Static and dynamic analysis: basic concepts and
examples
Ragnar Nymoen
Department of Economics, UiO
18 August 2009
ECON 3410/4410: Lecture 1
Lecture plan and web pages for this course
The lecture plan is at
http://folk.uio.no/rnymoen/ECON3410_h08_index.html,
which is the workpage of the course.
The workpage is for practical posting of slides, exercises sets etc.
But refer to the Department’s webpage
http://www.uio.no/studier/emner/sv/oekonomi/ECON4410/h09/
for all o¢ cial information: credits, overlap, exam dates and so on.
ECON 3410/4410: Lecture 1
3 main topics
1
Concepts and methods of dynamic analysis.
Introductory Dynamic Macroeconomics (IDM), posted on the
workpage.
2
Medium term macro dynamics: The dynamic AD-AS model.
Introducing Advanced Macroeconomics (IAM) by
Birch-Sørensen and Whitta Jacobsen
3
Critical assumptions of the standard model and alternative
models of the supply-side.
ECON 3410/4410: Lecture 1
The main focus: medium-run macro dynamics
Review of the "building blocks" of the dynamic AD-AS model
Closed economy AD-AS model:
The short run-and the long-run version of the model.
Full dynamic analysis
Application: Stabilization policy, rules versus discretion
A di¤erent perspective: The RBC model.
Open economy AD-AS model
Short-and long run (again)
Monetary policy regimes.
ECON 3410/4410: Lecture 1
Dynamics is a typical feature of the real world (1)
If it was not, what would the world look like?
Economic variables
would jump
whenever incentives
changed.
110. 0
Blue line:a static variable determined
by many small shocks
107. 5
Time graphs would
show:
105. 0
102. 5
100. 0
97. 5
Red line: static variable determined
by a single large shock.
95. 0
0
50
100
150
200
250
300
350
400
ECON 3410/4410: Lecture 1
a step-wise
evolution, or
very erratic
(volatile)
behaviour, or
a combination if
some incentives
are huge, and
some are small.
Dynamics is a typical feature of the real world (2)
For some real world variables graphs look a little like the blue
graph in picture.
Daily data of stock prices, and exchange rates (under some
monetary poly regimes) are examples
But for most macroeconomic variables, persistence is a
dominant feature: It takes times before a change in incentives,
or in legislation, or in policy, obtain full e¤ect on macro
economic variables.
Main sources of persistence (and therefore of dynamics) are:
Information and recognition lags,
Adjustments cost,
Uncertainty and expectations,
Aggregation of individual decisions to the macro level.
ECON 3410/4410: Lecture 1
Persistence in the response to a shock is typical of
dynamics
The graph shows
static (red) and
dynamic (blue)
responses to the
same sequence of
shocks
107
106
105
104
A static resp o n se pattern
103
102
A dynamic response pattern
101
100
99
98
0
50
100
150
200
250
300
350
400
Note how dynamics
add persistence to
the series, because
shocks are
propagated through
time
ECON 3410/4410: Lecture 1
Some Norwegian economic variables: GDP per capita
16
GDP per capita relative to 1900
14
GDP per capita can
‡uctuate in the
medium-run time
perspective
12
10
8
But in longer
perspective the
dominating trait is
growth!
6
4
2
1840
1860
1880
1900
1920
1940
1960
1980
2000
ECON 3410/4410: Lecture 1
Unemployment (long time series)
Ledighetsrate
0.10
The unemployment
rate can ‡uctuate
in the medium-run
time perspective
0.09
0.08
0.07
0.06
0.05
But in longer time
perspective, the
dominating trait is
no-growth!
0.04
0.03
0.02
0.01
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
ECON 3410/4410: Lecture 1
Norway today: In‡ation and unemployment
12
Annual rate of inflation (AET) in Norway
The “end of
in‡ation” is typical
for many countries
10
8
Un emp lo y men t rate
6
Note the …nancial
crisis at the end of
the sample?
