In fact, the fit of these lines is so good that I have become a bit suspicious over the exercise. I decided to do two things: 1) I would extend the forecast back to the early 1950s and 2) I would drop any measure of economic slack.
The reason for the first is obvious: The Fed seems to have made systematic policy mistakes during the 1970s after performing admirably in the 1960s. Then, if the Taylor rule is to be a decent guide as to the appropriateness of policy, it had better deviate systematically in the 70s.
The reason for the second is both econometric and philosophical. If the lagged policy rate responds to economic slack and slack evolves on slowly, the system is over-identified: we are more or less estimating an identity. Philosophically, economic slack is impossible to measure. We have no idea how to measure it or how this measure would relate to inflation. (I know: there are a thousand ways to measure slack. I am just saying none of them are meaningful.)
The result of the exercise is shown below. I too was stunned.
The estimated Fed funds rate lies almost exactly on top of the effective funds rate, shown as a dashed line. Either this is a meaningless measure of policy or monetary policy has been equally appropriate from 1956 through 2009. I choose the former as the more reasonable explanation.
I am not saying monetary policy has been bad of late. I am saying that using a Taylor rule to evaluate policy is meaningless. (Not the theory behind the Taylor rule; just the practice of estimating such a rule.)
What gives?: The Taylor Rule is an Identity
The Taylor rule is really something of an economic identity rather than a model of economic decision making. In effect, estimating a Taylor rule is no different than estimating the national income identity and finding out that Y really is equal to the sum of its parts.
To see this, use the old quantity theory equation:
P = v(φ)*M/Y
Prices are a function of Money (M), the quantity of goods in the economy (Y), and perhaps some measure of the current state of the economy (v(φ)), where the variable φ simply stands in for the current state of everything not written explicitly.
This equation is old fashioned but is fundamentally an identity: more money chasing fewer goods leads to higher prices.
We can transform the identity by taking logs and then first difference the equation.
dln(P) = dln(v(φ)) + dln(M) – dln(Y)
Then rearrange the equation to put money on the left hand side:
dln(M) = dln(P) + dln(Y) – dln(v(φ))
This is the Taylor rule.
Wait! We started with an identity (of sorts) and we ended with a Taylor rule. Logic then insists that the Taylor rule is an identity.
Okay, I hear you. The Fed does not target the money supply; the Fed targets a nominal short-term interest rate and the Taylor rule uses a short-term interest rate not the supply of money.
To see the link, how does the Fed enforce its nominal target. The Fed buys or sells bonds until short bonds are trading at the desired price. What does it use to buy and sell bonds? Money, of course.
So, the money supply is determined by the desired interest rate. The Fed, in effect, adjusts the money supply such that the short-term bond market is in equilibrium at the desired policy rate. M = f(r) and r = G(M). Where G is the inverse function of f.
Then, we have finally derived the Taylor rule.
dln(f(r)) = dln(P) + dln(Y) – dln(v(φ))
Finally, it is a small step to transform the above equation to the more familiar:
rt = αrt-1 + ϐ1Inft + ϐ2Growth Rate of Outputt – ϐ3Potential Somethingt
The coefficients in the equation can be estimated to minimize the information loss in the last transformation. The final term simply reinterprets our state variable. Recall, v(φ) was just some term reflecting the economic environment. In my specification, I set this coefficient to zero. In a standard specification, the restriction sets this to some measure of potential output. We don’t have to argue over signs or magnitudes because we may freely estimate the coefficients.
The Taylor rule fits because it is an identity.
The Quantity Theory
For those of you who don’t believe in money or at least who don’t believe in the link between inflation and money. Take a look at the following picture. The graph shows the five-year change in M2 divided by output against the five year cumulative change in the CPI. If M/Y rises rapidly, so do prices.
NorthGG asked if the relationship is between core or headline. I would say: yes. The five-year changes should completely eliminate the influence of high-frequency changes in food or energy. Only prolonged increases in either food or energy prices will show through. And, prolonged increases are also known as inflation.
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6 comments:
Great post.
What remains unclear to me is whether raising the level of inflation in an economy that is naturally deflating raises the real wealth and/or real income of the economy.
