Nonparametric Methods in Econometrics using

Size: px
Start display at page:

Download "Nonparametric Methods in Econometrics using"

Transcription

1 Density Estimation Nonparametric Methods in Econometrics using David T. Jacho-Chávez 1 1 Department of Economics London School of Economics Cemmap 2006

2 Density Estimation Packages: Ecdat Data sets for econometrics KernSmooth Functions for kernel smoothing for Wand & Jones (1995) Data: Earnings Description: 4266 observations from a cross section ( ) from USA age (age groups) A factor with levels (g1,g2,g3) y (average annual earnings) In 1982 US dollars Source: Mills, Jeffery A. and Sourushe Zandvakili (1997) Statistical Inference via Bootstrapping for Measures of Inequality, Journal of Applied Econometrics, 12(2), pp

3 Density Estimation package: stats density(x, bw = "nrd0", adjust = 1, kernel = c("gaussian", "epanechnikov", "rectangular", "triangular", "biweight", "cosine", "optcosine"), weights = NULL, window = kernel, width, give.rkern = FALSE, n = 512, from, to, cut = 3, na.rm = FALSE,...)

4 Density Estimation Sensitivity: Bandwidth Density Income

5 Density Estimation Sensitivity: 7 different kernels, same bandwidth Density gaussian epanechnikov rectangular triangular biweight cosine optcosine N = 1109 Bandwidth = 0.4

6 Density Estimation Local Constant Local Linear Income

7 Curve Estimation (Univariate) package: stats ksmooth(x, y, kernel = c("box", "normal"), bandwidth = 0.5, range.x = range(x), n.points = max(100, length(x)), x.points)

8 Curve Estimation (Univariate) Bandwidth= Bandwidth= Bandwidth=

9 Curve Estimation (Univariate) Bandwidth= Bandwidth= Bandwidth=

10 Curve Estimation (Univariate) Normal Q Q Plot: m(0.5) h=0.1 Theoretical Quantiles Sample Quantiles Normal Q Q Plot: m(0.5) h=0.3 Theoretical Quantiles Sample Quantiles Normal Q Q Plot: m(0.5) h=0.8 Theoretical Quantiles Sample Quantiles

11 Curve Estimation (Univariate) Packages: Ecdat Data sets for econometrics locfit Local Regression, Likelihood and Density Estimation Data: Housing Description: 546 observations from a cross section (1987) regarding sales prices of houses in the city of Windsor (Canada) price Sale price of a house lotsize The lot size of a property in square feet Source: Anglin, P.M. and R. Gencay (1996) Semiparametric estimation of a hedonic price function, Journal of Applied Econometrics, 11(6),

12 Curve Estimation (Univariate) package: locfit density.lf(x, n = 50, window = "gaussian", width, from, to, cut = if(iwindow == 4.) 0.75 else 0.5, ev = lfgrid(mg = n, ll = from, ur = to), deg = 0, family = "density", link = "ident",...)

13 Curve Estimation (Univariate) Cross Validation of Bandwidths for Curve Estimation Cross validation function Bandwidth

14 Curve Estimation (Univariate) Log Lot Size Log Sale Prices E^[log(price) log(lotsize)] 95% Pointwise C.I.

15 Curve Estimation (Univariate) Packages: Ecdat Data sets for econometrics locfit Local Regression, Likelihood and Density Estimation Data: Southafrica Description: Data taken from Living Standards Measurement Survey ltexp Log(Total monthly household expenditure) FoodShr Share of total expenditure on food Source: Yatchew, Adonis (2003), Semiparametric Regression for the Applied Econometrician, Cambridge University Press, First Edn

16 Curve Estimation (Univariate) Food Share E^[Food Share log(expenditure)] 95% Asymptotic Conf.Int. 95% Bootstrap Conf.Int Log Expenditure

17 Curve Estimation (Multivariate) Packages: JLLprod Nonparametric Estimation of Homothetic and Generalized Homothetic Production Functions akima Interpolation of irregularly spaced data Data: ecu Description: 406 observations at plant level for the Petroleum, Chemical & Plastics industry in Ecuador for the year 2002 lny (Log(y)) Output in thousands of current US dollars lnk (Log(K)) Capital in thousands of current US dollars lnl (Log(L)) The average number of employees Source: Jacho-Chávez, David T., A. Lewbel and O. B. Linton (2005) Identification and Nonparametric Estimation of a Transformed Additively Separable Model, Unpublished Manuscript

18 Curve Estimation (Multivariate) ln(k/l) ln(y) ln(l) ln(y) Ecuador 2002 Petroleum, Chemical & Plastics, 406 Plants

19 Curve Estimation (Multivariate) Ecuador 2002 Original Data ln(y) ln(k/l) 0 10 ln(l) 8

20 Curve Estimation (Multivariate) >library(jllprod,akima,locfit) >data(ecu) >fit <- locfit(lny lp(lnl,lnk-lnl,nn=0,h=4, deg=1,scale=t), data=ecu) >fitted <- fitted(fit) >persp(interp(lnl,lnk-lnl,fitted), axes=true,lty=1,lwd=1,,xlab="ln(l)", ylab="ln(k/l)", zlab="ln(y)", ticktype="detailed", nticks=4, font.lab=1, font.main=1, col="powderblue", theta= 320, phi=17, shade=0.45, main="ecuador ") mtext("nonparametric Estimate")

