Short overview
Slides to Lecture 1 of Introductory Dynamic
Macroeconomics
1. ’Statics and dynamics’
Concepts and definitions.
2. Dynamic analysis
Models and methods.
3. Wage-price dynamics (a dynamic view at the supply-side of macro models)
Ragnar Nymoen
University of Oslo, Department of Economics
4. Macro dynamics.
• Review of demand side (closed economy); Role of asset markets
• Stabilization policy, rules versus discretion
August 17, 2007
• Open economy AS-AD model. Short-and long run.
• Foreign exchange market. Regime dependency.
• Current monetary policy
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Consult (frequently!!) the detailed plan at
http://folk.uio.no/rnymoen/ECON3410 h07 index.html
which is the workpage of the course.
You can access the workpage from the Department of Economics
web page for ECON 4410.
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‘Statics and dynamics’, an introduction
Economic agents typically take time to adjust their behaviour to changes in
circumstances–because of habits, learning, norms and other institutions (for
example annual wage setting).
Instantaneous adjustment is the exception in economics. Adjustments lags
represent the rule.
At the aggregate (macro) level: a shock typically affects the economy several
periods after the it first occurred–the effects of a shock are dynamic.
Expectations:
Backward-looking expectations are another explanation of lags
Forward-looking expectations sometimes creates a particular form of dynamics:
large adjustments first (“over-shooting”), then more gradual adjustment.
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Time lags as a premise for decision making.
Norges Bank [The Norwegian Central Bank] is typical of many central banks’
view:
By the way, before it was changed in the summer of 2004, the same passage
on Norges Banks internet pages read:
“Monetary policy influences the economy with long and variable lags.
Norges Bank sets the interest rate with a view to stabilizing inflation
at the target within a reasonable time horizon, normally 1-3 years”
“A substantial share of the effects on inflation of an interest rate
change will occur within two years. Two years is therefore a reasonable
time horizon for achieving the inflation target of 2 12 per cent.”
Hence policy decisions–meaning interest rate setting–is based on Norges
Banks beliefs about the dynamic nature of the monetary transmission mechanism.
Taken at face value, this shows that Norges Bank’s belief/model of the transmission mechanism changed in the summer of 2004. Later in the cause we will
be able to assess the likely impact of such a change on policy decisions!
In economics, beliefs means models, implicit or explicit.
Hence, the statement illustrates two theses: policy is model based, and policy
models are dynamic.
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A static model
A static demand schedule, by definition:
Definition: ‘statics and dynamics’
Formal Dynamic analysis in economics is a relatively new invention.
It all began with Ragnar Frisch who worked intensively with the foundations of
the discipline he dubbed macrodynamics in the early 1930s. His definition of
dynamics is:
A dynamic theory or model is made up of relationships between variables that
refer to different 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.
Xt = aPt + b + εd,t,
with a < 0 and b > 0 as parameters.
The thre variables: X and P,and εd (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).
In theoretical models we usually set t = 0, 1, 2, ....T . Where t = 0 is referred
to as the initial period and T the terminal period. Sometimes though, the
terminal period is not specified, so we write t = 0, 1, 2, .....
In empirical models, t refers to calendar time periods: years, quarter, months
for example.
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If we supplement the demand equation with a static supply equation, we obtain
the static marked equilibrium model
Xt = a Pt + b + εd,t, demand, and
εs,t
Supply shocks
0.01
0.00
<0
Xt = c Pt + d + εs,t,
>0
supply.
determining the endogenous variables Xt and Pt for known values of the exogenous variables εd,t and εs,t (and fixed and known values of the 4 parameters
a − d).
We assume that εd,t and εs,t are random variables. Their role is to represent
shocks, or in Frischean terminology, impulses to the system. We do not need
to be specific about the distribution of εd,t and εs,t: but if it might be helpful
to fix ideas to think of them as normally distributed with zero mean and a
constant variances.
-0.01
0
75
20
40
60
80
100
120
140
time
Density
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25
-0.0175 -0.0150 -0.0125 -0.0100 -0.0075 -0.0050 -0.0025 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0175
Figure 1: Example of normally distributed supply shocks.
