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Short-run models and Error Correction Mechanisms. Professor Bill Mitchell Director, Centre of Full Employment and Equity Department of Economics University of Newcastle Australia. Objectives. To introduce the concept of a short-run model in economics.
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Short-run models and Error Correction Mechanisms Professor Bill Mitchell Director, Centre of Full Employment and Equity Department of Economics University of Newcastle Australia
Objectives • To introduce the concept of a short-run model in economics. • To show how short- and long-run models interact. • To explain the concept of an Error Correction Mechanism (ECM). • To show how ECM and cointegration work together.
Long-run model review • Economic theory is essentially static and mostly considers equilibrium relationships. • Equilibrium (long-run) relations are normally in terms of levels. • The problem is that with non-stationary variables we are prone to finding spurious relationships if we run regressions in levels.
Figure 1 Z1, Z2 and Z4 • The Z variables were simulated using random walk functions with r = 1: • Any relation between them is spurious and because they contain stochastic trends.
So this equation exhibits “good” econometric results but is in fact spurious and tells us nothing at all. The “good” is qualified b/c the DW statistic is the clue.
The long-run model quandary • So how do we proceed? • In the 1970s, the approach was to take differences?
Taking differences… • Do we still have a relationship? • To test it we would run DZ1t= b0 + b1DZ2t + b2DZ4t + et
Levels and differences Problems ? Question 1: What are the problems of estimating economic relationships in difference form like Equation (4), given that it can overcome the problem of non-stationarity in the levels of the variables concerned?
Error Correction Approach • This approach attempts to use differenced data to model the short-run adjustments but also take into account and estimate long-run information. • Consider this long-run model:
Equilibrium and disequilibrium Question 2: What are the properties of Equation (6)? Does it tell you about the path of adjustment for y if x changes? Question 3: What are some of the reasons why equilibrium may not hold in every period? In a forecasting environment why would it be necessary to know about the nature of disequilibrium adjustment paths?
Equilibrium and disequilibrium When Equation 6(b) holds we cannot observe the relationship in Equation (6). But we can observe the short-run, dynamic relationship that would reduce to Equation (6) whenever equilibrium occurs. So we need to learn a bit about the short-run models.
Short-run model • Short-run models are also called adjustment functions or dynamic models or lagged models. • A typical (simplified) version is the first-order model: • The order is selected to “soak” up the serial correlation (the “missing dynamics”)
Properties of short-run model Question 4: What are the properties of Equation (8)? Tell a story in words about the process through which the long-run relationship is re-established if x was to change in a particular period?
Properties of short-run model Question 4: Parameter b1 measures the immediate impact of a change in x on y. It is not the long-run impact that would occur from one equilibrium to another though. Why not? What is the difference between b1 and g1? Can you find an expression that links b1 and g1? Solve the steady-state properties of (8).
Questions 6 to 9 … • Question 6: Assume that a1 = 0.9, b1 = 0.6 and b2 = 0.3. Starting from an equilibrium position, how long does it take for y to return to that equilibrium, if x increases by a unit and remains at that new level? • Question 7: What is the change in y in the first period after the shock? What is the change in y in the second period? What is the total change? • Question 8: How is the shift in equilibrium dependent on the value taken by the AR parameter? • Spreadsheet demonstration.
Error Correction models • The basic dynamic model may also suffer from non-stationarity problems. • We have seen the differencing is unsatisfactory. • Error Correction Mechanism (ECM) models begin with the basic short-run model. • After re-parameterising, the ECM form has both dynamic and steady-state information in the one equation.
ECM questions Question 9: See if you can perform the re-parameterisation to get the ECM model which combines differences and levels. It is shown below as Equation (10).
ECM form and the steady-state Question 10: Would you say that Equation (8) and Equation (10) are equivalent? What are the advantages of Equation (10) relative to Equation (8)?
ECM form and the steady-state Question 11: Provide an interpretation of the expression in square brackets in Equation (10). Have you already encountered an expression like this earlier in this lecture?
ECM form and the steady-state You can see that the term in square brackets is equivalent to the expression for disequilibrium in the steady-state.
ECM form and the steady-state Question 12: Is the term in square brackets stationary given that it is in terms of levels? Under what conditions will it be stationary?
Cointegration and ECM model • Two-step procedure for estimating the model: • Test for cointegration in Equation (6). • If null accepted then the residuals would be stationary. • Estimate (10) with residuals from CI Equation (6) as the ECM term.
