Apportionment Cycles as Natural Experiments. Roy Elis Department of Political Science Stanford University

Transcription

1 Apporionmen Cycles as Naural Experimens Roy Elis Deparmen of Poliical Science Sanford Universiy Neil Malhora Graduae School of Business Sanford Universiy Marc Meredih Deparmen of Poliical Science Massachuses Insiue of Technology

2 ABSTRACT Alhough here are compelling heoreical reasons o believe ha unequal poliical represenaion in a legislaure leads o an unequal disribuion of funds, esing such heories empirically is challenging because i is difficul o separae he effecs of represenaion from he effecs of eiher populaion levels or changes. We leverage he naural experimen generaed by infrequen and discree Census apporionmen cycles o esimae he disribuional effecs of malapporionmen in he U.S. House of Represenaives. We find ha changes in represenaion cause changes in he disribuion of federal oulays o he saes. Our mehod is exporable o any democraic sysem in which reapporionmens are regular, infrequen, and non-sraegic.

3 Following Census 2000, he sae of Uah was allocaed hree seas in he U.S. House of Represenaives, falling shor of he hreshold for a fourh sea by 857 people less han 0.04% of is populaion. Uah vociferously challenged he Census coun, aking is case all he way o he Supreme Cour (Uah v. Evans 2001, 2002) where i conesed boh he impuaion mehods used by he Census Bureau o esimae apporionmen populaions and also he saue ha couns overseas miliary personnel bu no Mormon missionaries residing abroad. Uah los boh cases. As a resul, he average disric in Uah in 2003 represened 746,000 residens insead of 560,000 residens as would have been he case if he sae had been awarded four seas. The conesed sea wen o Norh Carolina, which increased is represenaion in he House from welve o hireen members. Alhough he U.S. House follows he principle of one person, one voe, significan dispariies in represenaion are unavoidable in pracice as demonsraed by he fac ha he 2000 apporionmen lef Uah wih 15% less represenaion han he average sae on a per capia basis. The exen o which Uah conesed he resuls of Census 2000 suggess ha differences in relaive represenaion have imporan policy consequences, no he leas of which is he disribuion of federal funds o he saes. The fundamenal problem of confirming his inuiion empirically is ha boh represenaion and populaion may direcly affec disribuional oucomes. Hence, observed associaions beween represenaion and disribuional oucomes are likely o joinly capure he effec of represenaion and any unmeasured direc effecs of populaion. To illusrae he idenificaion problem, consider he well-documened posiive relaionship beween changes in saes ne receips from federal expendiures and changes in represenaion per capia in he Senae (e.g. Alas e al. 1995; Hoover and Pecorino 2005; 1

4 Larcinese e al. 2007). Because each sae has a fixed number of senaors, per capia represenaion is direcly proporional o he inverse of sae populaion, and hence changes in Senae represenaion are driven solely by changes in sae populaion. In an observaional sudy, disenangling he effec of populaion changes from he effec of represenaional changes necessiaes making srong funcional form resricions on he effecs of changes in populaion. I is also likely ha here are imporan unobservables (e.g. economic developmen) ha drive boh he changes in sae populaion and also a sae s share of he disribuion of federal dollars. For insance, saes wih below-average populaion growh gain relaive represenaion in he conex of he Senae by definiion. If, for example, he federal governmen direcs financial assisance owards economically-depressed areas, regressions predicing changes in federal spending wih changes in relaive represenaion will pick up a spurious correlaion due o he economic processes driving boh populaion rends and federal spending rends. Thus, alhough hese sudies are insrucive a poining o a correlaion beween represenaion and disribuion, hey do no provide compelling evidence of he causal effec. Oher sudies examine he correlaions beween levels of represenaion and levels of expendiures (e.g. Lee 1998, 2000; Knigh 2008; Larcinese e al. 2007). Ye, as Alesina and Spolaore (1997) argue, geographically-large poliical unis exhibi diseconomies of scale and herefore require more public monies han geographically-small unis o obain he same level of services. Hence, he fac ha large, sparsely populaed saes such as Alaska and Monana receive higher per capia federal funds may mainly be driven by greaer need. In his paper, we uilize a naural experimen in he U.S. House of Represenaives in order o separae he disribuional effecs of populaion changes, populaion levels, and poenial unobservables from he disribuional effecs of changes in poliical represenaion. Specifically, 2

5 we use he infrequen and discree naure of reapporionmen in he U.S. House of Represenaives as our idenifying source of variaion. Previous work has overlooked he fac ha he very mechanisms designed o reapporion he House consiue a srucural source of variaion in represenaional equaliy. The House is reapporioned only once every en years despie coninuous populaion changes among he saes. This implies a srucural break in relaive represenaion following each Census-based reapporionmen. Our analysis leverages he discree shocks creaed by he Census cycles, allowing us o compare oulays received by saes immediaely before and afer reapporionmen. The effec is idenified by swichers, or saes ha gain or lose seas. By focusing on a narrow window of ime around each reapporionmen, we are able o develop a difference-in-firs-differences echnique o esimae he effecs of represenaion wihou imposing sric funcional form resricions. Changes in House represenaion significanly increase federal oulays a he sae level. Our poin esimaes imply ha he elasiciy of oal oulays wih respec o represenaion is abou In oher words, a 10 percen increase in a sae s share of represenaives equaes o a 0.7 percen increase in a sae s share of he federal budge, suggesing ha Uah s oulays were abou wo percen lower in 2004 han hey would have been had Uah been awarded a fourh Congressional sea, a loss of abou $100 per capia. We also find ha he effec of represenaion is conexual; large saes do no benefi as much from he same percen change in he number of represenaives as small saes. We find no evidence of asymmeric effecs beween gains and losses in represenaion. The aricle proceeds as follows. In he firs secion, we review recen lieraure linking represenaion o disribuion. Secion 2 describes he complex apporionmen process used by he Census Bureau o assign congressional seas o saes. Secion 3 presens wo idenificaion 3