9
Pt
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Nature of exogenous variables
Later in the course we will also introduce exogenous variables with a non-zero
average and with a deterministic component.
Demand curve
(average position)
P1
Supply curve (average position)
C
B
D
Such variables are exogenous economic explanatory variables.
P0
A
They may be determined on the world marked, or controlled by the government
for example.
But for the time being, in order to discriminate clearly between static and
dynamic models, it is convenient to only use purely random exogenous variables.
X1
X0
Xt
Figure 2: A static marked equilibirum model. IDM fig 1.1.
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Static marked equilibrium model
Characteristics of a static model
Static marked equilibrium model
1.00
0.03
market price
Dynamic multipliers
net demand shock
0.02
The whole effect of a shock is contained in the equilibrium values of P and X
in the period of the shock.
0.75
0.01
0.50
0.00
0.25
There are no spill-over effects of a shock in period t = 1 to period 2, 3, and
later periods
-0.01
10
20
30
40
50
Dynamic marked equilibrium model
0
1.0
0.050
10
15
20
Dynamic multipliers
market price
We say that impulses in period 1 are not propagated to later periods
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Dynamic marked equilibrium model
net demand shock
0.5
0.025
• The time series of Pt (and Xt) are perfect mirror images of the shocks εd,t
and εst. Fig 3 a).
0.0
0.000
-0.5
-0.025
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• The sequence of dynamic multipliers, for example ∂Pt/∂εs,1 (t = 1, 2, 3...)
are zero, expect for ∂Pt/∂εs,1. Fig 3 b)
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20
30
40
50
0
5
10
15
20
Figure 3: Static model and dynamic (cobweb) model. IDM fig 1.2.
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Let t = 0 denote the initial situation with εs,0 = 0. According to the dynamic
model, supply in period t = 1 is given by
A dynamic model (cobweb)
Xt = a Pt + b + εd,t, demand, and
<0
Xt = c Pt−1 + d + εs,t,
>0
supply.
The only change is in the supply equation, where Pt−1 replaces Pt.
By Frisch’s definition the supply equation is now dynamic, since the relationship
is in terms of variables from different time periods.
This is a seemingly trivial change in specification. But it affects both the
economic interpretation and the propagation of shocks fundamentally.
Interpretation: In some markets supply is fixed 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.
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X1 = cP0 + d.
Supply in period 1 is a function of P0 which is pre-determined from history,
and not the price in period 1. The supply in period 1 (short-run supply) is thus
completely inelastic with respect to the price, P1.
Pt−1 is therefore called a pre-determined variable.
The parameter c is thus not a short-run slope coefficient in the way is was in the
static model, instead it gives the response of supply to a lasting change in price.
We define c as the long-run slope coefficient, for the stationary relationship
X̄ = cP̄ + d,
where are stationary values of supply and price (Xt = Xt−1 = X̄ and Pt =
Pt−1 = P̄ )
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Xt = c Pt−1 + d + εs,t,
Pt
“Short-run” and “long-run” are not absolute terms, is relative to the modelspecificatin. Here, with
Long-run supply curve
supply.
>0
we only have to wait one period to see the full response of a price change in
period t on supply. Xt does not change, but Xt+1 changes with derivative
coefficient c.
Demand curve
(average position)
B
P1
D
A
P0
Supply is elastic with a one period lag. In other modes this will be different,
typically the response is more sluggish.
C
P2
But even this simple case of one-period supply lag has a large impact on the
behaviour of the equilibrium values of price and quantity, compared to the static
model.
To see how, assume that the initial period is also a stationary situation, with
X0 = X̄ and P0 = P̄ , and εd,0 = εs,0 = 0.
X0
X2
Xt
Figure 4: The cobweb model. IDM fig 1.3
Then, consider a demand shock in period 1: εd,1 > 0.
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Static marked equilibrium model
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Characteristics of dynamic models
Static marked equilibrium model
1.00
0.03
market price
Dynamic multipliers
net demand shock
0.02
The whole effect of a shock is no longer contained in the equilibrium values of
P and X in the period of the shock.
0.75
0.01
0.50
0.00
There are spill-over effects of a shock in period t = 1 to period 2, 3, ....
