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Chapter4. Datafiles
30
4.9 Assemblingdatafrommultiplesources
Inmanycontextsresearchersneedtobringtogetherdatafrommultiplesourcefiles,andinsome
casesthesesourcesarenotorganizedsuchthatthedatacansimplybe“stucktogether”byappend-
ingrowsorcolumnstoabasedataset. Ingretl,thejoincommandcanbeusedforthispurpose;
thiscommandisdiscussedindetailinchapter7.
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Chapter5
Sub-samplingadataset
5.1 Introduction
Somesubtleissuescanarisehere;thischapterattemptstoexplaintheissues.
Asub-samplemaybedefinedinrelationtoafulldatasetintwodifferentways:wewillrefertothese
as“setting”thesampleand“restricting”thesample;thesemethodsarediscussedinsections5.2
and5.3respectively. Inadditionsection5.4discussessomespecialissuesrelatingtopaneldata,
andsection5.5coversresamplingwithreplacement,whichisusefulinthecontextofbootstrapping
teststatistics.
Thefollowing discussion focuses s on n thecommand-line approach. . Butyou u can also o invoke e the
methodsoutlinedhereviatheitemsundertheSamplemenuintheGUIprogram.
5.2 Settingthesample
By“setting”thesamplewemeandefiningasub-samplesimplybymeansofadjustingthestarting
and/orendingpointofthecurrentsamplerange.Thisislikelytobemostrelevantfortime-series
data.Forexample,onehasquarterlydatafrom1960:1to2003:4,andonewantstorunaregression
usingonlydatafromthe1970s.Asuitablecommandisthen
smpl 1970:1 1979:4
Oronewishestosetasideablockofobservationsattheendofthedataperiodforout-of-sample
forecasting.Inthatcaseonemightdo
smpl ; 2000:4
wherethesemicolonisshorthandfor“leavethestartingobservationunchanged”. (Thesemicolon
mayalsobeusedinplaceofthesecondparameter,tomeanthattheendingobservationshouldbe
unchanged.)By“unchanged”here,wemeanunchangedrelativetothelastsmplsetting,orrelative
tothefulldatasetifnosub-samplehasbeendefineduptothispoint.Forexample,after
smpl 1970:1 2003:4
smpl ; 2000:4
thesamplerangewillbe1970:1to2000:4.
Anincrementalorrelativeformofsettingthesamplerangeisalsosupported.Inthiscasearelative
offsetshouldbegiven,intheformofasignedinteger(orasemicolontoindicatenochange),for
boththestartingandendingpoint.Forexample
smpl +1 1 ;
willadvancethestartingobservationbyonewhilepreservingtheendingobservation,and
smpl +2 2 -1
31
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Chapter5. Sub-samplingadataset
32
willbothadvancethestartingobservationbytwoandretardtheendingobservationbyone.
Animportantfeatureof“setting”thesampleasdescribedaboveis that it necessarilyresults in
theselectionofasubsetofobservationsthatarecontiguousinthefulldataset. Thestructureof
thedatasetis thereforeunaffected(forexample,ifitisaquarterlytimeseriesbeforesettingthe
sample,itremainsaquarterlytimeseriesafterwards).
5.3 Restrictingthesample
By“restricting”thesamplewemeanselectingobservationsonthebasisofsomeBoolean(logical)
criterion,orbymeansofarandomnumbergenerator. Thisislikelytobemostrelevantforcross-
sectionalorpaneldata.
Supposewehavedataonacross-sectionofindividuals,recordingtheirgender,incomeandother
characteristics.Wewishtoselectforanalysisonlythewomen.Ifwehaveagenderdummyvariable
withvalue1formenand0forwomenwecoulddo
smpl gender==0 --restrict
tothiseffect.Orsupposewewanttorestrictthesampletorespondentswithincomesover$50,000.
