Empirical Asset Pricing
|
|
- Collin Weaver
- 6 years ago
- Views:
Transcription
1 Department of Mathematics and Statistics, University of Vaasa, Finland Texas A&M University, May June, 2013 As of May 24, 2013
2 Part III Stata Regression
3 1 Stata regression Regression Factor variables Postestimation: test More about factor variables Robust standard errors Postestimation commands
4 Regression Stata has a very rich family of regression models and estimation methods. Full description is found from the manuals. The basic syntax in all alternatives are the same as in the basic regression: regress depvar [indepvars] [if] [in] [weight] [, options]
5 Regression options Description Model noconstant suppress constant term hascons has user-supplied constant tsscons compute total sum of squares with constant; seldom used SE/Robust vce(vcetype) Reporting level(#) beta eform(string) depname(varname) display_options vcetype may be ols, robust, cluster clustvar, bootstrap, jackknife, hc2, or hc3 set confidence level; default is level(95) report standardized beta coefficients report exponentiated coefficients and label as string substitute dependent variable name; programmer s option control column formats, row spacing, line width, and display of omitted variables and base and empty cells noheader suppress output header notable suppress coefficient table plus make table extendable mse1 force mean squared error to 1 coeflegend display legend instead of statistics
6 Regression Example: IBM FF-factor model (regression.do) IBM stock Fama-French 3-factor model (daily data) reg rete mkt_rf smb hml, cformat(%6.3f) pformat(%5.3f) sformat(%8.2f) Source SS df MS Number of obs = F( 3, 5813) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml _cons Formating printed output, see help cformat
7 Factor variables gen dow = dow(date) // day-of-week 0 = Sun, 1 = Mon,... i.dow is called a factor variable and defines virtual indicator variable (dummy variable) for each unique value of dow where the smallest forms the reference class. list i.dow in 1/5, clean 1b dow dow dow dow dow b. is the reference class with all values equal to zero. It is dropped from the regression.
8 Factor variables The base value (reference value/class) can be defined by ib. Base operator ib#. ib(##). ib(first). ib(last). ib(freq). ibn. Description use # as base, # = value of variable use the #th ordered value as base use smallest value as base (default) use largest value as base use most frequent value as base no base level The i may be omitted. E.g., you can type ib2.dow or b2.dow. For example, ib(#2). means to use the second value as the base.
9 Factor variables In fact, bn., rather than i., defines virtual indicator value for each class. list bn.dow in 1/5, clean dow dow dow dow dow
10 Factor variables Testing for day of the week effects // estimate ff-model with weekday dummies reg rete mkt_rf smb hml bn.dow, noconstant Source SS df MS Number of obs = F( 8, 5809) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml dow Monday (dow = 1) is statistically significant (Monday effect?).
11 Postestimation: test Given the Monday effect, we can test whether the rest of the weekday effects are jointly zero. This can be carried out by the postestimation command test test (spec) [(spec)...] [, test options] See help test for details.
12 Postestimation: test Example: Testing for linear hypotheses test 2.dow 3.dow 4.dow 5.dow ( 1) 2.dow = 0 ( 2) 3.dow = 0 ( 3) 4.dow = 0 ( 4) 5.dow = 0 F( 4, 5809) = 1.87 Prob > F = // note, e.g., i2.dow is // the same as 2.dow No empirical evidence of joint difference from zero. Note: Usually 2.dow 3.dow 4.dow 5.dow is equivalent to i( ).dow or i(2/5).dow but with test it does not seems to work.
13 Postestimation: test Equality of Tue through Fri effects test 2.dow = 3.dow = 4.dow = 5.dow // equality of coefficients ( 1) 2.dow - 3.dow = 0 ( 2) 2.dow - 4.dow = 0 ( 3) 2.dow - 5.dow = 0 F( 3, 5809) = 2.49 Prob > F =
14 More about factor variables Factor variable operators Operator Description i. unary operator to specify indicators c. unary operator to treat as continuous # binary operator to indicate interaction ## binary operator to specify full-factorial interactions E.g. i1.dow.##c.smb includes all the terms 1.dow, smb, and 1.dow#c.smb to the model. The c. means continuous variable.