How does the idea of an output gap reflect the underlying economies net liability structure including financial liabilities?
For example, if a company gets too levered, even running at max capacity may not generate profitability and long term health. Indeed the attempt to circumvent the liability overhang even if the company was operating at maximum volume by legislating price increases would have diasterous effects if the price effect made the financial and variable cost liability grow at the induced inflation rate or some multiple of it. Furthermore the policy of creating inflation in an economy with significant slack seems likely to have the price pressure manifest in the cost base.
Can induced price increases be really isolated from the liability structure of the economy?
If the liability structure exceeds the asset structure on both a stock and growth rate basis (yes agg Owners equity is negative), can inflation close that gap or worsen the basis?
Does the output gap incorporate the financial liability structure of the economy or is it independant of explicit and implict leverage in the economy?
The output increases required to sustain todays US liabilities and tomorrows are enormous. Even running the economy at MaxCapacity will not cover them hence the need for the deflationary cycle; liabilities have to be destroyed.
My view remains the US economy has too few assets to meet the liability structure of the economy and this gap accelerates on secular basis now as the boomer retirement cycle create havoc on the cashflow structure of the economy.
The aggregate US liability structure (PV) is not only much higher than potential GDP but grows at a much faster rate. There is a stock and a flow mismatch.
Is the financial liability structure incorporated into the output gap models?
North: "Naturally deflating" ??
Secret... In Money Mischief Friedman shows 100 years of comparability between M2 money and real output. But "real" output is calculated by factoring inflation out of actual prices.
Using it as a denominator under M2, Friedman factored inflation into his results.
In private correspondence I pointed this out to Friedman and he replied that the CPI and the output deflator are calculated independently.
I'd say that adds just enough "difference" to the money/output trendline to make it believably similar to the CPI trendline. Sort of like what you show with the Taylor rule.
Authurian: I am not sure I completely understand your comment. It has always seemed to me that we want to factor prices out of output before using it to normalized the money supply. If (and this is a big if) all prices are factored out, we are left with units of output. Money divided by units of output should give us prices (or at least something that trends with prices). I think of the quantity theory equation as reflecting money chasing goods.
NorthGG: Inflation does not raise real wealth. Inflation is, at most, a transfer from lenders to debtors. Then, IF the dollar-denominated liability structure of the economy is a hindrance to growth, THEN inflation can restructure this debt. In this instance, inflation is a default mechanism (happens to be legal without out need of a court order as well).
The household balance sheet can be remedied by inflation. The structure of household debt is almost all long term. The corporate balance sheet and the banking sector balance sheet may not be able to be remedied by inflation. Their debt is mostly short term and inflation will simply be reflected in the needed premium for rolling the debt. The same could be said for government debt.
Financial liabilities are never included in standard models of the output gap. One more reason to believe that measures of the output gap are consistently meaningless.
SE
I do not dispute the link between inflation and money. But I do dispute the validity of graphs such as the one under "The Quantity Theory" in your post above. I present three examples to make my argument.
My first graph compares two time series. I modeled mine after yours, so each series is expressed as a five-year percent change. The blue line represents the CPI trendline. The red line I will identify below. But you can see there is similarity between the two lines.
My second graph contains the same data as the first. But the similarity and closeness of the two trendlines is much greater here, almost as good as in your graph. I achieved this effect by indexing each series on its average value. That is the same technique used by Milton Friedman for his graphs.
Your graph, and Friedman's, compare the CPI to what Friedman called "money supply relative to output," where M2 is the money supply, and real values are used for output. As you say, "we want to factor prices out of output" so that "we are left with units of output." (I assume you use "real output," as Friedman did.)
My graphs compare the CPI to "real population," which is calculated just as real output is calculated: We take the actual number and divide it by the GDP Deflator.
This is just a stupid gimmick that makes my trendline similar to the price trendline. But Milton Friedman used exactly the same gimmick to make "money supply relative to output" similar to prices. And, yes, Friedman's choice of data is much more reasonable than mine. But that does not validate his graphs. It just makes it more difficult to see the stupid gimmick.
