| {smcl} | |
| {* 30July2015}{...} | |
| {hline} | |
| help for {hi:ivreg2} | |
| {hline} | |
| {title:Extended instrumental variables/2SLS, GMM and AC/HAC, LIML and k-class regression} | |
| {p 4}Full syntax | |
| {p 8 14}{cmd:ivreg2} {it:depvar} [{it:varlist1}] | |
| {cmd:(}{it:varlist2}{cmd:=}{it:varlist_iv}{cmd:)} [{it:weight}] | |
| [{cmd:if} {it:exp}] [{cmd:in} {it:range}] | |
| {bind:[{cmd:,} {cmd:gmm2s}} | |
| {cmd:bw(}{it:#}{cmd:)} | |
| {cmd:kernel(}{it:string}{cmd:)} | |
| {cmd:dkraay(}{it:integer}{cmd:)} | |
| {cmd:kiefer} | |
| {cmd:liml} | |
| {cmd:fuller(}{it:#}{cmd:)} | |
| {cmd:kclass(}{it:#}{cmd:)} | |
| {cmd:coviv} | |
| {cmd:cue} | |
| {cmd:b0}{cmd:(}{it:matrix}{cmd:)} | |
| {cmdab:r:obust} | |
| {cmdab:cl:uster}{cmd:(}{it:varlist}{cmd:)} | |
| {cmd:orthog(}{it:varlist_ex}{cmd:)} | |
| {cmd:endog(}{it:varlist_en}{cmd:)} | |
| {cmdab:red:undant(}{it:varlist_ex}{cmd:)} | |
| {cmd:partial(}{it:varlist}{cmd:)} | |
| {cmdab:sm:all} | |
| {cmdab:noc:onstant} | |
| {cmd:center} | |
| {cmd:smatrix}{cmd:(}{it:matrix}{cmd:)} | |
| {cmd:wmatrix}{cmd:(}{it:matrix}{cmd:)} | |
| {cmd:first} {cmd:ffirst} {cmd:savefirst} {cmdab:savefp:refix}{cmd:(}{it:prefix}{cmd:)} | |
| {cmd:sfirst} {cmd:savesfirst} {cmdab:savesfp:refix}{cmd:(}{it:prefix}{cmd:)} | |
| {cmd:rf} {cmd:saverf} {cmdab:saverfp:refix}{cmd:(}{it:prefix}{cmd:)} | |
| {cmd:nocollin} {cmd:noid} | |
| {cmdab:l:evel}{cmd:(}{it:#}{cmd:)} | |
| {cmd:bvclean} | |
| {cmdab:nohe:ader} | |
| {cmdab:nofo:oter} | |
| {cmdab:ef:orm}{cmd:(}{it:string}{cmd:)} | |
| {cmdab:dep:name}{cmd:(}{it:varname}{cmd:)} | |
| {bind:{cmd:plus} ]} | |
| {p 4}Replay syntax | |
| {p 8 14}{cmd:ivreg2} | |
| {bind:[{cmd:,} {cmd:first}} {cmd:sfirst} | |
| {cmd:ffirst} {cmd:rf} | |
| {cmdab:l:evel}{cmd:(}{it:#}{cmd:)} | |
| {cmdab:nohe:ader} | |
| {cmdab:nofo:oter} | |
| {cmdab:ef:orm}{cmd:(}{it:string}{cmd:)} | |
| {cmdab:dep:name}{cmd:(}{it:varname}{cmd:)} | |
| {cmd:plus} ]} | |
| {p 4}Version syntax | |
| {p 8 14}{cmd:ivreg2}, {cmd:version} | |
| {p}{cmd:ivreg2} is compatible with Stata version 8 or later. | |
| The most-up-to-date implementation of {cmd:ivreg2} requires | |
| Stata version 11 or later. | |
| If {cmd:ivreg2} is called under earlier versions of Stata, | |
| it will run a legacy version {cmd:ivreg2x}. | |
| See below under {help ivreg2##s_versions:Running ivreg2 under earlier versions of Stata} | |
| for details. | |
| {p}{cmd:ivreg2} may be used with time-series or panel data, | |
| in which case the data must be {cmd:tsset} | |
| before using {cmd:ivreg2}; see help {help tsset}. | |
| {p}All {it:varlists} may contain time-series operators or factor variables; | |
| see help {help varlist}. | |
| {p}{cmd:by}, {cmd:rolling}, {cmd:statsby}, {cmd:xi}, | |
| {cmd:bootstrap} and {cmd:jackknife} are allowed; see help {help prefix}. | |
| {p}{cmd:aweight}s, {cmd:fweight}s, {cmd:iweight}s and {cmd:pweight}s | |
| are allowed; see help {help weights}. | |
| {p}The syntax of {help predict} following {cmd:ivreg2} is | |
| {p 8 16}{cmd:predict} [{it:type}] {it:newvarname} [{cmd:if} {it:exp}] | |
| [{cmd:in} {it:range}] [{cmd:,} {it:statistic}] | |
| {p}where {it:statistic} is | |
| {p 8 23}{cmd:xb}{space 11}fitted values; the default{p_end} | |
| {p 8 23}{cmdab:r:esiduals}{space 4}residuals{p_end} | |
| {p 8 23}{cmd:stdp}{space 9}standard error of the prediction{p_end} | |
| {p}These statistics are available both in and out of sample; | |
| type "{cmd:predict} {it:...} {cmd:if e(sample)} {it:...}" | |
| if wanted only for the estimation sample. | |
| {title:Contents} | |
| {p 2}{help ivreg2##s_description:Description}{p_end} | |
| {p 2}{help ivreg2##s_robust:Robust, cluster and 2-way cluster, AC, HAC, and cluster+HAC SEs and statistics}{p_end} | |
| {p 2}{help ivreg2##s_gmm:GMM estimation}{p_end} | |
| {p 2}{help ivreg2##s_liml:LIML, k-class and GMM-CUE estimation}{p_end} | |
| {p 2}{help ivreg2##s_sumopt:Summary of robust, HAC, AC, GMM, LIML and CUE options}{p_end} | |
| {p 2}{help ivreg2##s_overid:Testing overidentifying restrictions}{p_end} | |
| {p 2}{help ivreg2##s_endog:Testing subsets of regressors and instruments for endogeneity}{p_end} | |
| {p 2}{help ivreg2##s_relevance:Tests of under- and weak identification}{p_end} | |
| {p 2}{help ivreg2##s_redundancy:Testing instrument redundancy}{p_end} | |
| {p 2}{help ivreg2##s_first:First-stage regressions, identification, and weak-id-robust inference}{p_end} | |
| {p 2}{help ivreg2##s_rf:Reduced form estimates}{p_end} | |
| {p 2}{help ivreg2##s_partial:Partialling-out exogenous regressors}{p_end} | |
| {p 2}{help ivreg2##s_ols:OLS and Heteroskedastic OLS (HOLS) estimation}{p_end} | |
| {p 2}{help ivreg2##s_collin:Collinearities}{p_end} | |
| {p 2}{help ivreg2##s_speed:Speed options: nocollin and noid}{p_end} | |
| {p 2}{help ivreg2##s_small:Small sample corrections}{p_end} | |
| {p 2}{help ivreg2##s_options:Options summary}{p_end} | |
| {p 2}{help ivreg2##s_versions:Running ivreg2 under earlier versions of Stata}{p_end} | |
| {p 2}{help ivreg2##s_macros:Remarks and saved results}{p_end} | |
| {p 2}{help ivreg2##s_examples:Examples}{p_end} | |
| {p 2}{help ivreg2##s_refs:References}{p_end} | |
| {p 2}{help ivreg2##s_acknow:Acknowledgements}{p_end} | |
| {p 2}{help ivreg2##s_citation:Authors}{p_end} | |
| {p 2}{help ivreg2##s_citation:Citation of ivreg2}{p_end} | |
| {marker s_description}{title:Description} | |
| {p}{cmd:ivreg2} implements a range of single-equation estimation methods | |
| for the linear regression model: OLS, instrumental | |
| variables (IV, also known as two-stage least squares, 2SLS), | |
| the generalized method of moments (GMM), | |
| limited-information maximum likelihood (LIML), and k-class estimators. | |
| In the language of IV/GMM, {it:varlist1} are the exogenous | |
| regressors or "included instruments", | |
| {it:varlist_iv} are the exogenous variables excluded | |
| from the regression or "excluded instruments", | |
| and {it:varlist2} the endogenous regressors that are being "instrumented". | |
| {p}{cmd:ivreg2} will also estimate linear regression models using | |
| robust (heteroskedastic-consistent), | |
| autocorrelation-consistent (AC), | |
| heteroskedastic and autocorrelation-consistent (HAC) | |
| and cluster-robust variance estimates. | |
| {p}{cmd:ivreg2} is an alternative to Stata's official {cmd:ivregress}. | |
| Its features include: | |
| two-step feasible GMM estimation ({cmd:gmm2s} option) | |
| and continuously-updated GMM estimation ({cmd:cue} option); | |
| LIML and k-class estimation; | |
| automatic output of overidentification and underidentification test statistics; | |
| C statistic test of exogeneity of subsets of instruments | |
| ({cmd:orthog()} option); | |
| endogeneity tests of endogenous regressors | |
| ({cmd:endog()} option); | |
| test of instrument redundancy | |
| ({cmd:redundant()} option); | |
| kernel-based autocorrelation-consistent (AC) | |
| and heteroskedastic and autocorrelation consistent (HAC) standard errors | |
| and covariance estimation ({cmd:bw(}{it:#}{cmd:)} option), | |
| with user-specified choice of kernel ({cmd:kernel()} option); | |
| two-level {cmd:cluster}-robust standard errors and statistics; | |
| default reporting of large-sample statistics | |
| (z and chi-squared rather than t and F); | |
| {cmd:small} option to report small-sample statistics; | |
| first-stage regressions reported with various tests and statistics for | |
| identification and instrument relevance; | |
| {cmd:ffirst} option to report only these identification statistics | |
| and not the first-stage regression results themselves. | |
| {cmd:ivreg2} can also be used for ordinary least squares (OLS) estimation | |
| using the same command syntax as official {cmd:regress} and {cmd:newey}. | |
| {marker s_robust}{dlgtab:Robust, cluster and 2-level cluster, AC, HAC, and cluster+HAC SEs and statistics} | |
| {p}The standard errors and test statistics reported by {cmd:ivreg2} can be made consistent | |
| to a variety of violations of the assumption of i.i.d. errors. | |
| When these options are combined with | |
| either the {cmd:gmm2s} or {cmd:cue} options (see below), | |
| the parameter estimators reported are also efficient | |
| in the presence of the same violation of i.i.d. errors. | |
| {p}The options for SEs and statistics are:{break} | |
| {bind:(1) {cmd:robust}} causes {cmd:ivreg2} to report SEs and statistics that are | |
| robust to the presence of arbitrary heteroskedasticity.{break} | |
| {bind:(2) {cmd:cluster}({it:varname})} SEs and statistics are robust to both | |
| arbitrary heteroskedasticity and arbitrary intra-group correlation, | |
| where {it:varname} identifies the group. | |
| See the relevant Stata manual entries on obtaining robust covariance estimates | |
| for further details.{break} | |
| {bind:(3) {cmd:cluster}({it:varname1 varname2})} provides 2-way clustered SEs | |
| and statistics (Cameron et al. 2006, Thompson 2009) | |
| that are robust to arbitrary heteroskedasticity and intra-group correlation | |
| with respect to 2 non-nested categories defined by {it:varname1} and {it:varname2}. | |
| See below for a detailed description.{break} | |
| {bind:(4) {cmd:bw(}{it:#}{cmd:)}} requests AC SEs and statistics that are | |
| robust to arbitrary autocorrelation.{break} | |
| {bind:(5) {cmd:bw(}{it:#}{cmd:)}} combined with {cmd:robust} | |
| requests HAC SEs and statistics that are | |
| robust to both arbitrary heteroskedasticity and arbitrary autocorrelation.{break} | |
| {bind:(6) {cmd:bw(}{it:#}{cmd:)}} combined with {cmd:cluster}({it:varname}) | |
| is allowed with either 1- or 2-level clustering if the data are panel data | |
| that are {cmd:tsset} on the time variable {it:varname}. | |
| Following Driscoll and Kray (1998), | |
| the SEs and statistics reported will be robust to disturbances | |
| that are common to panel units and that are persistent, i.e., autocorrelated.{break} | |
| {bind:(7) {cmd:dkraay(}{it:#}{cmd:)}} is a shortcut for the Driscoll-Kraay SEs | |
| for panel data in (6). | |
| It is equivalent to clustering on the {cmd:tsset} time variable | |
| and the bandwidth supplied as {it:#}. | |
| The default kernel Bartlett kernel can be overridden with the {cmd:kernel} option.{break} | |
| {bind:(8) {cmd:kiefer}} implements SEs and statistics for panel data | |
| that are robust to arbitrary intra-group autocorrelation | |
| (but {it:not} heteroskedasticity) as per Kiefer (1980). | |
| It is equivalent to to specifying the truncated kernel with {cmd:kernel(tru)} | |
| and {cmd:bw(}{it:#}{cmd:)} where {it:#} is the full length of the panel. | |
| {p}Details: | |
| {p}{cmd:cluster}({it:varname1 varname2}) provides 2-way cluster-robust SEs | |
| and statistics as proposed by Cameron, Gelbach and Miller (2006) and Thompson (2009). | |
| "Two-way cluster-robust" means the SEs and statistics | |
| are robust to arbitrary within-group correlation in two distinct non-nested categories | |
| defined by {it:varname1} and {it:varname2}. | |
| A typical application would be panel data where one "category" is the panel | |
| and the other "category" is time; | |
| the resulting SEs are robust | |
| to arbitrary within-panel autocorrelation (clustering on panel id) | |
| and to arbitrary contemporaneous cross-panel correlation (clustering on time). | |
| There is no point in using 2-way cluster-robust SEs if the categories are nested, | |
| because the resulting SEs are equivalent to clustering on the larger category. | |
| {it:varname1} and {it:varname2} do not have to | |
| uniquely identify observations. | |
| The order of {it:varname1} and {it:varname2} does not matter for the results, | |
| but processing may be faster if the category with the larger number of categories | |
| (typically the panel dimension) is listed first. | |
| {p}Cameron, Gelbach and Miller (2006) show how this approach can accommodate | |
| multi-way clustering, where the number of different non-nested categories is arbitary. | |
| Their Stata command {cmd:cgmreg} implements 2-way and multi-way clustering | |
| for OLS estimation. | |
| The two-way clustered variance-covariance estimator | |
| is calculated using 3 different VCEs: one clustered on {it:varname1}, | |
| the second clustered on {it:varname2}, and the third clustered on the | |