6 sraegies semming from Census-based apporionmen in he U.S. House of Represenaives. We describe he daa and measures in Secion 4. In he final secion, we presen he resuls and discuss heir implicaions. Secion 1. Recen Advances in he Sudy of Represenaion and Disribuion A fundamenal concep in he sudy of poliics is represenaion, or he degree o which eleced officials wih poliical power reflec he preferences of ciizens (Mansbridge 2003). Our paper focuses on esimaing he disribuive consequences of unequal represenaion in a legislaure. We assume ha legislaors respond o reelecion incenives and hus compee o procure argeable goods and benefis for heir disrics (e.g. Mayhew 1974; Fiorina 1989; Weingas e al. 1981). Moreover, we assume a posiive correlaion beween voing weighs and bargaining power, as is usually he case in disribuive models of legislaive bargaining (e.g. Baron and Ferejohn 1989). 1 Thus, we expec ha overrepresened poliical unis will receive a disproporionaely large share of disribuive goods. 2 Alhough he heoreical bases for he relaionship are sufficienly compelling, a general mehod for esimaing is magniude has proved elusive. A number of recen sudies have addressed he idenificaion problem in innovaive ways. Ansolabehere e al. (2002) use he naural experimen generaed by he Supreme Cour s decision in Baker v. Carr (1962), which mandaed one person, one voe in U.S. sae legislaures as an exogenous shock o sae-level apporionmen. They esimae ha he cour-ordered poliical equalizaion resuled in a ransfer 1 I should be noed ha examples can be consruced in a Baron and Ferejohn (1989) framework where expeced payoffs decrease from an increase in voing weighs. 2 The Baron-Ferejohn model has been exended in numerous ways o explain how he srengh of a consiuency s voing weigh significanly increases is abiliy o bargain and procure resources from a common pool (Banks and Duggan 2000; Snyder e al. 2005; Chen and Malhora 2007), as well as he condiions under which malapporionmen maers (Ansolabehere e al. 2003). 4

7 of abou $7 billion from counies ha were overrepresened o counies ha were underrepresened. Knigh (2008) and Hauk and Wacziarg (2007) examine differences in earmarks ha originae in he Senae versus he House and find ha relaively more earmarks are argeed o small saes in he Senae s version of he legislaion. Hirano (2006) and Hirano and Ting (2008) use legislaor deahs in he Japanese Die as an exogenous shock o esimae how argeed spending changes once a consiuency loses represenaion. The auhors find a significan effec of represenaion among weak consiuency groups. Finally, in a sudy closes o our own, Falk (2006) uses disconinuiies creaed by ineger consrains in he apporionmen formula in he House of Represenaive as an insrumenal variable for represenaion. His poin esimaes sugges ha he reurns o gaining a second member of Congress are abou $1,000 per capia. Even hese innovaive approaches, however, have cerain limiaions. Ansolabehere e al. (2002) use a one-ime experimen, which is specific o he Unied Saes in he 1960s and herefore heir research design does no generalize o oher eras in he U.S. or o comparaive conexs. Knigh (2008) and Hauk and Wacziarg s (2007) mehod can only be applied o a subse of bills and ress on he assumpion ha legislaors do no sraegically anicipae how he bills will be resolved in conference when voing wihin heir respecive chambers. Hirano (2006) and Hirano and Ting s (2008) approach would be difficul o apply ouside he Japanese conex due o he pauciy of deahs and he speed wih which members are replaced. Falk s (2006) approach limis him o esimaing a local-average-reamen-effec (LATE) of he effecs of represenaion in small saes. This brings ino quesion wheher his resuls also apply o larger saes. Moreover, he necessiy of looking a small saes resrics he sample size from which he gains 5

8 idenificaion o a smaller number of observaions, which raises concerns abou small sample insrumenal variable bias (see Ullah 2004 for an overview). Using he iming of Census apporionmen has several advanages over previous mehods. Firs, he mehod can be applied o mos any legislaive seing and o a broad se of oucomes so long as reapporionmen is relaively infrequen and non-sraegic, making i especially useful for he comparaive sudy of represenaion. Second, he mehod requires no assumpions abou sraegic ineracions beween he upper and lower chambers of he legislaure. Third, i leverages he full sample of U.S. saes and avoids poenial bias of small-sample insrumenal variables. Secion 2. The Apporionmen Mechanism as a Naural Experimen Populaion-Based Apporionmen Aricle 1, Secion 2, of he Consiuion esablished ha he apporionmen of he House of Represenaives shall be based upon a naional decennial census. The House has been regularly apporioned according o Census populaion esimaes since 1790, wih he excepion of he 1920 Census afer which here was no reapporionmen. The number of seas in he House has been fixed a 435 since 1911, wih he excepion of a emporary increase o 437 seas following he admission of Hawaii and Alaska in Since 1941, he House has been reapporioned wih perfec regulariy decennially, for a fixed size of 435, by he Mehod of Equal Proporions (also called he Hill Mehod) allowing us o consider reapporionmen as a regularly recurring naural experimen. 4 3 The emporary addiion of seas for Alaska and Hawaii did no affec eiher he 1950 or he 1960 reapporionmen, boh of which were based on 435 seas and he apporionmen populaions of all relevan saes. 4 See hp:// and Balinski and Young (2001) for a hisory. I is less clear ha reapporionmens prior o 1940 can be reaed as a naural experimen, 6

