Chadha, B. and E. Prasad, “Interpreting the Cyclical Behavior of Prices,” Staff Papers, International Monetary Fund (June 1993).
Coe, D. and R. Moghadam, “Capital and Trade as Engines of Growth in France,” Staff Papers, International Monetary Fund (September 1993).
Hodrick, R. and E. Prescott, “Postwar U.S. Business Cycles: An Empirical Investigation,” mimeo, Carnegie-Mellon University, (1980).
Laxton, D. and R. Tetlow, “A Simple Multivariate Filter for the Measurement of Potential Output,” Bank of Canada Technical Report No. 59 (June 1992).
Organization for Economic Cooperation and Development, “Estimating Potential Output, Output Gaps and Structural Budget Balances,” mimeo (1994).
Quah, D. and J. Rauch, “Openness and the Rate of Economic Growth,” Working Paper, University of California San Diego (October 1990).
Rudebusch, G. and D. Wilcox, “Productivity and Inflation: Evidence and Interpretations,” mimeo, Board of Governors of the Federal Reserve (May 1994).
Wilkins, C., F. Lee, and S. James, “Estimating Trend Total Factor Productivity Growth in Canada,” Department of Finance Working Paper No. 3 (1992).
Prepared by Alun H. Thomas.
A recent extension of the univariate filter is the multivariate HP filter. The multivariate filter minimizes the weighted average of the errors from a set of relationships rather than from a single output equation. In addition to the output equation, an inflation equation (often based on the Phillips curve), and an unemployment equation (often constructed so as to reflect Okun’s law) are usually included in the specification (see Laxton and Tetlow (1992) for example). The advantage of this approach is that--by construction--it produces an estimate of the output gap that has strong explanatory power in the inflation equation. The disadvantages include the standard end-point problem associated with the HP filter, and the need to arbitrarily choose the weights in the loss function assigned to the errors in each equation.
For example, the unemployment rate was at least 1 1/2 percent above most estimates of the natural rate of unemployment over the 1991-93 period.
The output variable is GDP in constant 1986 dollars, the employment variable is economy-wide employment from the Labor Force Survey and the capital stock series is gross fixed non-residential capital formation in constant 1986 dollars. All variables were obtained from DRI.
See Chapter II for more details on this issue.
A variable is said to be integrated of order 1 if first differencing renders it stationary.
In order to satisfy the basic assumptions of regression analysis variables must be transformed into stationary series or yield a linear combination that is stationary.
Substituting the CPI inflation rate for the GDP deflator inflation rate produced similar results. The capacity utilization rate is provided by Statistics Canada and is based on a trend fitted through the output-capital ratio and multiplied by an estimate of the capital stock. The estimate only covers the non farm goods-producing sector, which accounts for roughly 30 percent of GDP. The volume of tradeables is the sum of merchandise exports and imports in constant 1986 dollars and the GDP deflator is the implicit output deflator. All variables were obtained from DRI.
The coefficients on the level and the change in the ratio of total trade to GDP were insignificant.
t-statistics in parentheses.
The labor factor input differs slightly from the variable used to estimate total factor productivity because the long-run employment level is used instead of the actual level. The long-run level is defined as the labor force multiplied by one minus the natural rate of unemployment. See Chapter III for an analysis of the natural rate of unemployment.
Since, as discussed above, output, labor, and capital are integrated of order 1, it is valid to investigate the possibility of a long-run relationship between these variables in levels. See Coe and Moghadam (1993) for details of the methodology.
The preferred cointegrating vector was chosen on the basis that all of the estimated coefficients have the expected signs and are of reasonable magnitudes.
The excess demand gap in the labor market is defined as the difference between the actual rate of unemployment and the natural rate, adjusted for an Okun coefficient of 2.3. See Chapter III for an analysis of the natural rate of unemployment.