This post is from a set of comments I gave at the NBER Asset Pricing conference in early November at Stanford. Conference agenda here. My full slides here. There was video, but sadly I took too long to write this post and the NBER took down the conference video.
I was asked to comment on "Downward Nominal Rigidities and Bond Premia" by François Gourio and Phuong Ngo. It's a very nice clean paper, so all I could think to do as discussant is praise it, then move on to bigger issues. These are really comments about whole literatures, not about one paper. One can admire the play but complain about the game.
The paper implements a version of Bob Lucas' 1973 "International evidence" observation. Prices are less sticky in high inflation countries. The Phillips curve more vertical. Output is less affected by inflation. The Calvo fairy visits every night in Argentina. To Lucas, high inflation comes with variable inflation, so people understand that price changes are mostly aggregate not relative prices, and ignore them. Gourio and Ngo use a new-Keynesian model with downwardly sticky prices and wages to express the idea. When inflation is low, we're more often in the more-sticky regime. They use this idea in a model of bond risk premia. Times of low inflation lead to more correlation of inflation and output, and so a different correlation of nominal bond returns with the discount factor, and a different term premium.
I made two points, first about bond premiums and second about new-Keynesian models. Only the latter for this post.
This paper, like hundreds before it, adds a few ingredients on top of a standard textbook new-Keynesian model. But that textbook model has deep structural problems. There are known ways to fix the problems. Yet we continually build on the standard model, rather than incorporate known ways or find new ways to fix its underlying problems.
Problem 1: The sign is "wrong" or at least unconventional.
The basic sign is wrong -- or at least counter to the standard belief of all policy makers. In the model, higher interest rates cause inflation to jump down immediately, and then
rise over time. Everyone at the Fed uniformly believes that higher interest rates cause inflation to go nowhere immediately, and then gently
decline over time, with "long and variable lags."
Larry Ball pointed this out 30 years ago. The behavior comes straight from the forward-looking Phillips curve. Lower output goes with lower inflation, relative to future inflation. I.e. inflation rising over time.
To be clear, maybe the model is right and the beliefs are wrong. It's amazing that so much modeling and empirical work has gone in to massaging theory and data to conform to Milton Friedman's 1968 proclamation of how monetary policy works. The "long and variable lags" in particular are a trouble to modern economics. If you know prices are going up tomorrow, you raise prices today. But that's for another day. This model does not behave the way most people think the economy behaves, so if you're going to use it, at least that needs a major asterisk.
Well, we know how to fix this. You can see that sneaking lagged inflation into the Phillips curve is going to be a big part of that.
Christiano Eichenbaum and Evans, 20 years ago, produced a widely cited model that "fixes" this problem. It has a lot of ingredients. Most of all, it assumes that wages and prices are indexed. Firms and workers that don't get tapped by the Calvo fairy to change their price or wage nonetheless raise by observed inflation. This gives a Phillips curve with lagged inflation. Moreover, in preferences, investment, and this Phillips curve, CEE modify the model to put growth rates in place of levels. (More review in a
three part series on new-Keynesian models here.)
The result: If the funds rate goes down (right panel) unexpectedly, inflation goes down just a bit but then turns around and goes up a year later.
Great. But notice that neither Gourio and Pho nor pretty much anyone else builds on this model. We cite it, but don't use it. Instead, 20 more years of NK theorizing studies different extensions of the basic model, that don't solve the central conundrum.
Problem 2: Fed induced explosions
The standard new-Keynesian model says that if the Fed holds interest rates constant, inflation is stable -- will go away on its own -- but indeterminate. There are multiple equilibria. The standard new-Keynesian model thus assumes that the Fed deliberately destabilizes the economy. If inflation comes out more than the Fed wishes, the Fed will lead the economy to hyperinflation or hyper deflation. Under that threat, people jump to the inflation that the Fed wishes to see.
But the Fed does no such thing. Central bankers resolutely state that their job is to stabilize the economy, to bring inflation back from wherever it might go. Despite thousands of papers with new-Keynesian equations written at central banks, if anyone were ever to honestly describe those equations in the introduction, "we assume that the central bank is committed to respond to inflation by hyperinflation or deflation in order to select from multiple equilibria" they would be laughed out of a job.
This has been clear, I think, since 2000 or so. I figured it out by reading Bob King's "
Language and Limits." My "
Determinacy and Identification" in the JPE 2011 was all about this. We've also known at least one way to fix it, as shown: fiscal theory. OK, I'm a broken record on this topic.
Instead, we go on with the same model and its underlying widely counterfactual assumption about policy.
Problem 3: The fit is terrible
A model consists of a set of equations, with the thing you want to determine (say, inflation) on the left, the economic causes described by the model on the right, plus "shocks," which are things your model can't capture. In the explanation part, there are parameters (\(\sigma, \ \beta, \ \kappa, \ \phi\)), that control how much the things on the right affect the things on the left.