9 The Mehod of Equal Proporions Every Census a reapporionmen consan is consruced ha is approximaely equal o he U.S. apporionmen populaion divided by 435. Each sae s apporionmen populaion is divided by he reapporionmen consan o produce is deserved quoien of seas wih an ineger par Q and fracional par q. 5 A sae receives Q represenaives if Q.q Q (Q 1) and Q + 1 represenaives if Q.q Q (Q 1). For example, a sae wih a quoien of 3.48 receives four Represenaives, while a sae wih a quoien of 3.45 receives hree Represenaives, since Noice ha he cupoins are sea-specific and ha he fracional par converges o 0.5 as Q ges large (see Table 1). Also noice ha he Hill Mehod ensures he Consiuionally-mandaed minimum of one sea per sae. <TABLE 1 HERE> Two Naural Experimens Census-based apporionmen creaes wo disinc naural experimens. The firs occurs because he Mehod of Equal Proporions does no award seas on a fracional basis. Sea shares are herefore disconinuous in populaion shares near he sea-specific hresholds ha deermine wheher deserved fracions of a sea are rounded up or down. The hresholds creae variaion in relaive represenaion, defined as he raio of sea shares o populaion shares, which we explain in deail below (see Figure 1 for daa from he 2000 apporionmen cycle). Alhough we ypically hink of he House of Represenaives as a well-apporioned legislaure, i is no perfecly apporioned even immediaely following reapporionmen. In he 2000 cycle, for because Congress endogenously seleced a new apporionmen rule for each apporionmen. For example, Balinksi and Young (2001) noe ha he 1900 and 1910 apporionmen rules were designed so ha no sae los a represenaive in he House. 5 In pracice, he common divisor mus be modified slighly in order o ensure ha he size of he House remains exacly 435 afer rounding. 7

10 example, saes such as Monana, Uah, and Mississippi barely missed he populaion hresholds necessary for gaining an addiional sea while saes such as Rhode Island, Nebraska, and Iowa barely cleared heir respecive hresholds, leading o imbalanced represenaion. <FIGURE 1 HERE> The second naural experimen is embedded in he iming of apporionmen, which induces a regular en-year cycle in he relaive equaliy of saes represenaion. Saes are mos equally represened immediaely following reapporionmen, bu he House grows malapporioned over he years due o differenial populaion growh raes across saes. Assuming hese differences are relaively consan, he House reaches maximum malapporionmen by he end of each cycle. The nex census hen leads o he nex reapporionmen, equalizing represenaion in he firs year of he subsequen cycle and so on. The apporionmen cycle begins wih he Census in year zero of each decade. Official apporionmen populaions are repored o he Presiden by he end of he year and he assignmen of seas o saes is cerified soon afer. The firs elecions following reapporionmen occur in November of year wo and represenaives are seaed in January of year hree. The newly-eleced represenaives pass heir firs budge in Ocober of ha year, which deermines federal spending in he saes for year four. For example: April-December 2000: Census performed and resuls cerified November 2002: Elecions in newly-apporioned disrics January 2003: Reapporioned Congress begins session Ocober 2003: Budge is enaced for he 2004 fiscal year The mos imporan feaure of he cycle for our purposes is ha saes receive he las round of federal ransfers disribued under maximum malapporionmen in fiscal years ending 8

11 wih hree, and receive he firs round of federal ransfers legislaed by he newly apporioned House in year four of each decade. Figure 2 illusraes how he discree changes in represenaion creae sudden changes in relaive represenaion. Fas-growing saes such as Arizona and Florida are ofen lef wih subsanially less han average represenaion per capia. However, his disadvanage ends o be significanly lower in he years immediaely following reapporionmen han in he years immediaely before. For example, even hough Arizona s populaion grew by similar amouns in boh 2002 and 2003, Arizona was subsanially less underrepresened in 2003 following is sudden increase from six o eigh represenaives. Conversely, saes wih below-average growh, such as New York and Pennsylvania, end o be subsanially less overrepresened in years immediaely following a reapporionmen. 6 <FIGURE 2 HERE> Secion 3. Mehodological Overview In his secion, we discuss in deail he idenificaion problem involved in esimaing he effec of House represenaion on disribuion, which we operaionalize as federal oulays o he saes. We hen explain our mehodological sraegy based on esing wheher he srucural breaks in represenaion beween years wo and hree of each decade correspond o changes in shares of oulays beween years wo and four. Figure 3 provides he inuiion behind our esimaion sraegy. The op panel of Figure 3 highlighs ha beween 1992 and 1994 here was a sudden 4.3 percenage poin shif in relaive 6 Trends in populaion and sea shares from 1935 o 2007 are provided in he Appendix for all saes excep Alaska, Vermon, and Wyoming. The graphs make clear ha alhough sea shares are correlaed wih populaion shares, he shifs in sea shares a he ime of each reapporionmen are abrup whereas year-o-year populaion rends are smooh. Addiionally, Figure 4 below demonsraes ha our assumpion of smooh populaion rends is empirically jusified. 9

12 represenaion from saes ha los seas o saes ha gained seas (hereafer, swichers ). A he same ime, here was a relaively linear populaion rend among boh groups of saes (Figure 3, middle panel). If represenaion per se affecs disribuive oucomes hen we should see a greaer increase in he share of federal oulays going o saes gaining seas afer he sudden shif in represenaion in 1993 (Figure 3, boom panel). <FIGURE 3 HERE> We model he share of federal oulays going o sae s a ime as: oulays oulays s,, rep s, f (, pops,, pops,, s, s, ), (1) 435 where oulays s, is he amoun of federal dollars allocaed o sae s a ime, oulays, is he oal amoun of federal dollars allocaed o saes a ime, rep s, is he number of represenaives in sae s a ime, pop s, is he populaion of sae s a ime, pop s, is he change in populaion of sae s beween ime k and ime, s is an idiosyncraic sae-specific effec, and f () s, s, is a sochasic error. We expec ha 0 rep s, f () s, f () s,, 0, 0. pop pop s, s, Assume ha f() is muliplicably separable such ha we can rewrie (1) as oulays oulays s,, rep s, 435 f (1, pop s,, pop s,, s,1) s,. (2) Log boh sides of equaion (2) such ha: oulayss, rep s, ln ln ln( f (1, pops,, pops,, s,1)) ln( s, ). (3) oulays 435, In his equaion, capures he elasiciy of oulays wih respec o represenaion; ha is, represens he percen change in oulay share wih respec o a 1 percen change in represenaion 10

