Fisher Effect Under Deflation

8/3/2019 Fisher Effect Under Deflation

1/22Electronic copy available at: http://ssrn.com/abstract=1749062

THE FISHER EFFECT UNDER DEFLATIONARY

EXPECTATIONS

January 2011

David Glasner

Federal Trade Commission*[email protected]

Abstract: The response of nominal and real interest rates to expected deflation becomesproblematic when nominal interest rates fall toward zero while the expected rate of deflationis increasing. As nominal interest rates approach their lower bound, further increases inexpected deflation cannot cause the nominal rate to fall. Either the Fisher equation isviolated or the real rate must increase. One way for the real rate to rise is asset prices to fall.Regressions between 2003 and 2010 of the daily percentage change in the S&P 500 onthe TIPS spread measuring inflation expectations show little correlation between asset

prices and expected inflation from 2003 until early 2008. However, since early 2008 thecorrelation between changes in stock prices and in inflation expectations has been

strongly positive and statistically significant.

JEL Classification: E31, E43, E52, E63, F41

Key Words: Fisher Effect, Interest Rates, Nominal Interest Rates, Real Interest Rates,

Inflation, Deflation, Expectations, Asset Prices, Stock Prices, Monetary Policy, ExchangeRates, FOMC

* The views expressed in this paper do not necessarily reflect the views of the FederalTrade Commission or of individual Commissioners.
mailto:[email protected]:[email protected]:[email protected]


2/22Electronic copy available at: http://ssrn.com/abstract=1749062

THE FISHER EFFECT UNDER DEFLATIONARY EXPECTATIONS

I. Introduction

In most renditions, the Fisher equation relating the nominal interest rate to the real

rate and the expected rate of inflation is treated as if it followed necessarily from the axiom

of rationality, any violation of the Fisher equation becoming deeply problematic or

paradoxical. Of course, the Fisher equation, like the equation of exchange, is a mere

tautology, but it is usually interpreted in the light of the Fisherian theory of interest in which

the real rate of interest reflects real, not monetary, factors, so that the real rate of interest

should not, at least as a first approximation, be affected by monetary factors like a mere

change in the price level (Hirshleifer 1970). Gibsons Paradox, the observed correlation

between interest rates and price levels, is paradoxical precisely because, given the Fisherian

theory of interest, the Fisher equation seems to disallow it.

My objective in this paper is to explore another, less well known than Gibsons

Paradox, difficulty with the Fisher equation: the effect of deflationary expectations on

nominal and real interest rates. The adjustment of nominal and real interest rates to

expected deflation becomes problematic when nominal interest rates fall to the

neighborhood of zero at the same time that the expected rate of deflation increases. Because

the nominal rate of interest cannot fall any further should expected deflation increase, the

question arises, how can the Fisher equation hold when nominal rate of interest is at its

lower bound and the sum of the real rate and the expected rate of deflation is less than the

lower bound?1

1 I still recall when, during his graduate microtheory sequence, Jack Hirshleifer, whoresurrected the once neglected Firsherian theory of capital, interest, and investment, showinghow it could be applied to solve the problem of the optimal investment decision by firms(Hirshleifer 1958), discussed the Fisher equation, deriving it directly from the definition of


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Because the nominal rate of interest cannot fall below its lower bound (whether zero

or some positive number), for expected rates of deflation above some threshold, the Fisher

equation can be satisfied only by sadjustment in the real rate of interest. It may be

instructive to spell out the process by which the real rate of interest would adjust to an

expected rate of deflation above the real rate. Because the expected yield from holding

money would exceed the expected yield on any real asset or combination of real assets (i.e.,

any feasible real investment project), asset markets could not achieve equilibrium. Asset

prices would have to fall -- more likely, crash -- with asset holders vainly seeking to liquidate

their positions at current prices. Thus, during a disequilibrium involving inconsistent

expectations, the Fisher equation, having no economically feasible solution, becomes an

inequality. The Fisher equation is therefore a special case of a more general relation:

I= r+pee for i> 0 and

i r+pee for i = 0,

where iis the nominal rate of interest, rthe real rate of interest, andpee is the expected rate of

inflation.