15 More about factor variables Monday effect in risk in factor betas? gen mon = 1.dow // for convenience, define Monday dummy and interaction terms gen mkt_x_mon = mkt_rf * mon gen smb_x_mon = smb * mon gen hml_x_mon = hml*mon reg rete mkt_rf smb hml mon mkt_x_mon smb_x_mon hml_x_mon // regression with // monday effects in coefficient Source SS df MS Number of obs = F( 7, 5809) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon smb_x_mon hml_x_mon _cons
16 More about factor variables The enhanced model is of the form r e t = α + β mkt r e mt + s SMB t + h HML t + δ mon t (3) +δ m (r e m mon) t + δ s (HML mon) t + δ h (HML mon) t + u t which we can write r e t = α + δ mon t + (β mkt + δ m mon t )r e mt (4) +(s + δ s mon t ) SMB t +(h + δ h mon t ) HML t + u t. We see that on e.g. on Monday β mkt β mkt + δ m and thus δ m can be interpreted as the shift in market beta on Mondays. The significance of the δ m -estimate above indicates a change in IBM stock s market risk in Mondays (decreases).
17 Robust standard errors In financial data homoscedastisity and independence of regression errors are typically not satisfied. Stata has several options to adapt these problems by using the vce() option (see help vce option). If the errors are not correlated White (1980, Econometrica ) type corrected standard errors are typically utilized. Generally the OLS standard errors depend on the diagonal elements of the matrix X ΩX (5) where Ω is the covariance matrix of the error terms, which is diagonal if the error terms are not correlated.
18 Robust standard errors Under this assumption the diagonal elements of (5) are of the form n ωi 2 x ij x ik (6) i=1 j, k = 1,..., p = number of regressors, where ω 2 i = var[u i ] is the variance of the ith observation. In literature there are four different practices to estimate ω 2 i HC 0 : ûi 2 HC 1 : HC 2 : HC 3 : n n p 1û2 i û 2 i 1 h i û 2 i (1 h i ) 2 Stata : vcr(robust) Stata : vce(hc2) Stata : vce(hc3) (7) h i is the ith diagonal element of X(X X) 1 X.
19 Robust standard errors Generally the different scalings of ûi 2 in (7) result to different bias corrections to estimate the error variances ωi 2. HC 0 performs worst, HC 1 does better, HC 2 does better still, and HC 3 does best of all (usually), Davidson and MacKinnon (1993, p. 554) Estimation and Inference in Econometrics.
20 Robust standard errors OLS standard errors reg rete mkt_rf smb hml mon mkt_x_mon // OLS standard errors Source SS df MS Number of obs = F( 5, 5811) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons
21 Robust standard errors Huber-White heteroscedastic consistent standard errors (HC 1 ) // White-Huber heteroscedastic consistent standard errors reg rete mkt_rf smb hml mon mkt_x_mon, vce(robust) Linear regression Number of obs = 5817 F( 5, 5811) = Prob > F = R-squared = Root MSE = Robust rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons Notice the difference in the F -statistic and standard errors, in particular that of mkt x mon interaction and its t and p values!
22 Robust standard errors White-MacKinnon correction (HC 2 ) reg rete mkt_rf smb hml mon mkt_x_mon, vce(hc2) Linear regression Number of obs = 5817 F( 5, 5811) = Prob > F = R-squared = Root MSE = Robust HC2 rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons It is notable that mkt x mon is at best borderline significant!
23 Robust standard errors White-MacKinnon correction (HC 3 ) Linear regression Number of obs = 5817 F( 5, 5811) = Prob > F = R-squared = Root MSE = Robust HC3 rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons
24 Robust standard errors Stata regress has also Jackknife and Bootstrap standard errors and also cluster type robust standard errors. Jackknife reg rete mkt_rf smb hml mon mkt_x_mon, vce(jacknife, nodots) // nodots suppress intermediate results Linear regression Number of obs = 5817 Replications = 5817 F( 5, 5816) = Prob > F = R-squared = Adj R-squared = Root MSE = Jackknife rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons
25 Robust standard errors Bootstrap reg rete mkt_rf smb hml mon mkt_x_mon, vce(boot, nodots) // nodots suppress intermediate results Linear regression Number of obs = 5817 Replications = 50 Wald chi2(5) = Prob > chi2 = R-squared = Adj R-squared = Root MSE = Observed Bootstrap Normal-based rete Coef. Std. Err. z P> z [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons
26 Robust standard errors Finally Stata allows also to robustify standard errors with respect to correlation within clusters (autocorrelation corrections can be dealt with by time series regressions). Using dow as a cluster variable gives: reg rete mkt_rf smb hml mon mkt_x_mon, vce(cluster dow) Linear regression Number of obs = 5817 F( 3, 4) =. Prob > F =. R-squared = Root MSE = (Std. Err. adjusted for 5 clusters in dow) Robust rete Coef. Std. Err. t P> t [95% Conf. Interval] mkt_rf smb hml mon mkt_x_mon _cons Estimation seems to have some problems because F -statistic does not show up.
