## Advanced Lecture Notes for Hall and Taylor, Chapter 8

Course Instructor: Professor Leigh Tesfatsion
Email: tesfatsi@iastate.edu
Last Updated: 8 April 1996

# HT8: The Complete Hall and Taylor Model

```
Basic References:  Hall and Taylor, Chapter 8;
Study Guide, Chapter 8.

In previous chapters, HT develop two of the components of
their macro model: the "long-run growth model"  for the
determination of potential GDP in period T, Y*(T); and the IS-LM
model for the determination of actual GDP in period T, Y(T).  In
this chapter HT develop the third and last component of their
macro model: the "Phillips Curve" describing the way in which the
general price level adjusts over time in response to
discrepancies between potential and actual GDP in each period T.

Before detailing the nature of this price adjustment
process, we need to introduce a more comprehensive definition
of equilibrium than the notion of short-run equilibrium
introduced in HT7.

A. A MORE COMPREHENSIVE DEFINITION OF EQUILIBRIUM

Recall from HT7 that an economy is said to be in a #short-run
equilibrium# if both the money market and the product market for
the economy are in equilibrium.  Equivalently, by construction of
the IS and LM curves, an economy is in a short-run equilibrium if
and only if its current Y and R levels constitute an intersection
point of its IS and LM curves.  For this reason, a "short-run
equilibrium" is often referred to as an "IS-LM equilibrium."

By construction, the AD curve for an economy is derived from
the locus of intersection points of the economy's IS and LM
curves.  Consequently, yet another way to characterize short-run
equilibrium for an economy is to say that it is on its AD curve.

Note that the fact an economy is in a short-run equilibrium
say nothing about whether its labor market is in equilibrium.  In
particular, being in a short-run equilibrium gives no guarantee
that actual employment N is equal to potential (full) employment
N*, or equivalently, that actual GDP Y is equal to potential GDP Y*.

For the complete HT model, we need a more comprehensive
definition of equilibrium, "internal balance,"  that also takes
the labor market into consideration.  [Although HT make extensive
implicit use of the concept of internal balance, for some reason
they never refer to it by its conventional name.]

#Internal Balance#: An economy is said to be in internal balance
if #all# of its domestic markets (money, product, #and# labor)
are in equilibrium.  In particular, then, an economy is in
internal balance if two conditions hold: (i) it is in a short-run
equilibrium; and (ii) actual GDP is equal to potential GDP.

the early nineteen seventies, a commonly maintained assumption
was that the price level P(T) for period T would not change
immediately if firms found themselves producing above or below
the potential GDP level Y*(T).  Rather, it was assumed that the
existence of a gap in period T between potential and actual GDP
resulted in some change in the price level in the following
period T+1 at the earliest.

In particular, it was assumed that the inflation rate from
period T to T+1 was positively correlated with the GDP gap in
period T for each period T.  Such a relation between the inflation
rate and the GDP gap is referred to as a #Phillips Curve# in
honor of one of the first economists to popularize the relation,
in a 1957 #Economica# article.

A simple linear algebraic form for the traditional Phillips
Curve is as follows:

#A Simple Linear Specification for the Traditional Phillips Curve#:

Y(T)- Y*(T)
(8.1)     INF(T,T+1)       =        f [ ------------- ]  ,
Y*(T)

where

P(T+1) - P(T)
INF(T,T+1)    =     ---------------   =  inflation rate
P(T)           from T to T+1 ;

Y(T)- Y*(T)
--------------  =   GDP gap in period T ;
Y*(T)

f  =  positive exogenously given coefficient multiplying
the GDP gap which reflects the responsiveness of
the inflation rate to changes in the GDP gap.

Note that, by manipulating terms, relation (8.1) determines
the price level P(T+1) for period T+1 as a function of the period
T price level P(T), the period T GDP level Y(T), and the period T
potential GDP level Y*(T):

Y(T)- Y*(T)
(8.2)    P(T+1)    =     P(T)   +   P(T) f [-------------]   .
Y*(T)

Consequently, once a relation such as (8.1) is appended to the
IS-LM model developed in HT7, augmented by labor market relations
for the determination of Y*(T), one has a way of determining the
movement over time of P(T) as well as the movement over time of
Y(T), R(T), and other endogenous variables such as aggregate
household consumption C(T).

