Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Sunday, February 12, 2012

The trend is your friend (until it ends)

My previous post advertising Jim Bullard's recent speech seems to have generated a lot of discussion; see Mark Thoma, Scott Sumner, David Beckworth, Tyler CowenNoah Smith and, yes, even Princeton Charming himself.

Most commentators are rather negative on Bullard's view that a permanent (persistent) negative wealth shock should be associated with a permanent (persistent) decline in the level of real GDP, leaving it's long-run growth rate largely intact. Some question the logic of Bullard's explanation, but it is not inconsistent with what happens in a standard RBC model where productivity follows a random walk with drift. I'm not sure if that's what Jim had in mind (I will find out in due course), but just thought I'd put it out there. (Alternatively, see Steve Williamson.)

What I would like to talk about here is my own take on the matter, which is I think is subtly different from Jim's. In my previous post, I made the following comment:
I think that Bullard makes a persuasive case that the amount of household wealth evaporated along with the crash in housing prices should likely be viewed as "permanent" (highly persistent) negative wealth shock. Standard theory (and common sense) suggests a corresponding permanent decline in consumer spending (with consumption growing along it's original growth path). The implication is that the so-called "output gap" may be greatly overstated by conventional measures.
I think that the crossed out part above was a mistake in light of the theory I had working in the back of my head when I wrote that paragraph. But otherwise, what I said is fine. As long as you understand the theory; which, of course, I should have explained. Let me do so here.

It is probably fair to say that when most people take a look at a time-series for real GDP, in their mind's eye they decompose the time-series into a linear trend and deviations from linear trend. It is a perfectly natural thing to do. But that doesn't make it correct.

Implicit in any decomposition is a theory. The common decomposition assumes that trend (or potential) GDP follows a smooth upward path. Trend is labeled "supply." Actual GDP (the thing we observe) obviously fluctuates around trend (something we do not observe). And since trend is "supply," it follows that actual GDP must be "demand;" and that cyclical deviations from trend (the output gap) are caused by "demand shocks." A lot of people seem to take all this as self-evident truth. Unfortunately, the "right" data decomposition is not as obvious as people sometimes like to believe.

What is another way to decompose time-series data? Personally, I find Jim Hamilton's regime-switching model an interesting way to interpret the pattern of economic development. The basic idea here is that growth is driven by productivity, and that productivity growth is subject to infrequent, but random and persistent, regime changes. (Regime changes are possible along other dimensions, of course.) Sometimes we are in a high-growth regime, and sometimes we are in a low-growth regime--a view not inconsistent with Schumpeterian growth dynamics. And while these growth shocks are not likely the only reason behind our cyclical ups and downs, this is the type of shock I had in mind when I envisioned the large negative wealth shock mentioned by Bullard.

In particular, as Joseph Zeira has shown (Informational Overshooting, Booms and Crashes, JME 1999), the switch from a high to low growth regime generates equilibrium asset price dynamics that any econometrician is likely to interpret as a price bubble that booms and then crashes. The price crash (and consequent loss of wealth) however, is driven entirely by economic fundamentals (I suspect that one could generate something similar in a model with multiple equilibria and self-fulfilling prophesies). I discuss this possibility in a bit more detail here: The 2005 Real Wage Shock. In this latter post, I raised the question of whether the apparent slowdown in real wage growth may have led property owners to revise downward their estimates of future rental income, precipitating the crash in real estate prices.

Now, maybe all this sounds a little crazy to you and, of course, perhaps it is. But it is interesting to note that some recent evidence on U.S. productivity growth, reported by James Kahn and Robert Rich, seems to corroborate my hypothesis: The Productivity Slowdown Reaffirmed (Liberty Street Economics, Sept. 2011). Here is a snippet from their opening paragraph:

Economists generally agree that productivity is the primary ingredient for sustainable growth in GDP and wages. The August productivity data release provided some clarification regarding trend--or long-run--GDP growth, but the news was not good: Following a resurgence of strong productivity growth in the late 1990s and early 2000s after nearly a quarter-century of slow growth beginning in 1973, the latest reading from a trend tracking model now indicates that slow productivity growth returned in 2004.

