*! version 3.2.9 21feb2016

Title

reghdfe -- Linear and instrumental-variable/GMM regression absorbing multiple levels of fixed effects

Syntax

reghdfe
depvar [indepvars] [(endogvars = iv_vars)]
[if] [in] [weight] , absorb(reghdfe_old##absvar:absvars) [options]

Model [+]
* absorb(reghdfe_old##absvar:absvars) identifiers of the absorbed fixed effects; each absvar represents one set of fixed effects

absorb(..., savefe) save all fixed effect estimates (__hdfe* prefix); useful for a subsequent predict.
However, see also the resid option.

residuals(newvar) save residuals; more direct and much faster than saving the fixed effects and then running predict

summarize(tabstat##statname:stats) equivalent to estat summarize after the regression,
but more flexible, compatible with the fast option, and saves results on e(summarize)

suboptions(...) additional options that will be passed to the regression command (either regress, ivreg2, or ivregress)

SE/Robust [+]
+ vce(vcetype [,opt]) vcetype
may be unadjusted (default), robust or cluster fvvarlist (allowing two- and multi-way clustering)

suboptions bw(#), kernel(str), dkraay(#) and kiefer allow for AC/HAC estimates; see the avar package

Instrumental-Variable/2SLS/GMM [+]
estimator(str) either 2sls (default), gmm2s (two-stage GMM),
liml (limited-information maximum likelihood) or cue (which gives approximate results, see discussion below)

stages(list) estimate additional regressions; choose any of first ols reduced acid (or all)

ffirst compute first-stage diagnostic and identification statistics

ivsuite(subcmd) package used in the IV/GMM regressions;
options are ivreg2 (default; needs installing) and ivregress

Diagnostic [+]
verbose(#) amount of debugging information to show (0=None, 1=Some, 2=More, 3=Parsing/convergence details, 4=Every iteration)

timeit show elapsed times by stage of computation

Optimization [+]
+ tolerance(#) criterion for convergence (default=1e-8)

maxiterations(#) maximum number of iterations (default=10,000); if set to missing (.) it will run for as long as it takes.

poolsize(#) apply the within algorithm in groups of # variables (default 10). a large poolsize is usually faster but uses more memory

acceleration(str) acceleration method; options are conjugate_gradient (cg), steep_descent (sd), aitken (a), and none (no)

transform(str) transform operation that defines the type of alternating projection; options are Kaczmarz (kac), Cimmino (cim), Symmetric Kaczmarz (sym)

Speedup Tricks [+]
cache(save [,opt]) absorb all variables without regressing (destructive; combine it with preserve/restore)

suboption keep(varlist) adds additional untransformed variables to the resulting dataset

cache(use) run regressions on cached data; vce() must be the same as with cache(save).

cache(clear) delete Mata objects to clear up memory; no more regressions can be run after this

fast will not create e(sample); disabled when saving fixed effects, residuals or mobility groups

Degrees-of-Freedom Adjustments [+]
dofadjustments(list) allows selecting the desired adjustments for degrees of freedom;
rarely used

groupvar(newvar) unique identifier for the first mobility group

Reporting [+]
version reports the version number and date of reghdfe, and saves it in e(version). standalone option

level(#) set confidence level; default is level(95)

display_options control column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling.

particularly useful are the noomitted and noempty options to hide regressors omitted due to collinearity

Undocumented
keepsingletons do not drop singleton groups

old will call the latest 2.x version of reghdfe instead (see the old help file)

* absorb(absvars) is required.

+ indicates a recommended or important option.

indepvars, endogvars and iv_vars may contain factor variables; see fvvarlist.

all the regression variables may contain time-series operators; see tsvarlist.

fweights, aweights and pweights are allowed; see weight.

Absvar Syntax

absvar

i.varname categorical variable to be absorbed (the i. prefix is tacit)

i.var1#i.var2 absorb the interactions of multiple categorical variables

i.var1#c.var2 absorb heterogeneous slopes, where var2 has a different slope coef. depending on the category of var1

var1##c.var2 equivalent to "i.var1 i.var1#c.var2", but much faster

var1##c.(var2 var3) multiple heterogeneous slopes are allowed together. Alternative syntax: var1##(c.var2 c.var3)

v1#v2#v3##c.(v4 v5) factor operators can be combined

To save the estimates specific absvars, write newvar=absvar.