The basic underlying motivation for the Phillips Curve (8.1)
was a key empirical regularity, known as "Okun's Law," that still
holds today.

C. OKUN'S LAW

It is a well-established empirical fact that GDP and unemployment
are negatively correlated over time, in the sense that periods of
high GDP correspond to periods of low unemployment and conversely.
[See HT Chapter 1, figures 1-3 and 1-5.]  However, as briefly
discussed by HT in Chapter 3, it is also an empirical fact that
the magnitude of this negative correlation tends to be fairly
#constant# over time.  In particular, for each percentage point
that the unemployment rate U(T) is #above# the natural unemployment
rate U*(T), real GDP Y(T) tends to be about 3 percent #below#
potential real GDP Y*(T). [See HT Chapter 3, figure 3-5.]

This empirical regularity is known as Okun's Law in honor
of the economist (Arthur Okun) who first pointed it out.  In
algebraic terms, Okun's Law takes the following form:

#Algebraic Form of Okun's Law#:

Y(T)  -  Y*(T)
(8.3)       ----------------    =    -3.0 [U(T) - U*(T)]  ,
Y*(T)

GDP gap                discrepancy between actual
in period T                and natural rates of
unemployment in period T

Relation (8.3) predicts that a #3 percent decline# in Y(T)
will be associated with only about a #1 percent increase# in the
unemployment rate U(T).  Why should this be so?  Many economists,
including HT, answer that it reflects the tendency of firms to
engage in hedging behavior in response to demand shocks.

For example, in response to an unfavorable demand side
shock (a decrease in Y^D), firms tend to hedge against the
possibility that the negative shock is transient by keeping on
workers they don't actually need and demanding less work effort
from their workers per hour.  Thus, measured productivity
(average output per paid work hour) declines along with output Y
as firms try to bring Y down in line with the lower Y^D, but the
percentage increase in unemployment (laid off or fired workers)
is less in magnitude than the percentage decline in Y---in
particular, unemployment increases by only about 1 percent in
response to a 3 percent decline in Y.  A similar story can be
told in reverse for favorable demand side shocks.

In this way, firms keep up worker morale by providing
increased job security, and they also avoid some of the
transactions costs associated with the hiring and firing of
workers.  Of course, if demand shocks persist, most firms
ultimately will resort to changes in their employment levels
(firing and hiring) to bring these levels in line with output
levels.

D. RELATION BETWEEN OKUN'S LAW AND THE TRADITIONAL PHILLIPS CURVE

[See HT Figure 8-4.]

Consider an economy in internal balance in some period T,
with an aggregate consumption function given by C = a + b[1-t]Y.
Suppose consumer tastes suddenly change---in particular, suppose
the coefficient "a" in the consumption function suddenly decreases,
implying that households demand fewer goods and services at each
given level of Y.

In terms of the IS-LM model developed in HT7, the economy's
IS curve will shift down in period T in response to this change in
the consumption function.  Assuming that short-run equilibrium is
quickly restored---in particular, that firms act to keep their
short-run production levels in line with their demands so that
product market equilibrium is retained---actual GDP Y(T) will
then decrease to some lower level Y(T)'; for the intersection of
the IS and LM curves will now occur at a point where Y and R are
both lower.

Note that this decrease in Y(T) in response to the sudden
period T change in the consumption function coefficient "a"
occurs for any value of the current price level P(T), implying
that the AD Curve for period T is shifted #downward#.  On the
other hand, period T potential GDP is unaffected by the change in
the consumption function coefficient.  Consequently, a negative
GDP gap opens up at the current price level P(T), i.e., Y(T)
falls below Y*(T).

By Okun's Law, the opening up of this negative GDP gap
results in an unemployment rate U(T) that is #higher# than the
natural unemployment rate U*(T) as firms start to decrease their
employment levels in response to decreased demand for their goods
and services.  Assuming the unfavorable demand shock persists (so
that the AD curve is permanently shifted downwards), these
conditions ultimately lead to falling wage rates and also to a
fall in the prices charged to household for final goods and
services as consumption demand for goods and services weakens in
response to the fall in Y.

This commonly observed sequence of events, from the opening
up of a negative (or positive) GDP gap to a fall (or rise) in
the prices for final goods and services, is precisely what is
captured by the traditional Phillips Curve (8.1).

E. THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE

[See HT figure (8-5).]

Okun's Law and the traditional Phillips Curve (8.1) together
predict a #negative# correlation between the inflation rate
INF(T,T+1) and the unemployment rate U(T).  This prediction
seemed to fit U.S. data and policy experience fairly well during
the nineteen fifties and sixties.  However, in the mid-nineteen
seventies things started to go haywire.

Specifically, as can be seen from figures 3-1 and 3-4 in HT
Chapter 3, Chapter 3, the inflation rate and the unemployment
rate exhibited a #positive correlation# in the nineteen seventies,
in the sense that they tended to #increase together#---a phenomenon
labelled "stagflation."  By the end of the nineteen seventies
(1979=the second oil price shock), the inflation rate had soared
to historically unprecedented heights (over 12 percent) while at
the same time the unemployment rate appeared to be trending upwards.
However, this was followed, in 1982, by a sudden #drop# in the
inflation rate and a huge #increase# in unemployment---the

Numerous researchers subsequently attempted various fix-ups
of the basic Phillips curve relation (8.1) that could explain all
of these empirical observations.

One economically reasonable modification of the relation (8.1)
which provides a systematic explanation for these events is the
#expectations-augmented Phillips Curve#.  The expectations-augmented
Phillips curve was developed by Edmund Phelps and Milton Friedman
in the late 1960s, in response to perceived theoretical deficiencies
of (8.1); but the importance of their work was not accepted until
the nineteen seventies, when the empirical deficiencies of (8.1)
became obvious.

HT postulate and use a simple form of the expectations-augmented
Phillips curve, as follows:

Y(T)  -  Y*(T)
(8.4)   INF(T,T+1)   =   INF^e(T,T+1)   +    f [----------------]
Y*(T)

where

INF^e(T,T+1)  =  Expected inflation rate
from T to T+1 as perceived
by firms at the beginning of
period T;

f  =  positive exogenously given coefficient
multiplying the GDP gap

Important Note:  For simplicity, HT assume throughout
Chapter 8 that potential GDP Y*(T) takes on a #constant# value Y*
over time, i.e., Y*(T) = Y* for all T; compare (8.4) with the HT
text equation (8-1).  This assumption requires consumer tastes to
be constant over time (no shifts in the labor supply curve), and
also technology and the capital stock K(T) to be constant over
time (no shifts in the aggregate production function or in the
labor demand curve).  In particular, the assumption that K(T)
does not change over time means that gross investment I(T) in
each period T consists entirely of expenditures for the
replacement of depreciated capital, so that net investment (gross
investment less depreciation expenditures) is zero.  This is
clearly unrealistic, and is relaxed by HT after a more careful
discussion in chapter 11 of the investment decision.
For clarity, definitions and relations will be introduced
and motivated in class lectures in the more general form (8.4)
which does not presume constancy of potential GDP over time.

Under relation (8.4), in contrast to (8.1), firms are
assumed to have a more sophisticated understanding of inflation.
If firms expect the inflation rate to be INF^e(T,T+1) from period T
to period T+1, then firms will adjust their prices to keep them
in line with the expected change in the general price level #even
if the GDP gap is zero#.  And a #positive# GDP gap will induce
firms to increase their prices at a #faster# pace than the
expected rate of inflation.

Recall that internal balance requires the GDP gap to be
#zero#.  However, according to (8.4), having a zero GDP gap
does #not# guarantee that the inflation rate is zero.  Rather, a
zero GDP gap is consistent with #any# inflation rate #as long as
this inflation rate is fully anticipated in each period T#.

More generally, as will be clarified in the next section and
in later experiments with the complete HT model, (8.4) is consistent
with the stagflation experience of the 1970s.  That is, under
(8.4), it is possible to have a situation in which the inflation
rate is increasing at the same time that the GDP gap is becoming
more negative---or in other words, a situation of stagflation in
which inflation and unemployment are increasing together.

F.  DETERMINANTS OF EXPECTED INFLATION

The simplest postulate concerning how firms form inflation
expectations is that they expect the current inflation rate to be
the same as it was in the previous period.  More generally, they
could form some kind of weighted average over the inflation rates
they have observed over a number of previous periods.  Expectations
formed in this way---as weighted averages over past observations

#Example 1: Adaptive Expectations for the Inflation rate#

Firms determine their expected inflation rate INF^e(T,T+1)
for period T to T+1 by taking a simple weighted average over past
observed inflation rates:

(8.5)  INF^e(T,T+1)  =  a_1INF(T-1,T)  +  a_2INF(T-2,T-1)  + ...

