Inventories, Buffer Stocks, and Excess Capacity: Fractal Analysis of Antipersistence, Entrepreneurial Management, and Austrian Business Cycle Theory

0:00What does Austrian business cycle theory imply for buffer stocks, the necessary stockpiles of raw materials, goods in process and finished intermediate output required for each stage of the production process? The lower interest rates brought about by credit expansion force the accumulation of buffer stocks in earlier stages of production. Because lower interest rates also result in a reduction in saving and a corresponding increase in consumer spending, buffer stocks also accumulate in late stages of production. So buffer stocks are progressively reallocated to early and late stages being transferred there from middle stages. This unsustainable expansion leads to recession. How can we measure buffer stocks? In this paper I use the ratio of specific sectoral producer prices Price Indices divided by the Consumer Price Index.

0:54This ratio increases when the demand for sectoral buffer stocks rises faster than for consumption and falls when demand for consumption rises faster than for sectoral buffer stocks. There are at least two alternative measures. Buffer stocks can be measured directly as inventories of goods in process or intermediate output for each sector, or we could use capacity utilization rates for each sector. Neither was used in this paper, though either might be used in subsequent research. Regressions were estimated where the buffer stock measure was explained by the three-month Treasury bill rate. Since credit expansion lowers the interest rate, the slope on interest should be negative for early and late stages of production and positive for middle stages.

1:40These regressions, unfortunately, had very low r-squares. Higher r-squares were obtained by adding 10-year Treasury bill rates, significant negative Positive coefficients were found on 10 out of 18 sectors suggesting these sectors are either early or late based on the result that the buffer stock measure rises when interest rates fall, that is in response to credit expansion. This doesn't offer a statistical basis to distinguish early from late-state sectors however. Significant positive coefficients were found on 7 out of 18 sectors suggesting these are Intermediate Stages of Production. And that leaves out one which didn't have either coefficient significant. None of these results is too surprising.

2:26The question marks are indicating ones that I thought weren't completely obvious that they should necessarily be late, early stage sectors, but I didn't think it was such a bad outcome. More question marks here for the intermediate stages. Why some stages that we would expect A priori to be late stages appear here is problematic. For the late stages, which again, I arbitrarily decided this is a late stage versus this is an early stage, based on those that I got the outcome, these should be 10 out of 18 are early or late. All right, and there are no surprises here. Finally, the residuals from these regressions are subjected to power spectral density analysis.

3:12These residual series should be stationary and our linear functions of three stationary series. The buffer stock measure which is a ratio of the producer price index for the sector divided by the consumer price index and the two interest rates. The finding that the residuals are antipersistent with Hearst exponent less than one half indicates that the sector is dominated by interest rate movements which we would expect for normal, I'm sorry, for early sectors. The finding that residuals are persistent with first exponent greater than one half suggests the sector is dominated by normal ongoing entrepreneurial adjustment, which should be characteristic of late sectors.

3:57And if it's very close to one half, that indicates that the sector is dominated by normally distributed adjustments for middle stages. To perform spectral density analysis, the series is divided into various frequencies or subsample sizes analogous to interval lengths or windows in the rescale range and roughness length methods. The signal power, a Fourier transform measure of variation occurring within each wavelength, is computed for each frequency. In the log-log plot of this power measure graphed against the frequency, the slope is estimated by least squares as negative b, which is then used to compute h, the Hurst exponent. These are two examples. This compares the lowest sloped power spectrum graph for crude materials on the left with the highest for finished goods, less food and energy on the right.

4:52and because it has a low slope, it's significantly less than one half, we can infer anti-persistence for the adjustments in the crude materials buffer stock, which is and would be expected a priori to be an early stage sector of production and for finished goods, less food and energy and pretty much anything that's described as finished goods, finished consumer goods, However categorized, you would expect that's fairly likely to be a late stage of production, although that outcome is not absolutely universal. So based on the spectral density analysis, we see clearly that the earliest stages have the lowest Hearst exponents, meaning that the buffer stocks are anti-persistent and driven by credit expansion.

5:40Why finished consumer foods appears here is a bit of a mystery. The latest stages have the highest Hurst exponents and these results are intuitively appealing. Middle stages are defined somewhat arbitrarily as those with Hurst exponents closest to one half and the arbitrary limit that I set was within one sample standard deviation of one half. However, this appears to include some late stages which is a bit of a puzzle. This may occur because the producer price indices track the consumer price index fairly closely Mostly for Late Stages, which then would impose normality, the result that H is equal to one half. It's more difficult to explain why this category includes some apparently late stages.

6:28These results overall support and are mostly very easy to interpret according to Austrian Business Cycle Theory, although there are a few idiosyncratic quirks. However, the finding of anti-persistence in 10 out of 18 sectors is very, very difficult to reconcile with the alternative real business cycle theory. Does that music mean that my time is up? And I have to get off the stage. Thank you very much.