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.
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.
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 are the OLS residuals obtained from model 11, w is the number of observations used to estimate the model and h is the forecast horizon. The matrix Π is defined as follows:
where is the variance of the coefficients of the predictive regression and Ω is the Newey-West long-run covariance matrix of the residuals with bandwith parameter equal to mim(h, w1/3).
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 and The denominator, is a nonparametric estimator of the long-run variance of ft:
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 The variance is a non-parametric estimator of the long-run variance of gt, analogue to 15. Like in the model selection step we use a triangular window with w(j, m)=1–j/(m+1) and set m=1.5 h, in line with Busetti and Marcucci (2013).
Anzuini, A., M. J. Lombardi, and P. Pagano. 2012. “The Impact of Monetary Policy Shocks on Commodity Prices.” Temi di discussione (Economic working papers) 851, Bank of Italy, Economic Research Department.10.2139/ssrn.2030797Search in Google Scholar
Balke, N. S., S. P. Brown, and M. K. Yücel. 1998. “Crude Oil and Gasoline Prices: An Asymmetric Relationship?” Federal Reserve Bank of Dallas Economic and Financial Policy Review (First Quarter): 2–11.Search in Google Scholar
Blanchard, O. J., and J. Gal. 2009. “The Macroeconomic Effects of Oil Shocks: Why are the 2000s So Different from the 1970s?” In International Dimensions of Monetary Policy, edited by J. Gal and M. Gertler, 373–428. Chicago, IL: University of Chicago Press.10.7208/chicago/9780226278872.003.0008Search in Google Scholar
Blanchard, O. J., and M. Riggi. 2012. “Why Are the 2000s So Different From the 1970s? A Structural Interpretation of Changes in the Macroeconomic Effects of Oil Prices. Journal of the European Economic Association, forthcoming.10.2139/ssrn.2009899Search in Google Scholar
Borenstein, S., A. C. Cameron, and R. Gilbert. 1997. “Do Gasoline Prices Respond Asymmetrically to Crude Oil Price Changes?” The Quarterly Journal of Economics 112: 305–339.10.1162/003355397555118Search in Google Scholar
Bullard. 2011. “Measuring Inflation: The Core Is Rotten.” Money Marketeers of New York University New York, NY. May 18, 2011. Accessed on April 10, 2011. http://www.stlouisfed.org/newsroom/speeches/pdf/2011-05-18.pdf.Search in Google Scholar
Busetti, F., and J. Marcucci. 2013. “Comparing Forecast Accuracy: A Monte Carlo Investigation.” International Journal of Forecasting, 29(1):13–27.10.1016/j.ijforecast.2012.04.011Search in Google Scholar
Catao, L., and R. Chang. 2010. “World Food Prices and Monetary Policy.” NBER Working Papers 16563, National Bureau of Economic Research, Inc.Search in Google Scholar
Clark, T. E., and M. W. McCracken. 2001. “Tests of Equal Forecast Accuracy and Encompassing for Nested Models.” Journal of Econometrics 105: 85–110.10.1016/S0304-4076(01)00071-9Search in Google Scholar
Clark, T. E., and M. W. McCracken. 2005. “The Power of Tests of Predictive Ability in the Presence of Structural Breaks.” Journal of Econometrics 124: 1–31.10.1016/j.jeconom.2003.12.011Search in Google Scholar
Clark, T. E., and M. W. McCracken. 2012. “Advances in Forecast Evaluation.” forthcoming in Handbook of Economic Forecasting, Volume 2, edited by Allan Timmermann and Graham Elliott, Amsterdam: Elsevier.10.1016/B978-0-444-62731-5.00020-8Search in Google Scholar
Crone, T., K. Khettry, L. Mester, and J. Novak. 2011. “Core Measures of Inflation as Predictors of Total Inflation.” Working Papers 11–24, Federal Reserve Bank of Philadelphia.10.21799/frbp.wp.2011.24Search in Google Scholar
Diebold, P., and R. Mariano. 1995. “Comparing Predictive Accuracy.” Journal of Business and Economic Statistics 13: 253–265.Search in Google Scholar