Please be aware that in most cases these estimates are neither consistent nor econometrically identified.

Using categorical interactions (e.g. x#z) is faster than running egen group(...) beforehand.

Singleton obs. are dropped iteratively until no more singletons are found (see ancilliary article for details).

Slope-only absvars ("state#c.time") have poor numerical stability and slow convergence.
If you need those, either i) increase tolerance or
ii) use slope-and-intercept absvars ("state##c.time"), even if the intercept is redundant.
For instance if absvar is "i.zipcode i.state##c.time" then i.state is redundant given i.zipcode, but
convergence will still be much faster.

Description

reghdfe is a generalization of areg (and xtreg,fe, xtivreg,fe) for multiple levels of fixed effects
(including heterogeneous slopes), alternative estimators (2sls, gmm2s, liml), and additional robust standard errors (multi-way clustering, HAC standard errors, etc).

Additional features include:

a) A novel and robust algorithm to efficiently absorb the fixed effects (extending the work of Guimaraes and Portugal, 2010).

b) Coded in Mata, which in most scenarios makes it even faster than areg and xtreg for a single fixed effect (see benchmarks on the Github page).

c) Can save the point estimates of the fixed effects (caveat emptor: the fixed effects may not be identified, see the references).

d) Calculates the degrees-of-freedom lost due to the fixed effects
(note: beyond two levels of fixed effects, this is still an open problem, but we provide a conservative approximation).

e) Iteratively removes singleton groups by default, to avoid biasing the standard errors (see ancillary document).

Options

Model and Miscellanea

absorb(reghdfe_old##absvar:absvars) list of categorical variables (or interactions) representing the fixed effects to be absorbed.
this is equivalent to including an indicator/dummy variable for each category of each absvar. absorb() is required.

To save a fixed effect, prefix the absvar with "newvar=".
For instance, the option absorb(firm_id worker_id year_coefs=year_id) will include firm,
worker and year fixed effects, but will only save the estimates for the year fixed effects (in the new variable year_coefs).

If you want to predict afterwards but don't care about setting the names of each fixed effect, use the savefe suboption.
This will delete all variables named __hdfe*__ and create new ones as required.
Example: reghdfe price weight, absorb(turn trunk, savefe)

residuals(newvar) will save the regression residuals in a new variable.

This is a superior alternative than running predict, resid afterwards as it's faster and doesn't require saving the fixed effects.

summarize(tabstat##statname:stats) will report and save a table of summary of statistics of the regression
variables (including the instruments, if applicable), using the same sample as the regression.

summarize (without parenthesis) saves the default set of statistics: mean min max.

The complete list of accepted statistics is available in the tabstat help. The most useful are count range sd median p##.

The summary table is saved in e(summarize)

To save the summary table silently (without showing it after the regression table), use the quietly suboption. You can use it by itself (summarize(,quietly)) or with custom statistics (summarize(mean, quietly)).

suboptions(...)
options that will be passed directly to the regression command (either regress, ivreg2, or ivregress)

SE/Robust

vce(reghdfe_old##vcetype:vcetype, subopt)
specifies the type of standard error reported.
Note that all the advanced estimators rely on asymptotic theory, and will likely have poor performance with small samples
(but again if you are using reghdfe, that is probably not your case)

unadjusted/ols estimates conventional standard errors, valid even in small samples
under the assumptions of homoscedasticity and no correlation between observations

robust estimates heteroscedasticity-consistent standard errors (Huber/White/sandwich estimators), but still assuming independence between observations

Warning: in a FE panel regression, using robust will
lead to inconsistent standard errors if for every fixed effect, the other dimension is fixed.
For instance, in an standard panel with individual and time fixed effects, we require both the number of
individuals and time periods to grow asymptotically.
If that is not the case, an alternative may be to use clustered errors,
which as discussed below will still have their own asymptotic requirements.
For a discussion, see
Stock and Watson, "Heteroskedasticity-robust standard errors for fixed-effects panel-data regression," Econometrica 76 (2008): 155-174

cluster clustervars estimates consistent standard errors even when the observations
are correlated within groups.

