I spent final calendar week traveling too giving talks. I ever larn a lot from this. One insight I got: Real involvement rates are genuinely of import inwards making feel of financial policy too inflation.
Harald Uhlig got me thinking i time to a greater extent than close financial policy too inflation, inwards his skeptical comments on the financial theory discussion, available here. At left, 2 of his graphs, quest pointedly i of the touchstone questions close the financial theory: Ok, then, what close Japan? (And Europe too the US, too, inwards like situations. If you lot don't encounter the graphs or equations, come upwards to the original.) This interrogation came upwards several times too 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 toll level, \(R_{t,t+j}\) is the discount charge per unit of measurement or existent render on regime bonds betwixt \( t\) too \(t+j\) too \(s\) are existent primary (excluding involvement payments) regime surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, too forecasts for long-term financial policy are as dire, amongst aging populations, tiresome growth, too exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this i before. Of class the equation holds inwards whatsoever model; it's an identity amongst \(R\) equal to the existent render on regime debt; financial theory is close the machinery rather than the equation itself. Sure, markets seem to convey faith that rather than a grand global sovereign default via inflation, bondholders seem to convey faith that eventually governments volition wake upwards too do the correct thing close primary surpluses \(s\). And so forth. But that's non really convincing.
This all leaves out the remaining letter: \(R\). We alive inwards a fourth dimension of extraordinarily depression existent involvement rates. Lower existent rates heighten the existent value surpluses s. So inwards the financial theory, other things the same, lower existent rates are a deflationary force.
The resultant is quite powerful. For a uncomplicated dorsum of the envelope approach, nosotros tin sack apply the Gordon growth formula to steady states. Surpluses \(s\) grow at the charge per unit of measurement \(g\) of the overall economy. So, inwards 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 inwards continuous time). The left mitt side is the steady solid soil ratio of surpluses to debt. The correct mitt side is the deviation betwixt the existent involvement charge per unit of measurement too the long-run growth rate.
So, amongst (say) a 2% growth charge per unit of measurement g, too 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 spend upwards to 3%. This alter cuts inwards one-half the needed long-run surpluses! Or, belongings surpluses constant, if long-run involvement rates autumn to 3%, the toll grade falls yesteryear half.
You tin sack encounter the punchline coming. Long term existent involvement rates are genuinely depression correct now. If anything, we're flirting amongst \(r \lt g\), the magic indicate at which governments tin sack borrow all they desire too never repay the debt.
With this insight, Harald should convey been quest of the financial theory, where is the huge deflation? And the reply is, well, we're sort of there. The puzzle of the 2nd is declining inflation too fifty-fifty slight deflation despite all our key bankers' best efforts.
Pursuing this idea, in that place is a larger novel story hither close growth, involvement rates, too inflation.
Obviously, in that place 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 acquaint values, suppose a regime that is $20 Trillion inwards debt faces involvement rates that rising from 2% to 5%. Well, so it has to growth surpluses yesteryear $600 billion per year; too if it cannot do so inflation volition result.
Influenza A virus subtype H5N1 like story makes feel for the cyclical falls inwards inflation. What happened to our equation inwards 2008? Surpluses roughshod -- deficits exploded -- too futurity surpluses roughshod fifty-fifty more. Debt rose sharply. Why did nosotros encounter deflation? Well, existent involvement rates on regime debt roughshod to unprecedentedly depression levels. This genuinely isn't fifty-fifty economics, it's simply accounting. The equation holds, ex-post, as an identity!
To intend a flake to a greater extent than close existent rates, growth, too inflation, shout out upwards the touchstone 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 futurity consumption) summation a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is ordinarily thought to go a flake inwards a higher house one.
With \(\gamma=1\) (log utility), so nosotros convey \(r-g = \delta-n\). The magic solid soil of unbounded regime debt tin sack occur because regime surpluses tin sack grow at the population growth rate, piece involvement rates are determined yesteryear the private growth rate. But population growth is tapering off, too must eventually cease, too 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 directly convey earlier us the key 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 genuinely had a puzzle earlier us. Higher existent involvement rates would hateful lower values of the debt, too 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 upwards amongst higher economical growth, too 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 park example (a 1% rising inwards consumption growth comes amongst a to a greater extent than than 1% rising inwards existent involvement rates), higher growth g comes amongst higher nevertheless involvement rates r, too thence remains an inflationary force, i time to a greater extent than belongings surpluses constant.
All inwards all then, nosotros convey the hint of a financial theory Phillips curve: Inflation should go procyclical. In practiced times, involvement rates rising too the existent value of regime debt falls, producing to a greater extent than inflation. In bad times, involvement rates autumn too the existent value of regime debt rises, producing less inflation.
Central banks convey been absent inwards all this. The natural adjacent interrogation is, does this provide roughly other reinforcing channel yesteryear which key banks mightiness heighten inflation if they heighten involvement rates? I don't intend so, but i needs to a greater extent than equations to genuinely reply the question.
What matters hither are really long-term existent involvement rates, the form that discount expectations of surpluses -- yes, nosotros demand roughly surpluses! -- xx to xxx years from directly to flora bondholder's willingness to concur debt today.
