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The dynamic models of economic policy
in the depiction of System Dynamics
Marek Urbaniak
Poznan University of Economics
Al. Niepodlegtosci 10
60-967 Poznan
fax: +48 61 8569565
e-mail: urbaniak@tenbit.pl
Abstract:
The study is a scientific and teaching approach of the issues of economic policy in
depiction of System Dynamics. There has been presented the dynamic version of the model of
aggregated supply - aggregated demand: AS-AD, the model of rational expectations and the
model of the economic cycle. Conducted simulations concerning a theoretical economy
enable to indicate the general recommendation for decisions-makers.
Key words: macroeconomics, economic policy, aggregated supply, aggregated demand,
Keynes, AS-AD model, rational expectations, economic cycles
Table of content:
LT Introduction .........cececeeceeseeseseeseseseeseseeseseseseseeseaesseassesneacseeasaesesassessssessacsesesiesseacsesseaeseseeeereee
2 The AS-AD model
2.1 The algebraic form of the AS curve
2.2 Solution of the AS-AD model
2.3 The demand shocks AD .
2.4 The supply shocks AS....
3 The changes of aggregated demand AD and aggregated supply AS
3.1 The growth of the money supply Ms
3.2 The increase of the governmental expenses G
3.3 The short-term negative supply shock ..
4 The long-term aggregated supply AS curve.
5 The policy of a state during the negative long-term supply shock.
6 The theory of rational expectations
7 The model of the economic cycle
1 Introduction
The study is a scientific and teaching approach of the issues of economic policy in
depiction of System Dynamics.
The dynamic version of the model of aggregated supply - aggregated demand: AS-AD is
presented in the study. There are simulated the following cases:
- the positive demand shock caused by the growth of money supply Ms and government
expenses G;
- the negative exogenous supply shock;
every time at different assumptions of nominal wages W rigidity.
The effectiveness of demand and supply policy is studied, enabling to specify general
instructions for decision-makers.
The AS-AD model is analysed from the point of view of the rational expectations theory.
The model that includes forming rational expectations instead of adaptive ones is proposed.
In a separate model there has been carried out the analysis of economic cycles - an
approach of structural models researchers, including the co-relation between the delays of real
production Y.
The simulations concern a theoretical economy, being in at the beginning in the point of
balance. The parameters were selected in order to carry on correct calculations. I believe that
this article can be the basis of fruitful discussion and scientific co-operation. Empirical
verification of conducted simulations will be presented during the conference. Working
models in Vensim are available from the author on request.
2 The AS-AD model
The IS-LM model was used in the economic analysis till the second half of the 60s. In that
time the economy of the United States suffered stagflation - the phenomenon of recession
combined with high inflation. The AS-AD model turned out to be useful in the interpretation
of this phenomenon. The model consists of:
- the equations of the aggregated demand (the AD curve), which shows the real production
Y in the balance points of the IS-LM model for the average changeable level of prices P;
- the equations of the aggregated supply (the AS curve) - the formula presenting the
changes of the average level of prices P at different production capacities (different labour
L - in short run).
The average level of prices P
'
:
Y
The real production Y
Figure 1. AS-AD model
The AD curve can be derived by side-comparing the equation of the IS-LM model:
- the IS curve:
pasterrs (Laden ly oy
dt+n dt+n
where:
Y - real production;
R - real interest rate;
a - autonomous consumption demand;
b - marginal propensity to consume;
d - marginal propensity to invest;
e - autonomous investments;
G - governmental expenses;
g- autonomous net export;
m - marginal propensity to import;
n- sensibility of net export to the changes of interest rate;
t- income tax rate;
and
- the LM curve:
Ruom iP + ; Y (2)
where:
h- sensibility of money demand to the changes of the real interest rate R;
k - sensibility of money demand to the changes of the real production Y;
P - average price level;
Rnom - Nominal interest rate.
The real interest rate R equals
R= Rom Keon) G)
where:
T“«ny7 expected inflation between the ¢ moment and ft +1.
On the basis of equation 2, one can receive the equation of LM curve as a function of the real
interest rate R:
M. 7 k
a(t +" wn @)
The formula of the AD curve presents the negative dependence between the real
production Y and the average price level P:
M,; 4 atetG +2 ie
Te tat)
Ey din
=—O (5)
1-bd=t)+m k
d+n h
The second element of the AS-AD model is the AS curve - the dynamic formula
describing the values of the average price level P in the situation of not adjusting the level of
' Detailed introduction to the IS-LM model was omitted here because it is presented almost in every textbook in
macroeconomics.
the real production Y to the level of potential production Y? The short-term AS curve allows
only the changes of the employment L, caused by balancing the labour demand Lp and the
labour supply Ls at the given level of real wages ..
2.1 The algebraic form of the AS curve
Philips’s curve without inflation expectations is characterised by the equation:
Ws. equi" (6)
W,
where
W - nominal wage;
u - unemployment rate;
€- the indicator of the convertibility of the variability of the unemployment rate u to the
natural unemployment u’ and the rate of the expected growth of nominal wages.
The wage in the moment f¢+1 amounts to:
Wy =W[l-eu-w’)). 7)
The expected growth of real wages amounts to
Wo —T, 141) (8)
where
Wi - nominal wages growth rate.
Philips’s curve with the inflation expectations is equal to
WTG, sty =-e(u—u) +0 (9)
where
v_ - long-term exogenous supply shock (v >0 in case of a negative shock, v <0 in case of
positive shock).
