CENSORED DATA AND CENSORED NORMAL REGRESSION
|
|
- Isabel Lyons
- 5 years ago
- Views:
Transcription
1 CENSORED DATA AND CENSORED NORMAL REGRESSION Data censoring comes in many forms: binary censoring, interval censoring, and top coding are the most common. They all start with an underlying linear model for y, the variable of interest: y x u E u x 0, (1) (2) where x is 1 K with first element unity. Under (1) and (2), if we have random draws x i,y i from the population, then OLS is consisitent and N -asymptotically normal for the parameters of interest,. But suppose what we observe is a censored version of y. In the top coding example, suppose that wealth is measured in thousands of dollars and it is top coded at 1
2 $200,000. Then we can define the censored version of weath (for any unit that can be drawn from the population) as w min y,200. For each random draw i, w i min y i,200. What would the data set look like on x i and w i,where w i is called wealth? We should notice that the maximum value of the w i in the sample is 200, with a nontrivial fraction of observations at exactly 200. Because there are no behavioral reasons to see a focal point for wealth at 200 let alone, to observe no values greater than 200 we would recognize that the wealth variable has been top coded at 200. BINARY CENSORING Suppose we want to estimate the factors that affect willingness to pay. Hard to elicit a precise figure. So present families with a cost and allow them to simply state whether their wtp is above the cost. The model for 2
3 the population is first assumed to be wtp x u, E u x 0, (3) where x 1 1. Let r i denote the cost of the project to household i. Presented with this cost, the household either says it is in favor of the project or not. Thus, along with x i and r i, we observe the binary response w i 1 wtp i r i (4) whereweassumethechancethatwtp i equals r i is zero. We are given data on x i,r i,w i. What is the most natural way to proceed to estimate? If we impose some strong assumptions on the underlying population and the nature of r i, then we can proceed with maximum likelihood. In particular, assume u i x i,r i ~ Normal 0, 2. (5) Assumption (5) implies that (3) actually satisfies the classical linear model (CLM). It also requires that r i is 3
4 independent of wtp i conditional on x i,thatis, D wtp i x i,r i D wtp i x i. (6) This assumption is satisfied if r i is randomized or if r i is chosen as a function of x i, or some combination of these. P w i 1 x i,r i P wtp i r i x i,r i P u i / r i x i / x i,r i 1 r i x i / x i r i /. (7) So the estimating equation is a probit model with coefficients / and 1/. All parameters, including, are identified if x i does not contain perfect collinearity and r i varies across i (in a way not perfectly linearly related to x i ). If r i is the same for all i, cannot identify the parameters. Estimate, by MLE. The costs of the binary censoring scheme are severe. If we could observe wtp i,e wtp i x i x i would suffice for consistent estimation of ;infact,wecouldjust 4
5 specify a linear projection and use OLS. With censoring, we must assume the underlying model satisfies the CLM. Now, discussions of the deleterious effects of nonnormality and heteroskedasticity when using probit models makes much more sense. There are ways to estimate the slope parameters up to scale without without placing strong restrictions on D u i x i,r i. For example, if the distribution of x i,r i,y i implies linear conditional expectations for all elements conditional on y i, then the Chung and Goldberger (1984) results can be used for OLS. Manski s (1975, 1988) maximum score estimator requires only symmetry of D u i x i,r i (around zero), and Horowitz s (1992) smoothed version is more convenient for inference. But in every case these methods only estimate the slope coefficients up to scale (and the intercept cannot be estimated at all), and therefore we cannot learn the 5
6 magnitude of the effect of any element of x on willingness to pay, nor do we have a way of predicting willingness to pay for given values of the covariates. An interesting puzzle: What if the appropriate population model for WTP is the type I Tobit, wtp max 0,x u, under assumption (5). Now, for example, E wtp x has the (nonlinear) Tobit form, and we can easily compute it becaus we have consistent estimates of and. The estimation procedure is the same provided the r i are strictly positive. Because we do not observe wtp i, with our data x i,r i,w i we cannot distinguish between (3) and (8). But, if we believe that wtp is zero for some fraction of the population, any calculations should take that into account by using the type I Tobit formulas. Because estimation of and 2 can be sensitive to heteroskedasticity and nonnormality, it makes sense to 6
7 be flexible in specifying D u x. INTERVAL CODING We can generalize the WTP example to allow multiple intervals. Let y i be the (unobserved) response for random draw i. We only know whether y i falls into a specific interval. In many cases, these intervals are fixed across all i, such as surveys asking people about their income bracket. In this case we say we have interval-coded data. First let a 1 a 2... a J denote the known interval limits that are common across i; these are specified as part of the survey method. If u x ~Normal(0, 2, (8) we can estimate and 2 by MLE, provide J 2. Not surprisingly, the structure of the problem is similar that for an ordered probit for an ordered, qualitative response (such as a credit rating). But with ordered probit we 7
