The High Price of Low Interest Rates

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The High Price of Low Interest Rates:An Empirical Investigation of the Claim that Too Low Interest Rates

Contributed to the Current Financial Crisis

By

Lindsey A. Shelley

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

Submitted in partial fulfillmentof the requirements for

Honors in the Department of Economics

UNION COLLEGE

June, 2009


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Abstract

SHELLEY, LINDSEY: The High Price of Low Interest Rates: An Empirical Investigation ofthe Claim that Too Low Interest Rates Contributed to the Current Financial Crisis.Department of Economics, June 2009

ADVISOR: Eshragh Motahar

Over the past two years, the economy of the United States has plunged into dismal

territory. What started as a burst in the U.S. housing bubble has set off economic avalanches

across the global economy. But how did we get here in the first place? The standard explanation

for any financial crisis is a period of excess, in this case: monetary excess associated with low

interest rates. This crisis is no different, but how do we quantify what is too low?

The econometric model in this study is similar to the one used by Judd and Rudebusch

(1998), which is a Taylor-type reaction function that describes the changes in the U.S. Federal

Funds rate to CPI and the output gap in the current period and the Funds rate, change in Funds

rate, and output gap from the previous period.

We estimate the model for the Funds rate from 1981 to 1989 to determine the parameters

of a good monetary policy rule. Using the policy mistake framework from Taylor (1999), we

calculate the prescribed Fed behavior for the first half of the 2000s, when many have claimed

that interest rates were kept too low for too long.

We find strong empirical evidence from both our model and Taylors original model that

interest rates during the post-sample period were much lower and remained at low levels for

longer than either rule would have prescribed. We conclude that interest rates were too low in

a systematic way and provide quantitative evidence that monetary excess contributed to the

current financial crisis.


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Acknowledgements

I dont get no respect

Rodney Dangerfield

It is my pleasure to thank the people who made this thesis possible.

I cannot overstate my gratitude to my advisor, Professor Eshragh Motahar. This thesis would nothave been possible without his tireless enthusiasm, stimulating questions, and careful direction.From his willingness to schedule meetings late in the evening to replying to my many emails andmaking weekend office visits, his dedication was second to none. Over the past three years, hehas provided guidance, advice, and great company, but most importantly, I credit him for helpingme find my passion for macroeconomics. For this, I am especially grateful.

I thank Tricia Linden, my partner in crime, for helping me get through the difficult times, and forall the endless entertainment and camaraderie she provided.

Lastly, and most importantly, I am forever indebted to my parents. It is only because of theirunconditional support and encouragement that I have been able to pursue the wonderfulopportunities that have crossed my path. I thank them for allowing me to live a life that is oneadventure after another.


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Table of Contents

Abstract......................................................................................................................................i

Acknowledgements .................................................................................................................. ii

Introduction ..............................................................................................................................1

Chapter 2: Recent Economic History and Interest Rate Reaction Functions ........................5

2.1 Economic History..............................................................................................................5

2.2 Rules vs. Discretion...........................................................................................................7

2.3 John Taylors Original Rule ............................................................................................10

2.4 Econometric Literature....................................................................................................11

Chapter 3: Econometric Model and Rationale for Sample Period .......................................14

3.1 Econometric Model......................................................................................................... 14

3.2 Rationale for sample period.............................................................................................17

3.3 Data ................................................................................................................................19

Chapter 4: Analysis of the Results of the Econometric Model and Rationale for the Post-

Sample Period .........................................................................................................................21

4.1 Regression Estimation.....................................................................................................21

4.2 Rationale for post-sample period .....................................................................................24

4.3 Calculating prescribed policy action................................................................................26

4.4 Contribution to current financial crisis.............................................................................28

Chapter 5: Conclusions...........................................................................................................31

References ...............................................................................................................................33


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Tables and Figures

Tables

Table 3.1: Descriptive Statistics ................................................................................................20

Table 4.1: Determinants of Change of the Fed Funds rate..........................................................22

Table 4.2: Individual Components of Each Coefficient .............................................................22

Figures

Figure 3.1: The Misery Index....................................................................................................18

Figure 3.2: Rate of Growth of the Money Supply......................................................................19

Figure 4.3: Real Federal Funds Rate..........................................................................................24

Figure 4.4: Money Supply.........................................................................................................25

Figure 4.5: Rate of Growth of the Money Supply (post-sample)................................................25

Figure 4.6: Comparison of Prescribed Funds Rates and Actual Effective Funds Rates...............26

Figure 4.7: Magnitude of the Deviation from Actual to Prescribed Fed Funds Rates ................. 27

Figure 4.8: Case-Shiller Home Price Index................................................................................29

Figure 4.9: Price-to-Income Ratio .............................................................................................29


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Introduction

Over the past two years, the economy of the United States has plunged into dismal

territory. What started as a burst in the U.S. housing bubble has set off economic avalanches

across the global economy. Crumbling house prices and related securities have forced a

bailout and consolidations in the U.S. banking industry, collapsing the values of stock indices

and destroying the wealth of the man on the street. But how did we get here in the first place?

