I got a pair of deuces, what you got?

... and what's the game we're playing, again?

Anyways. There comes a time when every macroeconomist needs to lay their cards on the table. Form their expectations, rational, adaptive or otherwise, but commit to something or other. Like a forecast.

And this time is obviously one of those times. All this crazy stuff happening, we should be able to say something about it. Something specific, in particular, to be precise, without qualifications. Most of the commentary so far has been on intermediate aspects, caveats, details, or theoretical nuances.

Yeah yeah yeah, credit crunch or not. Greenspan made some mistakes or maybe he was a Trotskyite saboteur. If only Friedman didn't advise the junta of Liechtenstein while Martin Luther was busy nailing his monetary thesis to the door of Wittenberg cathedral (i.e. on his "blog") Icelandics would've never settled Greenland. And then the Easter Island economy's money supply consisting of big statues of very important looking faces would've never collapsed, prompting a bailout of the Long Term Capital Management causing Cardinal Mazarin to scuttle the Bretton Woods system, Athos to become a drunk, Aramis to become a cynical advisor to McCain and Porthos wouldn't have died trying to hold up the whole edifice of the American financial system while Paulson cackled, Wasilla burned and Nemo fiddled. Rock the Vote against the Global Warming and for the Moderate Progress Within the Bounds of the Law!

But seriously. How much is GDP gonna fall? How high will unemployment get? When you say "worst since the Great Depression", do you mean like a 32.5% decline in output, .1% lower than that between 1929 and 1933? Or do you mean a 5% decline,.1% higher than the 1973-1975 recession? There's a lot of freakin' percentage points between 33% and 5%, which means there's worst and then there's worster, so let's get specific.

But of course I'm not gonna tell you. Well, I will but it should be immediately understood that the forecasts that follow are just based on half-monkey-butt guesses and quick algebra which I haven't double checked, but I think it's at least a way to clarify some of the issues and stop some of the crazy talk. Of course, we live in crazy times, so crazy talk might not be all that inappropriate. Hmm, I've already started with the qualifications.

Casey Mulligan has laid his cards on the table. Whatever you think of his estimates, at least he's estimating and doing what a macroeconomist should be doing in a situation like this. Predictin'. Forecastin'. Not evadin' the issue. Obviously he's new to blogging but I'm sure he'll learn soon (there's a lot more there).

My approach here is going to involve much more pulling stuff out of thin air, but it does have the potential misbenefit of being simpler.

So national income is composed of the financial sector and the non-financial sector. Here I take the financial sector to include the real estate sector, since it's more or less the same mess.



where Y is output at time t, F is the financial sector and NF is the non-financial sector.

Some data here. Better data around if you look.

In 2007, "Finance, insurance, real estate, rental, and leasing" (note that this does not include Construction which is a separate category. Real estate is people who buy and sell houses and other land for other people) was 20.68% of GDP. In 1998, it was 19.26% of GDP. Ok, here's the first problem. About 20% of the 'real economy' is 'unreal economy'. In other words, the financial sector + real estate are big enough in and of themselves that even if all negative effects from the present crisis are confined to that sector, it will still be big enough to show up as a decent recession. Suppose the financial sector shrinks by 10%. That's still a 2% drop in overall GDP which is larger than the last two recessions - basically, since Volcker.

10% shrinkage in the size of the financial sector is pretty huge actually. But anyway, we'll get to that soon enough. Ok, some simple accounting. Based on the equation above we have







or diving through by Y_t-1, re-arranging and all that, we get




where alpha_t=F_t/Y_t, or the share of the financial sector in GDP at time t. Factoring out the growth rate of the financial sector (or in this case, it's shrinkage) and letting g(.) denote growth rates ((dX/dt)/X) and dropping time subscripts on the alphas (which basically means going to continuous time - this doesn't matter significantly) we have




This is just accounting (true by definition) and it just means that the growth rate (or the fall in it) in output is a weighted average of the growth rate of the financial and non financial sectors where the weights are the shares of each in output. Like I said, it's just accounting. But here's where the economics come in - we can give an economic interpretation to the ratio




as the elasticity of the non-financial sector to the financial sector. In other words, this would be the effect that the trouble in the financial sector has on "mainstream", the "real economy" or whatever you want to call this. When you hear people talking about "how will this crisis affect main street?", they're really talking about that elasticity. Except so far it's not really an elasticity, I'm only pretending it is, so far it's only accounting. Still, at this point I can start putting some numbers on these variables and start figuring out how much of a decline in output can happen. Basically two variables got identified which will determine the recession, if any, that's gonna happen. And these are two variables that have been mentioned in a lot of the commentary directly or indirectly, but which here I am putting at the forefront, which I'm gonna slap some number on. Which allows me to put my pair of deuces on the table and look triumphantly at... well, nobody in particular. But it will be a really triumphant look. Because it's at least a forecast.