13 share. There are wo complicaions ha make i difficul o esimae via direc esimaion of equaion (3). Firs, he funcional form of g() s, = f 1, pop s, pop,,1) is unknown o he (, s, s researcher. Second, represenaion in he House is iself a funcion of lagged populaion. Therefore, if he researcher does no correcly specify he direc effecs of levels and changes in populaion on oulays, he esimaed effecs of represenaion are likely o be conaminaed by omied variable bias. There are wo soluions o he idenificaion problem. The firs is o find an insrumenal variable (IV) ha affecs represenaion bu is independen of he measuremen error in he direc effec of populaion and s,. As described above, he indivisibiliy of seas inheren in he Mehod of Equal Proporions can serve as an insrumen o idenify he effecs of represenaion (Falk 2006). The principle advanage of he IV approach is ha he insrumen is likely o saisfy he exclusion resricion of being independen of he unobservables, including any measuremen error in he effec of populaion change and growh. However, he IV approach also has several limiaions. For saes wih seven or more represenaives, changes in populaion explain abou 93% of he variaion in he number of represenaives wihin saes across apporionmen cycles, compared o only abou 63% of he variaion in saes wih six or fewer represenaives. 7 Hence, he firs sage of he insrumenal variable approach lacks sufficien explanaory power o be used in a subsanial porion of he populaion of saes. This is problemaic for wo reasons. Firs, i severely limis he sample size from which he effec of apporionmen can be esimaed. We find ha one can only incorporae fewer han 20 changes in he number of represenaives ino he IV model, raising concerns abou small sample IV bias. Second, because IV can only provide us wih a local average reamen effec (LATE) of represenaion among he 7 These values come from he R-squared of a regression of acual changes in he number of represenaives on deserved changes in he number of represenaives based on a simulaed Congress ha awards fracional seas. 11

14 subpopulaion of saes affeced by changes in he insrumens, we can only use he IV model o assess he effecs of represenaion in small saes (Imbens and Angris 1994). The second mehod, which we adop in his paper, is o leverage he discree iming of apporionmen as he experimen. We develop an esimaion framework ha separaes he effecs of represenaion from he direc effecs of populaion as well as unobserved long-run processes of economic growh or decay associaed wih populaion changes by using periods wihou changes in represenaion o conrol for f() s, wihou having o know he exac funcional form. Our framework compares saes jus before and jus afer gaining represenaion, using a difference-in-firs-differences echnique o conrol for preexising rends in hose saes gaining or losing represenaion. The effec is idenified by swichers, or saes ha experience a change in he number of represenaives. The benefis of using he difference-in-firs-differences approach is ha we are able o incorporae a significan amoun of informaion ha is los in he insrumenal variables approach. Insead of using less han 20 swiches as in he IV model, our mehod incorporaes 53 swiches. Moreover, we are no limied o esimaing a local reamen effec for small saes and do no have he same concern abou small sample bias. Suppose ha Congress is reapporioned beween ime periods - 1 and. Taking firsdifferences in f() s, and f() s, - 2, 8 gives us ha: f() s, f() s, - 2 = (ln(rep s, ) ln(rep s, - 2 )) + g() s, + s,, (4) 8 We ake firs difference beween and 2 raher han and 1 for wo reasons. Subsanively, he lags in he budge cycle creae concerns ha reapporionmen may begin having some affec on he budge in ime period - 1. More pracically, we can only observe our primary dependen variable in wo-year incremens following he 1970 apporionmen cycle. The esimaed effecs of represenaion are subsanially smaller when we esimae (f() s, f() s, - 2) (f() s, - 1 f() s, - 3) for he years we do have daa. 12

15 where g() s, = (g(pop s,, pop s,, s) g(pop s, - 2, pop s, - 2, s)) and s, = s, s, - 2. Because represenaion only changes before he seaing of every fifh Congress, we know ha rep s, - 2 = rep s, - 4. Therefore, if we ake difference-in-firs-differences, we obain: (f() s, f() s, - 2) (f() s, - 2 f() s, - 4) = (ln(rep s, ) ln(rep s, - 2 )) +, (5) where = ( g() s, g() s, - 2 ) + ( s, s, - 2). If we assume ha E[ g() s, rep s,, rep s, - 2 ] = g() s, - 2 and E[ s, + 2 s, rep s,, rep s, - 2] = 0, hen we are able o obain an unbiased esimae of via OLS. We believe his is a reasonable assumpion. In our sample, growh raes wihin saes are very persisen across ime: pop s, and pop s, 2 are boh on average 2.5 percenage poins larger han he naional average in saes where rep s, > rep s, - 2 and are boh on average 1.1 percenage poins less han he naional average in saes where rep s, < rep s, - 2. We also plo he full disribuion of pop s, and pop s, 2 for swichers (see Figure 4). Mos observaions lie near he 45 degree line, suggesing ha populaion rends end o be smooh even in he saes ha experienced a change in heir sea allocaion. The slope of he regression line of he relaionship beween populaion shifs around he Census is (s.e. =.043). We fail o rejec he null hypohesis ha he slope is equal o he 45 degree line (p =.93). These paerns increase our confidence in he assumpions abou he similariies beween g(pop s, - 2, pop s, - 2, s) and g(pop s,, pop s,, s). <FIGURE 4 HERE> Secion 4: Daa and Measures Measuring Represenaion Our primary measure of represenaion is sea shares in he House of Represenaives. Daa on he sea apporionmen for each sae and on apporionmen populaions are from 13