The relation between the average price level P and wages W amounts to
pata y (10)
a
where
zZ - margin per production costs.
a - the number of product units per labour unit;
Ww - the cost of labour per product unit.
a
At the assumption of the constant quotient of the average level of prices P and the nominal
wages W
P_(1+z)_
Ww a
const
, ay
? In the study the constant level of the potential production Y* is assumed. This assumption does not distort the
results of the analysis. In a long period the full adaptation of the quantity of the production factors is possible.
The potential production Y* is calculated on the basis of the form of economic growth, i.e. Solow’s and
Kalecki’s growth formula.
the rate of nominal wages equals the rate of inflation
Wo =Ta un: (12)
Then, the modified Philips’s curve has the following form
Rett) Mant SEU) +0. (13)
On the basis of Okun’s law
y-Y +
= =-o(u-u ), 14
Y ( ) (14)
where
® - the indicator of the convertibility of a product and unemployment;
one can introduce the value of the demand gap to the formula of Philips’s curve and receive
the equation of the AS curve:
C (y-Y
Kory Kaan =f (4) (15)
where f af,
o
The inflation 2 is a positive function of not adjusting the real production Y to the potential
production Y”, corrected by the inflation expectation Re, my?
2.2 Solution of the AS-AD model
Iteration calculations in the AS-AD model are carried out according to the following
algorithm:
Input ee Output
variables Equations Variables
Foys By asT eo Expected Me eat) = Ma, FSM 2, 1-1) (16)| 7%, YR
inflation s - the weight of inflation from the previous period
at+e+Gt 1-b(1-t)+m
The IS curve R= = -( d=) Y a7)
d+n d+n
Ms; ; k
TheLMcurve R=-|— +7“ +—Y (18)
[ iP, Gey | F
Py. Tos Y, ¥ Inflation rate (19) Fun he
Phillips’s curve ™(, e41) =TG, an —e(u—u ) (20)
Okun’s law a =-o(u-u') (21)
Table 1. Equations in dynamic version of AS-AD model
Algebraic formulas of the AS and AD curves enabled to work out the dynamic version
of AS-AD model in Vensim.
Pt-L d Pt-2
+ flow2 flow3
f “8 ad
INFet a INF tl INF t-2
Ms ‘ ind] ind2
: G Sa By un
-_ of 3 “al
INFe t 48 op of INFet
NS
Raw
z-
- To
k.-
m “ap
Figure 2. AS-AD model in Vensim
The fixed delays used in the calculations between streams and the resource level in the
top part of the model meet the important role. The delays enable to maintain the value of
variables in the system. At the beginning of the next iteration the “flow 0” value
(corresponding to the P.
14
variable) is moved to the “Pt” reserve, being the basis of the
decision process in a next period. This situation is presented in the following example of a
situation chart:
Time (Year) "flow0" "Pt "flow!"
16
“pet “flow?”
w
Bw nN
Table 2. Calculations between streams and the resource level in time
2.3 The demand shocks AD
The AS-AD model enables to analyse demand shocks, which are caused by the
fluctuations of the aggregated demand AD. In case of the positive shock one can observe the
phenomenon of expansion: the real production Y and the average level of prices P is increased
(the AD curve moves to the right). The negative demand shock causes the opposite situation.
The effect of the expansive demand shock i.e. the growth of the money supply My is the
increase of the average level of prices P. The result of that is the decrease of the real wage
.. The labour L becomes cheaper, which results in employing the greater number of
employees and increase the real production Y above the level of the potential production x
The growth of the average price level P over the expected average price level P*, causes that
the current real wage . is lower than the expected real wage =. Employees notice the
decline of the real wage se and start to demand the higher nominal wage W. They start to
renegotiate the wage contracts. The increase of wages being the element of a cost structure of
running a business causes the movement of the AS curve to the left, which decrease the
deviation of the real production Y from the level of the potential production Y.
The average level of prices P
Py po-
Pitan
p be AD,
Y=Y=¥, ¥% The real production Y
Figure 3. Adjustments of AS curve in case of the positive demand shock
If the shock of the aggregated demand AD is not fully anticipated, the growth of the
nominal wage W will not be proportional to the growth of the average level of prices P. The
bigger surprise will result from the shock of the aggregated demand AD or the less elastic the
wages are, the bigger will be the increase of the real Y production in a short period.
Any growth of the average level of prices P, which is not caused by the changes of the
real values (i.e. increasing the asset capital, the growth of population, etc.) has to be
compensated by the equivalent change of the nominal wages W. The change has to maintain
the real wage . at the level providing the long-term balance on the labour market L”. The
contentious issue is the time of adaptations. The hypothesis of a partial rigidity of wages
seems the most realistic.
2.4 The supply shocks AS
The short-term supply shocks signify changes of the real production Y and the average
level of prices P (by the AS curve). The most common cause of fluctuations of the aggregated
supply AS are the changes of the prices of production resources. Although the prices of raw
materials are not an element of the function of production their increase causes the increase of
the costs of running a company. It will cause the increase of prices at the specified fixed
margin added to the costs of production.
The relationship between wages and prices modified with the cost of materials has the
form of:
(1+z)
a
P=
W +vP, (22)
where
v- the quantity of raw materials necessary to produce a single unit of a final product;
P, - the price of materials.
The share of the cost of a raw material in the price of the product P is defined by the
equation:
P
=. 23
Pn = (23)
The price of the product amounts to:
P= l+z W (24)
l-vp,, a
for vp, <1.
