|
| |
| Moisés A. Resende Filho |
| |
| ''When does an own-lag IV estimand identify a contemporaneous causal effect?'' |
| ( 2026, Vol. 0 No.0 ) |
| |
| |
| Researchers often use a lag of an endogenous treatment as an instrument for its current value, relying on dynamic orthogonality restrictions rather than temporal ordering alone. This note asks when the resulting population IV estimand equals a specified contemporaneous direct causal effect. In a linear dynamic system, equality holds exactly when the residualized lag is orthogonal to the target-specific structural residual. The contribution is not a new orthogonality condition, but a target-specific structural characterization of that condition. Deleting the target edge in the underlying DAG before latent projection yields an ADMG in which m-separation supplies a graphical sufficient condition, equivalent to d-separation in the edge-deleted underlying DAG. This analysis shows why contemporaneous treatment endogeneity alone need not invalidate the lag, whereas treatment carryover, outcome dynamics, persistent latent confounding, and persistent omitted shocks can create bypassing paths. A stationary benchmark yields a closed-form estimand-target gap, while Monte Carlo evidence shows that increasing panel length can improve precision around the wrong estimand without restoring identification. The practical implication is that own-lag instruments should be justified by the exact target-specific moment implied by the maintained dynamic model, rather than by lagging or first-stage strength alone. |
| |
| |
| Keywords: instrumental variables, dynamic panels, causal effects, latent projection, m-separation, estimand-target equivalence |
JEL: C1 - Econometric and Statistical Methods: General
C2 - Single Equation Models; Single Variables: General |
| |
| Manuscript Received : Sep 03 2026 | | Manuscript Accepted : Oct 10 2026 |
|