#Example 2: Rational Expectations for the Inflation Rate#

An alternative hypothesis concerning expectation formation
which has become very fashionable in recent years is to assume
that agents understand the actual mechanisms generating key
economic variables, and they use this information to form
"rational expectations."  In particular, agents understand the
structural relations which determine the inflation rate, and they
use this understanding in formulating their inflation rate
expectations.  They don't simply extrapolate over past
observations.

Suppose, for example, that the #actual# inflation rate from
T to T+1 is determined by the growth of the money supply from T
to T+1; i.e.,

M^S(T+1) - M^S(T)
(8.6)   INF(T,T+1)  =   -------------------
M^S(T)

=   actual percentage change in
the money supply M from T to T+1.

Then agents' have #rational expectations# concerning the inflation
rate from T to T+1 if these expectations are given by

(8.7)     INF^e(T,T+1)  =  the #expected# percentage
change in M^S from T to T+1.

Various factors might affect in some degree the way in which
firms formulate an expected inflation rate: for example, past
rates of inflation; monetary policy; and negotiated wage
contracts, especially if these wage contracts include cost of

Economists making use of the expectations-augmented Phillips
curve (8.4) generally assume that, regardless of how firms form
their expectations, they tend to adjust their expectations to
conform to their observations.  In particular, it is assumed that
firms continually adjust INF^e to conform more closely to
observed values of INF.

Given this assumption, relation (8.4) implies the following
#accelerationist property#, sometimes also referred to as the
#natural rate property#:

NATURAL RATE PROPERTY:  As long as actual GDP Y is maintained
above (below) potential GDP Y*, the inflation rate INF will
#perpetually increase (decrease)# as people keep attempting to
adjust their inflation rate expectations to the actual inflation
rate.  Conversely, a #zero# GDP gap is consistent with any
inflation rate INF #as long as this inflation rate is correctly
anticipated#.

G. SOME EMPIRICAL EVIDENCE

Economists have estimated the relation (8.4) over various
different time intervals, often relying on the following simple
adaptive assumption for the expected inflation rate: namely, the
expected inflation rate from T to T+1 is proportional to the
actual inflation rate from T-1 to T.  The following data is taken
from S. Sheffrin, #The Making of Economic Policy#, Blackwell,
1991, p. 1989.  The numbers in parentheses below the estimated
coefficient values denote measured standard deviations.

#Pre-WWII study:#

1873-1914:
Y(T) - Y*(T)
INF(T,T+1)   =   0.22INF(T-1,T)  +   0.34 [-------------]
Y*(T)
(0.14)              (0.19)

R^2  =  0.14   (goodness of fit measure, 1 = best possible)

#Post-WWII study:#

1953-1982:
Y(T) - Y*(T)
INF(T,T+1)  =   0.005 +  0.92INF(T-1,T) +  0.37 [------------]
Y*(T)
(0.07)           (0.003)

R^2  =  0.83  (goodness of fit measure, 1 = best possible)

Comparing the two regressions, the coefficient f on output
deviations is somewhat higher in the post-war era, indicating a
somewhat higher price responsiveness to the GDP gap.  The
regression for the earlier period does not explain nearly as much
variance in inflation as the postwar regression, however, as
evidenced by the small goodness of fit measure.  Inflation is
much more persistent in the postwar error, in the sense that the
coefficient on the lagged inflation term is much closer to 1.0
(implying that inflation in one period tends to spill over into
the next period).

In similar studies run for Italy, Sweden, and the U.K., all
countries exhibited increased responsiveness of inflation to
output movements in the post-war error (higher f estimates).
Although not as clear-cut, evidence for Canada, Norway and
Denmark shows that none of these countries exhibited any sharp
decrease in responsiveness (decline in f) during the postwar era.
On the other hand, for all these countries, the persistence of
inflation (as measured by estimates of the coefficient on lagged
inflation) was much higher in the post-war era.

