Abstract This paper develops integrated modified ordinary and generalized least squares estimation for systems of cointegrating multivariate polynomial regressions, i. e., systems of equations that include deterministic variables, integrated processes and (cross-)products of non-negative integer powers of these variables as regressors. The stationary errors are allowed to be correlated across equations, over time and with the regressors. The necessity to consider integrated modified generalized least squares estimation arises in the case of estimation under restrictions, which in general implies that ordinary and generalized least squares estimators cease to be identical. We discuss in detail hypothesis testing for the unrestricted and restricted estimators. Furthermore, we develop asymptotically pivotal fixed-b inference, shown to be available only in special cases. A brief illustration to modelling output and emissions as a Cobb-Douglas-Translog cointegrated production system with TFP, capital and labor as inputs indicates the potential usefulness of the developed methods for climate econometrics.
Summary We consider likelihood-ratio-type statistics for testing restrictions on parameters built from a convex M-estimation criterion. In general, these statistics are not asymptotically pivotal. We propose a general simple non-parametric bootstrap procedure that yields asymptotically valid critical values and p-values. The method modifies the bootstrap objective function to mimic what happens under the null hypothesis. A Monte Carlo study illustrates that our method controls level well and is powerful.
Abstract This paper studies identification and doubly robust (DR) estimation of quantile treatment effects (QTEs) in difference-in-discontinuities (diff-in-disc) designs when a new treatment is introduced in the post period and a confounding discontinuous policy is present in both periods. We show that QTEs are point identified under a conditional stable-distributional-effect assumption for the confounding treatment, a restriction that is analogous to the distributional parallel trends assumption in the recent difference-in-differences literature. We then propose a DR estimator and inference procedure that remain valid when either the outcome regression or the propensity score model is correctly specified, while avoiding high-dimensional nonparametric adjustment for covariates in the local estimation setting. We establish asymptotic normality of the proposed estimator, and Monte Carlo simulations illustrate its double-robustness and good finite-sample performance. In an application to Italian municipal fiscal data (Grembi et al. 2016),, the estimates suggest that relaxing fiscal constraints increases deficits primarily over the lower and central portions of the distribution, shifting municipalities from surplus or near balance into moderate deficits—a distributional pattern not captured by mean effects.
Summary This paper develops numerical and causal interpretations of two-way fixed effects (TWFE) regressions in settings with nonbinary, nonstaggered treatments and time-varying covariates. Using the equivalence between TWFE and pooled first-difference (FD) regressions, I express the TWFE coefficient as a weighted average of FD coefficients across all horizons, clarifying how short- and long-run changes contribute to the estimate. Causal interpretation of the TWFE coefficient relies on common trends assumptions at all horizons simultaneously, whereas each FD coefficient relies on the assumption only at its own horizon. This structure opens the identifying assumptions to empirical scrutiny: I propose diagnostic procedures that assess common trends horizon by horizon, and illustrate them by reexamining TWFE estimates of minimum wage effects on employment.
Summary Putting a price on carbon emissions helps mitigate climate change but may also raise overall price inflation. Using high-frequency event studies based on regulatory news in the European carbon market, we show that carbon price surprises generate significant increases not only in energy futures prices, but also in inflation swap rates and break-even inflation rates. These measures of inflation compensation respond positively at both short and long horizons, with significant effects up to ten years out. Such persistent effects of climate policy on market-based inflation expectations are relevant for central banks. However, despite the sustained effects on inflation compensation, forward-looking nominal interest rates show no meaningful response to the carbon policy shocks, suggesting that investors do not anticipate that the European Central Bank will lean against the inflationary effects of higher carbon prices.