OK, so I was off by a year. ;)

I would like to mention some related empirical work by Marco Lippi and Lucrezia Reichlin, Diffusion of Technical Change and the Decomposition of Output into Trend and Cycle (ReStud 1994). The authors argue against modeling productivity growth as a random walk, suggesting that it makes more sense to think of technology diffusing according to an S-shaped dynamic.  Of course, the S-shaped dynamic gives rise to the low/high/low growth regimes I mentioned above. The authors conclude:
Thus we have found what might be called a dynamic tradeoff: either we assume rich dynamics for the cycle and consequently a trivial trend, or else we assume more complicated dynamics for the trend, consequently impoverishing the dynamics of the cycle. All intermediate cases are rejected by the data. 

Interesting, don't you think? At the very least, I think it suggests there is some room for different interpretations of the cycle and that the relative merits of these different interpretations should be the subject of an open and respectful debate (I believe that this was the main motivation for Bullard's speech).

Why is understanding the true nature of the decomposition important for monetary policy? Kahn and Rich provide us with one answer to this question:

It is widely believed that the difficulty of detecting a change in trend growth contributed significantly to the economic instability of the 1970’s, as policymakers were unaware of the slowdown in productivity growth for many years, and only much later were able to date the slowdown at approximately 1973. This resulted in overestimating potential GDP (at least so the conventional wisdom goes) and setting interest rates too low, and double-digit inflation followed not long after.  

It is not surprising to discover that the memory of that event weighs on the mind of some Fed presidents. Now, it happens to be my personal opinion that the inflation threat this time around is overstated (largely because this time there is a huge worldwide demand for USD and US treasury debt that is keeping inflation and interest rates low; see here). But what I, or anyone else, thinks is beside the point I am trying to make here. One of  the Fed's most important jobs is to keep inflation expectations anchored. History shows that inflation expectations can change suddenly and capriciously. Whether one likes it or not, it is the job of Fed presidents to think about this possibility, and to voice concern if they see a danger of repeating past policy mistakes.

If we are indeed entering into 1970s era of relatively slow productivity growth, then current CBO measures of the output gap are likely overstated, and further LSAPs are probably not warranted. This does not mean, however, that there is no output gap, or that there should be no policies directed to those who are having a difficult time in the labor market. As I discuss here, there is considerable variation in regional labor market conditions and it is not at all clear that "looser" monetary policy is the tonic we want to employ (assuming that it will have any effect at all in current conditions). In particular, there may be ample scope for regional fiscal policies, education and retraining programs, or other more direct measures that are outside the realm of monetary policy.

Update: Related Links

Bleak Apologists (The New Arthurian Economics)
The Asset Price Decline IS a Negative Productivity Shock (Canucks Anonymous)
Chucking the Solow Growth Model Cont. (Noahpinion)
The Output Gap: Still Negative (hjeconomics)


  1. You seem to be echoing comments by Gary Gorton:

    "The way standard models deal with it is, I think, incorrect. A lot of macroeconomists think in terms of an amplification mechanism. So you imagine that a shock hits the economy. The question is: What magnifies that shock and makes it have a bigger effect than it would otherwise have? That way of thinking would suggest that we live in an economy where shocks hit regularly and they’re always amplified, but every once in a while, there’s a big enough shock … So, in this way of thinking, it’s the size of the shock that’s important. A “crisis” is a “big shock.”

    I don’t think that’s what we observe in the world. We don’t see lots and lots of shocks being amplified. We see a few really big events in history: the recent crisis, the Great Depression, the panics of the 19th century. Those are more than a shock being amplified. There’s something else going on. I’d say it’s a regime switch—a dramatic change in the way the financial system is operating."


    1. Ah yes, thanks for reminding me--I've heard Gary present this argument before.

  2. David,

    As you know, the Survey of Professional Forecasters show that the productivity growth rate is expected to slow down. This 'real' development is consistent with a smaller output gap. The question, though, is how much so. One reason I am not convinced that much of the output gap can be attributed to this slowdown is that we have yet to see sustained upward pressure on expected inflation. One would expect to see higher expected inflation if expected productivity growth was falling sufficient to explain a large part of the output gap.

    1. David, in fact I was not aware of the SPF showing a decline in forecast productivity growth! (Thanks for letting me know.)

      I am not so convinced either; but the point of my post is that we should at least be discussing the possibility.

      Your statement "One would expect to see higher inflation..." Well, I guess that depends on what sort of model you have operating in your head, right? I'm not sure one way or the other how I would expect inflation to behave, especially since I think that foreign influences are having a major impact on US inflation. Let's keep thinking about it!

