Three views of consumption and the slow economy

I'm still digesting New-Keynesian models. As part of that effort, today I offer some thoughts on how economists come to such different views of the current situation and desirable policies. It's a nice story, in the end. Real economists, unlike much of the commentary and blogging world, come to different conclusions by using much the same model, but making different assumptions and simplifications, each of which we can look at and evaluate, and hopefully come to some consensus.

The economy is not doing well. The black line in the graph shows log consumption. (The units are percent increase in consumption since 2002.) After trending up steadily at close to 3% per year through the previous decade, consumption -- along with output and everything else -- took a dive, totaling 10% loss relative to the red trendline. And consumption has been stuck there ever since.

So, the big questions: why, and what might be done about it?

All current macroeconomic theories start with the same basic story: when interest rates are higher, people consume less today, save, and then consume more in the future. Higher real interest rates mean higher consumption growth. In equations,

(c represents log consumption, i is the interest rate, pi is inflation, rho and gamma are parameters. Rho is a "discount rate" capturing how much people prefer the present to the future, and gamma captures how strongly people react to interest rate changes. I simplified, leaving out uncertainty.)

We build on this insight in different ways. 

I. New Keynesians 

Integrating forward, today's consumption reflects all expected future interest rates, and where we think consumption will be in the far-off future

This is the central equation of the new-Keynesian model and world-view. (For example, this is Johannes Wieland's equation 2, see my last post. I have taken out growth or trend, so these represent deviations from a steady growth path.)

The green line in the graph presents the New-Keynesian diagnosis of the current situation. New-Keynesians assume consumption will return to trend, so the last term in the equation is zero. In the graph, they anchor future consumption at the green dot. Then, a too-high interest rate means too-high consumption growth, which drives the level of today's consumption down.  (For example,  Ivan Werning's figure 3, discussed in an earlier post here.)

Why is the interest rate too high? The "zero lower bound" is to blame. The Fed cannot lower nominal interest rates (i) below zero. So if the inflation and discount rate terms (pi and rho) require a strongly negative nominal rate, the real rate will be stuck at a big positive number.

From this one equation and graph, you can make sense of lots and lots of new-Keynesian analysis and policy advice.

The level of today's consumption depends on the whole string of future interest rates, not just today's interest rate. So, if people expect the interest rate in 2014 to be lower, that is every bit as effective in raising today's consumption as would be lowering today's rate. Hence, "open mouth operations," "forward guidance," and "managing expectations."  If the Fed by just talking can persuade people it will hold interest rates low for a longer periods, when they are expecting rates to rise above zero, that expectation will "stimulate" today's consumption. If promises don't help, perhaps announcing a new "rule" which if followed would lead to lower rates for longer will help to change expectations.

In this equation, more inflation lowers the real interest rate too. So, anything that boosts inflation is a good thing. Boosting inflation isn't primarily about a Phillips curve, direct "monetary stimulus," encouraging investment, and so on. It's a way to lower real interest rates inside the integral and shift consumption from the future to the present.

Once again, increasing expected future inflation would be just as effective as increasing current inflation. Hence, calls for the Fed to announce a higher inflation target, or at least announce that it will tolerate more inflation before beginning to raise rates, as it has.

Fiscal stimulus, and many of the other seemingly magical properties of new-Keynesian models (see  last post) follow from the idea that inflation is good. Fiscal stimulus raises inflation. Broken windows, hurricanes, pointless public works projects, temporarily lowering the economy's productive capacity, all raise inflation (how is in other equations of the model), which lowers interest rates.

I'm not sold on this story, as you probably guessed, for a variety of reasons.  

New Keynesian models are a bit fuzzy on just why interest rates have to be so low -- why the "natural rate" is sharply negative and why zero interest rates aren't enough. Many of the formal models assume that consumer's discount rate (rho) has declined sharply, beyond the capacity of the interest rate to follow it. If rho goes to, say -5%, with our 2% inflation, then even a zero nominal interest rate is like a 3% real interest rate. (These are deviations from trend, so one might not need actually negative discount rates to hit the zero bound. But even adding growth, it's hard to avoid the need for a negative natural rate to cause a problem of this size.)

Now, a spontaneous outbreak of thrift, to the point of valuing the future a lot more than the present, seems a bit of a strained diagnosis for the fundamental trouble of the US economy. That a bit more thrift is a great danger to the economy, rather than the long awaited return to normal after decades of debt-financed consumption, seems strained as well.

To be fair, all the papers I've read say clearly that they regard the decline in the discount rate rho as a stand-in for some more complex process involving the financial crisis. For example, a more precise version of my first equation adds a "precautionary saving" term. When people are very uncertain about the future, they save more, just as if they had become much more patient. In equations,

This story seems possible for 2008 and 2009, in the depths of the financial crisis and recession. But I'm less convinced that it describes our current moment. Just look at the graph. Our state is one of steady but sclerotic growth, not one of great consumption volatility.