The increase of the share of a raw material in the price of a product p',, > p,, can be inserted
to the equation of the Philips’s curve’s formula:
W =W[l-eu-w’)). (25)
Then, the equation of the AS curve taking into account the increase of the prices of raw
materials has the following form:
p (aw'sa_ p=)
Tl ’ [l-e@-w’)}. (26)
l+z l+z
The new level of prices P,, will amount to:
P, =p Pe) ew’) 7)
a
“(l-yp',,)
The increase of the cost of the raw material P, in the price of the product P will cause the
movement of the AS curve to the left.
The average level of prices P
Y, Y= Y, The real production Y
Figure 4. The negative supply shock
The economy will be in the new point of a short-term balance at the higher average
level of prices P and the lower real production Y. The companies decrease the level of
. . . Ww.
employment L, in the same time as a result of the growth of prices P - the real wage 7 will
decrease.
The growth of production costs can signify specifying the new lower level of the real
production Y, at the higher unemployment level vu. This phenomenon will take place when
Acco Ww P
employees want to maintain the real wage y at the level from the period before the shock.
The different situation will take place when the growing unemployment forces
employees to accept the lower level of nominal wages W or when a cause of a supply shock
disappears. Then, the growth of prices P will be limited and the employment will return to the
potential level D
3 The changes of aggregated demand AD and aggregated supply AS
The changes of the balance are more often caused by the changes of the aggregated
demand AD, which is characterised by the bigger changeability, than the aggregated supply
AS.
The following issues were subjects of simulations with the assumption of the different
rigidity of nominal wages W:
- the positive demand shock (increasing the money demand Ms);
- the positive demand shock (increasing the governmental expenses or another
autonomous component of the AD curve);
- the negative short-term exogenous supply shock.
The simulations concern a theoretical economy, being at the beginning in the point of
balance. The parameters were selected in the way enabling to carry on correct calculations.
In case of every shock one has assumed that the s, parameter in the equation of the
expected inflation 7/, ,,,, (see equation 16) amounts to 0 and s, has one of the following
values: 0.7, 0.5 or 0.1. The lower value of the s, parameter means the bigger elasticity of the
average price level P, thanks to which the price and wage adaptations to the long-term level
are faster.
3.1 The growth of the money supply Ms
Increasing the money supply Ms causes the movement of the AD curve, which results in
mutual adaptations of the AS-AD curve.
The money supply Ms (auxiliary variable) is specified by the equation:
Ms = 900+STEP(300, 1). (28)
The growth of the money supply Ms does not cause any changes of the real production Y
and the real interest rate R in a long term. After initial deviation both variables go back to the
level from the period before the shock.
Yt
8,000
7,000
6,000
5,000
4,000
0 3 ey ne (
Time (Year)
Yt: ind1=0,1
Figure 5. The real production Y in case of the growth of the nominal money supply Ms
R
0.4
0.3
0
0 5 10 15 20 25 30 35 40 45 50
Time (Year)
R: ind1=0,7
R: ind1=0,5
R: ind!=0,1
Figure 6. The real interest rate R in case of the growth of the nominal money supply Ms
The average level of prices P increases proportionally to the increase of the nominal
money supply M,. The most of prices are increased already in the first iterations of the
adaptation process.
Pt
"TAL ALAA
w_U
N
0.8
0 3 mo 15 20 25 30 35 40 45 50
Time (Year)
Pt: ind1=0,7
Pt: ind1=0,5
Pt: ind1=0,1
Figure 7. The average level of prices P in case of the growth of the nominal money supply Ms
Because of the change of the nominal money supply M, (not the real money supply
“s) the rate of inflation m in a long run goes back to the level from the period before the
shock.
MS/P
2,000
1,650
1,300
950 is
600
0 > 10 Is 20. 25 30 35 40. 45 50
Time (Year)
"MS/P" : ind1=0,7
"MS/P" : ind1=0,5
"MS/P" : ind1=0,1
Figure 8. The real money supply in case of the growth of the nominal money supply Ms
The dynamics of the rate of inflation 1 is strongly related to the nature of the
adaptations of the average price level P. The rate of inflation 1 increases significantly at the
beginning of the analysis, then, it begins to decrease gradually to the level from the period
before the shock.
INF t
“NCA AAA
0 3 2 30.°«35°~=CO« 40S SO
Time (Year)
INF t:ind1=0,1
Figure 9. The rate of inflation 1 in case of the growth of the nominal money supply Ms
In case of the most elastic wage and price adaptations (s; = 0,1), on the basis of the
chart of the average price level P - the real production Y, one can notice almost direct
transition to the point of a long-term balance (from the level of the real production Y’ for P=
1 to the same level of the real production at P = 1.33). In other cases (s; = 0,5 or 0,7) the
adaptations occur with delays.
Price - production
2
0.8
5985 6209 6433. 6657 68817105. 732975537777
Production
Pt: ind1=0,7
Pt: ind1=0,5
Pt: ind1=0,1
Figure 10. The chart of the average price level P - the real production Y
in case of the growth of the nominal money supply Ms
The consequence of the changes of the quantity of production is the oscillating
character of adaptations within the confines of relations between unemployment wu and
inflation 2 . In each case of the simulation the long-term balance corresponds with the level
from the period before the shock.
Inflation (Rate of Unemployment)
0.2
-0.010 0.010 0.030 0.050 0.070 0.090
Rate of unemployment
Figure 11. The chart of the rate of inflation x in case
of the growth of the nominal money supply Ms
3.2 The increase of the governmental expenses G
The increase of the governmental expenses (or the exogenous component of the
aggregated demand AD) means, similarly like in case of the growth of the money supply Ms,
the movement of the AD curve, after which the adaptations of the AS and AD curve take
place.
