{"title":"Identification and inference for semiparametric single index transformation models","authors":"Yingqian Lin , Yundong Tu","doi":"10.1016/j.jeconom.2025.106084","DOIUrl":"10.1016/j.jeconom.2025.106084","url":null,"abstract":"<div><div>This paper considers a semiparametric single index model in which the dependent variable is subject to a nonparametric transformation. The model has the form <span><math><mrow><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>Y</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mo>⊤</mo></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>+</mo><mi>e</mi></mrow></math></span>, where <span><math><mi>X</mi></math></span> is a random vector of regressors, <span><math><mi>Y</mi></math></span> is the dependent variable and <span><math><mi>e</mi></math></span> is the random noise, the monotonic function <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the smooth function <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and the index vector <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> are all unknown. This model is quite general in the sense that it nests many popular regression models as special cases. We first propose identification strategies for the three unknown quantities, based on which estimators are then constructed. The kernel density weighted average derivative estimator of <span><math><mi>δ</mi></math></span> (proportional to <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) has a <span><math><mi>V</mi></math></span>-statistic representation and its asymptotical normality is established under the small bandwidth asymptotics. The kernel estimator of the transformation function <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is a functional of the conditional distribution estimator of <span><math><mi>Y</mi></math></span> given <span><math><mrow><msup><mrow><mi>X</mi></mrow><mrow><mo>⊤</mo></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> and is shown to be <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-consistent and asymptotically normal. The sieve estimator of <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is shown to enjoy the standard nonparametric asymptotic properties. A specification test for the single index structure and extension to allow for endogeneous regressors are also developed. In addition, data-driven choices of the smoothing parameters are discussed. Simulation results illustrate the nice finite sample performance of the proposed estimators and specification test. An empirical application to studying the impact of family income on child achievement demonstrates the practical merits of the proposed model.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106084"},"PeriodicalIF":4.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Bajari , Z. Cen , V. Chernozhukov , M. Manukonda , S. Vijaykumar , J. Wang , R. Huerta , J. Li , L. Leng , G. Monokroussos , S. Wang
{"title":"Hedonic prices and quality adjusted price indices powered by AI","authors":"P. Bajari , Z. Cen , V. Chernozhukov , M. Manukonda , S. Vijaykumar , J. Wang , R. Huerta , J. Li , L. Leng , G. Monokroussos , S. Wang","doi":"10.1016/j.jeconom.2025.106052","DOIUrl":"10.1016/j.jeconom.2025.106052","url":null,"abstract":"<div><div>We develop empirical models that efficiently process large amounts of unstructured product data (text, images, prices, quantities) to produce accurate hedonic price estimates and derived indices. To achieve this, we generate abstract product attributes (or “features”) from descriptions and images using deep neural networks. These attributes are then used to estimate the hedonic price function. To demonstrate the effectiveness of this approach, we apply the models to Amazon’s data for first-party apparel sales, and estimate hedonic prices. The resulting models have a very high out-of-sample predictive accuracy, with <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> ranging from 80% to 90%. Finally, we construct the AI-based hedonic Fisher price index, chained at the year-over-year frequency, and contrast it with the CPI and other electronic indices.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106052"},"PeriodicalIF":4.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Deep learning based residuals in non-linear factor models: Precision matrix estimation of returns with low signal-to-noise ratio","authors":"Mehmet Caner , Maurizio Daniele","doi":"10.1016/j.jeconom.2025.106083","DOIUrl":"10.1016/j.jeconom.2025.106083","url":null,"abstract":"<div><div>This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low signal-to-noise ratio environments typical for financial markets and is compatible with the weak factor framework. Our theoretical analysis establishes uniform bounds on expected estimation risk based on deep neural networks for an expanding number of assets. Additionally, we provide a new consistent data-dependent estimator of error covariance in deep neural networks. Our models demonstrate superior accuracy in extensive simulations and the empirical application.