8 estimate cut points, whereas here we know the intervals and hope to estimate the parameters of the underly CLM. In fact, we can define w 0 ify a 1 w 1 ifa 1 y a 2 w J if y a J (9) and easily obtain the conditional probabilities P w j x for j 0,1,...,J. The log-likelihood is l i, 1 w i 0 log a 1 x i / 1 w i 1 log a 2 x i / a 1 x i /... 1 w i J log 1 a J x i /. (10) The maximum likelihood estimators, and 2, are often called interval regression estimators, with the understanding that the underlying distribution is normal. Importantly, when we obtain the interval regression estimates, we interpret the as if we had been able to 8
9 run the regression y i on x i, i 1,...,N. Imposing the assumptions of the classical linear model allows us to estimate the parameters in the distribution D y x even though they data are censored by being put into intervals. Sometimes in applications of interval regression the observed, censored variable, w, is set to some value within the interval that y belongs to. For example, if y is wealth, we might set w to the midpoint of the interval that y falls into. (Of course, we have to use some other rule if y a 1 or y a J. Provided the definition of w determines the proper interval, the maximum likelihood estimators of and will be the same. In Stata, for each observation specify two dependent variables, which are the upper and lower bounds for each i. When w is defined to have the same units as y,itis tempting to ignore the grouping of the data and just to 9
10 run an OLS regression of w i on x i, i 1,...,N. Naturally, such a procedure is generally inconsistent for. Nevertheless, the results of Chung and Goldberger apply: if E x y is linear.in y, then the OLS regression produces consistent estimators up to a common scale factor (at least for the slope coefficients). If we allow the endpoints to depend on i, we encompass the case of binary censoring. More generally, we might have multiple endpoint that change across i. In Stata, specify the two endpoints for each observation. That is, a lower bound and an upper bound of the interval that observation is known to fall into. The command specifies these bounds as dependent variables: intreg lower upper x1 x2... xk When the interval limits change across i, we assume they do so exogenously, namely, 10
11 D y i x i,a i1,...,a ij D w i x i,a i1,...,a ij. (11) In the WTP example, this holds because the one limit value J 1 is randomly assigned. Generally, the limits can be a function of x i (because these are being conditioned on). Because of the underlying normality assumption, we can use the Rivers-Vuong (1988) control function approach to test and correct for endogeneity of explanatory variables. It is analog of the Smith-Blundell approach that we discussed for Tobit. The underlying model is linear y 1 z y 2 u 1. (12) We would just like to use 2SLS on this model, but y 1 is interval coded (and we have the lower and upper limits for each observation). reg y2 z1 z2... zl 11
12 predict v2h, resid intreg lower1 upper1 z1... zl1 y2 v2h where L 1 L. We are just interested in 1 and 1 here, because (12) is the equation of interest. Bootstrap is easy to implement for standard errors. Again, beware of schemes for discrete y 2 that involve plugging in fitted values. RIGHT AND LEFT CENSORING Now we consider the more common cases of left and right censoring (or censoring from below and above). In top coding cases (right censoring) and minimum wage or price floors (left censoring), the censoring point is typically fixed. But in other applications, particularly duration models, the censoring point changes with i. The right censoring case, where y i is again the underlying variable of interest, is 12
13 y i x i u i w i min w i,c i (13) (14) where c i 0 is the censoring point for unit i. Sometimes the linear model is specified for y i log durat i, and so, of course, the censoring values have to be logs, too. If we assume exogenous censoring (and exogenous explanatory variables) that is, D u i x i,c i D u i Normal 0, 2, (15) we can use censored normal regression (called censored Tobit, too). (In Stata, however, the tobit command does not allow limits to depend on i, soneed to use cnreg command.) Log likelihood is similar to type I Tobit: l i, 2 1 w i c i log x i c i / 1 w i c i log w i x i / /. (16) 13
14 MLE is straightforward, as before, and can focus just on. Note that we only have to observe c i when y i is actually censored; we just have to know which observations are censored. In some duration data sets, the censoring value is reported only when the duration is censored. This causes no problem for MLE (but does for certain semiparametric procedures). In Stata, need to have a variable that tells when an observation is censored (and whether it is left or right censored). So, cens is 1 for left censoring, 0 for uncensored, and 1 for right censoring. cnreg y x1 x2... xk, censored(cens) Smith-Blundell applies directly. Add reduced form residuals to cnreg, test for endogeneity. No need to compute complicated partial effects, but should bootstrap standard errors. 14