27 Robust standard errors The overall conclusion from the above estimation results is that while the Monday effect on IBM s returns seems evident, the Monday effect on IBM s market beta may eventually not exist. Using dow as a cluster variable to capture the potential similarity of regression residuals on particular weekdays (intraclass correlation among weekdays, e.g. Mondays) does not seem to work. In this case a better alternative is to use time series tools of which we will return later. Before that we look at some post estimation commands.
28 Postestimation commands Postestimation commands provide tools for model checking, testing, etc. purposes. Earlier we have already used test for testing linear hypotheses. Some regress postestimation commands The following postestimation commands are of special interest after regress: ================================================================================ Command Description -- dfbeta DFBETA influence statistics estat hettest tests for heteroskedasticity estat imtest information matrix test estat ovtest Ramsey regression specification-error test for omitted variables estat szroeter Szroeters rank test for heteroskedasticity estat vif variance inflation factors for the independent variables acprplot augmented component-plus-residual plot avplot added-variable plot avplots all added-variables plots in one image cprplot component-plus-residual plot lvr2plot leverage-versus-squared-residual plot rvfplot residual-versus-fitted plot rvpplot residual-versus-predictor plot ===============================================================================
29 Postestimation commands Some more More useful postestimation commands: ========================================================================== Command Description contrast contrasts and ANOVA-style joint tests of estimates estat AIC, BIC, VCE, and estimation sample summary estat(svy) postestimation statistics for survey data estimates cataloging estimation results hausman Hausmans specification test lincom point estimates, standard errors, testing, and inference for linear combinations of coefficients linktest link test for model specification lrtest1 likelihood-ratio test margins marginal means, predictive margins, marginal effects, and average marginal effects marginsplot graph the results from margins (profile plots, interaction plots, etc.) nlcom point estimates, standard errors, testing, and inference for nonlinear combinations of coefficients predict predictions, residuals, influence statistics, and other diagnostic measures predictnl point estimates, standard errors, testing, and inference for generalized predictions pwcompare pairwise comparisons of estimates suest seemingly unrelated estimation test Wald tests of simple and composite linear hypotheses testnl Wald tests of nonlinear hypotheses ============================================================================= For more information, see help (e.g. help estat).
30 Postestimation commands Postestimation commands apply to the last estimated model. We estimate the previous model wit HC 3 corrected standard errors. Examples predict res, residuals // generates residuals into res predict yhat, xb // generates fitted values into yhat avplots, msymbol(point) // added variable plots avplots, called added variable plots or partial-regression leverage plots, create two-dimensional scatter plots of projections of the multidimensional data. These can be used to identify visually outliers in the data.
31 Postestimation commands e( rete X ) e( mkt_rf X ) coef = , se = , t = e( rete X ) e( smb X ) coef = , se = , t = 6.84 e( rete X ) e( hml X ) coef = , se = , t = e( rete X ) e( mon X ) coef = , se = , t = 3.71 e( rete X ) e( mkt_x_mon X ) coef = , se = , t = 2.63
Statistical Modelling in Stata 5: Linear Models
Statistical Modelling in Stata 5: Linear Models Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester 07/11/2017 Structure This Week What is a linear model? How good is my model? Does
More informationDescription Syntax for predict Menu for predict Options for predict Remarks and examples Methods and formulas References Also see
Title stata.com logistic postestimation Postestimation tools for logistic Description Syntax for predict Menu for predict Options for predict Remarks and examples Methods and formulas References Also see
More informationPostestimation commands predict estat Remarks and examples Stored results Methods and formulas
Title stata.com mswitch postestimation Postestimation tools for mswitch Postestimation commands predict estat Remarks and examples Stored results Methods and formulas References Also see Postestimation
More informationoptions description set confidence level; default is level(95) maximum number of iterations post estimation results
Title nlcom Nonlinear combinations of estimators Syntax Nonlinear combination of estimators one expression nlcom [ name: ] exp [, options ] Nonlinear combinations of estimators more than one expression
More informationpoint estimates, standard errors, testing, and inference for nonlinear combinations