21 ln(y) Curve Estimation (Multivariate) Ecuador 2002 Nonparametric Estimate ln(k/l) 0 10 ln(l) 8

22 Additive Models Packages: Ecdat Data sets for econometrics gam Generalized Additive Models Data: Participation Description: 872 observations from a cross section regarding labor force participation in Switzerland lnnlinc The log of nonlabor income age Age in years divided by 10 educ Years of formal education nyc The number of young children (younger than 7) noc Number of older children Source: Gerfin, Michael (1996) Parametric and semiparametric estimation of the binary response, Journal of Applied Econometrics, 11(3),

23 Additive Models >library(ecdat,gam) >data(participation) >lab1.gam <- gam(lnnlinc s(educ)+s(age) +s(nyc)+s(noc), data=participation) >par(mfrow=c(2,2),pty="s",lwd=3,las=1) >plot.gam(lab1.gam,se=t,col="red")

24 Additive Models s(educ) s(age) educ age s(nyc) s(noc) nyc noc

Conditional density estimation: an application to the Ecuadorian manufacturing sector. Abstract

Conditional density estimation: an application to the Ecuadorian manufacturing sector. Abstract Conditional density estimation: an application to the Ecuadorian manufacturing sector Kim Huynh Indiana University David Jacho-Chavez Indiana University Abstract This note applies conditional density estimation

More information

Economics 620, Lecture 19: Introduction to Nonparametric and Semiparametric Estimation

Economics 620, Lecture 19: Introduction to Nonparametric and Semiparametric Estimation Economics 620, Lecture 19: Introduction to Nonparametric and Semiparametric Estimation Nicholas M. Kiefer Cornell University Professor N. M. Kiefer (Cornell University) Lecture 19: Nonparametric Analysis

More information

Section 7: Local linear regression (loess) and regression discontinuity designs

Section 7: Local linear regression (loess) and regression discontinuity designs Section 7: Local linear regression (loess) and regression discontinuity designs Yotam Shem-Tov Fall 2015 Yotam Shem-Tov STAT 239/ PS 236A October 26, 2015 1 / 57 Motivation We will focus on local linear

More information

Introduction to Nonparametric and Semiparametric Estimation. Good when there are lots of data and very little prior information on functional form.

Introduction to Nonparametric and Semiparametric Estimation. Good when there are lots of data and very little prior information on functional form. 1 Introduction to Nonparametric and Semiparametric Estimation Good when there are lots of data and very little prior information on functional form. Examples: y = f(x) + " (nonparametric) y = z 0 + f(x)

More information

Econ 582 Nonparametric Regression

Econ 582 Nonparametric Regression Econ 582 Nonparametric Regression Eric Zivot May 28, 2013 Nonparametric Regression Sofarwehaveonlyconsideredlinearregressionmodels = x 0 β + [ x ]=0 [ x = x] =x 0 β = [ x = x] [ x = x] x = β The assume

More information

UNIVERSITY OF CALIFORNIA Spring Economics 241A Econometrics

UNIVERSITY OF CALIFORNIA Spring Economics 241A Econometrics DEPARTMENT OF ECONOMICS R. Smith, J. Powell UNIVERSITY OF CALIFORNIA Spring 2006 Economics 241A Econometrics This course will cover nonlinear statistical models for the analysis of cross-sectional and

More information

Preface. 1 Nonparametric Density Estimation and Testing. 1.1 Introduction. 1.2 Univariate Density Estimation

Preface. 1 Nonparametric Density Estimation and Testing. 1.1 Introduction. 1.2 Univariate Density Estimation Preface Nonparametric econometrics has become one of the most important sub-fields in modern econometrics. The primary goal of this lecture note is to introduce various nonparametric and semiparametric

More information

Econometrics Homework 1

Econometrics Homework 1 Econometrics Homework Due Date: March, 24. by This problem set includes questions for Lecture -4 covered before midterm exam. Question Let z be a random column vector of size 3 : z = @ (a) Write out z

More information

A Simple Estimator for Binary Choice Models With Endogenous Regressors

A Simple Estimator for Binary Choice Models With Endogenous Regressors A Simple Estimator for Binary Choice Models With Endogenous Regressors Yingying Dong and Arthur Lewbel University of California Irvine and Boston College Revised June 2012 Abstract This paper provides

More information

A Simple Estimator for Binary Choice Models With Endogenous Regressors

A Simple Estimator for Binary Choice Models With Endogenous Regressors A Simple Estimator for Binary Choice Models With Endogenous Regressors Yingying Dong and Arthur Lewbel University of California Irvine and Boston College Revised February 2012 Abstract This paper provides

More information

Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case

Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case Arthur Lewbel Boston College December 2016 Abstract Lewbel (2012) provides an estimator

