Fundamentals versus the leading index–the forecasting of Canada's output growth since 1991: an encompassing approach

Abstract

We evaluate the ability of Statistics Canada's Composite Leading Index to forecast Canada's real Gross Domestic Product (GDP) growth rate in the backdrop of the Duguay (1994, JME) model and also the dynamic and the error-correction variants of the Duguay model, that already include the ‘fundamentals’ of the Canadian business cycle. The results show that integrating the index in these models substantially improve the in-sample fit of the models and also provide an explanation for the ‘perplexingly’ large influence of the US real GDP on aggregate spending in the Canadian economy. Out-of-sample forecasts over the inflation-targeting regime (January 1991–April 2004), evaluated using the forecast encompassing tests, confirm that the index contains an important amount of new information about the future growth rate, quite apart from the information contained in the fundamentals.

Notes

¹ The fundamental forces or prime movers include changes in government policies, price and interest rate movements, demographic and technological shifts and others (De Leeuw, 1989).

² The key intuition behind the index-based approach is that many cyclically-sensitive activities tend to move ahead of movements in aggregate output over the course of the business cycle. The index combines the most important of these variables based on a demonstrated ability to predict future economic activity (Vaccara and Zarnowitz, 1977; Diebold and Rudebusch, 1991).

³ Canada's leading index includes 10 monthly series including real M1 money, housing index (starts and resale), business and personal service employment, S&P/TSX stock price index, US leading index, average work week, new orders for durables, shipments/inventories of finished goods, furniture and appliances and other durable goods sales. In step one of the construction of the index, all 10 series are converted into zero-mean percentage changes and are standardized to make each series unit-free and to prevent the more volatile components from dominating the index. Next, the standardized series are aggregated into an equally weighted average or index. To ensure that the index has the same trend as the economy's coincident indicator of recession, the trend for real GDP is added to the index. Finally, the index is smoothed by applying an ARMA filter, which has a similar effect as a five-period moving average (Rhoades, 1982).

⁴ We are grateful to an anonymous referee for raising the issue of structural instability and pointing out to us the relevance of the FLS estimator.

⁵ To implement the cointegration tests, we have first tested for unit roots and found a single root in each of the variables of interest (ln Y, ln Y _US, and ln CLI). Next, we have tested whether the stochastic trends in these variables are related, using the Johansen and Juselius (1990) Trace test and L _max test. To implement this procedure, we estimated a VAR(4) model among the three variables, where the order of the VAR was determined using the likelihood ratio test. The test results indicated the presence of a single cointegrating vector, which we have normalized with respect to Canada's real GDP (ln Y):

Table

⁶ The motivation for examining the sub-period January 1996 to April 2004 separately derives from Freedman (2001), who documents evidence which shows the performance of the Canadian economy was much more robust in the sub-period after January 1996 compared to the sub-period before January 1996, due to tight monetary policy, private sector restructuring and a tight fiscal policy stance.

⁷ Tests of equal forecast accuracy are not valid when the forecasts being compared are from a pair of nested models. They break down because, under the null hypothesis of equal forecast accuracy, forecast errors from the restricted and unrestricted models are asymptotically perfectly correlated; see Clark and McCracken (2001).

⁸ For the case when the constant term is dropped from Equation 9, the weight attached to the unrestricted model increase substantially for all the models that include the index.