16 Balinski and Young (2001). We prefer his specificaion because i ensures ha our represenaion measure is independen of populaion. In our esimaions, we ransform represenaion shares as follows: we ake he difference in he naural log of represenaion share beween ime 2 and ime period. Noe ha because we are aking he difference in logs, his is approximaely equal o he percen change in he share of represenaives in he U.S. House. A populaion-normalized measure of represenaion, however, allows us o describe he daa in an inuiive manner and run alernaive specificaions of our main model. In addiion o sea shares, we adop he Relaive Represenaion Index (RRI) (David and Eisenberg 1961; Ansolabehere e al. 2002). The RRI for sae i a ime measures he number of seas per person in he sae relaive o he number of seas per person in he enire House of Represenaives. Thus, RRI s, = rep s, / pop 435/ pop s,,. If a sae s per capia represenaion is equal o average disric size in he House, RRI = 1. Values of RRI less han 1 indicae underrepresenaion whereas values of RRI greaer han 1 indicae overrepresenaion. Following Ansolabehere e al. (2002), Woon (2007), and Lee (1998), we ake he naural log of RRI o make gains and losses of equal represenaion symmeric and so ha coefficiens can be inerpreed as elasiciies. Table 2 shows he disribuion of logged RRI immediaely before and immediaely afer each of he pas four apporionmens he poins in each cycle when represenaion is mos unequal and equal, respecively. <TABLE 2 HERE> There is subsanial variaion in he RRI boh across saes and wihin saes over ime. Following he 2000 census, he bes-represened sae, Rhode Island, enjoyed 70% more represenaion per capia han Monana, he wors-represened sae. Monana was no, however, always poorly represened. In fac, Monana was among he bes represened saes jus before 14

17 he reapporionmen based on he 1990 census wih a ln(rri) of Afer losing is second sea in he 1991 reapporionmen, Monana s ln(rri) fell o Measuring Disribuion Our measure of disribuive spending is shares of oal federal oulays. These daa comprise a panel of repeaed observaions a he sae level over 33 years (1970, 1972, 1974, 1976, 1977, ). Oulays o he saes were published as Federal Expendiures by Sae (FES) saring in 1981, afer which he repors were folded ino he Consolidaed Federal Funds Repor (CFFR) series, boh published by he U.S Census Bureau. We could no locae he original daa for 1981 and 1982 and used he figures published in he Saisical Absrac of he Unied Saes for hose years. Earlier daa were published by he Office of Economic Opporuniy in an annual series, Geographic Disribuion of Federal Funds (GDFF). We use hese daa when possible bu supplemened hem wih daa published in The Almanac of American Poliics and CQ Weekly Repors when he GDFF was unavailable. The daa in he Almanac/CQ mach hose in he GDFF in years where we could locae boh sources. We use federal oulays o saes for a number of reasons. Firs, previous analyses by Alas e al. (1995) and Falk (2006) use his measure, allowing comparabiliy. Second, alhough here are good heoreical reasons for analyzing more specific caegories of federal funds (Lee (2003) offers a compelling argumen for analyzing earmarks in paricular), here is lile agreemen abou he ypes of funding over which legislaors have disribuive discreion. For example, Lee (1998) finds ha funds disribued on he basis of congressionally-mandaed formulas raher han discreionary funds are mos affeced by malapporionmen. Levi and Snyder (1995), on he oher hand, classify as discreionary only hose programs wih relaively 15

18 high coefficiens of variaion across disrics, leading hem o classify programs such as food samps as discreionary bu Medicare as non-discreionary. Analyzing oal federal oulays allows us o remain agnosic abou he heoreical mechanism for wha renders cerain ypes of programs more discreionary han ohers. I also makes i less likely ha we find a significan resul since non-discreionary porions of oal oulays are likely o add significan noise o he oulays daa. Finally, daa on oal federal oulays have been repored over muliple apporionmen cycles allowing us o conduc analyses saring wih he 1970 cycle. Toal federal oulays in 2004 amouned o $2.04 rillion. Toal oulays include federal grans-in-aid o sae and local governmens, wages and salaries of miliary and civilian governmen employees, direc paymens o individuals (e.g. Social Securiy, Medicare, Supplemenal Securiy Income, and Food Samps), federal procuremen conracs, as well as suppor for oher programs ranging from he Naional Endowmen for he Ars o he Corporaion for Naional Service. Direc paymens accouned for 54% of he $2.04 rillion disbursed in 2004, by he far he larges caegory. Grans-in-aid accouned for 19%, procuremens for 15%, salaries and wages for 10%, and he remaining 2% were spen on oher programs. The mean level of per capia oulays was $7,529 wih a sandard deviaion of $1,633. A he boom of he lis, Nevada, Uah, and Minnesoa each received less han $6,000 per capia while Maryland, Virginia and Alaska opped he lis, each receiving over $11,000 per capia. Toal oulays per capia increased in real erms by roughly 50 percen beween 1970 and 2006 (see Figure 5). The ime series also indicaes a sharp kink in oal oulays around he 1980 reapporionmen. Since he oulays daa for hese years come from he Saisical Absrac of he Unied Saes we were concerned ha hey may no be consisen wih he daa from oher sources. Figure 6 illusraes his poin by showing he wihin-sae correlaions of per capia 16

19 oulays beween fiscal year and fiscal year - 2 are much lower for 1982 and 1983 han for any oher se of years. Because comparable daa across ime for hese years are essenial for idenifying he effecs of he 1980 apporionmen using he difference-in-firs-differences echnique, we resric our analysis o he 1970, 1990, and 2000 reapporionmens. 9 <FIGURES 5 AND 6 HERE> In our esimaions, we ransform oal federal oulays as follows: we ake he firsdifference-in-difference in he naural log of a sae s share of disribuive spending. Noe ha his is approximaely equal o he difference in he percen change in he share of disribuive goods going o a sae beween ime period and ime period 2 compared o analogous changes beween ime periods 2 and 4. Populaion All populaion daa (oher han apporionmen populaions) are from midyear esimaes repored by he Bureau of Economic Analysis. Secion 5: Resuls We find ha gains in represenaion increase saes shares of federal oulays. Table 3 presens he esimaes of equaion (5). 10 As shown in column (1) of Table 3, he coefficien esimae of in equaion (1) is.067, which is saisically significan a he p<.10 level (woailed). This implies ha a 10% increase in he number of represenaives causes a 0.67% increase in a sae s share of federal oulays. To pu his effec size in perspecive, Uah s 9 The inconsisen daa source for he 1980 apporionmen cycle makes is inclusion problemaic. Including daa from he 1980 cycle produced dramaically differen resuls depending on small changes in specificaion. For example, when (f() s, 1984 f() s, 1982) (f() s, 1982 f() s, 1980) is used as he dependen variable, marginally significan negaive effecs of represenaion are esimaed. In conras, when using (f() s, 1985 f() s, 1983) - (f() s, 1983 f() s, 1981) as he dependen variable, large and significan posiive effecs of represenaion are esimaed. 10 Sandard errors are clusered by sae. 17