  3. David

    It is beyond me how GDP can trend when we have been below trend on investment, as % of GDP, and R & D, as % of GDP, for years.

    Drugger, I assume you know who he is, says that investment has fled because of tax cuts. Smart investors knew such was nuts, that starving the beast was nuts, so they have taken their money elsewhere. He doesn't date flight as early as do I, but the data collaborates.

  4. obviously, federal tax cuts have reduced R & D as a percent of GDP

    another paradox. I believe, if you asked businesses, they would tell you that what drives them nuts is that the tools to be productive are everywhere but that the friction of deploying them, of doing business, is unbelievable, especially now that all suppliers are in Asia.

  5. If you dislike Krugman so much, you should try being right for once. That would give you more credibility.

    But sadly for you Krugman-haters, HE's proved right on nearly every issue of import over this extremely complicated and unprecedented time.

    So let's give the guy a little credit, eh?

    1. RN, did you actually read this post? It's not about him. It's about an idea that I think deserves discussion.

    2. Oh please. The poster is referring to your "Princeton Charming". I've read Krugman for years and have never seen him use anything like that sort of ad hominem name calling toward you, he's never used anything but your name when he's linked to you, which he's done only recently.

      And yet you're the one going on about how uncivil he is.

    3. Timelagged, grab a sense of humor somewhere.

  6. Tim Duy's FedWatch weighs in on the issue:

  7. Why should GDP follow a smooth upward path? What is the theory behind this?


    1. If youre saying "why should potential GDP" follow a smooth upward path, then the answer is nobody said it did.

      anon 212 + 1

  8. David,

    Your presentation of this viewpoint is logically coherent and with more time and data will present a testable hypothesis. In addition, I think the importance of this discussion is in regards to how much weight is given to the output gap in the conduct of monetary policy. I think that differing opinions in and of themselves should give one pause about the usefulness of the output gap.

    BUT (you knew this was coming) doesn't wealth impact aggregate demand? For example, it is entirely possible to suggest that a slowdown in productivity caused a decline in "potential" output and asset prices. The latter of which reduces wealth and therefore real GDP through some sort of collateral channel. Thus, the output gap is substantially smaller than we might otherwise think. However, when I read Bullard, he seems to be suggesting that the wealth shock is causing the decline in potential. In other words, I see a coherent story in which wealth is endogenous whereas Bullard seems to be making the case that the shock to wealth is exogenous.

    Regardless, I don't know how much validity there is to this view, but you know what they say about opinions...

    1. "doesnt wealth impact AD "?

      Doesnt a wealth shock imply a supply shock - the supply shock is the primitive, not the wealth shock?

    2. Isnt that what josh said? read a bit further...

    3. Thanks, Josh. In terms of whether wealth impacts aggregate demand, well, you know that is difficult to separate "supply" and "demand" in general equilibrium models. But in any case, yes, and yes to the collateral channel. As for what Jim had in mind exactly, I guess we will have to wait and see whether he offers some clarification.

  9. "We should at least discuss the possibility..."

    and there are so many possibilities to discuss... especially if you are trying to muddle the discussion about what to do... maybe the answer is we should not do anything, right?

    For some reason all this feels awfully similar to rhetorical games... I mean, referencing an obscure article from 1999 (with a decent number of citations -91- according to Google Scholar, but not enough to be considered more than mere theoretical possibility) to back up the claim that changes in asset prices may affect output trend is not enough of an argument. The rest of your argument is conventional and accepted knowledge, but the challenge to Bullard's argument is the relation between asset prices and permanent output.

    1. I'm not sure what the right thing to do is. But I do know that whatever we decide to do, we should have contingency plans in place in the event that things don't turn out as expected. And this is why it is useful, in my view, to discuss alternate interpretations. I'm not sure what you mean by suggesting that I am engaging in "rhetorical games." I think I pointed out something interesting and potentially useful. Maybe you don't think so, but if not, explain why not.

  10. I have computed an alternative, and theory-based measure of the US output gap in this blog post:
    The US output gap is still quite negative currently according to this measure (which builds on the Gali, Gertler and Lopez-Salido, 2007, ReStat).

    Cheers, Henrik

    1. Hi Henrik,

      Yes, in fact I did see your post! How do you define gap? Is it the difference between flex price and sticky price equilibrium output? I also wonder what would happen in this class of models if trend was modeled the way I describe in this post. Still lot's to figure out. Thanks!