More information

Individual Counterfactuals with Multidimensional Unobserved Heterogeneity

Individual Counterfactuals with Multidimensional Unobserved Heterogeneity Individual Counterfactuals with Multidimensional Unobserved Heterogeneity Richard Blundell Dennis Kristensen Rosa Matzkin Provisional Draft, February 015 Abstract New nonparametric methods for identifying

More information

Identification and Nonparametric Estimation of a Transformed Additively Separable Model

Identification and Nonparametric Estimation of a Transformed Additively Separable Model Identification and Nonparametric Estimation of a Transformed Additively Separable Model David Jacho-Chávez Indiana University Arthur Lewbel Boston College May 5, 2008 Oliver Linton London School of Economics

More information

Package NonpModelCheck

Package NonpModelCheck Type Package Package NonpModelCheck April 27, 2017 Title Model Checking and Variable Selection in Nonparametric Regression Version 3.0 Date 2017-04-27 Author Adriano Zanin Zambom Maintainer Adriano Zanin

More information

Identification and Estimation of Semiparametric Two Step Models

Identification and Estimation of Semiparametric Two Step Models Identification and Estimation of Semiparametric Two Step Models Juan Carlos Escanciano Indiana University David Jacho-Chávez Emory University Arthur Lewbel Boston College First Draft: May 2010 This Draft:

More information

Nonparametric Methods

Nonparametric Methods Nonparametric Methods Michael R. Roberts Department of Finance The Wharton School University of Pennsylvania July 28, 2009 Michael R. Roberts Nonparametric Methods 1/42 Overview Great for data analysis

More information

12 - Nonparametric Density Estimation

12 - Nonparametric Density Estimation ST 697 Fall 2017 1/49 12 - Nonparametric Density Estimation ST 697 Fall 2017 University of Alabama Density Review ST 697 Fall 2017 2/49 Continuous Random Variables ST 697 Fall 2017 3/49 1.0 0.8 F(x) 0.6

More information

IDENTIFICATION OF MARGINAL EFFECTS IN NONSEPARABLE MODELS WITHOUT MONOTONICITY

IDENTIFICATION OF MARGINAL EFFECTS IN NONSEPARABLE MODELS WITHOUT MONOTONICITY Econometrica, Vol. 75, No. 5 (September, 2007), 1513 1518 IDENTIFICATION OF MARGINAL EFFECTS IN NONSEPARABLE MODELS WITHOUT MONOTONICITY BY STEFAN HODERLEIN AND ENNO MAMMEN 1 Nonseparable models do not

More information

Confidence intervals for kernel density estimation

Confidence intervals for kernel density estimation Stata User Group - 9th UK meeting - 19/20 May 2003 Confidence intervals for kernel density estimation Carlo Fiorio c.fiorio@lse.ac.uk London School of Economics and STICERD Stata User Group - 9th UK meeting

More information

Identification and estimation of semiparametric two-step models

Identification and estimation of semiparametric two-step models Quantitative Economics 7 (2016), 561 589 1759-7331/20160561 Identification and estimation of semiparametric two-step models Juan Carlos Escanciano Department of Economics, Indiana University David Jacho-Chávez

More information

Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case

Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case Arthur Lewbel Boston College Original December 2016, revised July 2017 Abstract Lewbel (2012)

More information

STAT 4385 Topic 01: Introduction & Review

STAT 4385 Topic 01: Introduction & Review STAT 4385 Topic 01: Introduction & Review Xiaogang Su, Ph.D. Department of Mathematical Science University of Texas at El Paso xsu@utep.edu Spring, 2016 Outline Welcome What is Regression Analysis? Basics

More information

Simple Estimators for Binary Choice Models With Endogenous Regressors

Simple Estimators for Binary Choice Models With Endogenous Regressors Simple Estimators for Binary Choice Models With Endogenous Regressors Yingying Dong and Arthur Lewbel University of California Irvine and Boston College Revised February 2012 Abstract This paper provides

More information

Nonparametric Econometrics

Nonparametric Econometrics Applied Microeconometrics with Stata Nonparametric Econometrics Spring Term 2011 1 / 37 Contents Introduction The histogram estimator The kernel density estimator Nonparametric regression estimators Semi-

More information

Regression and Inference Under Smoothness Restrictions

Regression and Inference Under Smoothness Restrictions Regression and Inference Under Smoothness Restrictions Christopher F. Parmeter 1 Kai Sun 2 Daniel J. Henderson 3 Subal C. Kumbhakar 4 1 Department of Agricultural and Applied Economics Virginia Tech 2,3,4

More information

SINGLE-STEP ESTIMATION OF A PARTIALLY LINEAR MODEL

SINGLE-STEP ESTIMATION OF A PARTIALLY LINEAR MODEL SINGLE-STEP ESTIMATION OF A PARTIALLY LINEAR MODEL DANIEL J. HENDERSON AND CHRISTOPHER F. PARMETER Abstract. In this paper we propose an asymptotically equivalent single-step alternative to the two-step

More information

Systems and Matrices CHAPTER 7

Systems and Matrices CHAPTER 7 CHAPTER 7 Systems and Matrices 7.1 Solving Systems of Two Equations 7.2 Matrix Algebra 7.3 Multivariate Linear Systems and Row Operations 7.4 Partial Fractions 7.5 Systems of Inequalities in Two Variables