Beginning in the early 2000s, the property markets were growing fast, interest rates

were low, and mortgage brokers began to relax lending standards. Low interest rates and lax

lending conditions established a climate where applicants were given loans that were unfit

for their economic situations. Credit was easy and to keep the initial monthly payments

affordable to these subprime borrowers, the lending industry marketed a range of

unconventional mortgage products. These included: loans that required no down payment or

documentation of income, interest-only monthly payments; and adjustable rate mortgages

(ARMs) with low introductory teaser rates below the market interest rate which would

reset to market rates after a predetermined period. For credit-stricken subprime borrowers

who wanted to buy and flip houses in a short period of time, this was a great way to obtain

cheap financing.

Many people, such as members of the Fed, foresaw this problem, but Greenspan was

unsympathetic to their concerns, citing that the benefits of broadened home ownership are

worth the risk (Friedman, 2008). Both President Clinton and Alan Greenspan argued that

the increase in home ownership across the U.S. was a positive development and Greenspan

rejected opportunities to regulate these practices. Without regulation, there was no incentive

for mortgage brokers to curb their practices. Brokers packaged these loans into complex


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investment vehicles and sold them off to financial institutions and other investors, freeing up

more cash for loans and generating commissions.

The increase in these lending practices, coupled with inflating house prices, led to a

building boom and surplus of houses on the market, which eventually put downward pressure

on house prices. The decline in the housing market set off a chain reaction through the

lending system and the economy as a whole. Once house prices began to decline, individuals

and investors riding the upward trend in the housing market could no longer flip their homes

for a quick profit. Borrowers who were practically unable to repay their mortgages during the

best of times found themselves unable to make the higher monthly payments once the ARMsreadjusted upwards. Unable to sell, make payments, or refinance, the defaults began to

skyrocket.

Once the value of mortgage-backed securities began to tumble, institutional investors

faced huge erosions in the value of their balance sheets. These massive losses caused many

banks to tighten their lending requirements and caused a crisis in the credit markets. This,

coupled with the massive deleveraging of the U.S. banking industry exacerbated a liquidity

crisis. What was once such a great deal has caused damage that will surely get worse before

it gets better.

Who is to blame for the current financial crisis? Fingers have been pointed in

numerous directions: the repeal of the Glass-Steagall Act in 1999; Greenspans distaste for

market regulation; the general disregard of the simple know your customer principle of

investing; high savings rates in other countries; and overly expansionary monetary policy.

The standard explanation for any financial crisis is a period of excess, in this case: monetary

excess associated with low interest rates. When interest rates are low, people invest in


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projects that would not be profitable at higher costs to borrow resulting in a boom and

inevitable bust. A number of economists, namely John Taylor, Benjamin Friedman, and Axel

Leijonhufvud have claimed that monetary excesses were the main cause of the boom, the

Feds actions were excessively expansionary, and these conditions were caused by interest

rates that were kept far too low for too long (Taylor, 2009, 1; Friedman, 2008, 6;

Leijonhufvud, 2009, 2). But what these noted economists do not explain is: how do we

quantify what is too low? The focus of this study is to empirically test the claim that too

low interest rates contributed to the current financial crisis.

In Chapter 2, we define the context of the problem and present a brief overview of theeconomic history leading up to the current crisis, paying close attention to how monetary

policy has changed throughout the Feds history. We give a brief overview of the rules versus

discretion debate which argues for the best way to set interest rates. In the following section,

we outline the fundamentals of John Taylors interest rate reaction function, commonly

named the Taylor Rule, with its ability to describe a complicated process in simple terms. We

review subsequent versions of the Taylor Rule and how these reaction functions are used in

practice, most notably to identify mistakes in monetary policymaking.

In Chapter 3, we set up our econometric model and explain the rationale for the

sample period used in our study. We explain the choice of data and describe the framework

used to determine the coefficients of good monetary policy. We investigate the behavior of

the Misery Index and the percent change in money supply to determine our sample period.

In Chapter 4, we explain the results of the regression estimation. We present our

rationale for the post-sample period and calculate the prescribed interest rates for this period

using both our model and the original Taylor Rule. We measure the difference between


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prescribed interest rates and actual interest rates, and we find a large gap between the

prescribed and actual Federal Funds rates during the post-sample period. We show the rapid

asset-price inflation that coincided with overly expansionary monetary policy.

We conclude that interest rates in the early to mid 2000s were too low in a

systematic way and explain how our model provides quantitative evidence that monetary

excess contributed to the current financial crisis.


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Chapter 2: Recent Economic History and

Interest Rate Reaction Functions

The Federal Reserve Bank is arguably the most powerful actor in the macroeconomic

arena of the United States. The Federal Reserve Act spells out the explicit goals of the Feds

monetary policy function, which specifies that the Board of Governors and the Federal Open

Market Committee shall maintain long-run growth while still promoting the goals of

maximum employment, stable prices, and moderate long-term interest rates. (Board, 1913,

2a) Price stability is noted as the core goal of monetary policy in the long run, since stable

prices are a prerequisite for stability in the growth of output, employment, and long-term

interest rates. However, in the short and medium terms, monetary policy focuses on

stabilizing the real income path by changing short-term interest rates to compensate for

demand and supply shocks. With only one significant tool, the raising or lowering of the

Federal Funds rate, the Fed is stuck in a tricky place: There is not one specialized interest

rate that can be raised to keep inflation in check, another that can be cut to stimulate more

jobs, and still another that can be raised to prevent home buyers from bidding up house

prices. (Friedman, 2008, 6) The Fed must use a blunt object to fulfill the many delicate

objectives of sound monetary policy. Over time, the Fed has gotten better at wielding this

tool and the following section explains the U.S.s economic improvement in the context of a

learning curve for making monetary policy.