Multi-way-clustering is allowed. Thus, you can indicate as many clustervars as desired
(e.g. allowing for intragroup correlation across individuals, time, country, etc).

Each clustervar permits interactions of the type var1#var2
(this is faster than using egen group() for a one-off regression).

Warning: The number of clusters, for all of the cluster variables, must go off to infinity.
A frequent rule of thumb is that each cluster variable must have at least 50 different categories
(the number of categories for each clustervar appears on the header of the regression table).

The following suboptions require either the ivreg2 or the avar package from SSC.
For a careful explanation, see the ivreg2 help file, from which the comments below borrow.

unadjusted, bw(#) (or just , bw(#)) estimates autocorrelation-consistent standard errors (Newey-West).

robust, bw(#) estimates autocorrelation-and-heteroscedasticity consistent standard errors (HAC).

cluster clustervars, bw(#) estimates standard errors consistent to common autocorrelated disturbances (Driscoll-Kraay). At most two cluster variables can be used in this case.

, kiefer estimates standard errors consistent under arbitrary intra-group autocorrelation (but not heteroskedasticity) (Kiefer).

kernel(str) is allowed in all the cases that allow bw(#)
The default kernel is bar (Bartlett). Valid kernels are Bartlett (bar); Truncated (tru); Parzen (par);
Tukey-Hanning (thann); Tukey-Hamming (thamm); Daniell (dan); Tent (ten); and Quadratic-Spectral (qua or qs).

Advanced suboptions:

, suite(default|mwc|avar) overrides the package chosen by reghdfe to estimate the VCE.
default uses the default Stata computation (allows unadjusted, robust, and at most one cluster variable).
mwc allows multi-way-clustering (any number of cluster variables), but without the bw and kernel suboptions.
avar uses the avar package from SSC. Is the same package used by ivreg2, and allows the bw, kernel, dkraay and kiefer suboptions.
This is useful almost exclusively for debugging.

, twicerobust will compute robust standard errors not only on the first but on the second step of the gmm2s estimation. Requires ivsuite(ivregress), but will not give the exact same results as ivregress.

Explanation: When running instrumental-variable regressions with the ivregress package,
robust standard errors, and a gmm2s estimator, reghdfe will translate
vce(robust) into wmatrix(robust) vce(unadjusted).
This maintains compatibility with ivreg2 and other packages, but may unadvisable as described in ivregress (technical note). Specifying this option will instead use wmatrix(robust) vce(robust).

However, computing the second-step vce matrix requires computing updated estimates (including updated fixed effects).
Since reghdfe currently does not allow this, the resulting standard errors
will not be exactly the same as with ivregress.
This issue is similar to applying the CUE estimator, described further below.

Note: The above comments are also appliable to clustered standard error.

IV/2SLS/GMM

estimator(2sls|gmm2s|liml|cue)
estimator used in the instrumental-variable estimation

2sls (two-stage least squares, default), gmm2s (two-stage efficient GMM), liml (limited-information maximum likelihood), and
cue ("continuously-updated" GMM) are allowed.

Warning: cue will not give the same results as ivreg2. See the discussion in
Baum, Christopher F., Mark E. Schaffer, and Steven Stillman. "Enhanced routines for instrumental variables/GMM estimation and testing." Stata Journal 7.4 (2007): 465-506
(page 484).
Note that even if this is not exactly cue, it may still be a desirable/useful alternative to standard cue, as explained in the article.

stages(list)
adds and saves up to four auxiliary regressions useful when running instrumental-variable regressions:

first all first-stage regressions

ols ols regression (between dependent variable and endogenous variables; useful as a benchmark)

reduced reduced-form regression (ols regression with included and excluded instruments as regressors)

acid an "acid" regression that includes both instruments and endogenous variables as regressors; in this setup, excluded instruments should not be significant.

