The identification in a nonseparable single-index models with correlated random effects is considered in panel data with a fixed number of time periods. The identification assumption is based on the correlated random effects structure. Under this assumption, the parameters of interest are identified up to a multiplicative constant and could be estimated by an average difference of derivatives estimator based on the local polynomial smoothing. We suggest to linearly combine the estimators obtained for different orders of differences and derive the variance-minimizing weighting scheme. The asymptotic distribution of the proposed estimators is derived both for stationary and non-stationary explanatory variables along with a test of the stationarity. Finally, Monte Carlo experiments reveal finite sample properties of the proposed estimator.
- average derivative estimation
- correlated random effects
- local polynomia smoothing
- nonlinear panel data
- nonseparable models