15 reg y2 z1... zl predict v2h, resid cnreg y1 z1... zl1 y2 v2h, censored(cens) With fixed censoring limits, can use the ivtobit command and use full MLE. We can combine corner solution responses and data censoring. For example, suppose that in a survey on charitable giving we observe several zero outcomes which represent no contributions and, in addition, contributions are top coded at, say, $10,000. Estimation is with two-limit tobit (with gift in $1000s): tobit gift inc educ married fsize age, ll(0) ul(10) predict gifth, ystar(0,.) How come I didn t put 20 as the upper bound? Because I want to estimate a model for gifts, which 15
16 follows a standard corner solution Tobit at zero. For response variables that may have very large values (wealth, income, charitable contributions), we might want to intentionally right censor a variable to guard against outliers. Of course, we might use somethink like LAD on the original data (if the original variable is not a corner). CENSORED LEAST ABSOLUTE DEVIATIONS FOR LEFT OR RIGHT DATA CENSORING If we assume the model in (13) with right censoring as in (14), but now assume then Med u i x i,c i 0, (17) Med w i x i,c i min x i,c i, (18) and we can use Powell s CLAD estimator of : 16
17 min b N w i min x i,c i. (19) i 1 Requires observing a censoring value for all individuals, which can be a problem in duration applications. Not for top coding, where the c i is a known value fixed across i. Currently, Stata only allows a fixed upper limit or a fixed lower limit (not both). clad nettfac inc incsq age agesq e401k, ul(20) Remember, we are doing this to estimate the parameters in Med nettfa x x, unlike in the corner solution case where we wanted Med hours x max 0,x. 17
What s New in Econometrics? Lecture 14 Quantile Methods
What s New in Econometrics? Lecture 14 Quantile Methods Jeff Wooldridge NBER Summer Institute, 2007 1. Reminders About Means, Medians, and Quantiles 2. Some Useful Asymptotic Results 3. Quantile Regression
More informationNew Developments in Econometrics Lecture 16: Quantile Estimation
New Developments in Econometrics Lecture 16: Quantile Estimation Jeff Wooldridge Cemmap Lectures, UCL, June 2009 1. Review of Means, Medians, and Quantiles 2. Some Useful Asymptotic Results 3. Quantile
More informationA 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 informationControl Function and Related Methods: Nonlinear Models
Control Function and Related Methods: Nonlinear Models Jeff Wooldridge Michigan State University Programme Evaluation for Policy Analysis Institute for Fiscal Studies June 2012 1. General Approach 2. Nonlinear
More informationA Course in Applied Econometrics Lecture 18: Missing Data. Jeff Wooldridge IRP Lectures, UW Madison, August Linear model with IVs: y i x i u i,
A Course in Applied Econometrics Lecture 18: Missing Data Jeff Wooldridge IRP Lectures, UW Madison, August 2008 1. When Can Missing Data be Ignored? 2. Inverse Probability Weighting 3. Imputation 4. Heckman-Type
More informationEconometric Analysis of Cross Section and Panel Data
Econometric Analysis of Cross Section and Panel Data Jeffrey M. Wooldridge / The MIT Press Cambridge, Massachusetts London, England Contents Preface Acknowledgments xvii xxiii I INTRODUCTION AND BACKGROUND
More informationRecent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data
Recent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data July 2012 Bangkok, Thailand Cosimo Beverelli (World Trade Organization) 1 Content a) Censoring and truncation b)
More informationJeffrey M. Wooldridge Michigan State University
Fractional Response Models with Endogenous Explanatory Variables and Heterogeneity Jeffrey M. Wooldridge Michigan State University 1. Introduction 2. Fractional Probit with Heteroskedasticity 3. Fractional
More informationTruncation and Censoring
Truncation and Censoring Laura Magazzini laura.magazzini@univr.it Laura Magazzini (@univr.it) Truncation and Censoring 1 / 35 Truncation and censoring Truncation: sample data are drawn from a subset of
More informationINVERSE PROBABILITY WEIGHTED ESTIMATION FOR GENERAL MISSING DATA PROBLEMS
IVERSE PROBABILITY WEIGHTED ESTIMATIO FOR GEERAL MISSIG DATA PROBLEMS Jeffrey M. Wooldridge Department of Economics Michigan State University East Lansing, MI 48824-1038 (517) 353-5972 wooldri1@msu.edu
More informationGibbs Sampling in Latent Variable Models #1
Gibbs Sampling in Latent Variable Models #1 Econ 690 Purdue University Outline 1 Data augmentation 2 Probit Model Probit Application A Panel Probit Panel Probit 3 The Tobit Model Example: Female Labor
More information1 Motivation for Instrumental Variable (IV) Regression
ECON 370: IV & 2SLS 1 Instrumental Variables Estimation and Two Stage Least Squares Econometric Methods, ECON 370 Let s get back to the thiking in terms of cross sectional (or pooled cross sectional) data
More informationA simple alternative to the linear probability model for binary choice models with endogenous regressors
A simple alternative to the linear probability model for binary choice models with endogenous regressors Christopher F Baum, Yingying Dong, Arthur Lewbel, Tao Yang Boston College/DIW Berlin, U.Cal Irvine,
More informationCHAPTER 7. + ˆ δ. (1 nopc) + ˆ β1. =.157, so the new intercept is = The coefficient on nopc is.157.