So ok. First question, how much will the financial sector shrink? In other words, what's . Above I said -10% or -.1. That was just an example, using a round number and all that. The truth is that neither I nor nobody else has any good idea of what that's going to be. We live in crazy times, as I said. But I'll try being rational in non-rational times, which is of course very irrational. Anyway. According to the data above, between 1998 and 2007 the Financial sector of the economy grew by about 7% more than overall GDP. So let's pretend that 1998 was a "normal year" and that if none of this crazy stuff happened the financial sector + real estate would've grown at about the same rate as overall GDP (I'm picking 1998 because it's far enough and close enough to "normal times". The share of the financial sector in GDP was increasing before that but 1) at least some of that increase DOES represent genuine innovation in the financial markets and 2) I'm too lazy to look for data that goes back before 1998). So our first monkey-guess is that the "correction" that's going on is going to involve the financial sector shrinking by 7%, down to where it was if that sector had grown at the same rate as overall output. So



This is actually the easy one. The tougher question is, what is going to be the spillover from the financial sector into "main street" or the non-financial sector, or what is . So far it's only really the ratio of the growth of the non-financial sector to the growth rate of the financial sector but if we assume it's some kind of a behavioral/social elasticity (i.e. do economics rather than accounting) then we can get some estimates. And here they are...

Oh wait. This is still too accounting based. Ok, let the size of the non-financial sector be a function of the F sector (which provides credit to the NF sector, as well uses up resources which have alternative uses in the NF sector) and a whole bunch of other stuff that we'll call A:



We could include a lag here and let it be a function of F_(t-1) but that would just unnecessarily complicate things. Let's also assume that the "whole bunch of other stuff", whatever that is, grows at a constant rate, g. So growth of A is g. In that case, the growth of the non-financial sector's going to be



where now is the spillover of financial markets to non-financial markets (rather than just an accounting ratio), g is an exogenous growth rate of the non-financial sector due to productivity increases which have nothing to do with the financial markets (technological progress and the like) and is how much the non-financial sector grows due to these productivity increases. In fact, at this point it's not too crazy to assume which would be equivalent to assuming the functional form (even if one objects to this formulation, it's still that data-wise phi*g would be the actual estimated growth rate of the non-financial sector which is not due to changes in the financial sector, which is what we actually care about here. Yes. It is difficult to write economics in a non-confusing manner. That's why there was comedy at the beginning of this post. To soften you up). So now our equation for the size of the recession becomes:




or




which is very similar to what we had previously except for that now we have an extra term (1-a)g, which represent increases in output due to exogenous growth in the non-financial sector and, more importantly, our interpretation of epsilon has changed - now it is truly an elasticity which measures the effect of changes in the financial sector on the main street economy.

Ok, but we still need to know what that epsilon is. I don't know. I know "g" though. If your horizon is a year than I'd say it's between 1% and 2%. Let's not be too optimistic and say it's actually .5% but now that we have actual formulas we can calculate the recession for various levels. Hmmm,... epsilon.

The epsilon or the how the financial crisis will affect the size of the "real economy". Thinking about it there's couple heuristics we can use here. First, there's a lot of talk about how the financial sector is too big and too bloated. A lot of that is crazy talk from people who ascribe to the Thomas Aquinas view that interest rate should be zero, but in these particular times there's probably something to it. What this means is that epsilon cannot be THAT big. I'd say less than one, and significantly so. Second, note that it can be positive or negative.

If epsilon > 0 this means that when the financial sector contracts, the non-financial sector does as well. The straightforward interpretation here is that as the financial sector collapses, the non-financial sector gets denied credit. And I'm sure you've been hearing stories about that.

A more counter-intuitive case would be that epsilon < 0, which you don't hear as much about. But this has a natural interpretation too. As a particular sector of the economy contracts, it releases resources, in terms of workers, capital, knowledge and yes, even re-directed credit, which can than be used by the non-financial sector. In fact, for most industries, this is exactly what happens when one industry contracts and another expands (and it is at least partly what Casey Mulligan's talking about in his post). That means that as the financial sector shrinks, the non-financial sector is given more resources to grow. So the elasticity is negative (which is good news for us here).

Additionally, in the long run (yes yes yes, I know that in the long run "we're all dead" but if you never think about the long run then when it comes it's gonna suck, and so will the medium run which comes around while you're still alive. (Rock the Vote against the metempsychosis of good quotes into empty cliches!)) insolvent financial institutions will be replaced by new, solvent ones, or their business overtaken by old, solvent ones. And that means the credit will resume and the negative aspects of epsilon will be reduced.

There's another aspect that should keep epsilon down in absolute terms ...

Oh.

The forecasts. Where are they? Hold up, hold up. Would anyone try to bluff by telling you they got a pair of deuces? They're coming.

... and that's the fact that by many accounts banks are withholding credit for two reasons. One, they wanna hoard because they're worried that they might go insolvent themselves. Two, they wanna hoard because they're worried that whoever they lend to will go insolvent and won't pay back. The first one applies generally. The second one though should not be a problem in terms of lending to non-financial institutions - provided that most "main street" firms are fine. Which if they're not, then we're in big trouble, but then, why are we worrying about the financial crisis in particular anyway? So while the supply side of credit may be a problem here, there shouldn't be much of a problem on the "effective" demand side - i.e. banks should be able to find non-financial firms to lend to.