Title xtreg postestimation Postestimation tools for xtreg Description The following postestimation commands are of special interest after xtreg: command description xttest0 Breusch and Pagan LM test for
More information8. Nonstandard standard error issues 8.1. The bias of robust standard errors
8.1. The bias of robust standard errors Bias Robust standard errors are now easily obtained using e.g. Stata option robust Robust standard errors are preferable to normal standard errors when residuals
More informationDescription Syntax for predict Menu for predict Options for predict Remarks and examples Methods and formulas References Also see
Title stata.com stcrreg postestimation Postestimation tools for stcrreg Description Syntax for predict Menu for predict Options for predict Remarks and examples Methods and formulas References Also see
More informationLab 11 - Heteroskedasticity
Lab 11 - Heteroskedasticity Spring 2017 Contents 1 Introduction 2 2 Heteroskedasticity 2 3 Addressing heteroskedasticity in Stata 3 4 Testing for heteroskedasticity 4 5 A simple example 5 1 1 Introduction
More informationxtdpdqml: Quasi-maximum likelihood estimation of linear dynamic short-t panel data models
xtdpdqml: Quasi-maximum likelihood estimation of linear dynamic short-t panel data models Sebastian Kripfganz University of Exeter Business School, Department of Economics, Exeter, UK UK Stata Users Group
More informationLabor Economics with STATA. Introduction to Regression Diagnostics
Labor Economics with STATA Liyousew G. Borga November 4, 2015 Introduction to Regression Diagnostics Liyou Borga Labor Economics with STATA November 4, 2015 64 / 85 Outline 1 Violations of Basic Assumptions
More informationA Journey to Latent Class Analysis (LCA)
A Journey to Latent Class Analysis (LCA) Jeff Pitblado StataCorp LLC 2017 Nordic and Baltic Stata Users Group Meeting Stockholm, Sweden Outline Motivation by: prefix if clause suest command Factor variables
More informationSyntax Menu Description Options Remarks and examples Stored results Methods and formulas Acknowledgments References Also see
Title regress Linear regression Syntax Menu Description Options Remarks and examples Stored results Methods and formulas Acknowledgments References Also see Syntax regress depvar [ indepvars ] [ if ] [
More informationGMM Estimation in Stata
GMM Estimation in Stata Econometrics I Department of Economics Universidad Carlos III de Madrid Master in Industrial Economics and Markets 1 Outline Motivation 1 Motivation 2 3 4 2 Motivation 3 Stata and
More informationECON Introductory Econometrics. Lecture 5: OLS with One Regressor: Hypothesis Tests
ECON4150 - Introductory Econometrics Lecture 5: OLS with One Regressor: Hypothesis Tests Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 5 Lecture outline 2 Testing Hypotheses about one
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 information1 Linear Regression Analysis The Mincer Wage Equation Data Econometric Model Estimation... 11
Econ 495 - Econometric Review 1 Contents 1 Linear Regression Analysis 4 1.1 The Mincer Wage Equation................. 4 1.2 Data............................. 6 1.3 Econometric Model.....................
More informationTitle. Description. stata.com. Special-interest postestimation commands. asmprobit postestimation Postestimation tools for asmprobit
Title stata.com asmprobit postestimation Postestimation tools for asmprobit Description Syntax for predict Menu for predict Options for predict Syntax for estat Menu for estat Options for estat Remarks
More informationHeteroskedasticity Example
ECON 761: Heteroskedasticity Example L Magee November, 2007 This example uses the fertility data set from assignment 2 The observations are based on the responses of 4361 women in Botswana s 1988 Demographic
More informationLongitudinal Data Analysis Using Stata Paul D. Allison, Ph.D. Upcoming Seminar: May 18-19, 2017, Chicago, Illinois
Longitudinal Data Analysis Using Stata Paul D. Allison, Ph.D. Upcoming Seminar: May 18-19, 217, Chicago, Illinois Outline 1. Opportunities and challenges of panel data. a. Data requirements b. Control
More informationOutline. Linear OLS Models vs: Linear Marginal Models Linear Conditional Models. Random Intercepts Random Intercepts & Slopes
Lecture 2.1 Basic Linear LDA 1 Outline Linear OLS Models vs: Linear Marginal Models Linear Conditional Models Random Intercepts Random Intercepts & Slopes Cond l & Marginal Connections Empirical Bayes
More informationBinary Dependent Variables
Binary Dependent Variables In some cases the outcome of interest rather than one of the right hand side variables - is discrete rather than continuous Binary Dependent Variables In some cases the outcome
More informationEconometrics. 9) Heteroscedasticity and autocorrelation
30C00200 Econometrics 9) Heteroscedasticity and autocorrelation Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Heteroscedasticity Possible causes Testing for
More informationSTATISTICS 110/201 PRACTICE FINAL EXAM
STATISTICS 110/201 PRACTICE FINAL EXAM Questions 1 to 5: There is a downloadable Stata package that produces sequential sums of squares for regression. In other words, the SS is built up as each variable