You can pass suboptions not just to the iv command but to all stage regressions with a comma after the list of stages. Example:

reghdfe price (weight=length), absorb(turn) subopt(nocollin) stages(first, eform(exp(beta)) )

By default all stages are saved (see estimates dir).
The suboption ,nosave will prevent that.
However, future replays will only replay the iv regression.

ffirst
compute and report first stage statistics (details); requires the ivreg2 package.

These statistics will be saved on the e(first) matrix.
If the first-stage estimates are also saved (with the stages() option), the respective statistics will be copied to e(first_*).

ivsuite(subcmd)
allows the IV/2SLS regression to be run either using ivregress or ivreg2.

ivreg2 is the default, but needs to be installed for that option to work.

Diagnostic

verbose(#) orders the command to print debugging information.

Possible values are 0 (none), 1 (some information), 2 (even more), 3 (adds dots for each iteration, and reportes parsing details), 4 (adds details for every iteration step)

For debugging, the most useful value is 3. For simple status reports, set verbose to 1.

timeit shows the elapsed time at different steps of the estimation. Most time is usually spent on three steps: map_precompute(), map_solve() and the regression step.

Degrees-of-Freedom Adjustments

dofadjustments(doflist) selects how the degrees-of-freedom, as well as e(df_a), are adjusted due to the absorbed fixed effects.

Without any adjustment, we would assume that the degrees-of-freedom used by the fixed effects is equal to the count of all the fixed effects
(e.g. number of individuals + number of years in a typical panel).
However, in complex setups (e.g. fixed effects by individual, firm, job position, and year),
there may be a huge number of fixed effects collinear with each other, so we want to adjust for that.

Note: changing the default option is rarely needed, except in benchmarks, and to obtain a marginal speed-up by excluding the pairwise option.

all is the default and almost always the best alternative. It is equivalent to dof(pairwise clusters continuous)

none assumes no collinearity across the fixed effects (i.e. no redundant fixed effects). This is overtly conservative, although it is the faster method by virtue of not doing anything.

firstpair will exactly identify the number of collinear fixed effects across the first two sets of fixed effects
(i.e. the first absvar and the second absvar).
The algorithm used for this is described in Abowd et al (1999), and relies on results from graph theory
(finding the number of connected sub-graphs in a bipartite graph).
It will not do anything for the third and subsequent sets of fixed effects.

For more than two sets of fixed effects, there are no known results that provide exact degrees-of-freedom as in the case above.
One solution is to ignore subsequent fixed effects (and thus oversestimate e(df_a) and understimate the degrees-of-freedom).
Another solution, described below, applies the algorithm between pairs of fixed effects to obtain a better (but not exact) estimate:

pairwise applies the aforementioned connected-subgraphs algorithm between pairs of fixed effects.
For instance, if there are four sets of FEs, the first dimension will usually have no redundant coefficients (i.e. e(M1)==1), since we are running the model without a constant.
For the second FE, the number of connected subgraphs with respect to the first FE will provide an exact estimate of the degrees-of-freedom lost, e(M2).

For the third FE, we do not know exactly.
However, we can compute the number of connected subgraphs between the first and third G(1,3),
and second and third G(2,3) fixed effects, and choose the higher of those as the closest estimate for e(M3).
For the fourth FE, we compute G(1,4), G(2,4) and G(3,4) and again choose the highest for e(M4).

Finally, we compute e(df_a) = e(K1) - e(M1) + e(K2) - e(M2) + e(K3) - e(M3) + e(K4) - e(M4);
where e(K#) is the number of levels or dimensions for the #-th fixed effect (e.g. number of individuals or years).
Note that e(M3) and e(M4) are only conservative estimates and thus we will usually be overestimating the standard errors. However, given the sizes of the datasets typically used with reghdfe, the difference should be small.

