{smcl}
{* 12jun2008 version 1.8.1}{...}
{cmd:help felsdvreg}{right: ({browse "http://www.stata-journal.com/article.html?article=st0143":SJ8-2: st0143})}
{hline}

{title:Title}

{p2colset 5 18 20 2}{...}
{p2col :{hi:felsdvreg} {hline 2}}Memory-saving estimation of a linear model with two high-dimensional fixed effects{p_end}


{title:Syntax}

{p 8 20}{cmd:felsdvreg}
varlist  
{ifin},
{opt i:var(varname)}
{opt j:var(varname)}
{opt p:eff(name)}
{opt f:eff(name)}  
{opt xb(name)}
{opt r:es(name)}
{opt m:over(name)}
{opt g:roup(name)}
{opt mnum(name)}
{opt pobs(name)}
[{opt cons}
{opt takegroup}
{opt grouponly}
{opt robust}
{opt cl:uster(varname)}
{opt noadji}
{opt noadjj}
{opt chol:solve}
{opt norm:alize}
{opt noi:sily}
{opt nocomp:ress}
{opt hat(varlist)}
{opt orig(varlist)}
{opt feffse(name)}]


{title:Description}

{pstd}{cmd:felsdvreg} computes a linear regression model with two
high-dimensional fixed effects: one effect
(e.g., the firm effect) is included as dummy variables, while the other effect
(e.g., the person effect) is eliminated by subtracting group means
(within-transformation).  This method has been termed "FEiLSDVj" by Andrews,
Schank, and Upward (2006) because it has features of both the classical
fixed-effects model and the least-squares dummy-variable model.  (Further
effects, e.g., time effects, can be specified by including the
corresponding dummies.)

{pstd}{cmd:felsdvreg} skips the step of creating the dummy variables.  Instead,
it exploits the information provided by the group identifiers to directly
create the cross-product matrices needed for the least-squares normal
equations.  This procedure is memory saving because the cross-product matrices
are of a much lower dimension than the design matrix.  The procedure is
described in more detail in Cornelissen (2008).

{pstd}{cmd:felsdvreg} incorporates the grouping algorithm proposed by Abowd,
Creecy, and Kramarz (2002) and programmed by Robert Creecy (original author),
Lars Vilhuber (current author), and Amine Ouazad (author of Stata command 
{net "from http://repository.ciser.cornell.edu/viewcvs-public/cg2/branches/stata/":{bf:a2group}}). 
The grouping algorithm allows you to determine which of the effects is
identified.  One firm effect per group (the reference) and all firm effects of
firms without movers are dropped from the estimation beforehand.

{pstd} In Cornelissen (2008), the use of {cmd:felsdvreg} and the
output are described.

{pstd}You may want to consider
{net "from http://repository.ciser.cornell.edu/viewcvs-public/cg2/branches/stata/":{bf:a2reg}}
by Amine Ouazad as an alternative estimation tool for a two-way fixed-effects
regression.


{title:Memory requirements}

{pstd}The moment matrices and the estimation are created in the
Mata environment.  Mata can use only memory that is not allocated to Stata by
the {cmd:set memory} command.  Therefore, you should not allocate too much
memory to Stata because any memory that is allocated in excess to Stata is
lost for Mata.  If you get the error message "unable to allocate real", then
Mata is running out of memory; in this case, try to reduce the memory you
allocated to Stata by using {cmd:set memory}.  If you get the error message "no
room to add more observations/variables", then Stata is running out of memory;
in this case, you need to increase the memory allocated to Stata by using
{cmd:set memory}.

{pstd} If you do not have enough memory available to run {cmd:felsdvreg} on the
complete sample, you may wish to run it on a subsample.  To have as
many identified firm effects as possible in this subsample, you may wish to
choose the subsample such that the mobility groups remain intact.  For example,
you may wish to choose a large mobility group as your subsample and remove 
the remaining groups.  In this case, you can use the option {cmd:grouponly}
(see description below) to run the grouping algorithm separately, and then use
the created group variable to choose your sample for the fixed-effects
estimation.


{title:Options} 

{phang}
{opt ivar(varname)} specifies the identification variable for the first effect,
which is omitted from the regression by a fixed-effect transformation
(subtracting group means).  This is, for example, the person ID.

{phang}
{opt jvar(varname)} specifies the identification variable for the second
effect, which is included as dummy variables.  This is, for example, the firm
ID.

{phang}
{opt peff(name)} specifies the name of a new variable to store the first
effect.

{phang}
{opt feff(name)} specifies the name of a new variable to store the second
effect.