| intersection of {it:varname1} and {it:varname2}. | |
| Cameron et al. (2006, pp. 8-9) discuss two possible small-sample adjustments | |
| using the number of clusters in each category. | |
| {cmd:cgmreg} uses one method (adjusting the 3 VCEs separately based on | |
| the number of clusters in the categories VCE clusters on); | |
| {cmd:ivreg2} uses the second (adjusting the final 2-way cluster-robust VCE | |
| using the smaller of the two numbers of clusters). | |
| For this reason, {cmd:ivreg2} and {cmd:cgmreg} will produce slightly different SEs. | |
| See also {help ivreg2##s_small:small sample corrections} below. | |
| {p}{cmd:ivreg2} allows a variety of options for kernel-based HAC and AC estimation. | |
| The {cmd:bw(}{it:#}{cmd:)} option sets the bandwidth used in the estimation | |
| and {cmd:kernel(}{it:string}{cmd:)} is the kernel used; | |
| the default kernel is the Bartlett kernel, | |
| also known in econometrics as Newey-West (see help {help newey}). | |
| The full list of kernels available is (abbreviations in parentheses): | |
| Bartlett (bar); Truncated (tru); Parzen (par); Tukey-Hanning (thann); | |
| Tukey-Hamming (thamm); Daniell (dan); Tent (ten); and Quadratic-Spectral (qua or qs). | |
| When using the Bartlett, Parzen, or Quadratic spectral kernels, the automatic | |
| bandwidth selection procedure of Newey and West (1994) can be chosen | |
| by specifying {cmd:bw(}{it:auto}{cmd:)}. | |
| {cmd:ivreg2} can also be used for kernel-based estimation | |
| with panel data, i.e., a cross-section of time series. | |
| Before using {cmd:ivreg2} for kernel-based estimation | |
| of time series or panel data, | |
| the data must be {cmd:tsset}; see help {help tsset}. | |
| {p}Following Driscoll and Kraay (1998), | |
| {cmd:bw(}{it:#}{cmd:)} combined with {cmd:cluster}({it:varname}) | |
| and applied to panel data produces SEs that are | |
| robust to arbitary common autocorrelated disturbances. | |
| The data must be {cmd:tsset} with the time variable specified as {it:varname}. | |
| Driscoll-Kraay SEs also can be specified using the {cmd:dkraay(}{it:#}{cmd:)}} option, | |
| where {it:#} is the bandwidth. | |
| The default Bartlett kernel can be overridden with the {cmd:kernel} option. | |
| Note that the Driscoll-Kraay variance-covariance estimator is a large-T estimator, | |
| i.e., the panel should have a long-ish time-series dimension. | |
| {p}Used with 2-way clustering as per Thompson (2009), | |
| {cmd:bw(}{it:#}{cmd:)} combined with {cmd:cluster}({it:varname}) | |
| provides SEs and statistics that are robust | |
| to autocorrelated within-panel disturbances (clustering on panel id) | |
| and to autocorrelated across-panel disturbances (clustering on time | |
| combined with kernel-based HAC). | |
| The approach proposed by Thompson (2009) can be implemented in {cmd:ivreg2} | |
| by choosing the truncated kernel {cmd:kernel(}{it:tru}{cmd:)} | |
| and {cmd:bw(}{it:#}{cmd:)}, where the researcher knows or assumes | |
| that the common autocorrelated disturbances can be ignored after {it:#} periods. | |
| {p}{cmd:Important:} Users should be aware of the asymptotic requirements | |
| for the consistency of the chosen VCE. | |
| In particular: consistency of the 1-way cluster-robust VCE requires | |
| the number of clusters to go off to infinity; | |
| consistency of the 2-way cluster-robust VCE requires the numbers of | |
| clusters in both categories to go off to infinity; | |
| consistency of kernel-robust VCEs requires the numbers of | |
| observations in the time dimension to go off to infinity. | |
| See Angrist and Pischke (2009), Cameron et al. (2006) and Thompson (2009) | |
| for detailed discussions of the performance of the cluster-robust VCE | |
| when the numbers of clusters is small. | |
| {marker s_gmm}{dlgtab:GMM estimation} | |
| {p}When combined with the above options, the {cmd:gmm2s} option generates | |
| efficient estimates of the coefficients as well as consistent | |
| estimates of the standard errors. | |
| The {cmd:gmm2s} option implements the two-step efficient | |
| generalized method of moments (GMM) estimator. | |
| The efficient GMM estimator minimizes the GMM criterion function | |
| J=N*g'*W*g, where N is the sample size, | |
| g are the orthogonality or moment conditions | |
| (specifying that all the exogenous variables, or instruments, | |
| in the equation are uncorrelated with the error term) | |
| and W is a weighting matrix. | |
| In two-step efficient GMM, the efficient or optimal weighting matrix | |
| is the inverse of an estimate of the covariance matrix of orthogonality conditions. | |
| The efficiency gains of this estimator relative to the | |
| traditional IV/2SLS estimator derive from the use of the optimal | |
| weighting matrix, the overidentifying restrictions of the model, | |
| and the relaxation of the i.i.d. assumption. | |
| For an exactly-identified model, | |
| the efficient GMM and traditional IV/2SLS estimators coincide, | |
| and under the assumptions of conditional homoskedasticity and independence, | |
| the efficient GMM estimator is the traditional IV/2SLS estimator. | |
| For further details, see Hayashi (2000), pp. 206-13 and 226-27. | |
| {p}The {cmd:center} option specifies that the moments in the GMM weighting matrix | |
| are centered so that they have mean zero. | |
| There is some evidence that the use of centered moments leads to better | |
| finite-sample performance; see e.g. Hall (2005), pp. 131-8 and 145-8. | |
| {p}The {cmd:wmatrix} option allows the user to specify a weighting matrix | |
| rather than computing the optimal weighting matrix. | |
| Estimation with the {cmd:wmatrix} option yields a possibly inefficient GMM estimator. | |
| {cmd:ivreg2} will use this inefficient estimator as the first-step GMM estimator | |
| in two-step efficient GMM when combined with the {cmd:gmm2s} option; | |
| otherwise, {cmd:ivreg2} reports the regression results | |
| using this inefficient GMM estimator. | |
| {p}The {cmd:smatrix} option allows the user to directly | |
| specify the matrix S, the covariance matrix of orthogonality conditions. | |
| {cmd:ivreg2} will use this matrix in the calculation of the variance-covariance | |
| matrix of the estimator, the J statistic, | |
| and, if the {cmd:gmm2s} option is specified, | |
| the two-step efficient GMM coefficients. | |
| The {cmd:smatrix} can be useful for guaranteeing a positive test statistic | |
| in user-specified "GMM-distance tests" (see {help ivreg2##s_endog:below}). | |
| For further details, see Hayashi (2000), pp. 220-24. | |
| {marker s_liml}{dlgtab:LIML, k-class and GMM-CUE estimation} | |
| {marker liml}{p} Maximum-likelihood estimation of a single equation of this form | |
| (endogenous RHS variables and excluded instruments) | |
| is known as limited-information maximum likelihood or LIML. | |
| The overidentifying restrictions test | |
| reported after LIML estimation is the Anderson-Rubin (1950) overidentification | |
| statistic in a homoskedastic context. | |
| LIML, OLS and IV/2SLS are examples of k-class estimators. | |
| LIML is a k-class estimator with k=the LIML eigenvalue lambda; | |
| 2SLS is a k-class estimator with k=1; | |
| OLS is a k-class esimator with k=0. | |
| Estimators based on other values of k have been proposed. | |
| Fuller's modified LIML (available with the {cmd:fuller(}{it:#}{cmd:)} option) | |
| sets k = lambda - alpha/(N-L), where lambda is the LIML eigenvalue, | |
| L = number of instruments (L1 excluded and L2 included), | |
| and the Fuller parameter alpha is a user-specified positive constant. | |
| Nagar's bias-adjusted 2SLS estimator can be obtained with the | |
| {cmd:kclass(}{it:#}{cmd:)} option by setting | |
| k = 1 + (L-K)/N, where L-K = number of overidentifying restrictions, | |
| K = number of regressors (K1 endogenous and K2=L2 exogenous) | |
| and N = the sample size. | |
| For a discussion of LIML and k-class estimators, | |
| see Davidson and MacKinnon (1993, pp. 644-51). | |
| {p} The GMM generalization of the LIML estimator | |
| to the case of possibly heteroskedastic | |
| and autocorrelated disturbances | |
| is the "continuously-updated" GMM estimator or CUE | |
| of Hansen, Heaton and Yaron (1996). | |
| The CUE estimator directly maximizes the GMM objective function | |
| J=N*g'*W(b_cue)*g, where W(b_cue) is an optimal weighting matrix | |
| that depends on the estimated coefficients b_cue. | |
| {cmd:cue}, combined with {cmd:robust}, {cmd:cluster}, and/or {cmd:bw}, | |
| generates coefficient estimates that are efficient in the presence | |
| of the corresponding deviations from homoskedasticity. | |
| Specifying {cmd:cue} with no other options | |
| is equivalent to the combination of the options {cmd:liml} and {cmd:coviv}. | |
| The CUE estimator requires numerical optimization methods, | |
| and the implementation here uses Mata's {cmd:optimize} routine. | |
| The starting values are either IV or two-step efficient GMM | |
| coefficient estimates. | |
| If the user wants to evaluate the CUE objective function at | |
| an arbitrary user-defined coefficient vector instead of having {cmd:ivreg2} | |
| find the coefficient vector that minimizes the objective function, | |
| the {cmd:b0(}{it:matrix}{cmd:)} option can be used. | |
| The value of the CUE objective function at {cmd:b0} | |
| is the Sargan or Hansen J statistic reported in the output. | |
| {marker s_sumopt}{dlgtab:Summary of robust, HAC, AC, GMM, LIML and CUE options} | |
| Estimator {col 20}No VCE option specificed {col 65}VCE option | |
| option {col 60}{cmd:robust}, {cmd:cluster}, {cmd:bw}, {cmd:kernel} | |
| {hline} | |
| (none){col 15}IV/2SLS{col 60}IV/2SLS with | |
| {col 15}SEs consistent under homoskedasticity{col 60}robust SEs | |
| {cmd:liml}{col 15}LIML{col 60}LIML with | |
| {col 15}SEs consistent under homoskedasticity{col 60}robust SEs | |
| {cmd:gmm2s}{col 15}IV/2SLS{col 60}Two-step GMM with | |
| {col 15}SEs consistent under homoskedasticity{col 60}robust SEs | |
| {cmd:cue}{col 15}LIML{col 60}CUE GMM with | |
| {col 15}SEs consistent under homoskedasticity{col 60}robust SEs | |
| {cmd:kclass}{col 15}k-class estimator{col 60}k-class estimator with | |
| {col 15}SEs consistent under homoskedasticity{col 60}robust SEs | |
| {cmd:wmatrix}{col 15}Possibly inefficient GMM{col 60}Ineff GMM with | |
| {col 15}SEs consistent under homoskedasticity{col 60}robust SEs | |
| {cmd:gmm2s} + {col 15}Two-step GMM{col 60}Two-step GMM with | |
| {cmd:wmatrix}{col 15}with user-specified first step{col 60}robust SEs | |
| {col 15}SEs consistent under homoskedasticity | |
| {p}With the {cmd:bw} or {cmd:bw} and {cmd:kernel} VCE options, | |
| SEs are autocorrelation-robust (AC). | |
| Combining the {cmd:robust} option with {cmd:bw}, SEs are heteroskedasticity- and | |
| autocorrelation-robust (HAC). | |
| {p}For further details, see Hayashi (2000), pp. 206-13 and 226-27 | |
| (on GMM estimation), Wooldridge (2002), p. 193 (on cluster-robust GMM), | |
| and Hayashi (2000), pp. 406-10 or Cushing and McGarvey (1999) | |
| (on kernel-based covariance estimation). | |
| {marker s_overid}{marker overidtests}{dlgtab:Testing overidentifying restrictions} | |
| {p}The Sargan-Hansen test is a test of overidentifying restrictions. | |
| The joint null hypothesis is that the instruments are valid | |
| instruments, i.e., uncorrelated with the error term, | |
| and that the excluded instruments are correctly excluded from the estimated equation. | |
| Under the null, the test statistic is distributed as chi-squared | |
| in the number of (L-K) overidentifying restrictions. | |
| A rejection casts doubt on the validity of the instruments. | |
| For the efficient GMM estimator, the test statistic is | |
| Hansen's J statistic, the minimized value of the GMM criterion function. | |
| For the 2SLS estimator, the test statistic is Sargan's statistic, | |
| typically calculated as N*R-squared from a regression of the IV residuals | |
| on the full set of instruments. | |
| Under the assumption of conditional homoskedasticity, | |
| Hansen's J statistic becomes Sargan's statistic. | |
| The J statistic is consistent in the presence of heteroskedasticity | |
| and (for HAC-consistent estimation) autocorrelation; | |
| Sargan's statistic is consistent if the disturbance is homoskedastic | |