CHAPTER 7 SOLUTIONS TO PROBLEMS 7. (i) The coefficient on male is 87.75, so a man is estimated to sleep almost one and one-half hours more per week than a comparable woman. Further, t male = 87.75/34.33
More informationSTOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods Course code: EC40 Examiner: Lena Nekby Number of credits: 7,5 credits Date of exam: Saturday, May 9, 008 Examination time: 3
More informationThoughts on Heterogeneity in Econometric Models
Thoughts on Heterogeneity in Econometric Models Presidential Address Midwest Economics Association March 19, 2011 Jeffrey M. Wooldridge Michigan State University 1 1. Introduction Much of current econometric
More informationCORRELATED RANDOM EFFECTS MODELS WITH UNBALANCED PANELS
CORRELATED RANDOM EFFECTS MODELS WITH UNBALANCED PANELS Jeffrey M. Wooldridge Department of Economics Michigan State University East Lansing, MI 48824-1038 wooldri1@msu.edu July 2009 I presented an earlier
More informationA Course in Applied Econometrics Lecture 7: Cluster Sampling. Jeff Wooldridge IRP Lectures, UW Madison, August 2008
A Course in Applied Econometrics Lecture 7: Cluster Sampling Jeff Wooldridge IRP Lectures, UW Madison, August 2008 1. The Linear Model with Cluster Effects 2. Estimation with a Small Number of roups and
More informationFinal Exam. Economics 835: Econometrics. Fall 2010
Final Exam Economics 835: Econometrics Fall 2010 Please answer the question I ask - no more and no less - and remember that the correct answer is often short and simple. 1 Some short questions a) For each
More information1 The problem of survival analysis
1 The problem of survival analysis Survival analysis concerns analyzing the time to the occurrence of an event. For instance, we have a dataset in which the times are 1, 5, 9, 20, and 22. Perhaps those
More informationESTIMATING AVERAGE TREATMENT EFFECTS: REGRESSION DISCONTINUITY DESIGNS Jeff Wooldridge Michigan State University BGSE/IZA Course in Microeconometrics
ESTIMATING AVERAGE TREATMENT EFFECTS: REGRESSION DISCONTINUITY DESIGNS Jeff Wooldridge Michigan State University BGSE/IZA Course in Microeconometrics July 2009 1. Introduction 2. The Sharp RD Design 3.
More informationNew Developments in Econometrics Lecture 9: Stratified Sampling
New Developments in Econometrics Lecture 9: Stratified Sampling Jeff Wooldridge Cemmap Lectures, UCL, June 2009 1. Overview of Stratified Sampling 2. Regression Analysis 3. Clustering and Stratification
More informationECON 594: Lecture #6
ECON 594: Lecture #6 Thomas Lemieux Vancouver School of Economics, UBC May 2018 1 Limited dependent variables: introduction Up to now, we have been implicitly assuming that the dependent variable, y, was
More informationCh 7: Dummy (binary, indicator) variables
Ch 7: Dummy (binary, indicator) variables :Examples Dummy variable are used to indicate the presence or absence of a characteristic. For example, define female i 1 if obs i is female 0 otherwise or male
More informationLecture 12: Application of Maximum Likelihood Estimation:Truncation, Censoring, and Corner Solutions
Econ 513, USC, Department of Economics Lecture 12: Application of Maximum Likelihood Estimation:Truncation, Censoring, and Corner Solutions I Introduction Here we look at a set of complications with the
More informationIntroduction to GSEM in Stata
Introduction to GSEM in Stata Christopher F Baum ECON 8823: Applied Econometrics Boston College, Spring 2016 Christopher F Baum (BC / DIW) Introduction to GSEM in Stata Boston College, Spring 2016 1 /
More informationCRE METHODS FOR UNBALANCED PANELS Correlated Random Effects Panel Data Models IZA Summer School in Labor Economics May 13-19, 2013 Jeffrey M.
