# Documents about Robust Standard Errors

• 2 Pages

#### lect2_part2

Berkeley, ARE 213

Excerpt: ... Imbens, Lecture Notes 2, ARE213 Fall '03 9 Let us look some variance estimates based on the various methods discussed here. We focus on a regression of log weekly earnings on a constant and years of education. The estimated regression function with conventional standard errors is is log(earnings)i = 5.0455 + 0.0667 educi (0.0849) (0.0062) ^ The estimate for 2 is 0.1744. The estimated covariance matrix for is -1 ^ V = 2 (X X) = ^ 0.0072066 -0.0005212 0.0000387 . With robust standard errors the estimated regression function is log(earnings)i = 5.0455 + 0.0667 educi (0.0858) (0.0063) The two sets of standard errors are obviously very similar. To see why, let us compare the matrix N N i=1 2 Xi Xi /N to 2 ^ i 01740 i Xi Xi /N. The first is 2.3632 32.9614 , 2 Xi Xi /N = i i=1 and the second N ^ i=1 2 Xi Xi /N = 01744 2.3491 32.4789 . It is not always the case that using robust standard errors makes no difference. Let us look at the same regression in levels rather than logs. The conven ...

• 2 Pages

#### non_spherical

Vassar, ECON 310

Excerpt: ... may get better results by using OLS and recalculating the variance covariance matrix of the estimators. The recalculated standard errors are called robust standard errors . If nothing is known about the matrix we are forced to use OLS with robust standard errors . A description of how robust standard errors are calculated can be found in Greene, Econometric Analysis. The estimator in the case of heteroskedasticity is known as Whites Heteroskedasticity Consistent Estimator. In STATA you can request robust standard errors in most regression procedures by simple adding , robust to the command. reg c yd r, robust ...

• 1 Pages

#### hw7

UConn, WEB 2

Excerpt: ... ECONOMICS 2311C (FALL 2008) PROBLEM SET 7 GAUTAM TRIPATHI Wooldridge Text1 3.8, 3.9, 7.1, 7.3, 7.8, C7.1, C7.2, C7.4, C7.8. Additional Problem 1 Suppose we estimate the wage regression log(w age) = 0 + 1 edu + u. (i) It is reasonable to believe that this model suers from an omitted variables problem since edu is correlated with ability which is unobserved. Can you determine the eect of unobserved ability on the estimated returns to schooling? (ii) It is also reasonable to believe that schooling is correlated with both ability and experience. Can you determine the eect of unobserved ability and experience on the estimated returns to schooling? Due: November 11, 2008. 1 Irrespective of what the text asks, I only need you to do hypotheses tests at 5% level of signicance. For computer exercises, make sure to report and use heteroscedasticity- robust standard errors when doing t-tests. Robust standard errors in Shazam are obtained by using the hetcov option when running the regression. In problems ...

• 12 Pages

#### LN+13+Instrumental+Variables

Harvard, HKS API202A

Excerpt: ... its (totcredb). Does this instrument satisfy the two conditions for a valid instrument? (1) Relevance: Is distance to college correlated with years of college? We check this below by assessing the statistical significance of the instrument in the first-stage regression. - Rule of thumb to assess relevance: Verify if the F statistic for the joint significance of the instruments is greater than 10. - If the F-test is less than 10 we say the instruments are weak. First stage regression: regress totcredb on instruments (Zs) and covariates (other Xs) dist2yr dist4yr = = distance to a 2-year college distance to a 4-year college . reg totcredb black hispanic female phsrank dist2yr dist4yr, robust Regression with robust standard errors Number of obs = 3292 R-squared = 0.2781 -| Robust totcredb | Coef. Std. Err. t P>|t| [95% Conf. Interval] -+-black | .0140185 .1317 ...