Governmental expenses are characterised by the equation:
G = 1200+STEP(300, 1). (29)
The increase of the governmental expenses G does not cause the changes of the real
production value Y in a long-term.
Yt
8,000
7,500
7,000 LN
6,500
6,000
0 3 io 15 20 25 30 35 40 45 30
Time (Year)
Yt: ind1=0,7
Yt: ind1=0,5
Yt: ind1=0,1
Figure 12. The real production Y in case of the increase of the governmental expenses G
The increase of the governmental expenses G causes the increase of the real interest rate
R ina long-term. This phenomenon is described in macroeconomics as “crowding-out effect“.
R
04
0.325
0 3 m0 15 20 25 30 35 40 45 50
Time (Year)
Figure 13. The real interest rate R in case of the increase of the governmental expenses G
The average level of prices P increases as a result of the increase of the governmental
expenses G.
Pt
5)
17
14
Ll
0.8
0 5 Cn
Time (Year)
Pt: ind1=0,7
Pt: ind1=0,5
Pt: ind1=0,1
Figure 14. The average level of prices P in case
of the increase of the governmental expenses G
Because the increase of the average level of prices P is not caused by the increase of the
nominal money supply M, , the real money supply “s is decreased.
MS/P
1,000
900
800 a
700 YY
600
0 3 10 15 20 25 30 35 40 45 50
Time (Year)
"MS/P" : ind1=0,7
"MS/P" : ind1=0,5
"MS/P" : ind1=0,1
Figure 15. The real money supply in case of the increase of the governmental expenses G
The rate of inflation in a long term stays at the level corresponding to the value from
the period before the shock.
INF t
0.1
0 3 m0 15 20 25 30 35 40 45 50
Time (Year)
INF t:ind1=0,1
Figure 16. The rate of inflation 7 in case of the increase of the governmental expenses G
On the chart presenting the average level of prices P and the real production Y one can
observe the gradually disappearing oscillations of the real production Y around the potential
production Y. The only difference in comparison to the initial state is the different average
level of prices P, increasing from P = 1 to P= 1.15.
Price - production
09
6436 6530 6624-6718 6812-6906 -~—«-7000-—S--7094.-—S 7188
Production
Pt: ind1=0,7
Pt: ind1=0,5
Pt: ind1=0,1
Figure 17. The chart of the average price level P - the real production Y
in case of the increase of the governmental expenses G
There are adaptations on the chart presenting the unemployment u and the inflation 1 in
the same time. In each case the level of the long-term balance corresponds to the situation
from the period before the shock.
Inflation (Rate of Unemployment)
0.1
0.05
-0.1
0.0250 0.0310 0.0370 ~—-0.0430 0.0490 0.0550 0.0610
Rate of unemployment
INF t: ind1=0,7
INF t: ind
INF t:ind1=0,1
Figure 18. The chart of the rate of inflation 1 in case of the growth
of the increase of the governmental expenses G
3.3. The short-term negative supply shock
The negative shock causes the growth of the average level of prices P and the decrease of
the real production Y. The AS curve moves to the left because of the increase of the costs of
business activity. With the assumption of a short-term character of the negative supply shock:
- the cause of the supply shock must disappear. In case of the growth of the prices of
raw materials the prices should return to the level from the period before the shock;
or
- employees have to agree to decrease the real wage to the level enabling the return of
the unemployment u to the natural level 1”.
The short-term supply shock described by the formula:
supply shock = STEP(0.2, 5)-STEP(0.2, 6), (30)
was inserted in the “flow 0” equation:
flow 0 = Pt*(f*(Yt-"Y*")/"Y*"+1+INFe tt+supply shock). (31)
The short-term supply shock causes the permanent decrease of the real production Y and
the growth of the average price level P.
Yt
0 3 Ce
Time (Year)
Yt: ind 1=0,1
Figure 19. The real production Y in case of the short-term negative supply shock
Pt
2
1.65
0.95
0.6
0 5 10 15 20 25 30 338 40 45 50
Time (Year)
Pt: ind1=0,1
Figure 20. The average level of prices P in case of the short-term negative supply shock
The rate of inflation 7 , after initial increase, comes to deflation, enabling the return of
the average level of prices P to the value from the period before the shock.
INF t
04
7 A
0
-0.2
-0.4
0 3 mo 15 20. 25 30 35 40 45 50
Time (Year)
INF t: ind1=0,1
Figure 21. The rate of inflation 7 in case of the short-term negative supply shock
The increase (decrease) of the average level of prices P causes the decrease (increase) of
M. r si é F ‘
the real money supply a , which results in increasing (decreasing) the real interest rate R.
In a long period the real money supply = and the real interest rate R reach the level from
the period before the shock.
MS/P
2,000
1,650
1,300
950
600
0 3 to 15 20. 25 30 35 40 45 50
Time (Year)
"MS/P" : ind1=0,7
"MS/P": ind1=0,5
"MS/P": ind1=0,1
Figure 22. The real money supply in case of the short-term negative supply shock
: AIA
OP
0 3 mo Is 20. 25 30 35 40 45 50
Time (Year)
R : ind 1=0,7
R : ind1=0,5
R: ind1=0,1
Figure 23. The real interest rate R in case of the short-term negative supply shock
The movements of the AS and AD curves representing the changes of the average level
of prices P and the real production Y show the oscillating character of fluctuations during the
return of the economy to the state from the period before the shock.
