Thursday, September 19, 2013

The New-Keynesian Liquidity Trap

I just finished a draft of an academic article, "The New-Keynesian Liquidity Trap"  that might be of interest to blog readers, especially those of you who follow the stimulus wars. 

New-Keynesian models produce some stunning predictions of what happens in a "liquidity trap" when interest rates are stuck at zero.  They predict a deep recession. They predict that promises work: "forward guidance," and commitments to keep interest rates low for long periods, with no current action, stimulate the current level of consumption.  Fully-expected future inflation is a good thing. Growth is bad. Deliberate destruction of output, capital, and productivity raise GDP. Throw away the bulldozers, let them use shovels. Or, better, spoons. Hurricanes are good. Government spending, even if financed by current taxation, and even if completely wasted, of the digging ditches and filling them up type, can have huge output multipliers.

Even more puzzling, new-Keynesian models predict that all of this gets worse as prices become more flexible.  Thus, although price stickiness is the central friction keeping the economy from achieving its optimal output, policies that reduce price stickiness would make matters worse.

In short, every law of economics seems to change sign at the zero bound. If gravity itself changed sign and we all started floating away, it would be no less surprising.

And of course, if you read the New York Times, people like me who have any doubts about all this are morons, evil, corrupt, and paid off by some vast right-wing conspiracy to transfer wealth from the poor to the secret conspiracy of hedge fund billionaires.

So I spent some time looking at all this.

It's true, the models do make these predictions. However, there is a crucial step along the way, where they choose one particular equilibrium. There is another equilibirum choice, where all of normal economics works again: no huge recession, no huge deflation, and policies work just as they ought to.

I took a setup from Ivan Werning's really nice 2012 paper: There is a negative "natural rate" from time 0 to time T, and the interest rate is stuck at zero. After that, the natural rate becomes positive again, and everyone expects the actual interest rate to follow. I solved the standard new-Keynesian model in this circumstance -- forward-looking "IS" and Phillips curves.

This is Werning's "standard" equilibrium choice, which shows all the new-Keynesian predictions. The liquidity trap lasts until T=5, shown as the vertical line in the middle of the graph.

The thick red line is inflation. As you see, there is huge deflation during the liquidity trap, though deflation is steadily decreasing.

The dashed blue line is output (deviation from  "potential".) As you see, there is a huge output gap, though strong expected output growth as it comes back to "trend" at the end of the trap. This is why growth is bad -- in these models you always come back to trend, so if you can lower growth, that raises today's level.

The thin red dashed lines marching toward the vertical axis show what happens as you reduce price stickiness. (I only showed inflation, output does the same thing.) As you reduce price stickiness, it all gets worse -- output at any given date falls dramatically. For price stickiness epsilon away from a frictionless market, output falls to zero and inflation to negative infinity.

I verify in the paper that all the claimed policy magic works in this equilibrium.  Even a small amount of "forward guidance" can dramatically raise output, wasted-spending multipliers can be as large as you like, and those policies get more effective as price stickiness gets smaller.

However, for the same interest rate path, there are lots and lots of equilibria.

This graph shows a different equilibrium. I call it the "local-to-frictionless" equilibrium. Again, the thick  red line is inflation. Now, during the liquidity trap, there is steady, mild inflation. The inflation pretty much matches the negative natural rate, so the zero interest rate during the trap (from t=0 to t=T=5) produces a the real interest rate near the natural rate.

As the trap ends, inflation slowly declines and then takes a "glide path" to zero -- i.e. zero deviation from trend, or back to the Fed's long-run target.

In this equilibrium, there is a small increase in potential output, shown in the dashed blue output line. The new-Keynesian Phillips curve says that when inflation today is higher than inflation tomorrow, output is above potential.

As we turn down price stickiness, the thin red lines show that inflation smoothly approaches the totally frictionless case, positive inflation from 0 to T and zero inflation immediately thereafter. I didn't have room to show it, but  output smoothly approaches a flat line as well.

The paper shows that all the magical policies are absent in this equilibrium: The multiplier is always negative, announcements about the far off future do no good, and deliberately making prices sticker doesn't help.