• 5 Pages

#### Hetero_Robust_WLS

Excerpt: ... Rockefeller College University at Albany PAD 705 Handout: Heteroskedasticity, Robust Standard Errors , and Weighted Least Squares There are two ways to cope with heteroskedasticity using robust standard errors or by doing a weighted least squares regression. This handout reviews both options, using the cps83.dta dataset. . . . . . . use "H:\Rockefeller Courses\PAD705\Problem Set Data\cps83.dta", clear gen hwage = wklywage/wklyhrs gen lhwage = log(hwage) gen exper2 = exper^2 gen fem = (sex = 2) graph lhwage union, saving(wls1) yrseduc exper exper2 fem union Number of obs F( 5, 994) Prob > F R-squared Adj R-squared Root MSE = = = = = = 1000 116.01 0.0000 0.3685 0.3653 .44384 . reg lhwage Source | SS df MS -+-Model | 114.270796 5 22.8541592 Residual | 195.81422 994 .196996197 -+-Total | 310.085016 999 .310395411 -lhwage | Coef. Std. Err. t P>|t| [95% ...

• 2 Pages

#### ps5

Purdue, ICS 671

Excerpt: ... Economics 671 Problem Set #5 Heteroscedasticity and FGLS (1) This problem set again makes use of the data house4.txt, which is available on the course website. To begin, estimate the following regression model P ricei = 1 + 2 Roomsi + 3 Lotsizei + 4 Sqrf ooti + 5 Agei + i . To make things a little more interpretable (and the estimated coecients smaller and easier to work with), divide the price and lot size variables by 1,000 and divide the sqrfoot variable by 100 before estimating this model. Calculate Whites heteroscedasticity- robust standard errors associated with the OLS estimator, using the technique discussed in the lectures. Compare these results to the standard ones that do not account for heteroscedasticity. (2) Using the same model above, add structure to the error variance by assuming: i |xi ind N [0, exp(xi )] , where xi = [1 Roomsi LotSizei Sqrf ti Agei ]. Obtain the FGLS estimate of in this case. Note: When doing this, interpret your estimate of . You should ...

• 2 Pages

#### hkas8

Georgia Tech, E 6160

Excerpt: ... (i) If spread is zero, there is no favorite, and the probability that the team we (arbitrarily) label the favorite should have a 50% chance of winning. (ii) The linear probability model estimated by OLS gives n favwin = .577 (.028) [.032] + .0194 spread (.0023) [.0019] n = 553, R2 = .111. where the usual standard errors are in ( ) and the heteroskedasticity- robust standard errors are in [ ]. Using the usual standard error, the t statistic for H0: 0 = .5 is (.577 - . 5)/.028 = 2.75, which leads to rejecting H0 against a two-sided alternative at the 1% level (critical value n 2.58). Using the robust standard error reduces the significance but nevertheless leads to strong rejection of H0 at the 2% level against a two-sided alternative: t = (.577 - .5)/.032 n 2.41 (critical value n 2.33). (iii) As we expect, spread is very statistically significant using either standard error, with a t statistic greater than eight. If spread = 10 the estimated probability that the favored team wins is .577 + .0194(10) = .771. ( ...

• 3 Pages

#### Anskey2

USC, ECON 513

Excerpt: ... timates with intercept are included here only for checking that people who did include the intercept did their math correct. The bootstrap standard errors are based on 100,000 bootstrap replications. 3. For the second regression model estimate the standard errors in four ways: (i) conventional ols standard errors, (ii), robust standard errors , (iii) parametric bootstrap with Problem Set II, Econ 513, Fall 205 2 Table 2: Estimates and Standard Errors for Coefficient on Education no intercept slope coefficient estimate ols s.e. robust s.e. parametric bootstrap s.e. nonparametric boostrap s.e. 0.1021 (0.0250) (0.0261) (0.0246) (0.0265) with intercept intercept slope coefficient -0.0756 (0.0460) (0.0456) (0.0457) (0.457) 0.1033 (0.0248) (0.0275) (0.0246) (0.0282) at least 10,000 bootstrap replications, (iv) nonparametric boostrap with at least 10,000 bootstrap replications. Which would you report if you were asked to report only one set of standard errors? See answer to previous question. Which one t ...