Price - production
0.9
0.7
5933 6160 6387: = 6614. 6841 = 7068 = 7295. 7522-7749.
Production
Pt: ind1=0,7
Pt: ind1=0,5
Pt: ind1=0,1
Figure 24. The chart of the average price level P - the real production Y
in case of the short-term negative supply shock
The influence of the demand gap (the gap of the real production Y) on the changes of the
unemployment u causes the oscillating fluctuations on the chart presenting the relation
between the inflation (rate) m and the unemployment (rate) uw.
Inflation (Rate of Unemployment)
-0.010 0.010 0.030 0.050 0.070 0.090
Rate of unemployment
INF t: ind1=0,7
INF t: ind1=0,5
INF t: ind1=0,1
Figure 25. The chart of the rate of inflation x in case
of the short-term negative supply shock
4 The long-term aggregated supply AS curve
The long-term AS curve shows the potential level of production Y’, which is created in
the conditions of the natural unemployment uw at the full usage of the production capacities.
The long-term AS curve has the shape of a vertical line on the chart showing the average level
of prices P and the real production Y, because prices have no influence on the production
capacities of an economy in a long term. Moving the long-term AS curve represents the
increase of the potential production Y and - ina longer perspective - the decrease of the
average level of prices P.
The average level of prices P
Y*, Y' The real production Y
Figure 26. The long-term positive supply shock
The causes of the movements of the long-term AS curve include the changes of real
values (i.e. increasing the quantity of production resources, improvements of technologies,
productivity increase, long-term supply shocks, etc.) This phenomenon took place in the USA
in the 90s, when the significant technological progress took place.
The long-term negative supply shock was simulated. The shock causes - as a result of the
permanent increase of business costs - moving the long-term AS curve to the left. The supply
shock described by the formula:
supply shock = STEP(0.2, 5), (32)
was introduces to the "flow 0" equation:
flow 0 = Pt*(f*(Yt-"Y*")/"Y*"+1+INFe tt+supply shock). (33)
The long-term supply shock causes the decrease of the real production Y and the increase
of the average price level P.
8,000
7,000
6,000
5,000
4,000
0 5 10 1s 20 25 30 35 40 45 50
‘Time (Year)
Yt: ind1=0,7
Yt: ind 1=0,5
Yt: ind1=0,1
Figure 27. The real production Y in case of the long-term negative supply shock
Pt
8
6
4
2
0
0 3 i Is 20 25 30 35 40 45 50
Time (Year)
Pt: ind1=0,7
Pt: ind1=0,5
Pt: ind1=0,1
Figure 28. The average level of prices P in case of the long-term negative supply shock
The dynamics of the rate of inflation 2, after the initial growth, gradually decreases
causing smaller and smaller increase of the average level of prices P.
INF t
0.4
0 5 1 15 20 25 30 35 40 45 50
Time (Year)
INF t: ind1=0,7
INF t: ind
INF t: ind1=0,1
Figure 29. The rate of inflation m in case of the long-term negative supply shock
The growth of the average level of prices P causes the decrease of the real money supply
M : ‘ r
> , which causes the increase of the real interest rate R.
MS/P
1,000
750
500
250
0
0 3 to 15 20. 25 30 35 40 45 50
Time (Year)
"MS/P": ind1=0,1
Figure 30. The real money supply in case of the long-term negative supply shock
0 3 mo 15 20 25 30 35 40 45 50
Time (Year)
R : ind1=0,7
R: ind1=0,5
R: ind1=0,1
Figure 31. The real interest rate R in case of the long-term negative supply shock
The crossing point of the curves AS and AD goes in the form of oscillating fluctuations
from the right bottom to the middle part of the chart.
Price - production
N
4084 4536 4988 5440 5892 6344 6796
Production
Pt: ind1=0,1
Figure 32. The chart of the average price level P - the real production Y
in case of the long-term negative supply shock
The balance points on the chart presenting the inflation x and the unemployment uw move
in an oscillating way from the left to the middle part of the chart.
Inflation (Rate of Unemployment)
0.4
-0.2
-0.4
0.040 0.060 :0.080~——0.100-— 0.120 0.140 0.160.180
Rate of unemployment
INF t: ind1=0,7
INF t: ind1=0,1
Figure 33. The chart of the rate of inflation x in case
of the long-term negative supply shock
5 The policy of a state during the negative long-term supply shock
As a result of a permanent increase of production costs there may appear the social
pressure on the short-term increase of the fluctuations of real production Y. There was
presented the analysis of the efficiency of the economic policy in the situation of the negative
exogenous supply shock, created (like in the point 4 in equation 32) by the formula:
supply shock = STEP(0.2, 5), (34)
inserted to the "flow 0" equation:
flow 0 = Pt*(f*(Yt-"Y*")/"Y*"+1+INFe t+supply shock). (35)
The case of the negative supply shock without taking up a policy is presented in the one of the
analysed situations.
There were used the instruments of an economic policy:
- stimulation of the aggregated demand AD by the growth of:
- the money supply Ms:
Ms = 900+STEP(400, 15); (36)
- the governmental expenses G:
G = 1200+STEP(400, 15); (37)
- the stimulation of the positive supply shock as a result of modification of the supply
shock equation:
supply shock = STEP(0.2, 5)-STEP(0.2, 15). (38)
The initial supply shock takes place in the moment ¢ = 5, the realisation of every policy takes
place in the moment ¢ = 15. In every situation there are assumed fast wage and price
adaptations (s, = 0.1).
