Managing A Liquidity Trap
I've been catching upward on my new-Keynesian economic science together with constitute a piddling precious rock yesteryear Ivan Werning, "Managing a liquidity trap"
The policy number is this: we're inwards a recession. Interest rates are zero, together with can't cash inwards one's chips lower. The Fed is desperately trying to goose the economy. Lots of people (most of the recent Jackson Hole Fed conclave) are advising "open-mouth operations," and "managing expectations," that the key to electrical flow prosperity is for the Fed to brand statements near what it volition do inwards the future; together with these statements on their own, alongside no concrete action, volition "increase demand" together with lower today's unemployment. The Fed has been convinced, alongside to a greater extent than together with to a greater extent than "forward guidance" equally business office of its strategy. For example, the latest FOMC statement made history yesteryear promising cipher involvement rates equally long equally unemployment stays inwards a higher house half dozen together with a one-half portion together with inflation below 2 together with a half.
Does whatever of this brand whatever sense?
There are piles of complicated new-Keynesian models on this topic. Ivan's newspaper gets right to the core, giving a real uncomplicated model that explains their logic. The version on p. xx is the simplest together with clearest of all. We alone genuinely request i equation
$$\frac{dc(t)}{dt} = \sigma^{-1} r(t) $$
(Hang inwards there, non-economists, y'all don't genuinely fifty-fifty request the equations; everything is inwards words too. Also, this is an experiment alongside Latex macros inwards blogger. You should regard a prissy equation above. Let me know if it doesn't operate inwards your browser.) When existent involvement rates are high, people guide to salve more, so consumption is lower today together with higher inwards the future. Thus, high consumption growth goes alongside high involvement rates, together with vice versa.
Now, forget near capital, so consumption equals output. Assume the Fed tin ready the existent involvement charge per unit of measurement to whatever it wants. Also, think of everything equally deviations from "potential output" or "trend." The degree of consumption becomes the "output gap." Thus, yesteryear controlling involvement rates, the Fed controls the growth rate of consumption, output, together with the output gap.
Now, here's the key. If the Fed raises the involvement rate, together with thence the growth rate of consumption, the level of consumption (now the output gap) falls. New-Keynesian models (correctly) anchor the degree inwards the future; consumption (output) sooner or after must live equal to "potential." This is the key new-Keynesian machinery yesteryear which higher involvement rates lower output, together with quite dissimilar from the static stories y'all may recall from old-Keynesian models. (I telephone telephone this "IS" bend the "interntemporal substitution" curve.)
You mightiness stimulate got thought that raising the growth charge per unit of measurement of consumption would only live a practiced thing; implicitly anchoring the degree of consumption at terminal year's value. That would live a mistake. The alone way to enhance the growth charge per unit of measurement of consumption side yesteryear side yr is for the degree this yr to drop. (In this economic scheme without capital.) Then nosotros grow faster yesteryear catching up.
Furthermore, if people aspect high involvement rates for many years, at that spot volition live many years of strong consumption growth, together with today's degree volition live real depressed. In equations, nosotros uncovering the degree of consumption (output gap) by integrating all its hereafter growth rates (bottom of p. 19)
$$x(t) = \sigma^{-1} \int_t^\infty r(t) dt$$
In sum, the degree of today's consumption, output, together with output gap all depend on today's involvement charge per unit of measurement and people's expectations of the path of hereafter involvement rates.
You tin showtime to regard how managing expectations of hereafter involvement rates mightiness live an attractive idea. If nosotros can't do anything near today's involvement rates, lowering expected hereafter rates volition stimulate got the same number on today's consumption.
In this paper's model, equally most new-Keynesian thinking, our electrical flow job is that the "natural rate" of interest, required to cash inwards one's chips on us at potential output, is sharply negative. (This is all exogenous.) With "only" 2% inflation together with nominal involvement rates stuck at zero, the Fed cannot deliver anything less than a negative 2% existent charge per unit of measurement of interest. If the "natural rate" is something similar negative 5%, together with then nosotros are stuck at a 3% "too high" existent involvement rate. Taking differences to "trend" or "potential," our province of affairs is equivalent to a too-high existent involvement charge per unit of measurement that the Fed can't do anything about.