2.1 Economic History

The path of the economic climate in the United States over the last quarter century,

except for the past two years, has been one of steady improvement. Many people have


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attributed this economic evolution from the Great Inflation of the 1970s to the Great

Moderation of the 1980s to better monetary policy (Taylor 1999; Bernanke, 2004). The

following review of literature examines monetary policy during the last half-century and

attempts to shed light on how the changes in economic climate are a result of changing Fed

behavior.

Sherman Maisel, who served as a Board member from May 1965 to June 1972, notes

that nowhere did I find an account of how monetary policy was made or how it operated

(Maisel, 1973, 77). He argues that, during this time, the understanding amongst the Fed

policymakers was that money market conditions cannot measure the degree to whichmarkets should be tightened or for how long restraint should be retained (Maisel, 1973, 82).

This lack of restraint is cited as one cause of the high and volatile inflation of the 1970s.

Taylor (1999) argues that interest rates did not go high enough to curb the inflation, which, in

hindsight, should have been reined in by policy.

Under Arthur Burns chairmanship from February 1970 to February 1978, Fed

policymakers showed an increased emphasis on the growth of the money supply (Maisel,

1973). It was a step in the right direction to identify a monetary target by which to guide

policy, but Taylor (1999) argues that necessary guidelines were not in place to make the most

of this change. Greenspan (1997) also claims that attempting to keep a constant growth rate

of the money supply did not provide a sufficient response of interest rates to inflation or

output during this period to keep inflation low and stable.

After the appointment of Paul Volcker in August 1979, the unstable economy took a

turn for the better. Both output and inflation variability, which had risen significantly in the

1970s, fell sharply under his chairmanship. Blanchard and Simon (2001) note that the


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standard deviation of quarterly output growth declined by a factor of three from the 1970s

to the mid-1980s (Blanchard & Simon, 2001, 135). The actual cause of the Great Moderation

has been debated, but economists generally agree that monetary policy played a part. During

this period, the Fed became more aggressive in their response to inflation and output, but

improved the timing of these interest rate movements for the least amount of shock to the

economy (Bernanke, 2004). Bernanke asserts, The historical pattern of changes in the

volatilities of output growth and inflation gives some credence to the idea that better

monetary policy may have been a major contributor to increased economic stability.

(Bernanke, 2004, 1)

2.2 Rules vs. Discretion

Taylor (1999) takes Bernankes (2004) point a step further with his claim that better

monetary policy is due to the growing movement away from discretionary monetary policy

towards a more rules-based approach. Economists have debated extensively on the

appropriate method for setting interest rates. The central focus of this debate attempts to

answer whether interest rates should be set according to a quantitative rule, or whether well-

meaning policymakers can be trusted to use their discretion to maintain good economic

conditions.

James Tobin, a major supporter of discretionary monetary policy, claims that a path

for instruments or immediate targets set according to a rule, without consideration for events

and observations, creates blind policy making (Tobin, 1983). For example, if we compare

interest rate setting to driving a car, a driver blindly following a rule adjusts the cars speed

according to previously estimated parameters that dictate how he should react to the


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obstacles that lie ahead, while a driver using his discretion can decide whether the obstacles

ahead are real, worth adjusting the speed for, and can account for new shocks that lie outside

the scope of a simple rule (Tobin 1983). Further, a simple rule cannot account for the

countless economic indicators worth consulting and lacks the ability to reason when facing

unprecedented economic shocks.

Until the mid 1970s, the general argument against rules focused on the idea that, if a

particular rule would stabilize the economy, policymakers could adopt its suggestions while

still using discretion to maintain flexibility as needed. While this may sound superficially like

a satisfactory approach, there is heavy opposition to this argument. Henry Simons (1936) pioneered the rules side of the debate in his classic paper, Rules versus Authorities in

Monetary Policy . He writes,

The monetary problem stands out today as the great intellectual challenge tothe liberal faith The liberal creed demands the organization of our economiclife largely through individual participation in a game with definite rules definite, stable, legislative rules of the game as to money are of paramountimportance to the survival of a system based on freedom of enterprise. 1

Even before specific quantitative rules were widely discussed in the literature, Simons

(1936) was fighting for the design of optimal rules focusing on price stability. Milton

Friedman (1948) added to this early body of literature by claiming that the destabilizing

shifts in monetary policy were caused by discretion, which had been clouded by public

opinion and political pressures. 2

Each side of the rules versus discretion debate received equal support until the

development of the theory of time inconsistency completely changed the debate. This theory

suggests that if a general attempt towards maintaining a prosperous economy is all that

1 Simons, 1936, 3.2 This is not to say that the Fed during this period was not autonomous, it just aims to point out thatwithout a rule the divide that separates a central bank from the government could become muddled.


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governs policy, there is nothing to say what should move, how far it should move, or when

the instrument should start or stop moving (Fischer, 1988). Furthermore, time inconsistency

describes a policymaker with one set of preferences at one point but another set at another

point in time. Kydland and Prescott (1977) address the major question of whether a monetary

policy that seeks to do what seems best in any given time period produces better results than

abandoning period-by-period discretion in order to follow a rule. According to this argument,

policy rules are the preferred solution, whereas discretionary policy may be inconsistent and

shortsighted (Kydland and Prescott, 1977). If policymakers are time consistent and follow the

same rule for all periods, monetary policy would be much more transparent and wouldincrease credibility and accountability among policymakers. Rudebusch and Svensson (1998)

argue that rules are crucial to maintaining credibility of a central banks commitment to

promoting economic well being. The contribution of the time inconsistency literature has

shown that a long-term commitment by monetary authorities could vastly improve the

behavior of monetary policy and decrease the volatility of the economy.