These are not different models. These are not different policies or different expected policies. Interest rates follow exactly the same path in each case, zero from t until T=5, and following the natural rate thereafter. These are different equilibrium choices of the same model. Each choice is completely valid by the rules of new-Keynesian models. I don't here challenge any of the assumptions, any of the model ingredients, any of the rules of the game for computation. Which outcome you choose is completely arbitrary.

The difference between the calamitous equilibrium and the mild local-to-frictionless equilibirum, in this model, is just expectational mulitple equilibria (with an implicit Ricardian regime.) If people expect the inflation glide path, we get the benign equilibrium. If they expect inflation to be zero the minute the trap ends, we get the disaster.

The paper goes on to compute all the magical policies, consider Taylor rules, and every other objection I can think of. So far.

What do I make of all this? Well obviously, maybe one isn't so dumb, evil, or corrupt for having doubts about changing the sign of all economic principles when interest rates hit zero.

Let me just quote from the conclusion
At a minimum, this analysis shows that equilibrium selection, rather than just interest rate policy, is vitally important for understanding these models' predictions for a liquidity trap and the effectiveness of stimulative policies. In usual interpretations of new-Keynesian model results, authors feel that interest rate policy is central, and equilibrium-selection policy by the Fed, or equilibrium-selection criteria, are details relegated to technical footnotes (as in Werning 2012), game-theoretic foundations, or philosophical debates, which can all safely be ignored in applied research. These results deny that interpretation.

....there really are multiple equilibria and choosing one vs. another is simply an arbitrary choice. Since there is an equilibrium with no depression and deflation, and no magical policy predictions, one cannot say that the new-Keynesian model makes a definite prediction of depression and policy impact.

I have not advocated a specific alternative equilibrium selection criterion. Obviously, the local-to-frictionless equilibrium has some points to commend it: It is bounded in both directions, it produces normal policy predictions, it has a smooth limit as price stickiness is reduced, and it does not presume an enormous fiscal support for deflation. But this is not yet economic proof that it is the "right" equilibrium choice.

We might consider which equilibrium choice is more consistent with the data. The US economy 2009-2013 features steady but slow growth, a level of output stuck about 6-7% below the previous trendline and the CBO's assessment of "potential," a stagnant employment-population ratio, and steady positive 2-2.5% inflation.

The local-to-frictionless equilibrium as shown in my second Figure can produce this stagnant outcome, but only if one thinks that current output is about equal to potential, i.e. that the problem is "supply" rather than "demand," and that the CBO and other calculations of "potential" or non-inflationary output and employment are optimistic, as they were in the 1970s, and do not reflect new structural impediments to output.

The standard equilibrium choice as shown in my first Figure cannot produce stagnation. It counterfactually predicts deflation, and it counterfactually predicts strong growth. One would have imagine a steady stream of unexpected negative shocks -- that each year, the expected duration of the negative natural rate increases unexpectedly by one more year -- to rescue the model. But five tails in a row is pretty unlikely.

The problem in generating stagnation is central to the new-Keynesian model. The "IS" curve and the assumption that we return to trend means that we can only have a low level of output and consumption if we expect strong growth. The Phillips curve says that to have a large output gap, we must have inflation today much below expected inflation tomorrow and thus growing inflation (or declining deflation). Thus if we are to return to a low-inflation steady state, we must experience sharp deflation today.  If one wants a model with stagnation resulting from perpetual lack of "demand," this model isn't it. Static old-Keynesian models produce slumps, but dynamic intertemporal new-Keynesian models do not.
I close with a few kinds words for the new-Keynesian model. This paper is really an argument to save the core of the new-Keynesian model -- proper, forward-looking intertemporal behavior in its IS and price-setting equations -- rather than to attack it. Inaccurate predictions for data (deflation, depression, strong growth), crazy-sounding policy predictions, a paradoxical limit as price stickiness declines, and explosive off-equilibrium expectations, are not essential results of the model's core ingredients.  A model with the core ingredients can give a very conventional view of the world, if one only picks the local-to-frictionless equilibrium. That model will build neatly on a stochastic growth model, represented here in part by the forward-looking "IS" equation and changes in "potential." Its price stickiness will modify dynamics in small but sensible ways and allow a description of the effects of monetary policy. This was the initial vision for new-Keynesian models, and it remains true.

