Lessons Learned Ane
Minggu, 01 Desember 2019
Academic Articles,
Monetary Policy,
negative interest rates,
Thesis topics
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I spent concluding calendar week traveling as well as giving talks. I ever larn a lot from this. One insight I got: Real involvement rates are truly of import inward making feel of financial policy as well as inflation.
Harald Uhlig got me thinking 1 time again most financial policy as well as inflation, inward his skeptical comments on the financial theory discussion, available here. At left, 2 of his graphs, bespeak pointedly 1 of the criterion questions most the financial theory: Ok, then, what most Japan? (And Europe as well as the US, too, inward like situations. If you lot don't run across the graphs or equations, come upwardly to the original.) This interrogation came upwardly several times as well as I had the exercise goodness of several creative seminar participants views.
The financial theory says
\[ \frac{B_{t-1}}{P_t} = E_t \sum_{j=0}^{\infty} \frac{1}{R_{t,t+j}} s_{t+j} \]
where \(B\) is nominal debt, \(P\) is the cost level, \(R_{t,t+j}\) is the discount charge per unit of measurement or existent render on authorities bonds betwixt \( t\) as well as \(t+j\) as well as \(s\) are existent primary (excluding involvement payments) authorities surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, as well as forecasts for long-term financial policy are as dire, amongst aging populations, dull growth, as well as exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this 1 before. Of course of teaching the equation holds inward whatsoever model; it's an identity amongst \(R\) equal to the existent render on authorities debt; financial theory is most the machinery rather than the equation itself. Sure, markets seem to bring organized religious belief that rather than a grand global sovereign default via inflation, bondholders seem to bring organized religious belief that eventually governments volition wake upwardly as well as exercise the correct thing most primary surpluses \(s\). And so forth. But that's non really convincing.
This all leaves out the remaining letter: \(R\). We alive inward a fourth dimension of extraordinarily depression existent involvement rates. Lower existent rates heighten the existent value surpluses s. So inward the financial theory, other things the same, lower existent rates are a deflationary force.
The final result is quite powerful. For a uncomplicated dorsum of the envelope approach, nosotros tin apply the Gordon growth formula to steady states. Surpluses \(s\) grow at the charge per unit of measurement \(g\) of the overall economy. So, inward steady state terms,
\[ \frac{B_{t-1}}{P_t s_t} = E_t \sum_{j=0}^{\infty} \frac{(1+g)^j}{(1+r)^j} \approx \frac{1}{ r - g} \]
\[ \frac{P_t s_t}{B_{t-1}} \approx r - g \; \; (1) \]
(and exact inward continuous time). The left mitt side is the steady state ratio of surpluses to debt. The correct mitt side is the departure betwixt the existent involvement charge per unit of measurement as well as the long-run growth rate.
So, amongst (say) a 2% growth charge per unit of measurement g, as well as a 4% long-run involvement charge per unit of measurement r, surpluses demand to last 2% of the existent value of debt. But suppose involvement rates turn down to 3%. This modify cuts inward one-half the needed long-run surpluses! Or, asset surpluses constant, if long-run involvement rates autumn to 3%, the cost degree falls yesteryear half.
You tin run across the punchline coming. Long term existent involvement rates are truly depression correct now. If anything, we're flirting amongst \(r \lt g\), the magic indicate at which governments tin borrow all they desire as well as never repay the debt.
With this insight, Harald should bring been bespeak of the financial theory, where is the huge deflation? And the respond is, well, we're sort of there. The puzzle of the minute is declining inflation as well as fifty-fifty slight deflation despite all our primal bankers' best efforts.
Pursuing this idea, at that spot is a larger novel story hither most growth, involvement rates, as well as inflation.
Obviously, at that spot is an contrary prediction for what happens when existent involvement rates rise. Higher existent rates, unless accompanied yesteryear higher surpluses, volition drive inflation upwards.
In conventional terms, looking at flows rather than introduce values, suppose a authorities that is $20 Trillion inward debt faces involvement rates that ascension from 2% to 5%. Well, so it has to growth surpluses yesteryear $600 billion per year; as well as if it cannot exercise so inflation volition result.
Influenza A virus subtype H5N1 like story makes feel for the cyclical falls inward inflation. What happened to our equation inward 2008? Surpluses savage -- deficits exploded -- as well as hereafter surpluses savage fifty-fifty more. Debt rose sharply. Why did nosotros run across deflation? Well, existent involvement rates on authorities debt savage to unprecedentedly depression levels. This truly isn't fifty-fifty economics, it's merely accounting. The equation holds, ex-post, as an identity!
To mean value a fight to a greater extent than most existent rates, growth, as well as inflation, think the criterion relation that the existent involvement charge per unit of measurement equals the subjective discount charge per unit of measurement (how much people prefer electrical current to hereafter consumption) addition a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is ordinarily thought to last a fight to a higher house one.