Historical rules for monetary policy have varied substantially, but focus on a

monetary target in some form: a constant growth rate of money supply, the exchange rate, a

target price level, or real output. According to John Taylor (1993), If there is anything about

which modern macroeconomics is clear. . . and on which there is substantial consensus

it is that policy rules have major advantages over discretion in improving economic

performance (Taylor, 1993, 197). Taylor (1993) believes that a policy rule need not be a

mechanical formula that adjusts short-term interests rates on autopilot, but instead could be a

simple rule derived from sound economic ideals. The policy rule can be implemented more

informally by policymakers as long as judgment is employed to sense check the interest rates


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prescribed by the rule. This would allow for use of both a rule that keeps the economy on

target and some discretion to cope with shocks and other unpredictable situations that cannot

be accounted for in a simple rule.

2.3 John Taylors Original Rule

In 1993, John Taylor demonstrated how the Feds interest-rate setting behavior could

be characterized by a simple reaction function. In his simple model, he set the nominal

Federal Funds rate equal to the rate of inflation plus the equilibrium real rate of interest plus

a weighted average of two gaps, the first being the inflation rate less a target rate of inflation,and the second, the percent deviation of real GDP from its potential:

it = r* + !

t + "

1(! t # ! *) + " 2 yt (2.1)

where: i is the Federal Funds rate operating target for the period, r * is the equilibrium real

interest rate, ! is the average inflation rate over the concurrent and prior three quarters as

measured by the GDP deflator, ! * is the target inflation rate, and yt is the output gap, which

is the percent deviation of real GDP from its potential.

Note that once simplified, the slope coefficient on the inflation gap is (1+ ! 1 ), which

indicates that for an increase in the inflation rate by k percent, the nominal interest rate must

be raised by more than k percent. Taylor (1993, 1999) stresses this as a necessity for sound

monetary policy, recognizing that if the coefficient on inflation is less than one, an increase

in inflation will bring about a decrease in the real interest rate, which stimulates demand.

Taylor argues that this is the wrong policy response to an increase in inflation, since it will


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generate more inflation and result in poor economic performance. 3 Therefore, if the

coefficient on the inflation gap is greater than one, an increase in inflation will cause a

greater increase in the real interest rate, which should help to stabilize the economy.

The ability of Taylors rule to describe a complicated process in a simple fashion

made it very popular and spurred significant growth of literature detailing Taylor-type

interest rate reaction functions. Subsequent research has attempted to provide evidence for

different forms of the Taylor Rule being relevant to monetary policy. These argue

extensively about whether Taylor-type reaction functions should be used as either a

description or prescription of monetary policy. Proponents of description focus on how bestto describe central bank behavior, which variables to include in the rule, how best to measure

these variables, and to what degree the response of the policy rule reacts to movements in

these variables. Economists supporting prescription favor optimal benchmark rules that can

be used to determine how policymakers should set interest rates and whether deviations from

these rules are policy mistakes (McCallum, 1999; Taylor, 1999).

2.4 Econometric Literature

Alternative modifications to the Taylor Rule in empirical papers investigate whether a

rule can represent a guideline for the central bank to follow when making interest rate

decisions. They address arguments that the original Taylor Rule is too restrictive to describe

actual changes in the Federal Funds rate. Modified rules attempt to make the original Taylor

Rule more realistic and appropriate, through changing the functional form, timing of

fundamentals, or the desired values of the coefficients (Carare and Tchaidze, 2005). The

3 We see evidence of this later in this study. Real interest rates were negative during part of the post-sample period for which we argue contributed to the asset-price inflation experienced shortlythereafter.


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original Taylor Rule assumes an immediate adjustment of the Federal Funds Rate to its target

level and ignores the Feds tendency to smooth changes in interest rates (Clarida, Gali, &

Gertler, 2000). Modifications to this effect include using lags of interest rates, inflation rates,

and the output gap. McCallum (1999) points out that the use of lags also makes timing more

realistic, since it is not possible to know the true output gap and inflation when changing

interest rates. We include lags of interest rates and output gap in our model, which is

discussed in detail in the following chapter.

Other contributions to the literature analyze whether Taylor Rules are optimal and

how the subsequent versions of Taylor Rules contribute to their optimality. These studiesevaluate backward and forward-looking Taylor Rules by designing structural models. Model

economies are simulated with different Rules to examine how they would operate under the

various policies. While model-based approaches have led to prescriptive monetary policy,

these black-box models cannot be the sole grounds for making policy decisions. Using

historical evidence to support these models aids their usage as prescriptions for policy in

practice.

Taylor (1999) outlines a method that combines the descriptive and prescriptive

powers of interest-rate reaction functions. He argues that, if there is sufficient evidence that a

period of economic history is good, the coefficients of the estimated Taylor Rule describe

good interest-rate setting behavior. The estimated coefficients can then be used in other

periods to calculate where interest rates should have been if the same Taylor Rule had been

followed, in effect prescribing good monetary policy. Further, he argues that the prescribed

interest rates can be compared to actual interest rates to identify sources of deviation from

where they should have been set. If it appears the economy was adversely affected as a


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result of these deviations, Taylor (1999) calls them policy mistakes. Simply measuring the

distance between the estimated rule and the actual rule provides the magnitude of these

mistakes.

