Nonparametric regresion models estimation in R

Transcription

1 Nonparametric regresion models estimation in R Maer Matei Monica Mihaela, Bucharest University Of Economic Studies National Scientific Research Institute for Labour and Social Protection Eliza Olivia Lungu National Scientific Research Institute for Labour and Social Protection

2 Theoretical background: Nonparametric estimation of regression functions with both categorical and continuous data (Racine and Li, 2004) Software solution: R np package (Hayfield, and Racine, 2008) Practical problem : Estimate the over education impact on earnings

3 Objectives: To model a dataset comprised of continuous, discrete, or categorical data (nominal or ordinal), or any combination. To construct a more flexible model. To let the data determine an appropriate model without specifying the functional forms for objects being estimated.

4 METHOD- nonparametric regression based on kernel methods Key notions - generalized product kernels - kernels for categorical data - bandwidth selection

5 R package np (Hayfield, and Racine, 2008): - density estimation - regression, and derivative estimation for both categorical and continuous data, - a range of kernel functions and bandwidth selection methods - tests of significance for nonparametric regression. - A variety of bootstrap methods for computing standard errors, nonparametric confidence bounds, and bias-corrected bounds are implemented. - A variety of bandwidth methods are implemented

6 FUNCTIONS npunitest - for testing equality of two univariate density/probability functions (Maasoumi and Racine,2002). npregbw - computes a bandwidth object for a p-variate kernel regression estimator defined over mixed continuous and discrete, using the method of Racine and Li (2004) and Li and Racine (2004). npreg - computes a kernel regression estimate of a one (1) dimensional dependent variable on p- variate explanatory data, given a set of explanatory data and dependent data), and a bandwidth specification using the method of Racine and Li (2004) and Li and Racine (2004).

7 The difficulties we encountered are related to the estimation time especially when the routines for significance testing based on bootstrap are called. - Execution time for most routines is exponentially increasing in the number of observations and increases with the number of variables involved. - Data-driven bandwidth selection methods involving multivariate numerical search can betime-consuming, particularly for large datasets. - A version of this package is under development to facilitate computation involving large datasets- Package nprmpi

8 Estimate the overeducation impact on earnings - REFLEX database includes information on early career outcomes of school leavers graduating ISCED 5 in 1999/2000 for 14 countries - UK sample 932 graduates - Main independent variable: { { }

9 Dependent variable

10 Other independent variables gender number of months employed since graduation (totworkdu) number of months at current job (workdu)

11 Testing equality of the density functions Srho : P Value: < 2.22e-16 *** Null of equality is rejected at the 0.1% level

12 Signifficance test for the estimated coefficients and Rsquared Country X1 (total work duration) X2 ( work duration current job) X1 (jobeducation match) UK X2 (gender) < 2.22e- 16 R squared 0.145

13 Partial local linear nonparametric response plots- UK case

14 Conclusions The results allow us to understand the overeducation impact on earnings distribution without assuming the functional form of the relationship between overeducation and higher education graduates earnings.