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

Transcription

1 Econometrics I Professor William Greene Stern School of Business Department of Economics 1-1/40

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3 Overview: This is an intermediate level, Ph.D. course in Applied Econometrics. Topics to be studied include specification, estimation, and inference in the context of models that include then extend beyond the standard linear multiple regression framework. After a review of the linear model, we will develop the theory necessary for analysis of generalized linear and nonlinear models. Topics to be examined: Regression modeling Instrumental variables Robust estimation and inference Causal inference Nonlinear modeling Cross section, time series and panel data Objective: Abstract Preparation to read and carry out empirical social science research using modern econometric methods. 1-3/40

4 Prerequisites A previous course that used linear regression Mathematical statistics Matrix algebra 1-4/40

5 Main text: Greene, W., Econometric Analysis, 8 th Edition, Prentice Hall, Readings A few articles Notes and materials on the course website: 1-5/40

6 No class on: Thursday, September 21 *Tuesday, November 21 Thursday, November 23 *Tuesday, November 28 Added class on: Tuesday, December 12 Midterm: October 24 Course Schedule Final: Take home; posted December 7, due December /40

7 Software Practicals NLOGIT provided, supported SAS, Stata, EViews optional, your choice R, Matlab, Gauss, others Questions and review as requested Problem Sets: (more details later) 1-7/40

8 Course Requirements Problem sets: 5 (30%) Midterm, in class (30%) Final exam, take home (40%) 1-8/40

9 Econometrics I Part 1 - Paradigm 1-9/40

10 Econometrics: Paradigm Theoretical foundations Behavioral modeling: Optimization, labor supply, demand equations, etc. Microeconometrics and macroeconometrics Mathematical Elements Statistical foundations Model building the econometric model Mathematical elements The underlying truth is there one? 1-10/40

11 1-11/40 Objectives Understanding covariation: What is the income elasticity of the demand for health care in an economy? Understanding a relationship: How will drivers respond to the availability of a new toll road? Causal Inference: The search for causal effects Did an antitrust intervention that broke up a British boarding schools cartel have an impact on fees charged? Prediction of an outcome of interest Does internet buzz help to predict movie success?

12 Small structural models Trends in Econometrics Pervasiveness of an econometrics paradigm Non- and semiparametric methods vs. parametric Robust methods / Estimation and inference Nonlinear modeling (the role of software) Behavioral and structural modeling vs. reduced form, covariance analysis Identification and causal effects 1-12/40

13 Data Structures Observation mechanisms Passive, nonexperimental (the usual) Randomly assigned experiment (wishful) Active, experimental (occasional) The natural experiment (occasional, limited) Data types Cross section Pure time series Panel Longitudinal data NLS Country macro data Penn W.T. Financial data 1-13/40

14 Paradigm: Classical Inference Population Imprecise inference about the entire population sampling theory and asymptotics Econometrics Measurement Characteristics Behavior Patterns Choices 1-14/40

15 Paradigm: Bayesian Inference Population Econometrics Sharp, exact inference about only the sample the posterior density. Measurement Characteristics Behavior Patterns Choices 1-15/40

16 An Application: Cornwell and Rupert Labor Market Data Is Wage Related to Education? Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years Variables in the file are EXP WKS OCC IND SOUTH SMSA MS FEM UNION ED LWAGE = work experience = weeks worked = occupation, 1 if blue collar, = 1 if manufacturing industry = 1 if resides in south = 1 if resides in a city (SMSA) = 1 if married = 1 if female = 1 if wage set by union contract = years of education = log of wage = dependent variable in regressions These data were analyzed in Cornwell, C. and Rupert, P., "Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators," Journal of Applied Econometrics, 3, 1988, pp /40

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18 Model Building in Econometrics Role of the assumptions Parameterizing the model Nonparametric analysis Semiparametric analysis Parametric analysis Sharpness of inferences 1-18/40

19 Application: Is there a relationship between (log) Wage and Education? Nonparametric Regression Kernel regression of log wage on education Semiparametric Regression: Least absolute deviations regression Parametric Regression: Least squares maximum likelihood regression 1-19/40

20 A First Look at the Data Descriptive Statistics Basic Measures of Location and Dispersion Graphical Devices Box Plots Histogram Kernel Density Estimator 1-20/40

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22 Box Plots Shows upward trend in median log wage 1-22/40

23 Histogram: Pooled data obscure within person variation What is the source of the variance, variation across people or variation over time? 1-23/40

24 Kernel density estimator suggests the underlying distribution for a continuous variable * 1 n 1 x i xm ˆf(x m) K i 1 n B B 1 n Q(x x,b), for a set of points x i 1 n B "bandwidth" K the kernel function * * * i m m x* the point at which the density is approximated. ˆf(x*) is an estimator of f(x*) 1-24/40

25 The kernel density estimator is a histogram (of sorts). * * * 1 n 1 xi xm ˆf(x m) K i 1, for a set of points x n B B B "bandwidth" chosen by the analyst K the kernel function, such as the normal or logistic pdf (or one of several others) x* the point at which the density is approximated. This is essentially a histogram with small bins. m 1-25/40

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28 From Jones and Schurer (2011) Stylized Box Plot 1-28/40

29 From Jones and Schurer (2011) 1-29/40

30 Objective: Impact of Education on (log) Wage Specification: What is the right model to use to analyze this association? Estimation Inference Analysis 1-30/40

31 Simple Linear Regression LWAGE = *ED 1-31/40

32 Multiple Regression 1-32/40

33 Nonlinear Specification: Quadratic Effect of Experience 1-33/40

34 Model Building in Econometrics A Model Relating (Log)Wage to Gender and Education & Experience 1-34/40

35 Partial Effects Coefficients may not tell the story Education Experience *.00068*Exp FEM /40

36 Effect of Experience = *.00068*Exp Positive from 1 to 30, negative after. 1-36/40

37 Interaction Effect Gender Difference in Partial Effects 1-37/40

38 Partial Effect of a Year of Education E[logWage]/ ED = ED + ED*FEM *FEM = *FEM Note, the effect is positive. The effect 43% is larger for women. 1-38/40

39 Gender Effect Varies by Years of Education E[logWage]/ FEM = FEM + ED*FEM *ED = *ED 1-39/40

40 Analysts are interested in interaction effects in models. 1-40/40