4
2
1980
1985
1990
1995
2000
2005
2010
ECON 3410/4410: Lecture 1
Norway and Sweden: In‡ation and unemployment
In flatio n (in red ) an d u n emp lo y men t (in b lu e). No rway : d ash ed lin es.
1 2 .5
Note again the
typical propagation
of shocks.
1 0 .0
7 .5
In Swedish
unemployment in
particular
5 .0
2 .5
0 .0
1980
1985
1990
1995
2000
2005
2010
ECON 3410/4410: Lecture 1
Beliefs about dynamics and propagation mechanism give
premises for decision making
Norges Bank [The Norwegian Central Bank] is typical of many
central banks’view:
“Monetary policy in‡uences the economy with long and
variable lags. Norges Bank sets the interest rate with a
view to stabilizing in‡ation at the target within a
reasonable time horizon, normally 1-3 years”
Policy decisions are based on Norges Banks beliefs about the
dynamic nature of the monetary transmission mechanism.
In economics, beliefs means models, implicit or explicit.
Therefore the citation illustrates two theses: policy is model
based, and policy models are dynamic.
ECON 3410/4410: Lecture 1
Dynamic and static model: de…nition
Formal dynamic analysis in economics is a relatively new
invention.
Ragnar Frisch worked intensively with the foundations of the
discipline he dubbed macrodynamics in the early 1930s. His
de…nition of dynamics was:
A dynamic theory or model is made up of
relationships between variables that refer to di¤erent time
periods. Conversely, when all the variables included in the
theory refer to the same time period (or, more generally,
the model is conceptualized without time as an entity),
the system of relationships is static.
In a dynamic model: time plays an essential role.
ECON 3410/4410: Lecture 1
A static model demand schedule
A linear demand function is
Xt = aPt + b + "d ;t ,
with a < 0 and b > 0 as parameters.
The three variables: X and P;and "d (denoting a random
demand shock) are all provided with time subscript t.
t might represent for example a year (the time period is
annual); or a quarter (the period is quarterly); or month (the
period is monthly).
This model of demand is static.
Note that the “appearance of time” (in the from of the time
subscript) is not enough to make the model dynamic, because
time does not play an essential role!
ECON 3410/4410: Lecture 1
A static equilibrium model
If we supplement the demand equation with a static supply
equation, we obtain the static market equilibrium model
Xt = a Pt + b + "d ;t ,
<0
Xt = c Pt + d + "s ;t ,
>0
determining the endogenous variables Xt and Pt for known
values of the exogenous variables "d ;t and "s ;t (and …xed and
known values of the 4 parameters a; b; c; d).
We assume that "d ;t and "s ;t are completely random variables.
Their role is to represent shocks, or in Frischean terminology,
impulses to the system. A variable that represents random
technology shocks is important in the Real Business Model
(RBC) that we will discuss later in the course.
ECON 3410/4410: Lecture 1
Solution of the static model (analytical)
The model written in structural form
1 Xt
aPt
= b + "d ;t
1 Xt
cPt
= d + "s ;t
Cramer’s rule gives:
Xt
=
Pt
=
1
a
c
b + "d ;t
d + "s ;t
c
1 b + "d ;t
1 d + "s ;t
1
a
a
c
=
=
d
ad
bc + a"s ;t c"d ;t
a c
b + "s ;t "d ;t
a c
ECON 3410/4410: Lecture 1
P
t
Solution of the static model (graphical)
D eman d cu rv e
(av erag e p o sitio n )
P
1
P
0
The initial (before
the shock)
equilibrium is at A
Su p p ly cu rv e (av erag e p o sitio n )
C
B
D
B, C and D are new
equilibria,
corresponding to
di¤erent types of
shocks.
A
X
1
X
0
X
t
ECON 3410/4410: Lecture 1
Solution of the static model (numerical)
Static marked equilibrium model
0.03
P
t
ε d ,t − ε s ,t
The graph shows 50
simulated
equilibrium values
for Pt .
