Taxes and the Fed: Theory and Evidence from Equities

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Taxes and the Fed: Theory and Evidence from Equities Anthony M. Diercks and William Waller 2017-104 Please cite this paper as: Diercks,AnthonyM.,andWilliamWaller(2017). “TaxesandtheFed: TheoryandEvidence from Equities,” Finance and Economics Discussion Series 2017-104. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2017.104. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Taxes and the Fed: Theory and Evidence from Equities AnthonyM.Diercks(cid:142),WilliamWaller(cid:142)(cid:142) Abstract We provide a critical theoretical and empirical analysis that suggests a key driver of fiscal effects on equity markets is the Federal Reserve. For the Post-1980 era, tax cuts lead to higher cash flow news and higher discount rates. The discount rate news tends to dominate such that tax cuts are associated with lower equity returns. This result is flipped for the Pre-1980 era. Our results are confirmed across multiple measures of tax shocks (narrative, SVAR, municipal bonds, etc.) at differentfrequencies(daily,quarterly,annual). Wemotivateourempiricalfindingswithastandard NewKeynesianmodel(inadditiontotheFRB/USmodel)thatexhibitsashiftintheaggressiveness of monetary policy. Moreover in our theoretical framework, downward nominal wage rigidities accountforobservedasymmetriesintheresponsetotaxcutsversustaxincreases. Keywords: fiscalpolicy,stockmarket,newsdecomposition JELClassification: E63,G12 Thisversion:August16,2017 Firstdraft:September12,2014 HelpfulcommentsandsuggestionsprovidedbyAnthonyDiercks’advisorMaxCroce, GeertBekaert, JohnCochrane, Thorsten Drautzburg, Yuriy Gorodnichenko, Urban Jermann, Arvind Krishnamurthy, Thomas Laubach, Martin Lettau, Karel Mertens, VirgiliuMidrigan,GlennRudebusch,PaulTetlock,AnnetteVissing-Jorgenson,LuZhang,andseminarparticipantsfrommultiple conferencesandinstitutions. (cid:142)FederalReserveBoard,MonetaryandFinancialMarketAnalysis20thStreetandConstitutionAvenueN.W.,Washington,D.C. 20551, Anthony.M.Diercks@frb.gov. http://www.anthonydiercks.com/ The analysis and conclusions set forth in this paper are thoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstaffortheBoardofGovernorsoftheFederal ReserveSystem. (cid:142)(cid:142)FinanceArea,TepperBusinessSchool,CarnegieMellonUniversity,Pittsburgh,PA15213,wwaller@andrew.cmu.edu. 1

1. Introduction Following the 2016 presidential election, the stock market, the value of the dollar, and inflation compensation measures increased significantly. Some observers suggest these observations provide evidence thatthepromiseoftaxcutssubstantiallyboostthestockmarket. Yetasoftheendofthesecondquarterin 2017,thevalueofthedollar,inflationcompensation,andtheimpliedtaxmeasuresbasedonmunicipalbond spreadshaveallreturnedtotheirpre-electionlevelssuggestinglittleeffectofpotentialtaxchangesonfinancialmarkets. Despitethesereversals,thestockmarketremains18%aboveitslevelpriortotheelection. The lackofequitymarketreversioncallsintoquestionhowimportantthepromiseoftaxcutsweretothestock market. In the vein of previous studies exploring the relationship between policy and equity markets,1 we provideacriticaltheoreticalandempiricalanalysisthatsuggeststhattheFederalReserveisakeydriverof fiscaleffectsonequitymarkets. TheFederalReserve’sreactionfunctionplaysacrucialroleindetermining therelativemagnitudesoftheeffectsoftaxesoncashflownewsanddiscountratenewsinequitymarkets. With the Federal Reserve’s more aggressive stance toward economic activity since 1980,2 we find that tax cuts are associated with lower excess equity returns, despite our findings of positive effects on cash flow news. Themoreaggressivemonetarypolicysince1980hastwoprimaryeffects: (1)monetarypolicyisraising rates to a greater extent in response to tax cuts, increasing the size of the discount rate channel and (2) the higher rates endogenously feed back negatively to economic activity in the form of less positive cash flow news in response to tax cuts. We conduct similar analysis for the Pre-1980 era and come to the opposite conclusion. Withalessaggressivemonetarypolicy,thecashflownewsislargerthanthediscountratenews, andtaxcutsareassociatedwithhigherequityreturns. Theseempiricalfindingsaremotivatedbyastandard theoreticalNewKeynesianmodelthatexhibitsashiftintheaggressivenessofmonetarypolicy. Ourresultsarenotdependentuponanyspecificcalibrationandinsteadholdforawidesetofcommonly used values, which we confirm across each of the parameters in the model. Moreover, the FRB/US model 1See Ai and Bansal (2016), Belo, Gala, and Li (2013), Croce, Kung, Nguyen, and Schmid (2012), Da, Warachka, and Yun (2016),Gallmeyer,Hollifield,andZin(2005),Gomes,Michaelides,andPolkovnichenko(2012),amongothersdiscussedinmore detailinourliteraturereview. 2See Coibion and Gorodnichenko (2011); Bhattarai, Lee, and Park (2016); Clarida, Gali, and Gertler (2000); Lubik and Schorfheide(2004);RomerandRomer(2002);andMeltzer(2005). 2

usedbytheFederalReservepredictstaxcutsbeingassociatedwithlowerreturns. We also document asymmetries with respect to tax changes. Specifically, we find that tax cuts have larger and more significant effects than tax increases. Again, this can be motivated by a nonlinear New Keynesianmodelthatexhibitsdownwardnominalwagerigidities. Thebasicintuitionisthatanincometax cutincentivizeshouseholdstoworkmorecausingwagestodecline. Howeverinthepresenceofdownward nominal wage rigidities, wages do not fully adjust to this change in labor supply such that the increase in labor demanded is reduced. With not as much labor demanded, output and dividends increase less so that cash flow news is less positive. Combining the less positive cash flow news with the increase in interest rates,theoveralleffectisalargernegativeeffectonequityreturns. Movingtotheempirics,wefirstusetaxshocksbasedonRomerandRomer(2010)andincorporatethem intoaCampbellandShiller(1988)newsdecompositiontobackouttheeffectsoncashflowanddiscountrate news. Wetakeadditionalstepstoensuretheexogeneityoftheseshocksbyfocusingalsoonthe“surprise” shocksasoutlinedbyMertensandRavn(2012),aswellastheorthogonalizedSVARshocksalsodiscussed inMertensandRavn(2014). Throughorderedprobittests,weshowthattheshocksarenotpredictablebased on financial market data, a concern raised by Leeper, Walker, and Yang (2013); Yang (2005); Mertens and Ravn(2013);andKueng(2015). Inadditiontoresultsbasedonatime-varyingparameterVAR,statisticaltestssuggestastructuralbreak in our data in 1980. Splitting the sample at this date, we demonstrate that the relative magnitudes of the cash flow and discount rate channels shift, with discount rate news becoming larger Post-1980. The larger effect on discount rate news dominates, so that tax cuts are associated with lower returns, consistent with ourtheoreticalmotivationbasedonamoreaggressivemonetarypolicy. Wefurtherempiricallyexaminewhethertaxincreasesortaxcutsyieldsignificantasymmetriceffectson equitymarkets. Wefindthattaxcutsaredrivingthesignificanceandthatwhenweisolatetheeffectsoftax increases,theeffectsaresmallerandlesssignificant. ThisisconsistentwithJones,Olson,andWohar(2015) in terms of macro effects and also consistent with our nonlinear New Keynesian model with downwardly nominalwagerigidities. Admittedly, the narrative shocks of Romer and Romer (2010) are quite heterogenous relative to the capital, labor, andincometaxesinourmodel. Tothisend, weexploremorenarrowlydefinedpersonaltax 3

shockstoensurethatourempiricsmirrorthechannelsoperatinginourtheory. Ourmainresultscarrythrough whenweshiftourdefinitionoftaxshockstothenarrativepersonaltaxshocksofMertensandRavn(2013) ortoadefinitionofexpectedpersonaltaxesbasedonmunicipalbondspreadsasinLeeper,Walker,andYang (2013)andKueng(2015). With the main empirical analysis conducted at the quarterly frequency, we show further robustness by usingchangesinexpectedfuturetaxratesathigherfrequenciesbasedonmunicipalbonddata. Wecontinue tofindapositiverelationshipbetweentaxratesandequityexcessreturnsbasedoneventwindowsranging from1weekto3months. Additionally, we replicate the results of Sialm (2009) using annual data and show that the effect of tax yields on equity returns flips signs if the sample is split in 1980 (rather than in 1960 as in Sialm (2009)). Usingmultiplerobustnesschecks,wefindthattheeffectoftaxesonequityreturnsswitchesfromnegative to positive for the post-1980 period, which is consistent with both our theoretical and empirical analysis. Furthermore, we note that Sialm (2005, 2006) does not model monetary policy, leaving open the theoretical possibility for the positive relationship between dividend taxes and equity returns in a non-endowment economy. We confirm these findings in a Real Business Cycle model, and show that once we incorporate nominal rigidities and a monetary policy rule that aggressively responds to economic activity, the results flip. The remainder of the paper proceeds as follows. Section 2 discusses the related literature. Section 3 providesthetheoreticalframeworkforouranalysis. Section4presentsourdataandmethodology. Section 5discussesourmainempiricalresults. Section6providessomeadditionaltestsandSection7concludes. 2. RelatedLiterature Theextantliterature,boththeoreticalandempirical,lacksconsensusregardingtheimpactoftaxchanges onequitymarkets. Inthetimeseries,TavaresandValkanov(2001)andSialm(2006,2009)findanegative relationship. However,studiesthatfocusonabroaderrangeofcountriesinadditiontotheUnitedStatestend tofindnoeffectorinfactapositiverelationship,asinArdagna(2009);AfonsoandSousa(2011,2012);and AgnelloandSousa(2013). Unlikeourresults,noneofthesestudiesexaminetheimpactofmonetarypolicy regimeonthestockresponsetotaxshocks. 4

Study SignofTaxIncrease Method TypeofTaxes Ayers,Cloyd,andRobinson(2002) Negative EventStudyof1993TaxCut,Panel Individualincome(i.e.dividendtaxrate) AuerbachandHassett(2005) Negative EventStudyof2003TaxCut,Panel CapGains,Dividend LangandShackelford(2000) Negative EventStudyof1997TaxCut,Panel CapitalGains McGrattanandPrescott(2005) Negative RBCmodel,IntangibleCapital Cons.,Divs,Interest,Labor,Property,Corp.Income Sialm(2009) Negative TimeSeriesandCrossSection,Ann Dividend,CapGain(SR,LR) Sialm(2005) Negative Theoretical,Endow.Economy ConsumptionTax Sialm(2006) Negative Theoretical,Endow.Economy DividendTax TavaresandValkanov(2001) Negative SVAR,1960-2000US Shareoftaxreceipts(exludingtransfers)inGDP Dai,Maydew,Shackelford,andZhang(2008) Ambiguous/Negative EventStudyof1997TaxCut,Panel – Arin,Mamun,andPurushothman(2009) NoEffect/Negative SVAR,1973-2005Intl LaborTax,Indirect(CorporateTax) Amromin,Harrison,andSharpe(2008) NoEffect EventStudyof2003TaxCut,Panel DividendTax Ardagna(2009) Positive 1960-2002Intl,Ann – AfonsoandSousa(2011) Positive(Small) SVAR,1970-2007Intl,Qtrly Govt.Revenue,NIPATable3.2,line36 AfonsoandSousa(2012) Positive(Small) B-SVAR,1970-2007Intl,Qtrly Govt.Revenue,NIPATable3.2,line36 AgnelloandSousa(2013) Positive(Temporary) P-VAR,Intl PrimaryDeficitShocks HanlonandHeitzman(2010) – LiteratureReview – TheoreticalimplicationsinMcGrattanandPrescott(2005)andSialm(2005,2006,2009)predictnegative stock returns in response to tax increases. In contrast to these theoretical models, we focus on a New Keynesianmodelthatexplicitlymodelsmonetarypolicy,whichwefindisacrucialmodelingchoice. Ayers, Cloyd, and Robinson (2002); Auerbach and Hassett (2005); Lang and Shackelford (2000); Dai, Maydew, Shackelford,andZhang(2008);andAmromin,Harrison,andSharpe(2008)runpanelregressionsandevent studies around various tax cuts in 1993, 1997, and 2003. Their findings range from negative to no effect with respect to a tax increase. However, this approach controls, at least in part, for discount rate news that isanintegralparttoourstory. Tothisend,weuseaCampbellandShiller(1988)newsdecomposition. News decompositions consist of splitting the movements in unexpected stock market returns into two fundamental components – news about future discount rates and news about future cash flows. The news component of both channels reflect changes in investors’ expectations, which can be proxied based on the methodsofCampbellandShiller(1988). Whileourfocusisonwhichchannelsareinfluencedbytaxshocks, our analysis speaks to the relative importance of discount rates versus cash flows, a central discussion of finance. CampbellandShiller(1988);Campbell(1991);CampbellandAmmer(1993);Vuolteenaho(2002); Chen and Zhao (2009) among others focus on the volatility of asset prices being driven by volatility in discount rate news. Cash flow news as the primary driver of asset volatility is emphasized by Bansal and Yaron (2004); Bansal, Dittmar, and Lundblad (2005); Lettau and Ludvigson (2005); Santos and Veronesi (2010);Cohen,Polk,andVuolteenaho(2009);Da(2009);Hansen,Heaton,andLi(2008). Previous studies have used similar empirical methods to derive the effects of monetary policy on the stockmarket,butnotfiscalpolicy. Patelis(1997);BernankeandKuttner(2005);andMaio(2014)haveall found monetary policy imposing significant effects on the stock market using a news decomposition. For instance, Bernanke and Kuttner (2005) find that unexpected monetary policy shocks impact stock market 5

returnspredominantlythroughthefutureexcessreturnschannel,whereastheeffectonrealinterestratesand dividendsaresmallerandlesssignificant. Thesefindingsalsoaddtoarichliteratureexploringtherelationshipbetweenpolicyandequityreturns, morebroadly. AiandBansal(2016)explorethemacroannouncementpremiuminthecontextofuncertainty aversion. Belo and Yu (2013) look at the relationship between government investment and returns at the aggregateandfirmlevel,whileBelo,Gala,andLi(2013)focusonindustryexposuretogovernmentspending and find predictable variation in cash flows and stock returns over political cycles. Croce, Kung, Nguyen, andSchmid(2012),Croce,Nguyen,Raymond,andSchmid(2017),andCroce,Nguyen,andSchmid(2012, 2013)studythelinkbetweendebt,taxation,andreturnsinageneralequilibriumRBCframework,whileDa, Warachka,andYun(2016)focusonstate-levelfiscalpolicies. PastorandVeronesi(2012,2013,2017)study the link between stock prices and risk premia with an explicit focus on political uncertainty along with the politicalcycle. Gallmeyer,Hollifield,andZin(2005)focusesontherelationshipbetweenvariousmonetary policyrulesandthetermstructureofinterestrates,whileKung(2015)studiestheequilibriumrelationship between monetary policy and the term structure of interest rates in a model with endogenous growth. In contrasttotheabovestudies,wedocumentthatashiftinmonetarypolicysignificantlychangestheresponse ofequityreturnstofiscalpolicywithinthecontextoftaxshocks. Finally,ourpaperisnotthefirsttosuggestthatbadnews(inourcase,taxincreases)canbeassociatedwith higher equity returns. Boyd, Hu, and Jagannathan (2005) find that bad news coming from unemployment data is usually good for stocks. Their empirical study suggests interest rate expectations fall on bad labor marketnewsduringexpansions,whichresultsinapositiveeffectonstockprices. Likewise,goodnews(in our case, tax cuts) can be associated with lower equity returns, as shown in McQueen and Roley (1993). Theyfindthatwhentheeconomyisstrong,thestockmarketrespondsnegativelytonewsabouthigherreal economic activity and this is caused by a larger increase in discount rates relative to expected cash flows. In a separate and independent manuscript completed after our paper, Mumtaz and Theodoridis (2017) find thatpositive(negative)shockstogovernmentspending(taxes)leadtoarise(fall)instockpricesintheUS post-1980.3 Additionally, Evans and Marshall (2009) show that an expansionary labor supply shock or a 3Ourpaperdiffersfromthispaperinseveralimportantways.Onthetheoreticalside,wemovebeyondafirst-orderapproximation to allow for potentially non-linear asymmetric effects, which allows us to determine that tax cuts could potentially have larger effectsinthepresenceofdownwardnominalwagerigidities.WeshowthatourtheoreticalimplicationsholdintheFRB/USmodel 6

