Measuring business cycles by saving for a rainy day

By Mario Crucini and Mototsugu Shintani

We propose a simple saving-based measure of the cyclical component in GDP. The measure is motivated by the prediction that the representative consumer changes savings in response to temporary deviations of income from its stochastic trend, while satisfying a present-value budget constraint. To evaluate our procedure, we employ the bivariate error correction model of Cochrane (1994) to the member countries of the G-7 and Australia. Our estimates reveal, that to a close approximation, the stochastic trend component of GDP is consumption and the transitory component is the error correction term, which justifies the use of our saving-based measure.

The HP-filter is a largely atheoretic way to measure cyclical components in the data. The choice of the penalty parameter is somewhat arbitrary, which makes that the cyclical component may include fluctuations that households consider to be permanent or miss fluctuations that are cyclical. Using realized consumption as a yardstick for what the households consider to be permanent fluctuations, this paper may give us a better measure of cyclical components, based on some minimal theory.

2 Responses to Measuring business cycles by saving for a rainy day

  1. M.H. says:

    The method uses HP-filtered consumption. Doesn’t that invalidate the whole purpose of the exercise?

  2. M.J.C. says:

    No. The method does not use HP-filtered consumption, it uses a Bivariate Error Correction Model in output and consumption growth. We show the decomposition arising using this ECM is very close to this very simple equation: y(t) = c(t) + [y(t)-c(t)] where the first term is the trend (consumption) and the second term is the cycle (saving).

    We simply use the HP-filter in one case to smooth consumption rather than use the raw series in the equation above. The key is to impose the co-integration of consumption and income and effectively have consumers identify the stochastic trend with their aggregated choices rather than predetermine the decomposition by choosing a smoothing parameter in the HP-filter.

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