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 ...
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 ...
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 ...
SUNY Albany, PAD 705
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% ...
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. ( ...
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 ...
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. ...
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 ...
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 ...
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, ...
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 ...
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 ...