preference/demand shock4 leads to a positive response in profits, but a much bigger response of interest rates. The overall effect on the market return is negative, so that “good news is bad news” for the stock market. Blanchard (1981) and Orphanides (1992) also provide equilibrium and empirical support for the notionthatgoodnewscanbebadforthestockmarket,dependingonthestateoftheeconomy. 3. Model 3.1. Households Theeconomyispopulatedbyacontinuumofidenticalinfinitelylivedhouseholds. Eachhouseholdhas preferencesdefinedforconsumption,c ,andlaborhours,h . PreferencesarebasedonthestandardCRRA t t utilityfunction E X 1 (cid:12)t .c t (cid:19).1 (cid:0) h t /1 (cid:0) (cid:19)/1 (cid:0) (cid:27) (cid:0) 1 (1) 0 1 (cid:27) t 0 (cid:0) D whereE denotestheexpectationsoperatorconditionaloninformationavailableattimet,(cid:12) .0;1/is t 2 thesubjectivediscountfactor,c istheconsumption,andh islabor. Theconsumptiongoodisassumedto t t be a composite good produced with a continuum of differentiated goods, c , i (cid:140)0;1(cid:141), via the aggregator it 2 function 1 1=.1 1=(cid:17)/ (cid:20)Z 1 1=(cid:17) (cid:21) (cid:0) c c di (2) t D it(cid:0) 0 where the parameter (cid:17) > 1 denotes the intratemporal elasticity of substitution across different varieties of consumptiongoods. Foranygivenlevelofconsumptionofthecompositegood,purchasesofeachvarietyiin 1 periodtmustsolvethedualproblemofminimizingtotalexpenditure,R 0 P it c it di subjecttotheaggregation constraint above, where P denotes the nominal price of a good of variety i at time t. Upon solving this it demonstratingthatneithertherelativelysmallscaleofourmodelnorthespecificformofourTaylorRuleisnecessarytodrive ourresults.Ontheempiricalside,weprovideevidenceusingavarietyofalternatespecificationsandidentificationstrategies,such ashigherfrequencyresultsusingmunicipalbonddata, resultsusingvaluationratiosratherthanreturnsasinSialm(2009), and cross-sectionalresults. 4Note,Mulligan(2002)interpretsthisshockasalabormarketdistortion,suchasachangeintaxrates. 7

(cid:17) problem, the optimal level of c is given by c (cid:16)Pit(cid:17)(cid:0) c and P is a nominal price index given it it D Pt t t 1=.1 (cid:17)/ by P t (cid:17) h R 0 1 P i 1 t(cid:0) (cid:17) dii (cid:0) . This price index has the property that the minimum cost of a bundle of intermediategoodsyieldingc unitsofthecompositegoodisgivenbyP c . t t t Householdsareassumedtohaveaccesstoacompletesetofnominalcontingentclaims. Thehousehold’s budgetconstraintisgivenby x x E t d t;s P t C 1 C c t C i t C (cid:28) t D P t C .1 (cid:0) (cid:28) t D/ (cid:1) .w t h t C u t k t / C (cid:14)q t (cid:28) t Dk t C (cid:30) t (3) t t whered isthestochasticdiscountfactor,definedsuchthatE d x isthenominalvalueinperiodtofa t;s t t;s s randomnominalpaymentx inperiods t. Thevariablei denotesinvestment,(cid:28) isthelumpsumtax,(cid:28)D s t t t (cid:21) isthedistortionaryincometaxrate,w istherealwage,u istherentalrateofcapital,k denotescapital,and t t t q denotesthemarketpriceofoneunitofinstalledcapital. Theterm(cid:14)(cid:28)Dq k denotesdeprecationallowance t t t t fortaxpurposesand(cid:30) denotesprofitsreceivedfromownershipoffirmsnetofincometaxes. t Theevolutionofcapitalisgivenby (cid:18) i t (cid:19) k .1 (cid:14)/k i (cid:137) (4) t 1 t t t C D (cid:0) C i t 1 (cid:0) where the function (cid:137) represents investment adjustment costs that take the form (cid:137).x/ 1 .x 1/2 D (cid:0) 2 (cid:0) and 0. Without adjustment costs on investment, the price of capital would never change because the (cid:21) supplywouldbeperfectlyelasticandalwaysequaltoone. Weshowintherobustnesssectionthatourresults donotdependonthisparameterandforparsimony,set 0. Householdsareassumedtobesubjecttoa D borrowinglimitthatpreventsthemfromengaginginPonzischemes. 3.1.1. WagesandLabor Householdsareassumedtohavedifferentiatedjobskillsthatprovidethemmonopolisticallycompetitive poweroverthelaborsupply. Theychoosetheirwageandlaborsupplytakingthefirms’demandfortheirlabor type. Following Kim and Ruge-Murcia (2009), labor market frictions create adjustment costs in nominal 8

wagesandtaketheformofthelinexfunction (cid:136)n (cid:136).Wn=Wn / (cid:30) (cid:18)exp. (cid:0) (cid:30).W t n=W t n 1(cid:0) 1// C (cid:30).W t n=W t n 1 / (cid:0) 1(cid:19) (5) t D t t 1 D (cid:0) (cid:30)2 (cid:0) (cid:0) whereWnisthenominalwageand(cid:30)and arecostparameters. Thisfunctionallowsforthecostsassociated t withwagedecreasestoriseexponentially, whilecostsassociatedwithwageincreasestoriselinearly. This createsanasymmetrythatisconsistentwiththenotionofdownwardnominalwagerigidities. WhenhouseholdschooseWn,theyequatethemarginalcostsandbenefitsofincreasingWn,asshown t t below 1 (cid:19) c t 1 (cid:20) h t 1 (cid:21) ! t (cid:136) 0 D (cid:18) (cid:0) (cid:19) leis t w t .1 (cid:28) t d/ (cid:0) .(cid:18) (cid:0) 1/.1 (cid:0) (cid:136)/ C E t m t;t C 1 h C t (cid:129)w t C 1 ! t C 1 (cid:136) 0t C 1 (6) (cid:0) where! Wn=Wn . AsnotedbyKimandRuge-Murcia(2009),thecostsdecreaseinhoursworkedas t D t t 1 (cid:0) firms substitute away from more expensive labor input and the wage adjustment cost. The benefits are the increaseinlaborincomeperhourworked,theincreaseinleisuretimeasfirmsreducetheirdemandforlabor oftype-n,andthereductionoffutureexpectedwageadjustmentcosts. 3.2. TheGovernment Thegovernmentissuesone-periodnominalrisk-freebonds,B ,collectstaxrevenuesP (cid:28) ,andspends t t t anexogenousamounteachperiod,g . Inrealterms,thegovernment’sbudgetconstraintis t R t 1 b t (cid:0) b t 1 g t (cid:28) t (7) D (cid:25) t (cid:0) C (cid:0) where lower case letters denote real values, (cid:25) P =P denotes gross consumer price inflation, R t t t 1 t (cid:17) (cid:0) denotesthegrossone-periodriskfreenominalinterestrateinperiodt. Total tax revenues are (cid:28) (cid:28)Dy (cid:28)L. The fiscal rule is defined so that tax revenues must rise with t t t t D C debt (cid:28) (cid:28) (cid:13) .R b R b / (8) t (cid:3) 1 t 1 t 1 (cid:3) (cid:3) D C (cid:0) (cid:0) (cid:0) 9

where (cid:13) denotes how fast taxes are paid back, (cid:28) and B denote the deterministic steady state values of 1 (cid:3) (cid:3) (cid:28) and B respectively. To isolate the effects of the tax rate, we allow lump sum taxes to adjust in order to t t balancethebudget. Notethatifwedidnotsetuptaxesinthisway,anydistortionarytaxratechangewould befollowedbyanoppositereactioninthefollowingperiods,comingfromtheaboveruleasdebtchanges.5 Toanalyzetheeffectoftaxshocks,anormal,meanzeroshockisappendedtothedistortionarytaxrate suchthat (cid:28)D (cid:28)D; utax: (9) t (cid:3) t D C utax (cid:26)(cid:28)utax (cid:15)tax (10) t t 1 t D C (cid:0) The standard deviation is set to match the standard deviation of the tax shocks coming from Romer and Romer(2010)andthepersistenceissettoahighvaluetobeconsistentwiththeempiricalanalysis. Weshow intherobustnesssectionthatourmainresultsdonotdependontheseparameters. Themonetaryauthoritysetstheshort-termnominalinterestrateaccordingtoasimplefeedbackrule. ln.R t =R (cid:3) / (cid:11) r ln.R t 1 =R (cid:3) / .1 (cid:11) r /(cid:2)(cid:11) (cid:25) ln.(cid:25) t =(cid:25) (cid:3) / (cid:11) y ln.(cid:129)y t =(cid:129)y (cid:3) /(cid:3) (11) D (cid:0) C (cid:0) C where(cid:129)y denotesthedeterministicsteadystateofoutputgrowth.6 (cid:3) 3.3. Firms Eachvarietyi (cid:140)0;1(cid:141)isproducedbyasinglefirminamonopolisticallycompetitiveenvironment. The 2 productiontechnologyisgivenbyz k(cid:18)h1 (cid:18) wherez denotesanexogenous,aggregateproductivityshock. t it it(cid:0) t Aggregatedemandforgoodi isdenotedbya c i g .P =P / (cid:17)a giventheaggregation it it it it it t (cid:0) t D C C D 5IsolatingtheeffectsoftaxratechangesinthiswayisalsoconsistentwithSimsandWolff(2016). 6Wefocusonoutputgrowthratherthantheoutputgapformultiplereasons:(1)Outputgrowthisobservablewhereastheoutput gapisafunctionoftwounobservedvariables,thenaturalrateofunemploymentandthepotentiallevelofoutput; (2)Real-time outputgapstendtosignificantlydifferfromex-postoutputgaps(BelkeandKlose,2011);(3)SmetsandWouters(2007),Orphanides (2004),andCampbell,Pflueger,andViceira(2017)findnosignificanceontheoutputgapforPost-Volcker.Incontrast,Smetsand Wouters(2007)dofindsignificanceonoutputgrowthforPost-Volcker.Inaddition,ourownestimatesbasedonGreenbookDatafind significanceforoutputgrowthbutnottheoutputgapforthePost-Volckertimeperiod. Furthermore,CoibionandGorodnichenko (2015)findsignificantchangestotheoutputgrowthvariableacrossthePreandPost-Volckerregimeswhereastheyfindnosignificant difference in the output gap level. Moreover, including an output gap level does not change our analysis so we exclude it for parsimony. 10

constraint. Itisassumedthatthefirmmustsatisfydemandatthepostedpricesothatfirmsmaximizeexpected profitssubjecttothefollowingconstraint z k(cid:18)h1 (cid:18) (cid:18)P it(cid:19)(cid:0) (cid:17) a (12) t it it(cid:0) (cid:21) P t t FirmsareassumedtofaceaquadraticcostofadjustingnominalpricesasinRotemberg(1982),withthecost beingmeasuredintermsofthefinalgoodandgivenby (cid:30) (cid:18) (cid:25) t (cid:19) 2 1 Y t 2 (cid:25) (cid:0) ss where(cid:30) capturesthedegreeofnominalrigidity. Theproblemforfirmjisthentomaximizethediscounted valueofnominalprofits 1 max E XQ (cid:132) t t;t s t s Pt.j/ 1t 0 s 0 C C D D wherenominalprofitsaredefinedas (cid:30) (cid:18) (cid:25) t (cid:19) 2 (cid:132) P .j/Y .j/ mc Y .j/P 1 Y P t t t t t t t t D (cid:0) (cid:0) 2 (cid:25) (cid:0) ss Firmscanchangetheirpriceineachperiodsubjecttotheadjustmentcosts. Therefore,allfirmsfacethefame problemandwillchoosethesamepriceandsamequantity. Thisyieldsasymmetricequilibrium,P .j/ P t t D andY .j/ Y foranyj,andthefirst-orderconditionis t t D (cid:25) t (cid:18) (cid:25) t (cid:19) " (cid:18)c t 1(cid:19) (cid:19).1 (cid:0) 1/ (cid:0) 1 (cid:18)1 h t 1(cid:19) .1 (cid:0) (cid:19)/.1 (cid:0) 1/ y t 1 (cid:25) t 1 (cid:18)(cid:25) t 1 (cid:19) # .1 (cid:17)/ (cid:17)mc t (cid:30) 1 (cid:30)(cid:12)E t C (cid:0) C C C C 1 0 (cid:0) C (cid:0) (cid:25) (cid:25) (cid:0) C c 1 h y (cid:25) (cid:25) (cid:0) D ss ss t t t ss ss (cid:0) Thisisthenon-linearPhillipscurvethatrelatescurrentinflationtofutureexpectedinflationandtothelevel ofoutput. Roundingoutthemodel,theresourceconstraintfortheentireeconomyis y c i g (cid:128) y w h (cid:136) (13) t t t t t t t t t D C C C C 11

where(cid:128) capturesthepriceadjustmentcostsand(cid:136) captureswageadjustmentcosts. t 3.4. Return Wefollowstandardtheoryanddefinethereturninourtheoreticalmodelasfollows P D RD t I 1 V D t C 1 P C t C 1 (14) C t where P t D E t (cid:2)M t C 1 RD t C I 1 V (cid:3) and D t D Y t (cid:0) w t L t (cid:0) I t .7 Typically, dividends are defined as a levered claimtoconsumptioninthefinanceliterature. Thisisbecauseconsumptionbasedassetpricingmodelsare frequentlymodeledasendowmenteconomieswhereconsumptionanddividendsareexogenous. Incontrast, oursetupisaricherandmorefullyspecifiedframeworkthatdefinesdividendsasafunctionofendogenous productionandinvestmentdecisions. Forthesakeofourtheoreticalincometaxexperiments,wemodifythecashflowinthereturnequation suchthat D (cid:16)1 (cid:28) (cid:17)D (15) t(cid:3) D (cid:0) D(cid:3);t t where(cid:28) (cid:13)(cid:28)Disthedividendtaxrateandisproportionaltotheincometaxrate. Ononeextreme,(cid:13) 0, D(cid:3);t D t D andthisassumesthat0%ofequityisheldbytaxableinvestors. Ontheotherextreme,(cid:13) 1,whichassumes D that 100% is held by taxable investors. Instead, we follow Sialm (2009) and use data from the FED2004 FlowofFundsthatsuggests(cid:13) 0:55,or55%ofequityisheldbytaxableinvestors. D 3.5. Calibration ManyofthedeepstructuralparametershavebeensettothevaluesinSchmitt-GrohéandUribe(2007). For completeness, we check the robustness of our results with respect to each parameter in Section 1 of the Appendix. Since the goal of Schmitt-Grohé and Uribe (2007) was to determine optimal policy and not necessarily to match empirical moments when specifying fiscal and monetary policy, we turn to prior literature to set the remaining parameters in our model. The four parameters that we are unable to obtain 7Alternatively,wecandefinedividendsasDt Ct Gt .1 (cid:136)t/WtHt. D C C (cid:0) 12