CRE METHODS FOR UNBALANCED PANELS Correlated Random Effects Panel Data Models IZA Summer School in Labor Economics May 13-19, 2013 Jeffrey M. Wooldridge Michigan State University 1. Introduction 2. Linear
More informationApplied Health Economics (for B.Sc.)
Applied Health Economics (for B.Sc.) Helmut Farbmacher Department of Economics University of Mannheim Autumn Semester 2017 Outlook 1 Linear models (OLS, Omitted variables, 2SLS) 2 Limited and qualitative
More informationWooldridge, Introductory Econometrics, 3d ed. Chapter 16: Simultaneous equations models. An obvious reason for the endogeneity of explanatory
Wooldridge, Introductory Econometrics, 3d ed. Chapter 16: Simultaneous equations models An obvious reason for the endogeneity of explanatory variables in a regression model is simultaneity: that is, one
More informationEstimating the Fractional Response Model with an Endogenous Count Variable
Estimating the Fractional Response Model with an Endogenous Count Variable Estimating FRM with CEEV Hoa Bao Nguyen Minh Cong Nguyen Michigan State Universtiy American University July 2009 Nguyen and Nguyen
More informationECONOMETRICS FIELD EXAM Michigan State University May 9, 2008
ECONOMETRICS FIELD EXAM Michigan State University May 9, 2008 Instructions: Answer all four (4) questions. Point totals for each question are given in parenthesis; there are 00 points possible. Within
More informationMultiple Linear Regression CIVL 7012/8012
Multiple Linear Regression CIVL 7012/8012 2 Multiple Regression Analysis (MLR) Allows us to explicitly control for many factors those simultaneously affect the dependent variable This is important for
More informationProbability and Samples. Sampling. Point Estimates
Probability and Samples Sampling We want the results from our sample to be true for the population and not just the sample But our sample may or may not be representative of the population Sampling error
More informationivporbit:an R package to estimate the probit model with continuous endogenous regressors
MPRA Munich Personal RePEc Archive ivporbit:an R package to estimate the probit model with continuous endogenous regressors Taha Zaghdoudi University of Jendouba, Faculty of Law Economics and Management
More informationSTOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods Course code: EC40 Examiner: Lena Nekby Number of credits: 7,5 credits Date of exam: Friday, June 5, 009 Examination time: 3 hours
More informationLimited Information Econometrics
Limited Information Econometrics Walras-Bowley Lecture NASM 2013 at USC Andrew Chesher CeMMAP & UCL June 14th 2013 AC (CeMMAP & UCL) LIE 6/14/13 1 / 32 Limited information econometrics Limited information
More informationLECTURE 10. Introduction to Econometrics. Multicollinearity & Heteroskedasticity
LECTURE 10 Introduction to Econometrics Multicollinearity & Heteroskedasticity November 22, 2016 1 / 23 ON PREVIOUS LECTURES We discussed the specification of a regression equation Specification consists
More informationAGEC 661 Note Fourteen
AGEC 661 Note Fourteen Ximing Wu 1 Selection bias 1.1 Heckman s two-step model Consider the model in Heckman (1979) Y i = X iβ + ε i, D i = I {Z iγ + η i > 0}. For a random sample from the population,
More informationNon-linear panel data modeling
Non-linear panel data modeling Laura Magazzini University of Verona laura.magazzini@univr.it http://dse.univr.it/magazzini May 2010 Laura Magazzini (@univr.it) Non-linear panel data modeling May 2010 1
More informationIntroduction to Regression Analysis. Dr. Devlina Chatterjee 11 th August, 2017
Introduction to Regression Analysis Dr. Devlina Chatterjee 11 th August, 2017 What is regression analysis? Regression analysis is a statistical technique for studying linear relationships. One dependent
More informationECNS 561 Multiple Regression Analysis
ECNS 561 Multiple Regression Analysis Model with Two Independent Variables Consider the following model Crime i = β 0 + β 1 Educ i + β 2 [what else would we like to control for?] + ε i Here, we are taking
More informationWorking Paper No Maximum score type estimators
Warsaw School of Economics Institute of Econometrics Department of Applied Econometrics Department of Applied Econometrics Working Papers Warsaw School of Economics Al. iepodleglosci 64 02-554 Warszawa,
More informationThe Simple Linear Regression Model
The Simple Linear Regression Model Lesson 3 Ryan Safner 1 1 Department of Economics Hood College ECON 480 - Econometrics Fall 2017 Ryan Safner (Hood College) ECON 480 - Lesson 3 Fall 2017 1 / 77 Bivariate
More informationPractice exam questions
Practice exam questions Nathaniel Higgins nhiggins@jhu.edu, nhiggins@ers.usda.gov 1. The following question is based on the model y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + u. Discuss the following two hypotheses.
