Identifying Canadian Regional Business Cycles Using the Plucking Model

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Abstract

Following the econometric specification suggested by Kim and Nelson (1999b), the plucking model (Friedmann 1964, 1993) is tested using output data from the Canadian regions. The empirical results give strong support to the theoretical predictions that negative transitory shocks hit the economy putting down the real regional output. After that, the regional economies enter into a recovery phase and after this they are operating again near the trend ceiling level. The only exception is the Atlantic region where the linear symmetric model of Clark (1987) cannot be rejected. Using the estimated filtered probabilities, a chronology of the regional business cycles is presented. It shows that there are clear and particular episodes corresponding to the regional dynamics which are not necessarily present at the aggregate level.

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It was Friedman (1964, 1993) who noted that the amplitude of a recession is strongly correlated with the following expansion, but the amplitude of an expansion is not correlated with the amplitude of the succeeding contraction. This striking asymmetry is the basic argument supporting the so named "plucking" model of business cycles. (1)

Neftci (1984) presented empirical evidence of the kind of asymmetry advanced by Friedman (1964, 1993), when he found that unemployment rates are characterized by sudden jumps and slower declines. Further evidence was found by Delong and Summers (1986), Falk (1986), and Sichel (1993). As Kim and Nelson (1999b) say, while these kind of asymmetries are consistent with the plucking model, they are also consistent with models where recessions are occasioned by infrequent permanent negative shocks as in the Markov-Switching models of Hamilton (1989) and Lain (1990). According to these authors, what distinguishes the plucking model is the prediction that negative shocks are largely transitory, while positive shocks are largely permanent. (2) Another important characteristic of the plucking model is the existence of an upper limit to the output, the so named ceiling output, which is set by the resources available in the economy.

The fact that recessions can essentially result from occasional transitory shocks may suggest that a recession, once it begins, will dissipate in a fairly predictable period of time. However, the length of an expansion is not helpful in predicting the next recession. This is what in the literature of business cycles is called duration dependence, which was investigated by Diebold and Rudebusch (1990), Diebold, Rudebusch and Sichel (1993), and Durland and McCurdy (1994) in an univariate context; and Kim and Nelson (1998) in a multivariate context. All these references found empirical support for the existence of duration dependence only for recession times.

Recently, Kim and Nelson (1999b) (3) suggested a formal econometric specification of the business cycle. Their specification allows us to decompose measures from economic activity into a trend component and deviations from the trend that show the types of asymmetries implied by the business cycle literature. In this sense, the approach offers more possibilities than standard linear models such as ARIMA models and the unobserved component model of Clark (1987), which cannot account for asymmetries. It may also perform better than other kind of models as the Markov-Switching (Hamilton 1989; Lam, 1990) where the asymmetric behavior is only accounted in the growth rate or stochastic trend component of real output.

Mills and Wang (2002) applied to the output of the G-7 countries the approach of Kim and Nelson (1999b). Galvao (2002) noted an interesting performance of this approach, where this model is one of the three models capable of reproducing the length of the United States business cycles, in this respect, see the special issue about business cycles published by Empirical Economics in 2002.

In this paper, I follow the same methodology of Kim and Nelson (1999b) applied to the logarithm of the real quarterly GDP of Canadian regions covering the period 1961:1 to 2000:1. …