A sufficiently large reduction in asset values could drive down the expected rate of

deflation below the real rate of interest. However, the very process that destroys asset values

the rate of interest as an intertemporal rate of exchange between present and futureconsumption. Since price level changes in one time period relative to another do not alterthe terms of intertemporal substitution determined by real factors, the real rate of interestmust be invariant to expected changes in the price level. That was all there was to the Fisher

equation. I raised my hand and asked how the Fisher equation would hold if expectedinflation exceeded the real rate of interest. Hirshleifers response, as I recall, was that he hadnever considered that contingency and would have to give it further thought. I neverfollowed up with him, but some later time, I found the question discussed in, I believe, oneof Harry Johnsons innumerable publications which I can no longer locate. The upshot ofJohnsons discussion, which still seems to me to be essentially correct, is that an increase inexpected deflation would cause investment to stop until the capital stock fell enough for thereal rate of interest to rise to match the expected rate of deflation.


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might well drive both the real rate and expected deflation further away from, not toward,

each other -- further away from, not toward, a new equilibrium. Such perverse dynamics

may characterize the panics and financial crises with which crashes in asset prices are

associated. In such situations, establishing an exogenous commitment to stabilizing asset

prices may be an essential condition for restoring asset market equilibrium.

A key problem for any explanation ofGibsons Paradox is how to make inferences

about the rate of expected inflation or deflation. The most successful study, that of Barsky

and Summers (1988), explained Gibsons Paradox by positing that, since the price level was

roughly constant under the classical gold standard from 1870 to 1913, the expected rate of

inflation could be taken to be roughly zero, so fluctuations in the nominal interest rate

corresponded to changes in the real rate of interest. Because gold is a durable commodity

demanded and willingly held by non-monetary users, its real value is sensitive, and inversely

related, to the real rate of interest. But under the gold standard, the real value of gold is

simply the inverse of the price level, so Gibsons Paradox follows directly from the

assumption that expected inflation is zero under the gold standard.

Because expected inflation is not directly observable, empirical studies of

Gibsons Paradox have had to rely on independently untestable assumptions about

inflation expectations and how they are formed. However, since 2003, when the US

Treasury began to issue inflation-indexed (TIPS) bonds, market data on both real interest

rates and expected inflation (TIPS spreads) have become available, providing a way to

observe the actual interaction of real and nominal interest rates with inflation

expectations. Inasmuch as prices generally, by most measures, were actually falling

during the financial crisis of 2008, while short- to medium-term inflation expectations (as

measured by TIPS spreads) turned negative or deflationary during the crisis, it is feasible


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to study the interaction of inflation expectations with asset prices to determine whether

the market dynamics implied by the Fisher equation when nominal interest rates are at or

near their lower bound were actually observed.2

In the following section I outline the basic theory of asset pricing on which my

empirical analysis is based. According to the basic theory, expected inflation, at least at

low or moderate levels, should have at most a weakly positive relationship to asset prices.

Similarly, real interest rates have an ambiguous relationship with asset prices, depending

on which underlying factors happen to be causing interest rates to change. Thus, in

normal periods, one would not expect to observe a strong correlation between either real

interest rates or inflation expectations and asset prices. In section 3, I show the results of

regressions between 2003 and 2010 testing the hypothesis that the normal weak or non-

existent relationship between real interest rates or inflation expectations on the one hand

and asset prices on the other is observed. I find that between 2003 and 2007 there was

little evidence of any correlation between the daily change in either real interest rates or

inflation expectations and the daily change in the S&P 500. Since 2008, however, the

relationship between the daily change in the S&P 500 and both real interest rates and

inflation expectations has been strongly positive. I interpret the increased correlation

between inflation expectations and stock prices since the financial crisis to mean that the

crisis and the recovery are evidence of a reverse Fisher effect in which the ex ante return

on holding real capital has been less or only marginally greater than the return on holding

money. In this environment increases in inflation expectations have generally been

2 In fact, even if expected inflation is positive, the perverse dynamics occasioned whenexpected deflation exceeds the real rate can arise as well if the expected yield on capital isnegative and exceeds (in absolute value) expected inflation.