European Central Bank. 2011. “Structural Features of Distributive Trades and Their Impact on Prices in the Euro Area.” Occasional Paper Series 128.Search in Google Scholar
Evans, C. 2011. “The Fed’s Dual Mandate Responsibilities and Challenges Facing U.S. Monetary Policy.” European Economics and Financial Centre, Distinguished Speaker Seminar London, UK, September 7, 2011. Accessed on April 10, 2011. http://www.chicagofed.org/digital_assets/publications/speeches/2011/09_07_11_dual_mandate.pdf.Search in Google Scholar
Ferrucci, G., R. Jimenez-Rodriguez, and L. Onorante. 2012. “Food Price Pass-Through in the Euro Area: Non-Linearities and the Role of the Common Agricultural Policy.” International Journal of Central Banking 8 (1): 179–217.Search in Google Scholar
Harvey, D., S. J. Leybourne, and P. Newbold. 1998. “Tests for Forecast Encompassing.” Journal of Business and Economic Statistics 16: 254–259.Search in Google Scholar
Herrera, A. M., G. L. Latika, and T. Wada. 2011. “Oil Price Shocks and Industrial Production: Is the Relationship Linear?” Macroeconomic Dynamics 15 (S3).10.1017/S1365100511000290Search in Google Scholar
Kilian, L. 2011. “Structural Vector Autoregressions.” CEPR Discussion Papers 8515, C.E.P.R. Discussion Papers.Search in Google Scholar
Kilian, Lutz, and Cheolbeom Park. 2008. “The Impact of Oil Price Shocks on the U.S. Stock Market.” International Economic Review 50 (4): 1267–1287.10.1111/j.1468-2354.2009.00568.xSearch in Google Scholar
Kilian, L., and R. J. Vigfusson. 2011a. “Are the Responses of the U.S. Economy Asymmetric in Energy Price Increases and Decreases?” Quantitative Economics 2 (3): 419–453.10.3982/QE99Search in Google Scholar
International Monetary Fund. 2008. “Is Inflation Back?” Commodity Prices and Inflation, World Economic Outlook, Chapter III, October, 93–128.Search in Google Scholar
L’Huillier, J. P. 2012. Consumers Imperfect Information and Price Rigidities. EIEF Working Papers Series 1209, Einaudi Institute for Economic and Finance (EIEF), revised Aug 2012.Search in Google Scholar
Manera, M., and G. Frey. 2007. “Econometric Models of Asymmetric Price Transmission.” Journal of Economic Surveys 21: 259–325.Search in Google Scholar
Marcellino, M., J. Stock, and M. Watson. 2006. “A Comparison of Direct and Iterated AR Methods for Forecasting Macroeconomic Series h-Steps Ahead.” Journal of Econometrics 135: 499–526.10.1016/j.jeconom.2005.07.020Search in Google Scholar
Meyer, C., and S. von Cramon-Taubadel. 2004. “Asymmetric Price Transmission: A Survey.” Journal of Agricultural Economics, Wiley Blackwell 55 (3): 581–611.10.1111/j.1477-9552.2004.tb00116.xSearch in Google Scholar
National Bank of Belgium. 2008. “Processed Food: Inflation and Price Levels.” NBB Economic Review, Special Edition, The Trend in Inflation in Belgium: An Analysis by the NBB at the Request of the Federal Government, April, Annex D, pp. 53–72.Search in Google Scholar
Pesaran, H. P., A. Pick, and A. Timmermann. 2011. “Variable Selection, Estimation and Inference for Multi-period Forecasting Problems.” Journal of Econometrics 164: 173–187.10.1016/j.jeconom.2011.02.018Search in Google Scholar
Rosengren, E. 2011. “A Look Inside a Key Economic Debate: How Should Monetary Policy Respond to Price Increases Driven by Supply Shocks?” Remarks to the Massachusetts Chapter of NAIOP, the Commercial Real Estate Development Association May 4, 2011. Accessed on April 10, 2011. http://www.bostonfed.org/news/speeches/rosengren/2011/050411/050411.pdf.Search in Google Scholar
Venditti, F. 2010. “Down the Non-linear Road From Oil to Consumer Energy Prices: No Much Asymmetry Along the Way.” Temi di discussione (Bank of Italy Economic working papers) 751.10.2139/ssrn.1670093Search in Google Scholar
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