In no model I convey played amongst tin sack key banks acquit on existent involvement rates for that long. I intend a quick expression out the window convinces us that key banks cannot substantially heighten involvement rates inwards a slump, amongst provide of global savings so rigid compared to demand for global investment. Long-term involvement rates genuinely must come upwards from provide too demand, non monetary machination. Higher existent involvement rates require higher marginal products of capital, too 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 toll level, \(R_{t,t+j}\) is the discount charge per unit of measurement or existent render on regime bonds betwixt \( t\) too \(t+j\) too \(s\) are existent primary (excluding involvement payments) regime surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, too forecasts for long-term financial policy are as dire, amongst aging populations, tiresome growth, too exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this i before. Of class the equation holds inwards whatsoever model; it's an identity amongst \(R\) equal to the existent render on regime debt; financial theory is close the machinery rather than the equation itself. Sure, markets seem to convey faith that rather than a grand global sovereign default via inflation, bondholders seem to convey faith that eventually governments volition wake upwards too do the correct thing close primary surpluses \(s\). And so forth. But that's non really convincing.
This all leaves out the remaining letter: \(R\). We alive inwards a fourth dimension of extraordinarily depression existent involvement rates. Lower existent rates heighten the existent value surpluses s. So inwards the financial theory, other things the same, lower existent rates are a deflationary force.
The resultant is quite powerful. For a uncomplicated dorsum of the envelope approach, nosotros tin sack apply the Gordon growth formula to steady states. Surpluses \(s\) grow at the charge per unit of measurement \(g\) of the overall economy. So, inwards 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 inwards continuous time). The left mitt side is the steady solid soil ratio of surpluses to debt. The correct mitt side is the deviation betwixt the existent involvement charge per unit of measurement too the long-run growth rate.
So, amongst (say) a 2% growth charge per unit of measurement g, too 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 spend upwards to 3%. This alter cuts inwards one-half the needed long-run surpluses! Or, belongings surpluses constant, if long-run involvement rates autumn to 3%, the toll grade falls yesteryear half.
You tin sack encounter the punchline coming. Long term existent involvement rates are genuinely depression correct now. If anything, we're flirting amongst \(r \lt g\), the magic indicate at which governments tin sack borrow all they desire too never repay the debt.
With this insight, Harald should convey been quest of the financial theory, where is the huge deflation? And the reply is, well, we're sort of there. The puzzle of the 2nd is declining inflation too fifty-fifty slight deflation despite all our key bankers' best efforts.
Pursuing this idea, in that place is a larger novel story hither close growth, involvement rates, too inflation.
Obviously, in that place 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 acquaint values, suppose a regime that is $20 Trillion inwards debt faces involvement rates that rising from 2% to 5%. Well, so it has to growth surpluses yesteryear $600 billion per year; too if it cannot do so inflation volition result.
Influenza A virus subtype H5N1 like story makes feel for the cyclical falls inwards inflation. What happened to our equation inwards 2008? Surpluses roughshod -- deficits exploded -- too futurity surpluses roughshod fifty-fifty more. Debt rose sharply. Why did nosotros encounter deflation? Well, existent involvement rates on regime debt roughshod to unprecedentedly depression levels. This genuinely isn't fifty-fifty economics, it's simply accounting. The equation holds, ex-post, as an identity!
To intend a flake to a greater extent than close existent rates, growth, too inflation, shout out upwards the touchstone 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 futurity consumption) summation a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is ordinarily thought to go a flake inwards a higher house one.
With \(\gamma=1\) (log utility), so nosotros convey \(r-g = \delta-n\). The magic solid soil of unbounded regime debt tin sack occur because regime surpluses tin sack grow at the population growth rate, piece involvement rates are determined yesteryear the private growth rate. But population growth is tapering off, too must eventually cease, too 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 directly convey earlier us the key 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 genuinely had a puzzle earlier us. Higher existent involvement rates would hateful lower values of the debt, too 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 upwards amongst higher economical growth, too 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 park example (a 1% rising inwards consumption growth comes amongst a to a greater extent than than 1% rising inwards existent involvement rates), higher growth g comes amongst higher nevertheless involvement rates r, too thence remains an inflationary force, i time to a greater extent than belongings surpluses constant.
All inwards all then, nosotros convey the hint of a financial theory Phillips curve: Inflation should go procyclical. In practiced times, involvement rates rising too the existent value of regime debt falls, producing to a greater extent than inflation. In bad times, involvement rates autumn too the existent value of regime debt rises, producing less inflation.
Central banks convey been absent inwards all this. The natural adjacent interrogation is, does this provide roughly other reinforcing channel yesteryear which key banks mightiness heighten inflation if they heighten involvement rates? I don't intend so, but i needs to a greater extent than equations to genuinely reply the question.
What matters hither are really long-term existent involvement rates, the form that discount expectations of surpluses -- yes, nosotros demand roughly surpluses! -- xx to xxx years from directly to flora bondholder's willingness to concur debt today.
In no model I convey played amongst tin sack key banks acquit on existent involvement rates for that long. I intend a quick expression out the window convinces us that key banks cannot substantially heighten involvement rates inwards a slump, amongst provide of global savings so rigid compared to demand for global investment. Long-term involvement rates genuinely must come upwards from provide too demand, non monetary machination. Higher existent involvement rates require higher marginal products of capital, too 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.