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markedly favorable to stock prices and have been the strongest indicator of a future

rebound in economic activity.

II. Asset Prices, Inflation Expectations, and Real Interest Rates

Asset values reflect expectations of the future. The basic theory of finance tells us

that asset values represent the expected future cash or service flows from those assets

appropriately discounted to the present. If, for simplicity, we take the market portfolio of

assets as a benchmark, changes in the value of that portfolio correspond either to changes in

the size or pattern of expected future cash flows, highly though not perfectly correlated with

the expected aggregate future output of the economy, or in the rates at which those future

flows are discounted to the present.

In this simple model, expected inflation ought to occasion precisely offsetting effects

on expected cash flows and (via the Fisher effect) on rates of discount, leaving present

values, and hence asset prices, unchanged. Because unanticipated inflation can have no

immediate effect on asset prices, though it might well affect them over the course of an

inflationary episode, our concern in this study is only with expected inflation. However, by

raising the nominal rate of interest, the opportunity cost of holding money, expected

inflation may exert an indirect effect on asset values, by reducing the quantity of money

demanded (at least that portion of the quantity of money not bearing competitively

determined interest), the consequent shift from holding money into holding real assets

causing a once and for all increase in the price level thereby raising asset prices (via increases

in expected future cash flows). A reduction in expected inflation would of course have the

opposite effect, reducing asset prices. These effects are well known, having been recognized

at least since the early 1960s in the literature on inflation and growth, which held that a shift

from money into real assets caused by inflation would encourage real capital accumulation


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and stimulate growth. Failing to distinguish either between inside and outside money, or

between interest-bearing and non-interest-bearing money, the inflation and growth literature

overstated the growth-enhancing effect of inflation. However, unless all money balances

yield competitive interest, expected inflation must, at least directionally, have some positive

effect on asset prices. The literature also implicitly assumed that holding money provides no

real service flow to money holders, raising the obvious question why anyone would be

willing to bear the opportunity costs of holding real cash balances in the first place. Without

assuming the real services generated by holding money out of existence, the literature could

not have arrived at the unambiguous conclusion that increasing inflation necessarily

increases growth.

Under normal conditions (i.e., when the nominal rate is not too close to its lower

bound, so that the real rate of interest exceeds the expected rate of deflation by more than a

trivial amount3), the effect on asset prices of a change in inflation expectations inducing a

shift from cash into real assets would not be very large, inasmuch as the shift would involve

only a rebalancing at the margin in the proportions of money and real assets in asset

portfolios. The extent of the rebalancing is given by the interest-elasticity of demand for the

non-interest-bearing portion of the cash holdings of the public. However, as noted above,

there are also plausible theoretical reasons to believe that expected inflation, even if the

above argument were unassailable, could tend to depress asset prices. Moreover, the

direction of the overall effect might well depend on the amount of expected inflation.

3 The real interest rate need not always be positive. If the real interest rate is negative, thenthe condition for avoiding a reverse Fisher effect is that the rate of expected inflation exceedthe real rate of interest. In other words, if the real rate is negative two percent, inflationmust be greater than two percent in order to avoid asset market disequilibrium and a flightfrom real assets into money, generating a crash in asset prices.


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Thus, although theoretically there is some basis for a conjecture that expected

inflation, under normal conditions, would tend to raise asset values, the effect, if it exists at

all, seems modest, and arguments are not lacking for why inflation would tend to reduce

asset prices, especially as the rate of inflation increases. However, under abnormal

conditions, when the ex ante real rate of interest is less than the expected rate of deflation, a

flight from real assets into cash implies a strong positive relationship between expected

inflation and asset prices.

Thus, in periods in which expected deflation exceeds the real rate of interest, one

would expect to observe at most a weekly positive correlation between between changes in

expected inflation and asset prices. However, in periods in which expected deflation was

less than the real rate of interest, the observed relationship between expected inflation and

asset prices ought to be strongly positive.