New-Keynesian introductions have something more complex in mind, involving the "frictions" of the financial crisis, and lots of models in this spirit add explicit financial frictions. That too seems to me a useful line to pursue to understand the onset of the recession and the financial crisis. But that too is really not our question. The  "frictions" of the financial crisis -- capital constraints at banks and financial intermediaries,  or the run in the shadow banking system -- passed quite a while ago, and the models with frictions are by and large not being used to address the current moment. 

The question before us is not really why consumption fell so drastically in 2008 and 2009. The question is, why did consumption get stuck at so low a level starting in 2010? For this question, it's much harder for me to understand what a strongly negative discount rate means.

This question and controversy is much like those surrounding the Great Depression. The controversy there has not been about why the stock market crash and recession happened in the first place. (Though perhaps it should, as we really don't know much about that process.) The controversy is, why did the US get stuck so low for so long? Was it bad monetary policy (Friedman and Schwartz), bad microeconomic policy, war on capital, and high marginal tax rates (Cole, Ohanian, Prescott, etc.), or inadequate fiscal stimulus (Keynesians)? 

Many new-Keynesian models (such as Ivan Werning's) generate the high real interest rate by predicting strong deflation. Yes, if inflation (pi) were negative 10% in (2), then a zero interest rate would be a 10% positive real rate. But our inflation has been positive throughout. Our zero interest rate has meant a negative 1.5% to 2.5% real rate all along. Deflation simply did not happen. Moreover, the other ingredient in new-Keynesian modeling -- the Phillips curve -- says that a big output gap should be accompanied by some action on inflation, not a steady 2%.  The Phillips curve part of the model suggests that "potential" dropped, not that current output is far below that potential.

I graphed the green line to 2010, a good date for supposing the crisis is over and we entered the period of sclerotic growth rather than swift return to trend. We've had some time since 2010. Again, the new-Keynesian model generates a low consumption level by saying that we have too-strong consumption growth. But we don't have strong consumption growth. Equation (2) does not produce a steadily depressed level of consumption, with (if anything) weaker than normal growth. I guess you could argue for a constant sequence of unexpected negative shocks, so that each quarter, people are expecting the big consumption growth which just ends up not happening. But you can see how strained that argument is. It would be much more appealing to refer to a model and analysis that describes slumponomics directly.  (Update: I just found Kathryn Dominguez and Matt Shaprio on a sequence of negative shocks.)

And, you might be exploding a bit at the economic logic of it all. How can it be that all we need to do is to decide how much to consume, and the output just magically appears? Doesn't consumption have to be limited a bit by income?

Well, the new-Keynesian models are coherent on this subject. The simple models have no capital; output is produced by more or less labor each period. The logical structure of the models, is, roughly, that you first decide how much you want to consume, then you'll work hard enough to make the required income. (This isn't a behavioral assumption, it's the equilibrium outcome of sticky prices and monopolistic competition.)

That's why fiscal stimulus works at all. You might think that if you have to pay taxes to the goverment, which buys output to throw it away, you'll have to consume less.  (Again, stimulus in these models is Ricardian so the same whether from taxed or borrowed money, and stimulus does not depend on the government doing anything useful with the output.) But if consumption is determined first by the above equation, then you just work harder to pay taxes and make the stuff the government wants to throw away. That gives us a multiplier of one, not zero, and then inflation kicks in to raise desired consumption and give us a larger multiplier. (Roughly! Again, I'm trying to explain the core simplest idea, not to fairly describe all the complexities of the models.)

The very simple new-Keynesian model also does not have investment or capital stock. Output is produced as you need it. That's why consumption "demand" immediately means changes in output. I've always wondered why buying a car is good (consumption) but buying a forklift is bad (investment) in new-Keynesian models. You just can't ask that question in the very simplified model here -- there is no investment. Now, real quantitative new-Keynesian models do have investment and capital (with adjustment costs and other wedges). But as far as I can tell, the same basic conclusions emerge from models with capital, so the intuition must be as here, in which consumption is everything.

II Permanent income

An alternative view asks, what about the second term on the right hand side of the basic equation (2)?  What if nothing's terribly wrong with the intertemporal allocation of consumption, but the long-run productive capacity of the economy has declined?

There is certainly an abundant litany of such complaints. What if all the over regulation (Obamacare, Dodd-Frank, EPA "crucifixions," etc.), sand in the gears, disincentives of social programs, crony capitalism, policy uncertainty, high and prospectively much higher marginal tax rates, and other litany of complaints, have permanently reduced the productive capacity of the US economy, or, worse, its long run growth rate? Then we are not returning to trend. The trend has shifted down.