20 represenaion in he House would have increased by approximaely 30% if is apporionmen populaion had been jus slighly larger in Our poin esimae suggess ha receiving a fourh represenaive would have increased Uah s receip of federal oulays by roughly $100 per capia in <TABLE 3 HERE> One concern abou equaion (5) is ha our difference-in-firs-differences specificaion may no sufficienly accoun for changes in populaion. To alleviae hese concerns, we esimae a varian of equaion (5) ha replaces difference in oulay shares wih difference in populaion shares as he righ-hand side variable. Our esimae of = is small and saisically insignifican (p = 0.773). This is unsurprising considering he smooh populaion shifs illusraed in Figure 4. In order o alleviae he concern ha a few dramaic changes in oulays or represenaion in he sample may be driving he resuls, we plo he 53 swiches ha produce our esimae (see Figure 7). One paricularly ineresing observaion is Norh Dakoa in he 1970 cycle. This observaion represens he larges decrease in represenaion, and consisen wih our heoreical expecaions, he larges decrease in per capia disribuion. Norh Dakoa did no experience a disconinuous shock in is populaion rend (see Figure 4: ND74 ), increasing our confidence ha is loss was no populaion driven. 11 We also esimae equaion (5) using a leas absolue deviaions (LAD) regression, which limis he influence of high-leverage observaions. 12 We coninue o find a posiive coefficien (see column (2) of Table 3), alhough he magniude 11 According o Fenno s (1992) sudy of Senaor Mark Andrews, he haling of he Garrison Diversion waer projec significanly decreased appropriaions o Norh Dakoa in he lae 1970s. I is possible ha increased represenaion could have offse his seback. 12 A leas absolue deviaions regression is jus a special case of a quanile regression a he median. Tha is, i esimaes he condiional median of he response variable raher han he condiional mean (as in OLS), hus making i robus o he influence of oulying cases. 18

21 aenuaes somewha and he sandard error increases. 13 Hence, when esimaing a condiional median, he seepness of he slope is similar o OLS esimaes of a condiional mean, bu is less precisely esimaed. <FIGURE 7 HERE> As discussed earlier, one advanage of our idenificaion sraegy is ha he idenifying source of variaion occurs in large saes as well as small saes, which allows us o es for conexual effecs. We find ha he effecs of represenaion on disribuion are concenraed in he smaller saes. We include an ineracion erm beween change in represenaion and a dichoomous measure of wheher he sae is big (see column (3) of Table 3). 14 We find he effecs o be solely concenraed in small saes, where a 10% increase in represenaion is associaed wih a 0.8 percen increase in per capia oulays ( =.079, p<.10). Conversely, in large saes he effec of represenaion is nearly zero. 15 The imporance of represenaion on Congressional commiees is one plausible explanaion for his effec since gaining an exra represenaive means a lo more o a small sae like Uah han i does o a large sae like California, which already has a represenaive on almos every commiee. Finally, we find no evidence of an asymmeric effec for gains versus losses in represenaion (see column (5) of Table 3). Alernaive Specificaion 13 Anoher approach o eliminaing he influence of ouliers is o conduc a non-parameric sign es evaluaing he paern of resuls displayed in Figure 7. We esed wheher he observaions were more likely o fall in quadrans I and III as opposed o he null of equal disribuion. We find ha 33 of he 53 observaions are in hese wo quadrans, and rejec he null of a homogenous disribuion a p= We define he big saes as hose wih a leas 15 represenaives in every Congress since he 1970 apporionmen (e.g. California, Florida, Illinois, Michigan, New York, Ohio, Pennsylvania, and Texas). The resul is robus o oher definiions of big. 15 Again, similar paerns hold when esimaing a LAD regression, alhough he coefficiens are slighly smaller and he sandard errors larger. 19

22 Following Ansolabehere e al. (2002) we consruc an alernae populaion-normalized measure of oulays o use as he dependen variable. The Relaive Oulays Index (ROI) is consruced in an analogous manner o he RRI, where ROI s, = oulays oulays s,, / pop / pop s,,. In order o make his specificaion comparable o our main model, we include an indicaor variable, Swich s,, ha is equal o 1 if rep s, rep s, - 2 and 0 oherwise. 16 We hen esimae he following regression model via ordinary leas squares, clusering sandard errors a he sae-level: [ln(roi s,) ln(roi s, - 2)] - [ln(roi s, - 2) ln(roi s, - 4)] = ([ln(rri s,) ln(rri s, - 2)] - [ln(rri s, - 2) ln(rri s, - 4)] )Swich s, + s,. (6) The alernaive specificaion produces slighly more precise esimaes han our main model (see Table 4). The poin esimae of in equaion (6) is 0.068, which is nearly idenical o he esimaed in equaion (4) (see column 1). Subsanively, a 10% increase in he number of represenaives causes a 0.68% increase in a sae s ROI. Again, he poin esimae becomes somewha smaller when esimaing a LAD regression model (see column 2). The ineracion effecs also confirm ha small saes experiencing swiches drive he resul. As shown in he hird column, a 10% increase in represenaion wihin small saes is associaed wih a 0.81 percen increase in per capia oulays (p<.05). This effec is somewha smaller bu sill approaches saisical significance when esimaing he LAD model (p<.11). Finally, as shown in he las wo columns, we do no observe any asymmeries beween saes ha gained and los seas. Secion 6: Conclusion 16 Non-swichers drop from he main specificaion of equaion (5) by consrucion via differences. 20