| and (for AC-consistent estimation) if it is also autocorrelated. | |
| With {cmd:robust}, {cmd:bw} and/or {cmd:cluster}, | |
| Hansen's J statistic is reported. | |
| In the latter case the statistic allows observations | |
| to be correlated within groups. | |
| For further discussion see e.g. Hayashi (2000, pp. 227-8, 407, 417). | |
| {p}The Sargan statistic can also be calculated after | |
| {cmd:ivreg} or {cmd:ivreg2} by the command {cmd:overid}. | |
| The features of {cmd:ivreg2} that are unavailable in {cmd:overid} | |
| are the J statistic and the C statistic; | |
| the {cmd:overid} options unavailable in {cmd:ivreg2} | |
| are various small-sample and pseudo-F versions of Sargan's statistic | |
| and its close relative, Basmann's statistic. | |
| See help {help overid} (if installed). | |
| {marker s_endog}{dlgtab:Testing subsets of regressors and instruments for endogeneity} | |
| {marker ctest}{p}The C statistic | |
| (also known as a "GMM distance" | |
| or "difference-in-Sargan" statistic) | |
| implemented using the {cmd:orthog} option, | |
| allows a test of a subset of the orthogonality conditions, i.e., | |
| it is a test of the exogeneity of one or more instruments. | |
| It is defined as | |
| the difference of the Sargan-Hansen statistic | |
| of the equation with the smaller set of instruments | |
| (valid under both the null and alternative hypotheses) | |
| and the equation with the full set of instruments, | |
| i.e., including the instruments whose validity is suspect. | |
| Under the null hypothesis that | |
| both the smaller set of instruments | |
| and the additional, suspect instruments are valid, | |
| the C statistic is distributed as chi-squared | |
| in the number of instruments tested. | |
| Note that failure to reject the null hypothesis | |
| requires that the full set of orthogonality conditions be valid; | |
| the C statistic and the Sargan-Hansen test statistics | |
| for the equations with both the smaller and full set of instruments | |
| should all be small. | |
| The instruments tested may be either excluded or included exogenous variables. | |
| If excluded exogenous variables are being tested, | |
| the equation that does not use these orthogonality conditions | |
| omits the suspect instruments from the excluded instruments. | |
| If included exogenous variables are being tested, | |
| the equation that does not use these orthogonality conditions | |
| treats the suspect instruments as included endogenous variables. | |
| To guarantee that the C statistic is non-negative in finite samples, | |
| the estimated covariance matrix of the full set orthogonality conditions | |
| is used to calculate both Sargan-Hansen statistics | |
| (in the case of simple IV/2SLS, this amounts to using the MSE | |
| from the unrestricted equation to calculate both Sargan statistics). | |
| If estimation is by LIML, the C statistic reported | |
| is now based on the Sargan-Hansen test statistics from | |
| the restricted and unrestricted equation. | |
| For further discussion, see Hayashi (2000), pp. 218-22 and pp. 232-34. | |
| {marker endogtest}{p}Endogeneity tests of one or more endogenous regressors | |
| can implemented using the {cmd:endog} option. | |
| Under the null hypothesis that the specified endogenous regressors | |
| can actually be treated as exogenous, the test statistic is distributed | |
| as chi-squared with degrees of freedom equal to the number of regressors tested. | |
| The endogeneity test implemented by {cmd:ivreg2}, is, like the C statistic, | |
| defined as the difference of two Sargan-Hansen statistics: | |
| one for the equation with the smaller set of instruments, | |
| where the suspect regressor(s) are treated as endogenous, | |
| and one for the equation with the larger set of instruments, | |
| where the suspect regressors are treated as exogenous. | |
| Also like the C statistic, the estimated covariance matrix used | |
| guarantees a non-negative test statistic. | |
| Under conditional homoskedasticity, | |
| this endogeneity test statistic is numerically equal to | |
| a Hausman test statistic; see Hayashi (2000, pp. 233-34). | |
| The endogeneity test statistic can also be calculated after | |
| {cmd:ivreg} or {cmd:ivreg2} by the command {cmd:ivendog}. | |
| Unlike the Durbin-Wu-Hausman tests reported by {cmd:ivendog}, | |
| the {cmd:endog} option of {cmd:ivreg2} can report test statistics | |
| that are robust to various violations of conditional homoskedasticity; | |
| the {cmd:ivendog} option unavailable in {cmd:ivreg2} | |
| is the Wu-Hausman F-test version of the endogeneity test. | |
| See help {help ivendog} (if installed). | |
| {marker s_relevance}{dlgtab:Tests of under- and weak identification} | |
| {marker idtest}{p}{cmd:ivreg2} automatically reports tests of | |
| both underidentification and weak identification. | |
| The underidentification test is an LM test of whether the equation is identified, | |
| i.e., that the excluded instruments are "relevant", | |
| meaning correlated with the endogenous regressors. | |
| The test is essentially the test of the rank of a matrix: | |
| under the null hypothesis that the equation is underidentified, | |
| the matrix of reduced form coefficients on the L1 excluded instruments | |
| has rank=K1-1 where K1=number of endogenous regressors. | |
| Under the null, | |
| the statistic is distributed as chi-squared | |
| with degrees of freedom=(L1-K1+1). | |
| A rejection of the null indicates that the matrix is full column rank, | |
| i.e., the model is identified. | |
| {p}For a test of whether a particular endogenous regressor alone is identified, | |
| see the discussion {help ivreg2##swstats:below} of the | |
| Sanderson-Windmeijer (2015) and Angrist-Pischke (2009) procedures. | |
| {p}When errors are assumed to be i.i.d., | |
| {cmd:ivreg2} automatically reports an LM version of | |
| the Anderson (1951) canonical correlations test. | |
| Denoting the minimum eigenvalue of the canonical correlations as CCEV, | |
| the smallest canonical correlation between the K1 endogenous regressors | |
| and the L1 excluded instruments | |
| (after partialling out the K2=L2 exogenous regressors) | |
| is sqrt(CCEV), | |
| and the Anderson LM test statistic is N*CCEV, | |
| i.e., N times the square of the smallest canonical correlation. | |
| With the {cmd:first} or {cmd:ffirst} options, | |
| {cmd:ivreg2} also reports the closely-related | |
| Cragg-Donald (1993) Wald test statistic. | |
| Again assuming i.i.d. errors, | |
| and denoting the minimum eigenvalue of the Cragg-Donald statistic as CDEV, | |
| CDEV=CCEV/(1-CCEV), | |
| and the Cragg-Donald Wald statistic is N*CDEV. | |
| Like the Anderson LM statistic, the Cragg-Donald Wald statistic | |
| is distributed as chi-squred with (L1-K1+1) degrees of freedom. | |
| Note that a result of rejection of the null | |
| should be treated with caution, | |
| because weak instrument problems may still be present. | |
| See Hall et al. (1996) for a discussion of this test, | |
| and below for discussion of testing for the presence of weak instruments. | |
| {p}When the i.i.d. assumption is dropped | |
| and {cmd:ivreg2} reports heteroskedastic, AC, HAC | |
| or cluster-robust statistics, | |
| the Anderson LM and Cragg-Donald Wald statistics are no longer valid. | |
| In these cases, {cmd:ivreg2} reports the LM and Wald versions | |
| of the Kleibergen-Paap (2006) rk statistic, | |
| also distributed as chi-squared with (L1-K1+1) degrees of freedom. | |
| The rk statistic can be seen as a generalization of these tests | |
| to the case of non-i.i.d. errors; | |
| see Kleibergen and Paap (2006) for discussion, | |
| and Kleibergen and Schaffer (2007) for a Stata implementation, {cmd:ranktest}. | |
| {cmd:ivreg2} requires {cmd:ranktest} to be installed, | |
| and will prompt the user to install it if necessary. | |
| If {cmd:ivreg2} is invoked with the {cmd:robust} option, | |
| the rk underidentification test statistics will be heteroskedastic-robust, | |
| and similarly with {cmd:bw} and {cmd:cluster}. | |
| {marker widtest}{p}"Weak identification" arises when the excluded instruments are correlated | |
| with the endogenous regressors, but only weakly. | |
| Estimators can perform poorly when instruments are weak, | |
| and different estimators are more robust to weak instruments (e.g., LIML) | |
| than others (e.g., IV); | |
| see, e.g., Stock and Yogo (2002, 2005) for further discussion. | |
| When errors are assumed to be i.i.d., | |
| the test for weak identification automatically reported | |
| by {cmd:ivreg2} is an F version of the Cragg-Donald Wald statistic, (N-L)/L1*CDEV, | |
| where L is the number of instruments and L1 is the number of excluded instruments. | |
| Stock and Yogo (2005) have compiled critical values | |
| for the Cragg-Donald F statistic for | |
| several different estimators (IV, LIML, Fuller-LIML), | |
| several different definitions of "perform poorly" (based on bias and test size), | |
| and a range of configurations (up to 100 excluded instruments | |
| and up to 2 or 3 endogenous regressors, | |
| depending on the estimator). | |
| {cmd:ivreg2} will report the Stock-Yogo critical values | |
| if these are available; | |
| missing values mean that the critical values | |
| haven't been tabulated or aren't applicable. | |
| See Stock and Yogo (2002, 2005) for details. | |
| {p}When the i.i.d. assumption is dropped | |
| and {cmd:ivreg2} is invoked with the {cmd:robust}, {cmd:bw} or {cmd:cluster} options, | |
| the Cragg-Donald-based weak instruments test is no longer valid. | |
| {cmd:ivreg2} instead reports a correspondingly-robust | |
| Kleibergen-Paap Wald rk F statistic. | |
| The degrees of freedom adjustment for the rk statistic is (N-L)/L1, | |
| as with the Cragg-Donald F statistic, | |
| except in the cluster-robust case, | |
| when the adjustment is N/(N-1) * (N_clust-1)/N_clust, | |
| following the standard Stata small-sample adjustment for cluster-robust. In the case of two-way clustering, N_clust is the minimum of N_clust1 and N_clust2. | |
| The critical values reported by {cmd:ivreg2} for the Kleibergen-Paap statistic | |
| are the Stock-Yogo critical values for the Cragg-Donald i.i.d. case. | |
| The critical values reported with 2-step GMM | |
| are the Stock-Yogo IV critical values, | |
| and the critical values reported with CUE | |
| are the LIML critical values. | |
| {marker s_redundancy}{dlgtab:Testing instrument redundancy} | |
| {marker redtest}{p}The {cmd:redundant} option allows a test of | |
| whether a subset of excluded instruments is "redundant". | |
| Excluded instruments are redundant if the asymptotic efficiency | |
| of the estimation is not improved by using them. | |
| Breusch et al. (1999) show that the condition for the redundancy of a set of instruments | |
| can be stated in several equivalent ways: | |
| e.g., in the reduced form regressions of the endogenous regressors | |
| on the full set of instruments, | |
| the redundant instruments have statistically insignificant coefficients; | |
| or the partial correlations between the endogenous regressors | |
| and the instruments in question are zero. | |
| {cmd:ivreg2} uses a formulation based on testing the rank | |
| of the matrix cross-product between the endogenous regressors | |
| and the possibly-redundant instruments after both have | |
| all other instruments partialled-out; | |
| {cmd:ranktest} is used to test whether the matrix has zero rank. | |
| The test statistic is an LM test | |
| and numerically equivalent to a regression-based LM test. | |
| Under the null that the specified instruments are redundant, | |
| the statistic is distributed as chi-squared | |
| with degrees of freedom=(#endogenous regressors)*(#instruments tested). | |
| Rejection of the null indicates that | |
| the instruments are not redundant. | |
| When the i.i.d. assumption is dropped | |
| and {cmd:ivreg2} reports heteroskedastic, AC, HAC | |
| or cluster-robust statistics, | |
| the redundancy test statistic is similarly robust. | |
| See Baum et al. (2007) for further discussion. | |
| {p}Calculation and reporting of all underidentification | |
| and weak identification statistics | |
| can be supressed with the {cmd:noid} option. | |