0.02
0.01
Pt is direct
re‡ection of “excess
demand”.
0.00
-0.01
5
10
15
20
25
30
35
40
45
50
ECON 3410/4410: Lecture 1
The e¤ect of a single shock
(A graph of a dynamic multiplier from a static model)
1 .0
Price resp o n se to temp o rary d eman d sh o ck . Static mark ed eq u ilib riu m mo d el
0 .8
0 .6
In the static model,
the full e¤ect of a
temporary shock
occurs in the …rst
period.
In the periods after
the shock, there are
no responses in Pt .
0 .4
0 .2
0
5
10
15
20
The impact
multiplier is
non-zero, all other
dynamic multipliers
are zero.
ECON 3410/4410: Lecture 1
Summary of properties of the static model
The whole e¤ect of a shock is contained in the equilibrium
values of P and X in the period of the shock.
There are no spill-over e¤ects of a shock in period t = 1 to
period 2; 3, and later periods
We say that impulses in period 1 are not propagated to later
periods
The time series of Pt (and Xt ) are perfect mirror images of the
shocks "d ;t and "st .
The sequence of dynamic multipliers, for example @Pt =@"s ;1
(t = 1; 2; 3:::) are zero, expect for @P1 =@"s ;1 .
ECON 3410/4410: Lecture 1
A dynamic equilibrium model
Xt = a Pt + b + "d ;t , demand, and
<0
Xt = c P t
>0
1
+ d + "s ;t ,
supply.
The only change is in the supply equation, where Pt
replaces Pt .
1
Interpretation: In some markets supply is …xed in the
short-run. No matter how high or low the price is in the
current period, the supply of the good is ‘frozen’by decisions
of the past.
Classic example: agricultural products such as pork and
wheat. Relevance today: “Salmon farming”, and China food
price in‡ation; but also the market for oil and for raw
materials.
ECON 3410/4410: Lecture 1
Solution of the dynamic model (graphical)
P
t
The long-run supply
function is
X = cP + d
Long-run supply curve
Demand curve
(average position)
P
After a temporary
demand shock, the
sequence of
equilibria is A
(t = 0), B (t = 1),
C (t = 2), D
(t = 3) and so on
in a cobweb pattern
B
1
D
P
0
P
2
A
C
X
0
X
2
X
t
In the long-run, the
equilibrium is back
at A
ECON 3410/4410: Lecture 1
Solution of the dynamic model (numerical)
D y n amic mark ed eq u ilib r iu m mo d el
0 .0 5 0
mark et p r ice
1 .0
Graph a) shows
solution of Pt from
the dynamic model,
D y n amic mark ed eq u ilib r iu m mo d el
D y n amic mu ltip liers
n et d eman d sh o ck
0 .5
0 .0 2 5
0 .0
0 .0 0 0
-0 .5
-0 .0 2 5
10
20
30
40
50
0
Static mark ed eq u ilib riu m mo d el
1 .0 0
0 .0 3
mark et p r ice
5
10
15
20
Static mark ed eq u ilib riu m mo d el
D y n amic mu ltip liers
n et d eman d sh o ck
0 .0 2
0 .7 5
0 .0 1
0 .5 0
0 .0 0
0 .2 5
-0 .0 1
10
20
30
40
50
0
5
10
15
20
b) shows the
sequence of
dynamic responses
in Pt ( @Pt =@"d ;1
t = 1; 2; :::)
Graph c) and d)
show the
corresponding for
the static model
ECON 3410/4410: Lecture 1
Characteristic di¤erences form the static model
In the dynamic model, the whole e¤ect of a shock is not
contained in the equilibrium values of P and X in the period
of the shock.
The sequence of the dynamic multipliers, for example
@Pt =@"d ;1 (t = 1; 2; 3:::) are generally non-zero, but may
approach zero for large values of t, if the dynamics is stable.
There are spill-over e¤ects of a shock in period t = 1 to
period 2; 3, ....