The fit of new-Keynesian models is usually terrible. In accounting for economic variables (\(x_t,\) \(\pi_t, \) \(i_t \) here), the error terms (\(\varepsilon\)) are much larger than the model's economic mechanisms (the \(x,\) \(\pi\) on the right hand side). Forecasts -- predicting \(\pi\), \(x\) ahead of time -- is worse. For example, where did inflation come from and why did it go away? Expected inflation hasn't moved much, and the economy just plugged along. Most of the rise and fall of inflation came from inflation shocks.
Related, the fit of the models is about the same amount of terrible for different values of the parameters. That means the parameters are "poorly identified" if identified at all. That means that the mechanisms of the model -- say, how much higher interest rates lower output, and then how much lower output affects inflation -- are weak, and poorly understood.
In part this isn't often noticed because we got out of the habit of evaluating models by fit in the 1980s. Most models are evaluated, as I showed above for CEE by matching select "identified" impulse response functions. But as those response functions also explain small variances of output and inflation, it's possible to match response functions well, yet still fit the data badly, i.e. fit the data only by adding big shocks to every equation.
I don't know of good fixes here. Old fashioned ISLM models had similar problems (See Sims 1980). But it is a fact that we just ignore and go on.
The Phillips curve is a central problem, which has only gotten worse lately. Unemployment was high and declining throughout the 2010s, with stable inflation. Inflation came with high unemployment in 2021. And inflation fell with no high real interest rates, no unemployment, and strong growth in 2022-2023. But what will replace it?
So where are we?
Macro is surprisingly un-cumulative. We start with a textbook model. People find some shortcomings and suggest a fix. But rather than incorporate that fix, the next paper adds a different fix to the same textbook model. One would think we would follow the path on the right. We don't. We follow the path on the left.
This is common in economics. The real business cycle literature followed much the same path. After the King Plosser Rebelo stochastic growth model became the standard, people spent a decade with one extension after another, each well motivated to fix a stylized fact. But by and large the next paper didn't build on the last one, but instead offered a new variation on the KPR model.
Posteriors follow priors according to Bayes' rule, of course. So another way of putting the observation, people seem to put a pretty high prior on the original model, but don't trust the variations at all.
I sin too. In
Fiscal Theory of the Price Level I married fiscal theory with the new-Keynsian IS and Phillips curve, exactly as above, despite problems #1 and #3. Well, it makes a lot of sense to change one ingredient at a time to see how a new theory works. I'm unhappy with the result, but I haven't been able to move on to a new and better textbook model, which is what has occasioned several of these related posts.
Wę need a digestion. Which of the new ingredients are reliable, robust, and belong as part of the new "textbook" model? That's not easy. Reliable and robust is very hard to find, and to persuade people. There are so many to choose from -- CEE's smorgasbord, capital, financial frictions, heterogeneous agents, different expectation formation stories, different pricing frictions, and so on. What's the minimal easy set of these to use?
Part of the trouble lies in how publishing works. It's nearly impossible to publish a paper that removes old ingredients, that digests the model down to a new textbook version. The rewards are to publishing papers that add new ingredients. Even if, like CEE, everyone cites them but doesn't use them.
I've asked many economists why they build on a model with so many known problems, and why they don't include known fixes. (Not just fiscal theory!) The answer is usually, yes, I know about all these problems, but nobody will bother me about them since every other paper makes the same assumptions, and I need to get papers published.
I went on a bit of a tear here as I referee lots of great papers like this one. Every part of the paper is great, except it builds on a model with big flaws we've known about for 30 years. It feels unfair to complain about the underlying model, since the journal has published and will publish a hundred other papers. But at what point can we, collectively, scream "Stop!"
The new-Keynesian model has been the standard model for an astonishing 30 years. None of ISLM, monetarism, rational expectations, or real business cycles lasted that long. It's even more amazing that it is so unchanged in all this time. It is definitely time for a better textbook version of the model! Maybe this is a plea for Woodford, Gali or one of the other NK textbook authors, which much better command of all the variations than I have, to bless us a new textbook model.
Or, perhaps it's time for something totally new.
That's not fiscal theory per se. Fiscal theory is an ingredient, not a model. You can marry it to new-Keynesian models, as I, Leeper, Sims, and others have done. But you can also marry it to old ISLM or anything else you want. Given the above, maybe there isn't an existing modification but a new start. I don't know what that is.
(My comments also have some similar comments about term premiums and how to think about them, but this post is long enough.)
Update:
The former is a VAR with high frequency measurement of the monetary policy shock. And..