{phang}
{opt xb(name)} specifies the name of a new variable to store the linear
prediction X'b.

{phang}
{opt res(name)} specifies the name of a new variable to store the residual.

{phang}
{opt mover(name)} specifies the name of a new variable to store an indicator
for movers.

{phang}
{opt group(name)} specifies the name of a new variable to store the group
identifier.  (Group 0 represents all firms without movers; all other groups
represent sets of firms that are connected to each other by worker mobility.)

{phang}
{opt mnum(name)} specifies the name of a new variable to store the number of
movers per firm.

{phang}
{opt pobs(name)} specifies the name of a new variable to store the number of
observations per person.  Similarly to {helpb xtreg}, the program will also
compute person effects for those persons with only one observation.  The
residual for these persons will be zero (in {helpb xtreg}, it is set to missing
in these cases).  The variable defined in {opt pobs()} allows you to identify
those persons.

{phang}
{opt cons} normalizes all person effects to the mean zero by subtracting the
mean person effect over all groups.  The mean is then displayed as the
regression constant.

{phang}
{opt takegroup}, if the group variable already exists, skips the
grouping algorithm.  The existing group variable must regroup all firms without
movers into group 0 and apply to exactly the same estimation sample.

{phang}
{opt grouponly} causes {cmd:felsdvreg} to run only the grouping algorithm and
produce the group indicator variable.  No estimates are computed.  This can be
useful if the sample is too big to run the estimation on the whole sample, but
the group variable is required to select a smaller sample.

{phang}
{opt robust} computes robust Huber/White/sandwich estimates of the covariance
matrix.

{phang}
{opt cluster(varname)} computes the clustered variant of the
Huber/White/sandwich estimates of the covariance matrix, where
{it:varname} defines the clusters.

{pmore} Notes: (1) If you choose {cmd:robust} or {cmd:cluster()}, the
conventional standard errors will be returned as {cmd:e(se)} for comparison. 

{pmore}(2) The clustered covariance matrix is multiplied by the scalar
N/(N-K)*M/(M-1), where N is the number of observations, M is the number of
clusters, and K is the number of parameters.  For this scalar adjustment,
{cmd:felsdvreg} computes K by default as the number of explicit regressors plus
the number of identified fixed effects (full degrees-of-freedom adjustment).
(Stata's {helpb xtreg} does this full degrees-of-freedom adjustment only when
the option {cmd:dfadj} is specified; otherwise, it leaves the fixed effects out
of the count.)  The options {opt noadji} and {opt noadjj} (see below) change the
default count of K.  The N-K used by {cmd:felsdvreg} is returned as a scalar,
{cmd:e(df_r)}.  If you want a different degrees-of-freedom adjustment than what
was done by {cmd:felsdvreg}, say, N-K*, then you can multiply the clustered
standard errors reported by {cmd:felsdvreg} by sqrt({cmd:e(df_r)}/(N-K*)).

{pmore} (3) Computing clustered or robust standard errors can take
substantially more time than the other steps of the estimation.  This is because
the memory-saving way in which {cmd:felsdvreg} operates consists of not storing
the time-demeaned dummy-variable matrix of the fixed effects but instead
computing elements of it each time they are needed.  For the robust and
clustered standard errors, this is more time consuming than for the preceding
generation of the moment matrices.

{phang}
{opt noadji} leaves out of the degrees-of-freedom adjustment for the clustered
covariance matrix the number of groups in the first effect.  This is the
default degrees-of-freedom adjustment used by Stata's
{helpb xtreg} with the option {cmd:vce(cluster} {it:clustvar}{cmd:)}.

{phang}
{opt noadjj} leaves out of the degrees-of-freedom adjustment for the clustered
covariance matrix the number of groups in the second effect.

{phang}
{opt cholsolve} directs Stata to use the {cmd:cholsolve()} function instead of
the {cmd:invsym()} function to solve for the estimates of the coefficients and
standard errors.  The advantage of the {cmd:cholsolve()} function may be its
greater internal precision, which can be important in large datasets.  However,
if the {cmd:cholsolve()} function is used, the program will only check for
collinearity between explicit regressors, not for collinearity between
regressors and fixed effects.  If the latter occurs and the option 
{cmd:cholsolve} is used, Stata will issue the error message "matrix has missing
values".

{phang}
{opt normalize} normalizes the group means of the firm effects to
zero.  In each group, the mean firm effect is subtracted from the firm effects
and added to the person effects.

{phang}
{opt noisily} provides additional output, including tables with summary
statistics.  These include the count of movers, persons, and firms, as well as
the mobility of persons between firms.

