Money, Inflation and the
Business Cycle
The Taylor Rule
Reverse Causation
Segmented Markets
Misperceptions Model
Commitment & Monetary Policy
• Readings:
* Williamson, Ch 11
* Williamson, Ch 17
• Recall that money in the CE model is either
(i) Neutral & Superneutral in the ad-hoc or CIA
model w/ exogenous income (Classical
Dichotomy).
(ii) Neutral but not Superneutral in CIA model w/
production.
• CIA model w/ production  money growth leads
to lower employment and output
(countercyclical).
• BC fact is money is procyclical and leading.
Figure 3.13 Money Supply (black line)
and Real GDP (colored line) for the
Period 1959–2003
• Three CE explanations of procyclical money:
(i) Reverse Causation  procyclical & neutral.
(ii) Segmented Markets  procyclical & nonneutral.
(iii) Misperceptions (Lucas-Friedman) Theory 
procyclical & non-neutral.
The Taylor Rule
• Movements in money supply are often
endogenous and react to economic events.
• Traditionally, FED has two primary objectives:
(i) Price Stability
(ii) Output Stability
• The Taylor Rule (J. Taylor – Stanford) quantifies
the observed decisions of the FOMC as
depending upon deviations of
(i)
inflation from a target level (p*)
(ii) GDP from “potential” or target y*
FOMC Statement – May 2000
• The Federal Open Market Committee voted
today to raise its target for the federal funds rate
by 50 basis points to 6-1/2 percent.
• Increases in demand have remained in excess
of even the rapid pace of productivity-driven
gains in potential supply … The Committee is
concerned that this disparity will continue, which
could foster inflationary imbalances.
• … The Committee believes the risks are
weighted mainly toward conditions that may
generate heightened inflation pressures in the
foreseeable future.
FOMC Statement – March 18,
2008
• The Federal Open Market Committee decided
today to lower its target for the federal funds rate
75 basis points to 2-1/4 percent.
• Recent information indicates that the outlook for
economic activity has weakened further …
Financial markets remain under considerable
stress …Inflation has been elevated, and some
indicators of inflation expectations have
risen. Uuncertainty about the inflation outlook
has increased.
• Downside risks to growth remain. The
Committee will act in a timely manner as needed
to promote sustainable economic growth and
price stability.
• Taylor Rule expressed in terms of a nominal interest rate
rule:
Rt  (1.5)(p * p t )  (0.5)( y *  yt )
* 1% increase in p > p*  1.5% increase in R
* 1% decrease in y < y*  0.5% decrease in R
• Taylor Rule expressed in terms of a money supply rule:
M ts  a1 (p * p t )  a2 ( y *  yt )
where a1 ,a2 > 0.
RBC View: Endogenous Money
(“Reverse Causation” View)
• If money is neutral in a CE model, can it explain
why the nominal money supply is procyclical and
leading the business cycle?
• Yes. Focus on Fed’s price stability objective.
• Combine the Taylor Rule with RBC model: Let
y* be the CE value of output and set yt = yt*:
M ts  a1 (p * p t )
where a1 > 0.
• Example: Productivity Shocks and Fed Reaction
Today (t): Fed forecasts negative productivity
shock ( zt 1 )
  future prices (Pt+1)
  p > p*
  Mts
Future (t+1): Productivity shock   Yt+1
and p  p*.
Conclusion:  Mts today and Yt+1 tomorrow.
 money is procyclical and leading but
neutral
Figure 3.13 Money Supply (black line)
and Real GDP (colored line) for the
Period 1959–2003
Non-Neutral Money
• There is evidence that monetary policy is nonneutral:
(i) Reverse causation cannot completely explain
procyclical money supply.
(ii) Statistical Evidence: Money  Output
(iii) The Taylor Rule implies FED operates as if it
can affect real output:
M ts  a2 ( y *  yt )
• Can this explained in CE models w/o assuming
fixed prices (e.g. IS-LM)?
Segmented Markets Theory
• Motivates by the “Bank Lending Channel” of monetary
policy emphasized by B. Bernanke and A. Blinder.
• Originates with works of Robert Lucas (1990) and
Timothy Fuerst (1992).
• Sometimes called “Limited Participation” models:
– Inventory Models of Money (Baumol/Tobin)
– Costly Portfolio Adjustment
• The traditional view of effect of monetary policy:
Short-Run  Liquidity Effect
Long-Run  Anticipated Inflation Effect
or Fisher Effect: R = r + pe
• Assumptions
(i) Segments goods and financial market.
(ii) Monetary policy works through financial markets.
(iii) Firms must use borrowed cash from financial
market to pay their wage bill (and/or
investment).
• Money Supply:
M ts1  M ts  X t  (1  mt ) M ts
where Xt = mtMts = transfer of money to financial market
and mt = money growth rate:
mt 1  (1   ) m  mt  e t 1
m
= “average” money growth rate, e = random money
growth shock.
M1 Money Supply, 2000-2010
Growth Rate
• Flow Chart
• Timing in Period t:
(i) Households begin with Mt money, Firms have Kt
capital stock.
(ii) Portfolio decision - Household deposits Dt into
financial market based on rational expectation of Xt.
Deposits pay interest rate Rt
(iii) Fed injects money Xt into financial market.
(iv) Firms borrow Qt from financial market to pay wages,
produces output from labor and capital, buys
investment goods. Loans are charged Rt.
(v) Households consume with cash Mt - Dt.
(vi) All loans and interest on deposits are paid. Ends
period with Mt+1, Kt+1.
• Key: Portfolio decision (ii) happens before (iii)!
• Modified Cash-in-Advance constraints.
Households: M t  Dt  Pt ct
Firms:
Qt  Ptt N td
• Household Deposits/Portfolio FOC:

(1  Rt ) 
Et 1uc (ct , lt )  Et 1 uc (ct 1 , lt 1 )

1 p t 

t
t 1
expected marginal cost of deposits = expected marginal benefit
or expected marginal value
of cash in goods market
• Let L =
=
expected marginal
value of cash in
financial market
(Actual Marginal Value of Cash in Goods Mkt)

(Actual Marginal Value of Cash in Financial Mkt)
L < 0  More than expected cash in goods market
L > 0  More than expected cash in financial market
Labor Supply FOC:
• Firm FOC:
Investment:
Labor Demand:
ul (ct , lt )  uc (ct , lt )
Et f K ( Kt 1 , Nt 1 )  rt  
f N ( Kt , Nt )  (1  Rt )t
• Market-Clearing Conditions.
Yt  ct  I t
Goods:
s
M
t  Mt
Money:
d
s
N

N
t
t
Labor:
Financial:
Qt  Dt  X t
• Household portfolio decision, i.e. money demand, based
upon expected nominal interest rate ( Et 1Rt  Rt e ):
Net-of-Deposits Money Demand
e
= M t  Dt  Pt L(Yt , Rt )
• The expected nominal interest rate obeys Fisher Effect:
(1  R e )  (1  r )(1  p e )
• The actual nominal interest rate follows
(1  R)  (1  r )(1  p )  L
e
• Unexpected positive money shock  Excess cash in
financial market  R < Re.
• Unexpected negative money shock  Excess cash in
goods market  R > Re .
• Recall Labor Demand will be inversely related to R:
f N ( Kt , Nt )  (1  Rt )t
Expected Money Shock
•
•
Purely temporary (0) and expected money
shocks are neutral.
An expected and persistent ( > 0) positive
money supply shock (e)  Similar to CIA
model w/ production:
* Increases expected inflation rate
* Increases nominal interest rates (R)
* Decreases ND and NS
* Decreases N*, c*, y*
* Money growth is countercyclical!
Simulation: Expected Monetary Shock in
Period 5
Money Growth Rate (m)
Nominal Interest Rate (R)
Simulation: Monetary Shock in Period 5
Labor (N)
Output (Y)
US DATA: Unexpected Negative Monetary
Shock (Bernanke & Gertler, 1995)
Unexpected Money Shock
•
An unexpected positive money supply shock (e):
Current Period:
(1) Excess cash in financial market  R < Re
(2) Lower R 
Firms borrow more to increase
labor demand.