0.25
-0.01
10
20
30
40
50
Dynamic marked equilibrium model
0
1.0
5
10
15
20
Dynamic marked equilibrium model
0.050
Impulses in period 1 are propagated to later periods
Dynamic multipliers
market price
net demand shock
• The time series of Pt (and Xt) are not perfect mirror images of the shocks
εd,t and εst.
0.5
0.025
0.0
0.000
-0.5
-0.025
10
20
30
40
50
0
5
10
15
20
• The sequence of the dynamic multipliers, for example ∂Pt/∂εd,1 (t =
1, 2, 3...) are generally non-zero, but may approach zero for large values of
t, if the dynamics is stable.
Figure 5: Copy of figure 3: Static model and dynamic (cobweb) model.
• Dynamics is a system property : even if only a single relationship in system
is dynamic, the response of the whole system is affected (in general)
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Dynamic market equilibrium model, habit formation.
Another example: effects of habit formation.
1.00
0.050
market price
Dynamic market equilibrium model, habit formation.
net demand shock
dynamic multipliers
0.75
0.025
0.50
Xt = aPt + b1Xt−1 + b0 + εd,t, demand and
Xt = c0Pt + c1Pt−1 + d + εs,t.supply
The demand function is now a dynamic equation. The parameter b1 instead
measures by how much an increase in Xt−1 shifts the demand curve. This can
be rationalized by habit formation, in which case we may set 0 < b1 < 1.
0.000
0.25
-0.025
10
20
30
40
Dynamic market equilibrium model, cobweb.
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1.0
0
5
10
15
Dynamic market equilibrium model, cobweb.
0.050
20
Dynamic multipliers
market price
net demand shock
0.5
0.025
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.
0.0
0.000
-0.5
-0.025
The supply equation is a generalization of the cobweb model, with supply
showing some within-period response to a price change (coefficient c0).
10
20
30
40
0
50
5
10
15
20
Figure 6: Two dynamic models. IDM fig 1.4.
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The short-run and the long-run
The cobweb model and habit model are both dynamic.
In the static model, the full effect of a shock on the endogenous variables were
reached in the same time period as the shock.
But their bproperties are different:
• Cobweb model amplifies shocks, the habit model dampens shocks (compare
panel c) and a))
The telling difference is that in the two dynamic models, the endogenous variables’ response to shocks were not instantaneous, and the system took several
periods to adjust to a shock in period t.
• Dynamic multiplier: changing signs (‘pork cycles’), and geometrically declining (habit formation)
The exact shapes of the responses, which we dubbed dynamic multipliers above,
depend on the detailed model specification.
The two model illustrates some of the capability of linear systems of equations
to represent many quite different dynamic behaviour of economic variables.
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We draw from this that static models as a framework for analysis, is best suited
when the speed of adjustment of the variables are so fast that we can ignore
that ‘actually’ there is some time delay between the impulse (or shock) and
the response.
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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.”
The choice between a static and a dynamic analysis will therefore vary from
application to application: Sometimes it might be a good simplifying assumption that there is a high speed of reaction to impulses. Nut typically, a more
realistic assumption to make is that there is a moderate or even long response
lag.
It is a paradox that phenomena which in an everyday meaning of the word are
really dynamic, with lots of volatility, as for example the market for foreign
exchange, can be analyzed scientifically with a static framework;
....at least as a first approximation, which brings out that the choice between
static and dynamic analysis may also be relative to the level of ambition of our
study, and to the time and other resources available for modelling
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Another example of the “relativism” of the static vs dynamic approaches:
The intellectual rationale for the IS-LM model is that we think it captures some
really important and dominant aspects of the macroeconomy over a period of
1-2 years for example.
This does not deny that for example fiscal policy stimulus have effects beyond
that short horizon. The static IS-LM model by definition cannot help us in
the modelling of those effects, which therefore remain beyond the scope and
ambition of the IS-LM based analysis.
One of the goals of our course is to extend the analysis of monetary and fiscal
policy into the realm of dynamic theory.
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However, apart from resource constraints and a need to simplify, the scales are
tilted in the favour of dynamic models in macroeconomics: Frisch:
“In real life both inertia and friction act as a brake on speed of
reaction”.