Under normal conditions, the relationship between asset prices and real interest rates

is as ambiguous as that between asset prices and expected inflation. Real interest rates

themselves respond to underlying fundamental causes. Real interest rates might, for

example, change because of expectations of increasing technological progress and future

economic growth. Those expectations would tend raise real interest rates, but they would

also tend to raise expectations of future cash flows. Under that scenario, it is likely that one

would observe rising asset prices along with rising real interest rates. However, if real

interest rate were caused by an increasing demand for present as opposed to future

consumption without any change in expected future technological progress, the rise in real

interest rates would likely be accompanied by falling asset prices. There is therefore no

strong theoretical basis for expecting that real interest rates would be either positively or

negatively correlated with asset values.


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Given the availability of market-generated data on inflation expectations since 2003

when the US Treasury began selling inflation adjusted bonds, it is possible to compare

market-based data on inflation expectations and real interest rates and to determine whether

there have been any periods in which expected deflation exceeded the real interest rate.

However, the real interest rate implied by the TIPS spread is not necessarily the relevant real

interest rate for our purposes. Nominal interest rates may reflect a liquidity premium,

especially in periods of crisis. In such situations, even though the real interest rate

corresponding to the ex ante rate of return on investment is likely to be negative even, the

nominal rate of interest rate may be, at least for a short period of time, well above zero.

Thus, even though market data on inflation expectations are now available, the relevant ex

ante real interest rate is not directly observable.

III. Expected Inflation and Asset Prices from 2003 to 2010.

I shall now examine the data on stock prices (as measured by the S&P 500) which

stand as a proxy for asset prices in general and their relationship to expected inflation and

real interest rates during the period from 2003 to 2010 for which real interest rates can be

inferred from the yield on TIPS securities and inflation expectations from the TIPS spread.

For real interest rates, I rely on the yields on 10-year constant maturity TIPS and for

inflation expectations I rely on the TIPS spreads between constant maturity 10-year

Treasuries and the corresponding constant maturity 10-year TIPS bonds as reported daily by

the St. Louis Federal Reserve Bank. TIPS securities at 5- and 10-year maturities became

available in January 2, 2003, the initial point of the data set with which I have been working.

TIPS securities of other maturities have since been issued, while inflation expectations over

time horizons shorter than 5 years may be empirically relevant in some time periods,

especially during the financial panic in the autumn of 2008, the meaning of TIPS yields and


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spreads during the crisis became doubtful during the crisis, because the yields on TIPS

bonds seem to have been spiked as the liquidity premia attaching to conventional Treasuries

during the crisis also increased, thus overstating the implied increase in deflation

expectations represented by the TIPS spread. Longer term TIPS Treasuries seem to have

been less subject to the liquidity effect than shorter term TIPS Treasuries, so that there is

less distortion in the yields on TIPS bonds and TIPS spreads at 10-year maturities than on

TIPS bonds and TIPS spreads at shorter maturities.

For observations since September 2005 I have also gathered data on the two-year

inflation expectations inferred from TIPS spreads as reported on the Bloomberg website.

Regressions on observations from October 2008 through January 2009 using the shorter

term using the shorter term TIPS yields and spreads lead to anomalous coefficient estimates

which tend to confirm that the shorter TIPS yields and spreads overstate real interest rates

and deflationary expectations as a result of liquidity premia on conventional Treasuries.

As an additional indicator of inflationary or deflationary expectations, I also used the

dollar/euro exchange rate inasmuch as many investment portfolios include both dollar and

euro assets with the relative proportions of dollars and euros depending on expectations of

future movements in the dollar/euro exchange rate, movements reflecting expectations of

relative future rates of inflation in terms of dollars and euros. Furthermore, the dollar/euro

exchange rate may, under certain conditions, also reflect expectations about future monetary

policy, as I will suggest in the discussion of the empirical results.4

4 I also estimated regressions with both the trade weighted foreign exchange value of thedollar and the Dow Jones/UBS commodity price index as supplementary indicators ofinflation expectations. The trade-weighted value of the dollar had little or no explanatoryvalue, suggesting that if the dollar/euro exchange rate had explanatory power it was becauseit was associated with the substitution of dollars for euros in individual or corporateportfolios. Although regressions with the DJUBS commodity index as an independent