H.  THE COMPLETE HT MODEL IN EQUATIONAL FORM

Combining the labor market equations for the determination of
potential GDP with the HT7 IS-LM model and the expectations-augmented
Phillips Curve developed above, one obtains the complete HT model.
This model will permit us to derive the movement of the economy from
one short-run equilibrium to the next as the price level adjusts
in response to either a nonzero GDP gap or a change in the
expected inflation rate.

#PERIOD T MODEL EQUATIONS FOR THE COMPLETE HT MODEL#

#Product and Money Markets#:

(1) [Adaptive Expectations]  INF^e(T,T+1)  =  zINF(T-1,T)

(2) [IS]  R(T) = [a + e + G + g]/[d + n] - (1-b[1-t] + m)/[d + n])Y(T)

(3) [LM]  R(T) =  - ( M/hP(T) + INF^e(T,T+1) )  +   [k/h]Y(T)

(4) [Potential Labor Supply]  N*(T)  =  (1+u)^Th(w*(T))

NOTE: "u" denotes the population growth rate; and "w*(T)"
denotes the period T benchmark #full employment# real wage,
not necessarily the actual period T real wage

(5) [Potential Labor Demand]   w*(T) = AF_N(N*(T),K(T))

(6) [Potential Product Supply]  Y*(T) = AF(N*(T),K(T))

(7) [Def of Inflation Rate]   INF(T,T+1) = [P(T+1) - P(T)]/P(T)

(8) [Phillips Curve]  INF(T,T+1) = INF^e(T,T+1) + f[Y(T) - Y*(T)]/Y*(T)

#Movement in Capital Stock over Time#:

(9)  [Gross Investment Function]  I(T) = e - dR(T)

(10) [Gross investment defined]   I(T)  =  K(T+1) - K(T) + xK(T)

Note: Here xK(T) denotes depreciated capital in period T.
Gross investment is defined to be net investment,
K(T+1)-K(T), plus depreciation expenditures, xK(T).

#PERIOD T CLASSIFICATION OF VARIABLES#

Ten Period T Endogenous Variables:

R(T), Y(T), INF^e(T,T+1), INF(T,T+1), P(T+1),
Y*(T), N*(T), w*(T), I(T), K(T+1)

Period T Predetermined Variables:

P(T), INF(T-1,T), K(T)

Exogenous Variables:

Positive Policy Variables  G, M , t with 0 less than t less than 1
Positive Coefficients a, e, g, d, n, b, m, k, h, z, A, u, f, x

#BOX DIAGRAM OF THE MOVEMENT OF THE ECONOMY OVER TIME#:

.....................
.                   .
.                   .
.   Period T Model  .
P(T),K(T),INF(T-1,T) --> . Equations (1)-(10).--> P(T+1),K(T+1),INF(T,T+1)
.                   .
State of the Economy     .                   .     State of the Economy
at the Beginning of      .                   .     at the Beginning of
Period T            .....................        Period T+1

#SOLVING THE PERIOD T MODEL (1)-(10)#:

By assumption, the period T predetermined variables P(T),
K(T), and INF(T-1,T) are known at the beginning of period T, along
with all exogenous variables.  The ten period T endogenous
variables can then be solved for as follows:

(a)  Given P(T) and INF(T-1,T), use (1), (2), and (3) to
determine INF^e(T,T+1), Y(T), and R(T).

(b)  Given K(T), use (4) and (5) to determine N*(T) and w*(T)

(c)  Given K(T) and N*(T), use (6) to determine Y*(T)

(d)  Given P(T), INF^e(T,T+1), Y(T), and Y*(T), use the two
equations (7) and (8) to determine the two unknowns
P(T+1) and INF(T,T+1)

(e)  Given R(T), use (9) to determine I(T)

(f)  Given K(T) and I(T), use (10) to determine K(T+1)

J.  DYNAMIC RESPONSE TO CHANGES IN ECONOMIC CONDITIONS

The dynamic model (1)-(10) permits the investigation of the
dynamic response of the economy to #changes# in economic conditions.
Here we give only a simple illustration, using various strong
simplifying assumptions used also by HT in Chapter 8.

In particular, following HT, suppose that the economy has a
constant potential GDP level Y* over all time periods 0,1,2,... .
In addition, suppose that money demand depends on the real rather
than the nominal interest rate, so that INF^e(T,T+1) does #not#
enter into the LM equation (3).