| {marker s_first}{dlgtab:First-stage regressions, identification, and weak-id-robust inference} | |
| {p}The {cmd:first}, {cmd:sfirst} and {cmd:ffirst} options report | |
| various first-stage results and identification statistics. | |
| The {cmd:first} option reports the individual first-stage regressions separately. | |
| The {cmd:sfirst} option reports all the first-stage regressions jointly | |
| in a single estimation table along with the reduced form equation | |
| for the dependent variable (see {help ivreg2##s_rf:below}); | |
| the output is similar in appearance and usage (e.g., in testing) | |
| as that generated by Stata's {cmd:mvreg}. | |
| {marker swstats}{p}Tests of both underidentification and weak identification are reported | |
| for each endogenous regressor separately, | |
| using the method of Sanderson-Windmeijer (2015) | |
| (a modification and improvement of the described by | |
| Angrist and Pischke (2009), pp. 217-18, and implemented | |
| in previous versions of {cmd:ivreg2}; | |
| the AP test statistics remain available in the {cmd:e(first) matrix}). | |
| {p}The Sanderson-Windmeijer (SW) first-stage chi-squared and F statistics | |
| are tests of underidentification and weak identification, respectively, | |
| of individual endogenous regressors. | |
| They are constructed by "partialling-out" linear projections of the | |
| remaining endogenous regressors. | |
| The SW chi-squared Wald statistic is distributed as chi2(L1-K1+1)) | |
| under the null that the particular endogenous regressor | |
| in question is unidentified. | |
| In the special case of a single endogenous regressor, | |
| the SW statistic reported is identical to underidentification statistics reported | |
| in the {cmd:ffirst} output, | |
| namely the Cragg-Donald Wald statistic (if i.i.d.) | |
| or the Kleibergen-Paap rk Wald statistic (if robust, cluster-robust, AC or HAC | |
| statistics have been requested); | |
| see {help ivreg2##idtest:above}. | |
| The SW first-stage F statistic is the F form of the same test statistic. | |
| It can be used as a diagnostic for whether a particular endogenous regressor | |
| is "weakly identified" (see {help ivreg2##widtest:above}). | |
| For further details and discussion, see Sanderson and Windmeijer (2015). | |
| {p}The first-stage results are always reported with small-sample statistics, | |
| to be consistent with the recommended use of the first-stage F-test as a diagnostic. | |
| If the estimated equation is reported with robust standard errors, | |
| the first-stage F-test is also robust. | |
| {p}A full set of first-stage statistics for each of the K1 endogenous regressors | |
| is saved in the matrix e(first). | |
| These include (a) the SW and AP F and chi-squared statistics; (b) the "partial R-squared" | |
| (squared partial correlation) corresponding to the SW and SP statistics; | |
| (c) Shea's (1997) partial R-squared measure (closely related to the SW and AP statistics, | |
| but not amenable to formal testing); (d) the simple F and partial R-squared | |
| statistics for each of the first-stage equations, | |
| with no adjustments if there is more than one endogenous regressor. | |
| In the special case of a single endogenous regressor, | |
| these F statistics and partial R-squareds are identical. | |
| {marker wirobust}{p}The first-stage output also includes | |
| two statistics that provide weak-instrument robust inference | |
| for testing the significance of the endogenous regressors in the structural equation being estimated. | |
| The first statistic is the Anderson-Rubin (1949) test | |
| (not to be confused with the Anderson-Rubin overidentification test for LIML estimation; | |
| see {help ivreg2##s_liml:above}). | |
| The second is the closely related Stock-Wright (2000) S statistic. | |
| The null hypothesis tested in both cases is that | |
| the coefficients of the endogenous regressors in the structural equation are jointly equal to zero, | |
| and, in addition, that the overidentifying restrictions are valid. | |
| Both tests are robust to the presence of weak instruments. | |
| The tests are equivalent to estimating the reduced form of the equation | |
| (with the full set of instruments as regressors) | |
| and testing that the coefficients of the excluded instruments are jointly equal to zero. | |
| In the form reported by {cmd:ivreg2},the Anderson-Rubin statistic is a Wald test | |
| and the Stock-Wright S statistic is an LM test. | |
| Both statistics are distributed as chi-squared with L1 degrees of freedom, | |
| where L1=number of excluded instruments. | |
| The traditional F-stat version of the Anderson-Rubin test is also reported. | |
| See Stock and Watson (2000), Dufour (2003), Chernozhukov and Hansen (2005) and Kleibergen (2007) | |
| for further discussion. | |
| For related alternative test statistics that are also robust to weak instruments, | |
| see {help condivreg} and {help weakiv}, | |
| and the corresponding discussions | |
| in Moreira and Poi (2003) and Mikusheva and Poi (2006), | |
| and in Finlay and Magnusson (2009), respectively. | |
| {p}The {cmd:savefirst} option requests that the individual first-stage regressions | |
| be saved for later access using the {cmd:estimates} command. | |
| If saved, they can also be displayed using {cmd:first} or {cmd:ffirst} and the {cmd:ivreg2} replay syntax. | |
| The regressions are saved with the prefix "_ivreg2_", | |
| unless the user specifies an alternative prefix with the | |
| {cmdab:savefp:refix}{cmd:(}{it:prefix}{cmd:)} option. | |
| The {cmd:savesfirst} and {cmdab:savesfp:refix}{cmd:(}{it:prefix}{cmd:)} options | |
| work similarly for the {cmd:sfirst} option if the user wishes to save | |
| the first-stage and reduced form estimations as a single estimated system. | |
| {marker s_rf}{dlgtab:Reduced form estimates} | |
| {p}The {cmd:rf} option requests that the reduced form estimation of the equation be displayed. | |
| The {cmd:saverf} option requests that the reduced form estimation is saved | |
| for later access using the {cmd:estimates} command. | |
| If saved, it can also be displayed using the {cmd:rf} and the {cmd:ivreg2} replay syntax. | |
| The regression is saved with the prefix "_ivreg2_", | |
| unless the user specifies an alternative prefix with the | |
| {cmdab:saverfp:refix}{cmd:(}{it:prefix}{cmd:)} option. | |
| {marker s_partial}{dlgtab:Partialling-out exogenous regressors} | |
| {marker partial}{p}The {cmd:partial(}{it:varlist}{cmd:)} option requests that | |
| the exogenous regressors in {it:varlist} are "partialled out" | |
| from all the other variables (other regressors and excluded instruments) in the estimation. | |
| If the equation includes a constant, it is also automatically partialled out as well. | |
| The coefficients corresponding to the regressors in {it:varlist} are not calculated. | |
| By the Frisch-Waugh-Lovell (FWL) theorem, in IV, | |
| two-step GMM and LIML estimation the coefficients for the remaining regressors | |
| are the same as those that would be obtained if the variables were not partialled out. | |
| (NB: this does not hold for CUE or GMM iterated more than two steps.) | |
| The {cmd:partial} option is most useful when using {cmd:cluster} | |
| and #clusters < (#exogenous regressors + #excluded instruments). | |
| In these circumstances, | |
| the covariance matrix of orthogonality conditions S is not of full rank, | |
| and efficient GMM and overidentification tests are infeasible | |
| since the optimal weighting matrix W = {bind:S^-1} | |
| cannot be calculated. | |
| The problem can be addressed by using {cmd:partial} | |
| to partial out enough exogenous regressors for S to have full rank. | |
| A similar problem arises when the regressors include a variable that is a singleton dummy, | |
| i.e., a variable with one 1 and N-1 zeros or vice versa, | |
| if a robust covariance matrix is requested. | |
| The singleton dummy causes the robust covariance matrix estimator | |
| to be less than full rank. | |
| In this case, partialling-out the variable with the singleton dummy solves the problem. | |
| Specifying {cmd:partial(_cons)} will cause just the constant to be partialled-out, | |
| i.e., the equation will be estimated in deviations-from-means form. | |
| When {cmd:ivreg2} is invoked with {cmd:partial}, | |
| it reports test statistics with the same small-sample adjustments | |
| as if estimating without {cmd:partial}, | |
| with the exception of the information in the output header | |
| (the model F, R-sqs and total sums-of-squares | |
| refer to the model after the variables are partialled-out). | |
| Note that after estimation using the {cmd:partial} option, | |
| the post-estimation {cmd:predict} can be used only to generate residuals. | |
| {marker s_ols}{dlgtab:OLS and Heteroskedastic OLS (HOLS) estimation} | |
| {p}{cmd:ivreg2} also allows straightforward OLS estimation | |
| by using the same syntax as {cmd:regress}, i.e., | |
| {it:ivreg2 depvar varlist1}. | |
| This can be useful if the user wishes to use one of the | |
| features of {cmd:ivreg2} in OLS regression, e.g., AC or | |
| HAC standard errors. | |
| {p}If the list of endogenous variables {it:varlist2} is empty | |
| but the list of excluded instruments {it:varlist_iv} is not, | |
| and the option {cmd:gmm2s} is specified, | |
| {cmd:ivreg2} calculates Cragg's "heteroskedastic OLS" (HOLS) estimator, | |
| an estimator that is more efficient than OLS | |
| in the presence of heteroskedasticity of unknown form | |
| (see Davidson and MacKinnon (1993), pp. 599-600). | |
| If the option {cmd:bw(}{it:#}{cmd:)} is specified, | |
| the HOLS estimator is efficient in the presence of | |
| arbitrary autocorrelation; | |
| if both {cmd:bw(}{it:#}{cmd:)} and {cmd:robust} are specified | |
| the HOLS estimator is efficient in the presence of | |
| arbitrary heteroskedasticity and autocorrelation; | |
| and if {cmd:cluster(}{it:varlist}{cmd:)} is used, | |
| the HOLS estimator is efficient in the presence of | |
| arbitrary heteroskedasticity and within-group correlation. | |
| The efficiency gains of HOLS derive from the orthogonality conditions | |
| of the excluded instruments listed in {it:varlist_iv}. | |
| If no endogenous variables are specified and {cmd:gmm2s} is not specified, | |
| {cmd:ivreg2} reports standard OLS coefficients. | |
| The Sargan-Hansen statistic reported | |
| when the list of endogenous variables {it:varlist2} is empty | |
| is a Lagrange multiplier (LM) test | |
| of the hypothesis that the excluded instruments {it:varlist_iv} are | |
| correctly excluded from the restricted model. | |
| If the estimation is LIML, the LM statistic reported | |
| is now based on the Sargan-Hansen test statistics from | |
| the restricted and unrestricted equation. | |
| For more on LM tests, see e.g. Wooldridge (2002), pp. 58-60. | |
| Note that because the approach of the HOLS estimator | |
| has applications beyond heteroskedastic disturbances, | |
| and to avoid confusion concerning the robustness of the estimates, | |
| the estimators presented above as "HOLS" | |
| are described in the output of {cmd:ivreg2} | |
| as "2-Step GMM", "CUE", etc., as appropriate. | |
| {marker s_collin}{dlgtab:Collinearities} | |
| {p}{cmd:ivreg2} checks the lists of included instruments, | |
| excluded instruments, and endogenous regressors | |
| for collinearities and duplicates. If an endogenous regressor is | |
| collinear with the instruments, it is reclassified as exogenous. If any | |
| endogenous regressors are collinear with each other, some are dropped. | |
| If there are any collinearities among the instruments, some are dropped; | |
| excluded instruments are dropped before included instruments. | |
| If any variables are dropped, a list of their names are saved | |
| in the macros {cmd:e(collin)} and/or {cmd:e(dups)}. | |
| {p}Starting with {cmd:ivreg2} v4.1, | |
| the Stata 11+ convention is followed and | |
| omitted variables are reported in the regression output | |
| and saved in the {cmd:e(b)} and {cmd:e(V)} macros. | |
| These omitted variables, as well as other omitted variables | |
| (e.g., empty factor variables) can be suppressed | |
| by use of the {cmd:bvclean} option. | |
| The Stata display options | |
