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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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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.

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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?

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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.

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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?

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

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

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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.

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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).

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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

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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.

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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):

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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)

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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.

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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

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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.

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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.

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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.

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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.

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

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

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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.

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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.

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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 …

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NONSTATIONARY PROCESSES 1 In the last sequence, the process shown at the top was shown to be stationary. The expected value and variance of X t were shown.

NONSTATIONARY PROCESSES 1 In the last sequence, the process shown at the top was shown to be stationary. The expected value and variance of X t were shown.

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