Note that this DOES NOT apply to the trouble that's currently starting in many emerging markets, as noted in some places, where many firms are potentially insolvent. In that case, both the number of potential supply of lenders and decent borrowers are low so ... well, this post is getting long and you probably want your forecasts, but yeah, much bigger trouble.

Anyways. I pick:

In the short run; epsilon = .3, in other words, if the financial system shrinks by 10%, the non-financial system shrinks by 3% due to lack of credit. I also pick g (exogenous growth in non-financial sector) g=0, reflecting, well, the short run.

In the medium run; epsilon = 0. I'm just gonna assume that the positive and negative effects described above offset each other. I'll let g=.005 in this case.

In the long run; epsilon = -.2. For symmetry I wanna go with -.3 but I also want to be a bit pessimistic. So if the financial system initially shrinks by 10%, it releases enough resources (I do wish I had some input/output tables here. It's true, people don't do that enough anymore) for the non-financial sector to increase by 2%. Going along with the pessimist I'll keep g at .5%.

What does that gives us?
Well, here's the values based on all this stuff above:
g_F - exogenous shrinkage in the financial system due to the present crisis = -.07
alpha - share of the financial sector in gdp, rounding it up = .2
g - exogenous improvements in the non financial sector = 0 in short run, .005 in medium and long run.
epsilon - .3 in short run, 0 in medium run, -.2 in long run.

Which means:
In short run



In other words a drop, peak to trough, in GDP of slightly more than 3%. How bad is this? Well, it's basically the second part of the Volcker recession. So not as bad as all of the Volcker recession of the early 80's (the whole thing was 5%+). But worse than the last two recessions we've had. If you want some good news, then there's the schadenfreude that the drop in the "main street" economy this implies is only about 2.1%

In the medium run:



Or something that looks like the 2000's recession if it looks like anything at all. You'll be able to see it if you squint really hard, but it will be there.

In the long run:



which means a slight gain due to the fact that the over bloated financial sector gets rid of some excess weight and due to the fact there's some productivity increases in the non-financial sector. Note that the productivity increases in the non-financial sector are assumed to be 1/2 of a percent, which would normally show up as .4% growth in GDP so this still represents some drag on the increases in incomes that would otherwise happen.

So there you go. There's my pair of dueces. They may not be much but they're spades.

But wait! We're not done actually.

One more thing we can do, since we're totally into the monkey-guess-ad-hoc-macro-make-up-elasticity-values territory (BTW. An empirical question related to a previous post. Did any of the efforts in macroeconomics to try and deal with the Lucas Critique and estimate the "deep" parameters actually lead to better forecasts? Or did they just lead to changes in the assumed utility functions/adjustment costs of capital/pushed back the ad-hociness another level? In other words, did they deal with Friedman?). It's called Okun's Law, which relates changes in output to changes in unemployment:



Usually u* is taken to be "natural rate" of unemployment but here we can just take it to be the present rate of unemployment. And xi is usually estimated to be between 2 and 3. And current unemployment rate is 6.1. Then the relevant unemployment rates we'll see according to the estimates above are:

Short run: Lower 6.1+(3.08)/3=7.13, Upper 6.1+(3.08)/2=7.64
Medium run: Lower 6.1+1/3=6.43, Upper 6.1+1/2=6.6
Long run: Lower 6.1-.12/3=6.06, Upper 6.1-.12/2=6.04

Alright, almost over. But obviously in these circumstances Bob's your uncle and the guesses above are just guesses although based on some assumptions. So here are some tables which allow you to question me (remember that this is all based on accounting and the behavioral assumptions are free) - maybe you think the crisis will cause a much greater fall in the size of the financial sector or maybe you think that epsilon's greater/smaller/insane. Here's some tables which do the calculations for you. I highlighted some values which I thought were relevant (click to enlarge).

The recession:



The effect on main street:



And the resulting unemployment rate:



Oh yeah. These were calculated under the assumption that g=0. Which means that if g=.005 - there's a 1/2 % improvement in productivity of the non financial sector - add .004 to the estimated growth rates of output. And then use Okun's Rule again. Basically this makes things a little bit, but not much, better.

Additional stuff:
* Ugh, now I gotta look for the links to anything that's relevant in all that crap I wrote above.
* This is also a useful framework to use when thinking about the bailout plan. What is it trying to achieve? Is it trying to contain the shrinkage of the financial sector? Well, that means less recession in short run, but less positive adjustment in the long run. Sure, it may be worth it. Or is trying to target the epsilon, the spillover from the financial sector to the non-financial sector? This also has some short run vs. long run implications (even if one's not a liquidationist - see previous post). Or is it just throwing money around hoping that it will hit something somewhere?
* I'm actually very much in favor of "moderate progress within the bounds of the law". In fact, I think that's my political bliss point. I still think that's pretty funny though. There's a difference between aesthetics/humor and ethics/politics.
* This stuff's peak to trough. If someone forces me to forecast the time frames as well I'd say; short run = 1 year, medium run = 1.5 years, long run = 2 years+
* I kept the Visigoths out of this