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106083"},"PeriodicalIF":4.0,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An order-invariant score-driven dynamic factor model","authors":"Mariia Artemova","doi":"10.1016/j.jeconom.2025.106073","DOIUrl":"10.1016/j.jeconom.2025.106073","url":null,"abstract":"<div><div>This paper introduces a novel score-driven dynamic factor model designed for filtering cross-sectional co-movements in panels of time series. The model is formulated using elliptical distribution for noise terms, allowing the update of the time-varying parameter to be potentially nonlinear and robust to outliers. We derive stochastic properties of time series generated by the model, such as stationarity and ergodicity, and establish the invertibility of the filter. We prove that the identification of the factors and loadings is achieved by incorporating an orthogonality constraint on the loadings, which is invariant to the order of the series in the panel. Given the nonlinearity of the constraint, we propose exploiting a maximum likelihood estimation on Stiefel manifolds. This approach ensures that the identification constraint is satisfied numerically, enabling joint estimation of the static and time-varying parameters. Furthermore, the asymptotic properties of the constrained estimator are derived. In a series of Monte Carlo experiments, we find evidence of appropriate finite sample properties of the estimator and resulting score filter for the time-varying parameters. We demonstrate the empirical usefulness of our factor model in constructing indices of economic activity from a set of macroeconomic and financial variables during the period 1981–2022. An empirical application highlights the importance of robustness, particularly in the presence of V-shaped recessions, such as the COVID-19 recession.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106073"},"PeriodicalIF":4.0,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144841156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bregman model averaging for forecast combination","authors":"Yi-Ting Chen , Chu-An Liu , Jiun-Hua Su","doi":"10.1016/j.jeconom.2025.106076","DOIUrl":"10.1016/j.jeconom.2025.106076","url":null,"abstract":"<div><div>We propose a unified model averaging (MA) approach for a broad class of forecasting targets. This approach is established by minimizing an asymptotic risk based on the expected Bregman divergence of a combined forecast, relative to the optimal forecast of the forecasting target, under local(-to-zero) asymptotics. It can be flexibly applied to develop effective MA methods across various forecasting contexts, including but not limited to univariate and multivariate mean forecasting, volatility forecasting, probabilistic forecasting, and density forecasting. As illustrative examples, we present a series of simulation experiments and empirical cases that demonstrate strong numerical performance of our approach in forecasting.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106076"},"PeriodicalIF":4.0,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144827730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Giuseppe Buccheri , Roberto Renò , Giorgio Vocalelli
{"title":"Taking advantage of biased proxies for forecast evaluation","authors":"Giuseppe Buccheri , Roberto Renò , Giorgio Vocalelli","doi":"10.1016/j.jeconom.2025.106068","DOIUrl":"10.1016/j.jeconom.2025.106068","url":null,"abstract":"<div><div>This paper rehabilitates biased proxies for the assessment of the predictive accuracy of competing forecasts. By relaxing the ubiquitous assumption of proxy unbiasedness adopted in the theoretical and empirical literature, we show how to optimally combine (possibly) biased proxies to maximize the probability of inferring the ranking that would be obtained using the true latent variable, a property that we dub proxy reliability. Our procedure still preserves the robustness of the loss function, in the sense of Patton (2011b), and allows testing for equal predictive accuracy, as in Diebold and Mariano (1995). We demonstrate the usefulness of the method with compelling empirical applications on GDP growth, financial market volatility forecasting, and sea surface temperature of the Niño 3.4 region.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106068"},"PeriodicalIF":4.0,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"High dimensional binary choice model with unknown heteroskedasticity or instrumental variables","authors":"Fu Ouyang, Thomas T. Yang","doi":"10.1016/j.jeconom.2025.106069","DOIUrl":"10.1016/j.jeconom.2025.106069","url":null,"abstract":"<div><div>This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous regressors. Our approaches extend the special regressor estimator originally proposed by Lewbel (2000). This estimator becomes impractical in high-dimensional settings due to the curse of dimensionality associated with high-dimensional conditional density estimation. To overcome this challenge, we introduce an innovative data-driven dimension reduction method for nonparametric kernel estimators, which constitutes the main contribution of this work. The method combines distance covariance-based screening with cross-validation (CV) procedures, making special regressor estimation feasible in high dimensions. Using this new feasible conditional density estimator, we address variable and moment (instrumental variable) selection problems for these models. We apply penalized least squares (LS) and generalized method of moments (GMM) estimators with an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> penalty. A comprehensive analysis of the oracle and asymptotic properties of these estimators is provided. Finally, through Monte Carlo simulations and an empirical study on the migration intentions of rural Chinese residents, we demonstrate the effectiveness of our proposed methods in finite sample settings.