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Figure 1 plots the natural log of the S&P 500 from the beginning of 2003 until the

end of 2010 along with the yield on the 10-year TIPS bond, 10-year TIPS spread, and the

dollar/euro exchange rate over the same period. The time period is divided almost at the

midpoint in March 2007, the housing bubble having peaked in the first quarter of 2007, and

the broader financial implications of the failure of housing prices to continue rising

becoming increasingly apparent. I divide the first and second periods into subperiods

reflecting my subjective impressions of more or less important events that may have been

economically significant. The sub-periods are enumerated in Table 1.

variable had higher R-squares and positive and significant coefficients for the variable, themeaning of a regression with commodity prices as an independent variable explainingmovements in the S&P 500 as a proxy for movements in asset prices in general isquestionable insamuch as commodities are also held as assets.


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TABLE 1

Period Beginning Ending Characteristics

1a Jan-03 Jun-03 weak recovery, high uncertainty about start of Iraq War

1b Jun-03 Jun-04Fed Funds cut to 1 percent, recovery strengthens,housing bubble begins

1c Jul-04 Oct-06Fed Funds rate gradually riased to 5.25 percent, housingbubble gains momentum, recovery continues

1d Oct-06 Mar-07 peak of housing bubble, first signs of financial stress

2a Mar-07 Aug-07 bursting of bubble, increasing financial stress

2b Aug-07 Mar-08increasing financial turbulence, start of recession, failureof Bear Stearns

2c Mar-08 Sep-08 deepening recession, rapidly rising food and oil prices

2d Sep-08 Mar-09 financial crisis, deflation, asset price collapse

2e Mar-09 Apr-10 QE1, bottom of recession, beginnings of recovery

2f Apr-10 Aug-10 Greek debt crisis, weakening euro, weakening recovery

2g Sep-10 Dec-10 QE2, strengthening recovery


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Although there is no obvious line of demarcation between the two periods, the

housing bubble bursting in the first quarter of 2007, with no major sell-off in stocks till

August 2007, and stocks staging a recovery and reaching their all-time high in October 2007

after the Fed to cut its discount rate in August and then the Fed Funds rate in September in

response to the August dip in stock prices. As is evident in the Table 2 in which I present

regression results, the March to August period emerges from the data as a transitional

period, and could have been assigned about as plausibly to period 1 as to period 2.

The discussion in the previous section implies that under normal conditions there

should be little or no correlation between asset prices and either real interest rates or

inflation expectations. However, if asset prices are falling because the expected yield from

holding cash -- the expected rate of deflation -- exceeds the expected yield from holding real

capital assets, the ex ante real rate of interest, so that asset holders are all attempting to shift

from real assets into cash, then we should observe a strong positive correlation between

asset prices and both inflation expectations and ex ante real interest rates. The same

correlation would presumably also hold in the post-crash recovery period in which asset

prices rise from the low levels reached during the crisis.

To test this theory of asset pricing during asset price crashes and recoveries, I posit a

simple econometric model with the natural log of the S&P 500 as the dependent variable,

and the yield on the 10-year constant maturity TIPS (a proxy for the real interest rate), the

constant maturity 10-year TIPS spread (a proxy for inflation expectations) and the

dollar/euro spot exchange rate (reflecting relative inflation expectations in terms of the

dollar and its closest substitute currency) as the independent variables. I estimated

regressions for the entire sample period and for the periods before and after the end of the

housing bubble and for the various sub-periods listed in Table 1. For each period, I


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estimated a regression in terms of levels and in terms of first differences.5 The results for

the level regressions are reported in Table 2, but being unable to attach any economic

meaning to those results, I shall discuss only the results for first differences in the remainder

of the paper.

