newey — Regression with Newey–West standard errors

1 Regression with newey West standard errorsSyntaxMenuDescriptionOptionsRemark s and examplesStored resultsMethods and formulasReferencesAlso seeSyntaxneweydepvar[indepvars] [if] [in] [weight], lag(#)[options]optionsDescriptionModel lag(#)set maximum lag order of autocorrelationnoconstantsuppress constant termReportinglevel(#)set confidence level; default islevel(95)displayoptionscontrol column formats, row spacing, line width, display of omittedvariables and base and empty cells, and factor-variable labelingcoeflegenddisplay legend instead of statistics lag(#)is musttssetyour data before usingnewey; see [TS] contain factor variables; see[U] Factor contain time-series operators; see[U] Time-series ,rolling, andstatsbyare allowed; see[U] Prefix are allowed; see[U] not appear in the dialog [U] 20 Estimation and postestimation commandsfor more capabilities of estimation >Time series> Regression with newey -West std.

2 ErrorsDescriptionneweyproduces newey West standard errors for coefficients estimated byOLSregression. Theerror structure is assumed to be heteroskedastic and possibly autocorrelated up to some Model lag(#)specifies the maximum lag to be considered in the autocorrelation structure. If you specifylag(0), the output is the same asregress, vce(robust).lag()is ; see [R]estimation newey Regression with newey West standard errors Reporting level(#); see [R]estimation :noomitted,vsquish,noemptycells,baseleve ls,allbaselevels,nofvla-bel,fvwrap(#),fv wrapon(style),cformat(%fmt),pformat(%fmt ),sformat(%fmt), andnolstretch; see [R]estimation following option is available withneweybut is not shown in the dialog box:coeflegend; see [R]estimation and Huber/White/sandwich robust variance estimator (see White [1980]) produces consistentstandard errors forOLSregression coefficient estimates in the presence of heteroskedasticity.

3 TheNewey West (1987) variance estimator is an extension that produces consistent estimates when thereis autocorrelation in addition to possible newey West variance estimator handles autocorrelation up to and including a lag ofm,wheremis specified by stipulating thelag()option. Thus, it assumes that any autocorrelation atlags greater thanmcan be (0)is specified, the variance estimates produced byneweyare simply the Hu-ber/White/sandwich robust variances estimates calculated byregress, vce(robust); see [R] 1newey, lag(0)is equivalent toregress, vce(robust):. use (1978 Automobile Data). regress price weight displ, vce(robust)Linear Regression Number of obs = 74F( 2, 71) = > F = = MSE = Std. Err. t P>|t| [95% Conf. Interval] .7808755 .2663445 generate t = _n.

4 Tsset ttime variable: t, 1 to 74delta: 1 unitnewey Regression with newey West standard errors 3. newey price weight displ, lag(0) Regression with newey -West standard errors Number of obs = 74maximum lag: 0 F( 2, 71) = > F = Std. Err. t P>|t| [95% Conf. Interval] .7808755 .2663445 the dataset to betsset, we generated a dummy time variablet, which inthis example played no role in the 2 Say that we have time-series measurements on variablesusrandidleand now wish to fit anOLSmodel but obtain newey West standard errors allowing for a lag of up to 3:. use , clear. tsset timetime variable: time, 1 to 30delta: 1 unit. newey usr idle, lag(3) Regression with newey -West standard errors Number of obs = 30maximum lag: 3 F( 1, 28) = > F = Std.

5 Err. t P>|t| [95% Conf. Interval] .0690927 newey Regression with newey West standard errorsStored resultsneweystores the following ine():Scalarse(N)number of observationse(dfm)model degrees of freedome(dfr)residual degrees of freedome(F)Fstatistice(lag)maximum lage(rank)rank ofe(V)Macrose(cmd) neweye(cmdline)command as typede(depvar)name of dependent variablee(wtype)weight typee(wexp)weight expressione(title)title in estimation outpute(vcetype)title used to label Std. (properties) b Ve(estatcmd)program used to implementestate(predict)program used to implementpredicte(asbalanced)factor variablesfvsetasasbalancede(asobserved)f actor variablesfvsetasasobservedMatricese(b)co efficient vectore(Cns)constraints matrixe(V)variance covariance matrix of the estimatorsFunctionse(sample)marks estimation sampleMethods and formulasneweycalculates the estimates OLS= (X X) 1X y Var( OLS) = (X X) 1X X(X X) 1 That is, the coefficient estimates are simply those ofOLSlinear (0)(no autocorrelation), the variance estimates are calculated using the White formulation:X X=X 0X=nn k i e2ix ixiHere ei=yi xi OLS, wherexiis theith row of theXmatrix,nis the number of observations,andkis the number of predictors in the model, including the constant if there is one.

6 The aboveformula is the same as that used byregress, vce(robust)with the Regression -like formula (thedefault) for the multiplierqc; seeMethods and formulasof [R] Regression with newey West standard errors 5 Forlag(m),m >0, the variance estimates are calculated using the newey West (1987)formulationX X=X 0X+nn km l=1(1 lm+ 1)n t=l+1 et et l(x txt l+x t lxt)wherextis the row of theXmatrix observed at timet. Whitney K. newey (1954 ) earned degrees in economics at Brigham Young University andMIT. After a period at Princeton, he returned toMITas a professor in 1990. His interests intheoretical and applied econometrics include bootstrapping, nonparametric estimation of models,semiparametric models, and choosing the number of instrumental D. West (1953 ) earned a bachelor s degree in economics and mathematics at WesleyanUniversity and then a PhD in economics atMIT.

7 After a period at Princeton, he joined theUniversity of Wisconsin in 1988. His interests include empirical macroeconomics and time-series econometrics. ReferencesHardin, J. W. 1997. sg72: newey West standard errors for probit, logit, and poisson Technical Bulletin39: 32 35. Reprinted inStata Technical Bulletin Reprints, vol. 7, pp. 182 186. College Station, TX: Stata , W. K., and K. D. West. 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistentcovariance : 703 , Q., and N. Wu. 2012. Long-run covariance and its applications in cointegration Journal12:515 , H. L., Jr. 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for : 817 see[TS] newey postestimation Postestimation tools for newey [TS]arima ARIMA, ARMAX, and other dynamic Regression models[TS]forecast Econometric model forecasting[TS]tsset Declare data to be time-series data[R]regress Linear Regression [U] 20 Estimation and postestimation commands