Since the gain from pairwise is usually minuscule for large datasets, and the computation is expensive, it may be a good practice to exclude this option for speedups.

clusters
will check if a fixed effect is nested within a clustervar.
In that case, it will set e(K#)==e(M#) and no degrees-of-freedom will be lost due to this fixed effect.
The rationale is that we are already assuming that the number of effective observations is the number of cluster levels.
This is the same adjustment that xtreg, fe does, but areg does not use it.

continuous
Fixed effects with continuous interactions (i.e. individual slopes, instead of individual intercepts) are dealt with differently.
In an i.categorical#c.continuous interaction, we will do one check: we count the number of categories where c.continuous is always zero.
In an i.categorical##c.continuous interaction, we do the above check but replace zero for any particular constant.
In the case where continuous is constant for a level of categorical, we know it is collinear with the intercept, so we adjust for it.

Additional methods, such as bootstrap are also possible but not yet implemented.
Some preliminary simulations done by the author showed a very poor convergence of this method.

groupvar(newvar) name of the new variable that will contain the first mobility group.
Requires pairwise, firstpair, or the default all.

Speeding Up Estimation

reghdfe varlist [if] [in], absorb(absvars) save(cache) [options]

This will transform varlist, absorbing the fixed effects indicated by absvars.
It is useful when running a series of alternative specifications with common variables, as the variables will only be transformed once instead of every time a regression is run.

It replaces the current dataset, so it is a good idea to precede it with a preserve command

To keep additional (untransformed) variables in the new dataset, use the keep(varlist) suboption.

cache(use) is used when running reghdfe after a save(cache) operation. Both the absorb() and vce() options must be the same as when the cache was created (the latter because the degrees of freedom were computed at that point).

cache(clear) will delete the Mata objects created by reghdfe and kept in memory after the save(cache) operation. These objects may consume a lot of memory, so it is a good idea to clean up the cache. Additionally, if you previously specified preserve, it may be a good time to restore.

Example:

. sysuse auto

. preserve

.

. * Save the cache

. reghdfe price weight length, a(turn rep) vce(turn) cache(save, keep(foreign))

.

. * Run regressions

. reghdfe price weight, a(turn rep) cache(use)

. reghdfe price length, a(turn rep) cache(use)

.

. * Clean up

. reghdfe, cache(clear)

. restore

fast avoids saving e(sample) into the regression.
Since saving the variable only involves copying a Mata vector, the speedup is currently quite small.
Future versions of reghdfe may change this as features are added.

Note that fast will be disabled when adding variables to the dataset (i.e. when saving residuals, fixed effects, or mobility groups), and is incompatible with most postestimation commands.

If you wish to use fast while reporting estat summarize, see the summarize option.

Optimization

tolerance(#) specifies the tolerance criterion for convergence; default is tolerance(1e-8)

Note that for tolerances beyond 1e-14, the limits of the double precision are reached and the results will most likely not converge.

At the other end, is not tight enough, the regression may not identify perfectly collinear regressors. However, those cases can be easily spotted due to their extremely high standard errors.

Warning: when absorbing heterogeneous slopes without the accompanying heterogeneous intercepts, convergence is quite poor and a tight tolerance is strongly suggested (i.e. higher than the default). In other words, an absvar of var1##c.var2 converges easily, but an absvar of var1#c.var2 will converge slowly and may require a tighter tolerance.

maxiterations(#)
specifies the maximum number of iterations; the default is maxiterations(10000); set it to missing (.) to run forever until convergence.

poolsize(#)
Number of variables that are pooled together into a matrix that will then be transformed.
The default is to pool variables in groups of 5. Larger groups are faster with more than one processor, but may cause out-of-memory errors. In that case, set poolsize to 1.

Advanced options:

acceleration(str) allows for different acceleration techniques, from the simplest case of
no acceleration (none), to steep descent (steep_descent or sd), Aitken (aitken),
and finally Conjugate Gradient (conjugate_gradient or cg).

Note: Each acceleration is just a plug-in Mata function, so a larger number of acceleration techniques are available, albeit undocumented (and slower).

transform(str) allows for different "alternating projection" transforms. The classical transform is Kaczmarz (kaczmarz), and more stable alternatives are Cimmino (cimmino) and Symmetric Kaczmarz (symmetric_kaczmarz)

Note: Each transform is just a plug-in Mata function, so a larger number of acceleration techniques are available, albeit undocumented (and slower).