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106069"},"PeriodicalIF":4.0,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Neural Conformal Inference for jump diffusion processes","authors":"Hyeong Jin Hyun, Xiao Wang","doi":"10.1016/j.jeconom.2025.106061","DOIUrl":"10.1016/j.jeconom.2025.106061","url":null,"abstract":"<div><div>Bayesian inference for jump diffusion processes (JDPs) remains challenging due to intractable transition densities and the latency of jump times and intensities. This paper introduces Neural Conformal Inference for JDPs (NCoin-JDP), a novel likelihood-free approach that leverages the power of deep neural networks (DNNs). NCoin-JDP bypasses the limitations of traditional methods by establishing a direct mapping between observed data and model parameters using a DNN. This approach eliminates the discretization errors inherent in likelihood-based methods, leading to more accurate inference. Despite the black-box nature of DNNs, we establish the asymptotic theory to quantify the approximation error of our algorithm. Additionally, we calibrate the uncertainty of our estimations using conformal prediction, providing theoretical guarantees of equivalence with the Bayesian posterior. NCoin-JDP demonstrates competitive performance compared to state-of-the-art methods. We showcase its effectiveness through numerical simulations and apply it to real-world data (S&P 500 and NASDAQ, 1993–2024) to investigate the impact of COVID-19 on the US economy. All numerical studies are reproducible in <span><span>https://github.com/anonymous1116/NCoin-JDP</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106061"},"PeriodicalIF":4.0,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized Lee bounds","authors":"Vira Semenova","doi":"10.1016/j.jeconom.2025.106055","DOIUrl":"10.1016/j.jeconom.2025.106055","url":null,"abstract":"<div><div>Lee (2009) is a common approach to bound the average causal effect in the presence of selection bias, assuming the treatment effect on selection has the same sign for all subjects. This paper generalizes Lee bounds to allow the sign of this effect to be identified by pretreatment covariates, relaxing the standard (unconditional) monotonicity to its conditional analog. Asymptotic theory for generalized Lee bounds is proposed in low-dimensional smooth and high-dimensional sparse designs. The paper also generalizes Lee bounds to accommodate multiple outcomes. Focusing on JobCorps job training program, I first show that unconditional monotonicity is unlikely to hold, and then demonstrate the use of covariates to tighten the bounds.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106055"},"PeriodicalIF":9.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A comparative analysis of two-way fixed effects estimators in staggered treatment designs","authors":"Jhordano Aguilar-Loyo","doi":"10.1016/j.jeconom.2025.106059","DOIUrl":"10.1016/j.jeconom.2025.106059","url":null,"abstract":"<div><div>Two-way fixed effects (TWFE) is a flexible and widely used approach for estimating treatment effects, and several TWFE estimators have been proposed for staggered treatment designs. This paper focuses on the extended TWFE estimator, introduced by Borusyak et al. (2024) and Wooldridge (2021), and compares it with alternative TWFE estimators. The main contribution is the derivation of an equation that connects the extended TWFE estimator with the difference-in-differences estimator. This equivalence provides a transparent decomposition of the components of the extended TWFE estimand. The results show that the extended TWFE estimand consists of two distinct components: one that captures meaningful comparisons and a residual term. The paper outlines the assumptions required to identify treatment effects. In line with previous literature, the findings show that the extended TWFE estimator relies on a parallel trends assumption that extends across multiple periods. Additionally, illustrative examples compare the TWFE estimators under violations of the parallel trends assumption. The results suggest that no single estimator outperforms the others. The choice of the TWFE estimator depends on the parameter of interest and the characteristics of the empirical application.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"251 ","pages":"Article 106059"},"PeriodicalIF":9.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}