More information

Nonparametric Inference via Bootstrapping the Debiased Estimator

Nonparametric Inference via Bootstrapping the Debiased Estimator Nonparametric Inference via Bootstrapping the Debiased Estimator Yen-Chi Chen Department of Statistics, University of Washington ICSA-Canada Chapter Symposium 2017 1 / 21 Problem Setup Let X 1,, X n be

More information

Nonparametric Econometrics in R

Nonparametric Econometrics in R Nonparametric Econometrics in R Philip Shaw Fordham University November 17, 2011 Philip Shaw (Fordham University) Nonparametric Econometrics in R November 17, 2011 1 / 16 Introduction The NP Package R

More information

Using Non-parametric Methods in Econometric Production Analysis: An Application to Polish Family Farms

Using Non-parametric Methods in Econometric Production Analysis: An Application to Polish Family Farms Using Non-parametric Methods in Econometric Production Analysis: An Application to Polish Family Farms TOMASZ CZEKAJ and ARNE HENNINGSEN Institute of Food and Resource Economics, University of Copenhagen,

More information

Day 4A Nonparametrics

Day 4A Nonparametrics Day 4A Nonparametrics A. Colin Cameron Univ. of Calif. - Davis... for Center of Labor Economics Norwegian School of Economics Advanced Microeconometrics Aug 28 - Sep 2, 2017. Colin Cameron Univ. of Calif.

More information

Time Series and Forecasting Lecture 4 NonLinear Time Series

Time Series and Forecasting Lecture 4 NonLinear Time Series Time Series and Forecasting Lecture 4 NonLinear Time Series Bruce E. Hansen Summer School in Economics and Econometrics University of Crete July 23-27, 2012 Bruce Hansen (University of Wisconsin) Foundations

More information

Semi-parametric estimation of non-stationary Pickands functions

Semi-parametric estimation of non-stationary Pickands functions Semi-parametric estimation of non-stationary Pickands functions Linda Mhalla 1 Joint work with: Valérie Chavez-Demoulin 2 and Philippe Naveau 3 1 Geneva School of Economics and Management, University of

More information

x i = 1 yi 2 = 55 with N = 30. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations.

x i = 1 yi 2 = 55 with N = 30. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations. Exercises for the course of Econometrics Introduction 1. () A researcher is using data for a sample of 30 observations to investigate the relationship between some dependent variable y i and independent

More information

Quantile methods. Class Notes Manuel Arellano December 1, Let F (r) =Pr(Y r). Forτ (0, 1), theτth population quantile of Y is defined to be

Quantile methods. Class Notes Manuel Arellano December 1, Let F (r) =Pr(Y r). Forτ (0, 1), theτth population quantile of Y is defined to be Quantile methods Class Notes Manuel Arellano December 1, 2009 1 Unconditional quantiles Let F (r) =Pr(Y r). Forτ (0, 1), theτth population quantile of Y is defined to be Q τ (Y ) q τ F 1 (τ) =inf{r : F

More information

Additional Material for Estimating the Technology of Cognitive and Noncognitive Skill Formation (Cuttings from the Web Appendix)

Additional Material for Estimating the Technology of Cognitive and Noncognitive Skill Formation (Cuttings from the Web Appendix) Additional Material for Estimating the Technology of Cognitive and Noncognitive Skill Formation (Cuttings from the Web Appendix Flavio Cunha The University of Pennsylvania James Heckman The University

More information

APEC 8212: Econometric Analysis II

APEC 8212: Econometric Analysis II APEC 8212: Econometric Analysis II Instructor: Paul Glewwe Spring, 2014 Office: 337a Ruttan Hall (formerly Classroom Office Building) Phone: 612-625-0225 E-Mail: pglewwe@umn.edu Class Website: http://faculty.apec.umn.edu/pglewwe/apec8212.html

More information

Econometrics I. Professor William Greene Stern School of Business Department of Economics 1-1/40. Part 1: Introduction

Econometrics I. Professor William Greene Stern School of Business Department of Economics 1-1/40. Part 1: Introduction Econometrics I Professor William Greene Stern School of Business Department of Economics 1-1/40 http://people.stern.nyu.edu/wgreene/econometrics/econometrics.htm 1-2/40 Overview: This is an intermediate

More information

Now what do I do with this function?

