It's an interesting paper (pdf). It's a very standard New Keynesian macro model with one twist. It's a twist worth doing. There are two types of people: the impatient, who borrow from; the patient. And there's an exogenous limit to the debt the impatient are allowed to accumulate.
It's a math model, of course. I'm not going to stick literally to the assumptions of the model, because many of those assumptions were made to make the math simple, and aren't really central. Here's my reading.
Start with an equilibrium in which all people and firms are lending or borrowing as much as they want. Now impose an exogenous borrowing constraint on some people and firms who have borrowed in the past and are now in debt. What happens?
1. For a given level of current and expected future income, the equilibrium real rate of interest will drop. That's because some people and firms who want to borrow won't be able to, or won't be able to borrow as much. The demand for loanable funds from qualified borrowers falls, and so does the equilibrium rate of interest. Equivalently, for a given level of expected future income and real interest rate, there is a fall in the level of current income at which desired savings equals desired investment (ignoring the desires of those who want to borrow and spend but can't). Whichever way you think about the IS curve, it shifts down, or it shifts left. Same thing.
2. The marginal propensity to spend out of current income increases. A change in current income that leaves future income unchanged has little effect on permanent income, and so will normally have little effect on the demand for goods. But borrowing-constrained people and firms will have a marginal propensity to spend out of current income of one. So anything that causes current income to change will have a bigger multiplier effect.
3. A change in the real rate of interest will have a smaller direct effect on the demand for goods. That's because the borrowing-constrained people and firms want to borrow and spend more if the rate of interest falls, but are unable to.
4. The IS curve may become either flatter or steeper, depending on whether 2 or 3 above dominates. A less interest-elastic demand for goods means a steeper IS curve. But a bigger multiplier means a flatter IS curve. With an exogenous borrowing constraint, a given fall in the rate of interest will have a smaller direct effect on increasing demand, but that direct effect will have a bigger multiplier effect. So the total effect of a fall in the rate of interest on demand for goods could be either bigger or smaller.
Now suppose an exogenous shock causes the borrowing constraint to bind more tightly. This causes the IS curve to shift left, and makes the natural rate of interest strongly negative. Since the nominal rate of interest cannot fall below zero, and since the expected rate of inflation isn't high enough, the economy goes into a recession. Any fall in the current price level increases the real value of existing nominal debt, and makes the borrowing constraint bind more tightly still. (That's the Fisher debt-deflation effect).
Monetary policy can only work if it can increase the expected future price level, and thereby increase expected inflation and lower the real rate of interest. Fiscal policy can work because a cut in current taxes will raise the current disposable income of borrowing-constrained people and firms, causing them to increase their demand for goods, even if they know that future taxes will be increased. In effect, the government is acting as lender to the borrowing-constrained, and relaxing that constraint.
One main problem with the model is the exogeneity of the level of real debt at which the borrowing constraint bites. I can think of three main channels in which making the borrowing constraint endogenous might change the results of the model:
B1. The amount that people and firms are allowed to borrow depends on their income. If a recession causes a decline in current and expected future income, this could tighten the borrowing constraints still further, deepening the recession. In effect, we get a borrowing-constraint multiplier.
B2. The amount that people and firms are allowed to borrow depends on the rate of interest. A fall in the rate of interest will lower the interest payments on a given debt, and would loosen borrowing constraints and help the economy escape the recession.
B3. A cut in current taxes implies an increase in expected future taxes, which reduces expected future disposable income, and reduces the ability of debtors to service debt in future, which may tighten the borrowing constraint. So fiscal policy may still fail, because the increased government lending may be fully offset by an equivalent tightening of the borrowing constraint. Ricardian Equivalence may still hold.
Let me add a quasi-monetarist gloss to the model: The recession is not caused by an excess of desired savings over investment. Instead, when lenders are unable to find borrowers they think are safe, they choose to save in the form of money instead. It is the excess demand for the medium of exchange that causes the recession. In a barter economy, those who desired to lend but who were unable to find borrowers they think are safe would be forced to consume or invest their income themselves.
Let me add a more monetarist objection (I'm trying to guess what Scott Sumner would say): It was the Fed, by having too tight a monetary policy, so that expected future nominal income fell, that caused the borrowing constraint to tighten. It wasn't exogenous at all.