fromSchmitt-GrohéandUribe(2007)are(cid:13) ,thespeedoftaxrepayment,(cid:11) ,theinflationcoefficient,(cid:11) , 1 (cid:25) y theoutputgrowthcoefficient, and(cid:11) , theinertiacoefficientinthemonetarypolicyrule. Forfiscalpolicy, R our choice for the speed of tax repayment comes from recent estimates by Drautzburg and Uhlig (2015), whichwesetto0.03. Sincelumpsumtaxeshelpbalancethebudget(whichallowsustoisolatetheeffects ofdistortionarytaxshocks),thisparameterdoesnotmeaningfullyalterthequantitativeresults. For monetary policy, we follow Coibion and Gorodnichenko (2015), who estimate parameters in the monetary policy rule for the Pre-Volcker and Post-Volcker eras. For the Post-Volcker era, we use their estimated coefficients of 0.90 for the inertia coefficient, 1.58 for the inflation coefficient, and 2.21 for the output growth coefficient. We show in Section 1 of the Appendix that our results are not highly sensitive to the values presented here. Moreover in Section 2 of the Appendix, we follow Orphanides (2004) and CoibionandGorodnichenko(2015)toestimatethepolicyrulewithGreenbookdatathrough2007.8 Again, theresultsofthesetestsareconsistentwiththetheoreticalimplicationspresentedbelow. ForthePre-Volckersetting, CoibionandGorodnichenko(2015)findaloweroutputgrowthcoefficient and a lower inflation coefficient and our estimates confirm these lower values in comparison to the Post- Volcker time period. Our own estimates suggest lowering the output growth coefficient to 0.94, lowering the inflation coefficient to 1.32, and setting an inertia coefficient to 0.91.9 We note that the change in the responsetooutputgrowthistheprimarydriverofourtheoreticalresults. 3.6. DSGEResults Our DSGE model results present the exact mapping from the initial tax shock to the endogenous responses of returns and cash flows implied by the solution to the model. We solve the model by taking a second order approximation of the nonlinear equilibrium conditions. We start with a discussion of the impactofanexogenousincometaxrateincreaseontheeconomyasdepictedinFigure1. Figure 1 presents the impulse response functions for an exogenous income tax rate increase under the Post-VolckerandPre-Volckercalibrations. Tobetterunderstandtheimportanceofthecashflowchannelversusthediscountratechannelindeterminingequityprices,wecomputetheexcessreturnsfortwoadditional 8WhileSimsandZha(2006)andothersfocusonashiftinthevolatilityofpolicyshockstoexplainchangesininflationthrough time,differencesinourestimatedloadingsacrossregimesaresufficienttogenerateourmaintheoreticalimplications. 9Section2oftheAppendixdetailsourestimation. 13

Parameter Value Description 1 0.2 IntertemporalElasticityofSubstitution (cid:27) (cid:18) 0.3 Costshareofcapital (cid:12) 0.999 Quarterlysubjectivediscountrate(Realrisk-freerate4%) (cid:17) 7 PriceElasticityofDemand (MidpointofSchmitt-GroheUribe(2007)=5andCoibionandGorodnichenko(2011)=10) (cid:14) 0.025 QuarterlyDepreciationRate (cid:30) 35 PriceAdjustmentCosts,(KimandRuge-Murcia,2007) (cid:19) 0.25 SettomatchLabor=0.25(SeeRobustnessSection) (cid:137) 0 InvestmentAdjustmentCostParameter (cid:26) 0.87 Serialcorrelationofgovernmentspending G (cid:27)(cid:15)G 0.016 Standarddeviationofinnovationtogovernmentpurchases (cid:26) 0.8556 Serialcorrelationofproductivityshock z (cid:27)(cid:15)z 0.0064 Standarddeviationofinnovationtoproductivityshock (cid:26) 0.9999 Serialcorrelationoftaxshock(SeeRobustnessSection) (cid:28) (cid:27)(cid:15)(cid:28) 0.0022 StandarddeviationofinnovationtotaxrateRomerandRomer(2007) (cid:30) 1000 Wageadjustmentcostsparameter(KimandRuge-Murcia,2007) 3800 Asymmetricwageadjustmentcostsparameter(KimandRuge-Murcia,2007) scenariosdefinedbelow: (1)DiscountRateOnlyand(2)CashFlowOnly. Specifically,wedefine DiscountRateOnlyScenario: P E (cid:140)M .P D /(cid:141) 1;t t t 1 t 1 SS D C (cid:1) C C CashFlowOnlyScenario: P M E (cid:140).P D /(cid:141) 2;t SS t t 1 t 1 D (cid:1) C C C whereM andD arethesteady-statevaluesoftheSDFanddividends,respectively. SS SS TheDiscountRateOnlyscenariocompletelyshutsdownvariationinthecashflowchannel,sothatthe price of equity is purely a function of the sum of future SDF values. As denoted by the dashed blue line, theexogenoustaxincreaseleadstoahigherexcessequityreturnasrealinterestratesdecline(therealSDF rises)duetothenegativewealtheffectsofthehighertaxrateonconsumptiongrowth. The Cash Flow Only scenario shuts down variation in the discount rate channel, so that the price of equity is purely a function of the future dividends discounted by the deterministic steady state of the real SDF.Asdenotedbythereddot-dashedline,itisclearthattheexcessequityreturnwouldbenegativewith only cash flow news. The higher income tax rate reduces output growth over the medium to long run, and thistranslatestolowerdividendgrowth. Byactivatingboththecashflowanddiscountratechannels,wearriveattheblacklinesinFigure1. In theleftpanel(Post-Volcker),thediscountrateeffectdominatessothattheexcessequityreturnhasapositive 14

response. ForthePost-Volckercalibration, asizableweightin theTaylorRuleis placedonoutputgrowth. Thisstabilizingeffectgeneratesagreaterrelativedeclineinrealinterestratesinresponsetotheexogenous incometaxrateincrease. Inaddition,thegreaterpolicyresponsetothenegativeeconomiceffectsofthetax shock also helps dampen the decline in cash flow news. We explore the effects of each coefficient in the TaylorRuleinmoredetailintheSection1oftheAppendix. In contrast, for the right panel (Pre-Volcker), a smaller coefficient on output growth in the monetary policyruleimpliesasmallerrelativedeclineinrealinterestrates. Inaddition,thesmallerpolicyresponseto thenegativeeconomiceffectsofthetaxshockamplifiesthedeclineincashflownews. Asaresult,thecash flownewsdominatesandtheeffectofthetaxincreaseisanegativecurrentexcessreturn. 3.6.1. Pre-Volcker Figure2presentstheimpulseresponsefunctionsforanexogenousincometaxrateincreaseforthePre- Volcker, Post-Volcker, and RBC calibrations. The difference between the Pre-Volcker and Post-Volcker calibrationsisisolatedtotheTaylorRule. Specifically,thePre-Volckercalibration(reddashedline)features a lower inflation coefficient, and a significantly lower output growth coefficient. With the lower output growth coefficient in the monetary policy reaction function, real interest rates do not decline as much and outputgrowthdeclinesmoreinthemediumtolongrun. For the Pre-Volcker calibration, the negative substitution effect dominates so that investment growth declinesinitially. Specifically,monetarypolicyrespondslesstothenegativeeffectsofthetaxincreasedue totheloweroutputgrowthcoefficient,whichreducestheincentivetoinvest. Sincethelevelofinvestment falls below its long-run level, investment growth is positive in the subsequent periods. While the initial decline in investment does lead to positive dividend growth at first, the increase in investment growth in later periods combined with the greater decline in output (compared to the Post-Volcker) leads to a larger negativesumofdividendgrowth. Therefore,thecashflowchannelislarger. Atthesametime,thediscount rate channel is smaller when compared to the Post-Volcker scenario. This combination of more negative cashflownewsandlessnegativediscountratenewscausesanegativeexcessequityreturnbecausethecash floweffectdominates. 15

3.6.2. Post-Volcker For the Post-Volcker scenario (the dashed blue line) , recall that dividends are an endogenous function oftheproductionandinvestmentdecisions(D Y w L I );thus,thedeclineindividendsiscaused t t t t t D (cid:0) (cid:0) by the incipient increase in investment due to the negative wealth effect. Dividend growth in the medium to long run is subdued as output growth also declines due to the higher income tax rate.10 As previously mentioned, real interest rates decline to a greater extent under the Post-Volcker regime because monetary policyrespondstoagreaterextentthroughthehighercoefficientonoutputgrowth.11 3.6.3. RBC The solid black line reflects the Real Business Cycle Model. The Real Business Cycle model differs from the New Keynesian model by eliminating the monetary policy rule and keeping inflation constant while removing wage rigidities. Doing so replicates the natural level of output, which is the output that wouldoccurwithflexibleprices. Itprovidesabenchmarktoshowtheimportanceofincorporatingarolefor monetary policy and nominal rigidities. As shown in Figure 2, dividends falls slightly more than the NK: Post-Volckermodelandrealinterestratesdonotfallasmuchinthemedium-longrun. Thisentailsalarger relativeeffectoncashflownewsversusdiscountratenews,sotheoveralleffectisanegativecurrentexcess return. IncontrasttothePre-VolckerandRBCsettings,thePost-Volckermonetarypolicyofputtinggreater weightonoutputgrowthleadstoalargereffectonrealinterestratenewsandasmallerdeclineindividends, sothatthediscountratechanneldominatesandthecurrentexcessreturnforPost-Volckerispositive. 3.6.4. AsymmetriesintheResponsetoFiscalPolicy This section explores the theory and intuition for why the tax shock generates asymmetric responses depending on its direction, as shown in Figure 3. Recall that for the Post-Volcker regime income tax rate 10Outputgrowthlargelyfollowstheresponseoflabor, andlaborbrieflyrisesbeforedeclininginresponsetothepositivetax shock. Thesedynamicsaresimilartotheresponsesonemightseeforanewsshock. Whiletheinitialriseinlabormightatfirst becounterintuitive,notethatcapitalispredetermined,sothatinthefirstperiod,thenegativeeffectsofthetaxshockonthecapital stock(vialowerinvestment)donotoccuruntillaterperiods,andthemarginalproductoflaborisatfirsthigherthanitwillbein subsequentperiodswhencapitalislower. 11Anotherwaytothinkabouttheeffectsontherealinterestratesistonotethatwiththepresenceofcapital, therealinterest ratesarelargelyequivalenttotheaftertaxmarginalproductofcapital.InthePost-Volckersetting,investmentishigherthaninthe Pre-Volckersettingandthecapitalstockishigherinthemediumtolongrun(duetothegreaterresponsetooutputinthePost-Volcker setting). Ahighercapitalstockmechanicallyreducesthemarginalproductofcapital,andalthoughthiseffectisslightlytempered bythehigherleveloflaborinthePost-Volckersetting,theoveralleffectisagreaterdeclineinrealinterestrateswhencomparedto thePre-Volckersetting. 16

increase(bluedashedline),thenegativewealtheffectdominatessothatconsumptiondeclines,whileinvestment and labor initially rise. Beyond the initial period of the shock, both labor and investment continue to declineuntiltheyreachtheirlong-runlevelsduetothehighertaxrate. Whilelaborandcapitalbothdecline (whichwouldhaveoppositeeffectsonthemarginalproductoflabor),thedeclineinlaborsupplydominates so that wages rise. When wages rise, wage adjustment costs are smaller compared to the case of falling wages(duetodownwardnominalwagerigidities). In contrast to the tax increase, the tax cut (black dashed line) generates a positive wealth effect so that consumption rises while investment and labor initially decline. Beyond the initial period of the shock, the benefitsofthetaxcutleadtoahigherlaborsupplyandhigherinvestment. Thehigherlaborsupplydominates sothatwagesdeclineinthemediumtolongrun. Howeverincomparisontoawageincrease,awagedecline generatesgreateradjustmentcosts,whichreflectthedownwardnominalrigiditiesinthemodel. Withwages declininglessduetothegreateradjustmentcosts,thedemandforlaborislower,andinvestmentandoutput donotriseasmuchduetothegreateradjustmentcosts. Relatingthesedynamicsbacktothecurrentexcessreturn,weseethattheexcessequityreturndeclines moreinresponsetothetaxcut(evidencedbytheredlineshowingthedifferenceinresponsestoataxincrease and tax cut). This decrease can mainly be attributed to the cash flow channel, as dividends do not rise as much in response to the tax cut. The dynamics for the dividends can be explained by separating the short runfromthemediumtolongrun. In the short run, investment does not decline as much (dividends do not increase as much) due to the positive wealth effect being dampened by the increased wage adjustment costs as wages decline over the medium to long run. In the medium to long run, investment does not rise as much (which should lead to a greaterincreaseindividends),butthiseffectisoffsetbythefactthatoutputalsodoesnotriseasmuch(recall thatD Y –w L –I ). Thesmallerincreaseinoutputoverthemediumtolongrunduetotheincreased t t t t t D wageadjustmentcostsdominatessothatdividendsdonotriseasmuchoverthemediumtolongrunforthe taxcutwhencomparedtotheeffectsofthetaxincrease. Combining both the short-run effect (relatively smaller decline in investment due to smaller positive wealtheffect)and mediumto long run effect(relatively smaller increase inoutputdue to wage adjustment costscomingfromlowerwages)leadstoanunambiguouslysmallerincreaseindividendsforthetaxcut. The 17

overalleffectisagreaterdeclineintheequityreturnforthetaxcut. Tosummarize,thepresenceofdownward nominalwagerigidities(i.e. asymmetricwageadjustmentcosts)providesatheoreticalfoundationforwhy taxcutscouldleadtolargereffectsonequitymarketsthantaxincreases. The right panel removes downward nominal wage rigidities, and shows that the difference across each impulse response function is essentially zero. This demonstrates the importance of including downward nominalwagerigiditiesinordertogenerateasymmetricresponsestotaxcutsandtaxincreases. 3.7. MeasuringtheImpactofNewsonEquityReturns In order to further decompose the impact of an exogenous tax increase on excess equity returns and to developaframeworkforwhichtoempiricallytestthepredictionsofourmodel,weturntothebasicframework of Campbell and Shiller (1988); Campbell (1991); and Campbell and Ammer (1993). Those studies show that according to a simple dynamic accounting identity, innovations in current equity excess returns can be decomposed as follows into revisions of future expected cash flows, revisions of future expected excessreturns,andrevisionsoffutureexpectedrealinterestrates. r E .r / .E E /X 1 (cid:26)j(cid:129)d .E E /X 1 (cid:26)jr ex;t 1 t ex;t 1 t 1 t t 1 j t 1 t ex;t 1 j C (cid:0) C D C (cid:0) C C (cid:0) C (cid:0) C C j 0 j 1 D D (16) .E E /X 1 (cid:26)jr t 1 t real;t 1 j (cid:0) C (cid:0) C C j 0 D r E .r / N N N (17) ex;t 1 t ex;t 1 CF;t 1 ex;t 1 real;t 1 C (cid:0) C (cid:17) C (cid:0) C (cid:0) C where N .E E /X 1 (cid:26)j(cid:129)d r E .r / N N (18) CF;t 1 t 1 t t 1 j ex;t 1 t ex;t 1 ex;t 1 real;t 1 C (cid:17) C (cid:0) C C D C (cid:0) C C C C C j 0 D N .E E /X 1 (cid:26)jr (19) ex;t 1 t 1 t ex;t 1 j C (cid:17) C (cid:0) C C j 1 D N .E E /X 1 (cid:26)jr f (20) real;t C 1 (cid:17) t C 1 (cid:0) t j 0 real;t C 1 C j D 18

represent revisions about future cash-flows, revisions in future expected excess returns, and revisions in future real interest rates, respectively. The monthly discount factor (cid:26) is set to 0.9962, following the previous literature (Campbell and Ammer, 1993; Bernanke and Kuttner, 2005) and is used to match the steady state average annual dividend yield of 5%. As previously stated, the above relationships reflect dynamic accountingidentitiesandhavenoeconomicorbehavioralcontent. Table1reportsthediscountedsumoftheseeffectsonequity,summarizestheIRFspresentedinFigure2, andprovidesabenchmarkforourempiricalresults. OverthePost-Volckerperiod,aonestandarddeviation increaseinthetaxes(0.22%)correspondstoa0.0515%increaseinexcessequityreturns. Withanexogenous increase in taxes, news about both future real interest rates and cash flows is negative. The decrease in discounted future cash flows of -0.2103% is offset by the decrease in discount rates of -0.2588%. Most of thischangeinfuturediscountratesisdrivenbynewsaboutfuturerealinterestratesratherthaninformation aboutfutureequitypremia,asmonetarypolicystabilizesoutputtoagreaterextent. Responsesforanegative taxshockexhibittheasymmetriesdiscussedinSection3.6.4withaonestandarddeviationdecreaseintaxes correspondingtoa-0.0528%contemporaneousexcessequityreturn. PanelBofTable1presentsresultsforthePre-Volckercalibration. Inthiscase,aonestandarddeviation increaseinthetaxrateleadstoa0.0502%decreaseinexcessequityreturns. Again,bothnewsaboutfuture real interest rates and cash flows is negative consistent with the findings in Gale and Orszag (2003) and Romer and Romer (2010), respectively. However in the Pre-Volcker period, the cash flow news channel dominates the real interest rate news channel such that the overall impact on equity returns is negative. Againasymmetriesexistduetodownwardnominalwagerigidities. Panel C of Table 1 presents results for the RBC calibration. Recall, the RBC calibration replicates the naturallevelofoutputbyremovingmonetarypolicyandnominalrigidities. Similartothepreviouspanels, ataxincreaseleadstonegativecashflowanddiscountratenews. SimilartothePre-Volckerframework,the cash flow news channel is larger so that the overall effect of tax increase is a 0.0555% decrease in excess equityreturns. 19