The enterprise occupation inwards Figure three of the paper, reproduced above, shows this situation. The lines plot differences relative to potential output, or "output gaps," so beingness on the horizontal axis is the best outcome. We stimulate got a "negative natural rate" until fourth dimension T, when the earth returns to normal, the Fed regains control, together with consumption together with output revert to the tendency line. You regard that the too-high growth of consumption betwixt straightaway together with T, together with the too-low degree of consumption (output gap) now.
Well, says Ivan, why non push clit the whole occupation up? Suppose the Fed could hope straightaway that, at fourth dimension T, it volition ready involvement rates too low, from the betoken of stance of that time? This volition encourage people to eat at fourth dimension T rather than inwards periods after that, i.e. it volition engineer the negatively sloped dashed occupation from T onwards. If people knew at that spot was going to live this nail at T, consumption today would live less depressed. (Again, the way the graph plant is that y'all operate from right to left, together with the Fed controls the output together with consumption growth rates from right to left inwards guild to make today's level.)
More formally, Ivan assumes that the Fed wants to minimize the squared deviations from potential. Influenza A virus subtype H5N1 policy similar the dashed i produces smaller sum-of-squared output deviations than the enterprise occupation we're facing now.
This pretty piddling graph illustrates lots of policy advice you're hearing from within together with exterior the Fed. According to this view, the key affair the Fed tin do to enhance "demand" today is to hope that it volition cash inwards one's chips on involvement rates depression longer than it usually would do -- inwards the menstruum after T -- technology scientific discipline a bout of output that is a piddling likewise high (in a bigger model, inflationary).
But the graph, together with the paper, illustrate the primal problem: At fourth dimension T, the Fed volition non desire to cash inwards one's chips on rates low. "Too much" consumption agency inflation, together with inwards this model likewise much output (beyond "potential") is only equally bad equally likewise little. When fourth dimension T hits, together with the "natural rate" returns to normal, the optimal affair for the Fed to do looking forrad is to ready the involvement charge per unit of measurement equal to the natural rate, together with follow the enterprise light-green line. In turn, people today know this, which is why their expectation for consumption at fourth dimension T is at the enterprise occupation level, which is why consumption today is depressed.
Chicago Fed Chair Charlie Evans describes the needed policy equally "Odyssean." As Odysseus realized inwards having himself tied to the mast, the powerfulness to commit yourself today that y'all volition do things tomorrow, things that y'all volition non guide tomorrow if y'all volition stimulate got the choice, tin improve overall performance. This is a deep regulation of practiced policy, together with its violation describes many of our electrical flow problems. If the regime refuses to commit today that it volition non bail people out inwards the future, together with then people volition accept risky actions, and the bailout volition recur.
And this is the primal job for this piddling parable inwards describing the Fed's actions. Let's read the Fed's Odyssean revelation (the FOMC statement) a piddling to a greater extent than carefully, alongside the model inwards mind:
The job is deep. How tin the Fed stimulate got the powerfulness to accept the "discretionary" activity today, inwards reply to the electrical flow situation, but that activity is somehow to commit itself to doing something inwards the hereafter that it real much volition non desire to do when the fourth dimension comes -- that it has so far explicitly together with loudly promised that it volition non do, together with has built upward xxx years of reputation against doing -- undershoot together with drive inflation? Why can't the Fed 2015 convene some other Jackson Hole conference, guide out Charlie Plosser together with Jeff Lacker's friends to say "we're heading to a repetition of the 1970s, it's fourth dimension to larn new-Monetarists together with hope that we'll live looking at monetary aggregates non unemployment rates?" It's so much hot air, together with people know it.
True commitment requires legal, institutional, or constitutional restraints. It at to the lowest degree needs linguistic communication similar "the Committee commits to cash inwards one's chips on a highly accomodative stance of monetary policy long after it is appropriate" or improve an institutional commitment "and to that terminate no farther FOMC meetings volition live scheduled until inflation hits 3%." But no establishment gives upward its discretion easily. (To live clear, I think this would all live a terrible idea; to a greater extent than below. I'm explaining the primal commitment/discretion job highlighted yesteryear Ivan's model.)