And I would add that monetary policy might actually be more powerful in this sort of model than it would be in a similar New Keynesian model with a liquidity trap but without a borrowing constraint. The higher marginal propensity to spend out of current income is higher, so the multiplier effect of anything that gets spending started will be higher. Plus, more importantly, the borrowing constraint creates its own multiplier, because any increase in current or expected future income relaxes the borrowing constraint which creates additional demand and income.
Worthwhile Canadian Initiative 
Olson argued in his book that there’s empirical evidence that wages have gotten more “sticky”. He cites Phillip Cagan on the tendency for prices to fall during recessions gradually declining over time from 1890. The endnote refers to an essay titled “Persisten Inflation”. He also writes that deflation did not have the present association with unemployment (in a more provocative note he argues that before the 1890s our concept of unemployment wasn’t common enough to have a term) or reduction in output, and that modern societies which have not developed a multitude of distributional coalitions also manage to combine lower unemployment rates with low inflation.
His explanation for why it is a sticky nominal wage which monetary policy can alleviate (or exacerbate) is that when distributional coalitions set prices (as in a collective bargaining agreement) it is in nominal terms. Such coalitions act slowly & deliberately to keep its members on board and they cannot quickly readjust the nominal prices they have set. But some “flexprice” sectors are more open to entry and so the unemployed may all try to rush to them, driving down prices in that sector much further than normal (agriculture and “selling apples on streetcorners” are his examples from the Great Depression).
Olson seemed to lump his theory in with Clower’s disequilibrium view, even using the term “Clower-Olson”. I’ve yet to come across any good popularization of the Clower/Leijonhufvud “post-walrasian” paradigm for laymen (possibly asking too much). I’d be interested in any pointers readers have.
Apologies for the two nicks. I blog under this name but decided I’d rather not have all my writings linked to a computer I use at the office.
TGGP,
I think wages have to be more sticky. The uncertainty costs of getting up each morning and not knowing how much you will earn that day are pretty high. We can’t all wait an interminable period of time, constantly revising our reversible bids, before the walrassian auctioneer finally announces what it costs us to buy a car into to drive to work, and earn enough money to buy the car ex-post. And in that case, we need some certainty of what our wage will be before we put in a bid for the car. Something has to break the loop and allow us to purchase long lived durable goods.
I also think that you have to have coalitions and rents, because there are many increasing return industries in which average costs are above marginal costs at pretty much all conceivable quantity levels, and unless you have labor coalitions that insure that average wages are above marginal product of labor, then you are not going to get market clearing. But that does not mean that the rents are split fairly in all cases. Look at managerial or CEO pay, for example, for a good example of out of control coalitions, in this case the cross membership on boards of directors.
And there are other examples of “natural” sticky prices — for example, many prices reflect expectations over longer periods of time. For example, a long term interest rate, or a long term cost of capital. By definition, when the price of something represents inputs that cover many time periods, then it cannot move as quickly in response to a current period demand shock. That’s not true for the price of eggs, obviously.
But none of that means that sticky prices prevent reaching some optimal output equilibrium. The optimal equilibrium could require some stickiness in some categories of goods in order to be reached in the first place.
The normative issues you bring up are more complicated than I’d care to get into right now (though I do agree that CEOs are overpaid, and Olson repeatedly noted that distributional coalition is not synonymous with labor union but they are merely a commonly recognized example), but I’d like for you to elaborate on the failure of markets to clear in the absence of labor coalitions. It’s a theory I hadn’t come across before (in the simplest classical models, markets always clear and frictions are introduced to explain why they might not). Is this some kind of monopsony theory, whose deadweight loss is analogous to the more well known monopolist who cannot price discriminate? Jobs aren’t exactly fungible goods whose differentials can be arbitraged away.
“Is this some kind of monopsony theory, whose deadweight loss is analogous to the more well known monopolist who cannot price discriminate?”
Yes, even without frictions, the assumption that workers are paid their marginal product relies on constant returns to scale, and doesn’t necessarily hold when there are different industries with different labor productivity levels hiring from the same labor pool.
For example, assume you have farming and manufacturing in a developing nation. Nothing forces the manufacturing wage to be bid up to the level that reflects the higher labor productivity in that sector. It could be just slightly higher than the agricultural wage. A “small” manufacturing firm would have lower labor productivity, so you cannot argue that some other firm will come along and bid up the wage. That argument pre-supposes scale-invariant labor productivity.