3.8. ModelRobustness 3.8.1. AlternativeParameterValues Asafirstpass, weverifythatourchoiceofparametersinourcalibratedmodeldonotimpactthetheoreticalpredictionsofthemodel. Namely,wedemonstratethatthedeclineinexcessreturnsinresponsetoa taxcutisrobusttoperturbingalltheparametersaboveandbelowtheirbenchmarkvalues. Specificresults alongwithafulldiscussionandintuitionareavailableinSection1oftheAppendix. 3.8.2. ResultsintheFRB/USModel While an exploration of the effects of monetary policy on real interest rates requires New Keynesian features,neithertherelativelysmallscaleofourmodelnorthespecificformofourTaylorRuleisnecessary todrivethechangestothediscountrateandcashflowmacroeconomicnewschannelsacrossmonetarypolicy regimes. Inthissection,weexploretherobustnessofourtheoreticalimplicationstoanalternativemodeling frameworkcloselyrelatedtothemodelpresentedinFleischmanandRoberts(2011),theFRB/USmodel.12 Thislarge-scalemodeloftheU.S.economyallowsfornonlinearinteractionsamongendogenousvariables andservesasoneofseveralworkhorsemodelsthattheFederalReserveBoardstaffconsultsforforecasting andtheanalysisofmacroeconomicissues,includingbothmonetaryandfiscalpolicy. Our approach is to take this model off the shelf and simulate the results of our fiscal policy experiment. Specifically,wepeturbnominalpersonaltaxreceipts(TFPN)by0.22%oftaxableincome(YPN (cid:0) GFTN GSTN)fortenyearsfrom2020Q1to2029Q4.13 Resultsaresimilartoourfindingsbasedonthe (cid:0) DSGE model. Current excess equity returns increase following an exogenous increase in the tax rate with bothcashflowanddiscountratenewsfallingfollowingtheshock. Asbefore,thediscountratenewschannels dominate the cash flow news driving the increase in equity returns. Specifically, the current excess return rises 0.28%, and the discount rate news declines by 0.98% and the cash flow news declines by 0.70%.14 In addition, when the output gap coefficient is decreased as in the case of our Pre-Volcker calibration, the discountratenewschanneldecreasesinabsolutemagnitudeleadingtoalowercurrentexcessequityreturn 12Formoreinformation,seeBrayton,Laubach,andReifschneider(2014)andcitestherein. 13Weshocknominalpersonaltaxreceiptsdirectlytopreventtheendogenouspersistenceinthetaxrate(TRFP)fromamplifying theeffectsofataxcutorstimulus. 14Onepotentialconcernisthatcashflowsfarinthefutureare(unrealistically)drivingourresults. Inthissetofexperiments wherewecanmoreeasilycontrolforthedurationofthefiscalpolicyexperiment,wefindthatourmainresultsremain. 20

response. 4. DataandMethodology Thissectiondescribesourempiricalimplementationoftheequityreturndecompositionpresentedinthe previoussection,thesourcesofdatawhichweemploy,andtheidentificationstrategyweusetoconstructa seriesofplausiblyexogenousshockstotaxpolicy. 4.1. DataandEstimation Inordertoempiricallyimplementthenewsdecompositiondescribedabove, werequireproxiesforthe expectationsappearinginEquation16. WefollowtheapproachofBernankeandKuttner(2005)andwrite ann-variable,p-lagvectorautoregression(VAR)asafirst-ordersystem Z AZ w (21) t 1 t t 1 C D C C whereZ isastackednp 1vectorcontainingtherealinterest rate, theexcessequityreturn, andother t 1 C (cid:2) variables that are considered useful for forecasting excess equity returns. The state vector we consider is givenby Z (cid:140)r ; r ; (cid:129)r ; SPREAD d p ; REL (cid:141) (22) t ex;t real;t t t; t t t 0 (cid:17) (cid:0) wherer istheCRSPvalue-weightedreturninexcessoftherisk-freerate;r istherealinterestrate, ex;t real;t definedasthe3-MonthTreasurybillratedividedbyquarterlyCPI;(cid:129)r denotesthechangeinthenominal t 3-MonthTreasurybillrate;SPREAD denotesthedifferencebetweentheyieldsonthe10-yearT-Billand t 3-monthT-Bill;d p denotesthelogdividend-priceratiofortheS&P500;REL isthedifferencebetween t t t (cid:0) the3-MonthT-Billandits12-monthmovingaverage. DataareasinWelchandGoyal(2008).15 Ouranalysisfocusesonthepost-WorldWarIIperiodforwhichwecanconstructaseriesoftaxpolicy shocks,1947Q1to2007Q4. Asdiscussedintheprevioussection,thehypothesizedresponseofequityprices tofiscalpolicyshocksishighlydependentonmonetarypolicyregime. TocapturethePre-andPost-Volcker 15WethankAmitGoyalforprovidingthesedata. 21

periodinourdata,wedefinethefollowingsubsamples: 1947Q1-1980Q2,and1980Q3-2008Q2. Weidentify the cutoff between 1980Q2 and 1980Q3 statistically. Specifically, we test for multiple unknown structural breaks in the VAR system given in Equation 21 using the SupW test of Andrews (1993). We allow for heteroskedasticitywithinregimesandimplementthefixedregressorbootstrapofHansen(2000)tocalculate thecriticalvaluesforourconditionalmodel. Thiscutoffalsohaseconomicimportanceasinflationpeaked inMarch1980followingthebeginningoftheVolckerpolicyexperimentinOctober1979.16 With the VAR expressed as above, the discounted sum of revisions in expectations are estimated as followsbyCampbell(1991);CampbellandAmmer(1993);andBernankeandKuttner(2005): N .E E /X 1 (cid:26)jr ex;t 1 t 1 t ex;t 1 j C (cid:17) C (cid:0) C C j 1 (23) D e1(cid:26)A.I (cid:26)A/ 1w 0 (cid:0) t 1 D (cid:0) C N .E E /X 1 (cid:26)jr real;t 1 t 1 t real;t 1 j C (cid:17) C (cid:0) C C j 0 (24) D e2.I (cid:26)A/ 1w 0 (cid:0) t 1 D (cid:0) C N .E E /X 1 (cid:26)j(cid:129)d CF;t 1 t 1 t t 1 j C (cid:17) C (cid:0) C C j 0 D (25) r E .r / N N ex;t 1 t ex;t 1 ex;t 1 real;t 1 D C (cid:0) C C C C C (cid:2)e1 0 e1 0 (cid:26)A.I (cid:26)A/ (cid:0) 1 e2 0 .I (cid:26)A/ (cid:0) 1 (cid:3)w t 1 D C (cid:0) C (cid:0) C In the above equations, e1 is a vector whose first element is equal to one and zero otherwise, which correspondstothepositionoftheexcessreturnontheCRSPvalue-weightedindexintheVAR,ande2isa vector whose second element is equal to one and zero otherwise, corresponding to the position of the real interest rate in the VAR. In the above equations, cash-flow news is the residual of the unexpected excess returnthatcannotbeexplainedbyfutureexcessreturnsandfuturerealinterestrates. Calculatingcash-flow news as the residual has the advantage of not having to directly model the dynamics of dividends, which 16OurmainresultsarequantitativelysimilarusingcutoffsthroughouttheVolckerpolicyexperimentof1979Q3to1984Q1. For example,CoibionandGorodnichenko(2015)use1983Q1asthecutoffbetweenthePre-andPost-Volckermonetarypolicyregimes. 22

oftenexhibitseasonalityandarenon-stationary. Includingvariablesbeyondtheexcessequityreturnandrealriskfreerateareimportantforimprovingthe forecastoffuturenewsaboutdiscountratesandcash-flows. Forinstance,both(cid:129)r andREL areknownto t t begoodpredictorsoftherealinterestrate. AspointedoutinCampbellandAmmer(1993),therelativebill rate helps to capture the longer-run dynamics of changes in the interest rate without introducing long lags that drive up the number of parameters to be estimated. The SPREAD variable has been popular in the t predictabilityofreturnsliteratureasCampbell(1991)showsittracksthebusinesscyclerelativelywell. The aggregatedividend-priceratioisanotherpopularpredictorofaggregatestockreturns(seeCochrane(2008)) andisappealingfromatheoreticalperspectivebasedontheCampbellandShiller(1988)decomposition. To gauge the impact of exogenous shocks to fiscal policy on these variables of interest, we include a proxyforchangestofiscalpolicyintheVARasanexogenousvariable. Specifically,welet w (cid:30)FISCAL u (26) t 1 t 1 t 1 C D C C C whereFISCAL representsanexogenousshocktofiscalpolicy. Theeffectsofthefiscalshockoncurrent t 1 C (unexpected)excessreturns,futureexcessreturnnews,realinterestratenews,andcashflownewsarethen givenby (cid:24) e1(cid:30) (27) ex;current 0 (cid:17) (cid:24) e1(cid:26)A.I (cid:26)A/ 1(cid:30) (28) ex;future 0 (cid:0) (cid:17) (cid:0) (cid:24) e2.I (cid:26)A/ 1(cid:30) (29) real 0 (cid:0) (cid:17) (cid:0) (cid:24) e1(cid:30) e1(cid:26)A.I (cid:26)A/ 1(cid:30) e2.I (cid:26)A/ 1(cid:30) (30) CF 0 0 (cid:0) 0 (cid:0) (cid:17) C (cid:0) C (cid:0) NotethatboththeVARdynamicsandcoefficient(cid:30)arerelevantforcharacterizingtheeffectsoffiscalpolicy. To calculate standard errors for our news decomposition, we compute a recursive wild bootstrap as in MertensandRavn(2013).17 Specifically,weestimatetheVARgiveninEquation21toobtainAandavector b 17TheVAR(1)systemweimplementremovesmuchoftheautocorrelationinthesystem’sresiduals. Specifically,theDurbin- Watsonteststatisticsforthepre-andpost-Volckerperiodsyieldp-valuesof0.605and0.743,respectively. TheLjung-Boxteston theresidualsofexcessequityreturnsalsofailstorejectthenullhypothesisofnoautocorrelationforbothsubsamplesatalaglength 23

ofresiduals,w . Foreachbootstrapreplicationb 1;:::;2500,wedrawaseriesofresiduals t 1 b C D wb w eb ; (31) t 1 t 1 t 1 b C D b C C whereeb isarandomvariabletakingonvaluesof-1or1withprobability0.5. Wealsogenerateaseries t 1 C offiscalpolicyshocks FISCALb FISCAL eb : (32) t 1 t 1 t 1 C D C C Afterestimating the effectsof the fiscalshock given by equations 27-30 for eachbootstrapped sample, we canconstructtheempiricalstandarderrorintheusualway. 4.2. IdentificationofTaxShocks Clearlyfromtheabovediscussion,obtaininganunbiasedestimateoftheeffectofafiscalpolicyshock oncurrentexcessreturnsreliesontheexogeneityofthefiscalpolicyshockusedinestimatingEquation26.18 Inthissubsection,wedescribethefourseriesofplausiblyexogenoustaxshocksusedtoobtainourprimary results: AllShocks,SVARShocks,SurpriseShocks,andSurpriseSVARShocks. We follow Romer and Romer (2010) in identifying All Shocks via a narrative approach. They conduct a narrative analysis that focuses on identifying all significant federal tax actions from 1947 to 2007. The sourcesusedtoidentifytheshocksarepublicgovernmentdocumentscomingfromboththeexecutivebranch (e.g. Economic Report of the President) and the legislative branch (e.g. Congressional Record). Fifty significant exogenous federal tax actions are identified and analysis is limited to tax actions that actually changetaxliabilities. Thesizeoftaxchangesaremeasuredatthetimeofimplementationandarenormalized bythepreviousperiod’snominalGDP. Commonmeasuresoftaxshockstypicallyfocusonchangesinoverallrevenuesandchangesincyclically adjustedrevenues(seeBlanchardandPerotti(2002)). Aconcernwithusingthesemeasuresfortaxshocks isthattheycouldreflectendogenouspolicyresponsestotheeconomicenvironment. Thegoalinusingthe of20. 18Whilemuchmacroeconomicliteraturehasfocusedonthisquestion,Leeper,Walker,andYang(2013)providesanoverviewof popularidentificationstrategiesusedinassessingtheeffectsoftaxpolicy. 24

narrativeanalysisistoavoidthepotentialcorrelationoftaxshockswithinfluencesonaggregateoutcomes. Toaccomplishthis,federaltaxactionsareclassifiedintofourcategories: spending-driven,countercyclical, deficit-driven,andforlong-rungrowth. Spending-drivenandcountercyclicaltaxactionsareconsideredendogenoustaxchangesbecausetheyaretypicallytakeninresponsetocurrentorfutureeconomicconditions. Onceweexcludesuchactionsfromouranalysis,wefocusontheremainingdeficit-driventaxchangeandthe long-runtaxchangeaimedatraisinggrowthinthelongrun. Bothofthesetypesoftaxchangesareclaimed to not be motivated by current or future short-run economic conditions. By focusing on these unexpected policyactions,wecanmoreclearlydiscernthestockmarketreactiontotaxchanges. ResearchbyMertensandRavn(2014)highlightsthepotentialformeasurementerrorinnarrativeshock seriessuchasourAllShocksvariableduetonecessaryjudgementcallsintheirconstruction,censoringproblems when changes to the tax code are deemed revenue neutral, and discrepancies between actual changes intaxrevenuesandtheprojectedchangesintaxliabilitiescapturedbynarrativeshockseries. Toovercome thesemeasurementerrorissues,weconstructtheseriesSVARShocksfollowingtheir“proxystructuralVAR (SVAR)”methodology. Specifically,thistechniqueusesaseriesofnarrativeshocks,AllShocks,toidentify the structural shocks to a VAR such as the one in Blanchard and Perotti (2002). We estimate the impact ofdiscretionarytaxshocksfromaVARusingdataontotaltaxrevenuesT , governmentspendingG , and t t outputY . ThedynamicsofthereducedformVARaregivenby t Z (cid:11) d (cid:14) Z u (33) t 0 t 0 t 1 t D C (cid:0) C whereZ (cid:140)T ;G ;Y (cid:141), d containsdeterministictermsincludingaconstant, linearandquadraticterms, t t t t 0 t D andadummyvariablefor1975Q2,andZ (cid:140)Z ;:::;Z (cid:141).19 Thestructuralshocks" arerelatedto t (cid:0) 1 D t0 (cid:0) 1 t0 (cid:0) 4 t thereduced-formresidualsu throughtheequation t u (cid:12)" (34) t t D 19DataarefromNIPA.OutputisGDPinline1fromTable1.1.5; governmentspendingisFederalGovernmentConsumption ExpendituresandGrossInvestmentinline6fromTable3.9.5;totaltaxrevenueisFederalCurrentTaxReceiptsinline2ofTable 3.2plusContributionsforGovernmentSocialInsuranceinline11ofTable3.2lesscorporateincometaxesfromFederalReserve Banks(line8inTable3.2).AllseriesaredeflatedbytheGDPdeflatorinline1fromTable1.1.9andbythecivilianpopulationages 16+obtainedfromFrancisandRamey(2009). 25

