Thursday, November 21, 2013

Liquidity Constraints

It's taken me a few days to make something out of this post by Paul Krugman, which is a comment on John Cochrane. See also my previous post.

Krugman is unhappy, and is accusing Cochrane of being a lazy reader. I think the subtext here is that Krugman wants us to read his paper with Gauti Eggertsson. I read the working paper, but that was a while back, so I looked at the published version to remind myself what is going on in their model.

The crux of Krugman's argument in his blog post comes for the most part from the Eggertsson/Krugman (EK) paper. Cochrane's point is that New Keynesian models and Old Keynesian models are very different. In New Keynesian models government spending increases consumption by increasing inflation; in Old Keynesian models government spending increases consumption by way of the multiplier process. Krugman says: hold on a minute. Government purchases in a typical New Keynesian model will actually increase output one-for-one. Add "liquidity-constrained" consumers and you can get multiplier effects, just like with Old Keynes.

Since these arguments come straight out of the EK paper, it's useful to dig into the EK model and figure out what is going on. First, I think anyone who attempts to capture credit and liquidity frictions and their implications for macro policy should be given a pat on the back. Certainly there was far too little work on these things before 2008 - particularly among New Keynesians - and that didn't work out so well. So, EK deserve some credit (no pun intended).

EK want to set up a model with credit and borrowing constraints, but they want it to be tractable. Standard incomplete markets models with such constraints (e.g. Krusell/Smith) are notoriously intractable - typically we're stuck with computational approaches. The trick in EK is to assume two types of economics agents - patient and impatient - who are identical except that they discount the future differently. It's well known that, in an endowment economy like this, with unlimited borrowing and lending, all the wealth goes to the patient agents in the limit. But, if we impose an exogenous debt constraint, then in the steady state the borrowing constraint binds for the impatient agents, and the patient people lend to the impatient ones. EK essentially involves linearizing around that steady state, and considering the effects of shocks to the debt limit when the zero lower bound on the nominal interest rate binds. There are also sticky prices, so the model has some basic New Keynesian features.

Thus, there are two key frictions in the model - sticky prices, which give rise to the possibility of typical Keynesian relative price inefficiencies (i.e. an inefficient real rate of interest); and a credit market friction. The relevant part of the paper for us is the section on policy - especially fiscal policy. The government has access to lump-sum taxes, and EK make some assumptions about the distribution of the tax burden, seemingly just to make life easier for the modelers. What does government spending do? Private goods are converted into public goods, which enter the utility function in a separable fashion.

What happens in the basic New Keynesian model (EK with one type of agent) if government spending increases? Consumption does not change, as that is determined from the Euler equation for the representative consumer. There is no investment, and firms are assumed to service whatever demand comes in the door, so the direct effect is for output to increase one-for-one with government spending. A good thing, right? Not necessarily. The increase in output did nothing to correct the fundamental inefficiency in the model, which is the sticky price friction. If we're at the zero lower bound, and the real interest rate is too high in this environment, then essentially we have a consumption gap, not an "output gap." If the government spends more, that doesn't shrink the consumption gap. There is some optimal quantity of public goods in this model - if government is providing less (more) than that quantity, then it should be spending more (less). A second effect is the one Cochrane discusses. By increasing output, the government can move us up the New Keynesian Phillips curve, inflation increases, this lowers the real interest rate, and the consumption gap falls. So, there's nothing wrong with Cochrane's analysis. Krugman is right in a sense, but he's focusing too much on the output effects, rather than the efficiency effects.

Next, go to the full-blown EK model. What happens here is that we get an additional effect from government spending, which Krugman discusses in his post. More output gets produced, as firms serve whatever demand comes in the door. Then, I think what is happening is that labor income must go up for everyone (higher wage and more employment), including the debt-constrained consumers, who will then consume more. As Krugman points out, that's a kind of standard Old-Keynesian effect coming from the non-Ricardian nature of this economy.

But hold on. This has the flavor of reverse engineering. We're supposed to get excited because we find some result that looks like something we think we already know. If all research proceeded like this, we wouldn't learn anything. Suppose we take this model at face value. What's the inefficiency problem or problems? What's a feasible government policy? Within that feasible set, what is optimal? Answers: (i) The economy is in a state of the world where the zero lower bound binds, consumption is too low for unconstrained agents because the real interest rate is too high, and consumption is too low for constrained agents - because they are constrained. (ii) The government has access to lump-sum taxes. If it can tax lump-sum, we'll suppose it can tax consumption as well. (iii) Policy solution? Easy. Given lump-sum taxation, the borrowing constraints can be relaxed - indeed eliminated - through a tax/transfer program. Then, we're back to the basic New Keynesian world, with a consumption gap. To fix that, all we need is a promise to tax consumption in the future when the zero lower bound threatens to bind. This gives us the correct (after-tax) real interest rate (see Correia et al.).

I think the bottom line is that we want to pay attention to what models tell us, not what we hope they might tell us. The model EK want us to pay attention to indeed has a role for fiscal policy. But that role isn't related to spending, multipliers, and Old Keynesian economics. It's about tax policy.


  1. If the government spends more, that doesn't shrink the consumption gap. There is some optimal quantity of public goods in this model - if government is providing less (more) than that quantity, then it should be spending more (less).