Thenwecoulduse
smpl income>50000 --restrict
Aquestionarises: ifweissuethetwocommandsaboveinsequence,whatdo o weendupwithin
our sub-sample: : allcases s withincomeover 50000, or justwomen with incomeover50000? ? By
default,theansweristhelatter:womenwithincomeover50000.Thesecondrestrictionaugments
thefirst,orinotherwordsthefinalrestrictionisthelogicalproductofthenewrestrictionandany
restrictionthatisalreadyinplace.Ifyouwantanewrestrictiontoreplaceanyexistingrestrictions
youcanfirstrecreatethefulldatasetusing
smpl --full
Alternatively,youcanaddthereplaceoptiontothesmplcommand:
smpl income>50000 --restrict --replace
Thisoptionhastheeffectofautomaticallyre-establishingthefulldatasetbeforeapplyingthenew
restriction.
Unlikeasimple“setting”of thesample, “restricting”thesamplemayresultinselectionof non-
contiguousobservationsfromthefulldataset. Itmaythereforechangethestructureofthedata
set.
Thiscanbeseeninthecaseofpaneldata.Saywehaveapaneloffivefirms(indexedbythevariable
firm)observedineachofseveralyears(identifiedbythevariableyear).Thentherestriction
smpl year==1995 --restrict
producesadatasetthatisnotapanel,butacross-sectionfortheyear1995.Similarly
smpl firm==3 --restrict
producesatime-seriesdatasetforfirmnumber3.
Forthesereasons(possiblenon-contiguityintheobservations,possiblechangeinthestructureof
thedata),gretlactsdifferentlywhenyou“restrict”thesampleasopposedtosimply“setting”it.In
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Chapter5. Sub-samplingadataset
33
thecaseofsetting,theprogrammerelyrecordsthestartingandendingobservationsandusesthese
asparameterstothevariouscommandscallingfortheestimationofmodels,thecomputationof
statistics,andsoon. Inthecaseofrestriction,theprogrammakesareducedcopyofthedataset
and bydefaulttreats thisreduced copyasasimple, undatedcross-section—butseethefurther
discussionofpaneldatainsection5.4.
Ifyouwishtore-imposeatime-seriesinterpretationofthereduceddatasetyoucandosousingthe
setobscommand,ortheGUImenuitem“Data,Datasetstructure”.
The fact that“restricting”the sample results s in the e creation of a reduced copy of the original
dataset mayraiseanissuewhenthedatasetis very large. . With h suchadataset in memory, the
creationofacopymayleadtoasituationwherethecomputerrunslowonmemoryforcalculating
regressionresults.Youcanworkaroundthisasfollows:
1. Openthefulldataset,andimposethesamplerestriction.
2. Saveacopyofthereduceddatasettodisk.
3. Closethefulldatasetandopenthereducedone.
4. Proceedwithyouranalysis.
Randomsub-sampling
Besidesrestrictingthesampleonsomedeterministiccriterion,itmaysometimesbeuseful(when
working withverylargedatasets, or perhaps to studytheproperties ofanestimator)to draw a
randomsub-samplefromthefulldataset.Thiscanbedoneusing,forexample,
smpl 100 0 --random
toselect 100cases. . Ifyouwantthesampleto o bereproducible, youshouldset t theseedfor r the
randomnumber generator first, using theset command. . This s sortof sampling falls under the
“restriction”category:areducedcopyofthedatasetismade.
5.4 Paneldata
ConsiderforconcretenesstheArellano–Bonddatasetsuppliedwithgretl(abdata.gdt). Thiscom-
prises dataon140firmsn 140)observedover theyears1976–1984T 9. Thedatasetis
“nominallybalanced”inthesensethatthatthetime-serieslengthisthesameforallcountries(this
beingarequirementforadatasettocountasapanelingretl),butinfacttherearemanymissing
values(NAs).
Youmaywanttosub-samplesuchadatasetineitherthecross-sectionaldimension(limitthesam-
pletoasubsetoffirms)orthetimedimension(e.g.usedatafromthe1980sonly). Thesimplest
(butlimited)waytosub-sampleonfirmskeysoffthenotationusedbygretlforpanelobservations.