Now what do I do with this function? Now what do I do with this function? Enrique Pinzón StataCorp LP December 08, 2017 Sao Paulo (StataCorp LP) December 08, 2017 Sao Paulo 1 / 42 Initial thoughts Nonparametric regression and about effects/questions

More information

Table 1. Answers to income and consumption adequacy questions Percentage of responses: less than adequate more than adequate adequate Total income 68.7% 30.6% 0.7% Food consumption 46.6% 51.4% 2.0% Clothing

More information

More formally, the Gini coefficient is defined as. with p(y) = F Y (y) and where GL(p, F ) the Generalized Lorenz ordinate of F Y is ( )

More formally, the Gini coefficient is defined as. with p(y) = F Y (y) and where GL(p, F ) the Generalized Lorenz ordinate of F Y is ( ) Fortin Econ 56 3. Measurement The theoretical literature on income inequality has developed sophisticated measures (e.g. Gini coefficient) on inequality according to some desirable properties such as decomposability

More information

12E016. Econometric Methods II 6 ECTS. Overview and Objectives

12E016. Econometric Methods II 6 ECTS. Overview and Objectives Overview and Objectives This course builds on and further extends the econometric and statistical content studied in the first quarter, with a special focus on techniques relevant to the specific field

More information

Econometrics Problem Set 3

Econometrics Problem Set 3 Econometrics Problem Set 3 Conceptual Questions 1. This question refers to the estimated regressions in table 1 computed using data for 1988 from the U.S. Current Population Survey. The data set consists

More information

Identi cation and Estimation of Semiparametric Two Step Models

Identi cation and Estimation of Semiparametric Two Step Models Identi cation and Estimation of Semiparametric Two Step Models Juan Carlos Escanciano y Indiana University David Jacho-Chávez z Indiana University Arthur Lewbel x Boston College original May 2010, revised

More information

Regression - Modeling a response

Regression - Modeling a response Regression - Modeling a response We often wish to construct a model to Explain the association between two or more variables Predict the outcome of a variable given values of other variables. Regression

More information

Inference in Regression Analysis

Inference in Regression Analysis ECNS 561 Inference Inference in Regression Analysis Up to this point 1.) OLS is unbiased 2.) OLS is BLUE (best linear unbiased estimator i.e., the variance is smallest among linear unbiased estimators)

More information

Discussion of the paper Inference for Semiparametric Models: Some Questions and an Answer by Bickel and Kwon

Discussion of the paper Inference for Semiparametric Models: Some Questions and an Answer by Bickel and Kwon Discussion of the paper Inference for Semiparametric Models: Some Questions and an Answer by Bickel and Kwon Jianqing Fan Department of Statistics Chinese University of Hong Kong AND Department of Statistics

More information

Testing for Bivariate Stochastic Dominance. Using Inequality Restrictions

Testing for Bivariate Stochastic Dominance. Using Inequality Restrictions Testing for Bivariate Stochastic Dominance Using Inequality Restrictions Thanasis Stengos and Brennan S. Thompson May 31, 2011 Abstract In this paper, we propose of a test of bivariate stochastic dominance

More information

11.5 Regression Linear Relationships

11.5 Regression Linear Relationships Contents 11.5 Regression............................. 835 11.5.1 Linear Relationships................... 835 11.5.2 The Least Squares Regression Line........... 837 11.5.3 Using the Regression Line................

More information

Causal Inference with General Treatment Regimes: Generalizing the Propensity Score

Causal Inference with General Treatment Regimes: Generalizing the Propensity Score Causal Inference with General Treatment Regimes: Generalizing the Propensity Score David van Dyk Department of Statistics, University of California, Irvine vandyk@stat.harvard.edu Joint work with Kosuke

More information

Volume 29, Issue 1. On the Importance of Span of the Data in Univariate Estimation of the Persistence in Real Exchange Rates

Volume 29, Issue 1. On the Importance of Span of the Data in Univariate Estimation of the Persistence in Real Exchange Rates Volume 29, Issue 1 On the Importance of Span of the Data in Univariate Estimation of the Persistence in Real Exchange Rates Hyeongwoo Kim Auburn University Young-Kyu Moh Texas Tech University Abstract

More information

A time series plot: a variable Y t on the vertical axis is plotted against time on the horizontal axis

A time series plot: a variable Y t on the vertical axis is plotted against time on the horizontal axis TIME AS A REGRESSOR A time series plot: a variable Y t on the vertical axis is plotted against time on the horizontal axis Many economic variables increase or decrease with time A linear trend relationship

More information

Math 112 Fall 2015 Midterm 2 Review Problems Page 1. has a maximum or minimum and then determine the maximum or minimum value.

Math 112 Fall 2015 Midterm 2 Review Problems Page 1. has a maximum or minimum and then determine the maximum or minimum value. Math Fall 05 Midterm Review Problems Page f 84 00 has a maimum or minimum and then determine the maimum or minimum value.. Determine whether Ma = 00 Min = 00 Min = 8 Ma = 5 (E) Ma = 84. Consider the function

More information

Statistics I Exercises Lesson 3 Academic year 2015/16

Statistics I Exercises Lesson 3 Academic year 2015/16 Statistics I Exercises Lesson 3 Academic year 2015/16 1. The following table represents the joint (relative) frequency distribution of two variables: semester grade in Estadística I course and # of hours

More information

Nonparametric Identification of a Binary Random Factor in Cross Section Data - Supplemental Appendix

Nonparametric Identification of a Binary Random Factor in Cross Section Data - Supplemental Appendix Nonparametric Identification of a Binary Random Factor in Cross Section Data - Supplemental Appendix Yingying Dong and Arthur Lewbel California State University Fullerton and Boston College July 2010 Abstract

More information

Nonparametric regresion models estimation in R

Nonparametric regresion models estimation in R 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

More information

Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions

Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions Duangkamon Chotikapanich Monash niversity William E. Griffiths niversity of Melbourne Abstract Hypothesis tests for dominance

More information

SiZer Analysis for the Comparison of Regression Curves

SiZer Analysis for the Comparison of Regression Curves SiZer Analysis for the Comparison of Regression Curves Cheolwoo Park and Kee-Hoon Kang 2 Abstract In this article we introduce a graphical method for the test of the equality of two regression curves.

