Lessons Learned Ane
I spent concluding calendar week traveling in addition to 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 in addition to inflation.
Harald Uhlig got me thinking i time to a greater extent than virtually financial policy in addition to inflation, inward his skeptical comments on the financial theory discussion, available here. At left, 2 of his graphs, cry for pointedly i of the measure questions virtually the financial theory: Ok, then, what virtually Japan? (And Europe in addition to the US, too, inward like situations. If y'all don't run across the graphs or equations, come upwardly to the original.) This interrogation came upwardly several times in addition to I had the do 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 \( t\) in addition to \(t+j\) in addition to \(s\) 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, in addition to forecasts for long-term financial policy are as dire, alongside aging populations, ho-hum growth, in addition to exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this i before. Of course of written report the equation holds inward whatever model; it's an identity alongside \(R\) equal to the existent render on authorities debt; financial theory is virtually the machinery rather than the equation itself. Sure, markets seem to accept faith that rather than a grand global sovereign default via inflation, bondholders seem to accept faith that eventually governments volition wake upwardly in addition to do the correct thing virtually 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 upshot is quite powerful. For a unproblematic 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 solid soil 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 solid soil ratio of surpluses to debt. The correct mitt side is the departure betwixt the existent involvement charge per unit of measurement in addition to the long-run growth rate.
So, alongside (say) a 2% growth charge per unit of measurement g, in addition to a 4% long-run involvement charge per unit of measurement r, surpluses demand to go 2% of the existent value of debt. But suppose involvement rates turn down to 3%. This alter 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 alongside \(r \lt g\), the magic indicate at which governments tin borrow all they desire in addition to never repay the debt.
With this insight, Harald should accept been cry for of the financial theory, where is the huge deflation? And the reply is, well, we're sort of there. The puzzle of the minute is declining inflation in addition to fifty-fifty slight deflation despite all our primal bankers' best efforts.
Pursuing this idea, at that spot is a larger novel story hither virtually growth, involvement rates, in addition to 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 rising from 2% to 5%. Well, in addition to then it has to increase surpluses yesteryear $600 billion per year; in addition to if it cannot do 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 cruel -- deficits exploded -- in addition to futurity surpluses cruel fifty-fifty more. Debt rose sharply. Why did nosotros run across deflation? Well, existent involvement rates on authorities debt cruel to unprecedentedly depression levels. This truly isn't fifty-fifty economics, it's but accounting. The equation holds, ex-post, as an identity!
To mean value a combat to a greater extent than virtually existent rates, growth, in addition to inflation, cry upwardly the measure relation that the existent involvement charge per unit of measurement equals the subjective discount charge per unit of measurement (how much people prefer electrical flow to futurity consumption) summation a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is unremarkably thought to go a combat higher upwardly one.
With \(\gamma=1\) (log utility), in addition to then nosotros accept \(r-g = \delta-n\). The magic solid soil 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, in addition to must eventually cease, in addition to 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 solid soil of magic.
More to the point, though, nosotros right away accept 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, in addition to would thence go inflationary if non accompanied yesteryear austerity to pay to a greater extent than to bondholders. But higher existent involvement rates must come upwardly alongside higher economical growth, in addition to higher economical growth would heighten surpluses, helping the province of affairs out. Which strength wins? Well, equation (2) answers that question: With \(\gamma \gt 1\), the park illustration (a 1% rising inward consumption growth comes alongside a to a greater extent than than 1% rising inward existent involvement rates), higher growth g comes alongside higher withal involvement rates r, in addition to thence remains an inflationary force, i time to a greater extent than asset surpluses constant.
All inward all then, nosotros accept the hint of a financial theory Phillips curve: Inflation should go procyclical. In practiced times, involvement rates rising in addition to the existent value of authorities debt falls, producing to a greater extent than inflation. In bad times, involvement rates autumn in addition to the existent value of authorities debt rises, producing less inflation.
Central banks accept been absent inward all this. The natural adjacent interrogation is, does this provide to a greater extent than or less other reinforcing channel yesteryear which primal banks powerfulness heighten inflation if they heighten involvement rates? I don't mean value so, but i needs to a greater extent than equations to truly reply the question.
What matters hither are really long-term existent involvement rates, the variety that discount expectations of surpluses -- yes, nosotros demand to a greater extent than or less surpluses! -- xx to xxx years from right away to institute bondholder's willingness to concord debt today.
