arXiv subjects

Xiyu Jiao

Publications and source records attributed to Xiyu Jiao.

3 recordsLinked to original sources

arXiv2026

Causal State-Dependent Local Projections

State-dependent local projections (LPs) are widely used to study how causal effects vary as a function of economic states, but shock exogeneity alone does not identify this response function. We show that identification follows when the underlying conditional mean is linear in the shock with a state-dependent coefficient, a condition satisfied in canonical micro-macro environments, including first-order perturbation solutions of heterogeneous-agent and macro-finance models. Even then, standard linear-interaction LPs generally recover only a projection of the response function, motivating LPs with nonparametric state dependence. We develop a sieve estimator and establish pointwise and uniform inference for micro-macro panels, where a distinctive challenge is that the estimator can converge at different rates across the state space. Applied to firm investment, the method uncovers a hump-shaped response to monetary policy shocks and shows that standard linear-interaction LPs substantially understate the aggregate role of financial heterogeneity.

econ.EM↗

arXiv2026

A Simple Robust Procedure in Instrumental Variables Regression

A common concern in empirical modelling centres around whether estimated regression coefficients are affected by a small set of outlying observations. To conduct outlier robustness checks in practical applications of instrumental variables regressions, the common practice is to run ordinary two stage least squares (2SLS) and remove observations with standardised residuals beyond a chosen cut-off value. Subsequently, the trimmed 2SLS is computed and compared to the original full-sample 2SLS. This paper aims to understand and improve the above heuristic procedure by establishing an asymptotic theory. Specifically, there are three main contributions of the paper. First, the trimmed 2SLS has a positive probability of removing observations even under the null hypothesis where the model contains no outliers. Under this situation, we derive a limiting Normal distribution of the trimmed 2SLS with the asymptotic variance as the ordinary one multiplied by a relative efficiency inflator. Furthermore, a bias correction factor is introduced for the variance estimator of structural errors, which otherwise would be downward biased. Second, a Hausman-type test is constructed to formalize the heuristic procedure of comparing between the two 2SLS estimators. Third, the trimmed 2SLS is a two-step procedure, which can be iterated until a fixed point is reached. The fixed point is shown to have the same first order asymptotics as the Huber-skip M-estimator. Our analysis involves a new class of empirical processes, whose theory would be of independent interest in applied probability. Simulation studies lend support to the asymptotic theory. An empirical illustration to Acemoglu et al. (2019) shows the utility of the proposed method.

econ.EM↗

arXiv2026

Inference on Common Trends in a Cointegrated Nonlinear SVAR

We consider the problem of performing inference on the number of common stochastic trends when data is generated by a cointegrated CKSVAR (a two-regime, piecewise affine SVAR; Mavroeidis, 2021), using a modified version of the Breitung (2002) multivariate variance ratio test that is robust to the presence of nonlinear cointegration (of a known form). To derive the asymptotics of our test statistic, we prove a fundamental LLN-type result for a class of stable but nonstationary autoregressive processes, using a novel dual linear process approximation. We show that our modified test yields correct inferences regarding the number of common trends in such a system, whereas the unmodified test tends to infer a higher number of common trends than are actually present, when cointegrating relations are nonlinear.

econ.EM↗