More informationEconometrics II. Seppo Pynnönen. Spring Department of Mathematics and Statistics, University of Vaasa, Finland
Department of Mathematics and Statistics, University of Vaasa, Finland Spring 2018 Part III Limited Dependent Variable Models As of Jan 30, 2017 1 Background 2 Binary Dependent Variable The Linear Probability
More informationIdentification 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 informationChapter 8. Linear Regression. The Linear Model. Fat Versus Protein: An Example. The Linear Model (cont.) Residuals
Chapter 8 Linear Regression Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8-1 Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Fat Versus
More informationECON3150/4150 Spring 2015
ECON3150/4150 Spring 2015 Lecture 3&4 - The linear regression model Siv-Elisabeth Skjelbred University of Oslo January 29, 2015 1 / 67 Chapter 4 in S&W Section 17.1 in S&W (extended OLS assumptions) 2
More informationA Guide to Modern Econometric:
A Guide to Modern Econometric: 4th edition Marno Verbeek Rotterdam School of Management, Erasmus University, Rotterdam B 379887 )WILEY A John Wiley & Sons, Ltd., Publication Contents Preface xiii 1 Introduction
More informationECON 450 Development Economics
ECON 450 Development Economics Statistics Background University of Illinois at Urbana-Champaign Summer 2017 Outline 1 Introduction 2 3 4 5 Introduction Regression analysis is one of the most important
More informationRecent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data
Recent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data July 2012 Bangkok, Thailand Cosimo Beverelli (World Trade Organization) 1 Content a) Classical regression model b)
More informationChapter 8. Linear Regression. Copyright 2010 Pearson Education, Inc.
Chapter 8 Linear Regression Copyright 2010 Pearson Education, Inc. Fat Versus Protein: An Example The following is a scatterplot of total fat versus protein for 30 items on the Burger King menu: Copyright
More informationIntro to Applied Econometrics: Basic theory and Stata examples
IAPRI-MSU Technical Training Intro to Applied Econometrics: Basic theory and Stata examples Training materials developed and session facilitated by icole M. Mason Assistant Professor, Dept. of Agricultural,
More informationECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria
ECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria SOLUTION TO FINAL EXAM Friday, April 12, 2013. From 9:00-12:00 (3 hours) INSTRUCTIONS:
More informationstatistical sense, from the distributions of the xs. The model may now be generalized to the case of k regressors:
Wooldridge, Introductory Econometrics, d ed. Chapter 3: Multiple regression analysis: Estimation In multiple regression analysis, we extend the simple (two-variable) regression model to consider the possibility
More informationEconometrics. Week 8. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague
Econometrics Week 8 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 25 Recommended Reading For the today Instrumental Variables Estimation and Two Stage
More informationLecture Notes 12 Advanced Topics Econ 20150, Principles of Statistics Kevin R Foster, CCNY Spring 2012
Lecture Notes 2 Advanced Topics Econ 2050, Principles of Statistics Kevin R Foster, CCNY Spring 202 Endogenous Independent Variables are Invalid Need to have X causing Y not vice-versa or both! NEVER regress
More informationApplied Econometrics (MSc.) Lecture 3 Instrumental Variables
Applied Econometrics (MSc.) Lecture 3 Instrumental Variables Estimation - Theory Department of Economics University of Gothenburg December 4, 2014 1/28 Why IV estimation? So far, in OLS, we assumed independence.