Frisch also noted that
“The static theory’s assumption regarding an infinitely great speed
of reaction contains one of the most important sources of discrepancy
between theory and experience.”
Therefore Frisch anticipated the increased use of dynamics in economics–it
would increase the degree of realism and scope of macroeconomic analysis.
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Short-run and long-run models
However, there is also another, quite different, interpretation of static models
which will figure prominently in this course.
It is that static equations express what the dynamic model would correspond to
in a counterfactual situation where no shocks, impulses or changes in incentives
occurred.
Recall the model with habit effects in the demand equation. Figure 6 a) above
(fig 1.4 in IDM) shows the full solution for Pt. Sometimes, when we are unable
to derive the solution of the dynamic model, we will still be able to answer two
important questions:
1. What are the short-run effect of a change in an exogenous variable? And
2. What are the long-run effects of the shocks.
As we become accustomed to dynamic analysis, we will refer to this correspondence by saying that static relationships can represent the stationary state (or
steady state) of a dynamic model.
The technique we will use is based on the distinction between the short-run
model given by
It is custom to use the terms stationary (or steady state) equation interchangeably with the term long-run equation.
Xt = aPt + b1Xt−1 + b0 + εd,t, (demand)
Xt = c0Pt + c1Pt−1 + d + εs,t, (supply),
taking the predetermined variables Xt−1 and Pt−1 as exogenous, and the longrun model which is defined for the stationary situation of Xt = Xt−1 = X̄, Pt =
Pt−1 = P̄ and εd,t = ε̄d = 0, εs,t = ε̄s = 0.
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P
Short-run supply curve
a
1
P̄ +
b0, long-run demand, and
1 − b1
1 − b1
X̄ = (c0 + c1)P̄ + d, long-run supply
Long-run supply curve
X̄ =
The long-run model applies to a hypothetical stationary situation where there
are no new shocks, and all past shocks have worked their way through (and
“out of”) the system.
C
B
A
Graphically we can represent the short-run and long-run models in one diagram,
using lines with different slopes to illustrate the difference between the shortand long-run.
Short-run demand curve
Long-run demand curve
X
We can then analyze the short-run, or impact, effect of a shock (to demand
for example), as well as the long-run effect.
Figure 7: Graphical analysis of a demand shock in the habit formation model
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Stock and flow variables
Starting from a stock variable like Pt, a flow variable results from obtaining
the change of that variable, hence
Dynamic models often include both flow 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, 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.
CPI in Norway
• zt ≈ yt by the properties of the (natural) logarithmic function, see for
example the appendix of IDM, if in doubt.
An typical empirical trait of stock variables are that they change gradually, as
a result of finite growth rates.
1500
Sometimes however, stock variables jump from one value in period t to quite
another in period t + 1.
1000
200
1.5
• yt × 100 is inflation in percentage points. In this course we often stick to
the rate formulation (hence, we omit the scaling by 100)
CPI in the UK
400
1760
are examples of flow variables. Note that:
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600
the (absolute) change
xt = Pt − Pt−1,
Pt − Pt−1
yt =
,
the relative change, and
Pt−1
zt = ln Pt − ln Pt−1 the approximate relative change
1780
1800
1820
1760
0.4
Inflation in Norway
1.0
1780
1800
1820
Inflation in the UK
Empirically, the rate of change then becomes very large. Norwegian “price
history” at the breakdown of the union with Denmark is an example (see graph)
0.2
When stock variables change gradually, we need explicit dynamic models to
account for their evolution.
0.5
0.0
0.0
-0.5
-0.2
1760
1780
1800
1820
1760
1780
1800
1820
Sometimes though, stock variables can be treated theoretically as if they are
jump-variables. An example of such a theory is the portfolio model of the
foreign exchange market. That model is static.
Figure 8: Consumer price indices (stock variables), and their rate of change
(flow). Norway and UK
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The Norwegian current account
Billion kroner
50
As noted, economic dynamics often arise from the combination of flow and
stock variables.
25
0
The behaviour of national debt (a stock) is linked to the value of the current
account (flow) in the following way
1980
1985
1990
1995
2000
1990
1995
2000
Norwegian net foreign debt
debt = − current account + last periods debt + corrections.