The simulations present the inefficiency of the supply policy increasing the money supply
Ms or the governmental expenses G in limiting the decrease of the real production Y. The
monetary policy is neutral for the real interest rate R and the fiscal policy causes its change in
a long period. The supply policy exerts a positive influence on the both mentioned variables
causing their return to the level from the period before the negative supply shock.
Yt
8,000
7,000
6,000
5,000
4,000
0 5 Cn Ce (CT)
Time (Year)
Yt: ind1=0,1 without policy
Yt : ind 1=0,1 with demand policy (G)
Yt: ind1=0,1 with demand policy (MS)
Yt: ind1=0,1 with supply policy
Figure 34. The real production Y in case of different policies
R
0.6
0.45
0.3
0.15
0
0 3 1 15 20 225 30 35 40 45 50
Time (Year)
1 with demand policy (MS)
1 with supply policy
Figure 35. The real interest rate R in case of different policies
The demand policy causes the inflation pressure and the average level of prices P is
increasing. The effect of the supply policy is different - there is the deflation pressure and the
average level of prices P goes back to the level from the period before the shock.
Pt
0 5 10 15 20.0 25.s30,'si35 (ss :C«‘i SCS
Time (Year)
Pt: ind1=0,1 without policy
Pt: ind1=0,1 with demand policy (G)
Pt: ind1=0,1 with demand policy (MS)
Pt : ind1=0,1 with supply policy
Figure 36. The average level of prices P in case of different policies
INF t
0.4
0.2
0
-0.2
-0.4
0 5 10 615) 20S 8's ( (tC
Time (Year)
INF t : ind 1=0,1 without policy
INF t : ind1=0,1 with demand policy (G)
INF t: ind1=0,1 with demand policy (MS)
INF t: ind 1=0,1 with supply policy
Figure 37. The rate of inflation 1 in case of different policies
. . M .
The monetary policy does not influence the real money demand po the fiscal policy
causes its decrease and the supply policy enables this variable to go back to the level from the
period before the shock.
MS/P
1,000
0 5 10 615) 20S 30's (tC
Time (Year)
. 1 with demand policy (G)
"MS/P" 1 with demand policy (MS)
"MS/P" : ind 1=0,1 with supply policy
Figure 38. The real money supply in case of different policies
The chart of the average level of prices P and the real production Y presents the
complexity of the correcting mechanism. The initial situation without any policy is presented
as the blue line starting from the right side of the chart and ending on its left side. The supply
policy causes the turn back of the real production Y from the initial target point to the initial
level, which is located on the right side of the chart. In case of the demand policy (specified
by the red and green lines) there occurs the parallel movement of the balance point to the
right, almost to the middle of the chart, and transition to the balance point on the left side, at
the new higher average price level P.
Price - production
0
5196 5356 5516 5676 5836 5996 6156 6316 6476 6636 6796
Production
ind1=0,1 without policy
1 with demand policy (G)
1 with demand policy (MS)
Pt: ind1=0,1 with supply policy
Figure 39. The chart of the average price level P -
- the real production Y in case of different policies
Similarly like in the earlier chart, the chart of inflation x and the unemployment u seems
to be complex, thus, almost unclear. The initial situation, without any policy, is presented as
the blue line, starting in the left part of the chart at the inflation 7 amounting to zero. Then,
the inflation increases to the level 0.2 and from this moment starts to decrease gradually,
going through to the right side of the chart. The demand policy causes a little distortion of the
changes of the unemployment rate u from the specified track, however, the new balance
corresponds to the long-term balance for the case of not realising any policy. The supply
policy causes temporary deflation at the high level of the unemployment wu and the gradual
return to the point of balance from the beginning of the analysis.
Inflation (Rate of Unemployment)
0.4
-0.2
-0.4
0.040 0.050 0.060 0.070 0.080 0.090 0.100 0.110 0.120 0.130
Rate of unemployment
INF t: ind1=0,1 without policy
INF t: ind 1=0,1 with demand policy (G)
INF t: ind1=0,1 with demand policy (MS)
INF t: ind1=0,1 with supply policy
Figure 40. The chart of the rate of inflation 7
in case of different policies
6 The theory of rational expectations
Adaptive expectations (i.e. 7(, ,,.)=5;-%q4,)) assume the persistence of inflation
expectations. The basis of forming rational expectations is all available information. The
expectations of inflation are inseparably connected with a state policy. The anticipation of
activities considers especially a fiscal policy, because the character of that policy depends on
the governing coalition and the realisation of that policy (i.e. passing a budget) is
characterised by a few month delay. One can discuss the anticipation of decisions in a
monetary policy, however, there is the need for transparency and credibility of the
institutions’ activities in this sphere.
The expected level of prices P* is a positive function of not adjusting the real production
Y to the potential production Y", increased by the value of a random error ¢, - which is made
at estimating the state policy:
Pe=P,+B,(%,-¥.) +8, (39)
Rational expectations assume the correctness of the prognoses of the average price level P:
FES =e, (40)
thus the real production Y is equal to:
Y,=¥/ +a¢,. (41)
The inflation expectations 2° are rational, when the random error ¢, has normal
distribution.
Rational inflation expectations assume the ineffectiveness of an economic policy.
Systematic and fully predictable interactions have no effect on the real production Y.