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| Source: Miranda-Agrippino and Ricco |
The price level as well as the inflation rate can jump down immediately when the interest rate rises! (I think the graph plots the level of CPI, not growth rate.) That's even stronger than the baseline model in which the price level, being sticky, does not move, but the inflation rate jumps on the interest rate rise.
The latter is a nice theoretical paper. It adds a lot of the CEE assumptions. I overstated a great deal that others have not used these ingredients. They are used in these "medium scale" models, just not in "textbook" models. However, it gets rid of indexed prices and wages with purely forward looking Phillips curves. It adds intermediate goods however. This makes prices changes work through the network of suppliers adding interesting dynamics, which has always struck me as a very important ingredient. And...
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| Source: Phaneuf, Sims ,and Victor |
The main estimate is the dark line. Here you see a model with the conventional response: inflation does not move on impact, and increases some time after the interest rate rise.
So, we can switch places! Estimates can replicate the conventional model, with an instant inflation response. Models can replicate the conventional estimates, with a slow inflation response. This one is much prettier than CEEs.
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Please also post on your thoughts on the term premium covered in your slides. Despite the volumes published in the popular press, I don’t feel enough emphasis is made on your simple but important point that the real term premium may be negative, especially when the risk people want to hedge against is inflation, and the true risk less asset may be long-term TIPS.
ReplyDeleteOf course, as I believe you commented on, that doesn’t mean investors should have locked in negative real rates 2 years ago. The level matters. But certainly the federal government should have!
Hello Cochrane, as always, excellent text! I'd like to elaborate on my impression regarding why people continue to build on NK models: simplicity. The simplest models offer a clear framework for discussing monetary policy and inflation. Introducing new ideas and corrections can be challenging to navigate, especially when they are built upon 20 older fixes that may not be widely known. This complexity makes achieving a cumulative understanding difficult.
ReplyDeleteI also believe it would be beneficial to advocate for Woodford, Gali, and others to produce more updated manuals. These manuals could incorporate model corrections as new benchmarks. I share your perspective on the stabilizing role of monetary policy, rather than providing a source of shocks.
Fiscal theory indeed provides a more reasonable source of shocks. In my view, a significant concern lies in the passive behavior of monetary policy within fiscal models. Historically, monetary policy has successfully controlled long-run inflation, or so I believe. My intuition suggests that both policies should exert influence on long-run values, rather than relying solely on one to determine how the model is closed.
Overall, a captivating read!
The model set down in the last slide (above) can be expected to be well-behaved in the open-loop sense: z(t) = A·ℒ⁻¹·z(t) + B·(1 - ρ·ℒ⁻¹)·zᵉ(t) + C·εᵢ(t) + D·(1 - ρ·ℒ⁻¹)·ϵ(t), where z(t)=(x(t) π(t))ᵀ, zᵉ(t)=(xᵉ(t) πᵉ(t))ᵀ , ϵ(t)=(εₓ(t) εₚᵢ(t))ᵀ are vectors, and A, B, and D are 2x2 matrices of constants while C is a 2x1 column vector (εᵢ(t) is a scalar), and ℒ⁻¹ is the one-period-lag shift operator, i.e., ℒ⁻¹·z(t) = z(t-1).
ReplyDeleteAs you note in the article, the inputs zᵉ(t) = Eₜ{z(t+1)} and εᵢ(t), εₓ(t), εₚᵢ(t) along with the parameters σ, κ, β, ρ, φₓ and φₚᵢ must be available (or, assumed if the model is for pedagogical purposes). It is to the modeller and his/her skill and access to estimates of the subjective expectations of x(t) and π(t) for t = 1, 2, …, n, …, T (where T is the measure of the model’s time horizon) that we must rely on for the insights into the economic problem that the model is constructed to answer.
On the question of the model's ability to predict (or, forecast) the path-wise evolution of an open (or, closed) economy, I have trouble seeing the model as useful for that application given its structural limitations (single representative household agent; single representative firm operating in an imperfect competition economy). From my limited reading of the literature, prompted by this discussion, it is my impression that the central banks in Europe and the Americas, rely on more complex DSGE models of their own devising to model their economies.
On the question of whether the FTPL and the simple NK-DSGE model can be merged, your expressed reservations are not greatly surprising. The absence of government produced private goods from the representative households utility function and the representative firm’s marginal cost function, is perhaps impeding the prospects of a successful merger of the FTPL and the NK-DSGE model. But, this is not a criticism, given the difficulty inherent in broadening the scope of the model and the elaborating on the theory.
As I wandered through the referenced papers and other related articles, it struck me that we have passed through, and may still be in, a period where both the monetary authority and the fiscal authority are both active. I am certain that that is not an original thought, but it is perhaps significant for those who might find research opportunities for ascertaining or confirming the various theories expounded in the macroeconomic literature. Just a thought.