{phang}
{opt nocompress} specifies not to compress the dataset.  By default, the
{cmd:felsdvreg} command uses the Stata {helpb compress} command to compress the
dataset.  Compressing is recommended.  You should only specify {opt nocompress}
if you are sure that you have enough memory and if you think compressing takes
too long.

{phang}
{opt hat(varlist)}, if you run the second-stage regression of a 2SLS
estimation, tells {cmd:felsdvreg} which regressors are predictions from a
first-stage regression so that it can adjust the residual sum of squares and
the standard errors of the second-stage regression (see, for example, Greene
[2003, 400]).  This option must be used with the option {opt orig()}.

{phang}
{opt orig(varlist)} specifies which original regressors belong to
the predicted regressors specified in {opt hat()}.  The order of the regressors
must match the order chosen in {opt hat()}.

{pmore}For example, in a regression of {cmd:y} on {cmd:z1}, {cmd:x2}, {cmd:x3},
and two-way fixed effects, the variables {cmd:x2} and {cmd:x3} are to be
instrumented by the IVs {cmd:z2} and {cmd:z3}.  A 2SLS estimation can be carried
out in the following way:

{pmore2}Run a first-stage regression for {cmd:x2}:

{phang3}{cmd:. felsdvreg x2 z1 z2 z3, ivar(i) jvar(j) xb(xb)}
         {cmd:peff(phat) feff(fhat)}

{pmore2}Predict {cmd:x2hat}:

{phang3}{cmd:. generate x2hat = xb + phat + fhat}

{pmore2}Run a first-stage regression for {cmd:x3}:

{phang3}{cmd:. felsdvreg x3 z1 z2 z3, ivar(i) jvar(j) xb(xb)}
         {cmd:peff(phat) feff(fhat)}

{pmore2}Predict {cmd:x3hat}:

{phang3}{cmd:. generate x3hat = xb + phat + fhat}

{pmore2}Run a second-stage regression:

{phang3}{cmd:. felsdvreg y z1 x2hat x3hat, ivar(i) jvar(j) xb(xb)}
            {cmd:peff(phat) feff(fhat) hat(x2hat x3hat) orig(x2 x3)}

{phang}
{opt feffse(varname)} specifies the name of a new variable to store the standard
errors of the fixed effects of the second effect.  For the nonidentified
effects, the variable for the standard errors will contain a missing value.
(Recovering the standard errors of the first effect is not implemented.)


{title:Saved results}

{pstd}
Besides the information saved in the variables named as determined by the
options {cmd:peff()}, {cmd:feff()}, {cmd:xb()}, {cmd:res()}, {cmd:mover()},
{cmd:group()}, {cmd:mnum()}, and {cmd:pobs()}, some e-class scalars and
matrices are returned and can be listed by typing {cmd:ereturn list}.  If the
{cmd:robust} or {cmd:cluster()} option is used, the e-class matrices include a
matrix {cmd:e(se)}, which contains the usual (nonrobust) standard errors that
would have been obtained without the {cmd:robust} or {cmd:cluster()} option.


{title:Example}

{phang}
{cmd:. felsdvreg y x w, ivar(i) jvar(j) feff(feff) peff(peff) mover(mover)}
         {cmd:group(group) xb(xb) res(res) mnum(mnum)}


{title:References}

{phang}Abowd, J., R. Creecy, and F. Kramarz.  2002.  Computing person and firm
effects using linked longitudinal employer-employee data.  Technical Report 
2002-06, U.S. Census Bureau. 
{browse "http://lehd.dsd.census.gov/led/library/techpapers/tp-2002-06.pdf"}.

{phang}Andrews, M., T. Schank, and R. Upward.  2006.  Practical fixed-effects
estimation methods for the three-way error-components model.
{it:Stata Journal} 6: 461-481.

{phang}Cornelissen, T. 2008.  The Stata command felsdvreg to fit a linear model
with two high-dimensional fixed effects.  {it:Stata Journal} 8: 170-189.

{phang}Greene, W.  2003.  {it:Econometric Analysis}.  5th ed.
Upper Saddle River, NJ: Prentice Hall.


{title:Author}

        Thomas Cornelissen, University of Hannover, Germany
        cornelissen@ewifo.uni-hannover.de


{title:Also see}

{psee}
Article: {it:Stata Journal}, volume 8, number 2: {browse "http://www.stata-journal.com/article.html?article=st0143":st0143}

{psee}Online:  {manhelp xtreg XT}
{p_end}
