the neo-fisher hypothesis william j. crowder presentation.pdfthe neo-fisher hypothesis increasing...

William J. Crowder Professor of Economics

Department of Economics University of Texas at Arlington

The Neo-Fisher Hypothesis


“A sustained burst of moderate inflation is not something to worry about. It should be embraced.” - Kenneth S. Rogoff, Project Syndicate, June 6, 2013. Why does the Fed want inflation? How do they get it?

The fundamental problem for the U.S. economy coming out of the 2007-09 financial crisis and recession is debt overhang. Low interest rates of the early 2000’s fueled excessive borrowing leading to a real estate bubble. The bursting bubble left asset prices (like housing) down but debt levels didn’t change much.


High debt coupled with low asset values makes debt service more difficult, constraining household spending and investment by firms. Higher inflation will reduce the real value of outstanding debt (and everything else).


Normally, the Fed creates inflation by increasing the growth rate of the money supply. The usual monetary transmission mechanism is: By stimulating economic activity through lower interest rates (AD shifts rightward) inflation rises over time.


Increasing Inflation – Old School

Federal Funds Rate

Reserves

id,1

iff,1

NBR1

RS1

RD1 (π1)


Federal Funds Rate

Reserves

id,1

iff,1

NBR1

RS1

RD1

NBR2

iff,2


Federal Funds Rate

Reserves

id,1

iff,1

NBR1

RS1

NBR2

iff,3

iff,2

RD1 (π1)

RD2 (π2)

Note the causal order in the creation of inflation before 2008. Nominal interest rates initially fall but as the economy heats up (presumably from the lower interest rates) inflation picks up leading to an increase in the nominal interest rate in the long run. In the short-run, nominal rates and inflation move in opposite directions. (Liquidity Effect) In the long-run, nominal interest rates and inflation move in the same direction. (Fisher Effect)


When nominal interest rates hit their floor (is zero interest the floor?) how does the Fed increase the money supply? Or more importantly inflation?

ZLB

Zero Lower Bound

Federal Funds Rate

Reserves

id,1

iff,1

NBR1

RS1

RD1

NBR2

iff,2

ZLB: Interest Paid on Bank Reserves

Federal Funds Rate

Reserves

id,1

ir = iff

NBR1

RS1

RD1

When the Fed pays interest on reserves held by banks, ir , it allows the Fed to control the “nominal interest rate floor”. The demand for bank reserves at interest rates below ir is zero, banks will just hold the reserves and collect the interest from the Fed. If the Fed wants to raise nominal rates economy-wide, they simply raise the rate paid on bank reserves. Competition among banks will do the rest.

Interest Paid on Bank Reserves

Interest Paid on Bank Reserves

Federal Funds Rate

Reserves

id,1

ir = iff

NBR1

RS1

RD1

The Neo-Fisher hypothesis was first proposed separately by John Cochrane and Stephen Williamson. The Neo-Fisher Hypothesis recognizes that when nominal interest rates are at ZLB, the traditional path to higher inflation will not work.

Higher Interest Rate → Higher Inflation?

When at the ZLB, increases in money will just be willingly held and the nominal interest rate will not go down any further. This is Keynes’ liquidity trap.


The first idea to deal with this situation was advocated by Michael Woodford. He suggested the Fed announce that they will keep interest rates very low for an extended time which should lead economic agents to rationally expect low real interest rates and encourage more spending and investment. So far, it hasn’t worked very well.


The failure of current Fed policy to create any significant inflation has led to the idea of the Neo-Fisher hypothesis. Since nominal interest rates and inflation are tied together in the long run, we should be able to increase one by increasing the other. Or so “the model” tells us.


The workhorse model for policy makers is the New-Keynesian model. The NK model has three important components: 1. NK AD - IS Equation 2. NK AS - Phillips curve 3. Taylor rule – Monetary Policy Rule This model is a dynamic simultaneous general equilibrium (DSGE) model.


The New Keynesian Model • The basic New Keynesian model with Calvo (sticky) price

setting simplifies to a system of three equations: 1. The New Keynesian Phillips curve relating inflation to the

output gap 2. A "Dynamic IS Equation" linking the evolution of

aggregate demand (and the output gap) to the nominal interest rate

3. A monetary-policy rule for setting the nominal interest rate (or, a money-supply rule plus a money-demand specification)

• These equations determine the nominal and real interest rate, inflation, and the output gap

The New Keynesian Model: The New Keynesian Phillips curve

The New Keynesian Phillips curve (NKPC) relates current inflation to expected future inflation and the output gap.

The New Keynesian Model: The Dynamic IS curve

Define the natural real interest rate rtn

as the real rate in the �flexible-price equilibrium. This interest rate is purely a function of real factors, i.e. productivity, preferences, etc., all of which is beyond the influence of the monetary authority.

This Dynamic IS equation relates the current output gap to (expected) future output gaps and the deviation of the current real interest rate from it’s natural value.

The New Keynesian Model: The Policy Rule

We can close the model by specifying an interest-rate rule for monetary policy.

The Taylor-rule equation results in a model in which the price level satisfies determinacy when the Taylor principle is applied, i.e. Φπ > 1 and Φy ≥ 0.


Output stabilization policy in the NK model depends on the ability of the central bank to manipulate the real interest rate. This is accomplished, theoretically, by targeting the nominal interest rate at a level that combined with the slow adjustment of inflation results in the desired real interest rate effect.


But when the nominal rate is already at its lower bound, this policy is stymied. Woodford’s idea was to generate higher expected inflation by keeping nominal rates low for a long time, thus keeping real rates low and presumably stimulating the economy.