The natural monopoly, or oligopoly depending on the elasticity of substitution, will be able to pay a wage just slightly higher than the less productive industries. Historically, industrialization was accompanied by natural monopolies and oligopolies not paying a substantially higher wage, and hence the birth of organized labor in the same era.
“Jobs aren’t exactly fungible goods whose differentials can be arbitraged away.”
That’s the key issue. There is no a priori reason to believe that differentiations in competency and skill will exactly match the differing labor productivities across industries, as the latter changes quickly with technology. When they don’t match, coalitions are formed to further differentiate the labor force by requiring certain levels of training or group membership that are not strictly required in order to perform the job, but whose purpose is to differentiate the labor force.
It doesn’t matter that workers are not perfect substitutes for each other. What matters is whether the full differential in labor productivity is passed onto the worker when they are pulled out of the less productive sector. If the costs of training someone to transition from the agricultural sector to the manufacturing sector are not too high — and they would need to be very high in NPV sense — then you can earn a profit by paying someone just a bit more than they are making in the less productive sector.
And let’s be honest, there is nothing intrinsically more difficult about doing repetitive tasks in a factory than working on a farm. And the manager of such a factory is not particularly more skilled than a manager of a farm. A lawyer is not particularly more skilled than a school teacher, etc. You can see this in the “training phases”, from apprentice to laborer journeyman to “wright” or master crafstman. It’s the same person, with more or less the same talents, but they have jumped through more hoops. They is learning, of course, but that learning is not strictly required to perform most of the daily tasks of the job. You don’t need someone with a PhD to teach econ 1. You require it because of coalitions.
The majority of daily tasks that most people perform can be replaced by someone with much less training and fewer skills. The remaining 10% can be handed off to a superstar. Coalitions exist to prevent this so that the doctor is not replaced by a registered nurse, even though the RN can do 90% of what a GP does. And an LPN can do 90% of what an RN does. And an orderly with a few semesters of training can do can do 90% of what an LPN does. You can can replace professors with instructors, etc. But when this happens, the savings will not be passed onto the consumer, but will appear as rents in the various sectors.
The “efficient” level of coalitions is when the coalition-augmented labor force is exactly as differentiated as the labor productivity differentials within industry, so that the wage differential of hiring a unionized factory worker is equal to the greater labor productivity in that industry. Note that this has nothing to do with “how hard” the union worker works, or what their natural talents are. The whole point is that there isn’t going to be a significant differential in natural endowments, and yet due to technology, labor productivity is higher in some industries.
They “is” learning! sorry for the Bush-ism 🙂
RSJ: “The whole concept of sticky prices is a bit strange. Imagine if physics took this approach, and their response to the Kepler problem was to declare that Mercury was “sticky”, rather than deciding that there was a theoretical deficiency in their current understanding of the laws of motion.”
We (sticky price macroeconomists) know it’s a bit strange. We “know* there is a theoretical deficiency in our current understanding of the laws of motion (of prices). We want a theory which explains sticky prices. We don’t have one yet. So we patch our existing theory. It’s the best we can do. It’s crap, but it’s better than ignoring the problem with the orbit of prices.
“And there are other examples of “natural” sticky prices — for example, many prices reflect expectations over longer periods of time. For example, a long term interest rate, or a long term cost of capital. By definition, when the price of something represents inputs that cover many time periods, then it cannot move as quickly in response to a current period demand shock. That’s not true for the price of eggs, obviously.”
Long-term interest rates move more slowly than short-term interest rates. That doesn’t mean they are sticky. They aren’t sticky at all (almost). There is (almost) never excess demand or supply of government bonds. The interest rates on long bonds moves less than on short bonds for the same reason that averages move more slowly than each of the items that makes up the average.
“Yes, even without frictions, the assumption that workers are paid their marginal product relies on constant returns to scale, and doesn’t necessarily hold when there are different industries with different labor productivity levels hiring from the same labor pool.”
If firms takes wages as given, in a competitive labour market, wages (for identical workers) will be equalised across all sectors, and will be equal to the Marginal Revenue Product (= Marginal Revenue x Marginal product) in each sector. But a firm that has monopoly power in its output market (it faces a downward-sloping demand curve) will have Price greater than Marginal Revenue. So the Value Marginal Product (= Price x Marginal Product) will be higher in firms that have monopoly power.