| {cmd:noomitted}, {cmd:vsquish}, {cmd:noemptycells}, {cmd:baselevels} and {cmd:allbaselevels} | |
| are also supported; see {helpb ereturn##display_options:ereturn}. | |
| Variable lists with collinear variables, duplicates marked with Stata's "o." operator, | |
| and factor variable base variables | |
| are saved in macros with a "0" appended to the corresponding macro names; | |
| lists with these variables removed are saved in macros with a "1" appended. | |
| {p}Collinearity checks can be supressed with the {cmd:nocollin} option. | |
| {marker s_speed}{dlgtab:Speed options: nocollin and noid} | |
| {p}Two options are available for speeding execution. | |
| {cmd:nocollin} specifies that the collinearity checks not be performed. | |
| {cmd:noid} suspends calculation and reporting of | |
| the underidentification and weak identification statistics | |
| in the main output. | |
| {marker s_small}{dlgtab:Small sample corrections} | |
| {p}Mean square error = sqrt(RSS/(N-K)) if {cmd:small}, = sqrt(RSS/N) otherwise. | |
| {p}If {cmd:robust} is chosen, the finite sample adjustment | |
| (see {hi:[R] regress}) to the robust variance-covariance matrix | |
| qc = N/(N-K) if {cmd:small}, qc = 1 otherwise. | |
| {p}If {cmd:cluster} is chosen, the finite sample adjustment | |
| qc = (N-1)/(N-K)*M/(M-1) if {cmd:small}, where M=number of clusters, | |
| qc = 1 otherwise. | |
| If 2-way clustering is used, M=min(M1,M2), | |
| where M1=number of clusters in group 1 | |
| and M2=number of clusters in group 2. | |
| {p}If the {cmd:partial(}{it:varlist}{cmd:)} option is used, | |
| the partialled-out exogenous regressors are included in K. | |
| {p}The Sargan and C (difference-in-Sargan) statistics use | |
| error variance = RSS/N, i.e., there is no small sample correction. | |
| {p}A full discussion of these computations and related topics | |
| can be found in Baum, Schaffer, and Stillman (2003) and Baum, Schaffer and | |
| Stillman (2007). Some features of the program postdate the former article and are described in the latter paper. | |
| Some features, such as two-way clustering, postdate the latter article as well. | |
| {marker s_options}{title:Options summary} | |
| {p 0 4}{cmd:gmm2s} requests the two-step efficient GMM estimator. | |
| If no endogenous variables are specified, the estimator is Cragg's HOLS estimator. | |
| {p 0 4}{cmd:liml} requests the limited-information maximum likelihood estimator. | |
| {p 0 4}{cmd:fuller(}{it:#}{cmd:)} specifies that Fuller's modified LIML estimator | |
| is calculated using the user-supplied Fuller parameter alpha, | |
| a non-negative number. | |
| Alpha=1 has been suggested as a good choice. | |
| {p 0 4}{cmd:kclass(}{it:#}{cmd:)} specifies that a general k-class estimator is calculated | |
| using the user-supplied #, a non-negative number. | |
| {p 0 4}{cmd:coviv} specifies that the matrix used to calculate the | |
| covariance matrix for the LIML or k-class estimator | |
| is based on the 2SLS matrix, i.e., with k=1. | |
| In this case the covariance matrix will differ from that calculated for the 2SLS | |
| estimator only because the estimate of the error variance will differ. | |
| The default is for the covariance matrix to be based on the LIML or k-class matrix. | |
| {p 0 4}{cmd:cue} requests the GMM continuously-updated estimator (CUE). | |
| {p 0 4}{cmd:b0(}{it:matrix}{cmd:)} specifies that the J statistic | |
| (i.e., the value of the CUE objective function) | |
| should be calculated for an arbitrary coefficient vector {cmd:b0}. | |
| That vector must be provided as a matrix with appropriate row and column names. | |
| Under- and weak-identification statistics are not reported | |
| in the output. | |
| {p 0 4}{cmd:robust} specifies that the Eicker/Huber/White/sandwich estimator of | |
| variance is to be used in place of the traditional calculation. {cmd:robust} | |
| combined with {cmd:cluster()} further allows residuals which are not | |
| independent within cluster (although they must be independent between | |
| clusters). See {hi:[U] Obtaining robust variance estimates}. | |
| {p 0 4}{cmd:cluster}{cmd:(}{it:varlist}{cmd:)} specifies that the observations | |
| are independent across groups (clusters) but not necessarily independent | |
| within groups. | |
| With 1-way clustering, {cmd:cluster}{cmd:(}{it:varname}{cmd:)} | |
| specifies to which group each observation | |
| belongs; e.g., {cmd:cluster(personid)} in data with repeated observations on | |
| individuals. | |
| With 2-way clustering, {cmd:cluster}{cmd:(}{it:varname1 varname2}{cmd:)} | |
| specifies the two (non-nested) groups to which each observation belongs. | |
| Specifying {cmd:cluster()} implies {cmd:robust}. | |
| {p 0 4}{cmd:bw(}{it:#}{cmd:)} impements AC or HAC covariance estimation | |
| with bandwidth equal to {it:#}, where {it:#} is an integer greater than zero. | |
| Specifying {cmd:robust} implements HAC covariance estimation; | |
| omitting it implements AC covariance estimation. | |
| If the Bartlett (default), Parzen or Quadratic Spectral kernels are selected, | |
| the value {cmd:auto} may be given (rather than an integer) | |
| to invoke Newey and West's (1994) automatic bandwidth selection procedure. | |
| {p 0 4}{cmd:kernel(}{it:string)}{cmd:)} specifies the kernel | |
| to be used for AC and HAC covariance estimation; | |
| the default kernel is Bartlett (also known in econometrics | |
| as Newey-West). | |
| The full list of kernels available is (abbreviations in parentheses): | |
| Bartlett (bar); Truncated (tru); Parzen (par); Tukey-Hanning (thann); | |
| Tukey-Hamming (thamm); Daniell (dan); Tent (ten); and Quadratic-Spectral (qua or qs). | |
| {p 4 4}Note: in the cases of the Bartlett, Parzen, | |
| and Tukey-Hanning/Hamming kernels, the number of lags used | |
| to construct the kernel estimate equals the bandwidth minus one. | |
| Stata's official {cmd:newey} implements | |
| HAC standard errors based on the Bartlett kernel, | |
| and requires the user to specify | |
| the maximum number of lags used and not the bandwidth; | |
| see help {help newey}. | |
| If these kernels are used with {cmd:bw(1)}, | |
| no lags are used and {cmd:ivreg2} will report the usual | |
| Eicker/Huber/White/sandwich variance estimates. | |
| {p 0 4}{cmd:center} specifies that the moments used to construct | |
| the efficient GMM weighting matrix are centered. | |
| If used with an inefficient 1-step estimator, | |
| the estimated coefficients and their standard errors are unaffected but | |
| centered moments will be used in the reported Hansen J statistic. | |
| {p 0 4}{cmd:wmatrix(}{it:matrix}{cmd:)} specifies a user-supplied weighting matrix | |
| in place of the computed optimal weighting matrix. | |
| The matrix must be positive definite. | |
| The user-supplied matrix must have the same row and column names | |
| as the instrument variables in the regression model (or a subset thereof). | |
| {p 0 4}{cmd:smatrix(}{it:matrix}{cmd:)} specifies a user-supplied covariance matrix | |
| of the orthogonality conditions to be used in calculating the covariance matrix of the estimator. | |
| The matrix must be positive definite. | |
| The user-supplied matrix must have the same row and column names | |
| as the instrument variables in the regression model (or a subset thereof). | |
| {p 0 4}{cmd:orthog}{cmd:(}{it:varlist_ex}{cmd:)} requests that a C-statistic | |
| be calculated as a test of the exogeneity of the instruments in {it:varlist_ex}. | |
| These may be either included or excluded exogenous variables. | |
| The standard order condition for identification applies: | |
| the restricted equation that does not use these variables | |
| as exogenous instruments must still be identified. | |
| {p 0 4}{cmd:endog}{cmd:(}{it:varlist_en}{cmd:)} requests that a C-statistic | |
| be calculated as a test of the endogeneity | |
| of the endogenous regressors in {it:varlist_en}. | |
| {p 0 4}{cmd:redundant}{cmd:(}{it:varlist_ex}{cmd:)} requests an LM test | |
| of the redundancy of the instruments in {it:varlist_ex}. | |
| These must be excluded exogenous variables. | |
| The standard order condition for identification applies: | |
| the restricted equation that does not use these variables | |
| as exogenous instrumenst must still be identified. | |
| {p 0 4}{cmd:small} requests that small-sample statistics (F and t-statistics) | |
| be reported instead of large-sample statistics (chi-squared and z-statistics). | |
| Large-sample statistics are the default. | |
| The exception is the statistic for the significance of the regression, | |
| which is always reported as a small-sample F statistic. | |
| {p 0 4}{cmd:noconstant} suppresses the constant term (intercept) in the | |
| regression. If {cmd:noconstant} is specified, the constant term is excluded | |
| from both the final regression and the first-stage regression. To include a | |
| constant in the first-stage when {cmd:noconstant} is specified, explicitly | |
| include a variable containing all 1's in {it:varlist_iv}. | |
| {p 0 4}{cmd:first} requests that the full first-stage regression results be displayed, | |
| along with the associated diagnostic and identification statistics. | |
| {p 0 4}{cmd:sfirst} requests that the first-stage and reduced form regressions | |
| are reported as a single system of equations (i.e., in a single regression output table). | |
| {p 0 4}{cmd:ffirst} requests the first-stage diagnostic and identification statistics. | |
| The results are saved in various e() macros. | |
| {p 0 4}{cmd:nocollin} suppresses the checks for collinearities | |
| and duplicate variables. | |
| {p 0 4}{cmd:noid} suppresses the calculation and reporting | |
| of underidentification and weak identification statistics. | |
| {p 0 4}{cmd:savefirst} requests that the first-stage regressions results | |
| are saved for later access using the {cmd:estimates} command. | |
| The names under which the first-stage regressions are saved | |
| are the names of the endogenous regressors prefixed by "_ivreg2_". | |
| If these use Stata's time-series operators, | |
| the "." is replaced by a "_". | |
| {p 0 4}{cmdab:savefp:refix}{cmd:(}{it:prefix}{cmd:)} requests that | |
| the first-stage regression results be saved using the user-specified prefix | |
| instead of the default "_ivreg2_". | |
| {p 0 4}{cmd:rf} requests that the reduced-form estimation of the equation | |
| be displayed. | |
| {p 0 4}{cmd:saverf} requests that the reduced-form estimation of the equation | |
| be saved for later access using the {cmd:estimates} command. | |
| The estimation is stored under the name of the dependent variable | |
| prefixed by "_ivreg2_". | |
| If this uses Stata's time-series operators, | |
| the "." is replaced by a "_". | |
| {p 0 4}{cmdab:saverfp:refix}{cmd:(}{it:prefix}{cmd:)} requests that | |
| the reduced-form estimation be saved using the user-specified prefix | |
| instead of the default "_ivreg2_". | |
| {p 0 4}{cmd:sfirst} requests that the first-stage and reduced form equations | |
| are estimated and displayed as a single system of equations. | |
| {p 0 4}{cmd:savesfirst} requests that the system of first-stage | |
| and reduced form estimations be saved for later access | |
| using the {cmd:estimates} command. | |
| The estimation is stored under the name of the dependent variable | |
| prefixed by "_ivreg2_sfirst_". | |
| If this uses Stata's time-series operators, | |
| the "." is replaced by a "_". | |
| {p 0 4}{cmdab:saverfp:refix}{cmd:(}{it:prefix}{cmd:)} requests that | |
| the reduced-form estimation be saved using the user-specified prefix | |
| instead of the default "_ivreg2_sfirst_". | |
| {p 0 4}{cmd:partial(}{it:varlist}{cmd:)} requests that | |
| the exogenous regressors in {it:varlist} be partialled out | |
| from the other variables in the equation. | |
| If the equation includes a constant, | |
| it is automatically partialled out as well. | |
| The coefficients corresponding to the regressors in {it:varlist} | |
| are not calculated. | |
| {p 0 4}{cmd:level(}{it:#}{cmd:)} specifies the confidence level, in percent, | |
| for confidence intervals of the coefficients; see help {help level}. | |
| {p 0 4}{cmd:bvclean} specifies that omitted variables (including factor base variables) | |
| are not reported in the estimation output and are not saved in the | |