Thefulldatarangeisprintedas1:1(firm1,period1)to140:9(firm140,period9).Theeffectof
smpl 1:1 1 80:9
is to limit thesampleto thefirst80firms. . Notethatifyouinsteadtriedsmpl l 1:1 80:4, , gretl
wouldinsistonpreservingthebalanceofthepanelandwouldtruncatetherangeto “complete”
firms,asifyouhadtypedsmpl 1:1 1 79:9.
Thefirms intheArellano–Bond dataset are e anonymous, , butsupposeyouhad apanelwith five
namedcountries. Withsuchapanelyoucaninformgretlofthenames s of thegroupsusing the
setobscommand.Forexample,given
string cstr = "Portugal Italy y Ireland d Greece Spain"
setobs country cstr r --panel-groups
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Chapter5. Sub-samplingadataset
34
gretlcreatesastring-valuedseriesnamedcountrywithgroupnamestakenfromthevariablecstr.
Then,toincludeonlyItalyandSpainyoucoulddo
smpl country=="Italy" || country=="Spain" " --restrict
ortoexcludeonecountry,
smpl country!="Ireland" --restrict
Tosub-sampleinthetimedimension,useof--restrictisrequired. Forexample,theArellano–
BonddatasetcontainsavariablenamedYEARthatrecordstheyearoftheobservationsandifone
wantedtoomitthefirsttwoyearsofdataonecoulddo
smpl YEAR >= 1978 --restrict
Ifadatasetdoesnotalreadyincudeasuitablevariableforthispurposeonecanusethecommand
genr timetocreateasimple1-basedtimeindex.
Notethatifyouapplyasamplerestrictionthatjustselectscertainunits(firms,countriesorwhat-
ever),orselectscertaincontiguoustime-periods—suchthatn>1,T >1andthetime-serieslength
is stillthesameacross allincludedunits—yoursub-samplewillstillbeinterpretedbygretlas a
panel.
Unbalancingrestrictions
Insomecases one e wants s to o sub-sampleaccording g to acriterionthat “cuts across thegrain” of
apaneldataset. For r instance, , supposeyouhaveamicro o datasetwith h thousandsof individuals
observed over r several years and you want to restrict the sample to o observations s on n employed
women.
IfwesimplyextractedfromthetotalnTrowsofthedatasetthosethatpertaintowomenwhowere
employedattimet t  1;:::;Twewouldlikelyendupwithadatasetthatdoesn’tcountas a
panelingretl(becausethespecifictime-serieslength,T
i
,woulddifferacrossindividuals). Insome
contextsitmightbeOKthatgretldoesn’ttakeyour sub-sampletobeapanel, butifyouwantto
applypanel-specificmethodsthisisaproblem. Youcansolveitbygivingthe--balancedoption
withsmpl.Forexample,supposingyourdatasetcontaineddummyvariablesgender(withthevalue
1codingforwomen)andemployed,youcoulddo
smpl gender==1 && employed==1 1 --restrict --balanced
Whatexactlydoesthisdo?Well,let’ssaytheyearsofyourdataare2000,2005and2010,andthat
somewomenwereemployedinallofthoseyears,givingamaximumT
i
valueof3. Butindividual
526isawomenwho wasemployedonlyintheyear2000(T
i
1). Theeffectofthe--balanced
optionisthentoinsert“paddingrows”ofNAsfortheyears2005and2010forindividual526,and
similarlyforallindividualswith0<T
i
<3.Yoursub-samplethenqualifiesasapanel.
5.5 Resamplingandbootstrapping
Givenanoriginaldataseriesx,thecommand
series xr = resample(x)
createsanewserieseachofwhoseelementsisdrawnatrandomfromtheelements ofx. . Ifthe
originalserieshas100observations,eachelementofxisselectedwithprobability1=100ateach
drawing.Thustheeffectisto“shuffle”theelementsofx,withthetwistthateachelementofxmay
appearmorethanonce,ornotatall,inxr.
