arXiv subjects

Mahrad Sharifvaghefi

Publications and source records attributed to Mahrad Sharifvaghefi.

6 recordsLinked to original sources

arXiv2026

Continuously Updating GMM in Linear IV Models: A Polynomial Approach

This paper characterizes the global minimum of the continuously updating generalized method of moments (CU-GMM) objective in linear instrumental variables models. We allow optimal weighting matrices under heteroskedasticity, autocorrelation, or clustering. We show that the objective is a ratio of polynomials. For one endogenous regressor, stationary points of CU-GMM objective function are real eigenvalues of a companion matrix. Comparing their objective values with the value at infinity gives the global minimum, extending the classical eigenvector approach to limited information maximum likelihood. With multiple endogenous regressors, algebraic elimination and checks for real solutions identify the minimum among finitely many candidate objective values, including boundary values. Galois theory rules out general formulas by radicals even with one endogenous regressor and two instruments, while numerical root finding remains possible. Finding the global minimum allows us to compute overidentification and likelihood ratio tests, including the conditional likelihood ratio (CLR) test.

econ.EM↗

arXiv2026

Properties of the Conditional Likelihood Ratio Test under Discrete Approximation

The conditional likelihood ratio (CLR) test is a valuable tool for inference under weak identification, with appealing theoretical properties in both linear and non-linear settings. Its implementation nevertheless requires minimizing a non-convex objective function, a difficulty long recognized even in the linear IV setting. While grid-based methods that provide a practical approximation may perform well in particular designs, such procedures do not guarantee that the resulting test preserves the theoretical properties of the CLR test uniformly across a class of data-generating processes. This paper examines the implementation challenges and their consequences for test size and power. In the linear IV settings, we contrast the grid-based method with the polynomial approach of Moreira, Newey, and Sharifvaghefi(2024), which guarantees global minimization and aligns computation with the theoretical properties of the CLR test.

econ.EM↗

arXiv2026

Power Bounds and Efficiency Loss for Asymptotically Optimal Tests in IV Regression

We characterize the maximal attainable power-size gap in overidentified instrumental variables models with heteroskedastic or autocorrelated (HAC) errors. Using total variation distance and Kraft's theorem, we define the decision theoretic frontier of the testing problem. We show that Lagrange multiplier and conditional quasi likelihood ratio tests can have power arbitrarily close to size even when the null and alternative are well separated, because they do not fully exploit the reduced-form likelihood. In contrast, the conditional likelihood ratio (CLR) test uses the full reduced-form likelihood. We prove that the power-size gap of CLR converges to one if and only if the testing problem becomes trivial in total variation distance, so that CLR attains the decision theoretic frontier whenever any test can. An empirical illustration based on Yogo (2004) shows that these failures arise in empirically relevant configurations.

econ.EM↗

arXiv2024

Variable Selection in High Dimensional Linear Regressions with Parameter Instability

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigate the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating model that includes all the signals and none of the noise variables. Properties of post selection regressions are also investigated, and in-sample fit of the selected regression is shown to have the oracle property. The theoretical results support the use of unweighted observations at the selection stage of OCMT, whilst applying down-weighting of observations only at the forecasting stage. Monte Carlo and empirical applications show that OCMT without down-weighting at the selection stage yields smaller mean squared forecast errors compared to Lasso, Adaptive Lasso, and boosting.

econ.EM↗

arXiv2021

Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors

This paper uses model symmetries in the instrumental variable (IV) regression to derive an invariant test for the causal structural parameter. Contrary to popular belief, we show that there exist model symmetries when equation errors are heteroskedastic and autocorrelated (HAC). Our theory is consistent with existing results for the homoskedastic model (Andrews, Moreira, and Stock (2006) and Chamberlain (2007)). We use these symmetries to propose the conditional integrated likelihood (CIL) test for the causality parameter in the over-identified model. Theoretical and numerical findings show that the CIL test performs well compared to other tests in terms of power and implementation. We recommend that practitioners use the Anderson-Rubin (AR) test in the just-identified model, and the CIL test in the over-identified model.

math.ST↗

arXiv2018

IPAD: Stable Interpretable Forecasting with Knockoffs Inference

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped in the econometric settings. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Candès, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods.

math.ST↗