More information

Econometrics I. Lecture 10: Nonparametric Estimation with Kernels. Paul T. Scott NYU Stern. Fall 2018

Econometrics I. Lecture 10: Nonparametric Estimation with Kernels. Paul T. Scott NYU Stern. Fall 2018 Econometrics I Lecture 10: Nonparametric Estimation with Kernels Paul T. Scott NYU Stern Fall 2018 Paul T. Scott NYU Stern Econometrics I Fall 2018 1 / 12 Nonparametric Regression: Intuition Let s get

More information

A Monte Carlo Comparison of Various Semiparametric Type-3 Tobit Estimators

A Monte Carlo Comparison of Various Semiparametric Type-3 Tobit Estimators ANNALS OF ECONOMICS AND FINANCE 4, 125 136 (2003) A Monte Carlo Comparison of Various Semiparametric Type-3 Tobit Estimators Insik Min Department of Economics, Texas A&M University E-mail: i0m5376@neo.tamu.edu

More information

Minimax Rate of Convergence for an Estimator of the Functional Component in a Semiparametric Multivariate Partially Linear Model.

Minimax Rate of Convergence for an Estimator of the Functional Component in a Semiparametric Multivariate Partially Linear Model. Minimax Rate of Convergence for an Estimator of the Functional Component in a Semiparametric Multivariate Partially Linear Model By Michael Levine Purdue University Technical Report #14-03 Department of

More information

Eco 391, J. Sandford, spring 2013 April 5, Midterm 3 4/5/2013

Eco 391, J. Sandford, spring 2013 April 5, Midterm 3 4/5/2013 Midterm 3 4/5/2013 Instructions: You may use a calculator, and one sheet of notes. You will never be penalized for showing work, but if what is asked for can be computed directly, points awarded will depend

More information

2. Linear regression with multiple regressors

2. Linear regression with multiple regressors 2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression Assumptions

More information

Introduction. Linear Regression. coefficient estimates for the wage equation: E(Y X) = X 1 β X d β d = X β

Introduction. Linear Regression. coefficient estimates for the wage equation: E(Y X) = X 1 β X d β d = X β Introduction - Introduction -2 Introduction Linear Regression E(Y X) = X β +...+X d β d = X β Example: Wage equation Y = log wages, X = schooling (measured in years), labor market experience (measured

More information

Bootstrap Approach to Comparison of Alternative Methods of Parameter Estimation of a Simultaneous Equation Model

Bootstrap Approach to Comparison of Alternative Methods of Parameter Estimation of a Simultaneous Equation Model Bootstrap Approach to Comparison of Alternative Methods of Parameter Estimation of a Simultaneous Equation Model Olubusoye, O. E., J. O. Olaomi, and O. O. Odetunde Abstract A bootstrap simulation approach

More information

A Local Generalized Method of Moments Estimator

A Local Generalized Method of Moments Estimator A Local Generalized Method of Moments Estimator Arthur Lewbel Boston College June 2006 Abstract A local Generalized Method of Moments Estimator is proposed for nonparametrically estimating unknown functions

More information

Density and Distribution Estimation

Density and Distribution Estimation Density and Distribution Estimation Nathaniel E. Helwig Assistant Professor of Psychology and Statistics University of Minnesota (Twin Cities) Updated 04-Jan-2017 Nathaniel E. Helwig (U of Minnesota) Density

More information

Modelling Non-linear and Non-stationary Time Series

Modelling Non-linear and Non-stationary Time Series Modelling Non-linear and Non-stationary Time Series Chapter 2: Non-parametric methods Henrik Madsen Advanced Time Series Analysis September 206 Henrik Madsen (02427 Adv. TS Analysis) Lecture Notes September

More information

Alternatives to Basis Expansions. Kernels in Density Estimation. Kernels and Bandwidth. Idea Behind Kernel Methods

Alternatives to Basis Expansions. Kernels in Density Estimation. Kernels and Bandwidth. Idea Behind Kernel Methods Alternatives to Basis Expansions Basis expansions require either choice of a discrete set of basis or choice of smoothing penalty and smoothing parameter Both of which impose prior beliefs on data. Alternatives

More information

Identification and Nonparametric Estimation of a Transformed Additively Separable Model

Identification and Nonparametric Estimation of a Transformed Additively Separable Model Identification and Nonparametric Estimation of a Transformed Additively Separable Model David Jacho-Chávez Indiana University Arthur Lewbel Boston College Oliver Linton London School of Economics November

More information

Nonparametric Regression

Nonparametric Regression Nonparametric Regression Econ 674 Purdue University April 8, 2009 Justin L. Tobias (Purdue) Nonparametric Regression April 8, 2009 1 / 31 Consider the univariate nonparametric regression model: where y

More information

University of California at Berkeley Fall Introductory Applied Econometrics Final examination. Scores add up to 125 points

University of California at Berkeley Fall Introductory Applied Econometrics Final examination. Scores add up to 125 points EEP 118 / IAS 118 Elisabeth Sadoulet and Kelly Jones University of California at Berkeley Fall 2008 Introductory Applied Econometrics Final examination Scores add up to 125 points Your name: SID: 1 1.

