Long run models in economics Professor Bill Mitchell Director, Centre of Full Employment and Equity School of Economics University of Newcastle Australia.
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Long run models in economics
Professor Bill MitchellDirector, Centre of Full Employment and Equity
School of EconomicsUniversity of Newcastle
Australia
http://e1.newcastle.edu.au/coffeeCentre of Full Employment and Equity
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Objectives
To introduce the concept of a long-run (steady-state) model in economics.
To demonstrate the hazards in using econometrics to estimate the steady-state.
To distinguish types of non-stationarity. To examine impulse responses and stability. To consider cointegration.
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Long run relations
Much of economic theory is comparative static. That means it considers equilibrium or steady-state
relationships. These are also called long-run relations. Usually these are cast in terms of relations between
levels. What does this mean? What are the problems in estimating these models?
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Figure 1 Z1 and Z2
Question 1:
Describe the pattern you observe and speculate a priori on whether you think there would be a relationship between these two variables and whether it would be a positive or negative relationship. -10
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Levels and Differences - Z1 and Z2
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DZ1
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t t t
t t t
y y y
y y y
Question 2:
What are the key differences?
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Question 3: Interpret results and confirm “eye balling”
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Question 4: Interpret as a money demand function?
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Question 6:
Assume all right hand side variables take their mean values in perpetuity?
Is there a unique steady-state value for Z1*? Mean values:
- Z1= 9.369454- Z2 = 8.435816- Z4 = -9.904742
We can thus compute Z1* from the regression.
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Steady-state
Means: Z1= 9.369454; Z2 = 8.435816, Z4 = -9.904742.
As long as there are no changes in Z2 and Z4 then Z1 will remain stable and only be subject to random shocks (with mean zero).
1 2 4
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Z - 0.796634 + 0.540610 Z - 0.565952 Z
Z = - 0.796634 + 0.540610*8.435816 - 0.565952*-9.904742
Z = 9.369453875
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Severe serial correlation present – invalidates inference.
The residuals are non-stationary.
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Residual Actual Fitted
Question 7: The alarm bells
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Concept of stationarity
Classical inference is based on strict assumptions about the residuals.
They must be white noise. These assumptions are typically violated when we use
non-stationary regressors. Spurious regression problem arises – a relationship
appears to exist but in fact it is just an artifact of contemporaneous correlation between the variables.
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Two types of non-stationarity
How were Z1 and Z2 generated? They were simulated as random walk functions ( = 1):
1
1t t ty y u
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Two types of non-stationarity
A general model to examine types of non-stationarity is:
Here yt is driven by three components all of which may be active:- a constant drift term ()- an autoregressive term (yt-1)- a deterministic trend term (t)- a stochastic error term (u)
1t t ty y t u
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Two types of non-stationarity
A general model to examine types of non-stationarity is:
We can capture various types of non-stationary time series processes within this general framework by placing appropriate restrictions on the coefficients.
1t t ty y t u
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Restrictions on general model
Model Restrictions
Random walk - drift
Random walk – no drift
Stationary process with deterministic trend
0, 1, 0
1t t ty y t u
0, 1, 0
?, 1, 0
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Two types of non-stationarity
In the latter case, we have what is called a trend-stationary processes.
This is because if we remove the deterministic trend (t) the remaining process is stationary because < 1.
1t t ty y ut
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Two types of non-stationarity
However, in the random walk case we cannot render the time series stationary in this way.
When = 1 (irrespective of whether b is non-zero or not), we have a difference-stationary process.
We can only render it stationary by differencing.
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if 1 and ( =0, 0)t t t
t t t
t t
y y t u
y y u
y u
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Two types of non-stationarity
The problem we have is in distinguishing the two types of non-stationarity.
In finite samples, their behaviour can look similar. It is crucial when modelling relationships to be able to
determine the difference and to take the appropriate actions to de-trend the time-series variables.
That is to extract the deterministic trend or to difference.
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Two types of non-stationarity
Show E-Views program for a random walk.
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The two types of non-stationarity
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Reaction to shocks
Spreadsheet simulation.
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Stationarity
How do you determine the source of stationarity?- De-trend- Unit roots tests.
What then? For a DS process you take differences. For a TS you take out the deterministic trend.
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Spurious regression
Occur when the variables are just correlated to an underlying time trend.
Regression 1! Z1 and Z2 cannot be related causally because they are
random walks. Yet the usual hypothesis tests would have said they were
statistically related. The tests are useless in this context.
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Cointegration
Problem is that economic theory casts equilibrium or long-run relations in levels.
But the levels are likely to be non-stationary. How to proceed? Cointegration helps …
End of Talk
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