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Dynamic Models for Dynamic Theories: The Ins and Outs of Lagged Dependent Variables
7/7 checkable references clean · checked 2026-08-27
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resolves10.1093/biomet/48.1-2.85
Asymptotic expansions for the mean and variance of the serial correlation coefficient
resolves10.2307/1911222
Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation
resolves10.2307/1914095
Tests for Serial Correlation in Regression Models with Lagged Dependent Variables and Serially Correlated Errors
resolves10.2307/2232053
Serial Correlation as a Convenient Simplification, Not a Nuisance: A Comment on a Study of the Demand for Money by the Bank of England
The 20 references without a DOI — listed, not checked
no DOI — not checkedStatistical Methods of Econometrics
no DOI — not checkedSociological Methodology 1973–1974
no DOI — not checkedEconometric Analysis
no DOI — not checkedEstimation and Inference in Econometrics
no DOI — not checkedComparing Dynamic Specifications: The Case of Presidential Approval
no DOI — not checkedEstimating Dynamic Models Is Not Merely a Matter of Technique
no DOI — not checkedFor processes such as budgets and arms races, if they are nonstationary, they are dynamic processes as well, the difference being that there is no decay in the effect of history on the current value of the process.
no DOI — not checkedThis approach may be of little help since it introduces all the difficulties of finding appropriate instruments.
no DOI — not checkedThe RMSE calculation here includes both model parameters: α and β.
no DOI — not checkedWe include OLS, since it should be unbiased so long as α is 0.0. The use of OLS without lags in the model would require an analyst to use Newey-West standard errors, which we do not calculate because we are concerned only with bias.
no DOI — not checkedThe common factor we refer to is (1 – β2 L). See Hendry (1995) for a more in-depth treatment.
no DOI — not checkedThat is not to say they are impossible to derive. Hurwicz (1950), White (1961), and Phillips (1977) have all derived the small sample properties of α analytically but only for the case in which φ is 0.0.
no DOI — not checkedSuch models are often referred to as partial adjustment models in the econometrics literature.
no DOI — not checkedThis is only roughly true; see the on-line appendix for the exact stationarity conditions.
no DOI — not checkedExercises in Econometrics
no DOI — not checkedAchen Christopher H. 2000. “Why Lagged Dependent Variables Can Supress the Explanatory Power of Other Independent Variables.” Presented at the Annual Meeting of Political Methodology, Los Angeles.
no DOI — not checkedThe steps required to go from the second to the third part of Eq. (4) are not entirely trivial in that the mathematics raise an important issue about the error term. The last line of Eq. (4) is actually the following: Yt = (1 – λ)α + λYt–1 + β0 Xt + ut – λut– 1. The nontrivial part of this equation is the error term, ut – λut– 1, which is an MA(1) error term. Most discussions of this model simply note that it is an MA(1) error term and move on. Beck (1992), however, has a nice treatment of this issue and notes that this MA(1) error term can be represented as an AR process (or is empirically impossible to distinguish from an AR process). The nature of the error term as an AR process is important for determining the properties of OLS when used with a lagged dependent variable and is taken up in the next section.
no DOI — not checkedThe reader should note that for some of the values of α and φ in the plot, the model is no longer stationary. We had to do this to make the surface rectangular.
no DOI — not checkedStatistical Inference in Dynamic Economic Models
no DOI — not checkedFor a nice discussion of ADL(1,1) models see (Hendry 1995).
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