Finally, suppose that the actual inflation rate INF(0,1) from
period 0 to period 1 is zero.  At the start of period 1, the
economy is in internal balance with a target money supply M, a
price level P(1), a real interest rate R*, a real GDP level equal
to Y*, and an expected inflation rate INF^e(1,2) = 0.  This
position of internal balance is graphically depicted below:

R
.
.
.
.                    E*
R* .
.
.
.
.
......................................    Y
0                    Y*

P
.
.
.
.
.                   A*
P(1)................................................
.                   .
.                   .
.                   .
.                   .
.                   .
.                   .
................................................ Y
0                   Y*

Price adjustment for the economy over periods T = 1, 2, ...
takes place in accordance with the following expectations-augmented
Phillips curve relation, which incorporates a simple adaptive
expectation for the inflation rate:

Y(T)  -  Y*
(8.8)   INF(T,T+1)  =   INF^e(T,T+1)    +    f [-------------]  ,
Y*

where

P(T+1) -  P(T)
INF(T,T+1)   =   ----------------   ;
P(T)

INF^e(T,T+1)  =  zINF(T-1,T)  =  adaptive expectation for the
inflation rate from T to T+1;

f,z  =  positive exogenously given coefficients
with z less than 1

Suppose the Fed unexpectedly #increases# the target money
supply M at the beginning of period 1 to a #higher# level M'.

QUESTION:  How is internal balance reestablished in
subsequent periods, if ever, assuming the Fed holds the
money supply #constant# at the higher level M' in all future
periods?

First-Round Effects: A new short-run equilibrium is established
in response to M --> M' at the initial price level P(1).

The increase in the target money supply leads to a
#downward# shift in the LM curve; the IS curve is not affected.

Since initially the economy was in internal balance at E*,
with M = M^D, and the new money supply M' is greater than M,
there is now an excess supply of money.  The interest rate will
thus tend to fall, encouraging #more# money demand---i.e., the
exchange of bonds (loan contracts) for money.  The fall in the
interest rate results in an increase in investment and net
exports, and hence also to an increase in Y through multiplier
effects.  The drop in the interest rate and the increase in Y
continue until a new IS-LM equilibrium is established at the
higher money supply M' at E'(1) = (Y'(1), R'(1)), say.  Thus,
Y'(1) is greater than Y* , implying the existence of a positive
GDP gap.  Since the period 1 price level P(1) is unchanged, this
implies an #outward# shift of the AD curve, say to the new curve AD'.

R
.
.
R* ..................... E*
.                   .
.                   .
.                   .
.                   .
R'(1) ...................................... E'(1)
.                   .                .
.                   .                .
.                   .                .
.                   .                .
..............................................Y
0                   Y*              Y'(1)

P
.
.
.
.
.                   A*              A'(1)
P(1)...............................................
.
.
.
.
.
.
...............................................  Y
0                   Y*              Y'(1)

Second Round:  The price level #increases# to P'(2) in response
to the #positive# GDP gap.

Since the #actual# inflation rate INF(0,1) from period 0 to 1
was zero, by assumption, the #expected# inflation rate INF^e'(1,2)
= zINF(0,1) from period 1 to 2 is zero.  However, after the
increase in the money supply, the level of GDP Y'(1) for period 1
is higher than potential GDP Y*, i.e., there is a positive GDP
gap (excess demand for goods).

It follows from (8.8) that the initial price level P(1) will
rise from period 1 to 2 to a new level P'(2) greater than P(1) as
firms adjust their prices upward in the face of the positive real
GDP gap:

P'(2)  -  P(1)                          Y'(1) - Y*
INF'(1,2)  =   ---------------   =   INF^e'(1,2)  +  f [----------]
P(1)                                   Y*

(+)                 (0)              (+)

Third Round: A new short-run equilibrium is established at the
higher price level P'(2).

The increase in the price level from P(1) to P'(2) shifts the
LM curve #up#; that is, in order to have money market clearing
for the smaller real money supply implied by the higher price
level P'(2), R must be higher for each GDP level Y to dampen money
demand.  Thus, at E'(1) with Y = Y'(1), the interest rate R'(1)
tends to rise; and this leads to a #decrease# in Y'(1) through
multiplier effects.  Suppose the IS-LM equilibrium corresponding
to the higher price level P'(2) is established at E'(2) =
(Y'(2),R'(2)) with Y* less than Y'(2) and Y'(2) less than Y'(1).