The demand policy consisting in the increase of the growth rate of the money supply Ms
is a special case in the AS-AD model. According to the theory of rational expectations
increasing the inflation 7 causes the increase of the nominal wage W to the level enabling to
Ww “ , ‘
keep the average level of the real wages P at a constant level. Assuming the inflation at the
constant level during the few previous periods (i.e. 1%) it is rational to have the inflation
expectations 2° on the similar level for the next period. In case of the growth of the inflation
t to the level of i.e. 4% employees should demand the higher (by 3%) increase of the average
level of nominal wages at the beginning of the next period.
In the AS-AD model with rational expectations the real production Y in a long term
reaches values exceeding the level of the potential production Y’. It should be emphasised that
such a situation occurs when the growth rate of the money supply Ms is bigger than the
growth rate of the real production Y. On the basis of Philips’s curve of the equation:
7 (Y-Y"
Keay —Keay = SF (4) (42)
at the assumption of adaptive inflation expectations:
Te, rat) = SMe, cary? (43)
the gap of the real production Y and the inflation meet the following equality in a long
(el)
term:
(44)
TM, 141)
Because for the different values of the parameters, the level of inflation x increases by
the same value the deviation of the real production Y from the potential level Y’ depends
positively on the coefficient f: The increase of the inflation 7 causes the underestimation of
the inflation expectations 1° and initial restraining of phenomena causing inflation. That is the
reason why the wage and price adaptations cannot keep up with the growth of the money
supply Ms.
The study of the AS-AD model with rational expectations requires modifying the model
of adaptive expectations. There is introduced the condition, according to which the rate of
inflation has the value of the growth rate of the money supply Ms. The scheme of the AS-AD
model with rational expectations is presented below.
4
7 ye
Yt \
a Pt 4X ae) —e Mst “4X
flow0 flow! Ms flow0 Ms flowl
ape ” w
‘ id
: Ms rate
INFe t Os
INF t-1
ind1 :
& «aN
. INFet
- -To
Figure 41. AS-AD model with rational expectations in Vensim
The increase of the rate of the growth of the money supply Ms from 1% in the given
period to the level of 4% occurs in the moment ¢ = 20. The money supply Ms is specified as
the level variable, and it is characterised by the equation:
Ms = Ms*(0.01+IF THEN ELSE(Time<20, 0, 0.03)).
awe)
(45)
The track of the growth of the money supply Ms is presented in the following chart. The
rate of the growth of the money supply Ms is represented by the inclination of a tangent to the
curve in a given point.
Ms
Ms : ind 1=0,1
Ms : ind 1=1
Figure 42. The nominal money supply in AS-AD model
with rational (red line) and adaptive expectations (blue line)
20
25
Time (Year)
30
35
40
45
50
The AS-AD model was put to the simulation with adaptive and rational expectations. In
case of the model with adaptive expectations there occurs the growth of the real production Y
over the level of the potential production Y’. In the model of rational expectations the real
production Y goes back to the point corresponding to the potential production ¥. Changes of
real production Y in case of the model with rational expectations in the moment t = | are due
to initial values variables of variables.
Yt
8,000
7,500
7,000
6,500
6,000
0 5 10 15 20 25 30 35 40 45 50
Time (Year)
Yt: ind1=0,1
Yt: indI=1
Figure 43. The real production Y in AS-AD model with rational and adaptive expectations
The increase of the money supply Ms causes in both cases the increase of the rate of
inflation 7.
INF t
0.06
0.045
0.03
0.015
0
0 5 Cn ne ()
Time (Year)
INF t: ind1=0,1
INF t: ind1=1
Figure 44. The rate of inflation 7 in AS-AD model with rational and adaptive expectations
Pt
6
4.5
3
1.5
0
0 5 10 615) 20—:—i«S a 8siS—( tC‘
Time (Year)
Pt: ind1=0,1
Pt: ind1=1
Figure 45. The average level of prices P in AS-AD model
with rational and adaptive expectations
The significant influence on the size of the real money supply is exerted by the speed of
the partially rigid price level P. It is the speed of the adaptation of the average price level P to
the money supply Ms that determines the final level of the real money supply us in a long
term.
MS/P
900
800
0 5 10 15 20 25 30 35 40 45 50
Time (Year)
"MS/P": ind1=0,1
"MS/P": ind1=1
Figure 46. The real money supply in AS-AD model with rational and adaptive expectations
x M, . F
The increase (decrease) of the real money supply 7s is accompanied by the decrease
(increase) of the nominal interest rate Ryom.
Rnom
0.4
0.325
0.25
0 5 CE ne ()
Time (Year)
R nom: ind1=0,1
R nom: indI=1
Figure 47. The nominal interest rate Rnom in AS-AD model
with rational and adaptive expectations
The real interest rate R is equal to the nominal interest rate Ryom diminished by the
inflation expectations 2°. In case of adaptive expectations the real interest rate R decreases
gradually to the new long-term level. In case of rational expectations the real interest rate R
stays at the initial level because the decrease of nominal interest rate Rnom is accompanied by
the increase of average price level P.
R
0.175
0.125
0 3 10 15 20. 25 30 35S 40 4550
Time (Year)
R : ind1=0,1
R: ind1=1
Figure 48. The real interest rate R in AS-AD model with rational and adaptive expectations
The dynamics of changes is clearly presented on the chart of the average price level P
and the real production Y as well as on the chart of the inflation 1 and the unemployment wu.
In case of adaptive expectations one can observe the increase of the real production Y in
comparison to its initial value. Next, the real production Y in the rational model of
expectations is equal to the potential production Y from the beginning of the analysis. The
patterns of adaptations are easier to analyse if one notices that in the simulation the average
price level P is increasing from period to period. The iterations for the following higher
values of the average price level P represent later and later simulations.