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 information5. Let W follow a normal distribution with mean of μ and the variance of 1. Then, the pdf of W is
Practice Final Exam Last Name:, First Name:. Please write LEGIBLY. Answer all questions on this exam in the space provided (you may use the back of any page if you need more space). Show all work but do
More informationSimultaneous Equations with Error Components. Mike Bronner Marko Ledic Anja Breitwieser
Simultaneous Equations with Error Components Mike Bronner Marko Ledic Anja Breitwieser PRESENTATION OUTLINE Part I: - Simultaneous equation models: overview - Empirical example Part II: - Hausman and Taylor
More information(a) Briefly discuss the advantage of using panel data in this situation rather than pure crosssections
Answer Key Fixed Effect and First Difference Models 1. See discussion in class.. David Neumark and William Wascher published a study in 199 of the effect of minimum wages on teenage employment using a
More informationECON2228 Notes 7. Christopher F Baum. Boston College Economics. cfb (BC Econ) ECON2228 Notes / 41
ECON2228 Notes 7 Christopher F Baum Boston College Economics 2014 2015 cfb (BC Econ) ECON2228 Notes 6 2014 2015 1 / 41 Chapter 8: Heteroskedasticity In laying out the standard regression model, we made
More informationCase of single exogenous (iv) variable (with single or multiple mediators) iv à med à dv. = β 0. iv i. med i + α 1
Mediation Analysis: OLS vs. SUR vs. ISUR vs. 3SLS vs. SEM Note by Hubert Gatignon July 7, 2013, updated November 15, 2013, April 11, 2014, May 21, 2016 and August 10, 2016 In Chap. 11 of Statistical Analysis
More informationEmpirical Application of Simple Regression (Chapter 2)
Empirical Application of Simple Regression (Chapter 2) 1. The data file is House Data, which can be downloaded from my webpage. 2. Use stata menu File Import Excel Spreadsheet to read the data. Don t forget
More informationEconometrics. 8) Instrumental variables
30C00200 Econometrics 8) Instrumental variables Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Thery of IV regression Overidentification Two-stage least squates
More informationLecture 3 Linear random intercept models
Lecture 3 Linear random intercept models Example: Weight of Guinea Pigs Body weights of 48 pigs in 9 successive weeks of follow-up (Table 3.1 DLZ) The response is measures at n different times, or under
More informationLecture 8: Heteroskedasticity. Causes Consequences Detection Fixes
Lecture 8: Heteroskedasticity Causes Consequences Detection Fixes Assumption MLR5: Homoskedasticity 2 var( u x, x,..., x ) 1 2 In the multivariate case, this means that the variance of the error term does
More informationHeteroskedasticity Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised January 30, 2015
Heteroskedasticity Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised January 30, 2015 These notes draw heavily from Berry and Feldman, and, to a lesser extent, Allison,
More informationApplied Statistics and Econometrics
Applied Statistics and Econometrics Lecture 5 Saul Lach September 2017 Saul Lach () Applied Statistics and Econometrics September 2017 1 / 44 Outline of Lecture 5 Now that we know the sampling distribution
More informationLecture 4: Multivariate Regression, Part 2
Lecture 4: Multivariate Regression, Part 2 Gauss-Markov Assumptions 1) Linear in Parameters: Y X X X i 0 1 1 2 2 k k 2) Random Sampling: we have a random sample from the population that follows the above
More informationSOCY5601 Handout 8, Fall DETECTING CURVILINEARITY (continued) CONDITIONAL EFFECTS PLOTS
SOCY5601 DETECTING CURVILINEARITY (continued) CONDITIONAL EFFECTS PLOTS More on use of X 2 terms to detect curvilinearity: As we have said, a quick way to detect curvilinearity in the relationship between
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression Sasivimol Rattanasiri, Ph.D Section for Clinical Epidemiology and Biostatistics Ramathibodi Hospital, Mahidol University E-mail: sasivimol.rat@mahidol.ac.th 1 Outline
More informationLecture notes to Stock and Watson chapter 8
Lecture notes to Stock and Watson chapter 8 Nonlinear regression Tore Schweder September 29 TS () LN7 9/9 1 / 2 Example: TestScore Income relation, linear or nonlinear? TS () LN7 9/9 2 / 2 General problem
More informationSociology Exam 1 Answer Key Revised February 26, 2007
Sociology 63993 Exam 1 Answer Key Revised February 26, 2007 I. True-False. (20 points) Indicate whether the following statements are true or false. If false, briefly explain why. 1. An outlier on Y will
More informationDescription Quick start Menu Syntax Options Remarks and examples Stored results Methods and formulas Acknowledgments References Also see
Title stata.com mixed Multilevel mixed-effects linear regression Description Quick start Menu Syntax Options Remarks and examples Stored results Methods and formulas Acknowledgments References Also see
More information4 Instrumental Variables Single endogenous variable One continuous instrument. 2
Econ 495 - Econometric Review 1 Contents 4 Instrumental Variables 2 4.1 Single endogenous variable One continuous instrument. 2 4.2 Single endogenous variable more than one continuous instrument..........................