Impulses in period 1 are propagated to later periods
The solution doe Pt (and Xt ) are not perfect mirror images of
the shocks "d ;t and "st . in each period.
The cobweb pattern is however not general, as a second
example will show.
ECON 3410/4410: Lecture 1
A second dynamic model of market equilibrium
Xt = aPt + b1 Xt
Xt = c0 P t + c1 P t
1
+ b0 + "d ;t , demand
1
+ d + "s ;t :supply
The demand function is now a dynamic equation. The
parameter b1 measures by how much an increase in Xt 1
shifts the short-run demand curve. This can be rationalized by
consumer habits for example.
0 < b1 < 1.
In any given period, Xt 1 is determined from history and
cannot be changed. Hence in this model there are two
pre-determined variables: Pt 1 and Xt 1 .
The supply equation is a generalization of the cobweb model:
If we set c0 > 0, short run supply is no longer completely
inelastic as in the cobweb model.
ECON 3410/4410: Lecture 1
Numerical solution of the model with habit formation
Dynamic market equilibrium model, habit formation.
1.00
0.050
market price
Dynamic market equilibrium model, habit formation.
Compare panel a)
with c), and panel
b) with d).
net demand shock
dynamic multipliers
0.75
0.025
0.50
0.000
0.25
-0.025
10
20
30
Dynamic market equilibrium model, cobweb.
40
50
1.0
0
5
10
Dynamic market equilibrium model, cobweb.
0.05
15
20
15
20
Dynamic multipliers
market price
net demand s hock
0.5
0.0
0.00
-0.5
10
20
30
40
50
0
5
10
It is typical that
small changes in
the model
speci…cation can
signi…cantly a¤ect
the solution of the
dynamic model.
ECON 3410/4410: Lecture 1
When is a static model relevant for the real world?
Frisch:
“Hence it is clear that the static model world is best
suited to the type of phenomena whose mobility (speed
of reaction) is in fact so great that the fact that the
transition from one situation to another takes a certain
amount of time can be discarded. If mobility is for some
reason diminished, making it necessary to take into
account the speed of reaction, one has crossed into the
realm of dynamic theory.”
We would add: Static models are also relevant when we only
claim to analyze the very short-run e¤ects (what we will call
the impact multiplier) of a shocks, i.e. we know that the
dynamic e¤ects of a shock “are there”, but we do not (know
how to) analyze them.
In this way we can interpret the Keynesian IS-LM model as a
short-run model.
ECON 3410/4410: Lecture 1
The three steps in a dynamic analysis
The question we typically want to answer is: “What are the
dynamic e¤ects of a shock (of a certain type) on the
endogenous variables of the model?”
It is often practical to break this question down to 3 “smaller”
questions:
1
2
3
What are the short-run e¤ects of the shock?
What are the long-run e¤ects of the shock, given that the
dynamic adjustment process is stable?
What are the properties of the dynamic adjustment process
(regarding stability in particular)?
To answer Q1 and Q2 we use two separate models!
ECON 3410/4410: Lecture 1
Market equilibrium: the short-run model
Xt = aPt + b1 Xt
1
Xt = c0 P t + c1 P t
+ b0 + "d ;t ,
(1)
+ d + "s ;t :
(2)
1
Since Pt 1 and Xt 1 are pre-determined from history in each
period t, they are exogenous in this short-run model. The
analytical solution:
Xt
=
Pt
=
ad
d
b 0 c0
b0
c0 b 1 Xt
+ ac1 Pt 1 + a"s ;t
a c0
b1 Xt 1 + c1 Pt 1 + "s ;t "d ;t
a c0
1
gives the short-run e¤ects of the shocks "d ;t and "s ;t as
derivatives,see Table 1.1 in IDM
ECON 3410/4410: Lecture 1
c0 "d ;t
Market equilibrium: The long-run model
The long-run model applies to a hypothetical (or counterfactual)
stationary situation where there are no new shocks, and all past
shocks have worked their way through the system.
