## Saturday, November 19, 2011

### The rising cost of financial intermediation

A lot of the recent debate on regulation in the finance industry has revolved around issues of size. How big is too big, in the financial sector? Should the largest financial corporations be taxed and monitored more than others? This set of issues has been dubbed "systemic risk", and a lot of measurement and theory work has gone into it.

Systemic risk, however, is about the size of one financial corporation relative to others. Thomas Philippon, in ongoing research, asks a different question: how big is the financial industry in the US as a whole? In relation to its output, does that size seem reasonable?

The graph above answers the question of the size of the financial sector. It shows the income share of the financial sector. Income is measured as wages and profits; there are some difficulties in obtaining those on a consistent basis, so Philippon looks at different data sources, which correspond to the different lines. Across sources, the message is the same: the income share of finance has changed over time, but it's larger than it ever used to be.

Now, of course, this need not be, per se, a bad thing. Perhaps there are good reasons to allocate a larger share of income to the financial industry. In fact, Baumol showed in 1967 that in a standard neoclassical growth model, the income share of a sector can grow over time if 1) it experiences higher technological progress than other sectors and 2) the elasticity of substitution across sectors is less than one.

The financial sector, however, is not just any type of sector: it does not produce a special variety of goods; instead, it provides intermediation services between different parts of the economy. Baumol's standard explanation for the apparent "superiority" of finance (relative technological progress, elasticity of substitution) does not apply. So Philippon sets out to construct variations of the neo-classical growth model that capture what he deems are the two most important roles of the financial sector: 1) it transfers funds from households to other households, corporate borrowers and the government, and in the process provides monitoring services 2) it provides liquidity services to households, ie it holds their cash and makes it available to them.

He then asks: what path of intermediation costs does the model need in order to match the observed path of finance's income share? This is the same type of approach that Mehra and Prescott took with the equity premium. They asked: given the large observed equity premium, and the comovement of equity values with consumption, what risk aversion is consistent with optimization of rational agents? The answer was: a really high risk aversion. Philippon's answer to his question (what intermediation cost is consistent with the rise in finance's income share in an efficient model of financial intermediation?) has the same flavor: you need pretty steeply rising costs.

How does he get to that answer? He focuses on the balanced growth path of his neoclassical economy with financial intermediation, on which he shows that the the following relationship has to hold:

$\phi = \psi_m \frac{m}{y} + \psi_c \frac{b_c}{y} + \psi_k \frac{b_k}{y} + \psi_e\frac{e}{y} + \psi_g \frac{b_g}{y}$

This relationship links the share of finance to gdp ($\phi$) to the "output to gdp" ratios corresponding to the various functions of the financial sector. For example, $\psi_m$ is the unit cost of intermediation for liquidity services, and $\frac{m}{y}$ is the ratio of total "liquidity services" (in his measure, bank deposits and assets of money market mutual funds) to nominal gdp. The following terms correspond, respectively, to household debt, corporate debt, corporate equity, and government debt. Note that this is a pretty standard decomposition: in a standard neoclassical growth model, labor's income share ($\alpha$) is equal to the unit cost of labor ($w$) times the output share of labor ($h/y$).

The key idea of the paper is to use this relationship to back out something akin to the "intermediation cost" of finance - in much the same way Mehra-Prescott backed out risk aversion from the equity premium. There are some measurement problems here, related to flows and funds, and which I do not understand, but the idea is to rewrite the relationship above as:

$\phi_t = (\gamma_m \frac{m_t}{y_t} + \gamma_b \frac{b_t}{y_t} + \gamma_e \frac{e_t}{y_t} ) \psi_t$

where now the terms are grouped by, respectively, liquidity services, debt (household, government and corporate), and equity. The term $\psi_t$ represents the average unit cost of financial intermediation, while $\gamma_m$, $\gamma_e$ and $\gamma_b$ represent the relative cost for a particular type of service. The implicit assumption here is that these relative costs are constant over time. (It's very unclear to me why he cannot just estimate the linear relationship above, with "output-specific" costs; it seems like he has all the data he needs).

Anyhow, one can now go ahead and compute a series for $\psi_t$, in what is probably the most straightforward estimation procedure ever: divide finance's share of income by what is, at its core, just a weighted measure of the output of the financial sector.
What he gets from this exercise is the picture below.
What do we learn from this? There are two points worth emphasizing.

First, intermediation costs have been moving in a stable range over the very long run - somewhere between 1.5 to 2.5 percent, ie a cost 1.5 to 2.5 cents per dollar of financial "stuff" produced. That is remarkable, given how variable the different series that go into the construction of the series are.

Second, it's been trending upwards for the better part of the last forty years.

This second fact is the main finding of the paper; and it is puzzling, for two reasons. The first one is that we tend to think of the early 1900's as times when the finance sector was highly monopolistic , and could have extracted higher rents (read: higher income per unit of financial stuff produced) than the current, probably slightly more competitive financial sector. Yet if you look at the graph, intermediation costs were lower then, than they are now. The second reason for which this rise in costs is puzzling is the IT boom. The financial sector invested heavily in IT; today most trade is conducted electronically; even the floor of the NYSE was closed down and replaced by computers. All of this suggests large productivity gains in intermediation, yet according to Philippon's measure, none of these gains were passed through in the form of lower intermediation costs.
So what happened? Philippon sees two possible types of answers. The first one are "efficient" answers. It is possible that the financial sector is providing services that he forgot to account for, and the remuneration of which increased in the past 40 years. Another way to put it is that there is an omitted variable in the decomposition above, which biases upwards the estimates of cost - because the financial sector actually produced more stuff. This other stuff could be services such as providing better information about financial assets. Think about portfolio managers, for example. This should still count as an increase in output - only one that the neoclassical model fails to capture. A second type of explanation is that the financial sector is doing something that would not contribute to an increase in output in any type of model, but for which financial intermediaries are still being rewarded. And indeed, the volume of asset trading has been booming in the financial sector in the past 20 years, suggesting that the increase in the financial sectors' share of income may be linked to a surge in transactions, some (or a lot) of which may not be creating any value added.
To be fair, this is a confusing paper. It sets out to do what Mehra and Prescott did, but in some sense, it only does half of it. The strength of Mehra-Prescott was that they could compare their high estimates of risk aversion to the low micro-founded estimates and say: ahah! there is an order of magnitude of difference; this is a puzzle. But Philippon does not really do this. He has -for now - no direct evidence that contradicts his model-based measure of the cost of financial intermediation. All he can say is that we have a hunch costs shouldn't have increased, especially given the IT revolution. But it's just a hunch. So this paper really needs further exploration of the "other half" of the puzzle: can we directly measure intermediation costs, and if so, have they gone up?

But imagine we do find stable or falling micro intermediation costs. Then we have a major puzzle. Where does might the wedge between macro and micro costs come from? Does it reflect some deep inefficiency in terms of resource allocation? Now, those questions are all fuzzy and predicated on the idea that there actually is a puzzle. But it looks like there might well be one, and making progress on accounting for it seems like a better use of our time than, say, setting up tents and clashing with police in public parks. Although it's probably a bit more austere.