23 Fairness in represenaion, embodied in he concep of one person, one voe, is one of he mos imporan normaive sandards agains which democraic insiuions are measured. Analyzing he impac of fairness empirically, however, is made difficul by he challenge of isolaing he disribuional effecs of represenaion from hose caused by underlying demographic and economic condiions. In his paper, we have developed a mehod of idenifying he causal effecs of represenaion per se ha can be expored across ime and space. Moreover, conrary o previous analyses ha have used apporionmen formulas as insrumens, we have developed a differences-in-firs-differences esimaor ha alleviaes concerns abou small samples and local reamen effecs. Scholars of comparaive poliics can apply he mehod in any democraic seing where Census-based apporionmen is carried ou regularly and nonsraegically. For insance, decennial censuses in he American syle are conduced in several naions including Ausria, India, and Greece, among ohers. One limiaion of our difference-in-firs difference esimaor is ha some effecs of represenaion migh no occur immediaely following reapporionmen. Our mehodology could be exended o look a differences in he growh raes of spending in periods before and afer swiches. We do no do so in his paper because we only currenly have daa from a consisen source for muliple periods in he pre- and pos- apporionmen period for he 1990 reapporionmen. Our mehodology could also be used o predic oher dependen variables of subsanive ineres. For insance, we can explore wheher commiee represenaion or federal appoinmens are affeced by having more members represening a sae in Congress. Alernaively, we can explore if increased represenaion improves he reelecion of members from a sae s enire delegaion, or has posiive spillover effecs in he elecoral prospecs of governors and sae 21

24 legislaors. Finally, we can use apporionmen cycles as an exogenous source of variaion in disribuion o analyze he effecs of money on a hos of oucomes, including axaion and spending (i.e. he flypaper effec ), economic growh, and he elecoral benefis of paricularisic spending. 22

25 Appendix: Sae Populaion and Seas Shares, Alabama Arizona Arkansas California Colorado Connecicu Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kenucky Louisiana Maine Maryland Massachuses Michigan Minnesoa Mississippi Missouri Monana Nebraska Nevada New Hampshire New Jersey New Mexico New York Norh Carolina Norh Dakoa Ohio Oklahoma Oregon Pennsylvania Rhode Island Souh Carolina Souh Dakoa Tennessee Texas Uah Virginia Washingon Wes Virginia Wisconsin Represenaion and Populaion U.S. House of Represenaives, Seas Populaion 23

26 References Alesina, A. and E. Spolaore. (1997). "On he Number and Size of Naions." Quarerly Journal of Economics 112(4): Angris, J. D. and V. Lavy. (1999). "Using Maimonides' Rule o Esimae he Effec of Class Size on Scholasic Achievemen." Quarerly Journal of Economics 114(2): Ansolabehere, S., A. Gerber, and J.M. Snyder. (2002). "Equal Voes, Equal Money: Cour- Ordered Redisricing and Public Expendiures in he American Saes." American Poliical Science Review 96(4): Ansolabehere, S., J. M. Snyder, and M.M. Ting. (2003). "Bargaining in Bicameral Legislaures: When and Why Does Malapporionmen Maer?" American Poliical Science Review 97(3): Alas, C. M., T. W. Gilligan, R.J. Hendersho, and M.A. Zupan. (1995). "Slicing he Federal Governmen Ne Spending Pie: Who Wins, Who Loses, and Why." American Economic Review 85: Balinski, M. L. and H. P. Young (2001). Fair Represenaion: Meeing he Ideal of One Man, One Voe. Washingon, D.C., Brookings Insiuion Press. Banks, J.S. and J. Duggan. (2000). A Bargaining Model of Collecive Choice. American Poliical Science Review. 94(1): Baron, D. and J. Ferejohn (1989). "Bargaining in Legislaures." American Poliical Science Review 83(4): Barone, M. and R.E. Cohen. The Almanac of American Poliics. Washingon, DC: Naional Journal Group. Various years. Chen, J. and N. Malhora. (2007). The Law of k/n: The Effec of Chamber Size on Governmen 24

27 Spending in Bicameral Legislaures. American Poliical Science Review. 101(4): Congressional Quarerly Weekly Repor. Various years. David, P. T. and R. Eisenberg (1961). Devaluaion of he Urban and Suburban Voe. Charloesville, VA: Universiy of Virginia Press. Falk, J. (2006). The Effecs of Congressional Disric Size and Represenaive's Tenure on he Allocaion of Federal Funds, Universiy of California, Berkeley. Manuscrip. Fenno, R.F. (1992). When Incumbency Fails: The Senae Career of Mark Andrews. Washingon, DC: Congressional Quarerly Press. Fiorina, M. P. (1989). Congress: Keysone of he Washingon Esablishmen. New Haven, CT: Yale Universiy Press. Hauk, W. and R. Wacziarg (2007). "Small Saes, Big Pork." Quarerly Journal of Poliical Science 2(1): Hirano, S. (2006). "Elecoral Insiuions, Homeowns, and Favored Minoriies: Evidence from Japan's Elecoral Reforms." World Poliics 59(1): Hirano, S. and M.M. Ting. (2008). "Direc and Indirec Represenaion." Columbia Universiy. Manuscrip Hoover, G. and P. Pecorino (2005). "The Poliical Deerminans of Federal Expendiure a he Sae Level." Public Choice 123(1): Knigh, B. G. (2008). "Legislaive Represenaion, Bargaining Power, and he Disribuion of Federal Funds: Evidence from he US Senae." Economic Journal 118(532): Larcinese, V., L. Rizzo, and C. Tesa (2007). "Do Small Saes Ge More Federal Monies? Myh and Realiy abou he US Senae Malapporionmen" London School of Economics. 25