For example: If there is a primary account surplus for some time (and ignoring
corrections for simplicity), this will lead to a gradual reduction of debt–or an
increase in the nation’s net wealth. Conversely, a consistent current account
deficit raises a nation’s debt.
Billion kroner
0
-250
-500
-750
1980
1985
Figure 9: The Norwegian current account (upper panel) and net foreign deb
(lower panel)t. Quarterly data 1980(1)-2003(4)
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Continuous and discrete time
An empirical example
In the relationship:
ẏ = ay(t) + ε(t), a < 0,
(1)
y(t) denotes a variable y which is a continuous function of time, t. The
exogenous variable ε(t) is also a continuous function of t. The left hand side
variable ẏ denotes the derivative of y with respect to time. a is a parameter,
assumed to be negative (with no loss of generality).
Time plays an essential role in model (1): If there is an increase in ε(t), ẏ will
be larger, and through time there will also be an increase in y. Hence, there
are propagation effects, just like in the corresponding formulation for discrete
time:
yt = αyt−1 + εt, α > 0,
or
yt − yt−1 = (α − 1)yt−1 + εt, α > 0,
(2)
The textbook consumption function, i.e., the relationship between real private
consumption expenditure (C) and real households’ disposable income (IN C)
is an example of a static equation
Ct = f (IN Ct), f 0 > 0.
(3)
Two examples of static consumption functions:
Ct = β0 + β1IN Ct + et,
ln Ct = β0 + β1 ln IN Ct + et,
(linear)
(log-linear)
(4)
If this is unfamiliar, read in IDM about the properties of these two functional
forms. For example for the interpretation of β1.
Using quarterly data for Norway, for the period 1967(1)-2002(4), we obtain,
by using the method of least squares:
to make the correspondence even clearer. In (2),yt − yt−1 corresponds to ẏ in
(1), and (α − 1) corresponds to a.
ln Ĉt = 0.02 + 0.99 ln IN Ct
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(5)
12.0
êt = ln Ct − ln Ĉt,
(6)
11.8
11.6
ln C t
where the “hat” in Ĉt is used to symbolize the fitted value. Next, use (4) and
(5) to define the residual êt:
11.4
which is the empirical counterpart to the static model’s disturbance et.
11.2
11.0
11.0
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
12.0
ln INCt
Figure 10: The estimated static consumption function.
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0.15
The dynamic consumption function:
Residuals of (1.7)
Residuals of (1.4)
0.10
ln Ct = β0 + β1 ln IN Ct + β2 ln IN Ct−1 + α ln Ct−1 + εt
(7)
0.05
is an example of a so called autoregressive distributed lag model, ADL, which
we treat in Ch. 2 of IDM. The emprical version is:
ln Ĉt = 0.04 + 0.13 ln IN Ct + 0.08 ln IN Ct−1 + 0.79 ln Ct−1
(8)
Compare graph of residuals ε̂t and êt to judge which model is best.
Which explanatory variables contribute most to the improved fit?
0.00
−0.05
−0.10
−0.15
−0.20
ln Ct−1 itself! Illustrates that the dynamic framework is important.
−0.25
The low estimated income elasticities (0.130 and 0.08) reflect that Norwegian
households have a low propensity to consume out of income rises that are
transitoy. As we shall see, the results imply that the propensity to consume a
permanent change in income is much larger.
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1965
1970
1975
1980
1985
1990
1995
2000
Figure 11: Residuals of the two estimated consumptions functions (5), and (8),
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The road immediately ahead
Next week we start a more systematic introduction to the modelling tools of
dynamics, see IDM Ch 2.
Present a general framework for dynamic single equation models, called the
autoregressive distributed lag model, ADL model.
In the ADL framework, the concept of the dynamic multiplier, used several
times already, can be made precise.
The dynamic multiplier is a key concept in this course
The ADL model also defines a typology of dynamic equations, as special cases,
each with their distinct features.
The analysis is extended to simple dynamic systems-of-equations.
Then we turn to wage-and-price setting, which is an essential part of the supply
side of modern macroeconomic model.
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