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 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 informationECON Introductory Econometrics. Lecture 4: Linear Regression with One Regressor
ECON4150 - Introductory Econometrics Lecture 4: Linear Regression with One Regressor Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 4 Lecture outline 2 The OLS estimators The effect of
More informationLab 10 - Binary Variables
Lab 10 - Binary Variables Spring 2017 Contents 1 Introduction 1 2 SLR on a Dummy 2 3 MLR with binary independent variables 3 3.1 MLR with a Dummy: different intercepts, same slope................. 4 3.2
More informationTitle. Description. Special-interest postestimation commands. xtmelogit postestimation Postestimation tools for xtmelogit
Title xtmelogit postestimation Postestimation tools for xtmelogit Description The following postestimation commands are of special interest after xtmelogit: Command Description estat group summarize the
More informationQuestion 1 carries a weight of 25%; question 2 carries 25%; question 3 carries 20%; and question 4 carries 30%.
UNIVERSITY OF EAST ANGLIA School of Economics Main Series PGT Examination 2017-18 FINANCIAL ECONOMETRIC THEORY ECO-7024A Time allowed: 2 HOURS Answer ALL FOUR questions. Question 1 carries a weight of
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 informationSoc 63993, Homework #7 Answer Key: Nonlinear effects/ Intro to path analysis
Soc 63993, Homework #7 Answer Key: Nonlinear effects/ Intro to path analysis Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 20, 2015 Problem 1. The files
More informationThe Simulation Extrapolation Method for Fitting Generalized Linear Models with Additive Measurement Error
The Stata Journal (), Number, pp. 1 12 The Simulation Extrapolation Method for Fitting Generalized Linear Models with Additive Measurement Error James W. Hardin Norman J. Arnold School of Public Health
More informationuse conditional maximum-likelihood estimator; the default constraints(constraints) apply specified linear constraints
Title stata.com ivtobit Tobit model with continuous endogenous regressors Syntax Menu Description Options for ML estimator Options for two-step estimator Remarks and examples Stored results Methods and
More informationNonlinear relationships Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 20, 2015
Nonlinear relationships Richard Williams, University of Notre Dame, https://www.nd.edu/~rwilliam/ Last revised February, 5 Sources: Berry & Feldman s Multiple Regression in Practice 985; Pindyck and Rubinfeld
More informationTopic 7: Heteroskedasticity
Topic 7: Heteroskedasticity Advanced Econometrics (I Dong Chen School of Economics, Peking University Introduction If the disturbance variance is not constant across observations, the regression is heteroskedastic
More informationLecture 8: Instrumental Variables Estimation
Lecture Notes on Advanced Econometrics Lecture 8: Instrumental Variables Estimation Endogenous Variables Consider a population model: y α y + β + β x + β x +... + β x + u i i i i k ik i Takashi Yamano
More informationIV and IV-GMM. Christopher F Baum. EC 823: Applied Econometrics. Boston College, Spring 2014
IV and IV-GMM Christopher F Baum EC 823: Applied Econometrics Boston College, Spring 2014 Christopher F Baum (BC / DIW) IV and IV-GMM Boston College, Spring 2014 1 / 1 Instrumental variables estimators
More informationEssential of Simple regression
Essential of Simple regression We use simple regression when we are interested in the relationship between two variables (e.g., x is class size, and y is student s GPA). For simplicity we assume the relationship
More information4 Instrumental Variables Single endogenous variable One continuous instrument. 2
Econ 495 - Econometric Review 1 Contents 4 Instrumental Variables 2 4.1 Single endogenous variable One continuous instrument. 2 4.2 Single endogenous variable more than one continuous instrument..........................