Note: The default acceleration is Conjugate Gradient and the default transform is Symmetric Kaczmarz. Be wary that different accelerations often work better with certain transforms. For instance, do not use conjugate gradient with plain Kaczmarz, as it will not converge.

precondition (currently disabled)

Reporting

level(#) sets confidence level; default is level(95)

display_options:
noomitted,
vsquish,
noemptycells,
baselevels,
allbaselevels,
nofvlabel,
fvwrap(#),
fvwrapon(style),
cformat(%fmt),
pformat(%fmt),
sformat(%fmt), and
nolstretch;
see [R] estimation options.

Postestimation Syntax

Only estat summarize, predict and test are currently supported and tested.

estat summarize

Summarizes depvar and the variables described in _b (i.e. not the excluded instruments)

predict
newvar
[if] [in]
[, statistic]

May require you to previously save the fixed effects (except for option xb).
To see how, see the details of the absorb option
Equation: y = xb + d_absorbvars + e

statistic

Main
xb xb fitted values; the default

xbd xb + d_absorbvars

d d_absorbvars

residuals residual

score score; equivalent to residuals

stdp standard error of the prediction (of the xb component)

although predict type newvar is allowed,
the resulting variable will always be of type double.

test Performs significance test on the parameters, see the stata help

suest Do not use suest. It will run, but the results will be incorrect. See workaround below

If you want to perform tests that are usually run with suest,
such as non-nested models, tests using alternative specifications of the variables,
or tests on different groups, you can replicate it manually, as described
here.

Possible Pitfalls and Common Mistakes

1. (note: as of version 2.1, the constant is no longer reported) Ignore the constant; it doesn't tell you much. If you want to use descriptive stats, that's what the summarize() and estat summ commands are for.
Even better, use noconstant to drop it (although it's not really dropped as it never existed on the first place!)

2. Think twice before saving the fixed effects. They are probably inconsistent / not identified and you will likely be using them wrong.

3. (note: as of version 3.0 singletons are dropped by default) It's good practice to drop singletons. dropsingleton is your friend.

4. If you use vce(robust), be sure that your other dimension is not "fixed" but grows with N, or your SEs will be wrong.

5. If you use vce(cluster ...), check that your number of clusters is high enough (50+ is a rule of thumb). If not, you are making the SEs even worse!

6. The panel variables (absvars) should probably be nested within the clusters (clustervars) due to the within-panel correlation induced by the FEs.
(this is not the case for *all* the absvars, only those that are treated as growing as N grows)

7. If you run analytic or probability weights,
you are responsible for ensuring that the weights stay
constant within each unit of a fixed effect (e.g. individual),
or that it is correct to allow varying-weights for that case.

8. Be aware that adding several HDFEs is not a panacea.
The first limitation is that it only uses within variation (more than acceptable if you have a large enough dataset).
The second and subtler limitation occurs if the fixed effects are themselves outcomes of the variable of interest (as crazy as it sounds).
For instance, imagine a regression where we study the effect of past corporate fraud on future firm performance.
We add firm, CEO and time fixed-effects (standard practice). This introduces a serious flaw: whenever a fraud event is discovered,
i) future firm performance will suffer, and ii) a CEO turnover will likely occur.
Moreover, after fraud events, the new CEOs are usually specialized in dealing with the aftershocks of such events
(and are usually accountants or lawyers).
The fixed effects of these CEOs will also tend to be quite low, as they tend to manage firms with very risky outcomes.
Therefore, the regressor (fraud) affects the fixed effect (identity of the incoming CEO).
Adding particularly low CEO fixed effects will then overstate the performance of the firm,
and thus understate the negative effects of fraud on future firm performance.

Missing Features

(If you are interested in discussing these or others, feel free to contact me)

Code, medium term:

- Complete GT preconditioning (v4)

- Improve algorithm that recovers the fixed effects (v5)

- Improve statistics and tests related to the fixed effects (v5)

- Implement a -bootstrap- option in DoF estimation (v5)

Code, long term:

- The interaction with cont vars (i.a#c.b) may suffer from numerical accuracy issues, as we are dividing by a sum of squares

- Calculate exact DoF adjustment for 3+ HDFEs (note: not a problem with cluster VCE when one FE is nested within the cluster)

- More postestimation commands (lincom? margins?)