The paper, of course of teaching achieves the same affair inwards much greater generality, piece also presenting this gorgeously transparent example. This instance makes it crystal clear that the argue for "forward guidance" inwards new-Keynesian models is non to enhance inflation together with thus lower existent involvement rates -- it plant hither alongside constant inflation. "The argue for asset the involvement charge per unit of measurement at cipher is non to promote inflation [and thence negative existent rates] equally is commonly assumed."..."The existent argue for committing to cipher involvement rates is to create the expectations of a hereafter consumption boom" (p. 4)
Cautioning implicitly against the Fed's "twist" policies aimed at lowering long-term involvement rates "I demo that optimal policy... genuinely raises long run involvement rates.... This cautions against uncomplicated assessments of monetary policy centered around the lowering of yields at long maturities." In the total model, promising the inflationary nail raises long term rates. I.e. precisely the reverse of the Fed's "quantitative easing" operations.
To live clear, I don't purchase whatever of this: that our electrical flow problems would all live solved if involvement rates could live negative 5%; i.e. that the "natural charge per unit of measurement of interest" is sharply negative; that the economic scheme is beingness strangled yesteryear tight credit; together with that committing to a repetition of the piece of cake 1970s would live a dandy way to escape our electrical flow troubles. I don't think y'all tin analyze the province of affairs inwards a model without capital, equally saving translates to investment demand when at that spot is capital. (Christiano, Eichenbaum together with Rebelo's When is the Government Spending Multiplier Large? makes this point, side yesteryear side on my review list.) I don't think a model that says nosotros are experiencing a depression degree together with high growth rates makes much sense. I think the Fed is fifty-fifty to a greater extent than powerless than these models posit.
But this is the dandy betoken of clean, theoretical models. They are non dark boxes that brand predictions. They are collections of clear "if, then" statements. I regard the nitty-gritty of the new-Keynesian forward-guidance declaration clearly inwards Ivan's model. If I disagree alongside the "then," I stimulate got to uncovering what I don't similar near the "if." And he real clearly shows the difference betwixt "commitment" inwards the new-Keynesian model vs. how it is translated to policy practice, for improve or worse.
The policy number is this: we're inwards a recession. Interest rates are zero, together with can't cash inwards one's chips lower. The Fed is desperately trying to goose the economy. Lots of people (most of the recent Jackson Hole Fed conclave) are advising "open-mouth operations," and "managing expectations," that the key to electrical flow prosperity is for the Fed to brand statements near what it volition do inwards the future; together with these statements on their own, alongside no concrete action, volition "increase demand" together with lower today's unemployment. The Fed has been convinced, alongside to a greater extent than together with to a greater extent than "forward guidance" equally business office of its strategy. For example, the latest FOMC statement made history yesteryear promising cipher involvement rates equally long equally unemployment stays inwards a higher house half dozen together with a one-half portion together with inflation below 2 together with a half.
Does whatever of this brand whatever sense?
There are piles of complicated new-Keynesian models on this topic. Ivan's newspaper gets right to the core, giving a real uncomplicated model that explains their logic. The version on p. xx is the simplest together with clearest of all. We alone genuinely request i equation
log consumption growth = (substitution elasticity) x existent involvement rate
$$\frac{dc(t)}{dt} = \sigma^{-1} r(t) $$
(Hang inwards there, non-economists, y'all don't genuinely fifty-fifty request the equations; everything is inwards words too. Also, this is an experiment alongside Latex macros inwards blogger. You should regard a prissy equation above. Let me know if it doesn't operate inwards your browser.) When existent involvement rates are high, people guide to salve more, so consumption is lower today together with higher inwards the future. Thus, high consumption growth goes alongside high involvement rates, together with vice versa.
Now, forget near capital, so consumption equals output. Assume the Fed tin ready the existent involvement charge per unit of measurement to whatever it wants. Also, think of everything equally deviations from "potential output" or "trend." The degree of consumption becomes the "output gap." Thus, yesteryear controlling involvement rates, the Fed controls the growth rate of consumption, output, together with the output gap.
Now, here's the key. If the Fed raises the involvement rate, together with thence the growth rate of consumption, the level of consumption (now the output gap) falls. New-Keynesian models (correctly) anchor the degree inwards the future; consumption (output) sooner or after must live equal to "potential." This is the key new-Keynesian machinery yesteryear which higher involvement rates lower output, together with quite dissimilar from the static stories y'all may recall from old-Keynesian models. (I telephone telephone this "IS" bend the "interntemporal substitution" curve.)