The GDP gap for period 2 is thus still positive, but smaller than
it was in period 1.

R
.
.
R*  .                   . E*
.
.
R'(2) .                                   E'(2)
.
R'(1) .                                         . E'(1)
.
.
.
....................................................Y
0                    Y*           Y'(2)  Y'(1)

P
.
.                    A'(N)
P'(N) ...................................................
.                    .
.                    .
.                    .
.                    .              A'(2)
P'(2) ...................................................
.                    .                     .
.                    .                     .
.                    . A*                  . A'(1)
P'(1) ...................................................
.                    .                     .
.                    .                     .
.                    .                     .
.                    .                     .
...................................................  Y
0                         Y*           Y'(2)  Y'(1)

Fourth Round:  The price level increases to P'(3) in response to
the positive GDP gap.

Fifth Round:   A new short-run equilibrium is established at
the higher price level P'(3).

and so forth......

The point is that the price level will keep on increasing as
long as there is a positive GDP gap and the expected inflation
rate is nonnegative.  According to (8.8), the price level will
cease changing from one period to the next---that is, the realized
inflation rate will be zero---when two conditions are met
simultaneously:

(1)  The GDP gap is zero [Y = Y*]

(2)  The expected inflation rate is zero

The first of these conditions is met at (Y*,P'(N)), but the
second need not be.  If the price level P'(T) during some period
T attains P(N) but agents still expect a positive inflation rate
from T to T+1, then the price level in the next period, P'(T+1),
will be greater than P'(T), and the economy will "overshoot" full
employment real GDP Y* to some level Y(T+1) less than Y*.  The
GDP gap then becomes #negative#, leading subsequently to downward
pressure on the price level through the Phillips Curve relation
(8.8).  Eventually this reverses the decline in real GDP,
bringing it back toward Y*.

Note from the IS-LM diagram above that the interest rate R
reestablished at Y = Y*.  Only the LM curve is shifting
internal balance requires the LM curve to once again attain its
original position in Y-R space.  In particular, #real# money
balances M/P must again equal M*/P(1).  But since M* has
increased to M', this requires the price level P(1) to increase
to a new level, say P'(N), given by

M'
P'(N) =   P(1) ---  .
M

Note that P'(N) is greater than P(1) since M' is greater than M.
Thus, in the internal balance position, both the nominal money
supply M' and the price level P'(N) are higher than they
originally were.

However, notice also that internal balance could be
re-established at Y=Y* with a #persistently# positive inflation
rate if government were to continually #accommodate# the inflation
rate by continually #increasing# the money supply, so that M/P
maintains the value M/P(1) with a continually increasing M and
P.  This observation is a reflection of the position maintained
by monetarists such as Milton Friedman that, in the long run,
inflation is "everywhere and always a monetary phenomenon."

The fact that real GDP Y and the real interest rate R
after the period 1 shock to the money supply is a key result of
the natural rate macro theory espoused by many economists.
According to this theory, a change in the money supply has no
long-run impact on real variables such as Y and R.  Rather, the
only long-run impact of a change in the money supply is a change
in the price level P.

Notice, however, that a lengthy price adjustment process
would realistically have significant affects on investment
(capital) spending, and hence on full employment income; so that
maintaining the constancy of Y* over time is not at all
realistic.  And if Y* is permanently affected by changes in
monetary policy, then so is the ultimate internal balance
position which emerges in response to a money supply shock.
Consequently, many economists argue that money is not "neutral"
in the sense of having no real affects unless the price level
adjusts #instantaneously# to keep the GDP gap always at zero
#and# expectations are always correct.

FINAL REMARK:  Suppose money demand depends on R^N = R + INF^e
rather than just on R as HT assume.  Does anything change?  The
answer is YES.  As before, the price level will go up in response
to the increase in M and consequent opening up of a GDP gap,
which tends to shift the LM curve #up#.  On the other hand, the
sudden rise in price will lead to a revised higher expectation
for the #inflation rate# INF, and this rise in INF^e causes a
#downward# shift in the LM curve.  If the latter effect
dominates, the economy might move further and further away from
the full employment level Y* in each successive period.

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