Really, the fault is not in the core of the new-Keynesian model. The fault is in its application, which failed to take seriously the fundamental problem of nominal indeterminacy.... Interest rate targets, even those that vary with output and inflation, or money supply control with interest-elastic demand, simply do not determine the price level or inflation.  In a model with price stickiness, nominal indeterminacy spills over in to real indeterminacy.

In that context, this paper shows there is an equilibrium choice that leads to sensible results. Alas, those sensible results are non-intoxicating. In that equilibrium, our present (2013) economic troubles cannot be chalked up to one big simple story, a "negative natural rate" (whatever that means) facing a lower bound on short term nominal rates; and our economic troubles cannot be solved by promises, or a sign reversal of all the dismal parts of our dismal science. Technical regress, wasted government spending, and deliberate capital destruction do not work. Growth is good, not bad. That outcome is bad news for those who found magical policies an intoxicating possibility, but good news for a realistic and sober macroeconomics.
If all this just whets your appetite, I hope you will read the paper. Similarly, if you're brimming with objections, take a look at my attempts to anticipate most objections -- what about the Taylor rule, etc. -- in the paper.

(This follows an earlier paper in the JPE (online appendix) looking deeply at multiple equilibria in new-Keynesian models. In that paper, I questioned whether ruling out multiple explosive equilibria made sense. In this paper, I accept that part of the rules of the game, and think about the mulitple non-explosive equilibria.)


  1. Thanks Prof. Cochrane. Good to know that the odd policy implication of New Keynesian model is purely due to equilibrium selection.

    BTW, I like the deterministic continuous formulation of NK model. Has people developed a stochastic one?

  2. It really bothers me when people consider out current economic efforts as Keynesian.

    Keynes' theories were based on "in an otherwise sound economy". We DO NOT have an otherwise sound economy.

    Applying Keynes is like trying to adjust the air/fuel mix on an engine that has thrown a rod out the bottom of the block.

    Keynes was a big proponent of balanced trade, both internationally and domestically. He knew that it would be impossible to persist trade imbalances indefinitely via unsustainable debt growth.

    But, that is exactly what we are trying to do, persist both domestic and international trade imbalances via unsustainable debt growth.

    What is Keynesian about attempting to persist imbalances forever via continuous, unsustainable debt growth?

    1. So much nonsense there I don't know where to start. But I'll just take your "rod" point. Your're assuming there is something wrong with the economy other than deficient demand (which is what Keynsian stimulus provides). But you don't tell us what. I therefor assume you don't know.

    2. Ralph,

      Back in 1978, Congress passed a law called the Humphrey Hawkins Act.


      That Act set specific economic goals for the U. S. Among those goals were:

      1. Full employment
      2. Growth in production
      3. Price stability
      4. Balance of trade and budget

      "You're assuming there is something wrong with the economy other than deficient demand..."

      I think Anonymous was pretty clear what is wrong with the economy - Hint: See lines #2 and #4.

    3. "Your're assuming there is something wrong with the economy other than deficient demand (which is what Keynsian stimulus provides). But you don't tell us what. I therefor assume you don't know."

      Limits on post size imposed by this board forced me to split my post into two.

      In the 1960s and 1970s we embraced a flatter income tax code and we embraced free international trade. This created large imbalances in trade, bot domestically and internationally.

      To fund those imbalances, we have relied on unsustainable debt growth.

      Check the Federal Reserve Z.1, table D3 and look at the 30 year history of total debt. Adjust it for inflation and population. You will see that total debt has been increasing at two-and-a-half times the sustainable rate.

      We love seeing the rich get richer, BUT then are unhappy with the debt that creates.

      Sorry, but this nation needs to wake up and accept that money is borrowed into existence. A few people can't be accumulating mass quantities of money, unless the majority is also accumulating mass quantities of debt.

      It is illogical, or plain old ignorant, to jump for joy at the mass amounts of money, then be unhappy about the offsetting debt.

  3. In the 1960s and 1970s we adopted free international trade and a way too flat tax code, creating the imbalances in the economy.