5 In the level equations a constant term was always included and was always significantlydifferent from zero. For first differences, I report results with the constant term suppressedinasmuch as in most cases the estimated constant term was insignificantly different fromzero and R-squares were higher for regressions in which the constant term was suppressed.Differences in estimated coefficients with and without the constant terms were slight and inno case did the significance of an estimated coefficient at the 95-percent confidence leveldepend on whether the constant term was suppressed.


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TABLE 2

TimePeriod Beginning Ending

Levels or

FirstDifferences

TIPS

coefficient(standarderror)

TIPS spread


$/euro


R2

Jan-03 Dec-10 Levels137.77(5.629)

256.683(5.156)

1049.756(28.438)

0.673

FirstDifferences

.06(.005)

.107(.007)

.234(.043)

0.153

1 Jan-03 Mar-07 Levels189.03(8.326)

98.494(11.888)

1689.921(56.488)

0.735

FirstDifferences

.022(.006)

.016(.009)

-0.043(0.044)

0.023

2 Mar-07 Dec-10 Levels144.672(7.183)

340.098(7.913)

201.845(65.319)

0.731

FirstDifferences

.078(.007)

.138(.011)

.312(.07)

0.226

1a Jan-03 Jun-03 Levels14.614(16.861

-369.359(31.202)

252.572(121.809)

0.853

FirstDifferences

.119(.022)

.091(.032)

-.211(.186)

0.288

1b Jun-03 Jun-04 Levels-31.497(7.708)

106.474(7.039)

654.417(41.171)

0.851

FirstDifferences

-.001(.009)

.023(.014)

.014(.073)

0.014

1c Jul-04 Oct-06 Levels138.711

(7.986)

27.422

(23.396)

-8.988

(58.86)0.417

FirstDifferences

.009(.007)

-.008(.012)

.022(.053)

0.003


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TimePeriod

Beginning EndingLevels or

FirstDifferences

TIPScoefficient(standard

error)

TIPS spreadcoefficient(standard

error)

$/eurocoefficient(standard

error)

R2

1d Oct-06 Mar-07 Levels 210.733(15.98)

105.877(35.004)

1468.454(79.007)

0.792

FirstDifferences

.04(.018)

.004(.31)

.168(.176)

0.048

2a Mar-07 Aug-07 Levels132.384(12.553)

254.306(43.809)

1508.745(218.912)

0.676

FirstDifferences

.059(.021)

0.078(.05)

.386(.262)

0.101

2b Aug-07 Mar-08 Levels295.309(13.913)

-17.696(48.231)

2117.36(216.471)

0.87

FirstDifferences

.093(.013)

.051(.042)

.145(.195)

0.276

2c Mar-08 Sep-08 Levels-25.868(23.363)

5.534(50.938)

567.031(256.031)

0.132

FirstDifferences

.108(.015)

.114(.029)

-.521(.148)

0.404

2d Sep-08 Mar-09 Levels95.669

(11.489)119.865(11.367)

2023.115(117.559)

0.809

FirstDifferences

.14(.028)

.195(.035)

.393(.243)

0.28

2e Mar-09 Apr-10 Levels-44.797(16.079)

282.392(9.606)

196.888(75.232)

0.827

First

Differences

.015

(.011)

.093

(.015)

.42

(.098)

0.206

2f Apr-10 Dec-10 Levels3.518

(12.089)167.662(8.788)

734.154(83.658)

0.854

FirstDifferences

.036(.012)

.148(.017)

.524(.099)

0.476


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Although the level regressions appear uninformative, the first-difference regressions

tell a clear story, supporting my conjecture that as the sum of the ex ante real interest rate

plus expected inflation falls toward zero, asset prices become highly sensitive to changes in

inflation expectations and in real interest rates. For period 1 as a whole, the coefficient of

the TIPS spread variable, .006, is insignificantly different from zero, and the R-squared of

the regression is only .023. Moreover, the only sub-period of period 1 in which the

coefficient estimate of the TIPS spread variable was significantly positive (.119) was sub-

period 1a (January to June 2003). In that sub-period, the recovery from the 2001 recession

was still faltering with expectations of inflation very low and, in the aftermath of the

September 11 attacks with a US invasion of Iraq on the verge of starting, uncertainty very

high. Thus, sub-period 1a, more than any other sub-period of period 1, resembles period 2,

characterized also by low inflation expectations, high uncertainty and unfavorable profit

expectations. The coefficient of the TIPS spread variable in period 2 was .138, the t-value

implying significance even at a 99.9 percent level.

