Are the prices of durable goods more flexible than those of non-durable goos?
Some empirical demonstrations in the business cycle literature lead to think so.
In this post, I have used Canadian data to show that this does not always hold.
I have done this by undertaking some spectral analyses and estimating price adjustment equations following Robert Gordon.
The data used are the Statistics Canada's quarterly price indices of durable and non-durable goods over the period 1961-2018.
Figure 1, below, plots the natural logarithm of these data.
Since the data are trended and not seasonally adjusted, I have worked instead with their year-to-year growth rates.
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| Figure 1: Natural Logarithm of the Prices of Durable and Non-Durables Goods, Canada, 1961:Q1-2018:Q4 |
The Spectral Analysis
The spectral analysis enables to break down the variance of a time series into portions that represent the contributions of cycles of various frequuencies. Figure 2, below, plots the estimates of the spectrum of the year-to-year growth rates of the price indices of durable and non-durable goods. The area under the plot of each of these two variables represent half of their respective variance. The variance of the year-to-year growth rate of the price index of durable goods is 8.12. That of non-durable goods is 12.8. |
| Figure 2: Estimates of the Spectrum of the Year-to-Year Growth Rates of the Quarterly Price Indices of Durables and Non-Durable Goods, Canada, 1962:Q1-2018:Q4 |
The variance of the growth rate of the prices of durable goods is lower than that of the prices of non-durable goods.
It appears in Figure 1 that part of the difference in these two variances is due cycles whose frequencies are between .2 and 1.
The duration of these cycles turns out to be between 6 and 32 months.
(By definition, the duration of a cycle equals 2π divided by its frequency.)
Cycles that last between 6 and 32 months are known as business cycles.
Most of the fluctuations in the year-to-year growth rates of the prices of durable and non-durable goods are attributable to low frequency cycles.
Cycles of frequency .2 or lower (i.e., cycles lasting at least 32 months) account for about two-thirds of the variance of these growth rates.
The estimates of their spectrum, which are respectively 31.8 and 96.6 at frequency .033, sharpely decline at frequency .2.
The prices of both durable and non-durable goods do not fluctuate much over business cycle frequencies.
Thus, stating that one is more flexible than the other over the business cyle does not seem quite appropriate.
The Price Adjustment Equations
In an article published in 1990, Robert Gordon attributed price stickiness to three effects: the inflation inertia, the level effect, and the rate-of-change effect. These three effects can be estimated by regressing the percentage change in the price level on its first lag, the cyclical component of real output, and the rate of change of this latter variable. I have used this model to estimate two price adjustment equatiuons: one for durable goods and the other one for non-durable goods. I have used the consumption of each of these two types of goods as a measure of their respective output. I have extracted their cyclical components using Hodrick and Prescott filter. To keep the rate-of-change effect (i.e., the coefficient associated to the rate of change of the cyclical output) in the interval [0,1], I have fitted the model to the data using the maximum likelihood method of estimation. The estimates are reported in the table below.| Durable Goods | Non-Durable Goods | |
|---|---|---|
| Intercept | .001 | .003 |
| Inertia Effect | .952 | .926 |
| Level Effect | -.009 | .177 |
| Rate-of-Change Effect | .000 | .000 |
The inertia effect (i.e., the coefficient on the lag of the percentage change in the price level) is very high for both goods, especially for durable goods.
This means, as firms producing both durable and non-durable goods do not all change their prices at the same time, the changes currently observed in the prices of these goods can be used to predict next period's price changes.
The level effect (i.e., the response to the cyclical consumption), which is negative for durable goods and positive for non-durable goods, also indicates that their prices are sticky.
The two estimates of this parameter are low, especially for durable goods.
During periods of economic expansion, the prices of durable goods only slightly fall in response to the increase in their production and the increase in the consumption of non-durable goods puts a moderate upward pressure on their prices.
According to the estimates of the rate-of-change effect, which are all null, the prices of both durable and non-durable goods are sticky.
Changes in the cyclical nominal demand for these two goods only result in fluctuations in their real outputs.
In conclusion, assuming that the prices of durable goods are flexible whereas those of non-durable goods are sticky helps improve the dynamics of the response of macroeconomic variables to monetary policy shock in two-sector new-Keynesian models.
But, this assumption does not always hold empirically.
Canadian data show that the prices of durable goods are as sticky as those of non-durable goods.