While Blanchard and Perotti (2002), outline a series of identifying restrictions to map the reduced-form residualsu tothestructuralresiduals" . MertensandRavn(2014)augmenttheapproachofBlanchardand t t Perotti(2002)viatwosetsofadditionalidentifyingrestrictionsincorporatingtheinformationinthenarrative shocksm t E(cid:140)m "T(cid:141) (cid:30) 0 (35) t t D ⁄ E(cid:140)m "G(cid:141) E(cid:140)m "Y(cid:141) 0 (36) t t t t D D suchthat (cid:30)(cid:12) E(cid:140)u m (cid:141) (37) T t t D where(cid:12) isthefirstcolumnof(cid:12). Equation35statesthatthenarrativeshockseriesiscontemporaneously T correlated with the structural tax shock. Equation 36 requires the narrative shock series to be uncorrelated withcontemporaneousspendingandoutputshocks. Takentogether,weobtainoursecondsetofexogenous taxshocks,SVARShocksby(1)estimatingthereducedformVARgivenbyEquation33,(2)regressingthe reduced form residuals on the narrative shocks series m (i.e. our All Shocks series), and (3) rescaling the t responsefunctionsasintheBlanchard–PerottiSVARtogeneratetheintendedeffectontaxrevenues. Itisimportanttonotethatthetimingofimplementationfortaxchangesmattersfromatheoreticalperspective. Yang (2005) and Leeper, Walker, and Yang (2013) point out the differences between anticipated andunanticipatedtaxchanges. RomerandRomer(2010)takethisintoaccountandfindonlyslightevidence of expectational effects. They find that the relationship between exogenous tax increases (when liabilities actuallychange)andoutputisrobustwhileincludingaproxyforfiscalnews. Moreover,Figure4ofMertens andRavn(2012)showsthatnotcorrectlytimingtheimplementationshouldbiasourresultstowardfinding no effect.20 However, this evidence of expectational effects may only be true with respect to other macro variables,andnotfinancialvariablesasweuse. Toaddresssomeoftheseconcernsandprovidefurtherevidence, we consider the series of surprise narrative shocks in Mertens and Ravn (2012) as a third series of 20Specifically, the longer the lag between announcement and implementation the more negative the effect on output postannouncementandthelowertheoveralleffectonoutputoncethetaxchangeisimplemented. 26

potentiallyexogenoustaxshocks,SurpriseShocks. Ourfinalseriesoftaxshocks,SurpriseSVARShocks,is aseriesconstructedbyusingtheSurpriseShocksseriesasinstrumentsm inthe“proxySVAR”ofMertens t andRavn(2014).21 Whilestatisticaltestsofexogeneityprovideonlyevidenceofexogeneity,wefollowMertensandRavn (2012)inrunningorderedprobitteststodetermineifourstatevariablecanpredictfuturesignedbinarytax shocksasmeasuredbyourfourseries. WhiletheoptimallaglengthdeterminedbyBICisone,wepresent theresultsoftheorderedprobittestsinTable2forbothlaglengthoneandlaglengthfour. Whileevidenceis somewhatmixedforourAllShocksseries,wefailtorejectthenullhypothesisofexogeneitywithrespectto thefinancialstatevariablesoverthefullsampleforeachofourotherthreetaxshockseries.22 Theseresults are consistent with the findings of Mertens and Ravn (2012), who find that tax shocks are not predictable basedonmacroeconomicdata. Theconcurrenteffectsofmonetarypolicyarealsofrequentlysuggestedasapossibleissuewithourestimation. Weaddressthisconcernintwoways. First,weincorporatethefederalfundsrateasanadditional statevariableandfindquantitativelysimilarresults. Second,weperformaHall(1986)andEvans(1992)test by regressing our tax shocks on the monetary policy shocks used in Bernanke and Kuttner (2005). Specifically, we regress our tax shocks on four lags of our tax shocks, contemporaneous monetary policy shocks andfourlagsofmonetarypolicyshocks. Wefailtorejectthehypothesisofexogeneity(p-value=0.4649) overtheperiodwherebothoftheseshocksareavailable,1989Q2to2007Q4. 5. Results Inthissection,wepresentourmainresultsontheimpactoftaxpolicyonequityreturnsforthePre-and Post-Volckerperiods. Wethenexamineasymmetriesinequityresponsestofiscalpolicyshocksaspredicted by our model. We finally turn to whether our estimated responses are a function of changes to personal or corporatetaxes. 21OurresultsarequantitativelysimilarusingfourseriesofunanticipatedshocksidentifiedbyMertensandRavn(2012). Two seriesdatedeffectivedatesofthetaxchanges,onerawseriesandoneseriesfilteredusingthe“proxySVAR”,andtwoseriesusing thedatesthatthetaxchangesweresigned,onerawseriesandoneseriesfilteredusingthe“proxySVAR”. 22Findings are quantitatively similar using linear probability models and Granger causality tests as in Hall (1986) and Evans (1992). 27

Table 3 presents some of the main results of our study and shows the impact of various tax shocks on eachassetpricingchannel. PanelsAandBreflectestimatesbasedonthePost-andPre-Volckertimeperiods, respectively,whilePanelCshowsthedifferenceacrosstimeperiods. ForthePost-Volckertimeperiod,we find a one standard deviation increase in the tax rate (0.22 percent) is associated with a quarterly positive equity excess return of 0.07 to 0.47 percent.23 The low end of this range of values is in line with with our theoreticalestimateof0.052percentinTable1. Foreachtypeofshock,PanelAalsoshowsthatthetaxincreasehashadanegativeeffectoncashflow news. However,theeffectonrealinterestratenewsisalsonegative,alongwithfutureexcessreturns,making thediscountratenewschannellargerthanthecashflownewschannel. Again,therelativemagnitudesofthe cashflowandrealinterestratechannel(1.5timesgreaterthanthecashflowchannelonthelowend)arein linewithourtheoreticalestimateofarealinterestratechannelthatis1.25timesgreaterthanthecashflow channel. Importantly,regardlessofthetypeofshock,thepositiveeffectoftaxshocksonthecurrentexcessreturn isfoundtobesignificantat1percentlevels. Additionally,ourmostexogenousmeasureoftaxshocksinthe farrightcolumn,theSurpriseSVARshocks,alsofindsignificanceforexplainingthiseffectwithregardsto therealinterestratenewsandcashflownewschannels. Panel B focuses on the Pre-Volcker time period. Regardless of the shock, we find that tax increases haveasignificantnegativeeffectonreturnsatthe1percentlevel. Thechannelsthatdrivethisresultarenot uniform across each shock, as the signs change depending on whether or not the shocks are based on the SVAR. 5.1. AsymmetricResponsestoTaxShocks Table 4 addresses the relevant question of whether or not equity markets respond symmetrically to tax cuts versus tax increases. Similar to Table 3, there are three panels reflecting the Post and Pre-Volcker timeperiodsalongwiththeirDifference,butnowweisolatetheeffectscomingfromPositiveandNegative shocks. Panel A shows that for 3 out of the 4 shocks, the tax cuts are associated with greater effects on equity 23Equivalently,a1percenttaxincreaseisassociatedwitha0.33to2.32percenthighercurrentexcessreturn. 28

markets and drive most of the significance. As was the case in Table 3 when both positive and negative werecombined,thetaxcutsareleadingtogreatercashflownews,butdiscountratenewsisalsoincreasing. The discount rate news is counteracting the positive cash flow news to such an extent that tax cuts are associatedwithlowercurrentexcessreturns. Thisfindingthattaxcutshavelargereffectsonequitymarkets isconsistentwiththetheoreticalanalysisinTable1,whichwasbasedonanonlinearNewKeynesianmodel with downward nominal wage rigidities. Recall, the mechanism is that downward nominal wage rigidities prevent wages from falling as much when supply of labor increases. These relatively higher wages reduce labor demand, which reduces output, dividends, and cash flow news and leads to a more negative current excessreturn. Thismechanismisnotpertinenttoataxincrease,whichcanleadtoalowerlaborsupplyand higherwages,andthatexplainstheasymmetry. PanelBshowsthePre-Volckertimeperiod. SimilartoPanelA,thetaxcutsseemtodrivethesignificance, with3outofthe4shockssuggestingtaxcutshavegreatereffectsthantaxincreases. AndincontrasttoPanel A, tax cuts are now associated with positive effects on current excess returns. These findings are roughly consistentwiththetheoreticalanalysisinTable1. Wefinditinterestingthatbothourtheoreticalandempirical analysissuggestthattaxcutstendtohavegreatereffectsthantaxincreases,regardlessofthetimeperiod. 5.2. TaxResponseChannels Of interest is ensuring that equity returns respond to the personal income tax channel identified in our model,ratherthanchangesincorporateincometaxes. Weinvestigatethischannelinthefollowingsubsection. While our four exogenous tax shock series do not differentiate between these two channels, we appeal tothreealternativemeasuresidentifiedinthemacroeconomicsandfinanceliteraturetoidentifythepersonal income tax channel, specifically. The first two measures, Personal Tax Shocks and Personal Tax SVAR Shocks,areidentifiedthroughnarrativeaccountsoffederaltaxliabilitychangesbyMertensandRavn(2013). Asbefore,thePersonalTaxSVARShocksseriesusesthenarrativeshocksasinstrumentsforstructuralshocks to tax revenues through the “proxy SVAR” methodology of Mertens and Ravn (2014). The third measure isamarket-basedmeasureusedbyLeeper,Walker,andYang(2013)andKueng(2015). Thesepapershave the insight that, in the United States, municipal bonds are exempt from federal taxes, and the differential 29

taxtreatmentofmunicipalandtreasurybondscanhelpidentifynewsabouttaxchanges.24 Specificallyifa municipalbondandataxablebondhavethesametermtomaturity,callability,marketrisk,creditrisk,and soon,then YM T (cid:28) 1 t X! (cid:28)e (38) t D (cid:0) Y D k k t k t D where YM is the yield at time t on a municipal bond maturing at time T, Y is the yield at time t on a t t taxable bond maturing at time T, and (cid:28)e is the expected future tax rate at time k. Put differently, the one k minusthecurrentmunicipalbondspreadisaweightedaverageofdiscountedexpectedfuturetaxrates. Our empiricalimplementationusesyieldsfromtheBondBuyerGo20-BondMunicipalBondIndex,consisting of20generalobligationbondsthatmaturein20years,andtheyieldsonthe20-yeartreasurytoconstructof timeseriesof(cid:28). SimilarinspirittotheaugmentedstructuralVARinLeeper,Walker,andYang(2013),we usechangesin(cid:28) asinstrumentsforstructuralshockstotaxrevenuesthroughthe“proxySVAR”methodology ofMertensandRavn(2014).25 Table 5 shows similar results to those presented in previous tables. Specifically, the Post-Volcker time periodshowninPanelAsuggestsataxincreaseresultsinasignificantlypositiveeffectonthecurrentexcess return. Acrosseachshock,thediscountratenewsdominatesthecashflownewssothattheoveralleffectis positive. PanelB,thePre-Volckertimeperiod,showstheoppositeeffect. Forthistimeperiod,thediscount ratenews(sumofrealinterestratesandfutureexcessreturns)tendstobelessnegativeacrossthedifferent shocks,sothattheoveralleffectissignificantlynegative. 6. AdditionalTests Thissectionprovidesadditionalrobustnesstestsofourmainresults. Wefirsttestourhypotheseswithin theframeworkofSialm(2009). Next,wetestequityresponsestochangesintaxpolicyatahigherfrequency thanthequarterlyresultspresentedabove. Wealsopresentevidencethatourdocumentedresponsesacross monetarypolicyregimesarerobusttoeconomicexpansionandcontractions,aswellasrecentperiodswhen 24SeePoterba(1989);Fortune(1996);Park(1997);Kueng(2015)forevidencethatchangesinmunicipalbondspreadspredict changesfiscalpolicy. 25Again,resultsarequantitativelysimilarusingtherawseriesof(cid:129)(cid:28) inplaceoftheSVARseries. 30

monetarypolicy’srolemaybediminishedduetothezerolowerboundonnominalinterestrates. Finally,we estimateourmodelusingatimevaryingparameterVARframeworkandverifythatourresultsarerobustto amoregeneralspecificationofparameterchangesthroughtime. 6.1. Sialm(2009)Regressions Sialm(2009)investigates,bothinthetime-seriesandcrosssection,whetherchangesintaxeshavehad an impact on US equity prices. Over the period between 1913 and 2006, an effective tax yield series is constructed for the marginal investor that takes into account variation over time in federal income taxes, dividendtaxes,andshort-andlong-termcapitalgains. Thistaxyield,alongwithnumerouscontrols,isused inannualtimeseriesregressionstobackoutitsrelationshipwithequityvaluations. WereplicateSialm(2009)usingtheexactsamedataandmethodology. Toshowfurtherrobustnessfor theresults,Sialm(2009)splitsthesampleinhalfat1960andshowsthatbothsub-samplescontinuetoreflect anegativerelationshipbetweentaxyieldandequityvaluations. Weperformasimilartest,butinsteadsplit thedatain1980. Wesplitthetimeseriesat1980toreflectthechangeinthestanceofmonetarypolicy,asour previoustheoreticalandempiricalresultssuggestthereshouldbeachangeinsignfromnegativetopositive. Table 6 shows our replication results with multiple robustness checks for the Pre-Volcker and Post- Volckerperiods. TheserobustnesschecksareborrowedexactlyfromTable4,p.1370ofSialm(2009). The additionalcontrolvariablesaretheinterestrate,inflationrate,growthrate,qualityspread,termspread,and timetrend. AspointedoutinSialm(2009),eachofthesevariablesareimportanttocontrolforwhentryingto extracttheeffectsoftaxyieldonequityvaluations. ResultsarequalitativelysimilarwhenthePost-Volcker sampleisextendedto2015andthesetofregressorsisexpandedtoincludeZLB,abinaryvariableequalto one in years after 2008 and zero, otherwise, designed to capture periods in which the zero lower bound on nominalratesbinds. As can be seen from Table 6, the signs flip from negative to positive, and continue to remain highly significant. Using a completely independent series from our own empirical analysis above, this provides additionalevidenceforourstorythattherelationshipbetweenequityandtaxeschangedafter1980. 31