Of the six sub-periods of period 2, only in the first two, 2a and 2b, was the estimated

coefficient of the TIPS spread not significantly positive at the 95-percent level. In the last

four periods, 2c-2f, the estimated coefficient is not less that .093, and, in period 2d, the

period of the financial crisis, as high as .195. These coefficients tell us that a 100 basis point

change in the expected rate of average inflation over a 10-year time horizon (say, from 0

percent annually to 1 percent) was associated with a change in the same direction in the S&P

500 between 9.3 and 19.5 percent. Only in period 2a is the R-squared less than .2, and for

period 2 as a whole the R-squared is .226.

Moreover, the coefficients of the TIPS variable estimated for period 2 as a whole,

and for four of its six sub-periods, were significantly positive. However, the conceptually


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relevant real rate of interest is the ex ante real rate reflecting the state of business confidence

and expectations of profitability. The real rate reflected in TIPS bonds, especially at shorter

maturities, is also influenced by current monetary policy and expectations about future

monetary policy, causing the interest rate on TIPS to diverge from the unobservable ex ante

real rate. The choice of a 10-year maturity was, in part, dictated by an attempt to minimize

the influence of short-term monetary conditions on the real rate.

In period 1, only in sub-period 1a was the estimated coefficient of the TIPS variable

significantly positive. In the other three sub-periods the estimated coefficient was

insignificantly different from zero. In period 2, the estimated coefficients of the TIPS

variable were significantly positive in all but one (2f) of the sub-periods. This suggests that

changes in real interest rates in period 2 reflected changes in expectations of profitability and

future cash flows, so that changes in real interest rates were positively related to asset values,

as opposed to periods of more stable expectations of future profitability (sub-periods 1b-1d)

when changes in real interest rates were not correlated with changes in asset values. If so,

the expressed rationale for the Feds quantitative easing policy(Bernanke 2010), namely to

reduce long term interest rates and stimulating spending on investment and consumption,

reflects a misapprehension of the mechanism by which the policy operates, increasing

expectations of inflation and future profitability and, hence, of the cash flows derived from

real assets, increasing asset values along with both with inflation expectations and real

interest rates. Rather than a policy to reduce interest rates, quantitative easing appears rather

a policy for increasing interest rates, though only as a byproduct of increasing expected

future prices and cash flows.

A few comments are also in order about the dollar/euro variable, whose coefficient

estimates differs systematically different in periods 1 and 2: insignificantly negative in period


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1 and strongly positive in period 2. The estimated value of the coefficient for period 2 as a

whole, .312, says that a 1 percent change in the $/euro exchange rate was associated with a

change in the S&P 500 of .31 percent. One way to interpret the result is that a fall in the

dollar relative to the euro reduced the incentive to hold dollars and thus reduced the

incentive to sell real assets in order to hold dollars. Perhaps another way to interpret the

result is that an appreciating dollar may have reflected a tightening money market and a

difficulty in obtaining dollars to meet liquidity needs. This was particularly true in the fall

and winter 2008 financial crisis during which the dollar appreciated sharply as firms and

individuals struggled to obtain cash to meet their obligations, obliging asset sales in order to

raise the needed cash.

One particular estimate of the coefficient of the $/euro variable requires special

attention. The estimated coefficient of the $/euro exchange rate variable in period 2c is

-0.521. In absolute value this is the highest estimated coefficient of the $/euro exchange rate

of any sub-period in the entire sample. In only two other sub-periods (1a and 1b), was the

estimated coefficient of this variable negative, and in neither case was the estimated

coefficient significant at a 95 percent confidence level. For sub-period 2c, however, the t-

value for the coefficient in sub-period 2c is over 3. The result seems extremely anomalous,

but it appears to me that the result reflects a unique set of conditions that prevailed during

sub-period 2c. The recession that began in December 2007 was rapidly worsening, especially

during period 2c when real GDP was falling at a 4 percent annual rate and the

unemployment rate was climbing rapidly. Despite the deterioration in the economy during

sub-period 2c, the Fed, showing more concern about inflation, because of rapidly rising food

and energy prices, than recession, fearing that a rapid rise in headline inflation would cause

inflation expectations to start rising uncontrollably. The minutes of the Federal Open