28 Manuscrip. Lee, F. E. (1998). "Represenaion and Public Policy: The Consequences of Senae Apporionmen for he Geographic Disribuion of Federal Funds." Journal of Poliics 60: Lee, F.E. (2000). Senae Represenaion and Coaliion Building in Disribuive Poliics. American Poliical Science Review 94(1): Lee, F. E. (2003). "Geographic Poliics in he US House of Represenaives: Coaliion Building and Disribuion of Benefis." American Journal of Poliical Science 47(4): Levi, S. D. and J. M. Snyder (1995). "Poliical Paries and he Disribuion of Federal Oulays." American Journal of Poliical Science 39: Mansbridge, J. (2003). "Rehinking Represenaion." American Poliical Science Review 97(04): Mayhew, D. (1974). The Elecoral Connecion. New Haven, CT: Yale Universiy Press. Office of Economic Opporuniy. Geographic Disribuion of Federal Funds. Various years. Snyder, J. M., M.M. Ting, and S. Ansolabehere. (2005). "Legislaive Bargaining under Weighed Voing." American Economics Review 95(4): Ullah, A. (2004). Finie Sample Economerics. Oxford: Oxford Universiy Press. U.S. Census Bureau. Consolidaed Federal Funds Repor. Various years. U.S. Census Bureau. Federal Expendiures by Sae. Various years. U.S. Census Bureau. Saisical Absrac of he Unied Saes. Various years. Weingas, B.R., K.A. Shepsle, and C. Johnsen. (1981). "The Poliical Economy of Benefis and Coss: A Neoclassical Approach o Disribuive Poliics." Journal of Poliical Economy 89(4):

29 Woon, J. (2007). Direc Democracy and he Selecion of Represenaive Insiuions: Voer Suppor for Apporionmen Iniiaives, Sae Poliics and Policy Quarerly 7(2):

30 ln(rri) Figure 1: Represenaion Per Capia Index for he 2000 Apporionmen Cycle (Saes wih 10 or Fewer Represenaives) WY RI NE IA VT HI AK NH WV NM CO ND ME ID AL LA MN AZ TNWAIN MA NV AR KS OR SC OK KY MD WIMO MS SD UT DE -0.4 MT 2000 Apporionmen Populaion (millions) 28

31 ln(rri) Figure 2: Represenaion Per Capia Index by Year for a Selecion of U.S. Saes Arizona Florida New York Pennsylvania 29

32 Share of Federal Oulays Share of Toal Populaion Share of House Represenaion Figure 3: Trends in House Represenaion, Populaion, and Oulays by 1990 Apporionmen Oucome Year Same Seas Gain Seas Lose Seas Year Same Seas Gain Seas Lose Seas Fiscal Year Same Seas Gain Seas Lose Seas 30

33 Diff. in ln(pop-2) Figure 4: Populaion Changes and Two Year Lagged Populaion Changes for Swichers ND Diff. in ln(pop ) 31

34 Oulays Per Capia ($90) Figure 5: Toal Federal Oulays Per Capia (1990 dollars) by Fiscal Year Fiscal Year 32

35 Figure 6: Wihin-Sae Correlaion in Per Capia Oulays a Time and Fiscal Year ( ) 33

36 Diff. in FD ln(oulay Share) Figure 7: Effec of Changes in House Represenaion on Changes in Federal Oulays AZ94 PA74 OH74 IA94 FL04 VA94 CA04 CO04 AZ04 KY94 OH94 MA94 TX04 WV94 NC04 KS94LA94 AL74 CA74 IL94 NY74 TX94 WA94 CA94 PA04 NV MT WI74 AZ74 OK04NY94 IL IN04 WV74MI94 WI04 NJ94 MI04 TX74 MS04 NC94 IA74 TN74 GA04 GA94 FL74 ND74 Diff. in ln(rep) 34

37 Table 1: Mehod of Equal Proporions Cupoins for he Firs Ten Seas Sae Sea Cupoin Populaion Needed (2000) , ,581, ,237, ,888, ,537, ,185, ,832, ,479, ,126,666 35

38 Table 2: Ln(RRI) Before and Afer Each Reapporionmen Year Median Range 10h Percenile 90h Percenile

39 Table 3: Effec of Changes in Logged Represenaion Shares on Firs Difference in Changes in Logged Oulay Shares N = 53 swiches (1) (2) (3) (4) (5) (6) Dep. Variable (all in difference log firs difference form) Share Oulays Share Oulays Share Oulays Share Oulays Share Oulays Share Oulays Regression Type OLS LAD OLS LAD OLS LAD ln(rep s, ) ln(rep s, 2 ) (0.039) (0.059) (0.042) (0.063) (0.072) (0.098) ln(rep s, ) ln(rep s, 2 ) X Large Sae (0.087) (0.190) ln(rep s, ) ln(rep s, 2 ) X Lose Sea(s) (0.010) (0.130) Noe: Regressions also include year fixed effecs. Sandard errors clusered by sae in parenheses. 37

40 Table 4: Effec of Changes in Logged RRI on Firs Difference in Changes in Logged ROI N = 53 swiches (1) (2) (3) (4) (5) (6) Dep. Variable (all in difference log firs difference form) ROI ROI ROI ROI ROI ROI Regression Type OLS LAD OLS LAD OLS LAD ln(rri s, ) ln(rri s, 2 ) X Swich (0.036) (0.047) (0.039) (0.039) (0.071) (0.084) ln(rri s, ) ln(rri s, 2 ) X Swich X Large Sae (0.089) (0.115) ln(rri s, ) ln(rri s, 2 ) X Swich X Lose Sea(s) (0.096) (0.110) Noe: Regressions also include year fixed effecs. Sandard errors clusered by sae in parenheses. 38