Appendix 6C Reply to Arcand, Berkes, and Panizza

In an earlier version of this chapter (Cline 2015b), I argued that statistical findings of a negative quadratic influence of finance on growth were ques­tionable. I showed that if causation went the other way, from rising per capita income to rising financial depth, for example, because home mort­gages are a luxury good, a quadratic term relating growth to finance would have a spurious negative coefficient.

Before turning to the critiques in their comment, it is important to em­phasize that even in their own study, the three authors (referred to as ABP hereafter) found virtually equal statistical performance of a formulation in which the influence of finance was logarithmic rather than quadratic. As a consequence, their own results suggest that there is little basis for stating that the influence of extra credit turns negative beyond some point rather than that this influence tapers off but remains positive. Thus, their table 1 shows in the quadratic formulation that a country with credit to the private sector at 150 percent of GDP could increase its growth rate by 1.57 percentage points by reducing credit back to an optimal 83 percent, but in the logarithmic formulation that reduction in credit would reduce the growth rate by 0.44 percentage point.^[244] The R² in the quadratic formulation is 0.458, almost indistinguishable from the R² of 0.435 in the logarithmic formulation. The finance variable is significant at the 5 percent level in both formulations.

The authors do apply a statistical test to verify that their quadratic func­tion relating growth to finance has a positive linear and negative quadratic term, yielding an inverse-U shape.^[245] However, they do not apply a similar test for whether an inverse-U is significantly superior to the monotonic logarithmic form.

If policies were aggressively pursued based on the inverse-U influence of finance on growth, punitive taxes could be required to shrink credit by more than 60 percent in economies such as the United States and the United Kingdom (where the 2010 levels reached 195 and 202 percent of GDP, respectively).^[247] But a difference in explanatory power that does not show up until the second decimal place in the R² is too slim to warrant such policies.

Regarding the critiques of my policy brief in their recent comment, ABP (2015b) first noted that my equations demonstrated not that the quadratic term on finance was necessarily negative and spuriously so, but rather that if the linear term was positive, then the quadratic term had to be negative. But the signs could also be the reverse. That observation is true, but it is also trivial and does not constitute a meaningful critique. Inspection of my relevant equation makes it clear that the sign of the linear term does indeed have to be the opposite of the sign of the quadratic term (subject to an ad­ditional specific threshold if the linear term is negative). Namely, I showed that if h alf of the observed reduction in growth as per capita income rises is spuriously attributed to a quadratic influence of finance (rather than un­derlying convergence), then:

Here, θ is the coefficient of growth on the quadratic term of finance and π is the coefficient on the linear term of finance, in a regression equation ex­plaining growth per capita on three variables: the level (or more accurately, logarithm) of per capita income; finance (e.g., private credit as a percent of GDP); and finance squared.

But the latter condition is only a curiosity. In the large empirical litera­ture relating growth to finance, there is to my knowledge not a single signif­icant finding that additional finance at first reduces growth but eventually (say after finance reaches 100 percent of GDP) increases growth again, such that π < 0 while θ > 0. So in the relevant application, estimating the influ­ence of finance on growth, it is strictly the case of positive linear influence that would generate a spurious negative quadratic influence. In any event, it is unclear why ABP should be so content that any spurious influence would have to show up with an opposite sign for the quadratic term from that on the linear term. If they agree to that proposition, then they would have to recognize that their own tests preclude the result that both the linear and quadratic terms are positive, yet that is the implied alternative to their test results in which the linear is positive and the quadratic negative. If that al­ternative is impossible, they have set up a test that cannot be rejected, and it is not a meaningful test.

The second critique of ABP is that if the quadratic term on finance is spuriously negative because of a pattern of greater financial depth as a con­sequence of higher per capita income, then by the same approach I used to arrive at equation 6C.1, it would follow that in a simple linear regression of growth on per capita income and a simple (linear only) finance variable the coefficient on the latter would be negative, yet the empirical literature finds it is positive.

But a more fruitful way to think about this issue would be to consider two types of finance: one that causes growth and the other that responds as a luxury good to rising relative demand as per capita income rises. For simplicity, the first would be business loans and the second, home mort­gages and loans for consumer durables. The system I spelled out would apply to the second category of finance, not the first. Empirical results pri­marily capturing the first type would find a positive coefficient of growth on finance. Those primarily reflecting the second type would find a negative simple linear coefficient of growth on finance, which may explain the nega­tive coefficients in the Cournede-Denk (2015) study. Importantly, in this interpretation, reduction of finance will not increase growth, any more than a luxury tax shifting consumption away from any other luxury good would increase overall growth.

Third, ABP take issue with my critique that their parameters indi­cate that implausibly large increases in growth rates could be achieved by shrinking the financial sector. I illustrated my point using the case of Japan, which (using their coefficients) could supposedly raise the growth rate by 1.6 percentage point by reducing credit to the private sector from 178 to 90 percent of GDP. They cite an alternative set of estimates, control­ling for banking crises, in which reducing credit from 178 to 90 percent of GDP in Japan would boost growth by “only” 0.95 percentage point. I would consider this alternative also implausible. They go on to insist that “regressions...are not meant to, and do not, fit all points (the regression's R² is never one)...[so] it is singularly inappropriate to pick out a specific data point to purportedly invalidate a result.” But the Japan example I gave does not involve Japan's actual residual but instead simply applies the regression line to two alternative credit levels (which the line would also predict for any other country at comparable credit levels).

Finally, ABP run new tests finding that if I had run my regressions of growth on doctors, R&D technicians, and telephones in what they believe is the right way—including country fixed effects—the spurious but statisti­cally significant negative quadratic terms would have disappeared in two of the three cases. I have argued above that on this issue it is more appropriate not to include country fixed effects, so my results arguably remain more relevant than their reversal of two out of three of them.