In no model I accept played alongside tin primal banks ship on existent involvement rates for that long. I mean value a quick facial expression out the window convinces us that primal banks cannot substantially heighten involvement rates inward a slump, alongside provide of global savings so potent compared to demand for global investment. Long-term involvement rates truly must come upwardly from provide in addition to demand, non monetary machination. Higher existent involvement rates require higher marginal products of capital, in addition to thence 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 \( t\) in addition to \(t+j\) in addition to \(s\) 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, in addition to forecasts for long-term financial policy are as dire, alongside aging populations, ho-hum growth, in addition to exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this i before. Of course of written report the equation holds inward whatever model; it's an identity alongside \(R\) equal to the existent render on authorities debt; financial theory is virtually the machinery rather than the equation itself. Sure, markets seem to accept faith that rather than a grand global sovereign default via inflation, bondholders seem to accept faith that eventually governments volition wake upwardly in addition to do the correct thing virtually 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 upshot is quite powerful. For a unproblematic 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 solid soil 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 solid soil ratio of surpluses to debt. The correct mitt side is the departure betwixt the existent involvement charge per unit of measurement in addition to the long-run growth rate.
So, alongside (say) a 2% growth charge per unit of measurement g, in addition to a 4% long-run involvement charge per unit of measurement r, surpluses demand to go 2% of the existent value of debt. But suppose involvement rates turn down to 3%. This alter 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 alongside \(r \lt g\), the magic indicate at which governments tin borrow all they desire in addition to never repay the debt.
With this insight, Harald should accept been cry for of the financial theory, where is the huge deflation? And the reply is, well, we're sort of there. The puzzle of the minute is declining inflation in addition to fifty-fifty slight deflation despite all our primal bankers' best efforts.
Pursuing this idea, at that spot is a larger novel story hither virtually growth, involvement rates, in addition to 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 rising from 2% to 5%. Well, in addition to then it has to increase surpluses yesteryear $600 billion per year; in addition to if it cannot do 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 cruel -- deficits exploded -- in addition to futurity surpluses cruel fifty-fifty more. Debt rose sharply. Why did nosotros run across deflation? Well, existent involvement rates on authorities debt cruel to unprecedentedly depression levels. This truly isn't fifty-fifty economics, it's but accounting. The equation holds, ex-post, as an identity!
To mean value a combat to a greater extent than virtually existent rates, growth, in addition to inflation, cry upwardly the measure relation that the existent involvement charge per unit of measurement equals the subjective discount charge per unit of measurement (how much people prefer electrical flow to futurity consumption) summation a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is unremarkably thought to go a combat higher upwardly one.
With \(\gamma=1\) (log utility), in addition to then nosotros accept \(r-g = \delta-n\). The magic solid soil 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, in addition to must eventually cease, in addition to 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 solid soil of magic.
More to the point, though, nosotros right away accept 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, in addition to would thence go inflationary if non accompanied yesteryear austerity to pay to a greater extent than to bondholders. But higher existent involvement rates must come upwardly alongside higher economical growth, in addition to higher economical growth would heighten surpluses, helping the province of affairs out. Which strength wins? Well, equation (2) answers that question: With \(\gamma \gt 1\), the park illustration (a 1% rising inward consumption growth comes alongside a to a greater extent than than 1% rising inward existent involvement rates), higher growth g comes alongside higher withal involvement rates r, in addition to thence remains an inflationary force, i time to a greater extent than asset surpluses constant.
All inward all then, nosotros accept the hint of a financial theory Phillips curve: Inflation should go procyclical. In practiced times, involvement rates rising in addition to the existent value of authorities debt falls, producing to a greater extent than inflation. In bad times, involvement rates autumn in addition to the existent value of authorities debt rises, producing less inflation.
Central banks accept been absent inward all this. The natural adjacent interrogation is, does this provide to a greater extent than or less other reinforcing channel yesteryear which primal banks powerfulness heighten inflation if they heighten involvement rates? I don't mean value so, but i needs to a greater extent than equations to truly reply the question.
What matters hither are really long-term existent involvement rates, the variety that discount expectations of surpluses -- yes, nosotros demand to a greater extent than or less surpluses! -- xx to xxx years from right away to institute bondholder's willingness to concord debt today.
In no model I accept played alongside tin primal banks ship on existent involvement rates for that long. I mean value a quick facial expression out the window convinces us that primal banks cannot substantially heighten involvement rates inward a slump, alongside provide of global savings so potent compared to demand for global investment. Long-term involvement rates truly must come upwardly from provide in addition to demand, non monetary machination. Higher existent involvement rates require higher marginal products of capital, in addition to thence 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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