You mightiness stimulate got thought that raising the growth charge per unit of measurement of consumption would only live a practiced thing; implicitly anchoring the degree of consumption at terminal year's value. That would live a mistake. The alone way to enhance the growth charge per unit of measurement of consumption side yesteryear side yr is for the degree this yr to drop. (In this economic scheme without capital.) Then nosotros grow faster yesteryear catching up.
Furthermore, if people aspect high involvement rates for many years, at that spot volition live many years of strong consumption growth, together with today's degree volition live real depressed. In equations, nosotros uncovering the degree of consumption (output gap) by integrating all its hereafter growth rates (bottom of p. 19)
$$x(t) = \sigma^{-1} \int_t^\infty r(t) dt$$
In sum, the degree of today's consumption, output, together with output gap all depend on today's involvement charge per unit of measurement and people's expectations of the path of hereafter involvement rates.
You tin showtime to regard how managing expectations of hereafter involvement rates mightiness live an attractive idea. If nosotros can't do anything near today's involvement rates, lowering expected hereafter rates volition stimulate got the same number on today's consumption.
In this paper's model, equally most new-Keynesian thinking, our electrical flow job is that the "natural rate" of interest, required to cash inwards one's chips on us at potential output, is sharply negative. (This is all exogenous.) With "only" 2% inflation together with nominal involvement rates stuck at zero, the Fed cannot deliver anything less than a negative 2% existent charge per unit of measurement of interest. If the "natural rate" is something similar negative 5%, together with then nosotros are stuck at a 3% "too high" existent involvement rate. Taking differences to "trend" or "potential," our province of affairs is equivalent to a too-high existent involvement charge per unit of measurement that the Fed can't do anything about.
The enterprise occupation inwards Figure three of the paper, reproduced above, shows this situation. The lines plot differences relative to potential output, or "output gaps," so beingness on the horizontal axis is the best outcome. We stimulate got a "negative natural rate" until fourth dimension T, when the earth returns to normal, the Fed regains control, together with consumption together with output revert to the tendency line. You regard that the too-high growth of consumption betwixt straightaway together with T, together with the too-low degree of consumption (output gap) now.
Well, says Ivan, why non push clit the whole occupation up? Suppose the Fed could hope straightaway that, at fourth dimension T, it volition ready involvement rates too low, from the betoken of stance of that time? This volition encourage people to eat at fourth dimension T rather than inwards periods after that, i.e. it volition engineer the negatively sloped dashed occupation from T onwards. If people knew at that spot was going to live this nail at T, consumption today would live less depressed. (Again, the way the graph plant is that y'all operate from right to left, together with the Fed controls the output together with consumption growth rates from right to left inwards guild to make today's level.)
More formally, Ivan assumes that the Fed wants to minimize the squared deviations from potential. Influenza A virus subtype H5N1 policy similar the dashed i produces smaller sum-of-squared output deviations than the enterprise occupation we're facing now.
This pretty piddling graph illustrates lots of policy advice you're hearing from within together with exterior the Fed. According to this view, the key affair the Fed tin do to enhance "demand" today is to hope that it volition cash inwards one's chips on involvement rates depression longer than it usually would do -- inwards the menstruum after T -- technology scientific discipline a bout of output that is a piddling likewise high (in a bigger model, inflationary).
But the graph, together with the paper, illustrate the primal problem: At fourth dimension T, the Fed volition non desire to cash inwards one's chips on rates low. "Too much" consumption agency inflation, together with inwards this model likewise much output (beyond "potential") is only equally bad equally likewise little. When fourth dimension T hits, together with the "natural rate" returns to normal, the optimal affair for the Fed to do looking forrad is to ready the involvement charge per unit of measurement equal to the natural rate, together with follow the enterprise light-green line. In turn, people today know this, which is why their expectation for consumption at fourth dimension T is at the enterprise occupation level, which is why consumption today is depressed.
Chicago Fed Chair Charlie Evans describes the needed policy equally "Odyssean." As Odysseus realized inwards having himself tied to the mast, the powerfulness to commit yourself today that y'all volition do things tomorrow, things that y'all volition non guide tomorrow if y'all volition stimulate got the choice, tin improve overall performance. This is a deep regulation of practiced policy, together with its violation describes many of our electrical flow problems. If the regime refuses to commit today that it volition non bail people out inwards the future, together with then people volition accept risky actions, and the bailout volition recur.