We use Taylors (1999) framework to argue that interest rates were too low in the

early to mid 2000s. First, we identify the period from 1981Q3 to 1989Q3 as being a good

period of economic history, when inflation and unemployment were low and stable, and

output growth was steady. We estimate a Taylor-type reaction function for the U.S. Federal

Funds rate over this period to determine the parameters of a good monetary policy rule.

Using the policy mistake methodology from Taylor (1999), we calculate the prescribedinterest rates for the post-sample period, where interest rates were said to have been too low

for too long. We measure the gap between actual interest rates and prescribed interest rates

to identify how much the Federal Funds rate deviated from what would have been prescribed

by the rule. We evaluate whether these policy mistakes support the claim that low interest

rates were one of the contributing factors to the asset-price inflation experienced during the

post-sample period. The following section explains our econometric model.


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Chapter 3: Econometric Model and

Rationale for Sample Period

3.1 Econometric Model

The econometric model used in this study is similar to the one used by Judd and

Rudebusch (1998), which is based on the original Taylor Rule. As discussed above, the

original Taylor Rule specifies that changes in the Federal Funds rate react to two key

variables: deviations of inflation from an inflation target and deviations of real output from

its potential. Taylors Rule set the nominal Federal Funds rate equal to the inflation rate, an

equilibrium real Funds rate, plus an equally weighted average of the four-quarter moving

average of actual inflation in the GDP deflator less a target rate and the percent deviation of

real GDP from an estimate of its potential level.

it = ! t + r* + "

1(! t # ! *) + " 2 yt (3.1)

where: i t is the Federal funds rate operating target for the period, r * is the equilibrium real

interest rate, ! t is the average inflation rate over the concurrent and prior three quarters as

measured by the GDP deflator, ! * is the target inflation rate, and yt is the output gap, which

is calculated as the percent deviation of real GDP from its potential,Y

t ! Y

t

*

Y t

* " 100 .

Taylor did not econometrically estimate this equation; rather, he assumed that the Fed

gave deviations in inflation and output equal weights of 0.5. Further, Taylor made the

assumption that the equilibrium real interest rate and the inflation target were both equal to

two percent:

it = 2 + 2 + 0.5( ! t " 2) + 0.5 yt (3.2)


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The fundamental principle underlying his assumptions is that if both inflation and real GDP

are on target, then the Federal Funds rate will equal four percent, or two percent in real terms

(Taylor 1993). Taylor (1993) argues that a two percent equilibrium real rate is close to the

assumed steady-state growth rate of 2.2 percent.

While Taylors original rule provided a simple way to describe monetary policy, we

address some shortcomings that warrant use of a more dynamic model. First, Taylors rule is

based on a static model, implying that changes in the independent variables in period t are

fully reflected in the changes in the Federal Funds rate in the same period. We consider this a

strong restriction in the model and unrealistic for several reasons. Most importantly, it is toosimplistic to assume the Fed looks only at current data and ignores the data from previous

periods. Also, Taylors original rule does not take into account the apparent slow adjustment

of the Federal Funds rate to target, which creates serial correlation in the error term (Clarida

et al., 2000). We resolve these issues by adding terms for lagged output gap and the Federal

Funds rate. We include the lagged output gap term in the following equation:

i t * = !

t + r * + " 1(! t # !

*) + " 2 yt + " 3 yt #1 (3.3)

Where i t *

is the target Federal Funds rate that will be achieved through gradual adjustment

and yt ! 1 , the additional lagged gap term, allows for the possibility that the Fed responds to

the output gap from both the current and previous period. Judd and Rudebusch (1998)

introduce the following equation to express the two stages of the gradual adjustment of the

actual level of the Funds rate to target ( i t *

) each quarter.

! i t = " (i t

* # i t # 1) + $ ! i t # 1

(3.4)


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Equation (3.4) shows that the change in the Funds rate at time t partially corrects the error

between the last periods change in the Federal Funds rate and the current target level

(i t * ! i

t ! 1) as well as maintaining some of the momentum from the Funds rate change ( ! " i t # 1 )

in the prior period. Estimates of ! , the coefficient on the first term, reveal the amount of the

gap between the target Fed Funds rate and the actual rate that the Fed attempts to close each

quarter. Estimates of ! , the coefficient on the second term, indicate how much the Fed is

constrained in the current period by where the Fed Funds rate was in the previous period. We

expect both ! and ! to be positive and less than one. By substituting Equation (3.3) into

(3.4), the equation to be estimated becomes:

! i t = "# $ " i t $ 1 + " (1 + % 1)& t + "% 2 yt + "% 3 yt $ 1 + ' ! i t $ 1 (3.5)

where ! = r * " # 1$ *

When estimated, Equation (3.5) provides an approximation on the weights on output and

inflation and on the speed of interest rate adjustments to the target. The constant term ( ! )

represents the combined equilibrium real Funds rate ( r* ) and the inflation target ( ! *

), which

is useful because neither of these variables is observable. If we were to assume a value for

one of the variables the other can be backed out through the estimates of ! and ! 1 (Judd and

Rudebusch, 1998). In this model, both the prior periods level of the Funds rate ( i t ! 1 ) and

change in the Funds rate ( ! i t " 1 ) influence the change in the Funds rate in the current period.