The assumption of constant returns to scale is not needed for this result. The only relevance of constant returns to scale is that increasing returns to scale is incompatible with long run equilibrium perfect competition in the output market.
“The recession is not caused by an excess of desired savings over investment.”
Yes, it is.
“they choose to save in the form of money instead. It is the excess demand for the medium of exchange that causes the recession.”
No, this is false for two reasons. Both sentences are completely wrong.
First, in the recession nobody increases their savings. The patient reduce their savings.
Secondly, the recession happens even in a world with no outside money. So the second sentence can’t be correct.
Adam: we disagree on the first, and have argued it over without a resolution.
On the second, the net stock of outside money can be zero in the limiting case of a Woodfordian NK model. But that does not mean that the net demand for outside money is identically equal to zero.
By analogy, the stock of net debt is identically equal to zero in any economy (barter or monetary). But that does not mean the net demand for debt is identically equal to zero.
Clarification on the first part of my above comment: (Actually scrap what I said in the first sentence above):
It depends whether we are talking about desired saving the existing rate of interest or actual saving at the new equilibrium rate of interest. It also depends on whether we interpret the actions of the impatient when the debt limit is reduced as something they choose to do or are required to do.
When the debt-limit is reduced: the patient do not change their desire to save (at the previous rate of interest); when the rate of interest falls, they desire to save less as a result. In the new equilibrium, they do actually save less. The impatient are required to save more (dissave less).
“But that does not mean that the net demand for outside money is identically equal to zero.”
But the demand for outside money, in equilibrium (even in the recession equilibrium) is zero!
You need to work through the appendix to see this but what actually happens is that as the debtors pay back the debt (denominated in the consumption good) the savers use the added consumption to simply maintain consumption and work less.
They don’t try to save more! (they don’t want to save in any medium).
Adam: “But the demand for outside money, in equilibrium (even in the recession equilibrium) is zero!”
Agreed. Normally, the central bank adjusts the rate of interest to ensure that the demand for money equals zero, at that rate of interest. But if the bank can’t or won’t adjust the rate of interest, income adjusts until the demand for money equals zero, at that level of income.
The debtors (the impatient) don’t really want to save more, but they are required to save more. It would be better if I said “planned” saving increases, rather than “desired” savings increases, (…and so interest rates fall or income falls until planned savings is zero.
The point here is that the proximate cause of the recession here is manifestly not an excess demand for or hoarding of the medium of exchange.
In this model, the recession happens even if it’s a barter economy. Even if their is no medium of exchange.
Adam: OK. That’s where we disagree. The GE/PK model is a model of monetary exchange. If it were a barter economy, firms would simply increase output and swap their output with other firms’ outputs.
NO! You’re wrong! It’s not a model of monetary exchange.
The firms don’t do that because the patient workers won’t supply more labour! They prefer to work less and use the labour of the deleveraging debtors to maintain their consumption.
And the debtors of course can’t consume more, they work as much as ever and hand over some of their output to the savers.
The firms can’t increase output and barter it.
Actually your last comment was also wrong for a more basic reason which is that firms don’t consume, the firms don’t desire the output of other firms, but I guess that’s not literally what you meant.
I know that we’ve already argued this and failed to agree. I’m just bringing it up again because it just hit me that when you construct examples you usually assume that labour is supplied inelastically.
But this model has a standard neoclassical labour market, workers have a disutility of supplying labour.
Nick,
“Long-term interest rates move more slowly than short-term interest rates. That doesn’t mean they are sticky. They aren’t sticky at all (almost). There is (almost) never excess demand or supply of government bonds. ”
Yes, the financial markets always clear — so what? Interest rates are not going to be set by the intersection of a supply curve of final borrowers with a demand curve of net savers. The prices will be set by all sellers of assets transacting with all buyers of assets. Moreover, in aggregate, the increase in savings necessary to fund investment comes from the investment itself.
The motivations of the sellers and buyers (e.g. whether they plan on spending the proceeds of their sale on the purchase of goods, or on the purchase of another financial asset) is not going to affect the auction price. Yet your argument crucially rests on someone only borrowing in order to spend, and only lending as a result of prior new savings.
One way to imagine this distinction is to look at the housing market. Most house purchases are by people already selling their existing home and moving into another used home. They could be moving to another location, trading up, trading down, etc. But in the vast majority of transactions, people are just swapping the houses that they currently have with each other, and in this way they are setting the overall price of housing. The price of housing is not going to be set by the supply of new homes being built by homebuilders intersecting with the demand of people without a house to buy one. Both of the above are insignificant, in terms of volume.
