Have structural changes eliminated the out-of-sample ability of financial variables to forecast real activity after the mid-1980s? Evidence from the Canadian economy

Abstract

This article evaluates how consistently reliable the information content of individual financial variables is for Canada's future output growth. We estimate the timing of structural changes in linear growth models and check robustness to specification changes, multiple breaks, and business cycle asymmetry. Our simulated out-of-sample forecast evaluation strategy, using the Mean Square Error F-type (MSE-F) and the new encompassing (ENC-NEW) tests, shows that the leading information content of most financial variables for Canada's future Gross Domestic Product (GDP) growth has deteriorated substantially after 1984:04, but the 1–3-year term spread exhibits a consistently reliable predictive ability at the 1 and 2 quarter horizons and has significant forecasting ability at the 8 quarter horizon. Also, the real M1 money growth has regained its ability to forecast output growth since 1991:01.

Keywords:

• forecasting
• GDP growth
• structural change
• in-sample tests
• out-of-sample tests

JEL Classification::

• C52
• C53
• E44

Notes

¹ Cross (2004) notes that diffusion indexes can provide useful additional information about business cycle dynamics. For example, diffusion indexes tend to be highly correlated to GDP growth, indicating that periods of expansion and contraction occur because the impulse to grow or contract is widely dispersed across many industries, not because a few industries are posting exceptional growth or decline.

² Bernanke (2004) notes that central bankers naturally turn to asset prices for this advance information, since asset markets are forward-looking, data on assets prices are available on a timely and continuous basis and financial data are not usually revised.

³ The MSE-F is a variant of the MSE-T statistic of Diebold and Mariano (1995) and West (1996) but has greater power. The ENC-NEW statistic has greater power over the MSE-F statistic Clark and McCracken (2001).

⁴ The results are the same when term spreads are defined using the 3-month t-bill rate.

⁵ Rapach and Weber (2004) use the specification given by Equation 1, while Stock and Watson (2003) redefine .

⁶ Observed changes in unconditional volatility may arise either from structural changes in conditional volatility or conditional mean or both (Kim and Nelson, 1999).

⁷ In the fixed-regressor bootstrap method, all regressors including the lagged dependent variables are held fixed in the simulation.

⁸ We wish to thank Rapach and Wohar (2006) whose Gauss codes, available at http://pages.slu.edu/faculty/rapachde/Research.htm, we modify for use in this article.

⁹ Davidian and Carroll (1987) have shown that if the errors ε _t are normally distributed, then represents an unbiased estimator of conditional SD of GDP growth in model (2).

¹⁰ The theoretical grounds for the predictive power of the yield spread for output growth is explained by Berk (1998) while its empirical relevance is noted by many others, including Estrella and Trubin (2006).

¹¹ To save space, the unit root test results are not reported in this article. They will be made available upon request.

¹² The second of these, the WD_max statistic, applies different weights to the individual UD_max statistics so that the marginal p-values are equal across values of m (see BP (1998) for details).

¹³ It should be noted that the sup F _T  (1|0) statistic is similar to Andrews's (1993) sup F statistic, and may have low power in the presence of multiple breaks.

¹⁴ Because of their close similarity of the results to those reported in Table 4, the results for a few of the financial variables are not reported in Table 4, in order to save space.

¹⁵ Clark and McCracken (2004) show that, for h > 1, both the MSE-F and the ENC-NEW statistics have nonnormal and nonpivotal limiting distributions so that inferences must be based on bootstrap procedures. The bootstrap procedure we employ in this study is a modification of the one used by Rapach and Weber (2004) which, in turn, is a variant of the procedure used by Clark and McCracken (2004). The Gauss code for the bootstrap procedure is available at http://pages.slu.edu/faculty/rapachde/Research.htm. For technical details about this procedure, we refer the reader to these previous studies.

¹⁶ Chan et al. (2005), however, argues that the removal of reserve requirements and other changes between 1992 and 1994 have made demand and notice deposits indistinguishable and this has adversely affected the information content of M1 (currency plus demand deposits) but not of M1+ (M1 plus notice deposits) money aggregates.