• 2 Pages

#### PS3

Northwestern, BIOL_SCI 164

Excerpt: ... e April 23 (g) Obtain heteroskedasticity- robust standard errors for the coefficients. How does this affect the statistical significance of the two policy variables? (h) Test the errors for AR(1) serial correlation, assuming strict exogeneity of the regressors. Is this a reasonable assumption here? Explain. (i) Obtain serial correlation- and heteroskedasticity- robust standard errors using six lags in the Newey-West estimator. How does this affect the statistical significance of the two policy variables? (j) Now estimate the model using Prais-Winsten and compare the estimates with the OLS estimates. Are there important changes in the policy variable coefficients or their statistical significance? (k) Now suppose you know that the error in the regression from part (f) follows an MA(2) process. How would you estimate the model efficiently? What are the estimated coefficients on the on and ? Discuss their statistical significance. ...

• 1 Pages

#### table1

BYU, ASSIGN 328

Excerpt: ... Political Science 328, Assignment 6 Table 1 Growth Regression Results Dependent variable: Growth Regressor Trade Share ( Years Schooling ( Capital Stock Coups Lack of Civil Society Intercept ( ) ( ) ( ) F-statistics testing the hypothesis that the population coefficients on the indicated regressors are all zero: Trade Share, Years Schooling ( ) ( ) ( ) Trade Share, Years Schooling, _ Capital Stock ( ) ( ) Coups, Lack of Civil Society _ _ ( ) Regression summary statistics _ ( _ _ _ ( _ ( ) ) ) ( ) ) ( ) ( ) (1) ) ( (2) ) ( (3) ) R2 R2 SER n Notes: Dependent variable is average annual percentage growth of real Gross Domestic Product (GDP) from 1960 to 1995. Heteroskedasticity- robust standard errors are given in parentheses under estimated coefficients, and p-values are given in parentheses under Fstatistics. The F-statistics are heteroskedasticity-robust. The regression results exclude data on Malta. ...

• 1 Pages

#### a7table2

BYU, GOODLIFFE 328

Excerpt: ... Political Science 328, Assignment 7 Table 2 Determinants of Terrorism (continued) Dependent variable: Terrorist Fatalities (4) Regressor: GDP/capita (logged) ( Lack of Political Freedoms ( (Lack of Political Freedoms)2 ( Ethnic Fractionalization ( Religious Fractionalization ( Middle East Other regional dummies? Intercept ( ) ( ) F-statistics testing the hypothesis that the population coefficients on the indicated regressors are all zero: Lack of Political Freedoms, (Lack of Political Freedoms)2 ( ) ( ) Ethnic Fractionalization, Religious Fractionalization ( ) ( ) Other regional dummies _ ( ) Regression summary statistics _ ( No Yes ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) (5) R2 R2 SER n Notes: Dependent variable is the natural logarithm of the number of fatalities from terrorist incidents in the country, 1998-2004, per million population. Heteroskedasticity- robust standard errors are given in parentheses under estimated coefficients, and p-values are given in parentheses under F- statistics. The F-statistics are ...

• 1 Pages

#### a7table1

BYU, ASSIGN 328

Excerpt: ... Political Science 328, Assignment 7 Table 1 Determinants of Terrorism Dependent variable: Terrorist Fatalities (1) Regressor: GDP/capita (logged) ( (GDP/capita (logged)2 Lack of Political Freedoms (Lack of Political Freedoms)2 Intercept ( ) ( ) F-statistics testing the hypothesis that the population coefficients on the indicated regressors are all zero: GDP/capita (logged), _ _ (GDP/capita (logged)2 Lack of Political Freedoms, _ _ (Lack of Political Freedoms)2 Regression summary statistics ( ) _ _ ( _ _ ( ) ) ( ) ) ( _ ( ) ) ( ) (2) (3) ( ( ) ) R2 R2 SER n Notes: Dependent variable is the natural logarithm of the number of fatalities from terrorist incidents in the country, 1998-2004, per million population. Heteroskedasticity- robust standard errors are given in parentheses under estimated coefficients, and p-values are given in parentheses under F- statistics. The F-statistics are heteroskedasticity-robust. Coefficients are significant at the +10%, *5%, *1% significance level. 1 ...