With \(\gamma=1\) (log utility), so nosotros bring \(r-g = \delta-n\). The magic set down of unbounded authorities debt tin occur because authorities surpluses tin grow at the population growth rate, spell involvement rates are determined yesteryear the private growth rate. But population growth is tapering off, as well as must eventually cease, as well as bondholders prefer their coin now. With \(\gamma \gt 1 \) ,
\[ r-g = \delta - n + (\gamma-1)(g-n) \; \; (2)\]
The novel term is the per capita growth rate, which is positive, farther distancing us from the set down of magic.
More to the point, though, nosotros at 1 time bring earlier us the primal determinant of long run existent involvement rates. Real involvement rates are higher when economical growth is higher. And \(r-g\) rises when economical growth \(g\) rises.
So, going dorsum to my equation (1), nosotros truly had a puzzle earlier us. Higher existent involvement rates would hateful lower values of the debt, as well as would hence last inflationary if non accompanied yesteryear austerity to pay to a greater extent than to bondholders. But higher existent involvement rates must come upwardly amongst higher economical growth, as well as higher economical growth would heighten surpluses, helping the province of affairs out. Which forcefulness wins? Well, equation (2) answers that question: With \(\gamma \gt 1\), the green example (a 1% ascension inward consumption growth comes amongst a to a greater extent than than 1% ascension inward existent involvement rates), higher growth g comes amongst higher all the same involvement rates r, as well as hence remains an inflationary force, 1 time again asset surpluses constant.
All inward all then, nosotros bring the hint of a financial theory Phillips curve: Inflation should last procyclical. In skillful times, involvement rates ascension as well as the existent value of authorities debt falls, producing to a greater extent than inflation. In bad times, involvement rates autumn as well as the existent value of authorities debt rises, producing less inflation.
Central banks bring been absent inward all this. The natural side yesteryear side interrogation is, does this provide to a greater extent than or less other reinforcing channel yesteryear which primal banks mightiness heighten inflation if they heighten involvement rates? I don't mean value so, but 1 needs to a greater extent than equations to truly respond the question.
What matters hither are really long-term existent involvement rates, the form that discount expectations of surpluses -- yes, nosotros demand to a greater extent than or less surpluses! -- twenty to thirty years from at 1 time to found bondholder's willingness to concur debt today.
In no model I bring played amongst tin primal banks impact existent involvement rates for that long. I mean value a quick expression out the window convinces us that primal banks cannot substantially heighten involvement rates inward a slump, amongst render of global savings so rigid compared to demand for global investment. Long-term involvement rates truly must come upwardly from render as well as demand, non monetary machination. Higher existent involvement rates require higher marginal products of capital, as well as hence higher economical growth, non louder promises, to a greater extent than speeches, or to a greater extent than energetic attempts to avoid the logic of a liquidity trap.
The financial theory says
\[ \frac{B_{t-1}}{P_t} = E_t \sum_{j=0}^{\infty} \frac{1}{R_{t,t+j}} s_{t+j} \]
where \(B\) is nominal debt, \(P\) is the cost level, \(R_{t,t+j}\) is the discount charge per unit of measurement or existent render on authorities bonds betwixt \( t\) as well as \(t+j\) as well as \(s\) are existent primary (excluding involvement payments) authorities surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, as well as forecasts for long-term financial policy are as dire, amongst aging populations, dull growth, as well as exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this 1 before. Of course of teaching the equation holds inward whatsoever model; it's an identity amongst \(R\) equal to the existent render on authorities debt; financial theory is most the machinery rather than the equation itself. Sure, markets seem to bring organized religious belief that rather than a grand global sovereign default via inflation, bondholders seem to bring organized religious belief that eventually governments volition wake upwardly as well as exercise the correct thing most primary surpluses \(s\). And so forth. But that's non really convincing.
This all leaves out the remaining letter: \(R\). We alive inward a fourth dimension of extraordinarily depression existent involvement rates. Lower existent rates heighten the existent value surpluses s. So inward the financial theory, other things the same, lower existent rates are a deflationary force.
The final result is quite powerful. For a uncomplicated dorsum of the envelope approach, nosotros tin apply the Gordon growth formula to steady states. Surpluses \(s\) grow at the charge per unit of measurement \(g\) of the overall economy. So, inward steady state terms,
\[ \frac{B_{t-1}}{P_t s_t} = E_t \sum_{j=0}^{\infty} \frac{(1+g)^j}{(1+r)^j} \approx \frac{1}{ r - g} \]
\[ \frac{P_t s_t}{B_{t-1}} \approx r - g \; \; (1) \]
(and exact inward continuous time). The left mitt side is the steady state ratio of surpluses to debt. The correct mitt side is the departure betwixt the existent involvement charge per unit of measurement as well as the long-run growth rate.