Theory:

- Add a more thorough discussion on the possible identification issues

- Find out a way to use reghdfe iteratively with CUE
(right now only OLS/2SLS/GMM2S/LIML give the exact same results)

- Not sure if I should add an F-test for the absvars in the vce(robust) and vce(cluster) cases.
Discussion on e.g. -areg- (methods and formulas) and textbooks suggests not;
on the other hand, there may be alternatives:
A Heteroskedasticity-Robust F-Test Statistic for Individual Effects

Examples

Setup

. sysuse auto

Simple case - one fixed effect

. reghdfe price weight length, absorb(rep78)

As above, but also compute clustered standard errors

. reghdfe price weight length, absorb(rep78) vce(cluster rep78)

Two and three sets of fixed effects

. webuse nlswork

. reghdfe ln_w grade age ttl_exp tenure not_smsa south , absorb(idcode year)

. reghdfe ln_w grade age ttl_exp tenure not_smsa south , absorb(idcode year occ)

Advanced examples

Save the FEs as variables

. reghdfe ln_w grade age ttl_exp tenure not_smsa south , absorb(FE1=idcode FE2=year)

Report nested F-tests

. reghdfe ln_w grade age ttl_exp tenure not_smsa south , absorb(idcode year) nested

Do AvgE instead of absorb() for one FE

. reghdfe ln_w grade age ttl_exp tenure not_smsa south , absorb(idcode year) avge(occ)

. reghdfe ln_w grade age ttl_exp tenure not_smsa south , absorb(idcode year) avge(AvgByOCC=occ)

Check that FE coefs are close to 1.0

. reghdfe ln_w grade age ttl_exp tenure not_smsa , absorb(idcode year) check

Save first mobility group

. reghdfe ln_w grade age ttl_exp tenure not_smsa , absorb(idcode occ) group(mobility_occ)

Factor interactions in the independent variables

. reghdfe ln_w i.grade#i.age ttl_exp tenure not_smsa , absorb(idcode occ)

Interactions in the absorbed variables (notice that only the # symbol is allowed)

. reghdfe ln_w grade age ttl_exp tenure not_smsa , absorb(idcode#occ)

Interactions in both the absorbed and AvgE variables (again, only the # symbol is allowed)

. reghdfe ln_w grade age ttl_exp not_smsa , absorb(idcode#occ) avge(tenure#occ)

IV regression

. sysuse auto

. reghdfe price weight (length=head), absorb(rep78)

. reghdfe price weight (length=head), absorb(rep78) first

. reghdfe price weight (length=head), absorb(rep78) ivsuite(ivregress)

Factorial interactions

. reghdfe price weight (length=head), absorb(rep78)

. reghdfe price weight length, absorb(rep78 turn##c.price)

Stored results

reghdfe stores the following in e():

Note: it also keeps most e() results placed by the regression subcommands (ivreg2, ivregress)

Scalars
e(N) number of observations

e(N_hdfe) number of absorbed fixed-effects

e(tss) total sum of squares

e(rss) residual sum of squares

e(r2) R-squared

e(r2_a) adjusted R-squared

e(r2_within) Within R-squared

e(r2_a_within) Adjusted Within R-squared

e(df_a) degrees of freedom lost due to the fixed effects

e(rmse) root mean squared error

e(ll) log-likelihood

e(ll_0) log-likelihood of fixed-effect-only regression

e(F) F statistic

e(F_absorb) F statistic for absorbed effect note: currently disabled

e(rank) rank of e(V)

e(N_clustervars) number of cluster variables

e(clust#) number of clusters for the #th cluster variable

e(N_clust) number of clusters; minimum of e(clust#)

e(K#) Number of categories of the #th absorbed FE

e(M#) Number of redundant categories of the #th absorbed FE

e(mobility) Sum of all e(M#)

e(df_m) model degrees of freedom

e(df_r) residual degrees of freedom

Macros
e(cmd) reghdfe

e(subcmd) either regress, ivreg2 or ivregress

e(model) ols, iv, gmm2s, liml or cue

e(cmdline) command as typed

e(dofmethod) dofmethod employed in the regression

e(depvar) name of dependent variable

e(indepvars) names of independent variables

e(endogvars) names of endogenous right-hand-side variables

e(instruments) names of excluded instruments

e(absvars) name of the absorbed variables or interactions

e(title) title in estimation output

e(clustvar) name of cluster variable

e(clustvar#) name of the #th cluster variable

e(vce) vcetype specified in vce()

e(vcetype) title used to label Std. Err.

