Nonparametric Methods in Econometrics using
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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
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