This paper presents robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach, deriving the conditional distribution of coefficient estimates given the group structure estimated from the data. Our procedure provides valid inference under possible violations of group separation, where distributional properties of group-specific coefficients remain unestablished. Furthermore, even when group separation does hold, our method demonstrates superior finite-sample properties compared to traditional asymptotic approaches. This improvement stems from our procedure's ability to account for statistical uncertainty in the estimation of group structure. We demonstrate the effectiveness of our approach through Monte Carlo simulations and apply the methods to two datasets on: (i) the relationship between income and democracy, and (ii) the cyclicality of firm-level R&D investment.

A triangular structural panel data model with additive separable individual-specific effects is used to model the causal effect of a covariate on an outcome variable when there are unobservable confounders with some of them time-invariant. In this setup, a linear reduced-form equation might be problematic when the conditional mean of the endogenous covariate and the instrumental variables is nonlinear. The reason is that ignoring the nonlinearity could lead to weak instruments As a solution, we propose a triangular simultaneous equation model for panel data with additive separable individual-specific fixed effects composed of a linear structural equation with a nonlinear reduced form equation. The parameter of interest is the structural parameter of the endogenous variable. The identification of this parameter is obtained under the assumption of available exclusion restrictions and using a control function approach. Estimating the parameter of interest is done using an estimator that we call Super Learner Control Function estimator (SLCFE). The estimation procedure is composed of two main steps and sample splitting. We estimate the control function using a super learner using sample splitting. In the following step, we use the estimated control function to control for endogeneity in the structural equation. Sample splitting is done across the individual dimension. We perform a Monte Carlo simulation to test the performance of the estimators proposed. We conclude that the Super Learner Control Function Estimators significantly outperform Within 2SLS estimators.

The paper uses structured machine learning regressions for nowcasting with panel data consisting of series sampled at different frequencies. Motivated by the problem of predicting corporate earnings for a large cross-section of firms with macroeconomic, financial, and news time series sampled at different frequencies, we focus on the sparse-group LASSO regularization which can take advantage of the mixed frequency time series panel data structures. Our empirical results show the superior performance of our machine learning panel data regression models over analysts' predictions, forecast combinations, firm-specific time series regression models, and standard machine learning methods.

In this paper we develop a data-driven smoothing technique for high-dimensional and non-linear panel data models. We allow for individual specific (non-linear) functions and estimation with econometric or machine learning methods by using weighted observations from other individuals. The weights are determined by a data-driven way and depend on the similarity between the corresponding functions and are measured based on initial estimates. The key feature of such a procedure is that it clusters individuals based on the distance / similarity between them, estimated in a first stage. Our estimation method can be combined with various statistical estimation procedures, in particular modern machine learning methods which are in particular fruitful in the high-dimensional case and with complex, heterogeneous data. The approach can be interpreted as a \textquotedblleft soft-clustering\textquotedblright\ in comparison to traditional\textquotedblleft\ hard clustering\textquotedblright that assigns each individual to exactly one group. We conduct a simulation study which shows that the prediction can be greatly improved by using our estimator. Finally, we analyze a big data set from didichuxing.com, a leading company in transportation industry, to analyze and predict the gap between supply and demand based on a large set of covariates. Our estimator clearly performs much better in out-of-sample prediction compared to existing linear panel data estimators.