More informationEconometrics II Censoring & Truncation. May 5, 2011
Econometrics II Censoring & Truncation Måns Söderbom May 5, 2011 1 Censored and Truncated Models Recall that a corner solution is an actual economic outcome, e.g. zero expenditure on health by a household
More informationComparing IRT with Other Models
Comparing IRT with Other Models Lecture #14 ICPSR Item Response Theory Workshop Lecture #14: 1of 45 Lecture Overview The final set of slides will describe a parallel between IRT and another commonly used
More informationECON5115. Solution Proposal for Problem Set 4. Vibeke Øi and Stefan Flügel
ECON5115 Solution Proposal for Problem Set 4 Vibeke Øi (vo@nupi.no) and Stefan Flügel (stefanflu@gmx.de) Problem 1 (i) The standardized normal density of u has the nice property This helps to show that
More informationIntroduction to Econometrics
Introduction to Econometrics T H I R D E D I T I O N Global Edition James H. Stock Harvard University Mark W. Watson Princeton University Boston Columbus Indianapolis New York San Francisco Upper Saddle
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Explained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationLecture 10: Alternatives to OLS with limited dependent variables. PEA vs APE Logit/Probit Poisson
Lecture 10: Alternatives to OLS with limited dependent variables PEA vs APE Logit/Probit Poisson PEA vs APE PEA: partial effect at the average The effect of some x on y for a hypothetical case with sample
More informationExtended regression models using Stata 15
Extended regression models using Stata 15 Charles Lindsey Senior Statistician and Software Developer Stata July 19, 2018 Lindsey (Stata) ERM July 19, 2018 1 / 103 Introduction Common problems in observational
More informationECO 310: Empirical Industrial Organization Lecture 2 - Estimation of Demand and Supply
ECO 310: Empirical Industrial Organization Lecture 2 - Estimation of Demand and Supply Dimitri Dimitropoulos Fall 2014 UToronto 1 / 55 References RW Section 3. Wooldridge, J. (2008). Introductory Econometrics:
More informationChapter 3: Examining Relationships
Chapter 3: Examining Relationships Most statistical studies involve more than one variable. Often in the AP Statistics exam, you will be asked to compare two data sets by using side by side boxplots or
More informationWISE International Masters
WISE International Masters ECONOMETRICS Instructor: Brett Graham INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This examination paper contains 32 questions. You are
More informationECON3150/4150 Spring 2016
ECON3150/4150 Spring 2016 Lecture 4 - The linear regression model Siv-Elisabeth Skjelbred University of Oslo Last updated: January 26, 2016 1 / 49 Overview These lecture slides covers: The linear regression
More informationMeasurement Error. Often a data set will contain imperfect measures of the data we would ideally like.
Measurement Error Often a data set will contain imperfect measures of the data we would ideally like. Aggregate Data: (GDP, Consumption, Investment are only best guesses of theoretical counterparts and
More informationPanel Data Exercises Manuel Arellano. Using panel data, a researcher considers the estimation of the following system:
Panel Data Exercises Manuel Arellano Exercise 1 Using panel data, a researcher considers the estimation of the following system: y 1t = α 1 + βx 1t + v 1t. (t =1,..., T ) y Nt = α N + βx Nt + v Nt where
More informationAnswer Key: Problem Set 6
: Problem Set 6 1. Consider a linear model to explain monthly beer consumption: beer = + inc + price + educ + female + u 0 1 3 4 E ( u inc, price, educ, female ) = 0 ( u inc price educ female) σ inc var,,,
More informationSTATS DOESN T SUCK! ~ CHAPTER 16
SIMPLE LINEAR REGRESSION: STATS DOESN T SUCK! ~ CHAPTER 6 The HR manager at ACME food services wants to examine the relationship between a workers income and their years of experience on the job. He randomly
More informationHandout 12. Endogeneity & Simultaneous Equation Models
Handout 12. Endogeneity & Simultaneous Equation Models In which you learn about another potential source of endogeneity caused by the simultaneous determination of economic variables, and learn how to
More informationNonlinear Regression Functions
Nonlinear Regression Functions (SW Chapter 8) Outline 1. Nonlinear regression functions general comments 2. Nonlinear functions of one variable 3. Nonlinear functions of two variables: interactions 4.
More informationNew Developments in Econometrics Lecture 11: Difference-in-Differences Estimation
New Developments in Econometrics Lecture 11: Difference-in-Differences Estimation Jeff Wooldridge Cemmap Lectures, UCL, June 2009 1. The Basic Methodology 2. How Should We View Uncertainty in DD Settings?
More information4.8 Instrumental Variables
4.8. INSTRUMENTAL VARIABLES 35 4.8 Instrumental Variables A major complication that is emphasized in microeconometrics is the possibility of inconsistent parameter estimation due to endogenous regressors.