The long-run model is therefore de…ned for the situation:
Xt = Xt 1 = X ; Pt = Pt 1 = P and "d ;t = "d , "s ;t = "s . The
model is given by
X = aP + b1 X + b0 + "d , long-run demand
X = c0 P + c1 P + d + "s ; long-run supply
or
X =
a
P+
1
(b0 + "d );
1 b1
1 b1
X = (c0 + c1 )P + (d + "s ).
Solve to obtain analytical expressions for long-run e¤ects, see
Table 1.1 in IDM.
ECON 3410/4410: Lecture 1
Graphically, we can
represent the
short-run and
long-run models in
one diagram,
P
Sh o rt- ru n su p p ly cu rv e
Lo n g - ru n su p p ly cu rv e
C
B
Lines with di¤erent
slopes de…ne the
short-run and the
long-run.
A
Sh o rt- ru n d eman d cu r v e
Lo n g - ru n d eman d cu r v e
X
We can then
analyze the
short-run e¤ect of a
shock, as well as
the long-run e¤ect.
ECON 3410/4410: Lecture 1
The third question
The short-run model and the long-run model of the
macroeconomy will be important tools in the following, in
particular for the medium-term AS-AS model covered by the
IAM book.
But we will also address systematically the third question:
What are the properties of the dynamic adjustment process
(regarding stability in particular)?
To do this we need to develop several concepts more precisely
than we have done in this introduction.
We do that within a class of dynamic equations which wide
enough to cover many economic interpretations as special
cases (Ch 2 of IDM).
ECON 3410/4410: Lecture 1
Discrete or continuous time?
The distinction between static models and dynamic modes is
fundamental.
Whether dynamic models are expressed in terms of discrete
time or continuous time is however not fundamental.
Often theories are expressed in continuous time, but since
actual data series are recorded in discrete time, choosing
discrete time keeps the theory closer to applications.
Refer to Box 1.1 in IDM for example. The point is that for
dynamics to occur, time must play an essential role in model
(discrete/continuous time is a secondary issue).
ECON 3410/4410: Lecture 1
Stock and ‡ow variables
Dynamic models often include both ‡ow and stock variables.
Flow: in units of (for example) million kroner per year
Stock: in units of (for example) million of kroner at a
particular period in time (for example start or end of the year).
Population size , and capital stock are examples of stock
variables. But so are also price indices: Pt may represent the
value of the Norwegian CPI in period t (a month, a quarter or
a year), and indicators of the wage level.
In practice: the values of P will be index numbers. The
number 100 (often 1 is used instead) refers to the base period
of the index. If Pt > 100 it means that relative to the base
period, prices are higher in period t.
ECON 3410/4410: Lecture 1
A ‡ow variable is often a change in a stock variable
Starting from a stock variable like Pt , a ‡ow variable results from
obtaining the change of that variable, hence
xt = Pt
Pt
yt =
zt = ln Pt
Pt
Pt
Pt
1,
1
the (absolute) change
,
the relative change, and
1
ln Pt
1
the approximate relative change
are examples of ‡ow variables. Note that:
yt 100 is in‡ation in percentage points. In this course we
often use to the rate formulation (hence, we omit the scaling
by 100)
zt yt by the properties of the (natural) logarithmic function,
see for example the appendix of IDM, if in doubt.
ECON 3410/4410: Lecture 1
A stock variable is the cumulated sum of a ‡ow
75
debt =
The Norwegian current account
Billion kroner
current account
+ lagged debt.
50
25
0
19 80
19 85
19 90
19 95
20 00
19 90
19 95
20 00
Norwegian net foreign debt
Billion kroner
0
-2 50
-5 00
-7 50
19 80
19 85
If there is a primary
account surplus for some
time, this will lead to a
gradual reduction of
debt— or an increase in
the nation’s net wealth.
Conversely, a consistent
current account de…cit
raises a nation’s debt.
ECON 3410/4410: Lecture 1