In my third graph I remove the population number and in its place use the constant value 1. I divide this value by the GDP Deflator to produce a "real constant" (which, of course, varies). Then I divide M2 by my "real constant" and compare it to prices -- again, indexing each series on its average value as Friedman did. Again, the result is a replica of the price trendline.
You said you didn't understand my previous comment. (It's no secret... I'm no economist.) Just for a moment take the economics out of your money-and-inflation graph, and consider the simple arithmetic. When you factor prices out of the denominator, you factor them into the result. This is the reason our graphs -- yours, mine, and Friedman's -- are all so similar to the price trend.
The similarities here are comparable to the similarity you show in your first graph of the above post, where the Taylor estimate so closely corresponds to the Federal Funds Rate. Fraudulent arithmetic all.
Call me crazy,
Art
Okay, Arthurian. I am going to have to do some homework. Your graphs are quite convincing. Too, I get the rationale behind the graphs. I am going to have to think about this and see how much of what I have done is just reflecting the price movements themselves ...
SE
Naturally deflating; simply that the US workforce will contract as the boomers retire. Much like it naturally inflated as the boomers entered the workforce.
An economy has some natural level of price pressure.
The balance between the two on a real rate of change basis is what determines the changes in the price equilibrium.
Inflation exploded in the 1970's in part due to an upward final demand shock that came from the boomers entering the workforce.
Demand simply outstripped capacity and prices rose.
Volcker's containment of inflation was succesful on a secular basis because of economic forces not monetary policy.
Raising interest rates above the the rate of inflation forces demand to cool and gives capacity time to catch up; Volcker enabled this.
What worked for the Volcker and the US overall was a peaking in the US workforce growth rate as well as the emergence of the US trade deficit (upward supply shock from the rest of the world that could and can grow indefinitely).
Peaking final demand growth and accelerating supply growth allowed inflation to fall in trend. Hence the strong coupling of the global production base to the US consumer base since the early 1980's! The ties are deep and broad for US$ set prices.
Fast forwarding, the boomers pursued secular leverage to capture capital gains to smooth wealth/income into retirement. The underlying price pressure needed to sustain collateral values has made a secular peak rooted in thier own demographics which they did not expect!
Capacity has grown to an excess state (as it depends on $ revenue to generate profits due to the coupling process). Demand was simply too high as the wealth and income effects from the peaking credit cycle were transitory but expected to be permanent.
The shortfall in demand can be seen in household sector; calculate gross payrolls. Total payrolls * average hours worked * average hourly earnings. That is your revenue line. Now subtract from this your expected US savings rate. Servicing of credit will get tougher and tougher.
This adjusted revenue line is going to weaken further and in trend forcing the delevering and deflation in the capital sector of the economy.
The boomers are a natural demand bubble. C+I+G; capacity and equity bubble, housing and consumption bubble and the last to unfold is the government spending bubble (entitlements). Each natural bubble (C+I have passed) h will be exacerbated by policy.
The entitlement spending boom will come (is here) with a weakening tax base; the bailouts make the deficit much worse.
However, the ability to consume in the future is now jeopordized by excess leverage throughout the economy. The boomer demand wave is essentially followed by a demand contraction. Myopic market expectations assumed the boomers could generate demand in trend and this allowed a massive credit overshoot in housing.
There is a strong relationship of the US workforce growth yoy to household sector borrowing yoy. Until 2001, the relationship was very strong.
This dynamic suggests to me a household sector credit overshoot of roughly 5 trillion USD. This will be the catalyst for a secular rise in household sector savings.
The natural deflation simply comes from the contraction in the workforce. The volatility of the deflationary pressure will be a function of the embedded credit structures price and volume expectations and previous policy overshoots.
Attempts to raise inflation only increase the deflationary pressure in my view. The economy is levered and is having a free cash flow problem. Inflation will exacerbate the free cash flow problem and threatens to weaken already scarce real demand that is in a natural weakening trend.
The economy was simply too dependant on cash flow from the credit cycle and the previously favorable demographics. Demand is scarce and inflation will make it more scarce.
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