Lagged Dependent Variable Predictors, Classical Measurement Error, and Path Dependency: The Conditions Under Which Various Estimators are Appropriate
Bibliographic record
Abstract
Lagged dependent variables (LDVs) are often used as predictors in ordinary least squares (OLS) models in the social sciences. Although several estimators are commonly employed, little is known about their relative merits in the presence of classical measurement error and different longitudinal processes. We assess the performance of four commonly used estimators: (1) the standard OLS estimator, (2) an average of past measures (AVG), (3) an instrumental variable (IV) measured at one period previously (IV), and (4) an IV derived from information from more than one time before (IV2). We also propose a new estimator for fixed effects models—the first difference instrumental variable (FDIV) estimator. After exploring the consistency of these estimators, we demonstrate their performance using an empirical application predicting primary school test scores. Our results demonstrate that for a Markov process with classic measurement error (CME), IV and IV2 estimators are generally consistent; LDV and AVG estimators are not. For a semi-Markov process, only the IV2 estimator is consistent. On the other hand, if fixed effects are included in the model, only the FDIV estimator is consistent. We end with advice on how to select the appropriate estimator.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.071 | 0.276 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".