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Market Committee in June, August and even September 16 (two days after the failure of

Lehman!) 2008 show that the Fed repeatedly refused to reduce interest rates to bolster a

weakening economy. In this strange economic and policy environment, the public could

well have assumed that any weakening in the dollar relative to the euro would reduce the

likelihood that the Fed would ease monetary policy, implying a further downward revision in

expected future cash flows and a further reduction in asset values.

IV. Conclusion

My results point to two important conclusions. First, and most obviously, sharp

downturns in asset prices are associated with deflationary expectations when ex ante real

interest rates are low. Thus if recessions are associated with falling real interest rates owing

to falling profit expectations, and if the expected rate of inflation falls below the possibly

negative real rate of interest, monetary attempts to reduce inflation may trigger a crash in

asset prices, and, in a highly leveraged economy, precipitate a financial crisis. Second, the

key to a recovery in asset prices is to raise inflation expectations above the real rate of

interest so that asset holders will be willing to shift out of holding cash into real assets.

This is not to say that inflation is always desirable. Indeed, the argument for

inflation depends on a very low, or negative, real rate of interest which seems to be an

exceptional circumstance. Moreover, my results also suggest that the danger of deflation,

which has led monetary authorities to generally aim at a low, and steady, rate of inflation, is

misplaced for two reasons. First, deflation is dangerous only in an environment of low real

interest rates, but in an environment of rapid growth and high real interest rates, mild

deflation poses little, if any, downside risk, while rapid monetary expansion to keep inflation

positive despite rapid economic growth may itself be destabilizing, though this of course is a

highly controversial issue. Second, seeking to stabilize the rate of inflation regardless of


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economic conditions can be highly destabilizing in the presence of adverse supply shocks.

Adverse supply shocks cause real output to fall, depressing profit expectations and reducing

real interest rates even as inflation expectations are increasing. A monetary policy that aims

at keeping inflation and inflation expectations constant during an adverse supply shock can

drive down profit expectations and real interest rates even further, starving the economy of

liquidity in the process.

The highly negative coefficient on the dollar/euro exchange rate variable in period

2c, spanning the six months before the financial crisis, supports the notion that transactors

were basing their expectations of the Feds policy on the assumption that the Fed was trying

to stabilize both inflation and inflation expectations. Thus, the dollar/euro exchange rate

became an indicator of future monetary policy so that any appreciation of the dollar signaled

that monetary policy would be eased, causing asset prices to rise, while a depreciation of the

dollar signaled the opposite. It was not until well after the financial crisis began in

September 2008, when inflation and inflation expectations were rapidly falling, that the Fed

shifted its policy enough so that transactors stopped using the dollar/euro exchange rate as

an indicator of the Feds future policy stance.


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REFERENCES

Barsky, R. B. and L. H. Summers. 1988. Gibsons Paradox and the Gold Standard.

Journal of Political Economy. 96(3):528-50.

Bernanke, B. 2010. Monetary Policy Objectives and Tools in a Low-Inflation

Environment.

http://www.federalreserve.gov/newsevents/speech/bernanke20101015a.htm

Hirshleifer, J. 1958. On the Theory of Optimal Investment Decision.Journal of Political

Economy. 66(4):329-52.

Hirshleifer, J. 1970. Investment, Interest, and Capital. Upper Saddle River, NJ: Prentice-Hall.
http://www.federalreserve.gov/newsevents/speech/bernanke20101015a.htmhttp://www.federalreserve.gov/newsevents/speech/bernanke20101015a.htmhttp://www.federalreserve.gov/newsevents/speech/bernanke20101015a.htm

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Fisher Effect Under Deflation