But there is a well known relationship between real interest rates and consumption growth called the intertemporal substitution effect. So that low real interest rates lead to low consumption growth. This is the departure point for the Neo-Fisherians.


Higher real interest rates will lead to higher consumption growth which will lead to higher inflation. Create higher inflation by raising the real interest rate. Raise the real interest rate by raising the nominal rate.

The Traditional Hypothesis


Note that both ideas, Woodford’s extended low rate leading to higher expected inflation, and the Neo-Fisherian idea that raising the nominal rate will eventually lead to higher inflation, are both consistent with the NK model. So theory cannot guide us to the correct answer.


The traditional monetary transmission mechanism implies that higher trend inflation causes higher nominal interest rates. The Neo-Fisher hypothesis claims that raising nominal interest rates will cause higher trend inflation. Let’s look at the empirical evidence.

The long-run relationship between nominal interest rates and inflation is known as the Fisher relation. Economic theory and empirical evidence tell us that the real interest rate, rt, is stationary such that changes in it will eventually fade away over time returning it to its long-run equilibrium value.


Stationary Real Interest Rate

In the long-run nominal interest rates and inflation must move together in order to yield a stationary real rate. Because the nominal interest rate and inflation are non-stationary, some part of any change in them will be permanent. We say that the two series are co-integrated.


Nominal Interest Rate Co-integrated with Inflation


We will use the implication of co-integration between nominal interest rates and inflation to form the basis of our empirical analysis. If series are co-integrated they must have an error-correction model (ECM) representation.

The Fisher ECM

If nominal interest rates cause changes to inflation in the long run, then αi = 0 in the ECM. If inflation cause changes to nominal interest rates in the long run, then απ = 0 in the ECM.


The first step in the empirical analysis is to test for co-integration between the nominal interest rate and inflation. The Johansen (1991) method is used and is based on the ECM.


The test of the rank of the П matrix in the ECM is called the trace test. Since Xt = [it , πt]́ we test the null hypothesis H0: rank(П) = 0 versus the alternative Ha: rank(П) ≤ 1.

The Data

Three inflation series are considered: 1) CPI-All (INFL1) 2) PCE Deflator (INFL2) 3) PCE Deflator – Less food and energy (INFL3)

And two nominal interest rates: 1) Federal Funds rate 2) Three-month Treasury Bill rate

The Data

-4

0

4

8

12

16

20

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

INFL1 INFL2 INFL3TB3 FEDFUNDS

The Data

Because of the extraordinary Fed policy following the financial crisis in 2008, the estimation sample is January 1964 to December 2007.

Test for Co-integration and Estimates from the ECM

Fisher Pair INFL1-FF INFL1-TB3 INFL2-FF INFL2-TB3 INFL3-FF INFL3-TB3

Tracea 18.18 18.31 16.83 16.18 16.92 15.78

Q-stat b 17.19 27.67 19.54 28.41 18.16 27.77

0.229 -0.277 0.827 0.697 1.085 0.943

0.325 0.394 0.276 0.248 0.260 0.231

-0.021 -0.011 -0.032 -0.030 -0.038 -0.036

0.008 0.006 0.010 0.010 0.011 0.011

-0.009 -0.009 -0.004 -0.006 0.000 -0.000

0.006 0.004 0.004 0.005 0.003 0.004

a - 5% critical value is 15.49 b - 5% critical value is 36.42

Test for Co-integration and Estimates from the ECM


1.75 1.95 0.21 0.61 0.08 0.04

-0.031 -0.025 -0.034 -0.030 -0.038 -0.036

0.011 0.010 0.010 0.010 0.011 0.011

0.000 0.005 -0.003 -0.001 0.000 0.000

0.006 0.006 0.004 0.005 0.003 0.004

1.76 2.70 0.70 0.68 0.08 0.05

10.53 8.96 11.07 10.15 13.46 11.91

What about after 2008?

The data are stationary after 2007 so co-integration is no longer appropriate. So I use a VAR and test for Granger non-causality. 5% critical value is 21.03


Q-stat 9.27 24.89 10.94 21.86 7.56 12.95

37.62 28.12 33.78 24.06 25.81 29.03

14.52 18.00 15.28 18.16 21.07 16.24

Impulse Response Functions 2008 - 2014

-.2

-.1

.0

.1

.2

.3

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of FEDFUNDS to FEDFUNDS

-.2

-.1

.0

.1

.2

.3

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of FEDFUNDS to INFL1

-2

0

2

4

6

8

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of INFL1 to FEDFUNDS

-2

0

2

4

6

8

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of INFL1 to INFL1

Accumulated Response to Generalized One S.D. Innovations ± 2 S.E.

Conclusions

Prior to 2007, the empirical evidence supports the following: 1) Nominal interest rates and inflation are co-

integrated. 2) The equilibrium relationship is statistically

consistent with the Fisher relationship. 3) Inflation causes nominal interest rates in the long

run. 4) Nominal interest rates do not cause inflation in

the long run.

Conclusions

After 2008, the empirical evidence supports the following: 1) Nominal interest rates and inflation are not co-

integrated. 2) The equilibrium relationship is not statistically

consistent with the Fisher relationship. 3) Inflation does not cause nominal interest rates in

the short and long run. 4) Nominal interest rates cause inflation in the short

and long run.

Conclusions

Using U.S. data from 1964 – 2007 there is no evidence in favor of the Neo-Fisher hypothesis. Evidence over this sample supports traditional view. Using the small sample from 2008 – 2014 there is evidence that nominal interest rates cause inflation. So there is weak support for the Neo-Fisher hypothesis after 2008.

the neo-fisher hypothesis william j. crowder presentation.pdfthe neo-fisher hypothesis increasing...

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