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 informationIntroductory Econometrics. Lecture 13: Hypothesis testing in the multiple regression model, Part 1
Introductory Econometrics Lecture 13: Hypothesis testing in the multiple regression model, Part 1 Jun Ma School of Economics Renmin University of China October 19, 2016 The model I We consider the classical
More informationMultivariate Regression: Part I
Topic 1 Multivariate Regression: Part I ARE/ECN 240 A Graduate Econometrics Professor: Òscar Jordà Outline of this topic Statement of the objective: we want to explain the behavior of one variable as a
More informationECON Introductory Econometrics. Lecture 7: OLS with Multiple Regressors Hypotheses tests
ECON4150 - Introductory Econometrics Lecture 7: OLS with Multiple Regressors Hypotheses tests Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 7 Lecture outline 2 Hypothesis test for single
More informationHomework Solutions Applied Logistic Regression
Homework Solutions Applied Logistic Regression WEEK 6 Exercise 1 From the ICU data, use as the outcome variable vital status (STA) and CPR prior to ICU admission (CPR) as a covariate. (a) Demonstrate that
More informationLab 07 Introduction to Econometrics
Lab 07 Introduction to Econometrics Learning outcomes for this lab: Introduce the different typologies of data and the econometric models that can be used Understand the rationale behind econometrics Understand
More informationEconometrics I KS. Module 2: Multivariate Linear Regression. Alexander Ahammer. This version: April 16, 2018
Econometrics I KS Module 2: Multivariate Linear Regression Alexander Ahammer Department of Economics Johannes Kepler University of Linz This version: April 16, 2018 Alexander Ahammer (JKU) Module 2: Multivariate
More informationLecture 4: Multivariate Regression, Part 2
Lecture 4: Multivariate Regression, Part 2 Gauss-Markov Assumptions 1) Linear in Parameters: Y X X X i 0 1 1 2 2 k k 2) Random Sampling: we have a random sample from the population that follows the above
More informationAnswer all questions from part I. Answer two question from part II.a, and one question from part II.b.
B203: Quantitative Methods Answer all questions from part I. Answer two question from part II.a, and one question from part II.b. Part I: Compulsory Questions. Answer all questions. Each question carries
More informationGraduate Econometrics Lecture 4: Heteroskedasticity
Graduate Econometrics Lecture 4: Heteroskedasticity Department of Economics University of Gothenburg November 30, 2014 1/43 and Autocorrelation Consequences for OLS Estimator Begin from the linear model
More informationIntroduction to Econometrics
Introduction to Econometrics STAT-S-301 Introduction to Time Series Regression and Forecasting (2016/2017) Lecturer: Yves Dominicy Teaching Assistant: Elise Petit 1 Introduction to Time Series Regression
More informationthe error term could vary over the observations, in ways that are related
Heteroskedasticity We now consider the implications of relaxing the assumption that the conditional variance Var(u i x i ) = σ 2 is common to all observations i = 1,..., n In many applications, we may
More informationECON Introductory Econometrics. Lecture 6: OLS with Multiple Regressors
ECON4150 - Introductory Econometrics Lecture 6: OLS with Multiple Regressors Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 6 Lecture outline 2 Violation of first Least Squares assumption
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 informationLecture 7: OLS with qualitative information
Lecture 7: OLS with qualitative information Dummy variables Dummy variable: an indicator that says whether a particular observation is in a category or not Like a light switch: on or off Most useful values:
More informationPlease discuss each of the 3 problems on a separate sheet of paper, not just on a separate page!
Econometrics - Exam May 11, 2011 1 Exam Please discuss each of the 3 problems on a separate sheet of paper, not just on a separate page! Problem 1: (15 points) A researcher has data for the year 2000 from
More informationGeneral Linear Model (Chapter 4)
General Linear Model (Chapter 4) Outcome variable is considered continuous Simple linear regression Scatterplots OLS is BLUE under basic assumptions MSE estimates residual variance testing regression coefficients
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 informationInstrumental Variables, Simultaneous and Systems of Equations
Chapter 6 Instrumental Variables, Simultaneous and Systems of Equations 61 Instrumental variables In the linear regression model y i = x iβ + ε i (61) we have been assuming that bf x i and ε i are uncorrelated
More informationCourse Econometrics I
Course Econometrics I 4. Heteroskedasticity Martin Halla Johannes Kepler University of Linz Department of Economics Last update: May 6, 2014 Martin Halla CS Econometrics I 4 1/31 Our agenda for today Consequences
More informationLecture#12. Instrumental variables regression Causal parameters III
Lecture#12 Instrumental variables regression Causal parameters III 1 Demand experiment, market data analysis & simultaneous causality 2 Simultaneous causality Your task is to estimate the demand function
More information1 A Review of Correlation and Regression
1 A Review of Correlation and Regression SW, Chapter 12 Suppose we select n = 10 persons from the population of college seniors who plan to take the MCAT exam. Each takes the test, is coached, and then
More informationGreene, Econometric Analysis (7th ed, 2012)
EC771: Econometrics, Spring 2012 Greene, Econometric Analysis (7th ed, 2012) Chapters 2 3: Classical Linear Regression The classical linear regression model is the single most useful tool in econometrics.