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Chapter5. Sub-samplingadataset
35
Theprimaryuseofthisfunctionisintheconstructionofbootstrapconfidenceintervalsorp-values.
Hereisasimpleexample.SupposeweestimateasimpleregressionofyonxviaOLSandfindthat
theslopecoefficienthasareported t-ratio of 2.5with40degrees of freedom. . Thetwo-tailedp-
valueforthenullhypothesisthattheslopeparameterequalszeroisthen0.0166,usingthet40
distribution. Dependingonthecontext,however,wemaydoubtwhethertheratioofcoefficientto
standarderrortrulyfollowsthet40distribution.Inthatcasewecouldderiveabootstrapp-value
asshowninExample5.1.
Underthenullhypothesisthattheslopewithrespecttoxiszero,yissimplyequaltoitsmeanplus
anerrorterm.WesimulatebyresamplingtheresidualsfromtheinitialOLSandre-estimatethe
model. Werepeatthisprocedurealargenumberoftimes,andrecordthenumberofcaseswhere
theabsolutevalueofthet-ratioisgreaterthan2.5: theproportionofsuchcasesisourbootstrap
p-value. For r agood discussionof simulation-based tests andbootstrapping, , seeDavidsonand
MacKinnon(2004,chapter4);DavidsonandFlachaire(2001)isalsoinstructive.
Example5.1: Calculationofbootstrapp-value
ols y 0 x
# save e the residuals
genr ui = $uhat
scalar ybar = = mean(y)
# number r of replications s for r bootstrap
scalar replics = 10000
scalar tcount t = = 0
series ysim
loop replics s --quiet
# generate e simulated d y y by y resampling
ysim = ybar r + + resample(ui)
ols ysim 0 0 x
scalar tsim m = = abs($coeff(x) / $stderr(x))
tcount += (tsim > 2.5)
endloop
printf "proportion of cases with |t| > 2.5 = %g\n", tcount / replics
Chapter6
Graphsandplots
6.1 Gnuplotgraphs
Aseparateprogram,gnuplot,iscalledtogenerategraphs.Gnuplotisaveryfull-featuredgraphing
programwithmyriadoptions. Itisavailablefromwww.gnuplot.info(butnotethatasuitablecopy
ofgnuplotisbundledwiththepackagedversions ofgretlforMSWindows and Mac OSX).Gretl
gives youdirectaccess, viaagraphicalinterface, to asubsetofgnuplot’soptionsandittries to
choosesensiblevaluesforyou;italsoallowsyoutotakecompletecontrolovergraphdetailsifyou
wish.
Withagraphdisplayed,youcanclickonthegraphwindowforapop-upmenuwiththefollowing
options.
 SaveasPNG:SavethegraphinPortableNetworkGraphicsformat(thesameformatthatyou
seeonscreen).
 Saveaspostscript:Saveinencapsulatedpostscript(EPS)format.
 SaveasWindowsmetafile:SaveinEnhancedMetafile(EMF)format.
 Savetosessionasicon:Thegraphwillappeariniconicformwhenyouselect“Iconview”from
theViewmenu.
 Zoom: : Lets s you select an area a within thegraphfor r closer inspection n (not availablefor r all
graphs).
 Print:(CurrentGTKorMSWindowsonly)letsyouprintthegraphdirectly.
 Copytoclipboard:MSWindowsonly,letsyoupastethegraphintoWindowsapplicationssuch
asMSWord.
 Edit:Opensacontrollerfortheplotwhichletsyouadjustmanyaspectsofitsappearance.
 Close:Closesthegraphwindow.