If so, the trouble is in the second term on the right hand side of the basic equation (2). And this basic equation has a dramatic and important lesson for us: Long-run ("supply") will depress today's consumption every bit as much as expected future interest rates ("demand") effects do. And improving the long-run "supply" effects can have a direct "stimulative" effect on consumption today.

I italicized, because I think this is an underappreciated consequence of the common world-view of all modern macroeconomics, both new-Keynesian and not, embodied in (2). The old-Keynesian view was,  take care of the short run now, because helping the long run only helps in the long run. You hear this over and over in policy circles. More stimulus now, and then talk about "structural reform" once the economy has recovered. Equation (2) denies that separation:  Improving the long run improves the present. 

I drew the blue line to reflect this view of matters. For an equation, we can turn to our old friend the permanent income model

Here W represents wealth (capital stock), r is the real rate r = i - pi, and y represents the stream of expected future income. This is an extremely oversimplified version of the standard stochastic growth model at the heart of... well, I don't know what to call us anymore. "Neoclassical?" "Anybody left who is a bit suspicous of the new-Keynesian juggernaut?"

The difference is really one of emphasis, not deep economics. (3) also derives from (1), but with a different set of auxiliary assumptions. The real interest rate is constant at r. There is capital W, and investment freely adds or subtracts from capital. Labor's product y is fixed rather than produced.

Again, this model is, like (2), extremely simplified. Yes, interest rates do vary, and it's easy enough to add that to the model.  Similarly, new-Keynesians know there is capital and investment.  We're outlining basic stories today, not constructing completely realistic, but often obscure and complex, models.

In this equation, the level of consumption shifts up and down along with expectations of permanent income. So, if you get news that the productive efficiency of the economy is permanently 10% lower, consumption drops 10%, and then goes on at the previous growth rate. As, by picking 2010 as the decision date, my graph suggests.

Like the new-Keynesians,  I won't be that specific here about just why consumption fell so drastically in the financial crisis.  The permanent income model does suggest that we look for changes in permanent income to explain the fall, rather than (only) a rise in discount rates or real interest rates, i.e. the desired intertemporal allocation of consumption.  From this perspective, consumers realized in fall 2008, that this recession was going to last forever rather than bounce back quickly, and they adjusted consumption downward accordingly. They were right. Just how they knew, when all the Government's forecasters thought we would quickly bounce back, is an interesting question.  Surely, my litany of free-marketer's complaints did not obvioulsy get suddenly worse in October 2008, just coincident with a run in the shadow banking system.  Well, maybe not so surely. Maybe consumers thought, we're in a horrible banking crisis, and our government is likely to prolong this one with ham-handed policies just like they did in the 1930s. But that's pretty speculative. And I do think (just as speculatively) there was a run in the shadow banking system, effective risk aversion spiked, and the financial crisis was more than just a signal of bad policy to come.

But all that is a topic for another day. The question is why consumption (and output) remain so low for so long after the crisis, when whatever outside-the-model chaos is over. The permanent income view suggests the problem is a poor long-term level, poor long-term prospects for the productive capacity of the economy, not too high growth, to an unchanged long-term level.

In this view, the Fed largely wasting its time with all its QEs and promises about future interest rates. The right policy answer is to forget about stimulating and fine tuning. Fix the long-run growth problem and the short run will take care of itself, much faster than you might have thought. This isn't the Fed's job. For Europe, do the "structural reforms" now and you'll start growing now in anticipation of their effect.

Moreover, in the underlying stochastic growth model, a rise in real interest rates is a good thing. Yes, we can get on the new-Keynesian green trajectory. What does that is a rise in the marginal product of capital, which raises interest rates, attracts investment, and leads to greater output. In that model, consumption is (very roughly) anchored at its position today, and increased interest rates raise future consumption, not the other way around. Of course, in the stochastic growth model, the Fed can't raise interest rates all on its own --  a higher marginal product of capital comes from greater efficiency or better technology. Still, it encapsulates the comments you read here and there that maybe the conventional sign is wrong -- maybe higher interest rates are desirable, as a sign of a good thing, not as a cause of a bad thing. There is always supply and demand in economics, and two sides to every question.

Which view is right? To my eyes, consumption seems stuck on a lower trend line, not growing sharply. Real interest rates are already negative -- we do not have deflation -- and I find it hard to believe that the discount rate and marginal product of capital are negative 5% or worse. The very large discount rate shock needed for the new-Keynesian story is pretty nebulous. The shocks to long-run productivity are staring us in the face.