    The optimal quantity of public goods in the model depends on the marginal disutility of labor. If the demand shortfall, combined with sticky prices, has opened up a wedge between productivity*MUC and -MUL, and -MUL is lower than usual, then additional government spending is indeed optimal. The extent to which this is true depends on the relative curvatures of labor disutility and utility from government purchases.

    I agree that Krugman was probably focusing too much on the output effect, and not thinking enough about welfare. But I think that his approach makes more sense if we think that labor doesn't adjust on the intensive margin (like in the basic NK model), and instead jobs are rationed along the extensive margin. In that case, there is a good chance that we would want to spend to fill the entire employment gap - because even if we are pushing into relatively unproductive government projects, there is essentially no cost at the margin to employing currently unemployed workers. (Believe it or not, the utility from "leisure" enjoyed while unemployed is not that great for most people.)

    To fix that, all we need is a promise to tax consumption in the future when the zero lower bound threatens to bind. This gives us the correct (after-tax) real interest rate.

    It is true that in theory, fiscal instruments can replicate the role of monetary policy and therefore save us at the zero lower bound. But there are many, many barriers to actually implementing this. If this is going to be held out as a refutation of standard NK policy prescriptions, there has to be more of a focus on how it would work in practice.

    1. "But there are many, many barriers to actually implementing this."

      Exactly. I'm not refuting anything. The model is what it is. Given the way it's written down, though, it looks like the policies that are being considered are suboptimal. Maybe people need to model the "barriers" you mention.

  2. "To fix that, all we need is a promise to tax consumption in the future when the zero lower bound threatens to bind."

    I suggest a re-wording, for clarity:

    'To fix that, when the zero lower bound threatens to bind, all we need do is promise to tax consumption in the future.'

  3. Given lump-sum taxation, the borrowing constraints can be relaxed - indeed eliminated - through a tax/transfer program. Then, we're back to the basic New Keynesian world

    This is exactly Miles Kimball's "Federal Lines of Credit" idea.

    1. If you want to take it seriously, you have to dig deeper. We want to understand exactly where that borrowing constraint comes from. Maybe it's limited commitment - people can run away from their debts, and we need to worry about collateral, etc. But the government also has to worry about getting people to pay their taxes. So, the argument would rest on whether the government has some advantage in getting people to pay their debts, or some other credit market advantage, as when we evaluate any government program or intervention.

    2. Noah and Steve,

      I had the same reaction when I read the working paper. If you take the model at face value, you don't need an increase in government spending, all you need is a Federal line of credit. Of course, in real life there are all the issues that Steve raises. But then again, are lump-sum taxes an option in real life?

      Second, if I remember correctly, in the model the recession is caused by a reduction in the debt limit for impatient households, which forces them to cut consumption in the short run more than in the long run, because they need to also pay off part of their debt. Therefore, an increase in transfers to impatient households helps them deleverage faster. But how does the drop in consumption correlate with income in the data? I am thinking that lower income households were more likely to be stuck in an upside down mortgage, and therefore more likely to deleverage by simply walking away from their home. In addition, it is easier for lower income households to file for Chapter 7 (as opposed to Chapter 13) bankruptcy, which dissolves much of the debt, so again it is easier for lower income households to deleverage without cutting consumption drastically. So what would Krugman say if we found that the drop in consumption of higher income households was greater? Would he still favor transfers to them?

      In addition, if I remember correctly, the consumption of patient households actually rises due to the decline in the rate of interest. Do we see such a discrepancy across households in the data? Is the share of constraint households in the data big enough to bring the natural rate below the ZLB? I do not think EK address this issue. Of course, all these question are absent from the Keynesian model.

      And one question for Steve. If the Euler equation of patient households is satisfied, why is their consumption sub-optimal? Is it because of the sticky prices?

    3. For the patient households, consumption is suboptimal because of the zero lower bound. Basically, there are two important binding constraints at work - the zero lower bound which constraints policy, and the debt limiit that constriains the impatient.

    4. To be patient you have to have a job. The issue is how many were pushed into the impatient camp by circumstance. It is a push not a pull problem. Government intervention via job programs would have had a stronger effect on the lower and middle parts of the income scale where the damage was greatest. Benefits would have trickled up through spending.

  4. Stephen, the issue isn't just the inclusion of credit constrained households in New Keynesian models (which is now quite routine in many policy models). Krugman's initial conclusion of a government spending multiplier of 1 in the New Keynesian model assumes prices are fully rigid. Otherwise as Cochrane argues, there are equilibria where price adjustment by firms dampens government spending multipliers significantly, as you yourself discussed in your posts on the anti Krugman. And these equilibria are in some ways much more reasonable in terms of people's expectations about monetary policy. Krugman manages to accuse Cochrane of misunderstanding New Keynesian models when he himself misunderstands the model badly (I'm suspecting ). My suspicion is that Krugman was responsible for some of the nice prose in the article with Eggertson, but most of the more subtle and complex thinking comes from Eggertson.

    1. Yes, I agree. It's hard to imagine that Krugman has this all figured out. You actually have to live with a model for a while, and play with it, to understand where all the bodies are hidden. Krugman doesn't have the time or inclination for that.