Error Correction Model Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

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An error correction model or equilibrium correction model (ECM) is a dynamic statistical model. Statistical models can be applied to time-series data—chronological sequences of observations—to examine the movement of political variables over time (e.g., public opinion, government policy, judicial court decisions). This allows the analyst to estimate relationships between political variables and test hypotheses. A dynamic model includes past values of the variable of interest as an explanatory variable. This captures the simple concept that what happens today affects what happens tomorrow.

A common dynamic model is the autoregressive distributed lag (ADL) model. In the ADL model, the variable of interest is a function of both past values of itself and current and past values of the independent variables. Any ADL model can be transformed linearly into an ECM without placing any restrictions on the parameters of the model. Other ECMs are equivalent to ADL models with restrictions placed on some parameters (e.g., setting a coefficient to zero). Simply put, the ECM contains exactly the same information as the ADL. The choice of using one over the other is purely a matter of convenience.

Within the context of political science, ECMs offer two advantages. The first is interpretation. ECMs model changes in the variable of interest as a function of the long-term equilibrium between the variable of interest and the independent variables in the absence of exogenous shocks, short-term movements due to exogenous shocks, and the rate at which the variable of interest returns to equilibrium (i.e., the rate of error correction). Explicitly separating the long-term equilibrium relationship from short-term movements is often appealing when fitting a model to theory.

The long-term equilibrium relationship component is the key to the second advantage of the ECM. Standard estimation techniques produce incorrect results if the time-series data violate an assumption called “stationarity.” A common violation is integrated data. However, a linear combination of integrated time series may exhibit stationarity; this is referred to as cointegration. This stationary linear combination can be interpreted as the long-term equilibrium relationship between the variables and incorporated in an ECM. This allows the relationship between integrated variables to be modeled.

Because of these advantages, the popularity of the ECM in political science has been on the rise since the early 1990s, particularly in political behavior and political economy. It also has been put to use in areas such as the study of judicial processes, conflict, and foreign policy. Most of these studies have justified the use of the ECM on the grounds of cointegrated data.

In the application of the ECM, there are two points to keep in mind. First, as the ECM is simply a reparameterization of the ADL model, any concerns about model specification that apply to the latter also apply to the former. These can include endogeneity issues, specifying the correct lag structure, and serially correlated errors. Second, there is more than one procedure for estimating an ECM. Estimation when using stationary data may require a different procedure than when using cointegrated data. The ECM allows certain relationships to be estimated using ordinary least squares, which would otherwise require more advanced procedures, but there are many ECMs that cannot be estimated using ordinary least squares.

Bibliography:

Banerjee, Anindya, J.W. Gilbraith, and Juan Dolado. Co-integration, Errorcorrection, and the Econometric Analysis of Non-stationary Data. Oxford, UK: Oxford University Press, 1993.
Beck, N. “Comparing Dynamic Specifications:The Case of Presidential Approval.” Political Analysis 3 (1991): 51–87.
Durr, Robert H. “An Essay on Co-integration and Error Correction Models.” Political Analysis 4 (1992): 185–228.
Engle, R. F., and C.W. J. Granger. “Co-integration and Error Correction: Representation, Estimation and Testing.” Econometrica 55 (1987): 251–276.
Granger, C.W. J. “Some Properties of Time Series Data and Their Use in Econometric Model Specification.” Journal of Econometrics 16 (1981): 121–130.
Hendry, David. F. Dynamic Econometrics. Oxford, UK: Oxford University Press, 1995.