6.2. HighFrequencyResults Apotentialconcernofourresultsisthattheresponsetofiscalpolicyshocksmaybeconflatedwithother newsoveraquarterlyhorizon. Inotherwords, thefrequencyofouranalysismaynotbenarrowenoughto preciselyidentifytheresponseofequityreturnstonewsaboutfuturetaxpolicy. Asimilarveinofdoubtis thecritiqueofLeeper,Walker,andYang(2013)whopointouttheoreticaldifferencesbetweentheresponse tounanticipatedandanticipatedtaxshocksandhighlighttheimportanceofinvestorforesightininterpreting fiscal policy responses. This point is especially important when dealing with a forward-looking efficient stockmarket,whichshouldhavealreadyincorporatedinformationregardingexpectedchangesinfuturetax rates. WhiletheseriesconstructedinSection4.2relyonquarterlymacroeconomicseriestoimplementthe “proxySVAR”methodofMertensandRavn(2014),the(cid:28) measureofexpectedfuturetaxratesintroduced in Section 5.2 is available at a higher frequency for a portion of our sample period. In this subsection, we estimate the responses of current excess equity returns to daily and weekly changes in expected future tax rates. Duetotheforecastingrequirementsofournewsdecomposition,wedonotfurtherdecomposecurrent excessequityreturnsduetonoiseintheforecastsoffuturereturnsathigherfrequencies. Tothisend,weestimateregressionsofthefollowingform r (cid:12) (cid:129)(cid:28) (cid:13) Controls (39) ex;t t j t t ! C D (cid:2) C (cid:2) wherer isthecumulativereturnintheCRSPvalue-weightedindexinexcessoftherisk-freerate ex;t t j ! C over the event window t to t j, (cid:129)(cid:28) is the change in the expected future tax rate over t 1 to t, and t C (cid:0) Controls isavectorofadditionalcontrols. AsdefinedinSection5.2,(cid:129)(cid:28) isequaltooneminustheratio t t of the yield on municipal bond and the yield on a treasury bond of equal maturity. Our primary variable of interest in these regressions is (cid:12) which captures the response in excess equity returns to changes in (cid:28). Given the limited time-series availability of (cid:28) at a high frequency, this variable is a natural complement to theestimateofthecurrentexcessequityreturnresponsespresentedinPanelBofTable3. We begin with results of daily return regressions. While these regressions have the tightest event windowsforidentificationpurposes,adailymeasureof(cid:129)(cid:28) isavailableforarelativelyshorttimeperiod. For t theseregressions,weusetheBloombergBVALMuniBenchmarksforyieldsonmunicipalbonds. Thisyield curveisconstructedwithyieldsfromhighqualityUSmunicipalbondswithanaverageratingofAaafrom 32

Moody’s and S&P and is available daily from 2009Q1 to 2015Q4. We consider maturities of 5, 10, and 30 years for our analysis. This data is only available over a limited sample period during the Post-Volcker regime. We consider specifications both with and without (cid:129)Spread even though some of the concern of creditspreadsdrivingchangesin(cid:28) aremitigatedbyyieldsbasedonAaainstruments. PanelAofTable7presentstheresultsofthesedailyreturnregressionsoveronedaywindowsandone weekwindows. Beginningwiththe5yearmaturity,weseeasignificantpositiverelationshipbetweenexcess returnsandthechangeinourimpliedtaxmeasure. Theimpliedeffectonexcessreturnbecomeslargerwith eachmaturity,suggestingahighpersistence,whichisconsistentwithouralternativemeasuresoftaxshocks, whichareallpermanent. Wealsoinvestigatetheimpactofchangesin(cid:28) onweeklyexcessreturns. Fortheseregressions,weuse theBondBuyerGo20-BondMunicipalBondIndexforyieldsonmunicipalbonds. Thisindexconsistsof20 generalobligationbondsthatmaturein20years. Theaverageratingofthe20bondsisroughlyequivalentto Moody’sInvestorsService’sAa2ratingandStandard&Poor’sCorporations’sAArating. Giventhelower ratingofthesemunicipalbonds,changesincreditspreadsduringthefinancialcrisis,ratherthanchangesin expectedfuturetaxrates,mayhavedrivenchangesin(cid:28). Forthisreason,weestimatetheseweeklyregressions overtwosampleperiods: 1980Q2to2008Q2and1980Q2to2015Q4. Thefirstperiodavoidsthefinancial crisis and lines up well with the sample period we explore in our main results. The second period controls forchangesincreditspreads,(cid:129)Spread,explicitlybyincludingthechangeinthespreadbetweenBaa-rated andAaa-ratedcorporatebondyieldsinourregressions. Researchsuggeststhatrecessionaryandexpansionaryenvironmentsdrivetheinterpretationofmacroeconomicnewsasgoodorbadratherthanbeingprimarilydrivenbymonetarypolicyregime.26 Totestthis hypothesiswithinoursetting,weincludeNBER,abinaryvariableequaltooneiftheobservationoccursduringanNBER-datedrecessionandequaltozerootherwise,anditsinteractionwithourfiscalpolicyvariable. Panel B of Table 7 presents the results of these regressions over one week windows, one month windows, twomonthwindows,andonequarterwindows. Acrosseachhorizon,wefindasignificantpositiveeffectof theimpliedtaxchangeontheexcessreturn. Theimpliedcoefficientonthe“(0,12)EventWindow”(quarter 26SeeMcQueenandRoley(1993);Boyd,Hu,andJagannathan(2005);GoldbergandGrisse(2013);Law,Song,andYaron(2016) amongothers. 33

horizon)correspondstoa0.3438%increaseintheexcessreturnfora1%increaseinourtaxrate. Forcomparison, our previous empirical estimates based on the SVAR Surprise tax shocks in Table 3 was 0.071% foraonestandarddeviationincreaseinthetaxrate(0.22%). Insteadofassuminga1%changebuta0.22% change,theexpectedeffectbasedonthisregressionis0.075%,whichisveryclosetotheestimatesbasedon theSVARSurprisetaxshocks. Intheseregressions,wedonotfindthatinteractionbetween(cid:129)(cid:28) andNBER Indicatorarestatisticallysignificant. This panel also enables us to examine the impact of the zero lower bound on nominal interest rates on ourfindings,asinLaw,Song,andYaron(2016). ComparedtoSpecifications7and8PanelA,weseelittle change in the parameter estimates in Specifications 1 and 2 of Panel B after including data outside of the financialcrisiswhen thezero lowerbound (ZLB)in interestrates wasbinding. In otherwords, thelack of slackinadjustingnominalinterestratesseemstohavelittleimpactontheresponseofrealequityreturnsto changesinexpectedtaxratesandisinsufficienttochangethesignofourestimates.27 6.3. Cross-sectionalEvidence Our previous results do not rule out an omitted variable, such as a change in an aggregate risk factor, beingcorrelatedwithbothmarketreturnsandfiscalpolicyshocks. Inthissection,weprovidecross-sectional evidencethatourmeasureoffiscalpolicyshocksfromthelastsection,(cid:129)(cid:28),isnotmerelyaproxyforchanges inaggregaterisk. WereplacethemarketreturnsinTable7withlong-shortportfolioreturnsformedonfirmcharacteristics that proxy for a firm’s exposure to personal income tax shocks. By forming a long-short portfolio, these returns should, at least partially, account for contemporaneous changes in risk insomuch as we are able to construct portfolio legs with similar quantities of risk. To motivate these measures, we note that revisions in future discount rates should be the same across the long and short legs if they have similar exposure toaggregaterisk. Thus, thetimingandsizeoffutureafter-taxcashflowsshoulddeterminethedifferential returns. Sincetheimpactoftaxincreaseoncashflownewsisnegative,wewouldexpectfirmswithrelatively lowafter-taxcashflowstooutperformfirmswithrelativelyhighafter-taxcashflows. 27EvidencefromtheFRB-USmodel(unreported)issimilar.Theequityreturnresponsefallsroughly14bpsfrom39.09bpswithout theZLBbindingto25.25bpswiththeZLBbinding. Moreover,therealinterestratechannelremainsactiveinbothscenarioswith andwithouttheZLBbinding. 34

First,wesortstocksintoportfoliosbasedontercileofPayoutRatio,equaltototaldividends(CompuStat field DVT) divided by net income (CompuStat field NI), as of June in the previous year following Fama and French (1993). Panel A of Table 8 presents the parameter estimates from the regression of long-short portfolio returns on (cid:129)(cid:28). As predicted, firms with low payout ratios outperform those with high payout ratios when expected future tax rates increase. While the differenceat short maturities, that is when future tax increases are expected to be short lived, are modest and often indistinguishable from zero. At longer horizons,thedifferentialreturnisstatisticallyandeconomicallysignificant. Fora30-yearmaturityof(cid:28),low payoutratiostocksoutperformhighpayoutratiostocksbyroughly1%foraonestandarddeviationincrease inthetaxrate(0.22%)atboththeonedayandoneweekwindow. Next,welookatInstitutionalOwnershipasaproxyoftheproportionofequityheldbytaxableinvestors. Institutional ownership may be positively correlated with payout ratio as documented by Allen, Bernardo, andWelch(2000)withtheseeffectsworkinginoppositedirectionswithrespecttoafirm’sexposuretofiscal policy. Therefore,wecontrolforafirm’spayoutratiobyformingportfoliosbasedonsortingfirmsfirstinto terciles of payout ratio and then terciles of institutional ownership. Institutional Ownership is equal to the dollaramountofpositionsreportedin13Ffilingsdividedbythemarketcapitalizationofthefirm,asJunein thepreviousyear. Againwefindthatfirmswithhighinstitutionalownershiporarelativelylowproportion ofequityheldbytaxableinvestors(lowexposuretochangesinfuturetaxrates)tendtooutperfomfirmswith lowinstitutionalownership(highexposuretochangesinfuturetaxrates),especiallyatlongermaturitiesof (cid:28) andforfirmswithhigherdividendspaid(largerpayoutratios). Forexampleatamaturityof(cid:28) oftenyears, wefindthathighinstitutionalownershipfirmsoutperformlowinstitutionalownershipfirmsbyroughly62 basis points in the middle tercile of payout ratio and 98 basis points for high payout ratio firms at the one daywindowwhenfuturetaxratesincreasebyonestandarddeviation. Admittedly, our portfolios may differ in their quantities of risk. Panel B of Table 8 repeats the above analysisreplacingtherawreturnsofeachportfoliolegwiththeabnormalreturnfromtheFama-Frenchthree factormodel. Specifically,wedefineabnormalreturnsas e R R (cid:11) (cid:12) .R R / (cid:12)SMB R (cid:12)HML R (40) i;t D i;t (cid:0) f;t (cid:0)b i;t (cid:0)b i;t (cid:3) m;t (cid:0) f;t (cid:0)bi;t (cid:3) SMB;t (cid:0)bi;t (cid:3) HML;t where (cid:11) and (cid:12) are estimated using rolling regressions over the previous twelve months. Panel B of i;t i;t b b 35

8 reports the loadings from the regression of long-short abnormal returns on (cid:129)(cid:28). The results are largely consistentwiththoseinPanelA. 6.4. TimeVaryingParameterVAR Whileweprovideboththeoreticalandstatisticalevidencesupportingafocusonbroadmonetarypolicy regimes, our choice of sample periods may seem somewhat ad hoc. To this end, we estimate a Bayesian timevaryingparameterVAR(TVP-VAR)inthespiritofPrimiceri(2005). ThismodelallowsboththeVAR loadings in Equation 21 and the loadings on fiscal policy in Equation 26. While specifics pertaining to the estimated model and our results within the framework of this model are available in Section 3 of the Appendix,webrieflysummarizeourmaintakeawaysfromthisanalysisbelow. Formanyoftheestimates,the68percentcoverageintervalsarequitewideanddonotallowustoreject thenullofzeroresponse. HoweverforboththeAllShocksandSurpriseShocksseries,thecoverageinterval foroverallequityresponseinthePost-Volckerperiodispositivewiththerangecoveringthefixed-loading responses reported in Table 3. Results are similar for the difference in the overall response across the two monetary policy regimes as well. The overall equity response increases with the onset of the Post-Volcker regime, and the size of the estimated difference in the TVP-VAR is in line with those reported in the main resultsofthepaper. 7. Conclusion With the recent increase in attention on fiscal policy, we provide a critical theoretical and empirical analysis that suggests a key driver of tax effects on equity markets is the Federal Reserve. With a more aggressive stance of monetary policy to inflation and/or real activity since 1980, we find that tax cuts are associatedwithlowerexcessequityreturns,despiteourfindingsofpositiveeffectsoncashflownews. We conduct similar analysis for the Pre-1980 era and come to the opposite conclusion. With a less aggressive monetary policy, the cash flow news is larger than the discount rate news, and tax cuts are associatedwithhigherequityreturns. Theseempiricalfindingsareeasilymotivatedbyastandardtheoretical NewKeynesianmodelthatexhibitsashiftintheaggressivenessofmonetarypolicy. Our empirical analysis is based on a wide range of measures for tax shocks, including those based on RomerandRomer(2010),MertensandRavn(2012),municipalbondyielddata,andalsothetaxyielddata 36

from Sialm (2009). These data series allow us to provide inference at the weekly, monthly, quarterly, and annual frequencies. And each of these series comes to the same conclusion: tax cuts are associated with lowerequityreturnssince1980. Overall,somewillsuggesttherecentrun-upinthestockmarketseemstocontradictbothourtheoretical andempiricalanalysis. Wepositthatourfindingsremainvalidandthattherecentexperiencecouldbedueto afewissues: (1)thereareadditionalfactorsatplaysuchaschangesinregulation,governmentspending,and repatriation that may be important, (2) because of the proximity to the zero lower bound monetary policy may not be acting as aggressively as it did in previous post-1980 tightening cycles, and (3) investors are unusuallyoptimistic. 37

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Figure1: Post-vsPre-Volcker: CashFlowversusDiscountRateChannels This figure shows the excess equity returns across the Pre and Post Volcker regimes in response to a one standard deviation income tax rate increase (0.22%). The only difference across the two calibrations is the definition of the monetary policy rule. In the Pre-Volcker, (cid:11) 1:32, (cid:11) (cid:25) (cid:129)y D D 0:94, (cid:11) 0:91. In the Post-Volcker, (cid:11) 1:58, (cid:11) 2:21, (cid:11) 0:9. We isolate the effects R (cid:25) (cid:129)y R D D D D of each channel by showing what the excess return would be if only one channel was active at a time. The left panel, the Post-Volcker, shows the excess return would be negative if the excess return was only a function of cash flow news (dashed red line). Instead, the discount rate channel dominates and the overall effect is positive. The right panel, the Pre-Volcker, shows the excess returnwouldbepositiveiftheexcessreturnwasonlyafunctionofdiscountratenews(dashedblue line). Instead,thecashflowchanneldominatesandtheoveralleffectisnegative. Thediscountrate channel dominates for the Post-Volcker because of the greater response to output growth, which generatesgreaterchangesinrealinterestratesanddampensthedeclineincashflownews. Post−Volcker: Excess Equity Return Pre−Volcker: Excess Equity Return Percent (deviation from steady state) Percent (deviation from steady state) 0.4 0.2 0.2 Discount Rate Only Discount Rate Only 0 Cash Flow Only 0 Cash Flow Only Both Both −0.2 −0.2 −0.4 5 10 15 20 0 5 10 15 20 25 Quarters (t) Quarters (t) Dividends Output Percent (deviation from steady state) 0 0.1 −0.1 0.05 −0.2 0 −0.3 −0.05 −0.4 −0.1 0 5 10 15 20 25 0 5 10 15 20 25 Quarters (t) Quarters (t) Real Interest Rate Consumption x 10−3 Percent (deviation from steady state) Percent (deviation from steady state) 0 0 −0.02 −2 47 −0.04 −4 −0.06 −6 −0.08 0 5 10 15 20 25 0 5 10 15 20 25 Quarters (t) Quarters (t)

