This is a post in response to some of the issues raised by SRW.

I appreciate the feedback.

First, I consolidated leverage by industry (e.g. 5 digit NAICS industry). Next, I looked only at downward deviations in price — e.g. I computed stddev( .5abs(x) – .5x), where x was the the month over month percent change in price for each BLS 5 digit price index.

Therefore now we have mappings between industry leverage, and the downward standard deviation of percent changes in price.

Finally, I weighted everything by equity, so that small industries (often with high leverage) do not contribute so much.

There were a few outliers — very small industries with Long Term Debt/Equity in excess of 4. I dropped those, and this is the result:

Here is the results of running a linear regression, weighted by equity:

Residuals: Min 1Q Median 3Q Max -30730 -2498 -1475 -444 93967 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.2108 0.3201 6.906 1.94e-10 *** x -0.8354 0.5565 -1.501 0.136 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 9898 on 131 degrees of freedom Multiple R-squared: 0.01691, Adjusted R-squared: 0.009409 F-statistic: 2.254 on 1 and 131 DF, p-value: 0.1357

As you can see, there *is *a negative correlation, but it is not significant and the R^2 is less than 0.1. Also, just by looking at the graph, we can see what is happening — the big blue dot at the top, which is industry 32411 — Petroleum Refineries. It has enormous downward price volatility and slightly below average long term debt to equity. If we remove this industry and run the linear regression again, we get:

Residuals: Min 1Q Median 3Q Max -13027.5 -1280.9 -404.1 601.1 15222.2 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.5321 0.1283 4.147 6.05e-05 *** x1 0.7277 0.2071 3.514 0.000607 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3562 on 130 degrees of freedom Multiple R-squared: 0.08677, Adjusted R-squared: 0.07974 F-statistic: 12.35 on 1 and 130 DF, p-value: 0.000607

Now there is a *positive* correlation between downward price volatility and debt to equity, which is also statistically significant. But I wouldn’t read anything into it, as the R^2 value is too low.

In either case, even after taking into account the issues of downward price deviations versus leverage (hint — not much difference between downward and upward deviations), and firm versus industry leverage, it still remains the case that there is no evidence that long term debt is a binding constraint that prevents firms from lowering prices.

My own “null hypothesis” is still that firms, in aggregate, do not lower prices because they cannot, regardless of whether they are funded by equity or debt. Of course the individual firm can (and does!) lower prices, but in aggregate firms * produce less*, meaning that supply decreases up until the amount supplied is the amount that is profitable to supply at the given overall cost of capital.

Just because there is an overall decline in demand does not mean that there is an overall decline in the cost of capital faced by firms. There is no rational reason to associate one with the other. But that is a topic for another day!

I appreciate any feedback. I’m not a data massaging expert, so if you have other suggestions or approaches, I would be interested in hearing them.

I’ve posted a spreadsheet so that others can massage the industry data. If you want csv db dumps of raw data — e.g. firm/price/financials mappings — send an email to rsj at windy at yahoo, but supply an ftp address or another transfer mechanism, since the files are too large to send as email attachments. Also specify if there is anything specific that you are interested in, since you may be better off downloading the db dumps from the BLS ftp site.

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Once you see r^2 that low, you should have gone back to refine your model before continuing the post. The first-order model doesn’t explain the variability of the dataset; any conclusion based on a model that explains under 10% of the data is.. not solid. Your graphs are colorful, the words are interesting thought experiments.. but the numbers don’t support your conclusion.

The sentence using the phrase “statistically significant” may be incorrect.. nobody knows until a chi square test is done. The point of the chisquare is to see if the relationship between your variables happens by chance or not.

The purpose was to show no correlation.

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