So, amongst (say) a 2% growth charge per unit of measurement g, as well as a 4% long-run involvement charge per unit of measurement r, surpluses demand to last 2% of the existent value of debt. But suppose involvement rates turn down to 3%. This modify cuts inward one-half the needed long-run surpluses! Or, asset surpluses constant, if long-run involvement rates autumn to 3%, the cost degree falls yesteryear half.
You tin run across the punchline coming. Long term existent involvement rates are truly depression correct now. If anything, we're flirting amongst \(r \lt g\), the magic indicate at which governments tin borrow all they desire as well as never repay the debt.
With this insight, Harald should bring been bespeak of the financial theory, where is the huge deflation? And the respond is, well, we're sort of there. The puzzle of the minute is declining inflation as well as fifty-fifty slight deflation despite all our primal bankers' best efforts.
Pursuing this idea, at that spot is a larger novel story hither most growth, involvement rates, as well as inflation.
Obviously, at that spot is an contrary prediction for what happens when existent involvement rates rise. Higher existent rates, unless accompanied yesteryear higher surpluses, volition drive inflation upwards.
In conventional terms, looking at flows rather than introduce values, suppose a authorities that is $20 Trillion inward debt faces involvement rates that ascension from 2% to 5%. Well, so it has to growth surpluses yesteryear $600 billion per year; as well as if it cannot exercise so inflation volition result.
Influenza A virus subtype H5N1 like story makes feel for the cyclical falls inward inflation. What happened to our equation inward 2008? Surpluses savage -- deficits exploded -- as well as hereafter surpluses savage fifty-fifty more. Debt rose sharply. Why did nosotros run across deflation? Well, existent involvement rates on authorities debt savage to unprecedentedly depression levels. This truly isn't fifty-fifty economics, it's merely accounting. The equation holds, ex-post, as an identity!
To mean value a fight to a greater extent than most existent rates, growth, as well as inflation, think the criterion relation that the existent involvement charge per unit of measurement equals the subjective discount charge per unit of measurement (how much people prefer electrical current to hereafter consumption) addition a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is ordinarily thought to last a fight to a higher house one.
With \(\gamma=1\) (log utility), so nosotros bring \(r-g = \delta-n\). The magic set down of unbounded authorities debt tin occur because authorities surpluses tin grow at the population growth rate, spell involvement rates are determined yesteryear the private growth rate. But population growth is tapering off, as well as must eventually cease, as well as bondholders prefer their coin now. With \(\gamma \gt 1 \) ,
\[ r-g = \delta - n + (\gamma-1)(g-n) \; \; (2)\]
The novel term is the per capita growth rate, which is positive, farther distancing us from the set down of magic.
More to the point, though, nosotros at 1 time bring earlier us the primal determinant of long run existent involvement rates. Real involvement rates are higher when economical growth is higher. And \(r-g\) rises when economical growth \(g\) rises.
So, going dorsum to my equation (1), nosotros truly had a puzzle earlier us. Higher existent involvement rates would hateful lower values of the debt, as well as would hence last inflationary if non accompanied yesteryear austerity to pay to a greater extent than to bondholders. But higher existent involvement rates must come upwardly amongst higher economical growth, as well as higher economical growth would heighten surpluses, helping the province of affairs out. Which forcefulness wins? Well, equation (2) answers that question: With \(\gamma \gt 1\), the green example (a 1% ascension inward consumption growth comes amongst a to a greater extent than than 1% ascension inward existent involvement rates), higher growth g comes amongst higher all the same involvement rates r, as well as hence remains an inflationary force, 1 time again asset surpluses constant.
All inward all then, nosotros bring the hint of a financial theory Phillips curve: Inflation should last procyclical. In skillful times, involvement rates ascension as well as the existent value of authorities debt falls, producing to a greater extent than inflation. In bad times, involvement rates autumn as well as the existent value of authorities debt rises, producing less inflation.
Central banks bring been absent inward all this. The natural side yesteryear side interrogation is, does this provide to a greater extent than or less other reinforcing channel yesteryear which primal banks mightiness heighten inflation if they heighten involvement rates? I don't mean value so, but 1 needs to a greater extent than equations to truly respond the question.
What matters hither are really long-term existent involvement rates, the form that discount expectations of surpluses -- yes, nosotros demand to a greater extent than or less surpluses! -- twenty to thirty years from at 1 time to found bondholder's willingness to concur debt today.
In no model I bring played amongst tin primal banks impact existent involvement rates for that long. I mean value a quick expression out the window convinces us that primal banks cannot substantially heighten involvement rates inward a slump, amongst render of global savings so rigid compared to demand for global investment. Long-term involvement rates truly must come upwardly from render as well as demand, non monetary machination. Higher existent involvement rates require higher marginal products of capital, as well as hence higher economical growth, non louder promises, to a greater extent than speeches, or to a greater extent than energetic attempts to avoid the logic of a liquidity trap.
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