More informationPhD/MA Econometrics Examination January 2012 PART A
PhD/MA Econometrics Examination January 2012 PART A ANSWER ANY TWO QUESTIONS IN THIS SECTION NOTE: (1) The indicator function has the properties: (2) Question 1 Let, [defined as if using the indicator
More informationHandout 11: Measurement Error
Handout 11: Measurement Error In which you learn to recognise the consequences for OLS estimation whenever some of the variables you use are not measured as accurately as you might expect. A (potential)
More informationChapter 11. Regression with a Binary Dependent Variable
Chapter 11 Regression with a Binary Dependent Variable 2 Regression with a Binary Dependent Variable (SW Chapter 11) So far the dependent variable (Y) has been continuous: district-wide average test score
More informationA 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 informationWarwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation
Warwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation Michele Aquaro University of Warwick This version: July 21, 2016 1 / 31 Reading material Textbook: Introductory
More informationUNIVERSITY 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 informationContest Quiz 3. Question Sheet. In this quiz we will review concepts of linear regression covered in lecture 2.
Updated: November 17, 2011 Lecturer: Thilo Klein Contact: tk375@cam.ac.uk Contest Quiz 3 Question Sheet In this quiz we will review concepts of linear regression covered in lecture 2. NOTE: Please round
More informationSIMPLE SOLUTIONS TO THE INITIAL CONDITIONS PROBLEM IN DYNAMIC, NONLINEAR PANEL DATA MODELS WITH UNOBSERVED HETEROGENEITY
SIMPLE SOLUTIONS TO THE INITIAL CONDITIONS PROBLEM IN DYNAMIC, NONLINEAR PANEL DATA MODELS WITH UNOBSERVED HETEROGENEITY Jeffrey M Wooldridge THE INSTITUTE FOR FISCAL STUDIES DEPARTMENT OF ECONOMICS, UCL
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Eplained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationNinth ARTNeT Capacity Building Workshop for Trade Research "Trade Flows and Trade Policy Analysis"
Ninth ARTNeT Capacity Building Workshop for Trade Research "Trade Flows and Trade Policy Analysis" June 2013 Bangkok, Thailand Cosimo Beverelli and Rainer Lanz (World Trade Organization) 1 Selected econometric
More informationA 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 informationappstats8.notebook October 11, 2016
Chapter 8 Linear Regression Objective: Students will construct and analyze a linear model for a given set of data. Fat Versus Protein: An Example pg 168 The following is a scatterplot of total fat versus
More information1. Basic Model of Labor Supply
Static Labor Supply. Basic Model of Labor Supply.. Basic Model In this model, the economic unit is a family. Each faimily maximizes U (L, L 2,.., L m, C, C 2,.., C n ) s.t. V + w i ( L i ) p j C j, C j
More informationChapter 9: The Regression Model with Qualitative Information: Binary Variables (Dummies)
Chapter 9: The Regression Model with Qualitative Information: Binary Variables (Dummies) Statistics and Introduction to Econometrics M. Angeles Carnero Departamento de Fundamentos del Análisis Económico
More informationLinear Regression. Linear Regression. Linear Regression. Did You Mean Association Or Correlation?
Did You Mean Association Or Correlation? AP Statistics Chapter 8 Be careful not to use the word correlation when you really mean association. Often times people will incorrectly use the word correlation
More informationMore on Specification and Data Issues
More on Specification and Data Issues Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) Specification and Data Issues 1 / 35 Functional Form Misspecification Functional
More informationIdentification 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 informationSimultaneous Equation Models (Book Chapter 5)
Simultaneous Equation Models (Book Chapter 5) Interrelated equations with continuous dependent variables: Utilization of individual vehicles (measured in kilometers driven) in multivehicle households Interrelation
More informationLinear Regression With Special Variables
Linear Regression With Special Variables Junhui Qian December 21, 2014 Outline Standardized Scores Quadratic Terms Interaction Terms Binary Explanatory Variables Binary Choice Models Standardized Scores:
More informationModels of Qualitative Binary Response
Models of Qualitative Binary Response Probit and Logit Models October 6, 2015 Dependent Variable as a Binary Outcome Suppose we observe an economic choice that is a binary signal. The focus on the course
More informationEconometric Modelling Prof. Rudra P. Pradhan Department of Management Indian Institute of Technology, Kharagpur
Econometric Modelling Prof. Rudra P. Pradhan Department of Management Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 28 LOGIT and PROBIT Model Good afternoon, this is doctor Pradhan
More information1. Overview of the Basic Model
IRP Lectures Madison, WI, August 2008 Lectures 3 & 4, Monday, August 4, 11:15-12:30 and 1:30-2:30 Linear Panel Data Models These notes cover some recent topics in linear panel data models. They begin with
More information