• 1 Pages

#### Assignment2

USC, ECON 513

Excerpt: ... 1 Problem Set II For this problem set you will have to use the data set TWINSAK 2004.MAT which is available on the website for the course. These data were collected and analyzed by Ashenfelter and Krueger in a study of twins (American Economic Review, Vol. 84, No. 5. Dec., 1994, pp. 1157-1173.). The data set has 143 observations on six variables, lwage1 (log weekly wage for first member of twin pair), lwage2 (log weekly wage for second member of twin pair), educ1 (years of education for first member of twin pair), educ2 (years of education for second member of twin pair), age (age of twins), male1 (gender of twins which is identical for both given that all twin pairs are monozygotic in this subsample). 1. Treat both members of the twin pairs as independent observations and estimate a linear regression function for log wages on a constant, years of education, age and age-squared. Report conventional and heteroskedasticity robust standard errors . 2. Estimate a linear regression model for the difference in log w ...

• 12 Pages

#### heteroskedasticity

Iowa State, ECON 371

Excerpt: ... ifferent formulas. Homoskedasticity-only standard errors are the default setting in regression software sometimes the only setting (e.g. Excel). To get the general "heteroskedasticity-robust" standard errors you must override the default. If you don't override the default and there is in fact heteroskedasticity, you will get the wrong standard errors (and wrong t-statistics and confidence intervals). 4-10 The critical points: If the errors are homoskedastic and you use the heteroskedastic formula for standard errors (the one we derived), you are OK If the errors are heteroskedastic and you use the homoskedasticity-only formula for standard errors, the standard errors are wrong. The two formulas coincide (when n is large) in the special case of homoskedasticity The bottom line: you should always use the heteroskedasticity-based formulas these are conventionally called the heteroskedasticity- robust standard errors . 4-11 Heteroskedasticity- robust standard errors in STATA regress testscr str, robu ...

• 26 Pages

#### LN2+Mechanics+and+Interpretation+of+OLS

Harvard, HKS API202A

Excerpt: ... LN2API202A Spring 2009 Harvard Kennedy School We run OLS with the 420 observations (N=420) and estimate 0 and 1 . The Stata output: variable testscr=test scores variable str=student-teacher ratio .reg testscr str, robust Regression with robust standard errors Number of obs F( 1, 418) Prob > F R-squared Root MSE = = = = = 420 19.26 0.0000 0.0512 18.581 -| Robust [95% Conf. Interval] testscr | Coef. Std. Err. t P>|t| -+-str | -2.279808 .5194892 -4.39 0.000 -3.300945 -1.258671 _cons | 698.933 10.36436 67.44 0.000 678.5602 719.3057 - Question 2: What is the estimated value of 0 and 1 ? How would you write the SR with this values? Question 3: How would you interpret 1 ? Question 4: Can we infer the causal eect of class size on students test scores from this OLS estimate? That is, ...

• 2 Pages

#### Assign4

Arizona, E 418

Excerpt: ... Professor R.L. Oaxaca Econ 418 Due in class Tuesday, November 13 (20 points) Assignment #4 Fall 2007 The data for this assignment are contained in both the Excel le hprice1.xls and the STATA le hprice1.dta available at http:/u.arizona.edu/~rlo. These data pertain to a cross-section sample of 88 homes in a certain locale. Be sure to attach the supporting computer print out to the completed assignment, show your work, and make clear where your answers are shown. The variables of interest for this exercise are assess (assessed value \$1,000s), sqrf t (size of house in square feet), bdrms (number of bedrooms), and lotsize (size of lot in square feet). Some basic STATA commands that might be useful To create the square of a variable named Z and give this new variable the name ZSQRD, type the command generate ZSQRD = Z^2 To estimate a regression model Yi = 0 + 1 X1i + 2 X2i + ui that generates robust standard errors , type the command regress Y X1 X2, robust 1. Use OLS to estimate the f ...