Increases * and N*
(3) Higher N*  Shifts Output Supply right

Increases y* and decreases r*
(secondary effect on NS)
•
This is often called the LIQUIDITY EFFECT
Simulation: Unexpected Monetary Shock in
Period 5
Segmented Markets Model
Money Growth Rate (m)
Nominal Interest Rate (R)
Simulation: Unexpected Monetary Shock in
Period 5, Segmented Markets Model
Labor (N)
Output (Y)
Future Period:
(1) Excess cash is pulled out of financial market by
households  R = Re
(2) Persistence of money shock  increase expected
future money growth and inflation  increase in R.
The ANTICIPATED INFLATION EFFECT
(3) N*,y*, c* will be temporarily lower than their long-run
steady state values but eventually converge.
•
Money is procyclical and non-neutral in the “short-run”.
•
Shortcoming: No persistence effect of monetary policy
on nominal interest rates and real GDP.
Table 11.2 Data Versus Predictions of
the Segmented Markets Model with
Monetary Shocks
• Non-neutrality of money is caused by imperfect
(unexpected) information about monetary policy.
• Remarks about optimal policy:
(i) Generally inefficient to create unexpected
monetary shocks to boost output (lowers
utility).
(ii) If the Fed can react faster to productivity
shocks then a procyclical money supply may be
welfare improving:
 z > z e  Optimal ND greater than expected
but limited cash in financial market. FED
adds liquidity to support ND and increase Y to
its “efficient level”
Misperceptions Theory
(Money Surprise Model – Williamson Ch 17)
Origins:
M. Friedman (1968) – “The Role
of Monetary Policy”
The Worker “Surprise” Model
Formalized:
R. Lucas (1973) – “Some
International Evidence on
Output-Inflation Trade-Offs”
The Producer “Island” Model
Worker Surprise Model
• What should matter to workers are real wages 
= W/P.
• Labor Market with Nominal Wages.
• Workers confuse W and .
• Recall W = P. It can increase because
(i) positive productivity shocks  increases 
(ii) an increase in Ms  increases P.
• An unexpected increase in P 
increases N* and Y*.
Lucas Island Model
• Supply of individual firms depends positively on local
price relative to aggregate price level.
• Time-Line of Information:
(i) Period t-1: Form Et-1Pt (expected value of Pt given
information up to time t-1).
(ii) Period t:
Observe local price NOT Pt.
• Let 0 < q < 1 represent the correlation between local
price and aggregate price Pt:
q0

No Correlation
q1

100% Positive Correlation
0<q<1

Some Correlation
• The AS Curve:
yt  y * (1  q )Pt  Et 1Pt 
• where y* = CE value for output (w/ perfect info)
• If q  1

y = y*
• If q < 1 then
Et-1Pt = Pt 
y = y*
Et-1Pt < Pt 
y > y*
Et-1Pt > Pt 
y < y*
• The Lucas Critique: Expectations about
(monetary) policy affects the impact of the
policy.
• Value of q is based on rational expectations
High inflation countries  q = 1  AS steep
Low inflation countries  q = 0  AS flat
Application: Rational Expectations and
Monetary Policy
• T. Sargent and N. Wallace (U. of Minnesota)
• Consider the following “reduced form” macro
model (let a  1q).
(AS Curve)
yt  y * a  pt  Et 1 pt 
(AD Curve)
mt  pt  yt
(Monetary Policy)
mt  mt 1  e t
Variables are in logs. y* is the CE value of output w/
complete info.
• Tools of Fed:
e
surprise shock to money supply.

anticipated (systematic) policy rule.
• Results:
 1 
e t
pt  y *  mt 1  
 1  a 
 a 
e t
yt  y * 
 1  a 
• Anticipated or systematic changes in monetary
policy () have no effect on real output (y).
• Unexpected shocks matter for real output:
yt
a