Price - production
6795 6829 6863 6897 6931 6965 6999 7033 7067
Production
Pt: ind1=0,1
Pt: ind1=1
Figure 49. The chart of the average price level P - the real production Y
in AS-AD model with rational and adaptive expectations
In case of adaptive expectations there occurs the decrease of the rate of unemployment wu.
In the model of rational expectations unemployment goes back to the point of the long-term
balance uv’.
Inflation (Rate of Unemployment)
0.06
0.045
0.03
0.015
0
0.0300 0.0320 0.0340 0.0360 0.0380 0.0400 0.0420 0.0440
Rate of unemployment
INF t: ind1=0,1
INF t: ind1=1
Figure 50. The chart of the rate of inflation 2
in AS-AD model with rational and adaptive expectations
7 The model of the economic cycle
According to the theory of rational expectations, the basis of the real production Y
equation
Y,=Y,/ +a, (46)
is the assumption of the random character of the production deviations to the potential level
Y’. Econometric analyses indicate that there is the opposite situation: there is the co-relation
between the real production Y from different periods. This phenomenon is presented in the
equation:
¥=Y'+BY +e, (47)
where B > 0, even in case of a delay longer than one single period.
The persistence in the form of the positive parameter B is the basis of an economic
cycle. The B parameter limits the range of the changes of the real production Y, during the
transition to the potential level Y’.
The proposal of the model of economic cycle in a closed economy is presented below.
The aggregated demand for goods and services is defined by the equation:
Yip =C+1+G. (48)
The consumption demand of households C is defined by the remaining income being to
the disposal of Y, from the previous period:
CaatbY, = at+b(Y,-T,)=atb0-t,,)¥- (49)
Investments are specified by the formula:
P=ylt+%Qi-Ya)-nR+z (50)
for y (Lat. gamma) from the range (0; 1), positive y (Lat. chi) and y (Lat. ni) and the
parameter z - the random variable with the normal distribution.
The real money supply us is defined by the formula:
M,_,Y
P R 6D
where the positive / defines the liquidity preference.
The level of production capacity utilisation is presented in Okun’s law; the relation
between the unemployment wu and the average price level P - in Philips’s curve.
The scheme of the model is presented below:
Yeoh
el vil 4%» Yt2 | 4X
flow0(Y) . _ fowl (Y) flow2(Y)
a
INFmin. - .p-INFt
nie
» gamma
ati —4X—e)
> Ly :
flow0(1) flow | (1) flow0(t) flow (t)
pf Woe 4
t
Figure 51. The model of the economic cycle in Vensim
The iterations received on the basis of the simulation model enable the analysis of
fluctuations of an economic cycle. On the chart of the real production Y there are visible the
economic cycles which last about 15 years. The economy at the beginning of the simulation is
in the state of a recession gap.
Yt
600
500
400
300
200
0 5 10 15 20 25 30 35 40 45 50
Time (Year)
Yt:rbe
Figure 52. The real production Y in the model of the economic cycle
The periods of expansion are characterised by an increased inflation and vice versa: the
recession is characterised by the lower rate of inflation.
INFt
wv
0 5 10 61S 20S 80's 30
Time (Year)
INFt: tbe
Figure 53. The rate of inflation in the model of the economic cycle
The average level of prices oscillates together with the changes of the real production Y.
Price - Production
Ll
1,025
0.95
0.8750
0.8
334. «355.376 397 418 439° 460 481 502 523
Production
Pt:rbe
Figure 54. The chart of the average price level P -
- the real production Y in the model of the economic cycle
Short-term Philips’s curve is visible on the chart of the unemployment u and inflation 7 .
Inflation (Rate of Unemployment)
wv
5 6 Gi 8 9 10 1 12 13 14 15
Rate of unemployment
INFt: tbe
Figure 55. The chart of the rate of inflation m in the model of the economic cycle
8 The summary
The conducted simulations enable to indicate the general recommendation for decision-
makers.
In the situation when the cause of recession is the insufficient aggregated demand AD, it
is advisable to use an expansive monetary and fiscal policy for the short-term aims. However,
it should be noticed that there is the danger of the inflation pressure 2 when the basis of the
policy will include the growth of the money supply Ms.
A special threat to the economy poses the negative supply shock causing the increase of
the costs of business. In such a situation one has to choose the problem, which the decision -
makers will try to cope with:
- decreasing the rate of unemployment u is carried out by using the expansive demand
policy;
- the reduction of the inflation 2 is possible thanks to the restrictive demand policy.
Within the confines of the policy one should try to avoid the situations when shocks,
especially the supply shocks, generate the inflation expectations x and cause the significant
decrease of the real production Y. It is advisable for decision makers to carry out actions
supporting positive supply shocks.
The model of rational expectations and the model of the economic cycle can show some
advanced aspects of the analysis of an economic policy.
References:
1. Blanchard O.: Macroeconomics, Upper Saddle River, NJ, Prentice Hall, 1997.
2. Cahill M., Kosicki G: Exploring Economic Models Using Excel, Southern Economic
Journal, Vol. 66, No. 3 (January 2000),
http://www. holycross.edu/departments/economics/mcahill/sejpaper.html
3. Hall R.E, Taylor J.B.: Makroekonomia, PWN, Warszawa 2000 (polish edition of
Macroeconomics).
4. Vensim User’s guide, http://www.vensim.com/ffiles/VensimUsersGuide.zip
5. Vienneau R.: Computer application Keynes from
http://csf.colorado.edu/pkt/authors/Vienneau.Robert/
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