| {cmd:e(b)} and {cmd:e(V)} macros. | |
| {p 0 4}{cmd:noheader}, {cmd:eform()}, {cmd:depname()} and {cmd:plus} | |
| are for ado-file writers; see {hi:[R] ivreg} and {hi:[R] regress}. | |
| {p 0 4}{cmd:nofooter} suppresses the display of the footer containing | |
| identification and overidentification statistics, | |
| exogeneity and endogeneity tests, | |
| lists of endogenous variables and instruments, etc. | |
| {p 0 4}{cmd:version} causes {cmd:ivreg2} to display its current version number | |
| and to leave it in the macro {cmd:e(version)}. | |
| It cannot be used with any other options. | |
| and will clear any existing {cmd:e()} saved results. | |
| {marker s_versions}{title:Running ivreg2 under earlier versions of Stata} | |
| {p}The most-up-to-date implementation of {cmd:ivreg2} requires Stata version 11 or later. | |
| If {cmd:ivreg2} is called under earlier versions of Stata, | |
| it will automatically run a legacy version {cmd:ivreg2x}, | |
| where "x" denotes the required Stata version. | |
| These versions of {cmd:ivreg2} - {cmd:ivreg28}, {cmd:ivreg29} and {cmd:ivreg210} - | |
| are self-contained and require a minimum of Stata version 8/9/10, respectively. | |
| "Self-contained" means these legacy versions (unlike the main up-to-date {cmd:ivreg2} code) | |
| do not require access to any external Mata library or user-written Stata routines. | |
| These legacy versions are installed with the {cmd:ivreg2} package, | |
| can also be called directly from the Stata command line or in do files, | |
| and come with their own help files. | |
| {p}For example, if a user has Stata 8 installed and calls {cmd:ivreg2}, | |
| it will invoke the legacy version {cmd:ivreg28}. | |
| If a user has a later version of Stata | |
| but wants to run the Stata 8 legacy version of {cmd:ivreg2}, | |
| s/he can estimate either calling {cmd:ivreg28} directly | |
| or by calling {cmd:ivreg2} under version control (i.e., "{cmd:version 8: ivreg2}"). | |
| To see what options are/aren't available with this particular legacy version, | |
| the user can see {helpb help ivreg28}. | |
| {marker s_macros}{title:Remarks and saved results} | |
| {p}{cmd:ivreg2} does not report an ANOVA table. | |
| Instead, it reports the RSS and both the centered and uncentered TSS. | |
| It also reports both the centered and uncentered R-squared. | |
| NB: the TSS and R-squared reported by official {cmd:ivreg} is centered | |
| if a constant is included in the regression, and uncentered otherwise. | |
| {p}{cmd:ivreg2} saves the following results in {cmd:e()}: | |
| Scalars | |
| {col 4}{cmd:e(N)}{col 18}Number of observations | |
| {col 4}{cmd:e(yy)}{col 18}Total sum of squares (SS), uncentered (y'y) | |
| {col 4}{cmd:e(yyc)}{col 18}Total SS, centered (y'y - ((1'y)^2)/n) | |
| {col 4}{cmd:e(rss)}{col 18}Residual SS | |
| {col 4}{cmd:e(mss)}{col 18}Model SS =yyc-rss if the eqn has a constant, =yy-rss otherwise | |
| {col 4}{cmd:e(df_m)}{col 18}Model degrees of freedom | |
| {col 4}{cmd:e(df_r)}{col 18}Residual degrees of freedom | |
| {col 4}{cmd:e(r2u)}{col 18}Uncentered R-squared, 1-rss/yy | |
| {col 4}{cmd:e(r2c)}{col 18}Centered R-squared, 1-rss/yyc | |
| {col 4}{cmd:e(r2)}{col 18}Centered R-squared if the eqn has a constant, uncentered otherwise | |
| {col 4}{cmd:e(r2_a)}{col 18}Adjusted R-squared | |
| {col 4}{cmd:e(ll)}{col 18}Log likelihood | |
| {col 4}{cmd:e(rankxx)}{col 18}Rank of the matrix of observations on rhs variables=K | |
| {col 4}{cmd:e(rankzz)}{col 18}Rank of the matrix of observations on instruments=L | |
| {col 4}{cmd:e(rankV)}{col 18}Rank of covariance matrix V of coefficients | |
| {col 4}{cmd:e(rankS)}{col 18}Rank of covariance matrix S of orthogonality conditions | |
| {col 4}{cmd:e(rmse)}{col 18}root mean square error=sqrt(rss/(N-K)) if -small-, =sqrt(rss/N) if not | |
| {col 4}{cmd:e(F)}{col 18}F statistic | |
| {col 4}{cmd:e(N_clust)}{col 18}Number of clusters (or min(N_clust1,N_clust2) if 2-way clustering) | |
| {col 4}{cmd:e(N_clust1)}{col 18}Number of clusters in dimension 1 (if 2-way clustering) | |
| {col 4}{cmd:e(N_clust2)}{col 18}Number of clusters in dimension 2 (if 2-way clustering) | |
| {col 4}{cmd:e(bw)}{col 18}Bandwidth | |
| {col 4}{cmd:e(lambda)}{col 18}LIML eigenvalue | |
| {col 4}{cmd:e(kclass)}{col 18}k in k-class estimation | |
| {col 4}{cmd:e(fuller)}{col 18}Fuller parameter alpha | |
| {col 4}{cmd:e(sargan)}{col 18}Sargan statistic | |
| {col 4}{cmd:e(sarganp)}{col 18}p-value of Sargan statistic | |
| {col 4}{cmd:e(sargandf)}{col 18}dof of Sargan statistic = degree of overidentification = L-K | |
| {col 4}{cmd:e(j)}{col 18}Hansen J statistic | |
| {col 4}{cmd:e(jp)}{col 18}p-value of Hansen J statistic | |
| {col 4}{cmd:e(jdf)}{col 18}dof of Hansen J statistic = degree of overidentification = L-K | |
| {col 4}{cmd:e(arubin)}{col 18}Anderson-Rubin overidentification LR statistic N*ln(lambda) | |
| {col 4}{cmd:e(arubinp)}{col 18}p-value of Anderson-Rubin overidentification LR statistic | |
| {col 4}{cmd:e(arubin_lin)}{col 18}Anderson-Rubin linearized overidentification statistic N*(lambda-1) | |
| {col 4}{cmd:e(arubin_linp)}{col 18}p-value of Anderson-Rubin linearized overidentification statistic | |
| {col 4}{cmd:e(arubindf)}{col 18}dof of A-R overid statistic = degree of overidentification = L-K | |
| {col 4}{cmd:e(idstat)}{col 18}LM test statistic for underidentification (Anderson or Kleibergen-Paap) | |
| {col 4}{cmd:e(idp)}{col 18}p-value of underidentification LM statistic | |
| {col 4}{cmd:e(iddf)}{col 18}dof of underidentification LM statistic | |
| {col 4}{cmd:e(widstat)}{col 18}F statistic for weak identification (Cragg-Donald or Kleibergen-Paap) | |
| {col 4}{cmd:e(arf)}{col 18}Anderson-Rubin F-test of significance of endogenous regressors | |
| {col 4}{cmd:e(arfp)}{col 18}p-value of Anderson-Rubin F-test of endogenous regressors | |
| {col 4}{cmd:e(archi2)}{col 18}Anderson-Rubin chi-sq test of significance of endogenous regressors | |
| {col 4}{cmd:e(archi2p)}{col 18}p-value of Anderson-Rubin chi-sq test of endogenous regressors | |
| {col 4}{cmd:e(ardf)}{col 18}degrees of freedom of Anderson-Rubin tests of endogenous regressors | |
| {col 4}{cmd:e(ardf_r)}{col 18}denominator degrees of freedom of AR F-test of endogenous regressors | |
| {col 4}{cmd:e(redstat)}{col 18}LM statistic for instrument redundancy | |
| {col 4}{cmd:e(redp)}{col 18}p-value of LM statistic for instrument redundancy | |
| {col 4}{cmd:e(reddf)}{col 18}dof of LM statistic for instrument redundancy | |
| {col 4}{cmd:e(cstat)}{col 18}GMM distance test statistic of exogeneity | |
| {col 4}{cmd:e(cstatp)}{col 18}p-value of GMM distance test statistic of exogeneity | |
| {col 4}{cmd:e(cstatdf)}{col 18}Degrees of freedom of GMM distance test statistic of exogeneity | |
| {col 4}{cmd:e(estat)}{col 18}GMM distance test statistic of endogeneity | |
| {col 4}{cmd:e(estatp)}{col 18}p-value of GMM distance test statistic of endogeneity | |
| {col 4}{cmd:e(estatdf)}{col 18}Degrees of freedom of GMM distance test statistic of endogeneity | |
| {col 4}{cmd:e(cons)}{col 18}1 when equation has a Stata-supplied constant; 0 otherwise | |
| {col 4}{cmd:e(center)}{col 18}1 when moments are mean-centered; 0 otherwise | |
| {col 4}{cmd:e(partialcons)}{col 18}as above but prior to partialling-out (see {cmd:e(partial)}) | |
| {col 4}{cmd:e(partial_ct)}{col 18}Number of partialled-out variables (see {cmd:e(partial)}) | |
| Macros | |
| {col 4}{cmd:e(cmd)}{col 18}ivreg2 | |
| {col 4}{cmd:e(cmdline)}{col 18}Command line invoking ivreg2 | |
| {col 4}{cmd:e(ivreg2cmd)}{col 18}Version of ivreg2 (ivreg2, ivreg28, ivreg29, etc.) | |
| {col 4}{cmd:e(version)}{col 18}Version number of ivreg2 | |
| {col 4}{cmd:e(model)}{col 18}ols, iv, gmm, liml, or kclass | |
| {col 4}{cmd:e(depvar)}{col 18}Name of dependent variable | |
| {col 4}{cmd:e(instd)}{col 18}Instrumented (RHS endogenous) variables | |
| {col 4}{cmd:e(insts)}{col 18}Instruments | |
| {col 4}{cmd:e(inexog)}{col 18}Included instruments (regressors) | |
| {col 4}{cmd:e(exexog)}{col 18}Excluded instruments | |
| {col 4}{cmd:e(collin)}{col 18}Variables dropped because of collinearities | |
| {col 4}{cmd:e(dups)}{col 18}Duplicate variables | |
| {col 4}{cmd:e(ecollin)}{col 18}Endogenous variables reclassified as exogenous because of | |
| {col 20}collinearities with instruments | |
| {col 4}{cmd:e(clist)}{col 18}Instruments tested for orthogonality | |
| {col 4}{cmd:e(redlist)}{col 18}Instruments tested for redundancy | |
| {col 4}{cmd:e(partial)}{col 18}Partialled-out exogenous regressors | |
| {col 4}{cmd:e(small)}{col 18}small | |
| {col 4}{cmd:e(wtype)}{col 18}weight type | |
| {col 4}{cmd:e(wexp)}{col 18}weight expression | |
| {col 4}{cmd:e(clustvar)}{col 18}Name of cluster variable | |
| {col 4}{cmd:e(vcetype)}{col 18}Covariance estimation method | |
| {col 4}{cmd:e(kernel)}{col 18}Kernel | |
| {col 4}{cmd:e(tvar)}{col 18}Time variable | |
| {col 4}{cmd:e(ivar)}{col 18}Panel variable | |
| {col 4}{cmd:e(firsteqs)}{col 18}Names of stored first-stage equations | |
| {col 4}{cmd:e(rfeq)}{col 18}Name of stored reduced form equation | |
| {col 4}{cmd:e(sfirsteq)}{col 18}Name of stored system of first-stage and reduced form equations | |
| {col 4}{cmd:e(predict)}{col 18}Program used to implement predict | |
| Matrices | |
| {col 4}{cmd:e(b)}{col 18}Coefficient vector | |
| {col 4}{cmd:e(V)}{col 18}Variance-covariance matrix of the estimators | |
| {col 4}{cmd:e(S)}{col 18}Covariance matrix of orthogonality conditions | |
| {col 4}{cmd:e(W)}{col 18}GMM weighting matrix (=inverse of S if efficient GMM estimator) | |
| {col 4}{cmd:e(first)}{col 18}First-stage regression results | |
| {col 4}{cmd:e(ccev)}{col 18}Eigenvalues corresponding to the Anderson canonical correlations test | |
| {col 4}{cmd:e(cdev)}{col 18}Eigenvalues corresponding to the Cragg-Donald test | |
| Functions | |
| {col 4}{cmd:e(sample)}{col 18}Marks estimation sample | |
| {marker s_examples}{title:Examples} | |
| {p 8 12}{stata "use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta" : . use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta }{p_end} | |
| {p 8 12}(Wages of Very Young Men, Zvi Griliches, J.Pol.Ec. 1976) | |
| {col 0}(Instrumental variables. Examples follow Hayashi 2000, p. 255.) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt)} | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), small ffirst" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), small ffirst} | |
| {col 0}(Testing for the presence of heteroskedasticity in IV/GMM estimation) | |
| {p 8 12}{stata "ivhettest, fitlev" : . ivhettest, fitlev} | |
| {col 0}(Two-step GMM efficient in the presence of arbitrary heteroskedasticity) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s robust" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s robust} | |
| {p 0}(GMM with user-specified first-step weighting matrix or matrix of orthogonality conditions) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), robust" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), robust} | |
| {p 8 12}{stata "predict double uhat if e(sample), resid" : . predict double uhat if e(sample), resid} | |
| {p 8 12}{stata "mat accum S = `e(insts)' [iw=uhat^2]" : . mat accum S = `e(insts)' [iw=uhat^2]} | |
| {p 8 12}{stata "mat S = 1/`e(N)' * S" : . mat S = 1/`e(N)' * S} | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s robust smatrix(S)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s robust smatrix(S)} | |
| {p 8 12}{stata "mat W = invsym(S)" : . mat W = invsym(S)} | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s robust wmatrix(W)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s robust wmatrix(W)} | |
| {p 0}(Equivalence of J statistic and Wald tests of included regressors, irrespective of instrument choice (Ahn, 1997)) | |
| {p 8 12}{stata "ivreg2 lw (iq=med kww age), gmm2s" : . ivreg2 lw (iq=med kww age), gmm2s} | |
| {p 8 12}{stata "mat S0 = e(S)" : . mat S0 = e(S)} | |
| {p 8 12}{stata "qui ivreg2 lw (iq=kww) med age, gmm2s smatrix(S0)" : . qui ivreg2 lw (iq=kww) med age, gmm2s smatrix(S0)} | |
| {p 8 12}{stata "test med age" : . test med age} | |
| {p 8 12}{stata "qui ivreg2 lw (iq=med) kww age, gmm2s smatrix(S0)" : . qui ivreg2 lw (iq=med) kww age, gmm2s smatrix(S0)} | |
| {p 8 12}{stata "test kww age" : . test kww age} | |