Displayingdatalabels
ForsimpleX-Yscatterplots,somefurtheroptionsareavailableifthedatasetincludes“casemark-
ers”(thatis, labelsidentifyingeachobservation).Withascatter plotdisplayed, whenyoumove
themousepointeroveradatapointitslabelis shownonthegraph. . Bydefaulttheselabelsare
transient:theydonotappearintheprintedorcopiedversionofthegraph.Theycanberemovedby
selecting“Cleardatalabels”fromthegraphpop-upmenu. Ifyouwantthelabelstobeaffixedper-
manently(sotheywillshowupwhenthegraphisprintedorcopied),selecttheoption“Freezedata
labels”fromthepop-upmenu;“Cleardatalabels”cancels thisoperation. . Theotherlabel-related
option,“Alldatalabels”,requeststhatcasemarkersbeshownforallobservations. Atpresentthe
displayofcasemarkersisdisabledforgraphscontainingmorethan250datapoints.
1
Foranexampleofsuchadataset,seetheRamanathanfiledata4-10:thiscontainsdataonprivateschoolenrollment
forthe50statesoftheUSAplusWashington,DC;thecasemarkersarethetwo-lettercodesforthestates.
36
Chapter6. Graphsandplots
37
GUIploteditor
SelectingtheEditoptioninthegraphpopupmenuopensaneditingdialogbox,showninFigure6.1.
Noticethatthereareseveraltabs, allowingyoutoadjustmanyaspectsofagraph’sappearance:
font,title,axisscaling,linecolorsandtypes,andsoon.Youcanalsoaddlinesordescriptivelabels
toagraph(under theLines andLabels tabs). . The“Apply”buttonapplies s yourchanges without
closingtheeditor;“OK”appliesthechangesandclosesthedialog.
Figure6.1: gretl’sgnuplotcontroller
Publication-qualitygraphics: advancedoptions
The GUI plot editor r has s two o limitations. . First, , it cannot represent all the e myriad options that
gnuplotoffers. Userswho o aresufficientlyfamiliarwithgnuplotto knowwhatthey’remissing in
theploteditorpresumablydon’tneedmuchhelpfromgretl,solongastheycangetholdofthe
gnuplotcommandfilethatgretlhasputtogether.Second,eveniftheploteditormeetsyourneeds,
intermsoffine-tuningthegraphyouseeonscreen,afewdetailsmayneedfurtherworkinorder
togetoptimalresultsforpublication.
Eitherway,thefirststepinadvancedtweakingofagraphistogetaccesstothegraphcommand
file.
 Inthegraphdisplaywindow,right-clickandchoose“Savetosessionasicon”.
 Ifit’snotalreadyopen,opentheiconviewwindow—eitherviathemenuitemView/Iconview,
orbyclickingthe“sessioniconview”buttononthemain-windowtoolbar.
 Right-clickontheiconrepresentingthenewlyaddedgraphandselect“Editplotcommands”
fromthepop-upmenu.
 Yougetawindowdisplayingtheplotfile(Figure6.2).
Hereare the basic c things you can do inthis window. . Obviously, , you u can edit thefile you just
opened. Youcanalsosenditforprocessingbygnuplot,byclickingthe“Execute”(cogwheel)icon
inthetoolbar.Oryoucanusethe“Saveas”buttontosaveacopyforeditingandprocessingasyou
wish.
Chapter6. Graphsandplots
38
Figure6.2:Plotcommandseditor
Unlessyou’reagnuplotexpert,mostlikelyyou’llonlyneedtoeditacoupleoflinesatthetopof
thefile,specifyingadriver(plusoptions)andanoutputfile.Weofferhereabriefsummaryofsome
pointsthatmaybeuseful.
First,gnuplot’soutputmodeissetviathecommandset termfollowedbythenameofasupported
driver (“terminal”in n gnuplot parlance) plus various possibleoptions. . (The e top line inthe plot
commandswindowshowstheset termlinethatgretlusedtomakeaPNGfile,commentedout.)