> 0 if a > 0
e t 1  a
• In this situation (exogenous) changes in money
supply is procyclical (& non-neutral).
– Note that unlike CIA model w/ production, money is
also superneutral (no anticipated inflation effects)
• Policy Evaluation: a matters for the effect of
monetary policy:
q = 1  a = 0  dy/dm = 0
• Result became know as the Policy
Ineffectiveness Proposition: Anticipated
changes in monetary policy are neutral and
unexpected changes are non-neutral.
• Information regarding monetary policy and the
Fed matters for the effect of money on real
output.
• If goal is to minimize output fluctuations (yt – y*),
ala the Taylor Rule, it is optimal for FED to set
et= 0. (monetarist “constant growth rate rule”)
Phillips Curve
• The Phillips Curve is a statistical
(i) Positive relationship between inflation
and real GDP.
(ii) Negative relationship between inflation
and unemployment rate.
Figure 17.2 The Phillips
Curve, 1947–1959
Figure 17.3 The Phillips
Curve, 1960–1969
Figure 12.1 The Phillips curve and the U.S.
economy during the 1960s
PC in Keynesian Model
• If nominal wages (W) are slow to adjust there will
be a
(i) Positive relation between p and Y
(ii) Negative relation between p and
unemployment rate u.
p  h(u * u )
where u* is the “natural unemployment rate”
• Trade-off can be permanent
• Fed can exploit this trade-off and control UR by
choosing p.
Some Historical Facts about US
Inflation
•
•
•
•
•
Stable and low inflation in 1950s and 60s
High inflation and unemployment in 1970s
Low inflation and unemployment in 1990s
PC “broke down” since 1970s.
Failure of Keynesian models to account for
PC break down (see Mankiw article).
Figure 17.3 The Phillips
Curve, 1960–1969
Figure 17.4 The Phillips
Curve, 1970–1979
Figure 17.5 The Phillips
Curve, 1980–1989
Figure 17.6 The Phillips
Curve, 1990–2003
Figure 12.2 Inflation and unemployment in
the United States, 1970–2002
CE Model View of PC
• Both segmented markets & misperceptions
models imply expectations about monetary
policy, prices, and inflation affect PC trade-off.
• Expectations augmented PC
p  p )  h(u * u)
e
where u* = “natural” rate of unemployment.
• Natural Unemployment is due to worker-job
“mismatches” caused by
(i) Frictional reasons (search theory  may be
optimal)
(ii) Structural reasons
• Generic macro policy cannot & should not be used to
affect natural unemployment. Only targeted policies:
– Worker retraining, education, employment agencies,
unemployment insurance reform, ect.
• There are costs of inflation in CEM: high nominal interest
rates, lower output. (recall the “Friedman Rule”)
• Robert Barro studies money supply and inflation across
83 countries (1950-90). Finds
* Median Inflation = 8% (23 > 10%)
* Median Money Growth = 11% (57 > 10%)
WHY??
Central Bank Commitment
• If inflation is “bad” why do we see it in
almost every country around the world?
• Two possibilities
(i) Inflation tax.
(ii) Central bank commitment problem
• Kydland and Prescott (2004 Nobel
Winners) pioneered work on policy rules
and discretion.
• Should Fed follow rules or discretion?
• The time consistency problem arises when
the best plan is made and then there are
incentives to abandon it at a future date.
• Hostages, Speeding, Exams.
• PC and central bank commitment.
* Fed preferences
* Credibility problem and pe
Commitment: A Simple Example
• Assume that FED can directly set inflation rate
p.
• FEDs Loss Function:
L = p2 + u2
• Phillips Curve:
p  p )
e
• Initially pe = p = 0
1
 (u * u )
2
 u = u* and L = (u*)2
• FED takes pe = 0 as given and sets p to
minimize loss function L:
p = 2u*/5 > 0
• Public has rational expectations and
understands the incentives of FED:
p = pe = 2u*/5 > 0.
• Rational expectations equilibrium w/ no
commitment:
p = pH = 2u*/5 > 0
u = u*
L = (pH)2 + (u*)2 > (u*)2.
• Rational expectations equilibrium with
commitment:
p = pH = 0
u = u*
L = = (u*)2.
• Solutions to commitment problem
(i) Tough central banker
(ii) Tougher consequences for not meeting
inflation targets.
(iii)Central bank independence.
Senate Testimony of Ben Bernanke, Fed
Chairman Nominnee (11/15/05)
• “the Federal Reserve's success in reducing and
stabilizing inflation and inflation expectations is a
major reason for this improved economic
performance.”
• “Monetary policy is most effective when it is as
coherent, consistent, and predictable as
possible.”
• One possible step toward greater transparency
would be for the FOMC to state explicitly the
numerical inflation rate or range … consistent
with the goal of long-term price stability
Figure 14.10 Central bank independence
and inflation
• Another reason for expansionary monetary
policies: CE is wrong, markets fail, involuntary
(cyclical) unemployment is a big problem, and
there is a role for Keynesian stabilization
policies.
(i) Sticky price (non-market-clearing)
(e.g., IS-LM model)
(ii) Coordination failure