| {p 8 12}{stata "qui ivreg2 lw (iq=age) med kww, gmm2s smatrix(S0)" : . qui ivreg2 lw (iq=age) med kww, gmm2s smatrix(S0)} | |
| {p 8 12}{stata "test med kww" : . test med kww} | |
| {p 0}(Continuously-updated GMM (CUE) efficient in the presence of arbitrary heteroskedasticity. NB: may require 30+ iterations.) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), cue robust" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), cue robust} | |
| {col 0}(Sargan-Basmann tests of overidentifying restrictions for IV estimation) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt)} | |
| {p 8 12}{stata "overid, all" : . overid, all} | |
| {col 0}(Tests of exogeneity and endogeneity) | |
| {col 0}(Test the exogeneity of one regressor) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s orthog(s)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s orthog(s)} | |
| {col 0}(Test the exogeneity of two excluded instruments) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s orthog(age mrt)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age mrt), gmm2s orthog(age mrt)} | |
| {col 0}(Frisch-Waugh-Lovell (FWL): equivalence of estimations with and without partialling-out) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns i.year (iq=kww age), cluster(year)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age), cluster(year)} | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns i.year (iq=kww age), cluster(year) partial(i.year)" : . ivreg2 lw s expr tenure rns smsa i.year (iq=med kww age), cluster(year) partial(i.year)} | |
| {col 0}({cmd:partial()}: efficient GMM with #clusters<#instruments feasible after partialling-out) | |
| {p 8 12}{stata "ivreg2 lw s expr tenure rns i.year (iq=kww age), cluster(year) partial(i.year) gmm2s" : . ivreg2 lw s expr tenure rns smsa (iq=med kww age), cluster(year) partial(i.year) gmm2s} | |
| {col 0}(Examples following Wooldridge 2002, pp.59, 61) | |
| {p 8 12}{stata "use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta" : . use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta } | |
| {col 0}(Equivalence of DWH endogeneity test when regressor is endogenous...) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6)" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6)} | |
| {p 8 12}{stata "ivendog educ" :. ivendog educ} | |
| {col 0}(... endogeneity test using the {cmd:endog} option) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), endog(educ)" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), endog(educ)} | |
| {col 0}(...and C-test of exogeneity when regressor is exogenous, using the {cmd:orthog} option) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq educ (=age kidslt6 kidsge6), orthog(educ)" : . ivreg2 lwage exper expersq educ (=age kidslt6 kidsge6), orthog(educ)} | |
| {col 0}(Heteroskedastic Ordinary Least Squares, HOLS) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq educ (=age kidslt6 kidsge6), gmm2s" : . ivreg2 lwage exper expersq educ (=age kidslt6 kidsge6), gmm2s} | |
| {col 0}(Equivalence of Cragg-Donald Wald F statistic and F-test from first-stage regression | |
| {col 0}in special case of single endogenous regressor. Also illustrates {cmd:first}, {cmd:sfirst} | |
| {col 0}and {cmd:savefirst} options.) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), first sfirst savefirst" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), first sfirst savefirst} | |
| {p 8 12}{stata "di e(widstat)" : . di e(widstat)} | |
| {p 8 12}{stata "estimates restore _ivreg2_educ" : . estimates restore _ivreg2_educ} | |
| {p 8 12}{stata "test age kidslt6 kidsge6" : . test age kidslt6 kidsge6} | |
| {p 8 12}{stata "di r(F)" : . di r(F)} | |
| {col 0}(Equivalence of Kleibergen-Paap robust rk Wald F statistic and F-test from first-stage | |
| {col 0}regression in special case of single endogenous regressor.) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust savefirst" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust savefirst} | |
| {p 8 12}{stata "di e(widstat)" : . di e(widstat)} | |
| {p 8 12}{stata "estimates restore _ivreg2_educ" : . estimates restore _ivreg2_educ} | |
| {p 8 12}{stata "test age kidslt6 kidsge6" : . test age kidslt6 kidsge6} | |
| {p 8 12}{stata "di r(F)" : . di r(F)} | |
| {col 0}(Equivalence of Kleibergen-Paap robust rk LM statistic for identification and LM test | |
| {col 0}of joint significance of excluded instruments in first-stage regression in special | |
| {col 0}case of single endogenous regressor. Also illustrates use of {cmd:ivreg2} to perform an | |
| {col 0}LM test in OLS estimation.) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust} | |
| {p 8 12}{stata "di e(idstat)" : . di e(idstat)} | |
| {p 8 12}{stata "ivreg2 educ exper expersq (=age kidslt6 kidsge6) if e(sample), robust" : . ivreg2 educ exper expersq (=age kidslt6 kidsge6) if e(sample), robust} | |
| {p 8 12}{stata "di e(j)" : . di e(j)} | |
| {col 0}(Equivalence of an LM test of an excluded instrument for redundancy and an LM test of | |
| {col 0}significance from first-stage regression in special case of single endogenous regressor.) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust redundant(age)" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust redundant(age)} | |
| {p 8 12}{stata "di e(redstat)" : . di e(redstat)} | |
| {p 8 12}{stata "ivreg2 educ exper expersq kidslt6 kidsge6 (=age) if e(sample), robust" : . ivreg2 educ exper expersq kidslt6 kidsge6 (=age) if e(sample), robust} | |
| {p 8 12}{stata "di e(j)" : . di e(j)} | |
| {col 0}(Weak-instrument robust inference: Anderson-Rubin Wald F and chi-sq and | |
| {col 0}Stock-Wright S statistics. Also illusrates use of {cmd:saverf} option.) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust ffirst saverf" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust ffirst saverf} | |
| {p 8 12}{stata "di e(arf)" : . di e(arf)} | |
| {p 8 12}{stata "di e(archi2)" : . di e(archi2)} | |
| {p 8 12}{stata "di e(sstat)" : . di e(sstat)} | |
| {col 0}(Obtaining the Anderson-Rubin Wald F statistic from the reduced-form estimation) | |
| {p 8 12}{stata "estimates restore _ivreg2_lwage" : . estimates restore _ivreg2_lwage} | |
| {p 8 12}{stata "test age kidslt6 kidsge6" : . test age kidslt6 kidsge6} | |
| {p 8 12}{stata "di r(F)" : . di r(F)} | |
| {col 0}(Obtaining the Anderson-Rubin Wald chi-sq statistic from the reduced-form estimation. | |
| {col 0}Use {cmd:ivreg2} without {cmd:small} to obtain large-sample test statistic.) | |
| {p 8 12}{stata "ivreg2 lwage exper expersq age kidslt6 kidsge6, robust" : . ivreg2 lwage exper expersq age kidslt6 kidsge6, robust} | |
| {p 8 12}{stata "test age kidslt6 kidsge6" : . test age kidslt6 kidsge6} | |
| {p 8 12}{stata "di r(chi2)" : . di r(chi2)} | |
| {col 0}(Obtaining the Stock-Wright S statistic as the value of the GMM CUE objective function. | |
| {col 0}Also illustrates use of {cmd:b0} option. Coefficients on included exogenous regressors | |
| {col 0}are OLS coefficients, which is equivalent to partialling them out before obtaining | |
| {col 0}the value of the CUE objective function.) | |
| {p 8 12}{stata "mat b = 0" : . mat b = 0} | |
| {p 8 12}{stata "mat colnames b = educ" : . mat colnames b = educ} | |
| {p 8 12}{stata "qui ivreg2 lwage exper expersq" : . qui ivreg2 lwage exper expersq} | |
| {p 8 12}{stata "mat b = b, e(b)" : . mat b = b, e(b)} | |
| {p 8 12}{stata "ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust b0(b)" : . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6), robust b0(b)} | |
| {p 8 12}{stata "di e(j)" : . di e(j)} | |
| {col 0}(LIML and k-class estimation using Klein data) | |
| {col 9}{stata "webuse klein" :. webuse klein} | |
| {col 9}{stata "tsset yr" :. tsset yr} | |
| {col 0}(LIML estimates of Klein's consumption function) | |
| {p 8 12}{stata "ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), liml" :. ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), liml} | |
| {col 0}(Equivalence of LIML and CUE+homoskedasticity+independence) | |
| {p 8 12}{stata "ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), liml coviv" :. ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), liml coviv} | |
| {p 8 12}{stata "ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), cue" :. ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), cue} | |
| {col 0}(Fuller's modified LIML with alpha=1) | |
| {p 8 12}{stata "ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), fuller(1)" :. ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), fuller(1)} | |
| {col 0}(k-class estimation with Nagar's bias-adjusted IV, k=1+(L-K)/N=1+4/21=1.19) | |
| {p 8 12}{stata "ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), kclass(1.19)" :. ivreg2 consump L.profits (profits wagetot = govt taxnetx year wagegovt capital1 L.totinc), kclass(1.19)} | |
| {col 0}(Kernel-based covariance estimation using time-series data) | |
| {col 9}{stata "use http://fmwww.bc.edu/ec-p/data/wooldridge/phillips.dta" :. use http://fmwww.bc.edu/ec-p/data/wooldridge/phillips.dta} | |
| {col 9}{stata "tsset year, yearly" :. tsset year, yearly} | |
| {col 0}(Autocorrelation-consistent (AC) inference in an OLS Regression) | |
| {p 8 12}{stata "ivreg2 cinf unem, bw(3)" :. ivreg2 cinf unem, bw(3)} | |
| {p 8 12}{stata "ivreg2 cinf unem, kernel(qs) bw(auto)" :. ivreg2 cinf unem, kernel(qs) bw(auto)} | |
| {col 0}(Heteroskedastic and autocorrelation-consistent (HAC) inference in an OLS regression) | |
| {p 8 12}{stata "ivreg2 cinf unem, bw(3) kernel(bartlett) robust small" :. ivreg2 cinf unem, bw(3) kernel(bartlett) robust small} | |
| {p 8 12}{stata "newey cinf unem, lag(2)" :. newey cinf unem, lag(2)} | |
| {col 0}(AC and HAC in IV and GMM estimation) | |
| {p 8 12}{stata "ivreg2 cinf (unem = l(1/3).unem), bw(3)" :. ivreg2 cinf (unem = l(1/3).unem), bw(3)} | |
| {p 8 12}{stata "ivreg2 cinf (unem = l(1/3).unem), bw(3) gmm2s kernel(thann)" :. ivreg2 cinf (unem = l(1/3).unem), bw(3) gmm2s kernel(thann)} | |
| {p 8 12}{stata "ivreg2 cinf (unem = l(1/3).unem), bw(3) gmm2s kernel(qs) robust orthog(l1.unem)" :. ivreg2 cinf (unem = l(1/3).unem), bw(3) gmm2s kernel(qs) robust orthog(l1.unem)} | |
| {col 0}(Examples using Large N, Small T Panel Data) | |
| {p 8 12}{stata "use http://fmwww.bc.edu/ec-p/data/macro/abdata.dta" : . use http://fmwww.bc.edu/ec-p/data/macro/abdata.dta }{p_end} | |
| {p 8 12}{stata "tsset id year" :. tsset id year} | |
| {col 0}(Two-step effic. GMM in the presence of arbitrary heteroskedasticity and autocorrelation) | |
| {p 8 12}{stata "ivreg2 n (w k ys = d.w d.k d.ys d2.w d2.k d2.ys), gmm2s cluster(id)": . ivreg2 n (w k ys = d.w d.k d.ys d2.w d2.k d2.ys), gmm2s cluster(id)} | |
| {col 0}(Kiefer (1980) SEs - robust to arbitrary serial correlation but not heteroskedasticity) | |
| {p 8 12}{stata "ivreg2 n w k, kiefer": . ivreg2 n w k, kiefer} | |
| {p 8 12}{stata "ivreg2 n w k, bw(8) kernel(tru)": . ivreg2 n w k, bw(8) kernel(tru)} | |
| {col 0}(Equivalence of cluster-robust and kernel-robust with truncated kernel and max bandwidth) | |
| {p 8 12}{stata "ivreg2 n w k, cluster(id)": . ivreg2 n w k, cluster(id)} | |
| {p 8 12}{stata "ivreg2 n w k, bw(8) kernel(tru) robust": . ivreg2 n w k, bw(8) kernel(tru) robust} | |
| {col 0}(Examples using factor variables) | |
| {p 8 12}{stata "sysuse auto" : . sysuse auto }{p_end} | |
| {p 8 12}{stata "ivreg2 price i.foreign i.rep78": . ivreg2 price i.foreign i.rep78} | |
| {p 8 12}{stata "ivreg2 price i.rep78 (foreign = weight turn trunk)": . ivreg2 price i.rep78 (foreign = weight turn trunk) } | |
| {p 8 12}{stata "ivreg2 price i.rep78 (c.mpg#c.mpg = weight length turn)": . ivreg2 price i.rep78 (c.mpg#c.mpg = weight length turn)} | |
| {col 0}(Examples using Small N, Large T Panel Data. NB: T is actually not very large - only | |
| {col 0}20 - so results should be interpreted with caution) | |
| {p 8 12}{stata "webuse grunfeld" : . webuse grunfeld }{p_end} | |
| {p 8 12}{stata "tsset" : . tsset }{p_end} | |
| {col 0}(Autocorrelation-consistent (AC) inference) | |
| {p 8 12}{stata "ivreg2 invest mvalue kstock, bw(1) kernel(tru)": . ivreg2 invest mvalue kstock, bw(1) kernel(tru)} | |
| {col 0}(Heteroskedastic and autocorrelation-consistent (HAC) inference) | |
| {p 8 12}{stata "ivreg2 invest mvalue kstock, robust bw(1) kernel(tru)": . ivreg2 invest mvalue kstock, robust bw(1) kernel(tru)} | |