• 2 Pages

#### spring04_study_sheet3

Virginia Tech, ASHLEYMAC 3254

Excerpt: ... agnostically check a multiple regression model for a. fitting error outliers b. coefficient stability c. gaussian errors (graphically) d. heteroskedastic errors (graphically & via auxiliary regression & by comparing to results using robust standard errors if N is large enough) e. serially correlated errors (for a time series regression) f. possible nonlinear dependence on an explanatory variable 7. Show how to use STATA to deal with heteroskedasticity of form var(,i) proportional to (zi)2, where zi is observable and how to obtain and interpret robust standard error estimates. 8. Interpret (and perhaps deal with) nongaussianity in an error term e.g., log transformation to deal with asymmetric error distribution or an additional explanatory variable to deal with a bimodal error distribution. 9. Interpret a regression parameter on an explanatory variable e.g., a gender dummy variable or a years-of-schooling variable. If the dependent variable is in logarithmic form e.g., ln(income) you should ...

• 10 Pages

#### hwk5sol.09

N.C. State, ST 732

Excerpt: ... the p-value for treatment by year interaction is .18 (Wald) or .19 (score) compared to the p-scale version .05. (c) The null hypothesis is simply H0 : 2 = 0. Thus, with the definition of in (b), the appropriate L is L= 0 0 1 . We can read the test statistic and p-value right off the table Analysis Of GEE Parameter Estimates using either the model-based or robust standard errors . Alternatively, we could invoke a contrast statement (we did this, too - note that the robust standard errors are used). If we used the robust standard errors , we get a Z test statistic of 0.87 (equivalently a 2 statistics from the constrast statement of 1.342 1.81) with a p-value of 0.18. The model-based analysis gives Z = 1.48 with a o-value of 0.14. Either way, there does not seem to be enough evidence to suggest that the pattern of change is different. (In fact, from (a), it seems that there may not be change at all in either group, so that this is reflecting that both patterns are "flat.") (d) Now the investigators are interest ...

• 37 Pages

#### eco2408_slides_lecture08_spring2009

Toledo, ECO 2408

Excerpt: ... Heteroskedasticity Variance of u is not constant 1 OUTLINE 1. What is Heteroskedasticity? Why Worry about Heteroskedasticity? Robust Standard Errors and Tests about Parameters Testing for (Detecting) Heteroskedasticity Weighted Least Squares (WLS) Generalized Least Squares (GLS) Feasible Generalized Least Squares (FGLS) 2 1. 1. 1. 1. 1. 1. 1.WhatisHeteroskedasticity Homoskedasticity implies that, conditional on the explanatory variables, the variance of the error u is constant (does not depend on x): Var( u | x) = constant If the variance of u is different for different values of the xs, then the errors are heteroskedastic: Var( u | x) = f(x) 3 Example of Heteroskedasticity f(y|x) y . x1 x2 x3 . . E(y|x) = 0 + 1x x 4 Example: Sample with Heteroskedasticity 5 Example: Sample with Heteroskedasticity 6 Example: Sample with Heteroskedasticity 7 Example: Film Revenue (Y) versus Production Costs (X) 8 Example: Sample with Heteroskedasticity 9 2.WhyWorry ...

• 1 Pages

#### a8table1

BYU, ASSIGN 328

Excerpt: ... PlSc 328 Assignment 8 Table 1 Estimated Effect on the Probability of Smoking of a Workplace Smoking Ban on Two Hypothetical Workers Mr. A: male, white, non-Hispanic, 20 years old, high school dropout Ms. B: female, black, 40 years old, college gradua ...

