2. Long run models in economics Professor Bill Mitchell Director, Centre of Full Employment and Equity School of Economics University of Newcastle Australia

3. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 3 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.

4. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 4 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?

5. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 5 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.

6. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 6 Levels and Differences - Z1 and Z2 Question 2: What are the key differences?

7. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 7 Question 3: Interpret results and confirm “eye balling”

8. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 8 Question 4: Interpret as a money demand function?

9. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 9 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.

10. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 10 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).

11. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 11 Severe serial correlation present – invalidates inference. The residuals are non-stationary. Question 7: The alarm bells

12. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 12 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.

13. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 13 Two types of non-stationarity  How were Z1 and Z2 generated?  They were simulated as random walk functions (  = 1):

14. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 14 Two types of non-stationarity  A general model to examine types of non-stationarity is:  Here y t is driven by three components all of which may be active: -a constant drift term (  ) -an autoregressive term (  y t-1 ) -a deterministic trend term (  t) -a stochastic error term (u)

15. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 15 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.

16. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 16 Restrictions on general model ModelRestrictions Random walk - drift Random walk – no drift Stationary process with deterministic trend

17. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 17 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.

18. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 18 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.

19. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 19 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.

20. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 20 Two types of non-stationarity  Show E-Views program for a random walk.

21. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 21 The two types of non-stationarity

22. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 22 Reaction to shocks  Spreadsheet simulation.

23. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 23 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.

24. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 24 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.

25. http://e1.newcastle.edu.au/coffee Centre of Full Employment and Equity 25 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 …

26. End of Talk