## Sunday, August 12, 2012

### Why I'm skeptical of fiscal stimulus

First, let me lay out a definition.  When I say "fiscal stimulus," I mean: discretionary countercyclical spending.  I don't mean: military spending; necessary infrastructure spending; welfare; sanitation; or any other function that government is expected to serve regardless of the economic climate.  I do mean: Tax cuts; make-work; the WPA; ARRA; extravagant (Japanese-style, bridge-to-nowhere) infrastructure spending; and other spending that occurs because the fiscal authority has identified that the economy is in the recessionary phase of the business cycle.  (Implicitly, when I say "discretionary fiscal stimulus," I really mean "expansive fiscal stimulus."  It is rare for a democratic government to engage in discretionary fiscal contraction.)

Here are two of the main reasons I'm skeptical of fiscal stimulus.

### 1: Timing

The first, due to Friedman, is very nicely laid out in this Marginal Revolution post.  I reproduce the argument here.

Let's set up a simple model.  At time $$t$$, represent total income by $$Z(t)$$, income in the absence of fiscal policy by $$X(t)$$, and the amount added to (or subtracted from) $$X(t)$$ by all the history of fiscal policy denote by $$Y(t)$$.  Here's the identity at the heart of the model:
$Z(t) = X(t) + Y(t).$
Since we hope for our policy to be countercyclical -- that is, we hope for $$Y$$ to reduce the fluctuations of $$X$$ so that $$Z$$ has low variance -- we want $$X$$ and $$Y$$ to be correlated.  The variance of a sum of correlated variables is
$V(Z) = V(X) + V(Y) + 2Cov(X,Y) = V(X) + V(Y) + 2r(X,Y)\sigma(X)\sigma(Y).$
(Here $$\sigma$$ is the standard deviation, $$\sigma^2 = V$$, and $$r$$ is the correlation of two random variables.)

Following Friedman and dividing both sides, we have
$\frac{V(Z)}{V(X)} = 1 + \frac{V(Y)}{V(X)} + 2r(X,Y)\frac{\sigma(Y)}{\sigma(X)}.$
Remember that $$X$$ measures fluctuations in the economy absent any countercyclical policy.  If the left side of the equation is $$1$$, then the countercyclical policy has no effect.  If it is less than $$1$$, the countercyclical policy has some positive effect.  If it is greater than $$1$$, the countercyclical policy has negative effect.

The key question here is, how closely does the cumulative effect of policy, $$Y$$, need to track incomes, $$X$$?  This tracking is measured by the correlation $$r(X,Y)$$; if $$Y$$ is perfectly timed and opposite to income fluctuations, $$r(X,Y) = -1$$; if $$Y$$ is independent from $$X$$, $$r = 0$$; and if $$Y$$ is perfectly harmful, so that policy is perfectly procyclical, $$r = 1$$.

Friedman goes on to show that policy is countercyclical if $$r(X,Y) < -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)}$$, has no effect if $$r(X,Y) = -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)}$$, and procyclical if $$r(X,Y) > -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)}$$.

The first thing to note is that it is harder to conduct countercyclical policy than procyclical policy: to be effective, we need $$r(X,Y) = -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)} < 0$$.  Why?  Note that if $$Y$$ is independent from $$X$$, then $$r = 0$$, so $$V(Z) = V(X) + V(Y)$$.  The variance of after-government income will be greater than the variance of the private economy's income because some of the time, spending will be procyclical, exacerbating the business cycle.

The next thing to note is that if policy were to attempt to mitigate, say, half the magnitude of the business cycle, one would need $$\frac{\sigma(Y)}{\sigma(X)} = \frac{1}{2}$$ so that $$-1 \leq r(X,Y)\leq -\frac{1}{4}$$.  The window of the target for effective business cycle amelioration narrows the more of the business cycle you want to eliminate.

The last thing to note is that for any correlative ability, there is an optimal level of countercyclical spending.  Using calculus to find $$\sigma(Y)$$ maximizing $$\frac{V(Z)}{V(X)}$$ for a fixed $$r(X,Y)$$, one sees that this optimum occurs at
$\sigma(Y) = -r(X,Y)\sigma(X).$
So to see the effectiveness of stabilization policy, assume the best $$\sigma(Y)$$ can be found and substitute:
$\frac{V(Z)}{V(X)} = 1 - r(X,Y)^2.$
Boom.  Right there.  This is how difficult discretionary fiscal stimulus is.  For example, if we want to cut the standard deviation of the business cycle in half with discretionary spending, the cumulative effect of all discretionary spending must be pegged to within 70% of the business cycle.

You should read both the Marginal Revolution post and Friedman's article.

This is reason number one that I'm skeptical of discretionary fiscal stimulus.  If you want to positively mitigate the business cycle, you need to be able to target your fiscal response very precisely.  Your discretionary fiscal authority has to be able to do three things:
1. Correctly identify current income - what we've been calling $$X(t)$$
2. Determine what level of spending is appropriate (including correctly estimating secondary and tertiary effects) to mitigate some of the deviation of $$X(t)$$ from its expected value
3. Enact that spending quickly enough to actually mitigate $$\sigma(X)$$.
Even correctly identifying current income is tricky enough (the BEA didn't announce the US was in a recession until December 2008, an entire year after the recession began), estimating the appropriate level of spending is almost as tricky (quarterly real GDP figures from 2008 are still being revised), and enacting that spending quickly ... well, anybody who's been watching Congress knows how tough this is.