    2. The welfare relevant gap is defined as the difference between output and the efficient output level. The monetary policy-relevant output gap fluctuations are the variations around the mean of this gap. In essence, one adds the average inefficiencies to the output gap measure, and one gets indeed an output gap that is the difference between output and output under flexible prices (with all kinds of distortions that monetary policy cannot cope with). I guess this gap it is what has normally been called output relative to the natural rate of output (I think that well-established label is more adequate than "potential output" which is confusing to many for purely semantic reasons.) Best, Henrik

  11. David A, dont you think that the concept of potential GDP is useless ? It conceals the useful information. Its like if a drug company were to try to develop a new drug just using 2-D Lewis dot formulas when what they really need is a 3-D representation of the molecular structure. GDP is 2-D, it conceals all the input output interconnections, all the cost complementarities, all the creative destructive churn/ reallocation and coordination issues.

    1. I'm not sure I would go so far as to say it is useless. What we should keep in mind is that it is simply a theoretical construct that may or may not be useful for organizing our thinking on a particular matter. There may be better ways of doing things. We should abandon the construct if we find a better way.

  12. "If youre saying "why should potential GDP" follow a smooth upward path, then the answer is nobody said it did."

    So what explains the demands that GDP should return to its pre-crisis trend?

  13. From the previous Anonymous @ 215pm (Anon 212):

    to be clear, I have seen a number of commentators claim 'GDP is x% below trend' and should return to trend (usually in the context of an argument why the Fed should do more). The distance of GDP from trend is also used as a measure of the output gap.

    As far as I know, there is no theory that explains why GDP should stick to a prior trend; it is simply an empirical regularity subject to the usual problem of induction/Peso problem (etc).

    Further to that, it seems that assuming a stable trend rate of growth is implicitly assuming stable trend rate of growth of inputs (labor, capital, TFP), which seems implausible (e.g. for demographic reasons).

    I am simply looking for some clarification on this matter, having failed to get that from other bloggers I have asked.

    1. you should definitely read

  14. Anon,

    I'm not exactly sure how to answer your question. One can certainly make assumptions about how the economy functions, with different assumptions leading to different conclusions about what to expect in terms of mean-reversion. In some models, shocks to the economy move GDP off trend for a while, but with GDP moving back to trend in finite time. In other models, shocks lead to a permanent change in trend. Which of these interpretations one accepts depends on how well the model predictions fit the data, and whether or not the economic mechanisms highlighted in the model seem "plausible."

  15. You write, "As I discuss here, there is considerable variation in regional labor market conditions and it is not at all clear that "looser" monetary policy is the tonic we want to employ (assuming that it will have any effect at all in current conditions). In particular, there may be ample scope for regional fiscal policies, education and retraining programs, or other more direct measures that are outside the realm of monetary policy. "

    We all know this isn't going to happen, so why did you mention such.

    1. I'm not so sure of that. A good part of the "Obama stimulus" included transfers to state and local governments. Maybe this is not going to happen again, but it has happened, and could in principle happen again. And even if it isn't going to happen, not sure why you don't want me to mention it.

  16. slow productivity growth returned in 2004.

    Robert Dugger argues that the Bush tax cuts lead to disinvestment/underinvestment through a process he calls fiscal adjustment discounting. People moved their money because it was going to go to hell in a hand basket here

    1. Robert Dugger is a whole lot of crazy packed into one person. I know its you, John D, you can't hide your crazy here.

  17. Can't find the article you refer to. However, I do see that this guy pointed out that Gross' call on Treasuries was wrong. Good call. But I thought you needed IS-LM to make that sort of right call. Don't tell

  18. Mark Thomas has more from Bullard on his website today. Bullard references a good paper from the St.Louis Fed

  19. David, maybe the model of Brunnermeir and Sannikov is consistent with your regime switch idea?

    "We build a model to study full equilibrium dynamics, not just near the steady state. While the system is characterized by relative stability, low volatility and reasonable
    growth around the steady state, its behavior away from the steady state is very diff erent and best resembles crises episodes as large losses plunge the system into a regime
    with high volatility. These crisis episodes are highly nonlinear, and strong amplifying adverse feedback loops during these incidents may take the system way below the
    stochastic steady state, resulting in signi cant ineffciencies, disinvestment, and slow recovery."