More informationGeneralized linear models
Generalized linear models Christopher F Baum ECON 8823: Applied Econometrics Boston College, Spring 2016 Christopher F Baum (BC / DIW) Generalized linear models Boston College, Spring 2016 1 / 1 Introduction
More informationWorking with Stata Inference on the mean
Working with Stata Inference on the mean Nicola Orsini Biostatistics Team Department of Public Health Sciences Karolinska Institutet Dataset: hyponatremia.dta Motivating example Outcome: Serum sodium concentration,
More informationExercices for Applied Econometrics A
QEM F. Gardes-C. Starzec-M.A. Diaye Exercices for Applied Econometrics A I. Exercice: The panel of households expenditures in Poland, for years 1997 to 2000, gives the following statistics for the whole
More information****Lab 4, Feb 4: EDA and OLS and WLS
****Lab 4, Feb 4: EDA and OLS and WLS ------- log: C:\Documents and Settings\Default\Desktop\LDA\Data\cows_Lab4.log log type: text opened on: 4 Feb 2004, 09:26:19. use use "Z:\LDA\DataLDA\cowsP.dta", clear.
More informationЭконометрика, , 4 модуль Семинар Для Группы Э_Б2015_Э_3 Семинарист О.А.Демидова
Эконометрика, 2017-2018, 4 модуль Семинар 3 160418 Для Группы Э_Б2015_Э_3 Семинарист ОАДемидова * Stata program * copyright C 2010 by A Colin Cameron and Pravin K Trivedi * used for "Microeconometrics
More informationEconomics 471: Econometrics Department of Economics, Finance and Legal Studies University of Alabama
Economics 471: Econometrics Department of Economics, Finance and Legal Studies University of Alabama Course Packet The purpose of this packet is to show you one particular dataset and how it is used in
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 informationSelf-Assessment Weeks 8: Multiple Regression with Qualitative Predictors; Multiple Comparisons
Self-Assessment Weeks 8: Multiple Regression with Qualitative Predictors; Multiple Comparisons 1. Suppose we wish to assess the impact of five treatments while blocking for study participant race (Black,
More informationsociology 362 regression
sociology 36 regression Regression is a means of modeling how the conditional distribution of a response variable (say, Y) varies for different values of one or more independent explanatory variables (say,
More informationECON3150/4150 Spring 2016
ECON3150/4150 Spring 2016 Lecture 6 Multiple regression model Siv-Elisabeth Skjelbred University of Oslo February 5th Last updated: February 3, 2016 1 / 49 Outline Multiple linear regression model and
More informationMarginal effects and extending the Blinder-Oaxaca. decomposition to nonlinear models. Tamás Bartus
Presentation at the 2th UK Stata Users Group meeting London, -2 Septermber 26 Marginal effects and extending the Blinder-Oaxaca decomposition to nonlinear models Tamás Bartus Institute of Sociology and
More informationLab 6 - Simple Regression
Lab 6 - Simple Regression Spring 2017 Contents 1 Thinking About Regression 2 2 Regression Output 3 3 Fitted Values 5 4 Residuals 6 5 Functional Forms 8 Updated from Stata tutorials provided by Prof. Cichello
More informationMediation Analysis: OLS vs. SUR vs. 3SLS Note by Hubert Gatignon July 7, 2013, updated November 15, 2013
Mediation Analysis: OLS vs. SUR vs. 3SLS Note by Hubert Gatignon July 7, 2013, updated November 15, 2013 In Chap. 11 of Statistical Analysis of Management Data (Gatignon, 2014), tests of mediation are
More informationHeteroskedasticity-Robust Inference in Finite Samples
Heteroskedasticity-Robust Inference in Finite Samples Jerry Hausman and Christopher Palmer Massachusetts Institute of Technology December 011 Abstract Since the advent of heteroskedasticity-robust standard
More informationProblem Set 10: Panel Data
Problem Set 10: Panel Data 1. Read in the data set, e11panel1.dta from the course website. This contains data on a sample or 1252 men and women who were asked about their hourly wage in two years, 2005
More information. *DEFINITIONS OF ARTIFICIAL DATA SET. mat m=(12,20,0) /*matrix of means of RHS vars: edu, exp, error*/
. DEFINITIONS OF ARTIFICIAL DATA SET. mat m=(,,) /matrix of means of RHS vars: edu, exp, error/. mat c=(5,-.6, \ -.6,9, \,,.) /covariance matrix of RHS vars /. mat l m /displays matrix of means / c c c3
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 informationImplementing Conditional Tests with Correct Size in the Simultaneous Equations Model
The Stata Journal (2001) 1, Number 1, pp. 1 15 Implementing Conditional Tests with Correct Size in the Simultaneous Equations Model Marcelo J. Moreira Department of Economics Harvard University Brian P.
More informationEconometrics Homework 4 Solutions
Econometrics Homework 4 Solutions Computer Question (Optional, no need to hand in) (a) c i may capture some state-specific factor that contributes to higher or low rate of accident or fatality. For example,
More information