We expect the change in the Federal Funds rate at time t to respond directly to current

inflation, output gap in t and t-1 , and the prior periods change in the Federal Funds rate, but

indirectly to the prior periods Federal Funds rate level.


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3.2 Rationale for sample period

The first step of Taylors (1999) framework is to identify a good period of

economic history for which to estimate our econometric model. As explained by Taylor

(1999), the coefficients estimated for the good period of monetary policy serve as a

description of good interest rate setting behavior. We narrow history based on the

literature and then look at various relevant indicators within those periods to determine the

best period for our study.

The 1980s are generally considered to have been a good period of economic history,

as selected by major contributors to the literature. Judd and Rudebusch (1998) estimate theirreaction function for 1987Q3 to 1997Q4, Kozicki (1999) estimates from 1983 to 1997, and

Clarida, Gali, and Gertler (1999) estimate from 1979Q3 to 1996Q4. Of these three, Clarida et

al. (1999) is the only paper to explain the rationale for the sample-period choice, stating it is

widely believed that U.S. monetary policy took an important turn for the better with the

appointment of Paul Volcker as Fed Chairman. (Clarida et. al, 1999, 1697) While most of

these authors address the behavior of one policymaker versus another, we are more interested

in evaluating a good period of economic history. To enrich the rationale for our sample

period choice, we investigated the behavior of the Misery Index and the percent change in the

money supply (M1). 4 The Misery Index is a simple index originally put forth by Arthur

Okun, in which the rate of inflation is added to the unemployment rate. Basic economic

theory supports the concept that high unemployment and high inflation often create a

miserable economic climate.

4 M1 is a strict measure of money supply, which includes only the assets that can be used to pay for agood or service or to repay debt.


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We calculate the Misery Index using quarterly annual percent change of the consumer

price index as a proxy for inflation and the unemployment rate from the Bureau of Labor

Statistics:

Figure 3.1: The Misery Index

The graph above shows two distinct periods when the Misery Index declines: from

1981Q2 to 1986Q4 the index dropped 63% over five and a half years; and from 1990Q4 to

1999Q1 the index dropped 46% over eight and a half years. Since the latter period contains a

number of technology shocks, which do not occur in the post-sample period, the former

period is better suited for our purposes. While the Misery Index begins its decline in 1980Q1,

examination of the error terms reveals many outliers at the beginning of the sample. We

believe these are caused by a combination of noise left over from the 1979 energy crisis and

Volckers goal to reverse inflationary pressures built up under his predecessor. We truncated

the sample period by removing the first year and a half to exclude these outliers, choosing the

quarter after the uptick in 1981Q2 as our starting point. The Misery Index continued to

4

8

12

16

20

24

1980 1985 1990 1995 2000 2005

Misery Index


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decline until 1986Q4, remained relatively flat until 1989Q4, and rallied for four of the next

five quarters.

We also examined the rate of growth of the money supply, which bottomed in

1989Q3, as seen in Figure (3.2) below:

Figure 3.2: Rate of Growth of the Money Supply(Sample Period)

We find that the period from 1981Q3 to 1989Q3 exhibits the characteristics of

good monetary policy and thus we choose it for our sample period. We outline the data we

use for estimating our model in the following section.

3.3 Data

The data used in this study are quarterly real GDP data from the Bureau of Economic

Analysis, annualized percentage change of the consumer price index from the Bureau of

Labor Statistics, the effective Federal Funds Rate from the Federal Reserve Bank of New

-4

0

4

8

12

16

20

1980 1982 1984 1986 1988 1990 1992

Annual quarterly percentage change in M1


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York, and potential GDP, which is estimated by the Congressional Budget Office using a

structural model. Descriptive statistics are shown in Table (3.1):

Table 3.1: Descriptive Statistics

Sample Period Post-Sample Period(81.Q3 - 89.Q3) (2000.Q3 - 2006.Q1)

Average Fed Funds rate (%) 9.79 2.71Average Real Fed Funds rate (%) 4.68 0.04Average Inflation (%) 5.11 2.68Percentage point change in inflation -8.20 -2.06End-of-sample inflation 4.67 3.67Average GDP Gap (%) -2.04 -0.33

Note: The change in inflation (in percentage points) is calculated as the difference inone quarter inflation from the first quarter to the last quarter of the sample. End-of-

sample inflation is average inflation over the last four quarters of the sample.

In the following chapter, we estimate our econometric model for the sample period

and explain our results.


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Chapter 4: Analysis of the Results of the Econometric Model

and Rationale for the Post-Sample Period

4.1 Regression Estimation

We estimate the following equation using ordinary least squares for the sample period

1981Q3 to 1989Q3 and then re-estimate the equation after eliminating the insignificant

terms.

