  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.
