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Martin Weidner

Publications and source records attributed to Martin Weidner.

At least 19 recordsLinked to original sources
arXiv2026

A Neyman-Orthogonalization Approach to the Incidental Parameter Problem in Likelihood Models

A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is zero. Such first-order orthogonalization allows the estimator of the nuisance parameters to converge at a slower-than-parametric rate. It may, however, not suffice when the nuisance parameters are very imprecisely estimated. Leading examples are models for panel and network data that feature fixed effects. In this paper, we show how, in the conditional-likelihood setting, estimating equations can be constructed that are orthogonal to any chosen order q, in that their leading q expected derivatives are zero. This yields estimators of target parameters that are unaffected by the presence of nuisance parameters to order q. In an empirical illustration, we apply our method to a fixed-effect model of team production.

econ.EM↗
arXiv2026

Higher-Order Neyman Orthogonality in Moment-Condition Models

We construct moment functions that are Neyman-orthogonal to a chosen order in parametric moment condition models. These moment functions reduce sensitivity to nuisance estimation error and, as such, offer a unified and tractable route to higher-order debiasing in a wide range of econometric models. The number of additional nuisance parameters required by our construction, beyond those already present in the original moment conditions, is independent of the order of orthogonalization and can be reduced to a single scalar if desired.

econ.EM↗
arXiv2026

Bounding Treatment Effects by Pooling Limited Information across Observations

We provide novel bounds on average treatment effects (on the treated) that are valid under an unconfoundedness assumption. Our bounds are designed to be robust in challenging situations, for example, when the conditioning variables take on a large number of different values in the observed sample, or when the overlap condition is violated. This robustness is achieved by only using limited "pooling" of information across observations. Namely, the bounds are constructed as sample averages over functions of the observed outcomes such that the contribution of each outcome only depends on the treatment status of a limited number of observations. No information pooling across observations leads to so-called "Manski bounds", while unlimited information pooling leads to standard inverse propensity score weighting. We explore the intermediate range between these two extremes and provide corresponding inference methods. We show in Monte Carlo experiments and through two empirical application that our bounds are indeed robust and informative in practice.

econ.EM↗
arXiv2026

Approximate Operator Inversion for Average Effects in Nonlinear Panel Models

We study the estimation of average effects in nonlinear panel data models with fixed effects when the time dimension $T$ is only moderately large. Our approach, called approximate operator inversion (AOI), offers a new perspective on bias correction. Instead of first estimating unit-specific fixed effects and then correcting the resulting plug-in bias, AOI approximately inverts the likelihood-induced mapping from the fixed-effect distribution to the outcome distribution. AOI can be interpreted as the limit of an infinitely iterated bias correction scheme, and this limit is available in closed form. We show that the bias of the AOI estimator has a rate double robustness property and converges to zero at an exponential rate in $T$ under regularity conditions. Our asymptotic theory requires $T \to \infty$, but the exponential convergence rate of the bias means that finite-sample performance is very good even for moderately large $T$. We establish asymptotic normality and provide feasible inference.

econ.EM↗
arXiv2026

Estimation of random coefficients logit demand models with interactive fixed effects

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete-choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodates endogeneity and, at the same time, captures strong persistence in market shares across products and markets. We propose a two-step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical illustration to US automobile demand.

econ.EM↗
arXiv2026

Dynamic Linear Panel Regression Models with Interactive Fixed Effects

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross-sectional dimension and the number of time periods become large. We find two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the idiosyncratic error term, and bias due to predetermined (as opposed to strictly exogenous) regressors. We provide a bias-corrected LS estimator. We also present bias-corrected versions of the three classical test statistics (Wald, LR, and LM test) and show their asymptotic distribution is a chi-squared distribution. Monte Carlo simulations show the bias correction of the LS estimator and of the test statistics also work well for finite sample sizes.

econ.EM↗
arXiv2026

Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross-sectional units jointly go to infinity. The main result of the paper is that under certain assumptions the limiting distribution of the LS estimator is independent of the number of factors used in the estimation, as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed effects consistently.

econ.EM↗
arXiv2026

Factor-Augmented Panel Regressions and Variance-Weighted Treatment Effects

We revisit panel regressions with unobserved heterogeneity through the lens of variance-weighted average treatment effects. Building on established results for cross-sectional OLS and one-way fixed effects panels, we show that two-way panel estimators with latent factors, specifically the principal components estimator of Greenaway-McGrevy, Han and Sul (2012) and the interactive fixed effects estimator of Bai (2009), also converge to interpretable estimands under fully nonparametric assumptions. Both estimators consistently estimate the same variance-weighted average of unit-time-specific treatment effects, where the weights are proportional to the conditional variance of the regressor given the unobserved heterogeneity. The result requires the number of estimated factors to grow with the sample size and applies to the single regressor case. We discuss the challenges that arise when extending to multiple regressors and to inference.

econ.EM↗
arXiv2026

Nuclear Norm Regularized Estimation of Panel Regression Models

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are defined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identification problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a finite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.