FFCHG = ! 0 + ! 1 FFACT (" 1) + ! 2CPI + ! 3GAP + ! 4GAP (" 1) + ! 5 FFCHG (" 1) + #

(4.1)

where FFCHG is the change in the level of the effective Federal Funds rate between t and t-

1, FFACT(-1) is the effective Federal Funds rate in t-1 , CPI is the percent change in the CPI

inflation index from t-1 to t, GAP is the percent deviation of real GDP from its potential level

Y t ! Y

t

*

Y t

* " 100 , GAP(-1) is the GAP during the previous period, and FFCHG(-1) is the change

in the Federal Funds rate during the previous period. Tables (4.1) and (4.2) on the following

page report the regression estimates of our model:


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Table 4.1: Determinants of Change of the Fed Funds rate(Dependent variable: change in the mean effective Fed Funds rate from t-1 to t)

Sample: 1981Q3 to 1989Q3Included observations: 33

Explanatory Variable (1) (2)

C 1.305(1.852)*

1.475(2.366) **

FFACT (-1) -0.361(-2.543) **

-0.389(-2.989) ***

CPI 0.413(2.313) **

0.426(2.440) **

GAP 0.579

(1.884) *

0.469

(2.048) ** GAP(-1) -0.569

(-2.199) **-0.494(-2.288) **

FFCHG(-1) -0.105(-0.543)

--

R 2 0.48 0.48S.E. 0.88 0.88

Prob (F-stat) 0.0018 0.0008Durbin-Watson 1.98 2.05

Note: t-statistics in parenthesis*Significant at 10% significance level**Significant at 5% significance level***Significant at 1% significance level

Table 4.2: Individual Components of Each Coefficient

$ $ $ 3 % (1) 3.615 0.361 0.143 1.603 -1.557 -0.105

(2) 3.787 0.389 0.094 1.205 -1.267 --

Several interesting results stand out. First, the lagged Federal Funds rate is

insignificant in the first regression. This indicates that, of the two stages of the Federal Funds

rate adjustment process, the primary consideration of Feds interest rate smoothing behavior


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concerns how much of the gap to close each quarter, rather than the momentum of interest

rates from the previous period. We eliminate the lagged Federal Funds rate in the second

regression. Regression (2) is not rejected at conventional significance levels over the sample

period, explains 48 percent of the quarterly variation in the change of the Funds rate (with an

adjusted R 2 = 41), and has a Durbin-Watson of 2.05. All coefficients are significant at the

10% significance level.

Second, as seen above in Table (4.2), the value of # suggests that the Fed typically

adjusts the Federal Funds rate enough to eliminate 38.9 percent of the difference between the

lagged actual and target Funds rate each quarter. Third, the negative sign on the coefficient of

the lagged GDP gap indicates that the Fed corrects the adjustment made in the previous

period in the current period. Finally, it should be noted that the coefficient on the rate of

inflation is lower than expected. While Taylor (1993, 1999) stresses that an inflation

coefficient of greater than one is necessary to stop inflation in its tracks, we look at the

change in the Federal Funds rate ( ! i t ) rather than the level ( i t ), so that a coefficient of less

than one is not necessarily inflationary.

The results above describe how the Fed reacts during a good period of monetary

policy. The following section explains how we can use these coefficients to calculate the

prescribed Funds rates to evaluate the actual policy response of the Fed during the post-

sample period.


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4.2 Rationale for post-sample period

Our basic hypothesis is that we can use the coefficients estimated for a good period

of economic history to calculate the prescribed Federal Funds rate for a post-sample period.

In this section we explain the rationale for our post-sample period choice and compare the

actual and prescribed interest rates during this period to operationalize what Taylor,

Friedman, and Leijonhufvud consider being too low.

To find the appropriate post-sample period, we examine the real Federal Funds rate, 5

the money supply (M1), and the percent change in the money supply during the first half of

the 2000s. First, real interest rates began declining steadily in 2000Q4 with only one uptickin 2001Q4 before dropping below zero. Figure (4.3) below shows real interest rates for the

post-sample period. Notice that positive real interest rates did not re-surface above zero until

2005Q3.

Figure 4.3: Real Federal Funds Rate(Post-Sample Period)

5 The real Federal Funds rate is the nominal effective Federal Funds rate less the rate of inflation asmeasured by CPI

-2

-1

0

1

2

3

4

2000 2001 2002 2003 2004 2005 2006

Real Federal Funds Rate


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Second, the money supply had leveled off in the late 1990s but began a steady

upward trend in 2004Q1 and peaked in 2006Q1 as seen in Figure (4.4) below:

Figure 4.4: Money Supply

Third, we present the rate of growth in the money supply in Figure (4.5). The rate of

growth of the money supply bottomed in 2000Q4 but over the next five years grew to over

8% before settling back down after 2005Q4.

Figure 4.5: Rate of Growth of the Money Supply

We use the period from 2000Q4 to 2006Q1 as our post-sample period.

1,050

1,100

1,150

1,200

1,250

1,300

1,350

1,400

98 99 00 01 02 03 04 05 06

M1 Money Supply

-2

0

2

4

6

8

10

2000 2001 2002 2003 2004 2005 2006

Percent Change in M1


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4.3 Calculating prescribed policy action

We use the coefficients estimated during the sample period and the raw data for

interest rates, inflation, and output gap from 2000Q4 to 2006Q1 to calculate the prescribed

Federal Funds rates. Figure (4.6) plots the prescribed and actual Federal Funds rate during

the post-sample period. From our calculations, our model prescribes that the Fed Funds rate

should have been above the actual Funds rate for the entire post-sample period. We also

calculate the Funds rate that is prescribed by Taylors original rule using the assumptions

shown in Equation (3.2). While we explained the shortcomings of Taylors simple model, we

find it interesting that both models show that interest rates were too low during the post-sample period. Figure (4.6) plots the actual Fed Funds rate and the rates prescribed by both

our model and Taylors original model:

Figure 4.6: Comparison of Prescribed Funds Rates and ActualEffective Funds Rates

0

1

2

3

4

5

6

7

2000 2001 2002 2003 2004 2005 2006

Funds Rates Prescribed by O riginal Taylor Rule Actu al F ed Funds RateFunds Rates Prescribed by our Model

Prescribed Fed Funds Rates vs. Actual Fed Funds Rates


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Figure (4.7) shows the magnitude of the difference between the actual Funds rate and

the values estimated by our model. 6 According to our calculations, the Federal Funds rates

during the post-sample period should have been an average of 159 basis points higher than

they were and as high as 271bps higher in 2003Q3. It is clear from these calculations that

there was a systematic difference in the dynamics of monetary policy from what good

policy would have prescribed.

Figure 4.7: Magnitude of the Deviation from Actual toPrescribed Fed Funds Rates

As shown in Figures (4.6) and (4.7), we find that there is a considerable difference between

where the Fed set interest rates and where the models prescribed. But what does this mean

for the current financial crisis? The following section explains the link between overly

expansionary policy and asset-price inflation.

6 This is calculated by subtracting the actual rates from the prescribed rates.

-2

-1

0

1

2

3

2000 2001 2002 2003 2004 2005 2006

Taylor 's Original ModelOur Model

Difference Between Actual and Prescribed Funds Rates


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4.4 Contribution to current financial crisis

Our post-sample period began with a major exogenous shock: the September 11 th

attacks. As seen above in Figure (4.4), our model supports the rate cuts that the Fed made

following the attacks to pump liquidity into financial markets. Markets stabilized quickly so

interest rates should have come back up, but the Fed continued to cut interest rates until the

first quarter of 2004. Our model suggests that interest rates should have come back up in the

second quarter of 2002, three quarters earlier than they actually did. As stated previously, the

standard explanation for any financial crisis is a period of excess. Absent any further

exogenous shocks to the economy, these low interest rates created a situation of monetaryexcess. Money in the economy needs somewhere to go; if not taken out once it is no longer

needed to support markets, it can enable the misallocation of resources, and also cause

inflation.

We present the following three pieces of evidence to support our argument that there

was a fundamental change in the monetary situation in the U.S. First, we refer to Figure (4.3)

above, the graph of real interest rates over the post-sample period. As seen in Figure (4.3),

real interest rates were negative over a major portion of the post-sample period. This means

that the Fed was essentially paying people to borrow. Second, we present the Case-Shiller

index of house prices. The shaded sections highlight the sample and post-sample periods. It is

clear from this graph that house prices during the post-sample period accelerated by much

more than was experienced over the prior fifty years.


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Figure 4.8: Case-Shiller Home Price Index

Third, Figure (4.9) shows the house price-to-income ratio, calculated as the Case-

Shiller index over nominal median household income from the Census Bureau (Calculated

Risk, 2008). This graph shows that the increases in house prices were not supported by

increases in income and thus were unsustainable.

Figure 4.9: Price-to-Income Ratio

100

120

140

160

180

200

220

1950 1960 1970 1980 1990 2000

Home Price Index

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

88 90 92 94 96 98 00 02 04 06 08

Ratio of House Prices to Median Household Income


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The fact that the rapid asset price inflation coincides with loose monetary policy

suggests that too low interest rates may have contributed. Our evidence suggests that

monetary excess during the post-sample period exacerbated the asset-price inflation that led

to the current financial crisis.


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Chapter 5: Conclusions

This study provides quantitative support for the argument that excessively

expansionary monetary policy with interest rates that were too low for too long in the first

half of the 2000s contributed to the current financial crisis. We identify 1981Q3 to 1989Q3

as a good period of monetary policy and estimate a Taylor-type reaction function over this

period for the U.S. Federal Funds rate, to determine parameters of a good monetary policy

rule for our model. Our results provide an interesting picture of how the Fed reacted during

this period. We use the estimated coefficients to calculate prescribed Federal Funds rates for

the post-sample period and find strong evidence from both our model and Taylors original

model to support the claim that interest rates were much lower than if the Fed set interest

rates according to either rule. These results provide quantitative evidence that interest rates

should not have been cut as far, or remained at low levels for as long, as they did from

2000Q4 to 2006Q1.

The major contributions of this study are three-fold. First, we operationalize Taylors

(1999) framework and identify it as the appropriate method to test our hypothesis. Second,

we identify a period of time for which we present a reasonable argument as to what is

good monetary policy. Third, we explain how the difference between the estimates of our

model and actual interest rates validate the claim that interest rates were kept far too low for

too long to connect expansionary monetary policy to bubble-causing asset-price inflation.

We acknowledge some shortcomings in our method. The sample period chosen for

estimating the reaction function were somewhat arbitrary, similar to all Taylor-type reaction

functions. We have also used revised data in both the estimation period and post-sample

period. Further research could remedy this.


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Despite these shortcomings, the results provided by the simple Taylor Rule and by

our model both provide evidence to support the claim that too low interest rates during the

post-sample period contributed to the asset-price inflation leading to the current financial

crisis. Other contributing factors, which should be examined, include market deregulation,

lax enforcement of existing regulation, high savings rates in other countries, and moral

hazard.


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Documents

The High Price of Low Interest Rates