An Introduction to Error Correction Models An Introduction to ECMs ...

Engle and Granger Two-Step ECM
� Viewed from this perspective, it is easy to see why error correction
models have become so closely associated with cointegration (we will
come back to this later).
� Integrated time series present a problem for time series analysis - at
least in terms of long term relationships.
� When integrated time series variables are also cointegrated, error
correction models provide a nice solution to this problem.
Cointegration and Error
Correction in Political Science
� Prime Ministerial Statisfaction (U.K.) and Conservative Party
Support
� Arms transfers by the U.S. and Soviet Union
� Economic expectations and U.S. Presidential Approval
� U.S. Domestic Policy Sentiment and Economic Expectations
� Support for U.S. Social Security and the Stock Market
X and Y: Cointegrated?
0 5 10 15 20 25
1960m1 1961m1 1962m1 1963m1 1964m1 1965m1
months
Y X
Cointegration and Error Correction
� One of the first instances of error correction was Davidson et. al.’s
(1978) study of consumer expenditure and income in the U.K..
� The Engle and Granger approach to error correction models follows
nicely from the field of economics, where integration and cointegration
among time series is theoretically common.
� Error correction models were imported from economics.
� Would we expect data from the social sciences to follow similar
patterns of integration and cointegration?
The Engle and Granger Two-Step
ECM: Putting it into Practice
� Lets imagine we have two time series - perhaps the drunk and her dog -
but lets call the drunk ‘X’ and the dog ‘Y’.
� From a theoretical perspective, we believe changes in X will have both
short and long term effects on Y, since we expect X and Y to have an
equilibrium relationship.
� We expect changes in X to produce long run responses in Y, as Y
adjusts back to the equilibrium state.
Engle and Granger Two-Step ECM
First, we need to determine that both X and Y are integrated of the same order.
• Which means we first need to demonstrate that both X and Y are, in fact,
integrated processes.
• We should also think about the likely stationary or nonstationary nature of our
time series from a theoretical perspective.
Tests for unit-root process tend to be controversial, primarily due to their low power.
For our purposes, we will focus on Dickey-Fuller (DF) and Augmented Dickey-Fuller
tests to examine the (non)stationarity of our time series.
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