Figure2: PostvsPre-VolckervsRBCResponsestoIncreaseinIncomeTaxRate This figure displays economic variables across the Pre and Post Volcker regimes and the RBC model, in response to a one standard deviation income tax rate increase (0.22%). The only difference across the two calibrations is the definition of the monetary policy rule. In the Pre-Volcker, (cid:11) 1:32,(cid:11) 0:94,(cid:11) 0:91. InthePost-Volcker,(cid:11) 1:58,(cid:11) 2:21,(cid:11) 0:9. The (cid:25) (cid:129)y R (cid:25) (cid:129)y R D D D D D D RBC framework eliminates the monetary policy rule and removes nominal rigidities. This figure showstheimportanceofincorporatingaroleformonetarypolicyandnominalrigidities. Incontrast to the Pre-Volcker (dashed red line) and RBC (solid black line) settings, the Post-Volcker (dashed blueline)monetarypolicyofputtinggreaterweightonoutputgrowthleadstoalargereffectonreal interest rate news and a smaller decline in dividends, so that the discount rate channel dominates andthecurrentexcessreturnforPost-Volckerispositive. Excess Equity Return Investment Percent (deviation from steady state) Percent (deviation from steady state) 0.1 0.5 0.05 NK: Post−Volcker, 0 0 NK: Pre−Volcker RBC Model −0.5 −0.05 −0.1 −1 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters (t) Quarters (t) Dividends Output Percent (deviation from steady state) Percent (deviation from steady state) 1 0.2 0 0 −0.2 −1 −0.4 −2 −0.6 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters (t) Quarters (t) Real Interest Rate Consumption Percent (deviation from steady state) Percent (deviation from steady state) 0.01 0 −0.1 0 −0.2 −0.01 −0.3 −0.02 −0.4 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters (t) Quarters (t) 48

Figure3: AsymmetricResponsesDuetoDownwardNominalWageRigidities This figure shows the responses in the Post-Volcker regime to a tax cut (dashed black line), a tax increase (dashed blue line), and the difference (multiplied by 10 for ease of exposition) in responses to the tax cut and tax increase (solid red line). The left panel, which exhibits downward nominal wage rigidities, shows that in response to an income tax cut, labor supply rises with the increasedincentiveto workcausing wagestodecline. However,wagesdonot fallas muchinthe presenceof downwardnominal wage rigidities so that labor demand doesn’t rise as much. With not as much labor demand, output along with dividends increase lesssothatcashflownewsislesspositiveandtheoveralleffectisalargernegativeeffectonequityreturnswhencomparedtothe positive effects coming from tax increases. The right panel shows the case with no downward nominal wage rigidities, and the difference(solidredline)isnearlyzeroacrosseachresponse. Thisdemonstratesthepotentialimportanceofincludingdownward nominalwagerigiditiestogeneratetheasymmetricresponses. With Downward Nominal Wage Rigidities No Downward Nominal Wage Rigidities Excess Equity Return Output Excess Equity Return Output Percent (deviation from steady state) Percent (deviation from steady state) Percent (deviation from steady state) Percent (deviation from steady state) 0.1 0.2 0.1 0.2 0.05 0.1 0.05 0.1 Tax Inc. Tax Inc. 0 Tax Cut 0 0 Tax Cut 0 Difference*10 Difference*10 −0.05 −0.1 −0.05 −0.1 −0.1 −0.2 −0.1 −0.2 0 2 4 6 8 10 0 10 20 30 40 50 0 2 4 6 8 10 0 10 20 30 40 50 Quarters (t) Quarters (t) Quarters (t) Quarters (t) W Investment W Investment Percent (deviation from steady state) Percent (deviation from steady state) Percent (deviation from steady state) Percent (deviation from steady state) 0.04 0.4 0.04 0.4 0.02 0.2 0.02 0.2 0 0 0 0 −0.02 −0.2 −0.02 −0.2 −0.04 −0.4 −0.04 −0.4 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 Quarters (t) Quarters (t) Quarters (t) Quarters (t) Labor (H) Dividends Labor (H) Dividends Percent (deviation from steady state) Percent (deviation from steady state) Percent (deviation from steady state) Percent (deviation from steady state) 0.2 0.4 0.2 0.4 0.1 0.2 0.1 0.2 0 0 0 0 −0.1 −0.2 −0.1 −0.2 −0.2 −0.4 −0.2 −0.4 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 Quarters (t) Quarters (t) Quarters (t) Quarters (t) 49

Table1: Theimpactofexogenousfiscalpolicyshocksonsimulatedreturns This table reports the impact of positive and negative exogenous tax shocks on the current excess equityreturn,andthediscountedsumsoffutureexcessequityreturns,currentandfuturerealinterest rates, and current and future cash flows. Data are the solutions to the DSGE model described inSection3. DatafromthePre-VolckerandPost-VolckercalibrationsarereportedinPanelAand B,respectively. Positive Negative Difference PanelA:Post-Volcker CurrentExcessReturn 0:0515 0:0528 0:0013 (cid:0) FutureExcessReturn 0:0030 0:0034 0:0005 (cid:0) RealInterestRateNews 0:2588 0:2574 0:0014 (cid:0) (cid:0) CashFlowNews 0:2103 0:2080 0:0023 (cid:0) (cid:0) PanelB:Pre-Volcker CurrentExcessReturn 0:0502 0:0494 0:0008 (cid:0) (cid:0) FutureExcessReturn 0:0513 0:0523 0:0011 (cid:0) RealInterestRateNews 0:2272 0:2258 0:0014 (cid:0) (cid:0) CashFlowNews 0:3287 0:3276 0:0011 (cid:0) (cid:0) PanelC:RealBusinessCycle(RBC)Model CurrentExcessReturn 0:0555 0:0550 0:0005 (cid:0) (cid:0) FutureExcessReturn 0:0118 0:0119 0:0000 (cid:0) RealInterestRateNews 0:1882 0:1880 0:0002 (cid:0) (cid:0) CashFlowNews 0:2556 0:2549 0:0007 (cid:0) (cid:0) 50

Table2: Testsforexogeneityoftaxshocks The table reports the results for tests of exogeneity of the tax shocks using ordered probit regressions. The values reported are p-values of likelihood ratio tests of the hypothesis that 1 lag and 1 to 4 lags of the state variables have no predictive power for the timing of tax changes. The state variables are the excess return, real interest rate, change in the 3-month T-bill rate, the difference inyieldsonthe10-yearT-Noteand3-monthT-Bill,thelogdividendpriceratio,andthedifference betweenthe3-monthT-Billandits12-monthmovingaverage. AlltestsarespecifiedasH (cid:12) 0 0 W D against H (cid:12) 0 where (cid:12) is the coefficient vector of lagged observables. Tax shocks are de- 1 W ⁄ scribedinSection4.2. Surprise SVAR Surprise AllShocks SVAR Shocks Shocks Shocks PanelA:1980Q3-2007Q4 Lag1 0:5747 0:7077 0:1414 0:7596 Lags1-4 0:0261 0:2716 0:0349 0:8943 PanelB:1947Q1-1980Q2 Lag1 0:0129 0:5696 0:7008 0:6041 Lags1-4 0:0925 0:3762 0:5690 0:4422 PanelC:1947Q1-2007Q4 Lag1 0:0574 0:7391 0:4682 0:7913 Lags1-4 0:0125 0:2782 0:2281 0:7819 51

Table3: Theimpactofexogenoustaxshocksonequityreturns This table reports the impact of exogenous tax shocks on the current excess equity return, and the discounted sums of future excess equity returns, current and future real interest rates, and current andfuturedividends(cashflows). Thesix-variableVAR(1)usedtoconstructexcessequityreturn and real interest rate forecasts is estimated over the sample indicated in the column headings. The VARstatevariablesaredefinedinthetext. TaxshocksaredescribedinSection4.2. Standarderrors arecalculatedbythebootstrapalgorithmdiscussedinSection4. ; ;and denotesignificance (cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) atthe10percent,5percent,and1percentlevels,respectively. Surprise Surprise AllShocks SVARShocks Shocks SVARShocks PanelA:1980Q3-2007Q4 CurrentExcessReturn 0:4662 0:1200 0:0998 0:0710 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) FutureExcessReturn 0:2250 0:0772 0:0712 0:0328 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:5520 0:0790 0:0800 0:0885 (cid:3)(cid:3)(cid:3) (cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:3108 0:0362 0:0515 0:0503 (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) PanelB:1947Q1-1980Q2 CurrentExcessReturn 0:2072 0:0563 0:0823 0:0470 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) FutureExcessReturn 0:2910 0:0968 0:1375 0:0890 RealInterestRateNews 0:1005 0:0843 0:0485 0:0645 (cid:0) (cid:0) CashFlowNews 0:1842 0:0440 0:1037 0:0227 (cid:0) (cid:0) PanelC:Difference CurrentExcessReturn 0:6735 0:1762 0:1820 0:1180 (cid:3)(cid:3) (cid:3) (cid:0) (cid:0) (cid:0) (cid:0) FutureExcessReturn 0:5162 0:1740 0:2087 0:1217 (cid:3) (cid:3) RealInterestRateNews 0:6525 0:0053 0:1283 0:0240 (cid:3)(cid:3) (cid:0) CashFlowNews 0:4950 0:0050 0:1552 0:0278 (cid:0) 52

Table4: Asymmetriesintheimpactofexogenoustaxshocksonequityreturns Thistablereportstheimpactofpositiveandnegativeexogenoustaxshocksonthecurrentexcessequityreturn,andthediscounted sums of future excess equity returns, current and future real interest rates, and current and future dividends (cash flows). The six-variable VAR(1) used to construct excess equity return and real interest rate forecasts is estimated over the sample indicated in the column headings. The VAR state variables are defined in the text. Tax shocks are described in Section 4.2. Responses for negative tax shocks are multiplied by negative one to ease exposition. Standard errors are calculated by the bootstrap algorithm discussedinSection4. ; ;and denotesignificanceatthe10percent,5percent,and1percentlevels,respectively. (cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) AllShocks SVARShocks SurpriseShocks SurpriseSVARShocks Positive Negative Positive Negative Positive Negative Positive Negative PanelA:1980Q3-2007Q4 CurrentExcessReturns 0:1225 0:6255 0:0922 0:1427 0:1913 0:0395 0:0272 0:1163 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) FutureExcessReturns 0:0495 0:3065 0:0605 0:0910 0:0938 0:0565 0:0152 0:0510 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2475 0:6930 0:0643 0:0910 0:2707 0:0457 0:0437 0:1348 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1742 0:3740 0:0328 0:0393 0:1732 0:0290 0:0318 0:0695 (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelB:1947Q1-1980Q2 CurrentExcessReturns 0:1000 0:2315 0:0420 0:0720 0:0077 0:1143 0:0060 0:0855 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) FutureExcessReturns 0:0085 0:3147 0:0823 0:1125 0:0815 0:1618 0:0355 0:1390 (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:3827 0:0783 0:1055 0:0612 0:0182 0:0770 0:0810 0:0493 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:4740 0:1613 0:0653 0:0205 0:0555 0:1247 0:0515 0:0043 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelC:Difference CurrentExcessReturns 0:0225 0:8572 0:1343 0:2147 0:1993 0:1537 0:0333 0:2015 (cid:3)(cid:3) (cid:3) (cid:3) (cid:0) (cid:0) (cid:0) FutureExcessReturns 0:0408 0:6212 0:1427 0:2035 0:1752 0:2182 0:0508 0:1900 (cid:3) (cid:3) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:6302 0:7712 0:0410 0:0300 0:2527 0:0312 0:0372 0:0855 (cid:3)(cid:3) (cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:6485 0:5353 0:0325 0:0187 0:2288 0:0958 0:0198 0:0740 (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 53

Table5: Personalincometaxchangeandequityreturns This table reports the impact of personal income tax changes on the current excess equity return, and the discounted sums of future excess equity returns, current and future real interest rates, and currentandfuturedividends(cashflows). Thesix-variableVAR(1)usedtoconstructexcessequity returnandrealinterestrateforecastsisestimatedoverthesampleindicatedinthecolumnheadings. TheVARstatevariablesaredefinedinthetext. Ourpersonalincometaxshockseriesaredescribed in Section 5.2. The column All Shocks from Table 3 is included for reference. Standard errors are calculatedbythe bootstrapalgorithmdiscussed inSection 4. ; ;and denotesignificanceat (cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) the10percent,5percent,and1percentlevels,respectively. PersonalTax PersonalTax (cid:28) SVAR AllShocks Shocks SVARShocks Shocks PanelA:1980Q3-2007Q4 CurrentExcessReturn 0:4662 0:2243 0:0762 0:0473 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) FutureExcessReturn 0:2250 0:1938 0:0365 0:0425 (cid:3)(cid:3) (cid:3) (cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:5520 0:1903 0:0907 0:0073 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) CashFlowNews 0:3108 0:1598 0:0508 0:0023 (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) PanelB:1947Q1-1980Q2 CurrentExcessReturn 0:2072 0:1715 0:0563 0:0480 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) FutureExcessReturn 0:2910 0:2457 0:0803 0:058 (cid:3)(cid:3) RealInterestRateNews 0:1005 0:0565 0:0925 0:0873 (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1842 0:0180 0:0685 0:0775 (cid:3) (cid:0) (cid:0) PanelC:Difference CurrentExcessReturn 0:6735 0:3957 0:1323 0:0955 (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) FutureExcessReturn 0:5162 0:4395 0:1165 0:1005 (cid:3) (cid:3) RealInterestRateNews 0:6525 0:1340 0:0020 0:0800 (cid:3)(cid:3) (cid:0) (cid:0) CashFlowNews 0:4950 0:1777 0:0177 0:0750 (cid:0) (cid:0) 54

Table6: Taxesandvaluationratios ThistablereplicatestheregressionresultsofSialm(2009)splittingthesampleonmonetarypolicy regimes. The dependent variable is equity Q and is obtained from the Federal Reserve Board’s FlowofFundsAccountsastheratiobetweenthemarketvalueofequitiesoutstandingofnonfinancialcorporatebusiness(FL103164003)andthenetworthatmarketvalueofnonfarmnonfinancial corporate business (FL102090005). Tax yield is defined as in Sialm (2009) as the sum of the dividend tax rate times the dividend yield, the short-term capital gains tax rate times the short-term capitalgainsyield,andthelong-termcapitalgainstaxratetimesthelong-termcapitalgainsyield. Growth rate is the per capita real growth rate of aggregate output. Quality spread is the difference in yields between Baa and Aaa bonds. Term spread is the difference between yields in Aaa bonds andtheone-yearinterestrateoncommercialpaperbyShiller. Dataareannual. Standarderrorsare Newey-Westadjustedusingafour-yearlag. ; ;and denotesignificanceatthe10percent,5 (cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) percent,and1percentlevels,respectively. Pre-Volcker Post-Volcker (1) (2) (3) (4) (5) (6) Taxyield 21:9137 24:8777 26:1699 94:8644 73:4594 83:8285 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (-6.93) (-9.08) (-7.33) (3.21) (2.76) (3.10) Interestrate 2:2804 2:3816 6:9016 0:0542 3:6974 10:232 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (-1.48) (-2.06) (-4.26) (-0.02) (1.50) (-1.67) Inflationrate 1:0218 1:2312 0:9899 7:9740 5:5663 8:0374 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (-2.46) (-3.64) (-2.33) (-2.30) (-2.99) (-3.33) Growthrate 0:7142 0:5901 0:8446 0:1992 2:4128 0:5071 (cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (1.89) (2.42) (2.59) (-0.09) (-1.20) (0.21) Qualityspread 13:2198 58:6862 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (-4.01) (-3.98) Termspread 9:9800 14:7938 (cid:3)(cid:3) (cid:0) (cid:0) (-2.45) (-1.51) Timetrend 0:0062 0:0037 0:0084 0:0738 0:0550 0:0422 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (2.58) (1.66) (4.96) (3.00) (2.82) (1.48) Constant 0:8332 1:1546 1:0888 5:7105 3:5845 2:133 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3) (cid:0) (cid:0) (cid:0) (8.36) (9.07) (7.45) (-2.60) (-1.91) (-0.73) Timeperiod 1919-1979 1919-1979 1919-1979 1980-2006 1980-2006 1980-2006 N 60 60 60 27 27 27 R2 0:4291 0:5474 0:5346 0:5702 0:7251 0:6150 55