More information

Supplement to Quantile-Based Nonparametric Inference for First-Price Auctions

Supplement to Quantile-Based Nonparametric Inference for First-Price Auctions Supplement to Quantile-Based Nonparametric Inference for First-Price Auctions Vadim Marmer University of British Columbia Artyom Shneyerov CIRANO, CIREQ, and Concordia University August 30, 2010 Abstract

More information

Econ 273B Advanced Econometrics Spring

Econ 273B Advanced Econometrics Spring Econ 273B Advanced Econometrics Spring 2005-6 Aprajit Mahajan email: amahajan@stanford.edu Landau 233 OH: Th 3-5 or by appt. This is a graduate level course in econometrics. The rst part of the course

More information

Department of Economics, Vanderbilt University While it is known that pseudo-out-of-sample methods are not optimal for

Department of Economics, Vanderbilt University While it is known that pseudo-out-of-sample methods are not optimal for Comment Atsushi Inoue Department of Economics, Vanderbilt University (atsushi.inoue@vanderbilt.edu) While it is known that pseudo-out-of-sample methods are not optimal for comparing models, they are nevertheless

More information

Estimation for nonparametric mixture models

Estimation for nonparametric mixture models Estimation for nonparametric mixture models David Hunter Penn State University Research supported by NSF Grant SES 0518772 Joint work with Didier Chauveau (University of Orléans, France), Tatiana Benaglia

More information

Time Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY

Time Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY Time Series Analysis James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY & Contents PREFACE xiii 1 1.1. 1.2. Difference Equations First-Order Difference Equations 1 /?th-order Difference

More information

Introduction to Econometrics. Heteroskedasticity

Introduction to Econometrics. Heteroskedasticity Introduction to Econometrics Introduction Heteroskedasticity When the variance of the errors changes across segments of the population, where the segments are determined by different values for the explanatory

More information

Maximum Smoothed Likelihood for Multivariate Nonparametric Mixtures

Maximum Smoothed Likelihood for Multivariate Nonparametric Mixtures Maximum Smoothed Likelihood for Multivariate Nonparametric Mixtures David Hunter Pennsylvania State University, USA Joint work with: Tom Hettmansperger, Hoben Thomas, Didier Chauveau, Pierre Vandekerkhove,

More information

STAT 705 Nonlinear regression

STAT 705 Nonlinear regression STAT 705 Nonlinear regression Adapted from Timothy Hanson Department of Statistics, University of South Carolina Stat 705: Data Analysis II 1 / 1 Chapter 13 Parametric nonlinear regression Throughout most

More information

Economics 270c Graduate Development Economics. Professor Ted Miguel Department of Economics University of California, Berkeley

Economics 270c Graduate Development Economics. Professor Ted Miguel Department of Economics University of California, Berkeley Economics 270c Graduate Development Economics Professor Ted Miguel Department of Economics University of California, Berkeley Economics 270c Graduate Development Economics Lecture 2 January 27, 2009 Lecture

More information

Stat 5101 Lecture Notes

Stat 5101 Lecture Notes Stat 5101 Lecture Notes Charles J. Geyer Copyright 1998, 1999, 2000, 2001 by Charles J. Geyer May 7, 2001 ii Stat 5101 (Geyer) Course Notes Contents 1 Random Variables and Change of Variables 1 1.1 Random

More information

Estimation of Treatment Effects under Essential Heterogeneity

Estimation of Treatment Effects under Essential Heterogeneity Estimation of Treatment Effects under Essential Heterogeneity James Heckman University of Chicago and American Bar Foundation Sergio Urzua University of Chicago Edward Vytlacil Columbia University March

More information

Heteroskedasticity (Section )

Heteroskedasticity (Section ) Heteroskedasticity (Section 8.1-8.4) Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) Heteroskedasticity 1 / 44 Consequences of Heteroskedasticity for OLS Consequences

More information

Rank Estimation of Partially Linear Index Models

Rank Estimation of Partially Linear Index Models Rank Estimation of Partially Linear Index Models Jason Abrevaya University of Texas at Austin Youngki Shin University of Western Ontario October 2008 Preliminary Do not distribute Abstract We consider

More information

MGEC11H3Y L01 Introduction to Regression Analysis Term Test Friday July 5, PM Instructor: Victor Yu

MGEC11H3Y L01 Introduction to Regression Analysis Term Test Friday July 5, PM Instructor: Victor Yu Last Name (Print): Solution First Name (Print): Student Number: MGECHY L Introduction to Regression Analysis Term Test Friday July, PM Instructor: Victor Yu Aids allowed: Time allowed: Calculator and one