| {col 0}(HAC inference, SEs also robust to disturbances correlated across panels) | |
| {p 8 12}{stata "ivreg2 invest mvalue kstock, robust cluster(year) bw(1) kernel(tru)": . ivreg2 invest mvalue kstock, robust cluster(year) bw(1) kernel(tru)} | |
| {col 0}(Equivalence of Driscoll-Kraay SEs as implemented by {cmd:ivreg2} and {cmd:xtscc}) | |
| {col 0}(See Hoeschle (2007) for discussion of {cmd:xtscc}) | |
| {p 8 12}{stata "ivreg2 invest mvalue kstock, dkraay(2) small": . ivreg2 invest mvalue kstock, dkraay(2) small} | |
| {p 8 12}{stata "ivreg2 invest mvalue kstock, cluster(year) bw(2) small": . ivreg2 invest mvalue kstock, cluster(year) bw(2) small} | |
| {p 8 12}{stata "xtscc invest mvalue kstock, lag(1)": . xtscc invest mvalue kstock, lag(1)} | |
| {col 0}(Examples using Large N, Large T Panel Data. NB: T is again not very large - only | |
| {col 0}20 - so results should be interpreted with caution) | |
| {p 8 12}{stata "webuse nlswork" : . webuse nlswork }{p_end} | |
| {p 8 12}{stata "tsset" : . tsset }{p_end} | |
| {col 0}(One-way cluster-robust: SEs robust to arbitrary heteroskedasticity and within-panel | |
| {col 0}autocorrelation) | |
| {p 8 12}{stata "ivreg2 ln_w grade age ttl_exp tenure, cluster(idcode)": . ivreg2 ln_w grade age ttl_exp tenure, cluster(idcode) }{p_end} | |
| {col 0}(Two-way cluster-robust: SEs robust to arbitrary heteroskedasticity and within-panel | |
| {col 0}autocorrelation, and contemporaneous cross-panel correlation, i.e., the cross-panel | |
| {col 0}correlation is not autocorrelated) | |
| {p 8 12}{stata "ivreg2 ln_w grade age ttl_exp tenure, cluster(idcode year)": . ivreg2 ln_w grade age ttl_exp tenure, cluster(idcode year) }{p_end} | |
| {col 0}(Two-way cluster-robust: SEs robust to arbitrary heteroskedasticity and within-panel | |
| {col 0}autocorrelation and cross-panel autocorrelated disturbances that disappear after 2 lags) | |
| {p 8 12}{stata "ivreg2 ln_w grade age ttl_exp tenure, cluster(idcode year) bw(2) kernel(tru) ": . ivreg2 ln_w grade age ttl_exp tenure, cluster(idcode year) bw(2) kernel(tru) }{p_end} | |
| {marker s_refs}{title:References} | |
| {p 0 4}Ahn, Seung C. 1997. Orthogonality tests in linear models. Oxford Bulletin | |
| of Economics and Statistics, Vol. 59, pp. 183-186. | |
| {p 0 4}Anderson, T.W. 1951. Estimating linear restrictions on regression coefficients | |
| for multivariate normal distributions. Annals of Mathematical Statistics, Vol. 22, pp. 327-51. | |
| {p 0 4}Anderson, T. W. and H. Rubin. 1949. Estimation of the parameters of a single equation | |
| in a complete system of stochastic equations. Annals of Mathematical Statistics, Vol. 20, | |
| pp. 46-63. | |
| {p 0 4}Anderson, T. W. and H. Rubin. 1950. The asymptotic properties of estimates of the parameters of a single | |
| equation in a complete system of stochastic equations. Annals of Mathematical Statistics, | |
| Vol. 21, pp. 570-82. | |
| {p 0 4}Angrist, J.D. and Pischke, J.-S. 2009. Mostly Harmless Econometrics: An Empiricist's Companion. | |
| Princeton: Princeton University Press. | |
| {p 0 4}Baum, C.F., Schaffer, M.E., and Stillman, S. 2003. Instrumental Variables and GMM: | |
| Estimation and Testing. The Stata Journal, Vol. 3, No. 1, pp. 1-31. | |
| {browse "http://ideas.repec.org/a/tsj/stataj/v3y2003i1p1-31.html":http://ideas.repec.org/a/tsj/stataj/v3y2003i1p1-31.html}. | |
| Working paper version: Boston College Department of Economics Working Paper No. 545. | |
| {browse "http://ideas.repec.org/p/boc/bocoec/545.html":http://ideas.repec.org/p/boc/bocoec/545.html}. | |
| Citations in {browse "http://scholar.google.com/scholar?oi=bibs&hl=en&cites=9432785573549481148":published work}. | |
| {p 0 4}Baum, C. F., Schaffer, M.E., and Stillman, S. 2007. Enhanced routines for instrumental variables/GMM estimation and testing. | |
| The Stata Journal, Vol. 7, No. 4, pp. 465-506. | |
| {browse "http://ideas.repec.org/a/tsj/stataj/v7y2007i4p465-506.html":http://ideas.repec.org/a/tsj/stataj/v7y2007i4p465-506.html}. | |
| Working paper version: Boston College Department of Economics Working Paper No. 667. | |
| {browse "http://ideas.repec.org/p/boc/bocoec/667.html":http://ideas.repec.org/p/boc/bocoec/667.html}. | |
| Citations in {browse "http://scholar.google.com/scholar?oi=bibs&hl=en&cites=1691909976816211536":published work}. | |
| {p 0 4}Breusch, T., Qian, H., Schmidt, P. and Wyhowski, D. 1999. | |
| Redundancy of moment conditions. | |
| Journal of Econometrics, Vol. 9, pp. 89-111. | |
| {p 0 4}Cameron, A.C., Gelbach, J.B. and Miller, D.L. 2006. | |
| Robust Inference with Multi-Way Clustering. | |
| NBER Technical Working paper 327. | |
| {browse "http://www.nber.org/papers/t0327":http://www.nber.org/papers/t0327}. | |
| Forthcoming in the Journal of Business and Economic Statistics. | |
| {cmd:cgmreg} is available at | |
| {browse "http://www.econ.ucdavis.edu/faculty/dlmiller/statafiles":http://www.econ.ucdavis.edu/faculty/dlmiller/statafiles}. | |
| {p 0 4}Chernozhukov, V. and Hansen, C. 2005. The Reduced Form: | |
| A Simple Approach to Inference with Weak Instruments. | |
| Working paper, University of Chicago, Graduate School of Business. | |
| {p 0 4}Cragg, J.G. and Donald, S.G. 1993. Testing Identfiability and Specification in | |
| Instrumental Variables Models. Econometric Theory, Vol. 9, pp. 222-240. | |
| {p 0 4}Cushing, M.J. and McGarvey, M.G. 1999. Covariance Matrix Estimation. | |
| In L. Matyas (ed.), Generalized Methods of Moments Estimation. | |
| Cambridge: Cambridge University Press. | |
| {p 0 4}Davidson, R. and MacKinnon, J. 1993. Estimation and Inference in Econometrics. | |
| 1993. New York: Oxford University Press. | |
| {p 0 4}Driscoll, J.C. and Kraay, A. 1998. Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data. | |
| Review of Economics and Statistics. Vol. 80, No. 4, pp. 549-560. | |
| {p 0 4}Dufour, J.M. 2003. Identification, Weak Instruments and Statistical Inference | |
| in Econometrics. Canadian Journal of Economics, Vol. 36, No. 4, pp. 767-808. | |
| Working paper version: CIRANO Working Paper 2003s-49. | |
| {browse "http://www.cirano.qc.ca/pdf/publication/2003s-49.pdf":http://www.cirano.qc.ca/pdf/publication/2003s-49.pdf}. | |
| {p 0 4}Finlay, K., and Magnusson, L.M. 2009. Implementing Weak-Instrument Robust Tests | |
| for a General Class of Instrumental-Variables Models. | |
| The Stata Journal, Vol. 9, No. 3, pp. 398-421. | |
| {browse "http://www.stata-journal.com/article.html?article=st0171":http://www.stata-journal.com/article.html?article=st0171}. | |
| {p 0 4}Hall, A.R. Generalized Method of Moments. 2005. Oxford: Oxford University Press. | |
| {p 0 4}Hall, A.R., Rudebusch, G.D. and Wilcox, D.W. 1996. Judging Instrument Relevance in | |
| Instrumental Variables Estimation. International Economic Review, Vol. 37, No. 2, pp. 283-298. | |
| {p 0 4}Hayashi, F. Econometrics. 2000. Princeton: Princeton University Press. | |
| {p 0 4}Hansen, L.P., Heaton, J., and Yaron, A. 1996. Finite Sample Properties | |
| of Some Alternative GMM Estimators. Journal of Business and Economic Statistics, Vol. 14, No. 3, pp. 262-280. | |
| {p 0 4}Hoechle, D. 2007. Robust Standard Errors for Panel Regressions with Cross�sectional Dependence. | |
| Stata Journal, Vol. 7, No. 3, pp. 281-312. | |
| {browse "http://www.stata-journal.com/article.html?article=st0128":http://www.stata-journal.com/article.html?article=st0128}. | |
| {p 0 4}Kiefer, N.M. 1980. Estimation of Fixed Effect Models for Time Series of Cross-Sections with | |
| Arbitrary Intertemporal Covariance. Journal of Econometrics, Vol. 14, No. 2, pp. 195-202. | |
| {p 0 4}Kleibergen, F. 2007. Generalizing Weak Instrument Robust Statistics Towards Multiple Parameters, Unrestricted Covariance Matrices and Identification Statistics. Journal of Econometrics, forthcoming. | |
| {p 0 4}Kleibergen, F. and Paap, R. 2006. Generalized Reduced Rank Tests Using the Singular Value Decomposition. | |
| Journal of Econometrics, Vol. 133, pp. 97-126. | |
| {p 0 4}Kleibergen, F. and Schaffer, M.E. 2007. ranktest: Stata module for testing the rank | |
| of a matrix using the Kleibergen-Paap rk statistic. | |
| {browse "http://ideas.repec.org/c/boc/bocode/s456865.html":http://ideas.repec.org/c/boc/bocode/s456865.html}. | |
| {p 0 4}Mikusheva, A. and Poi, B.P. 2006. | |
| Tests and Confidence Sets with Correct Size When Instruments are Potentially Weak. The Stata Journal, Vol. 6, No. 3, pp. 335-347. | |
| {p 0 4}Moreira, M.J. and Poi, B.P. 2003. Implementing Tests with the Correct Size in the Simultaneous Equations Model. The Stata Journal, Vol. 3, No. 1, pp. 57-70. | |
| {p 0 4}Newey, W.K. and K.D. West, 1994. Automatic Lag Selection in Covariance Matrix Estimation. Review of Economic Studies, Vol. 61, No. 4, pp. 631-653. | |
| {p 0 4}Sanderson, E. and F. Windmeijer, 2015. A Weak Instrument F-Test in Linear IV Models with Multiple Endogenous Variables. | |
| Journal of Econometrics (forthcoming). | |
| Working paper version: University of Bristol Discussion Paper 14/644. | |
| {browse "http://ideas.repec.org/p/bri/uobdis/14-644.html":http://ideas.repec.org/p/bri/uobdis/14-644.html}. | |
| {p 0 4}Shea, J. 1997. Instrument Relevance in Multivariate Linear Models: A Simple Measure. | |
| Review of Economics and Statistics, Vol. 49, No. 2, pp. 348-352. | |
| {p 0 4}Stock, J.H. and Wright, J.H. 2000. GMM with Weak Identification. | |
| Econometrica, Vol. 68, No. 5, September, pp. 1055-1096. | |
| {p 0 4}Stock, J.H. and Yogo, M. 2005. Testing for Weak Instruments in Linear IV Regression. In D.W.K. Andrews and J.H. Stock, eds. Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg. Cambridge: Cambridge University Press, 2005, pp. 80�108. | |
| Working paper version: NBER Technical Working Paper 284. | |
| {browse "http://www.nber.org/papers/T0284":http://www.nber.org/papers/T0284}. | |
| {p 0 4}Thompson, S.B. 2009. Simple Formulas for Standard Errors that Cluster by Both Firm and Time. | |
| {browse "http://ssrn.com/abstract=914002":http://ssrn.com/abstract=914002}. | |
| {p 0 4}Wooldridge, J.M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press. | |
| {marker s_acknow}{title:Acknowledgements} | |
| {p}We would like to thanks various colleagues who helped us along the way, including | |
| David Drukker, | |
| Frank Kleibergen, | |
| Austin Nichols, | |
| Brian Poi, | |
| Vince Wiggins, | |
| and, not least, the users of {cmd:ivreg2} | |
| who have provided suggestions, | |
| spotted bugs, | |
| and helped test the package. | |
| We are also grateful to Jim Stock and Moto Yogo for permission to reproduce | |
| their critical values for the Cragg-Donald statistic. | |
| {marker s_citation}{title:Citation of ivreg2} | |
| {p}{cmd:ivreg2} is not an official Stata command. It is a free contribution | |
| to the research community, like a paper. Please cite it as such: {p_end} | |
| {phang}Baum, C.F., Schaffer, M.E., Stillman, S. 2010. | |
| ivreg2: Stata module for extended instrumental variables/2SLS, GMM and AC/HAC, LIML and k-class regression. | |
| {browse "http://ideas.repec.org/c/boc/bocode/s425401.html":http://ideas.repec.org/c/boc/bocode/s425401.html}{p_end} | |
| {title:Authors} | |
| Christopher F Baum, Boston College, USA | |
| baum@bc.edu | |
| Mark E Schaffer, Heriot-Watt University, UK | |
| m.e.schaffer@hw.ac.uk | |
| Steven Stillman, Motu Economic and Public Policy Research | |
| stillman@motu.org.nz | |
| {title:Also see} | |
| {p 1 14}Articles:{it:Stata Journal}, volume 3, number 1: {browse "http://ideas.repec.org/a/tsj/stataj/v3y2003i1p1-31.html":st0030}{p_end} | |
| {p 10 14}{it:Stata Journal}, volume 7, number 4: {browse "http://ideas.repec.org/a/tsj/stataj/v7y2007i4p465-506.html":st0030_3}{p_end} | |
| {p 1 14}Manual: {hi:[U] 23 Estimation and post-estimation commands}{p_end} | |
| {p 10 14}{hi:[U] 29 Overview of model estimation in Stata}{p_end} | |
| {p 10 14}{hi:[R] ivreg}{p_end} | |
| {p 1 10}On-line: help for {help ivregress}, {help ivreg}, {help newey}; | |
| {help overid}, {help ivendog}, {help ivhettest}, {help ivreset}, | |
| {help xtivreg2}, {help xtoverid}, {help ranktest}, | |
| {help condivreg} (if installed); | |
| {help weakiv} (if installed); | |
| {help cgmreg} (if installed); | |
| {help xtscc} (if installed); | |
| {help est}, {help postest}; | |
| {help regress}{p_end} | |