Optimal Fiscal Policy with a Liquidity Trap and Gridlock

Robert Waldmann

I’m still thinking about Krugman’s excellent little model which gives the very clear result that optimal macro policy implies that unemployment is always at the natural rate and so, if the nominal interest rate is zero, the optimal fiscal stimulus should drive unemployment all of the way to the natural rate.

Krugman’s model is a simple inter-temporal model with rational expectations. This means that it has the odd feature that tax cuts have no effect on demand — people rationally understand that they will have to pay for Government consumption (G) sooner or later so they don’t count the federal debt as part of their net wealth.

Government consumption can still stimulate the economy. The multiplier is exactly 1 whether it is tax financed or deficit financed (this also requires that money demand depends on private consumption, that is that the Treasury doesn’t have to keep a significant amount of money in its checking account).

The model is exactly what a model should be — it is comprehensible (to me only on a second reading the explanation is very brief) and clarifies thought. Also, of course, it is much simpler than reality.

Krugman is puzzled as to why the Obama administration in waiting proposed a much more modest stimulus. They make two arguments.

First that the President isn’t the fiscal authority — he proposes but Congress decides. Obama clearly said that he expects congress to increase spending beyond the proposal, since that is what congress usually does.

Second that a larger stimulus would burden the economy with excessive debt.

Do these arguments make any sense ? What happens when we combine them ? I present a “model” after the jump which suggests that the answer is yes.

Before deciding whether or not to take the jump, ask yourself 2 questions.

Krugman’s argument does not depend on the duration of the period of trapped liquidity. If unemployment were above the natural rate for 10 years with the nominal interest rate equal to zero, then he would recommend fiscal stimulus for 10 years. Might that lead to an unsustainable deficit and default in the future ? Would that be optimal ?

OK I will present 2 pseudo models. One is a parody of Krugman’s model which takes it a few decades back in time. It is the dear old IS-LM Phillips curve model. Here fiscal policy affects aggregate demand directly via G or indirectly via disposable income Yd = GNP minus Taxes plus Transfers = Y-T. In this case, a fiscal stimulus can be turned off and on as quickly as G and T can be changed. The model is static except for the Phillips curve so the Federal debt doesn’t matter (it doesn’t appear at all in the IS-LM model). Now this model has been out of fashion since before I took my first course in economics. However, it still affects the way people think, because it is neat and simple and you can come up with an optimizing model which is more or less the same when you have to present your reasoning. In this case, I think, the “more or less” matters a lot.

I’m going to stick to an IS-LM model except that I will change the assumptions about consumption. I’m pretty sure that Krugman can translate my argument to an argument in his model in a minute. This means I won’t do the New-Keynesian formal analysis and I will consider investment (isn’t there in Krugman’s model). Being ad hoc, I will just assume investment is a shift variable times decreasing function of the real interest rate. The crisis is a sharp decline in that shift variable. I will assume a closed economy, but I really think that doesn’t matter much.

The model of consumption is rational optimization with overlapping generations of infinite lived agents (due to O.J. Blanchard). Huh ? Let me explain. A standard macro optimizing model of consumption assumes that all consumers are rational, immortal and identical. It implies that the timing of taxes has no effect on anything (shows Ricardian equivalence). This feature is not realistic. Krugman assumes Ricardian equivalence.

A way to avoid this result is to have new agents arrive who will help repay the debt even though they didn’t benefit from the tax cuts or G increase which caused it. Say half of the debt (in present value) will be paid by people who haven’t arrived yet arrivals. This means that government bonds are net wealth for current inhabitants, not at their full market value but, on average, at half of it (the value of the bonds I own minus my share of the extra taxes to pay for them). Barro might argue that, with bequests, taxes paid by the children of the current residents count as taxes paid by current residents. Now I think he is fundmantally wrong, because I don’t think people are approximately rational. However, here and now I am assuming full rationality, so I appeal to immigrants. US residents clearly don’t care much about foreigners and about a million of them are (legally) entering the US a year and paying taxes.

OK now I assume logarithmic utility, this makes things simple, it means that optimal consumption is the rate of time preference (rho) times total wealth which consists of physical wealth plus the present discounted value of future labor income minus the present value of future tax payments. Future labor income depends on the future capital stock and on future unemployment rates, but I will mostly assume it is exogenous.

This means that consumption depends on the federal debt. It is what it would be with no federal debt + 0.5rho times the federal debt. There is an effect of fiscal policy on consumption, but it depends on the debt and not on current taxes as in the original IS-LM model.

Now Obama (and Krugman) clearly believe that, for a given path of G, a huge national debt is a bad thing in normal times, that is when unemployment is set equal to the natural rate by the FED. This means that output is the same no matter what the federal debt is. Consumption is greater if there is more debt, so investment is lower. They guess that the market is about right without distortion so the optimal debt is roughly zero. Higher debt distorts consumption savings decisions and crowds out investment. Krugman just decided that this is a separate issue. He was talking about optimal G not optimal debt. Now in his model as written, it doesn’t matter when the government taxes because the model has Ricardian equivalence. Krugman doesn’t believe in Ricardian equivalence. I’m pretty sure that the policy which he really thinks is the one true optimal policy is a balanced budget expansion of G whcih will stimulate the economy and won’t build up increased federal debt. Obviously this is politically impossible and so Krugman doesn’t mention taxes in his little model.

Now to get his result he doesn’t strictly need that the increased G is financed at the time it is spent. With Ricardian non-equivalence, he could even get a larger effect of G by running up a deficit. However, as soon as the interest rate gets to be positive, he wants the debt to be as low as possible. In my “model” as unwritten, this would require the extra G of fiscal stimulus to be financed with taxes collected during the period of trapped liquidity. That’s not going to happen either.

Another model says that there are political limits on the budget (imposed by congress) and especially on taxes, so there is a minimum feasible deficit. This would mean that, once we are out of the crisis, Krugman would set the deficit to this minimum value (which might be a surplus). this means that all debt built up while the economy is in the liquidity trap will distort the mix between consumption and investment for a long long time, that is, until Krugman would have gotten the debt to the level he likes, which, I would guess, is zero.

The argument for accepting unemployment over 4.8% makes sense. In the “model” and in reality, the federal debt matters. Obama is not the fiscal authority. He won’t be able to pay back the debt built up during the crisis as fast as he would like. Therefore he doesn’t want to build up too much.