Therefore supply and demand of new home-builders and the new home buyers will have little effect on the price of house. And in the same way, the supply and demand of final borrowers and final lenders will have little effect on the price of a financial asset.
Now why would houses just sit in foreclosure, unsold? A bank forecloses on a houses and the new buyer can only afford a cheaper price. Why wouldn’t the bank sell the house to the buyer at the lower price? Is it because we don’t barter?
No, it’s because the seller believes that next period, a higher bid will appear. It may well be in their economic interest, in the sense of expected utility, to leave the resource idle, rather than transacting at the current price. And in this sense the prices will appear to be “sticky”, as you have empty houses waiting to be sold, as well as willing buyers waiting to buy, but they cannot agree on a price. The price doesn’t fall enough for the market to clear in the current period, because of possibly of a divergence of expectations of the future prices.
OK, that is a partial equilibrium analysis. But the general case holds as well. Because the cost of capital is not the intersection of the demand of net investors with the supply of net savers, but is determined by expectations of the future return on capital over many periods, it could be that, in a give period, the rate demanded is higher than the return available for increasing the capital stock in that period. In that case, it would be better, from the point of view of the individual investor, to defer investment and wait until the situation improves. But that deferral of investment means that the current period of would-be savers will be disappointed — they will not receive the income arising from the investment that they need to save, and if they require that level of savings in order to repay debts, then they will try to save even more, causing current periods to be even lower, curtailing investment in the present period even further, etc, up until a default occurs or their income adjusts to a sufficiently low level that they do not wish to save anymore.
None of this has anything to do with a desire to “hold the medium of exchange”. All of the above works equally well in a barter economy with long lived (real) assets purchased with long term debt.
Thank you, Nick and Matt, for your replies to my query about Ricardian Equivalence. I don’t completely understand your answers, but at least I know that you have good reasons for thinking that the demand-side Laffer Curve argument doesn’t work in the E-K model, but may work in a different model.
Adam: “I know that we’ve already argued this and failed to agree. I’m just bringing it up again because it just hit me that when you construct examples you usually assume that labour is supplied inelastically.
But this model has a standard neoclassical labour market, workers have a disutility of supplying labour.”
That’s true. I ought to be able to make essentially the same argument even when the supply of labour is not perfectly inelastic. But it does make it harder for me to put that argument into words. And when firms are imperfectly competitive, it’s even harder for me. (Actually, thinking about Bertrand Competition in a Barter economy is conceptually hard as well, because what is the medium of account in which each of the n firms sets its price? I would have to re-formulate it as Cournot equilibrium, plus I would need the proof that Bertrand and Cournot converge in the limit as n approaches infinity, with or without differentiated products (which I did prove once, decades ago).
“That’s true. I ought to be able to make essentially the same argument even when the supply of labour is not perfectly inelastic.”
But you can’t because your argument won’t end up being true and the Krugman/Eggertson paper is a counter example.
Now, I imagine that you’re thinking that the recessionary outcome must involve hoarding money because it’s caused by the debtors retire some debt and thus reducing their expenditure on new production while the savers don’t increase their expenditure by the full amount of the transfer that they receive. If there is money in the economy and the debt contracts are paid off by monetary transfer then you’d be right, the savers would end up increasing their money holdings as a saving medium and that could be correctly taken as the cause of the recession.
However, suppose it is a barter economy and the debt contracts are settled by a transfer of a specified nominal quantity of the consumption basket (the index). Here we have some nominal unit of account (numeraire) which we can call dollars but dollars are not the medium of exchange. (this works because if the individual wants a basket different from the index he can trade to the basket he wants).
Now, when the deleveraging comes the debtors pay back some of their debt aquiring the consumption basket in the market and transfering it to the savers. What do the savers do?
If the savers supplied labour inelastically then you’d be right, no recession, there’d be extra output available and the savers would consume it instead of throwing it away (suppose consumption basket is entirely non-storable).
In this model though that isn’t what happens. The savers optimality conditions mean that they simply use the consumption goods they receive in payment of the debt to maintian their consumption while supplying less labour. Since they supply less labour there is no excess of consumption goods available.
There is no money, nobody hoards the medium of exchange since it doesn’t exist. The economy is pure barter yet has a recession.