    By the 1980s, with most of household savings gone, we turned to debt to create the new money that was needed to fund the imbalances we created.

    Look at the Federal Reserve Z.1, table D3. $4T total debt to $40T total debt in 30 years. Even adjusted for population and inflation, we see that debt has exploded at an unsustainable pace.

    $4T * 309M/227M * 230/78 = $16T

    So, sustainable debt growth based on population and inflation would have been 4x from $4T to $16T, but we actually increase total debt 10x, from $4T to $40T.

    Put simply, households are tapped out and continue to try to reduce debt. Businesses have returned to adding debt at an unsustainable pace (from 1Q2012 to 1Q2013, business debt increased 7.5% while their revenues increased less than 2%), but that is still only half the new debt needed to fund our massive imbalances.

    The government has been adding the bulk of the $1.5T a year we need, but patients on that is wearing thin.

    Rather than looking for new ways to shove $1.5T a year new debt into the economy through either monetary policy (low interest rates and loose lending conditions) or through fiscal policy (taxing $2T and spending $3.5T), isn't long past time to attack and reverse the massive imbalance that drain 10% of GDP worth of money from active circulation every year?

    What is Keynesian about attempting to persist trade imbalances through unsustainable debt growth?

    Only by attacking and reversing the imbalances, international AND domestic, can we make the economy function without the unsustainable debt growth.

    Everything else is just rearranging deck chairs on the Titanic.

    1. Anonymous,

      The easiest way to reduce debt is to do a debt for equity swap. John's paper is interesting in its appraisal of New Keynesian economics but it misses an equally valid point:

      New Keynesian models are three good (money, debt, other goods). We live in a four good world (money, debt, equity, other goods).

    2. A top tax rate of 70% is "way too flat?"

    3. Anonymous,

      70% tax rates won't guarantee a reduction in federal debt. At any tax rate (30%, 70%, 99%, or anything in between) the government can always choose to spend more than it takes in revenue.

      Selling equity would guarantee a reduction in federal debt.

    4. "The easiest way to reduce debt is to do a debt for equity swap."

      Government prints bonds, sells them to the Fed for "money", then spends the money. The money quickly flows through the economy into the hands of the top 1%. The top 1% then buys government bonds with the money, or corporate bonds, or deposits the money into money market accounts or bank accounts.

      This allows new money to be borrowed into existence again, spent into the economy, and then end up in the hands of the 1% again....

      This is how we have increased total debt from $4T to $40T over the last 40 years as GDP increased from $3T to $15T. That is a doubling of debt/gdp ratio.

      So, what is your suggestion to the imbalance that drains money from active circulation into the hands of the 1%? Sell them some government land?

      We sell them $10T in land, use the money to buy back bonds, and we have paid down the national debt.... now what?

      We still have the same imbalances, if not wider as the 1% can now profit off the assets it just purchased. We still have to borrow money into existence to replace the money being accumulated at the top.

    5. Anonymous,

      "So, what is your suggestion to the imbalance that drains money from active circulation into the hands of the 1%? Sell them some government land?"

      Do you honestly believe that guys like Warren Buffett and Bill Gates (the top 1%) have all of their money tied up in U. S. government bonds?

      A government bond is a claim on future tax revenue. More than that it is a guaranteed claim - a government bond holder always gets his / her money back plus interest no matter the economic circumstances.

      The present non-discounted value of all the tax revenue the federal government is ever going to collect is infinite.

      Government equity is a non-guaranteed claim on the same future tax revenue. A government equity holder must have a tax liability at some point in the future to realize the return on investment. A government bond holder has to do nothing but sit back and collect the interest payments.

    6. Anonymous,

      "Only by attacking and reversing the imbalances, international AND domestic, can we make the economy function without the unsustainable debt growth."

      Like I said, the easiest way to reduce federal debt would be a debt for equity swap. Government equity is sold domestically, foreign creditors are paid off with proceeds. International balance is restored.

      Restoring domestic imbalances are harder because of differences in philosophy on the role of government - equalization of opportunity versus equalization of outcome.

