this hypothesis the linear model is said to encompass the one with asymmetric terms.
The test statistics are defined as follows. Let T be the total number of observations, R be the number of in-sample observations used to estimate the model, P the number of out-of-sample predictions, h the forecast horizon and et,m the forecast errors of model m, where m=1, 2. The DM test statistics is the following:
where
Taking into account the results of Clark and McCraken (2012) we set m=h–1 and w(j, m)=1.
Turning to forecast encompassing, the forecast errors of the competing models and those of the combined forecast satisfy the relationship et,1=λ(et,1–et,2)+et,c. In population, under the null hypothesis that et,1 encompasses et,2λ=0, or equivalently, gt=et,1(et,1–et,2)=0. The HLN test statistics is:
where
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The online version of this article (DOI:10.1515/snde-2012-0077) offers supplementary material, available to authorized users.
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