As part of the Federal Communication Commission’s *Tariff Investigation Order and Further Notice of Proposed Rulemaking on Special Access Services*, the Agency included as Appendix B a commissioned empirical study by Dr. Marc Rysman of Boston University. While there’s a lot to say about Dr. Rysman’s analysis, because it just came out two days ago I want to take the time to make sure I fully understand Dr. Rysman’s technique and modeling choices before passing judgement. That said, while I won’t provide a thorough analysis of Dr. Rysman’s econometric analysis in this blog, there are some glaring items that are readily apparent even upon my first read of the document.

First, I cannot help but note that my recent Perspective, *The Road to Nowhere: Regulatory Implications of the FCC’s Special Access Data Request*, seems spot on. Dr. Rysman sends a clear message that the FCC’s Special Access data is of very limited use in assessing the price effects of competition. Also, the estimated effects of competition are much smaller than I expected. Dr. Rysman’s evidence showing that regulation appears to facilitate collusion was interesting, since that effect was the basis for the FCC’s detariffing of long-distance services.

I also feel obligated to point out one well-known problem that implicates the magnitude of the price effects of competition estimated by Dr. Rysman’s model. Since these effects are at the center of his analysis, I think it’s important to correctly (or precisely) interpret the size of these effects, at least as they are estimated by his model.

In his price regressions, Dr. Rysman specifies the dependent variable in natural log form. Competition is measured using dummy variables. So, his model looks something like this:

ln*P* = b_{0} + b_{1} **COMP* + b_{2}*X* + *e*

where *P* is price, *COMP* is a competition dummy variable (taking values of 1 where competition exists, 0 otherwise), *X* is other stuff included in the model, and *e* is the econometric disturbance term. In Dr. Rysman’s model, the coefficient b_{1} is used to quantify the effects of competition. For example, he claims in one of his model’s that “for DS3 lines, the effect is a 10.9% decrease in price (at p. 229).” This number is, in fact, taken from the first estimated coefficient listed in the second column of Table 14 (-0.109 with standard error 0.021).

Yet, this is not the correct effect of competition.

As detailed by Halvorsen and Palmquist in the American Economic Review in 1980 and discussed by Dave Giles in his 2011 blog Dummies for Dummies, when the dependent variable is measured in log form, the percentage change in the dependent variable for a change in the dummy variable (from 0 to 1) is calculated using the expression: 100[exp(b_{1}) – 1], or even better 100[exp((b_{1})-0.5∙v(b_{1})) – 1], where b_{1} is the estimate of b_{1} and v(b) is the variance of the estimator. The latter formula accounts for a bias inherent in using b_{1} instead of b_{1} in the simpler formula under the assumption of normality of the disturbances. In many cases, the two formulas produce very similar results. Various alternatives have been offered when the disturbances are not so well behaved. (Note: If going from 1 to 0, then you need to use exp(-b1) in the formula.)

As Dave Giles notes in Dummies for Dummies,

… in general, these values will be quite different from the 100[b

_{1}] that some of our chums insist on using. For example, if [b_{1}] = 0.6, the naïve econometrician will conclude that there is a 60% impact; whereas it is really an 82.2% positive impact as [COMP] changes from 0 to 1, and a 45.1% negative impact as [COMP] goes from 1 to 0!

Inserting the estimated coefficient of -0.109 for DS3s from Table 14, the price effect is -10.35%, not -10.9% as Rysman reports. Dr. Rysman has overstated the price effect by about 5.3%. For DS1, the estimated competitive effect is reported (at Table 14) to be a paltry 3.2%, which is very close to the properly calculated effect of 3.15%.

You’ll notice two things about the difference between using the coefficient and the proper formula to measure the effect. First, when the coefficient on the dummy is negative, using the coefficient always results in an overstatement of the competitive effect. Second, the more negative the coefficient, the bigger the difference between the correct and incorrect impact. For example, if the coefficient is -0.05, then the percentage difference in price is -4.9%; if the coefficient is -0.20, then the percentage difference in price is 18%.

Since Dr. Rysman’s estimated competition effects are quite small, the improper interpretation of the results is not fatal. In almost all cases (using the tract fixed effects), the competitive price effect for DS1s is less than 5%. Price effects for DS3s are typically around 10% or less. Given these very small price effects (from “monopoly” to “duopoly” no less), the incorrect interpretation of the regression coefficients does not produce huge interpretive errors. Nevertheless, it’s worth interpreting the effects of the variables in the model correctly before the FCC uses Dr. Rysman’s results to regulate a business with annual revenues of $45 billion.