  4. "We might consider which equilibrium choice is more consistent with the data. The US economy 2009-2013 features steady but slow growth, a level of output stuck about 6-7% below the previous trendline and the CBO's assessment of "potential," a stagnant employment-population ratio, and steady positive 2-2.5% inflation. "

    The TV show, in an early episode, featured a joke about a chicken rancher asking a physicist to help improve the efficiency of his operations. They physicist goes off and works on the problem for awhile then comes back to the rancher and says that he's come up with a model that will help, but it only works for spherical chickens in a vacuum.

    Does the liquidity trap model of new-Keynesian economics not also require a vacuum?

    Does your "Let's look at conditions" statement exclude the effects of $3.5T in fiscal stimulus over those same years?

    More importantly, does the liquidity trap model account for a situation where, despite 0% interest rates, there is little to no net new borrowing, because businesses and households are already tapped out and unable or unwilling to take on more debt?

    Total private sector debt at the start of 2009: $24.7T. Inflation adjusted 2009 to 2012 (cpi * 230/211) that is $26.9T.

    Total private sector debt at the end of 2012: $25.5T.

    We're limited in our ability to evaluate things such as the liquidity trap paradigm, by the minor issue that an economy does not exist in a vacuum, unaffected by all else that is occurring in the economy.

    It could be argued that the flaw in the liquidity trap model is that it does not account for conditions that created the liquidity trap (entities unable or unwilling to borrow).

    1. yes Krugman Eggertson 2011 does all the things you are talking about. Krugman puts in credit constrained heterogeneous agents, and then shows it's just business as usual as far as the new-Keynesian literature (like in Eggertson's or Woodford's older papers).

      Here is a link to it:

      I think it was Shakespeare who once said: "there are more things in mathematical modelling than are dreamed of in your philosophy."


    2. Re: "exclude the effects of $3.5T in fiscal stimulus over those same years?"

      Lol, that fiscal stimulus never happened. Most of that was partial Bush tax cut extensions, nobody had ever thought that was going away completely. State and local austerity were actually much larger than the original stimulus...

  5. Thanks a lot for this post John!

    New Keynesian models are often log-linearised around a steady state. This paper by Braun, Korber and Waki shows that the log linearisation itself removes some of the equilibria that you mention. Hence this might lead to the (possibly erroneous) selection of the first type of equilibrium that you discuss (their paper relates to fiscal policy but I suspect that the results carry over to the "puzzles" you mention).

    In response I believe that Christiano argues that you should focus on "learnable" equilibria (but I can't find the reference). This might be a way of refining the equilibria you discuss here?

  6. Haven't you just more or less proven that the market monetarist's theory exists even in nk models? If you had (credibly) targeted NGDP you would have been in the equilibrium of 5% inflation and the recession would have been much milder?

    Or have I misunderstood?

  7. ...people like me who have any doubts about all this are morons, evil, corrupt, and paid off by some vast right-wing conspiracy ...

    OK, Doc, so what do I owe you?

  8. Well just to be Satin's Lawyer, what Prof. Cochrain has shown is the Neo-Keynesian model in question has multiple equilibria, not that the model is wrong. So it's quite possible that the equilibrium that the advocates of the N-K model hope for (namely, the economy getting better by the government dropping money out of a helicopter) in fact does transpire. And the N-K advocates would argue the only way to find out is to try it! :-P

  9. Nick Rowe has been very interesting on New Keynesianism recently:
    He also seems to be trying to "save it from itself", although he's more irritated that they haven't already noticed how wrong they went by leaving money out of the model and talking about interest rates instead.

    1. Wonks Anonymous,

      The New Keynesian model concentrates on money flows through the interest rate mechanism. It doesn't address money originating as debt and balance sheets.

      To do a full macro model you really need both. I have not seen an attempt by Nick (or anyone else) to put money or debt levels back into the New Keynesian model.

  10. Excellent analysis! However, most of the models in modern economic theory, including the new Keynesian models do not consider the biomedical progress rates leading to the unprecedented life extension and the shift in the dependency ratio and will be useless going forward.