More information

Course Description. Course Requirements

Course Description. Course Requirements University of Pennsylvania Spring 2007 Econ 721: Advanced Microeconometrics Petra Todd Course Description Lecture: 9:00-10:20 Tuesdays and Thursdays Office Hours: 10am-12 Fridays or by appointment. To

More information

Economics 250 Midterm 1 17 October 2013 three

Economics 250 Midterm 1 17 October 2013 three Economics 250 Midterm 1 17 October 2013 Instructions: You may use a hand calculator. Do not hand in the question and formula sheets. Answer all three questions in the answer booklet provided. Show your

More information

Model Specification Testing in Nonparametric and Semiparametric Time Series Econometrics. Jiti Gao

Model Specification Testing in Nonparametric and Semiparametric Time Series Econometrics. Jiti Gao Model Specification Testing in Nonparametric and Semiparametric Time Series Econometrics Jiti Gao Department of Statistics School of Mathematics and Statistics The University of Western Australia Crawley

More information

A Course in Applied Econometrics Lecture 14: Control Functions and Related Methods. Jeff Wooldridge IRP Lectures, UW Madison, August 2008

A Course in Applied Econometrics Lecture 14: Control Functions and Related Methods. Jeff Wooldridge IRP Lectures, UW Madison, August 2008 A Course in Applied Econometrics Lecture 14: Control Functions and Related Methods Jeff Wooldridge IRP Lectures, UW Madison, August 2008 1. Linear-in-Parameters Models: IV versus Control Functions 2. Correlated

More information

A Bootstrap Test for Conditional Symmetry

A Bootstrap Test for Conditional Symmetry ANNALS OF ECONOMICS AND FINANCE 6, 51 61 005) A Bootstrap Test for Conditional Symmetry Liangjun Su Guanghua School of Management, Peking University E-mail: lsu@gsm.pku.edu.cn and Sainan Jin Guanghua School

More information

On Fractile Transformation of Covariates in Regression 1

On Fractile Transformation of Covariates in Regression 1 1 / 13 On Fractile Transformation of Covariates in Regression 1 Bodhisattva Sen Department of Statistics Columbia University, New York ERCIM 10 11 December, 2010 1 Joint work with Probal Chaudhuri, Indian

More information

A Distributional Framework for Matched Employer Employee Data

A Distributional Framework for Matched Employer Employee Data A Distributional Framework for Matched Employer Employee Data (Preliminary) Interactions - BFI Bonhomme, Lamadon, Manresa University of Chicago MIT Sloan September 26th - 2015 Wage Dispersion Wages are

More information

Econ 444, class 11. Robert de Jong 1. Monday November 6. Ohio State University. Econ 444, Wednesday November 1, class Department of Economics

Econ 444, class 11. Robert de Jong 1. Monday November 6. Ohio State University. Econ 444, Wednesday November 1, class Department of Economics Econ 444, class 11 Robert de Jong 1 1 Department of Economics Ohio State University Monday November 6 Monday November 6 1 Exercise for today 2 New material: 1 dummy variables 2 multicollinearity Exercise

More information

Inference on distributions and quantiles using a finite-sample Dirichlet process

Inference on distributions and quantiles using a finite-sample Dirichlet process Dirichlet IDEAL Theory/methods Simulations Inference on distributions and quantiles using a finite-sample Dirichlet process David M. Kaplan University of Missouri Matt Goldman UC San Diego Midwest Econometrics

More information

Multiple nonparametric regression and model validation for mixed regressors

Multiple nonparametric regression and model validation for mixed regressors Multiple nonparametric regression and model validation for mixed regressors Dissertation zur Erlangung des Grades eines Doktors der Wirtschaftswissenschaft Eingereicht an der Fakultät für Wirtschaftswissenschaften

More information

Estimation of cumulative distribution function with spline functions

Estimation of cumulative distribution function with spline functions INTERNATIONAL JOURNAL OF ECONOMICS AND STATISTICS Volume 5, 017 Estimation of cumulative distribution function with functions Akhlitdin Nizamitdinov, Aladdin Shamilov Abstract The estimation of the cumulative

More information

Inference on distributional and quantile treatment effects

Inference on distributional and quantile treatment effects Inference on distributional and quantile treatment effects David M. Kaplan University of Missouri Matt Goldman UC San Diego NIU, 214 Dave Kaplan (Missouri), Matt Goldman (UCSD) Distributional and QTE inference

More information

Density Estimation (II)

Density Estimation (II) Density Estimation (II) Yesterday Overview & Issues Histogram Kernel estimators Ideogram Today Further development of optimization Estimating variance and bias Adaptive kernels Multivariate kernel estimation

More information

Chapter 1 Introduction. What are longitudinal and panel data? Benefits and drawbacks of longitudinal data Longitudinal data models Historical notes

Chapter 1 Introduction. What are longitudinal and panel data? Benefits and drawbacks of longitudinal data Longitudinal data models Historical notes Chapter 1 Introduction What are longitudinal and panel data? Benefits and drawbacks of longitudinal data Longitudinal data models Historical notes 1.1 What are longitudinal and panel data? With regression

More information