econ.EM↗
arXiv2026

Bounds on Average Effects in Discrete Choice Panel Data Models

In discrete choice panel data, estimation of average effects is crucial for quantifying the effect of covariates, and for policy evaluation and counterfactual analysis. However, in short panels with individual-specific effects, challenges arise due to partial identification and the incidental parameter problem. In particular, estimating the sharp identified set on average effects becomes impractical when covariates have large support sets, such as when they are continuous. This paper proposes a method for estimating outer bounds on the identified set of average effects, which are easy to construct, converge at the parametric rate, and remain computationally feasible even for moderately large samples. Asymptotically valid confidence intervals are also provided.

econ.EM↗
arXiv2026

Forecasted Treatment Effects

We consider estimation and inference of the effects of a policy in the absence of an untreated or control group. We obtain unbiased estimators of individual (heterogeneous) treatment effects and a consistent and asymptotically normal estimator of the average treatment effect. Our estimator averages, across individuals, the difference between observed post-treatment outcomes and unbiased forecasts of their counterfactuals, based on a (short) time series of pre-treatment data. The paper emphasizes the importance of focusing on forecast unbiasedness rather than accuracy when the end goal is estimation of average treatment effects. We show that simple basis function regressions ensure forecast unbiasedness for a broad class of data generating processes for the counterfactuals. In contrast, forecasting based on a specific parametric model requires stronger assumptions and is prone to misspecification and estimation bias. We show that our method can replicate the findings of some previous empirical studies but it does so without using an untreated or control group.

econ.EM↗
arXiv2025

Binary choice logit models with general fixed effects for panel and network data

This paper systematically analyzes and reviews identification strategies for binary choice logit models with fixed effects in panel and network data settings. We examine both static and dynamic models with general fixed-effect structures, including individual effects, time trends, and two-way or dyadic effects. A key challenge is the incidental parameter problem, which arises from the increasing number of fixed effects as the sample size grows. We explore two main strategies for eliminating nuisance parameters: conditional likelihood methods, which remove fixed effects by conditioning on sufficient statistics, and moment-based methods, which derive fixed-effect-free moment conditions. We demonstrate how these approaches apply to a variety of models, summarizing key findings from the literature while also presenting new examples and new results.

econ.EM↗
arXiv2025

Unified Quantum Dynamics: The Emergence of the Born Rule

While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schrödinger equation that includes "small-signal truncation". This parallels the way quantum decoherence gives rise to the branches of the multiverse in the "Many-Worlds Interpretation", eliminating the need for a separate measurement postulate. Our approach thus offers a unified framework in which both the emergence of multiple branches of the multiverse and their statistical properties follow from a single fundamental law of motion. We model "small-signal truncation" in a somewhat stylized manner, but we argue that the precise details of its underlying physical mechanism do not affect the emergence of the Born rule.

quant-ph↗
arXiv2025

Robust Estimation and Inference in Panels with Interactive Fixed Effects

We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We demonstrate that existing estimators and confidence intervals (CIs) can be heavily biased and size-distorted when some of the factors are weak. We propose estimators with improved rates of convergence and bias-aware CIs that remain valid uniformly, regardless of factor strength. Our approach applies the theory of minimax linear estimation to form a debiased estimate, using a nuclear norm bound on the error of an initial estimate of the interactive fixed effects. Our resulting bias-aware CIs take into account the remaining bias caused by weak factors. Monte Carlo experiments show substantial improvements over conventional methods when factors are weak, with minimal costs to estimation accuracy when factors are strong.

econ.EM↗
arXiv2024

Dynamic Ordered Panel Logit Models

This paper studies a dynamic ordered logit model for panel data with fixed effects. The main contribution of the paper is to construct a set of valid moment conditions that are free of the fixed effects. The moment functions can be computed using four or more periods of data, and the paper presents sufficient conditions for the moment conditions to identify the common parameters of the model, namely the regression coefficients, the autoregressive parameters, and the threshold parameters. The availability of moment conditions suggests that these common parameters can be estimated using the generalized method of moments, and the paper documents the performance of this estimator using Monte Carlo simulations and an empirical illustration to self-reported health status using the British Household Panel Survey.

econ.EM↗
arXiv2023

Moment Conditions for Dynamic Panel Logit Models with Fixed Effects

This paper investigates the construction of moment conditions in discrete choice panel data with individual specific fixed effects. We describe how to systematically explore the existence of moment conditions that do not depend on the fixed effects, and we demonstrate how to construct them when they exist. Our approach is closely related to the numerical "functional differencing" construction in Bonhomme (2012), but our emphasis is to find explicit analytic expressions for the moment functions. We first explain the construction and give examples of such moment conditions in various models. Then, we focus on the dynamic binary choice logit model and explore the implications of the moment conditions for identification and estimation of the model parameters that are common to all individuals.

econ.EM↗
arXiv2023

Approximate Functional Differencing

Inference on common parameters in panel data models with individual-specific fixed effects is a classic example of Neyman and Scott's (1948) incidental parameter problem (IPP). One solution to this IPP is functional differencing (Bonhomme 2012), which works when the number of time periods T is fixed (and may be small), but this solution is not applicable to all panel data models of interest. Another solution, which applies to a larger class of models, is "large-T" bias correction (pioneered by Hahn and Kuersteiner 2002 and Hahn and Newey 2004), but this is only guaranteed to work well when T is sufficiently large. This paper provides a unified approach that connects those two seemingly disparate solutions to the IPP. In doing so, we provide an approximate version of functional differencing, that is, an approximate solution to the IPP that is applicable to a large class of panel data models even when T is relatively small.

econ.EM↗