  11. Dr. Cochrane,

    If you're right, how do you explain what happened between 1939 - 1946? The Federal Government spent a lot of taxed/borrowed/printed money to produce very little goods of value (oil pipelines, radar, airports might be the entire list), yet on one side of the period, you had the Depression, on the other you had the post-War prosperity. If your approach to economics is right (here, and generally), then shouldn't all that debt and wasted spending have left the country in a worse state then prior to the war?

    1. That would be a great example for Bob Murphy on the insufficiency of crude empiricism, since anti-Keynesians love to point out how the economy boomed after government spending/deficits were reduced, even as Paul Samuelson predicted disaster. But really I think your question is a poor one. Everyone agrees that civilian consumption was very low during the war, but Keynesians would emphasize that we did actually have a lot of useful output: the military materiel which won the war.

      "shouldn't all that debt and wasted spending have left the country in a worse state then prior to the war?"
      Not if the normal trend is growth, under anti-Keynesian theory it would only leave us worse off compared to the counter-factual in which we didn't do that.

  12. Dr Cochrane

    First, when you were describing the wild predictions of New Keynesian Liquidity Traps, you forgot to mention that

    a) People like Paul Krugman, who don't use this exact framework but their variation of it, got almost everything right about the recession, while you got everything wrong

    b) You seem to be interested only in the theoretical "models", and that would indeed be appropriate if this was a journal discussion. This isn't. This should have been you answering why people like Krugman have been right (i.e. what is right in their models), but this isn't that because it seems you value your ego too highly, and will not admit that had your policy prescriptions been followed, the recession would have been far worse.

    Warm regards.

    1. I'm sorry but what exactly, did Krugman get right?

      he predicted a deflationary spiral, which I'm not sure if you've noticed...but it didn't cant argue with that, Krugman admits it in multiple places...

      he predicted we would be poorer because of things like payroll taxcuts...doesn't seem to be true...

      please help me out here...

  13. Very cute. I would never have the patience to take IS curves so seriously. I could never get past the New Keynesian refrain that "savings are too high". But don't savings equal investment? Isn't investment closely related to growth? Years on I still haven't read or heard a sensible New Keynesian response to those basic objections.

  14. Professor Cochrane --

    Is the nominal indeterminacy you mention a result of interest rate targeting? If not, what is the nominal indeterminacy caused by?


    -- UChicago 2015 undergrad

    1. "Nominal indeterminacy" means that if the Fed sets the interest rate to 5%, the price level can be 100 200 or 500. Furthermore, if the real rate is 3% the Fed sets expected inflation to 2%, but actual inflation can come out to anything. Heads, 4%, tails 0%. Thus, just setting an interest rate does not determine the price level, or the actual inflation rate. MV=PY can determine P..If V is constant. If V is a function of interest rates, then even MV=PY leads to mulitple P paths. That's the short version...

    2. V is a function of a lot of factors (nominal interest rates being one of them). Credit demand, liquidity preference, and productivity are other factors that determine V.

  15. "Thus if we are to return to a low-inflation steady state, we must experience sharp deflation today"--Cochrane.

    Ouch. If the road to prosperity is through deflation, I think we will never get there.

    We have this problem in the USA. Banks lend heavily on real estate, both commercial and residential. Borrowers are very leveraged. Deflation, especially sharp deflation in real estate, will crush the banks (and the borrowers).

    Deflation and crushing banks will not get you to economic recovery.

    These are what used to be called "institutional imperfections" in economic models.

    Can we devise another model, one that shows robust monetary growth leading to increased output and then mild inflation?

    1. Benjamin,

      "Deflation, especially sharp deflation in real estate, will crush the banks (and the borrowers)."

      Unless some other asset (government equity) or flow (trade surplus) rebuilds balance sheets.

  16. "You may object that nobody has written any op-eds or policy essays castigating the Fed for its equilibrium-selection policies."

    I think the market monetarist critique of the Fed failing to "target the forecast" fits this, that is the Fed has chosen to implement policy which will fail to hit the target even according to its own forecasts.

  17. Hey John, thanks for your post.

    I'm a bit skeptical of two things. First, you wrote that in standard New-Keynesian models, "Growth is bad". This wasn't something I'd heard New-Keynesians assert, and clearly doesn't apply to Krugman-Eggertson, as more growth implies improving balance sheets.