e(stage) stage within an IV-regression; only if stages() was used

e(properties) b V

Matrices
e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

Functions
e(sample) marks estimation sample

Author

Sergio Correia

Fuqua School of Business, Duke University

Email: sergio.correia@gmail.com

User Guide

A copy of this help file, as well as a more in-depth user guide is in development and will be available at http://scorreia.com/reghdfe.

Latest Updates

reghdfe is updated frequently, and upgrades or minor bug fixes may not be immediately available in SSC.
To check or contribute to the latest version of reghdfe, explore the
Github repository.
Bugs or missing features can be discussed through email or at the Github issue tracker.

To see your current version and installed dependencies, type reghdfe, version

Acknowledgements

This package wouldn't have existed without the invaluable feedback and contributions of Paulo Guimaraes, Amine Ouazad, Mark Schaffer and Kit Baum. Also invaluable are the great bug-spotting abilities of many users.

In addition, reghdfe is build upon important contributions from the Stata community:

reg2hdfe, from Paulo Guimaraes,
and a2reg from Amine Ouazad,
were the inspiration and building blocks on which reghdfe was built.

ivreg2, by Christopher F Baum, Mark E Schaffer and Steven Stillman, is the package used by default for instrumental-variable regression.

avar by Christopher F Baum and Mark E Schaffer, is the package used for estimating the HAC-robust standard errors of ols regressions.

tuples by Joseph Lunchman and Nicholas Cox, is used when computing standard errors with multi-way clustering (two or more clustering variables).

References

The algorithm underlying reghdfe is a generalization of the works by:

Paulo Guimaraes and Pedro Portugal. "A Simple Feasible Alternative Procedure to Estimate
Models with High-Dimensional Fixed Effects".
Stata Journal, 10(4), 628-649, 2010.
[link]

Simen Gaure. "OLS with Multiple High Dimensional Category Dummies".
Memorandum 14/2010, Oslo University, Department of Economics, 2010.
[link]

It addresses many of the limitation of previous works, such as possible lack of convergence, arbitrary slow convergence times,
and being limited to only two or three sets of fixed effects (for the first paper).
The paper explaining the specifics of the algorithm is a work-in-progress and available upon request.

If you use this program in your research, please cite either
the REPEC entry
or the aforementioned papers.

Additional References

For details on the Aitken acceleration technique employed, please see "method 3" as described by:

Macleod, Allan J. "Acceleration of vector sequences by multi-dimensional Delta-2 methods."
Communications in Applied Numerical Methods 2.4 (1986): 385-392.

For the rationale behind interacting fixed effects with continuous variables, see:

Duflo, Esther. "The medium run effects of educational expansion: Evidence from a large school construction program in Indonesia."
Journal of Development Economics 74.1 (2004): 163-197. [link]

Also see:

Abowd, J. M., R. H. Creecy, and F. Kramarz 2002.
Computing person and firm effects using linked longitudinal employer-employee data.
Census Bureau Technical Paper TP-2002-06.

Cameron, A. Colin & Gelbach, Jonah B. & Miller, Douglas L., 2011.
"Robust Inference With Multiway Clustering,"
Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 238-249.

Gormley, T. & Matsa, D. 2014.
"Common errors: How to (and not to) control for unobserved heterogeneity."
The Review of Financial Studies, vol. 27(2), pages 617-661.

Mittag, N. 2012.
"New methods to estimate models with large sets of fixed effects with an application to matched employer-employee data from Germany."
FDZ-Methodenreport 02/2012.