It's time for a long overdue edition in my "Review of the week" series!!!! For anyone just joining the fun, this series was inspired by an experimental class I took where a teacher would RI published academic papers every other week. Part 1 and Part 2 for reference.

That said, I'm flying on my own this week. I'm writing a fairly extensive critical literature review of returns to scale in the banking sector and happened upon a paper I thought was worth bringing here.

Trigger warning: this post will get technical

The paper we are looking at today is "Too big to be efficient? The impact of implicit funding subsidies on scale economies in banking" by Davies and Tracey.

This paper wants to test if implicit funding (from expected government bailouts) in banks considered "too big to fail" could be a driving factor in cost economies of scale. They use a proxy variable for this "implicit funding subsidy" which is the difference between the "support" and "standalone" credit rating of each bank.

They model the costs of banks using a translog cost function (see p.4-5 for details) and estimate the returns to scale by computing the inverse of the cost elasticity of output. Note that output is a right hand side variable in the estimated cost function, this will come back later.

The data used is panel data on 172 banks from 37 countries with assets ranging from $5Bn to $4Tr, dating from 2001 to 2010.

The study finds increasing increasing returns to scale with size without accounting for implicit funding subsidy (see figure 3, p.9) and decreasing decreasing returns to scale when accounting for it (figure 4, p.12).

Notably, they find much milder results (largely constant returns to scale) when restricting their sample from 2001 to 2007 (eg. taking out the crisis). This is p.14, table 1, panel c for all you nerds following at home.

RI

To start this RI, let's bring everyone up to speed in the literature of returns to scale in banking. If you have one paper to read, it's Loretta Mester's chapter in the handbook of financial intermediation. The consensus is fairly clear at this point (and has been since ~2003), that there are increasing returns to scale, though recent studies hint towards the fact that these may become exhausted (and revert to constant returns to scale) around the $1Tr mark. There is not much of a consensus as to what causes these increasing returns to scale.

Take note that I said the consensus is clear at this point. That was not always the case. In fact, especially in the 20th century, the literature had varying and conflicting results. A 1993 paper called "Resolving the Scale Efficiency Puzzle in Banking" came to the conclusion that this was because globally fitting a single translog cost function across various banks of various sizes in various regulatory environment with various output mixes led to specification bias, which led to goofy results. This is because the globally fitted cost function will inevitably misrepresent some banks in the sample and lead to bias in some of the estimations.

At this point, you should be raising an eyebrow.

Modern studies (like the one I linked above) use nonparametric statistical models to avoid functional form mispecification. One example of a scenario where parametric methods are appropriate is for small sample of homogenous banks, like in this study on the "Big Six" banks in Canada by the Bank of Canada. Also note that in this study, the BoC uses panel data and, as such, does tests to see if non-stationarity is a problem in the model used.

Your eyebrow should now be seriously cocked.

Now, we have two major and completely undealt with problems in the Davies and Tracey paper, both of which should be known to anyone who spent a few hours doing a literature review. Fitting a global translog cost function on banks whose size range across 4 orders of magnitude and 37 countries to estimate returns to scale in banking should not be a thing serious researchers do in 2002, let alone 2012. Not testing for non-stationarity problems in panel data is also very sloppy.

But I have further criticisms!

I told you to remember that output was a RHS variable in the cost function, the model being estimated. Now, everyone who took introductory statistics knows right hand side variables are supposed to be exogenous, and anyone who took intermediate micro should now be wondering how output can truly be exogenous on costs. Of course this issue is not addressed at all in the paper.

In the interest of piling on, their proxy measure of implicit funding subsidy, the difference between two credit ratings, changed severely during (and after) the financial crisis. Now credit ratings and the financial crisis aren't exactly the best friends in the world, so it wouldn't be outlandish to say that there's probably some sort of bias in the proxy used, at least before, and during, the GFC. That said, the authors mention this issue, so there's that.

The idea in this paper is really cool, and I think it definitely merits further study. What causes increasing returns to scale in banks is still an open question.

However, we can't take any results this paper presents seriously with all the potential bias that isn't addressed. As such, I have to stamp it with the official Review of the Week stamp of BadEconomics.