    Secondly, I'm a bit skeptical of this "negative multiplier". What you are saying is that if an agent who has no liquidity constraints begins spending money like mad in a liquidity trap, total output of the economy will fall. I'm curious what aspect of your model gives rise to this result. As you know, even Barro's standard Ricardian Equivalence implies a multiplier greater than zero, and that's with no sticky prices and fully rational, optimizing agents with perfect knowledge and foresight of future economic conditions and government spending.

    Since you are a good writer, you should be able to spell out what mechanism makes this happen.

    1. Dear Anonymous:

      Thanks so much for making this comment. You caused me to go back and look and find a small sign error, which cleans up the multiplier graph. I posted a new version of the paper that fixes this bug.

      Now, to your question. Look at my IS and Phillips curves, with the g in it. g only enters in the Phillips curve, with (x_t + g_t). So in a steady state, raising g by one lowers x by one, leaving everything else constant.

      I computed d x / d g, the "private GDP" multiplier. and called that a negative one multiplier; the more conventional calculation is d (x+g)/dg and you'd call that a zero multiplier.

      Dynamics change the picture, but not much when dynamics are limited as they are in the local to frictionless equilibrium

      I hope this helps

    2. I reread your paper again but am still thinking about your multiplier. Could you please clarify two points? i) Why dx/dg - the "private" multiplier - instead of dY/dg or dY/dG, as in Woodford or Christiano et al? ii) Why need to "be evaluated at g=0"?

    3. Because it's easier and simpler. The point here is not a quantitative evaluation of policy, it's to show how calculations are sensitive to equilibrium choice. Also when g represents capital destruction or other phillips curve shifters, it doesn't add in. See new version just uploaded Aug 14 2017 BTW.

    4. Thanks a lot for your explanation! I misunderstood. Also, good to know that this paper is finally forthcoming in JME.

  18. Dear Commenters:

    I have deleted quite a few comments lately along the lines of "Krugman says you forecast inflation and it didn't happen so you must not know anything." Some are even polite enough to pass the usual no insults test.

    First, this is simply a lie. (With Krugman, there's no point in trying to use polite language. That's what it is. Lie, slander, calumny, deliberate falsehood, untruth, and all its cousins.) The lie is made worse by the fact he never bothers to actually read what people he is slandering have to say. I never forecast anything -- I know how hard it is to forecast.

    I have said, and continue to do, that our large and as yet unresolved debt puts us at risk -- small, but not negligible -- of a run on the dollar sort of event, which would imply inflation. To say that, is like saying a building lies on an earthquake fault, one of the chambers you're playing Russian roulette with is loaded, or in 2003 that subprime mortages and greek government bonds look a bit risky relative to their prices. That you go several years without an earthquake or that the gun goes click click does not deny the analysis. I have written quite explicitly that it is a danger that might well never happen, and in fact since the US has underlying great strength and our economic problems are self-inflicted, we should be able to grow quickly and pay back the debt. This is risk management, not a forecast.

    But even that is not the point. We don't test economic theories by listening to the "predictions" of soothsayers, any more than you test meteorological theoories by whether their authors can tell you if it will rain next week. We test economic theories with careful comparison to data, and that's a lot harder than having your intern dredge up one quote out of context and say "see, he predicted inflation."

    Soo... Comments about who predicted what when will still get deleted, along with the usual ban on insults and overly partisan commentary. Try to make some sense, please.

    John Cochrane

    1. So there's a grey area between actually predicting something and just routinely and dramatically (earthquake, bullet to the head, etc.) talking it up. I think you may have trouble convincing open-minded readers you've been treated awfully unjustly.

    2. Lets go back to '09. You're insisting (here, so that nothing is taken out of context: ) that the big danger is inflation, now that we've avoided deflation. The danger is Argentina, not 1932. The danger is severe inflation, not a crushing slump with no growth.

      You're completely correct you didn't say this WILL happen, and the distinction between probability forecasts outright predictions is a crucial one. But the response at the time by the New Keynesians was that you were seeing a danger where there was none. You said 'I would say it's a greater danger than most of the other people have said'. They said the opposite: the risk of high inflation was lower than usual, because factors like slumping demand and a flight to safety by investors meant there was very little inflation pressure. And the financial markets agreed with them.