And this is the primal job for this piddling parable inwards describing the Fed's actions. Let's read the Fed's Odyssean revelation (the FOMC statement) a piddling to a greater extent than carefully, alongside the model inwards mind:
"..the Committee expects that a highly accommodative stance of monetary policy volition remain appropriate for a considerable time...;" "currently anticipates that this exceptionally depression gain for the federal funds charge per unit of measurement volition live appropriate at to the lowest degree equally long equally the unemployment charge per unit of measurement remains inwards a higher house 6-1/2 percent..." "the Committee volition also consider other information."There is no commitment at all inwards this. It's a description of how the Fed thinks it volition experience inwards the future, but nowhere inwards hither is what the new-Keynesian model demands: a commitment to do things inwards the hereafter that the Fed volition non desire to do when the fourth dimension comes.
The job is deep. How tin the Fed stimulate got the powerfulness to accept the "discretionary" activity today, inwards reply to the electrical flow situation, but that activity is somehow to commit itself to doing something inwards the hereafter that it real much volition non desire to do when the fourth dimension comes -- that it has so far explicitly together with loudly promised that it volition non do, together with has built upward xxx years of reputation against doing -- undershoot together with drive inflation? Why can't the Fed 2015 convene some other Jackson Hole conference, guide out Charlie Plosser together with Jeff Lacker's friends to say "we're heading to a repetition of the 1970s, it's fourth dimension to larn new-Monetarists together with hope that we'll live looking at monetary aggregates non unemployment rates?" It's so much hot air, together with people know it.
True commitment requires legal, institutional, or constitutional restraints. It at to the lowest degree needs linguistic communication similar "the Committee commits to cash inwards one's chips on a highly accomodative stance of monetary policy long after it is appropriate" or improve an institutional commitment "and to that terminate no farther FOMC meetings volition live scheduled until inflation hits 3%." But no establishment gives upward its discretion easily. (To live clear, I think this would all live a terrible idea; to a greater extent than below. I'm explaining the primal commitment/discretion job highlighted yesteryear Ivan's model.)
The paper, of course of teaching achieves the same affair inwards much greater generality, piece also presenting this gorgeously transparent example. This instance makes it crystal clear that the argue for "forward guidance" inwards new-Keynesian models is non to enhance inflation together with thus lower existent involvement rates -- it plant hither alongside constant inflation. "The argue for asset the involvement charge per unit of measurement at cipher is non to promote inflation [and thence negative existent rates] equally is commonly assumed."..."The existent argue for committing to cipher involvement rates is to create the expectations of a hereafter consumption boom" (p. 4)
Cautioning implicitly against the Fed's "twist" policies aimed at lowering long-term involvement rates "I demo that optimal policy... genuinely raises long run involvement rates.... This cautions against uncomplicated assessments of monetary policy centered around the lowering of yields at long maturities." In the total model, promising the inflationary nail raises long term rates. I.e. precisely the reverse of the Fed's "quantitative easing" operations.
To live clear, I don't purchase whatever of this: that our electrical flow problems would all live solved if involvement rates could live negative 5%; i.e. that the "natural charge per unit of measurement of interest" is sharply negative; that the economic scheme is beingness strangled yesteryear tight credit; together with that committing to a repetition of the piece of cake 1970s would live a dandy way to escape our electrical flow troubles. I don't think y'all tin analyze the province of affairs inwards a model without capital, equally saving translates to investment demand when at that spot is capital. (Christiano, Eichenbaum together with Rebelo's When is the Government Spending Multiplier Large? makes this point, side yesteryear side on my review list.) I don't think a model that says nosotros are experiencing a depression degree together with high growth rates makes much sense. I think the Fed is fifty-fifty to a greater extent than powerless than these models posit.
But this is the dandy betoken of clean, theoretical models. They are non dark boxes that brand predictions. They are collections of clear "if, then" statements. I regard the nitty-gritty of the new-Keynesian forward-guidance declaration clearly inwards Ivan's model. If I disagree alongside the "then," I stimulate got to uncovering what I don't similar near the "if." And he real clearly shows the difference betwixt "commitment" inwards the new-Keynesian model vs. how it is translated to policy practice, for improve or worse.
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