  20. I am a Brit living in the States and am certainly no academic economist. However, I have become quite a voracious reader and one issue has always caused me to wonder. This is related to productivity growth. I relate productivity growth to things like increasing automation in factories. However, is it possible that in a certain sense that this type of automation may raise productivity in a broad sense, yet reduce employment as machines replace people? In theory, people should be "retrained" or perhaps our educational system needs to be better as manufacturing becomes increasingly complicated (note - read the front page article in latest issue of Atlantic Magazine). But I do sometimes wonder about the broad relationshipm between productivity growth and employment.

    1. Good question. The broad long-run relationship between productivity growth and employment roughly zero.

      While the employment/population ratio has grown over the last century, the average work week has declined. Consequently, hours worked per capita is roughly constant. Over the same time, productivity has risen dramatically.

      So, to the extent that new technologies are labor-saving, the long-run effect is to allow labor to flow sectors where it will be better rewarded. At one time, almost everybody worked in the agricultural sector; today, almost no one does. Society seems no worse for this; and indeed, is better off (food has never been cheaper, measured in how much you have to work for your dinner). Of course, this is not to diminish the fact that there are winners and losers in transition episodes.

    2. Dave,

      We've had this argument before. That is, the profession has had it before.

      This is the difference stationary GDP argument of Peter Phillips and coauthors versus the trend stationary GDP argument of DeJong and Whiteman. The former argued from a frequentist point of view versus the latter's Bayesian point of view.

      Blough (1992) and Faust (1993) came along to show that stationary and non-stationary processes are observationally equivalent in that every stationary process is approximated arbitrarily well by a NS process and vice versa.

      Thus, we cannot know whether GDP is difference stationary as Jim Bullard seems to imply or trend stationary as his opponents seem to think.

    3. Chris,

      And if what you say is true (and I believe you), then what say you to those who assert we are presently below potential GDP?

    4. David:

      Is there any field within economics that deals with the wide difference between potential and actual GDP based on the human condition.

      For example, I have talked with many lawyers and other service providers who state that technology has given them unlimited productivity but that such cannot be applied due to the fact that they are dealing with people and all sorts of resistance and psychological misjudgment.

      Take the simple procedure of getting an xray or MRI and look at the inefficiency of the process. The machines can take a picture every 15 seconds, but take one every 5 to 10 minutes

  21. Unfortunately, from an empirical point of view, I think that we can't know.

    We might have to turn to theory. [Gasp in horror.]

    1. Can you give me an example of how one might use theory to help empiricists grapple with this question?

    2. Well, what does theory say about variation in output?

      Are shocks to output permanent or temporary?

      Different models imply different persistence of shocks to output.

      Now we are on your territory so I'm sure that you can fill in the blanks better than I can.

  22. One more thing: Tim Duy's comment about how potential GDP tracked GDP so well made me laugh.

    Tim attempts to do by eyeball what some of the best econometricians in the profession cannot agree on. The funny thing is, Tim thinks that the problem is simple. I wish he were correct.

  23. Keep going quotes I just read through this posting and had to express gratitude personally. Very clear and succinct!

  24. You can plot a straight line through real GDP per capita going back to the great depression and 2% per year pops out. There are no "level adjustments" including the great depression. According to this decomposition, output was below trend by 50% in 1933, but "caught up" by the early 40s. Given the experience of the great depression, why would anything different be expected to occur now? Why would there be a level adjustment to trend now?

    1. You could plot a straight line through the data, I agree. But one could plot other decompositions that would fit just as well, if not better -- read Lippi and Reichlin, for example (though the statement I just made is well known among econometricians).

  25. I agree since we don't have a great theory explaining the growth rate of TFP, we are left to econometrics. That seems to always get us into trouble.

  26. "Why would there be a level adjustment to trend now?"

    Because the cross-country evidence suggests that's what happens after a financial crisis. I say "suggests" because (among other things) the sample for developed markets is small.

    Anon 212

  27. You're overdue for a new blog post, Dave. How am I supposed to keep procrastinating when you don't blog?

    1. Sorry, travelling. But nice to know someone misses me! You must be one of my two

  28. Once again great post. You seem to have a good understanding of these themes.When I entering your blog,I felt this . Come on and keep writting your blog will be more attractive. To Your Success!
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  31. Bullard's view that a permanent (persistent) negative wealth shock should be associated with a permanent (persistent) decline in the level of real GDP, leaving it's long-run growth rate largely intact. buy from china