      Now, your risk assessment could have been correct; the US may have just been fortunate to avoid the high-inflation risk. But we've had a whole host of countries go through this crisis, and none of them experienced the sort of inflation you talked about. Add them to all the previous countries that have experienced ZLB-scale slumps (mostly GD-era), and that's a lot of data points. Your assessment of risk has a lot less immunity than you make out.

      And you seem to think they are ignoring your objection. Here's DeLong, Smith, and, yes, Krugman responding last year when you made the risk-not-prediction objection:

      Last year, you made the analogy, 'To Mr. Krugman, we are sailing in smooth waters, nobody has seen an iceberg yet, so it must be safe, so stoke the boilers. All I am saying is, there are icebergs out there in the middle of the night.' You didn't realize that we're actually at the equator.

    3. Touché. Seeing he's not been as ill-treated as he supposed, we may hope the grumpy one, who, bravely acknowledging his ignorance, humbly tutored himself in New Keynesian theory, will now show us the exercise wasn't merely to legitimize caricaturing his opponents.

  19. What is the appropriate size and form of a policy response to a low probability inflation risk?

  20. Forecasting is hard, I agree. But at some point, don't you have to forecast conditional on salient features of current economic climate? Otherwise, how do we evaluate real life out of sample performance of economic models?

  21. Let's do some Bayesian model averaging. There is no need to decide which equilibrium is at play: we should give each one a probability.

  22. I think there's a typo in the equation at the bottom of page 3 in your paper. Shouldn't it read "inflation = *minus* r"?

    I'm still working through your paper. I think I get what you are saying. But I think you have missed (unless I haven't got there yet) a second indeterminacy in NK models. Even if we ignore the zero lower bound, and assume the central bank always sets a real interest rate equal to the natural rate, the *level* of the output gap is indeterminate. Because the Euler IS only determines the *growth rate* of consumption as a function of the real interest rate. New Keynesian modellers just pick the equilibrium path which converges to zero output gap asymptotically. (I've been blogging about this )

  23. Another sorta typo in your paper, bottom of page 6. You say "This is a standard and
    much-criticized feature of the usual new-Keynesian Phillips curve (2), that output rises when
    inflation is declining, i.e. when inflation today is higher than expected future inflation."

    I think you mean that output *is high* when inflation is declining.

    Picky, I know, but all this stuff depends on the distinction between levels and rates of change.

  24. Dr. Cochrane,

    In section 5 of the paper, you study a simple Taylor rule in which the policymaker adjusts the interest rate in response to contemporaneous inflation. You note: "The Taylor rule policy often includes output responses, lagged responses and other complexities. That generality is inessential to the current point."

    Have you also considered forward-looking Taylor-like rules in which the Fed responds to expected inflation? I ask because part of your argument later in the paper is based on the intuition that the Taylor principle implies a commitment to out-of-equilibrium policy actions that are not credible. Evans and Honkapohja (2003, RES) showed that in a simple New Keynesian model, a forward-looking Taylor rule satisfies the policymaker's optimality condition for discretionary policy after all histories and for all possible values of private sector expectations, and also achieves equilibrium determinacy and E-stability. Would that result have any bearing on your analysis?


  25. I've tried to explain what you are saying simply and clearly, and discussed possible responses. Not sure if I have succeeded.

  26. Why was Nero fiddling while Rome was burning? One, he loved his fiddle. Two, he knew he was irrelevant to the proceedings.

    There, my friends, is modern macro in a nutshell.

    Or maybe he was just a very foresighted neo-Keynesian and wanted to cause some new growth opportunities?

  27. "In short, every law of economics seems to change sign at the zero bound. If gravity itself changed sign and we all started floating away, it would be no less surprising. "

    This statement is very representative of the bad abstractions that go on throughout cochrane's work.
    Economic data is not produced by scientific rules, economic data is produced by humans, this means literal interpretations of what happens at limits, is not reasonable, as it might be in physics or mathematics.


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