I wish, of course, for more serious structural investigation to separate the two stories. I haven't seen a serious attempt to look at the structure of the US economy and measure a sharp negative "natural rate." (I welcome pointers from commenters.) I would welcome a quantitative assessment of how much the level of GDP is depressed from my litany of free-market complaints. With trillions of dollars of GDP, and potentially trillions of wasted stimulus at stake, you'd think we could do better.  

I want to emphasize, this is not a fight between models. This is the same model, with different emphasis, and different simplifications. There is nothing in the new-Keynesian modeling paradigm that forbids one to ask the question, what if the long-run productivity of the economy has sunk and high real rates are not the problem? The models were developed to talk about other things, to talk about historical "cycles" defined as deviations from "trend." Nothing but old habits prohibits one from asking the opposite questions.

III. Old Keynesians

A traditional view of consumption has been conspicuously absent so far, the textbook old-Keynesian consumption function

Consumption depends on today's income through the "marginal propensity to consume" mpc.

Modern new-Keynesian models are utterly different from this traditional view. Lots of people, especially in policy, commentary, and blogging circles, like to wave their hands over the equations of new Keynesian models and claim they provide formal cover for traditional old-Keynesian intuition, with all the optimization, budget constraints, and market clearing conditions that the old-Keynesian analysis never really got right taken care of. A quick look at our equations and the underlying logic shows that this is absolutely not the case.

Consider how lowering interest rates is supposed to help. In the old Keynesian model, investment I = I(r) responds to lower interest rates, output and income Y = C + I + G, so rising investment raises income, which raises consumption in (4), which raises income some more, and so on. By contrast, the simple new-Keynesian model needs no investment, and interest rates simply rearrange consumption demand over time.

Similarly, consider how raising government spending is supposed to help. In the old Keynesian model,  raising G in Y = C + I + G raises Y, which raises consumption C by (4), which raises Y some more, and so on. In the new-Keynesian model, the big multiplier comes because raising government spending raises inflation, which lowers interest rates, and once again brings consumption forward in time.

Old-Keynesians spent two generations fighting against the intertemporal view of consumption embodied in my first two equations, and now at the heart of the new-Keynesian model, in favor of the last equation. They said consumers were "liquidity constrained," or "rule of thumb," their expectations (if they had any) "adaptive," either too stupid to look forward in time or unable to do so.

I must confess a little sympathy to some of these views. A long long time ago I wrote a paper on "near-rationality" criticizing excessive zeal in the application of equation (1). Really, if the Fed today raises interest rates to 12% (annual rate) for a month, would everybody's consumption fall one percent today, so that it could rise one percentage point over the next month? Or is the relation between consumption and interest rates one of those looser relations that yes, applies roughly, for large sustained changes, and over long time periods, but not necessarily instantly?

In any case, a look at (1) and its application in (2) tells us that Friedman won more than he could possibly have imagined. Intertemporal optimization is now not the heretical pariah suggesting a low marginal propensity to consume and low multiplier, but it is the heart of the model. The Lucas-Sargent-Prescott revolution pervades new-Keynesian models as much as their more classical counterparts. Consumers are forward-looking. Expectations matter. No self-respecting mid 1970s Keynesian would have said that Fed pronouncements about what interest rates were going to be in 2016 -- or how the future unemployment rate would condtion that choice -- would have the slightest effect at all on today's consumption. Consumers are myopic, he would say. Expectations are adaptive.
But as a result, the new-Keynesian model really has nothing to do with the old-Keynesian intuition.

IV. Bottom line

Enough history of thought, though. The relevant choice today is between the first two alternatives. Are we in a situation where the long run is just fine, but the zero bound is forcing us to have too high interest rates, so consumption growth is too high and the level is depressed? Or are we in a situation that consumers doubt the long-run productive capacity of the economy, and are consuming little today because they expect to consume little tomorrow and little 10 years from now?

The answer matters: whether the economy can be stimulated merely by more solemn promises from the Fed about future interest rates and inflation, by broken-window interventions that reduce supply today to engender some inflation, or whether the economy must be stimulated today by ignoring short-run stimulus, fixing the long run, and counting on the permanent income model to increase consumption, and the present value model (q theory) to increase investment today.


P.S. It's 2013. Why is displaying math in html so hard?! The people who developed the internet are all nerd engineers who took calculus! I'm back to  pasting in png files to show equations. I tried mathjax, but it only seems to work on traditional screens, not in mobile, rss, etc. Suggestions welcome.

P.P.S. Martin Boulanger and Absalon below asked if maybe consumption wasn't growing unsustainably before the crash. Here's a longer view of the first graph, with my 2000-2007 trend line.
Or, even go back to 1945.
A big boom in the 2000's does not stick out from the consumption data. If anything, it was a little weaker than usual.

Also, yes, this is total consumption. Nondurable and services does not look much different. I started to break out the components but the post was getting too long.

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