"This paper, like hundreds before it, adds a few ingredients on top of a standard textbook new-Keynesian model. But that textbook model has deep structural problems. There are known ways to fix the problems. Yet we continually build on the standard model, rather than incorporate known ways or find new ways to fix its underlying problems."
ReplyDeleteThis maps so closely to Kuhn's "Structure of Scientific Revolutions" - which describes (among other things) a process of scientific paradigms having more and more flaws discovered until they are replaced. Do you think that there's much of a chance that the field might actually have a paradigm shift?
The political charge behind "Keynesianism" does not give me hope - where political squabbling might block the normal course of scientific discovery.
Excellent post - you're killing with the Monetary Econ/VAR/FTPL/NK posts. Keep them coming. Now a question: you show that carefully specified/estimated VARs can be made consistent with the simple model. Why throw them out? Isn't competition in academia and CBs going to take care of replacing models if they don't work just as Friedman, then Lucas/Sargent took care of the K models pre-68/69? What is different this time? Cheers.
ReplyDeleteThe following paper might be of some interest, in as much as it incorporates capital in the NK-DSGE model framework with the FTPL included. The author works with the continuous-time versions, avoiding the discrete-time approximations.
ReplyDeleteCitation:
Liemen, Max Ole, "The Fiscal Theory of the Price Level in New Keynesian Models with Capital" (September 30, 2022). Available at SSRN: https://ssrn.com/abstract=4234795 or ttp://dx.doi.org/10.2139/ssrn.4234795
Abstract:
"In this paper, I embed the fiscal theory of the price level (FTPL) in a simple continuous-time New Keynesian (NK) model with capital and capital adjustment costs. I offer an elaborate analysis of determinacy, model dynamics, transmission channels and the importance of capital adjustment costs in the continuous-time NK-FTPL framework. My results indicate that FTPL lives up to its name, as the exact specification of fiscal policy is crucial for model implications and predictions. Equipped with the fiscal theory, I evaluate the Great East Japan Earthquake of 2011 and show how to explain and solve the puzzling behavior of expansionary effects of capital destruction at the Zero Lower Bound of the nominal interest rate. I then address and solve the Crowding-In Consumption Puzzle that refers to a discrepancy between the empirically observed and theoretically predicted responses of consumption to government consumption shocks. My model supports consumption dynamics in either direction and at the same time suggest a crowding-in of investment. Finally, FTPL models in the literature usually introduce long-term debt in order to obtain a negative correlation between inflation and the nominal interest rate. I show that the inclusion of capital and its effect on fiscal policy rules is able to induce the negative correlation even under short-term debt."
Keywords: Continuous-time NK models, FTPL, Capital Adjustment Costs
JEL Classification: E31, E12, E22, C61
One difference between the current bout of inflation above "target" and earlier bouts of inflation that exceeded the then-current accepted level of inflation is the greater proportion of imports vs. domestic production in goods (trade-exposed) sectors vs. services sectors which have lower or non-existent exposure to international trade. The PRC is experiencing deflation at the present time and it is very likely this situation which is contributing to the tailing off of inflation in the goods sectors of the economy. But, we should keep in mind the preponderant weight placed (30% +/-) on the index by the residential housing sub-index. Not only is that sub-index protected from international competition, but it is constructed in a manner that ensures a long lag between market cost adjustment and adjustment of the sub-index.
ReplyDeleteThe simple NK-DSGE model is not capable of replicating the PCE index changes (inflation rate), nor is the model representative of the U.S. economy which as a large open economy has many more moving parts that adjust and influence every other moving part in the economy in a manner that the NK model simply cannot mimic. What is more, a real-world economy is populated by rational agents that are able to anticipate, and therefore run in front of the fiscal and monetary authorities, in a way that no econometric model can hope to replicate. The FTPL is increasingly recognized as a useful framework for understanding the role of government as a fiscal agent in the determination of inflationary pressures. An interesting aside -- The Wall Street Journal reported this week on the effects of IMF and World Bank encouragement of EMEs to issue domestic-currency denominated government bonds to avoid the known hazards of foreign-currency denominated bonds to finance government expenditures. The recent rapid growth in domestic currency denominated bonds issued by EMEs has grown geometrically and is now causing dislocation in the international bond markets. The charts accompanying the WSJ article are truly astonishing in the manifest rate of growth of this category of financial security. FTPL has a place there as a solvent and lodestone.
In case John is too modest to mention, "The best books of 2023, as chosen by The Economist" includes "The Fiscal Theory of the Price Level" which the Economist notes is "Not for the faint-hearted, this book is provocative to economists and well-timed for an age of big deficits and high inflation."
ReplyDelete