ThegraphicformatsthataremostsuitableforpublicationarePDFandEPS.Thesearesupported
bythegnuplottermtypespdf, pdfcairoandpostscript (withtheepsoption). . Thepdfcairo
driverhasthevirtuethatisbehavesinaverysimilarmannertothePNGone,theoutputofwhich
youseeonscreen.Thisisprovidedbytheversionofgnuplotthatisincludedinthegretlpackages
forMSWindowsandMacOSX;ifyou’reonLinuxitmayormaybesupported. Ifpdfcairoisnot
available,thepdfterminalmaybeavailable;thepostscriptterminalisalmostcertainlyavailable.
Besidesselectingatermtype,ifyouwanttogetgnuplotto writetheactualoutputfileyouneed
toappendaset outputlinegivingafilename. . Hereareafewexamplesofthefirsttwolinesyou
mighttypeinthewindoweditingyourplotcommands.We’llmakethesemore“realistic”shortly.
set term m pdfcairo
set output ’mygraph.pdf’
set term m pdf
set output ’mygraph.pdf’
set term m postscript eps
set output ’mygraph.eps’
Thereareacoupleofthingsworthremarkinghere. First,youmaywanttoadjustthesizeofthe
graph, and secondyoumay want to changethefont. . Thedefaultsizes s produced by theabove
driversare5inchesby3inchesforpdfcairoandpdf,and5inchesby3.5inchesforpostscript
eps. Ineachcaseyoucanchangethisbygivingasizespecification,whichtakestheformXX,YY
(examplesbelow).
Chapter6. Graphsandplots
39
Youmayask,whybotherchangingthesizeinthegnuplotcommandfile?Afterall,PDFandEPSare
bothvectorformats,sothegraphscanbescaledatwill.True,butauniformscalingwillalsoaffect
thefontsize,whichmayendlookingwrong. Youcangetoptimalresults s byexperimentingwith
thefontandsizeoptionstognuplot’sset termcommand. . Herearesomeexamples(comments
followbelow).
# pdfcairo, regular r size, , slightly amended
set term m pdfcairo o font "Sans,6" size 5in,3.5in
# or small size
set term m pdfcairo o font "Sans,5" size 3in,2in
# pdf, regular size, slightly y amended
set term m pdf f font "Helvetica,8" size 5in,3.5in
# or small
set term m pdf f font "Helvetica,6" size 3in,2in
# postscript, regular
set term m post t eps solid font "Helvetica,16"
# or small
set term m post t eps solid font "Helvetica,12" size 3in,2in
On thefirstlineweset asansseriffontfor r pdfcairo at t asuitablesizefor r a53.5inchplot
(whichyoumayfindlooksbetterthantherather“letterboxy”defaultof53).Andonthesecond
weillustratewhatyoumightdotogetasmaller32inchplot. Youcanspecifytheplotsizein
centimetersifyouprefer,asin
set term m pdfcairo o font "Sans,6" size 6cm,4cm
Wethenrepeattheexerciseforthepdfterminal. Noticethatherewe’respecifyingoneofthe35
standardPostScriptfonts,namelyHelvetica. Unlikepdfcairo, , theplainpdfdriverisunlikelyto
beabletofindfontsotherthanthese.
Inthethirdpair oflinesweillustrateoptionsforthepostscript driver(which,asyousee,can
be abbreviated as s post). . Note e thatherewe have added the option solid. . Unlike e most other
drivers, this oneuses dashed lines unless s you u specifythe solid option. . Also o notethat t we’ve
(apparently)specifiedamuchlargerfontinthiscase. That’sbecausetheepsoptionineffecttells
thepostscriptdriver to workathalf-size(amongother things), soweneedto doublethefont
size.
Table6.1summarizesthebasicsforthethreedriverswehavementioned.
Terminal
defaultsize(inches) suggestedfont
pdfcairo
53
Sans,6
pdf
53
Helvetica,8
post eps
53.5
Helvetica,16
Table6.1:Driversforpublication-qualitygraphics
Tofindoutmoreaboutgnuplotvisitwww.gnuplot.info.Thissitehasdocumentationforthecurrent
versionoftheprograminvariousformats.
Additionaltips
Tobewritten.Linewidths,enhancedtext.Showa“beforeandafter”example.
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