• 1 Pages

#### a7table3

BYU, ASSIGN 328

Excerpt: ... Political Science 328, Assignment 7 Table 3 Determinants of Terrorism (continued) Dependent variable: Terrorist Fatalities (6) Regressor: High GDP/capita ( Lack of Political Freedoms ( (Lack of Political Freedoms)2 High GDP/capita Lack of Political Freedoms High GDP/capita (Lack of Political Freedoms)2 Intercept ( _ ( ( ) ) _ ( ) ( ) ) ) ( ) ) ( ) (7) ( ) F-statistics testing the hypothesis that the population coefficients on the indicated regressors are all zero: _ High GDP/capita Lack of Political Freedoms, 2 High GDP/capita Lack of Political Freedoms (Lack of Political Freedoms)2, _ High GDP/capita (Lack of Political Freedoms)2 Lack of Political Freedoms, _ (Lack of Political Freedoms)2 Regression summary statistics: ( ( ( ) ) ) R2 R2 SER n Notes: Dependent variable is the natural logarithm of the number of fatalities from terrorist incidents in the country, 1998-2004, per million population. Heteroskedasticity- robust standard errors are given in parentheses under estimated coefficients ...

• 17 Pages

#### eco2408_slides_lecture11_spring2009

Toledo, ECO 2408

Excerpt: ... Serial Correlation and Heteroskedasticity with Time Series Data yt = 0 + 1xt1 + . . .+ kxtk + ut 1 Lecture 11: TIME SERIES DATA: SERIAL CORRELATION AND HETEROSKEDASTICITY Professor Victor Aguirregabiria OUTLINE 1. Properties of OLS with Serial Correlation Testing for Serial Correlation - 1. Test for AR(1) with Strictly Exogenous Regressors Test for AR(1) with Lagged Endogenous Regressors Test for Higher Order Serial Correlation 1. Correcting for Serial Correlation - Serial Correlation- Robust Standard Errors Feasible GLS (Cochrane-Orcutt and Prais-Winsten) 1. Heteroskedasticity 2 1.Properties of OLS with Serial Correlation If we have stationary data and E(ut | xt) = 0, the OLS is consistent and asymptotically normal, regardless the serial correlation of the error term. There are three main implications of serial correlation on the OLS properties. 1. 2. 3. OLS is not efficient. OLS standard errors do not have the form that we have used so far. For some dynamic TS models (wi ...

• 21 Pages

#### panel2

Berkeley, E 244

Excerpt: ... For this model, the matrices (T by TK) and (T2K by T2K) are sufficient to describe the data: = E [y i x i ']E [x i x i ']-1 = E [(y i - x i )(y i - x i ) ' -1 (x i x i ') -1 ] X X where y i = (y i 1 , y i 2 ,., y iT ) ' 1 2 K x i = (x i11 ,., x iT ; x i21 ,., x iT ;.; x iK1 ,., x iT ) ' (TxTK) (T 2KxT 2K ) (Tx 1) (TKx 1) (TKxTK ) -1 = E [x i x i '] X 2/10/02 Economics 244 - Lecture 2 15 4. PI Matrix and can be estimated consistently from the SUR (seemingly unrelated regression) estimate of the {yi} on all the {xi}, together with the robust standard errors from that regression: ^ = ( 1 , 2 ,., T ) ' ^ ^ ^ N -1 or ^ = vec = ( 1 ', 2 ',., T ') ' ^ ^ ^ ^ N x i x i ' x i y it t = ^ i =1 i =1 - - ^ ^ ^ = E [(y i - x i )(y i - x i ) ' S X 1 (x i x i ')S X 1 ] where S -1 X Note: This estimator is easily computed in any software package with SUR and robust standard errors . Treat the y for each year as a separate equation and regress it on ALL the x's. By performing the esti ...