Even when Democrats controlled both houses and the White House, fiscal stimulus wasn't even signed into law until February 2009.  The worst of the economic contraction had passed by then, and the economy returned to growth well before the bulk of stimulus spending occurred (ARRA was authorized for two years, so it was in effect until August 2011).

### 2: The Sumner Critique

As Paul Krugman said in 1997:
If you want a simple model for predicting the unemployment rate in the United States over the next few years, here it is: It will be what Greenspan wants it to be, plus or minus a random error reflecting the fact that he is not quite God.
How? I have a series of posts on the omnipotence of your local central bank coming up, so I'll save all the gory details until then. Instead, I'll just point out that the Fed controls aggregate demand by controlling the supply of money. The total amount of spending in the economy at any price level -- aggregate demand -- is a product of the Fed's policies.

If the Fed were to decide that spending was too low and needed to rise, it would increase the money supply, spending would rise, and -- depending on underlying real factors, such as unemployment, productivity, etc. -- some of that increased spending would cause an increase in output, while the rest of it would push up prices.

If the Fed were to decide that spending was too high and needed to fall, it would decrease the money supply, spending would fall, and both output and prices would fall.

(This discussion holds in the short run only; in the long run, as expectations adjust, output adjusts so that all monetary expansion and contraction translate into price changes.)

The Fed makes decisions about spending based on its assessment of monetary variables such as inflation, interest rates, unemployment.  It also (sadly) incorporates political assessments - would a policy decision hurt the independence and credibility of the Fed?

You can see where this is going.  If the government engages in discretionary fiscal policy, it also boosts total spending.  Ultimately, fiscal stimulus has the same short-run effect on total spending as monetary expansion, and hence the same short-run effects on unemployment and on inflation.

If the Fed has decided that it prefers current levels of unemployment and inflation, then it will initiate contractionary monetary policy when the government engages in discretionary fiscal stimulus and the fiscal stimulus will have no effect.  (To see the effects of this, look no further than our erstwhile Pacific protege).

If the Fed has decided that it does not prefer current levels of unemployment and inflation, then it will initiate expansionary monetary policy.  If the government engages in discretionary fiscal stimulus, the Fed will only loosen money to the extent that the fiscal stimulus does not meet the Fed's goals for unemployment and inflation.  In other words, discretionary fiscal stimulus is unnecessary: If it had not occurred, the Fed would just have instituted looser monetary policy.

This is the weakest form of the Sumner critique: one cannot measure the gains from fiscal stimulus without a counterfactual of central bank policy.  A stronger form is: the fiscal multiplier is always zero.  (The strongest form is: If the central bank targets nominal income, all macroeconomic effects are classical.)

Here's a little bit of play (inspired by these posts) using accounting identities to shore up the Sumner critique.  We know that income is consumption plus investment plus government spending plus net exports,
$Y = C + I + G + NX,$
and, by the equation of exchange,
$Y = \frac{MV}{P}.$
Therefore,
$C + I + G+ NX = \frac{MV}{P}.$
Claiming that discretionary fiscal stimulus works amounts to asserting that we can control $$G$$, and therefore at our discretion we can affect $$Y$$ by changing the right hand side of the last equation.  But the central bank exerts continuous and complete control over the right hand side of the equation.

If $$G$$ rises but the central bank does not permit the money ratio $$\frac{MV}{P}$$ to change, then necessarily the other components of $$Y$$ fall.  On the other hand, if the central bank changes $$\frac{MV}{P}$$, then the components of income will rise.

### Conclusion

There are other, weaker reasons I'm skeptical of fiscal stimulus -- how do we know that the projects being undertaken are valuable investments of time and resources?  Is it really worthwhile to pay people to dig holes and fill them back in?  And so on.  They're not so hard to reasonably answer ("They're still better than leaving resources idle," "It's the same as printing money and handing it out, and they'll spend the money and incomes will rise,"), so I'll leave considering them to a future post.

These two reasons, however, seem damning to me.  There's just no way an institution like Congress can gather enough information on the state of the economy, identify projects to engage in or taxes to cut, craft legislation, trade all the horses, and pass a bill to counteract a downturn (or counteract an upturn, but let's not get into why Congress might not want to quench a booming economy) quickly enough to correlate the economy and the government's response tightly enough to make discretionary fiscal stimulus effective.

(This begs the question of why the Fed would be able to do so, which I will answer in future posts regarding the Fed's omnipotence.)  But the central bank does control the macroeconomy, which means that either discretionary fiscal policy will be offset by contractionary monetary policy or it can simply be replaced by expansive monetary policy.

The take-home lesson from all this is, the fiscal authority should not worry itself with the business cycle.  Instead, the fiscal authority should set the monetary authority on a rule that does its best to eliminate the business cycle, because recessions are everywhere and always monetary phenomena, and focus on long-run policies that correct market failures and optimize growth against humane considerations.

Whether a policy is good or bad doesn't depend on the condition of the economy.  If a policy is a good idea in a boom, then it's a good idea in a recession: it's a good idea, period.  If a policy is a bad idea in a recession, then it's a bad idea in a boom: it's a bad idea, period.