Table7: Excessreturnsaroundchangesinexpectedfuturetaxrates This table reports parameter estimates from the regression of excess returns on changes in expected future tax rates ((cid:28)) and other controls. ThedependentvariableineachregressionistheCRSPvalue-weightedindexreturninexcessoftherisk-freerateoverthe window specified in the column header. (cid:129)(cid:28) is the change in the expected future tax rate equal to one minus the ratio of the yield on municipal bond and the yield on a treasury bond of equal maturity. NBER is a binary variable equal to one if the observation occurs during an NBER-dated recession and equal to zero otherwise. Panel A reports parameter estimates for regressions using daily excess returns. For this panel, the sample period is 2009Q1 to 2015Q4 (n 1743). (cid:28) is constructed using the Bloomberg D BVAL Muni Benchmark with maturity reported in the row (cid:28) Maturity. Panel B reports parameter estimates for regressions using weekly excess returns. For these panels, the sample period for odd columns is 1980Q2 to 2008Q2 (n 1455), while the sample D period for even columns is 1980Q2 to 2015Q4 (n 1851). (cid:28) is constructed using the Bond Buyer Go 20-Bond Municipal Bond D Index, which has maturity of 20 years. Standard errors are Newey-West adjusted with lag length eight. ; ; and denote (cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) significanceatthe10percent,5percent,and1percentlevels,respectively. PanelA:DailyEventWindows (0,1)EventWindow (0,5)EventWindow (1) (2) (3) (4) (5) (6) (7) (8) Intercept 0:0005 0:0005 0:0005 0:0005 0:0026 0:0026 0:0026 0:0026 (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:129)(cid:28) 0:0208 0:1000 0:1702 0:2253 0:0486 0:0989 0:1652 0:2225 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:28) Maturity 2yr 5yr 10yr 30yr 2yr 5yr 10yr 30yr PanelB:WeeklyEventWindowswithNBERIndicators (0,1)EventWindow (0,4)EventWindow (0,8)EventWindow (0,12)EventWindow (1) (2) (3) (4) (5) (6) (7) (8) Intercept 0:0013 0:0016 0:0049 0:0061 0:0093 0:0114 0:0132 0:0164 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) NBER 0:0007 0:0030 0:0002 0:0094 0:0017 0:0137 0:0074 0:0147 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:129)(cid:28) 0:2252 0:1638 0:4689 0:2404 0:6804 0:3023 0:6239 0:3438 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:129)(cid:28) NBER 0:0743 0:2777 0:0283 0:0433 0:1536 0:1312 0:0940 0:0668 (cid:2) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 56

Table8: Long-shortportfolioreturnsaroundchangesinexpectedfuturetaxrates Thistablereportsparameterestimatesfromtheregressionofportfolioreturnsonchangesinexpectedfuturetaxrates((cid:28))andother controls. (cid:129)(cid:28) isthechangeintheexpectedfuturetaxrateequaltooneminustheratiooftheyieldonmunicipalbondandtheyield onatreasurybondofequalmaturity. (cid:28) isconstructedusingtheBloombergBVALMuniBenchmarkwithmaturityreportedinthe row (cid:28) Maturity. The sample period is 2009Q1 to 2015Q4 (n 1743). The dependent variable in Panel A is the value-weighted D return of the long portfolio in excess of the value-weighted return of the short portfolio. HiPR, MidPR, and LoPR denote the high,medium,andlowtercileofPayoutRatio,respectively. HiIO,MidIO,andLoIO denotethehigh,medium,andlowtercile of Institutional Ownership, respectively. The dependent variable in Panel B is the abnormal portion of the value-weighted return of the long portfolio with respect to the Fama-French three factor model in excess of the abnormal return for the short portfolio. StandarderrorsareNewey-Westadjustedwithlaglengtheight. ; ;and denotesignificanceatthe10percent,5percent,and (cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) 1percentlevels,respectively. (0,1)EventWindow (0,5)EventWindow (1) (2) (3) (4) (5) (6) (7) (8) PanelA:RawReturns RLoPR RHiPR 0:0046 0:0143 0:0268 0:0498 0:0001 0:0139 0:0240 0:0496 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) RLoPR HiIO RLoPR LoIO 0:0018 0:0006 0:0141 0:0020 0:0252 0:0298 0:0138 0:0186 (cid:2) (cid:2) (cid:0) (cid:0) (cid:0) RMidPR HiIO RMidPR LoIO 0:0014 0:0257 0:0283 0:0397 0:0076 0:0163 0:0286 0:0337 (cid:2) (cid:2) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3) (cid:0) RHiPR HiIO RHiPR LoIO 0:0012 0:0171 0:0445 0:0538 0:0108 0:0210 0:0407 0:0872 (cid:2) (cid:2) (cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) PanelB:AbnormalReturns eLoPR eHiPR 0:0079 0:0019 0:0015 0:0129 0:0122 0:0003 0:0017 0:0211 (cid:3) (cid:3) (cid:0) (cid:0) (cid:0) (cid:0) eLoPR HiIO eLoPR LoIO 0:0014 0:0058 0:0147 0:0041 0:0201 0:0228 0:0124 0:0161 (cid:2) (cid:2) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) eMidPR HiIO eMidPR LoIO 0:0041 0:0015 0:0058 0:0054 0:0125 0:0099 0:0039 0:0067 (cid:2) (cid:2) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) eHiPR HiIO eHiPR LoIO 0:0055 0:0153 0:0258 0:0295 0:0031 0:0215 0:0308 0:0612 (cid:2) (cid:2) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:28) Maturity 2yr 5yr 10yr 30yr 2yr 5yr 10yr 30yr 57

Appendix for Taxes and the Fed 1. AlternativeParameterValues 1.1. MonetaryPolicyRuleParameters The monetary policy rules we consider involve three parameters: the inertia coefficient, the inflation coefficient,andtheoutputgrowthcoefficient. Withthebenchmarkvaluesof0.9,1.58,and2.2,respectively, we show that the inertia coefficient (weight on previous period’s interest rate) does not meaningfully alter the results for values between 0 and 0.95. Intuitively, the greater the inertia coefficient, the less monetary policyrespondsintheshortrunandthemoreitinfluencesthelong-run. ThisisconsistentwithPanelAof TableA.1whichshowsthatrealinterestratesfallmoreasthecoefficientrises,andthecurrentexcessreturn becomesmorepositive. Theinflationcoefficientalsoexhibitsamonotonicrelationshipwithrealinterestratesandthecashflow newschannel. Wefindthatforahigherinflationcoefficient,inflationriseslessandisstabilizedtoagreater extent. As a result, real interest rates do not decline as much in the medium-long term as the inflation coefficientrises. Incontrast,anincreaseintheoutputgrowthcoefficienttendstostabilizeoutputwhilegeneratinggreater decreasesintherealinterestrates. Increasesinthecoefficientsoninflationandoutputgrowthhaveopposite effectsbecauseinflationrises(highertaxesincreasecostsofproduction)andoutputdeclinesinresponseto thetaxincrease. Therefore,increasingtheoutputgrowthcoefficientgenerateshigherinflationandlowerreal interestrates,whileincreasingtheinflationcoefficientgenerateslowerinflationandsmallerdeclinesinreal interestrates. WhiletheeffectsofvariousoutputgrowthcoefficientsarerelativelystableatthePost-Volcker benchmark calibration, when moving to the benchmark values for the Pre-Volcker calibration, we see that theresultsdodependontheoutputgrowthcoefficient. Whentheinertiacoefficientandinflationcoefficientare0.91and1.32,respectively,weobserveachange insignforthecurrentexcessreturnastheoutputgrowthcoefficientincreases. Asexplainedintheprevious section,thehigheroutputgrowthcoefficientgeneratesgreaterdeclinesinrealinterestratesasmonetarypolicytriestostabilizethedeclineinoutput. Inaddition,asmonetarypolicystabilizesoutputtoagreaterextent, dividendsdonotdeclineasmuchsothatthediscountchannelisrelativelylargerandexcessreturnsincrease. While the relationship between output growth and the asset pricing channels for the Post-Volcker framework is not strictly monotonic, as the output coefficient rises from 1.2 to 2.4, the results are quantitatively consistent. 1.2. NewKeynesianParameters The two main parameters of the New Keynesian block are the price adjustment costs and elasticity of substitutionacrossgoods,whichcapturesthedegreeofmonopolisticcompetition. InPanelBofTableA.1, wecanseethatasthepriceadjustmentcostsincrease,realinterestratesdonotdeclineasmuchanddividends 1

fallmore.1 Bothoftheseeffectscombinetomakethecurrentexcessreturnlesspositiveinresponsetothetax increase. Theintuitionforthesmallerdeclineinrealinterestratesisthataspriceadjustmentcostsbecome larger,theaggregatesupplycurvebecomesflattersothatthetaxincreaseinfluencestheeconomyless. The dividends(D Y w L I )fallmorebecauseinvestmentdoesnotfallasmuchinthemedium-long t t t t t D (cid:0) (cid:0) run(theflattersupplycurvereducestheeffectsofthetaxincreaseoninvestmentsoinvestmentisrelatively higheranddividendsarerelativelylower). Withregardstomarketpower,astheelasticityofsubstitutionacrossgoodsincreases,themarketpower declines. Whilethisdoesnotlargelyinfluencetherealinterestratechannel,itdoesinfluencethedividends. Thedividendsareafunctionofthefirm’sprofitsandasmarketpowerdecreases,profitsbecomesmallerand lessvolatile. Withdividendsdeclininglessoverthemedium-longrun,currentexcessreturnsbecomemore positiveasthemarketpowerdecreases. 1.3. UtilityParameters Thesubjectivediscountfactorcapturesthepatienceofhouseholdsandfirmsandthedegreetowhichthey areforwardlooking. Withalowersubjectivediscountfactor,householdsarelesspatientandrequiregreater interestratesformarketstoclear. Thisleadstolargersteadystateinterestratesandlargerfluctuations. As a result, real interest rates decline more in response to the tax increase and this can lead to a more positive currentexcessreturn.2 The intertemporal elasticity of substitution (IES) captures how sensitive households are to interest rate fluctuations. The greater the IES, the less interest rates need to fluctuate in order for markets to clear. As showninPanelCofTableA.1,valuesbetween0.15to0.25leadtoresultsthatarequalitativelyconsistent. 3 AstheIESdeclinestozero,thediscountratechannelbecomeslargerandthecurrentexcessreturnrises. Riskaversioncapturestheaversionofhouseholdstochangesinconsumptionacrossstates. Higherrisk aversionincreasestheprecautionarysavingsmotiveandtendstoreducesteadystaterealinterestrates. The overall effects of higher risk aversion in the model have little influence over the channels and largely does notaltertheexistingresults. Theleisureshareparameterintheconsumption-leisurebundlepinsdownthesteadystateleveloflabor. The higher the value, the less households work and the more inelastic the labor supply. As labor becomes moreinelastic,itdeclineslessinresponsetothetaxincrease,andthisresultsinmorestableinvestmentand output responses. With greater stability in investment and output, dividends (D Y w L t I ) t t t t D (cid:0) (cid:0) (cid:0) donotdeclineasmuchaslaborbecomeslesselastic. Withasmallerdeclineincashflownews,thecurrent excessreturnbecomesmorepositiveaslaborbecomeslesselastic. 1Beyondthepriceadjustmentcostsvalueof35,thereisamonotonicrelationship. 2Thismonotonicallyholdsforvaluesdeclininguntil(cid:12) 0:994. Forvalueslessthan0.994forthesubjectivediscountfactor, D therealinterestratesdonotdeclineasmuchandresponsesleveloff,asshownbythechannelsfor0.99inTableA.1. 3Intertemporalelasticityofsubstitutionvaluesaround0.2areconsistentwithasubstantialliteratureinmacroeconomics, see forexampleChari, Kehoe, andMcGrattan(2002);HouseandShapiro(2006);Piazzesi, Schneider,andTuzel(2007), aswellas empiricalworkbyBarsky,Juster,Kimball,andShapiro(1997);CampbellandMankiw(1989);Hall(1988). 2

1.4. ProductionParameters The capital share of income and depreciation rate parameters pin down the amount of capital. With a highershareofcapitalorlowerdepreciationrate,investmentdoesnotriseasmuchinitially(investmentrises initiallyduetothenegativewealtheffect)intheshort-mediumtermascapitalmakesupalargerpercentage ofGDP and becomesless volatile. Withinvestment notrising as much, dividendsdo not decline asmuch, sothatthecurrentexcessreturnbecomesmorepositiveasthecapitalshareofincomerisesordepreciation ratedeclines. 1.5. TaxRateParameters Thepersistenceofthetaxrateshockdetermineshowpermanentthetaxratechangeis. Wefindthatfor awiderangeofpersistenceparameters,therelativemagnitudesofthecashflowanddiscountratechannels are unaltered. The discount rate channel is almost always larger and this implies positive current excess returns in response to the tax increase. The cash flow channel dominates only when the persistence value is less than 0.5. However, at such a low persistence, the tax shock is very short-lived and has almost no effectoncurrentexcessreturns. Thepredictedeffectoncurrentexcessreturnsatapersistencevalueof0.5is minus4one-hundredthsofabasispoint. Giventhatthepriceofequitytakesintoaccountallfutureexpected discountedcashflows,itisintuitivethatatemporarytaxshockwouldhavealmostnoeffect. Different levels of the marginal tax rate have also been tested, and the results in Panel D of Table A.1 areshowntoberobust. 1.6. WageParameters Increasing the wage adjustment costs makes wages stickier. By making wages less volatile, both labor and investment do not rise as much initially. With a smaller rise in investment, dividends do not decline as much initially compared to the scenario with more flexible wages. After the initial period, both labor and investment begin to decline due to the tax increase but again, do not decline as quickly due to the stickier wages. This keeps output relatively higher in the medium-long term for the sticky wage scenario, and dividends do not decline as much in the medium-long term. Both the short-run and medium-long run effectssuggestthegreaterthewageadjustmentcosts,thelessdividendsdecline. Real interest rates also decline by less due to the higher marginal product of capital coming from the smallerdeclineinlabor withstickywages. However, inthemedium-long run, therelatively highercapital stockmechanicallyentailsrelativelylowerrealinterestrates,whichslightlyoffsetsthepreviouseffect. Theoveralleffectofthecashflowanddiscountratechannelsisthatthecashflowchanneldeclinesby less,andthecurrentexcessreturnbecomesmorepositivewithgreaterwageadjustmentcosts. Theasymmetricwagecostparameteraltersthequadratic-costfunctionsothatdeclineshavelargercosts, andincreaseshavesmallercosts. Asaresult,thehighertheasymmetryparameter,thelowerthestickiness of wage increases. This is confirmed by the table, which shows that the higher asymmetry parameter has the opposite effect of the wage adjustment costs parameter (because wage increases are less sticky). The dividendsbecomemorenegative,andtheoveralleffectoncurrentexcessreturnsbecomeslesspositive. 3

The elasticity of substitution across labor inputs pins down the market power of households in labor supply. The table shows that as market power increases, the cash flow news declines more. This is consistentwithmorevolatileresponsesoflaborandinvestment. Themoremarketpower, themoreelasticthe household’slaborsupplysothatinvestmentandlaborrisemoreinitially,resultinginagreaterinitialdecline individends. Overthemedium-longrun,labordeclinestoagreaterextentwithmoremarketpower,sothat outputdeclinesmoreasdodividends. Theoveralleffectisgreaterdeclinesindividendsandalesspositive responseofcurrentexcessreturnsasthemarketpowerofworkersrises. 1.7. TimingoftheTaxShock Wealsochangethetimingofthetaxshocktocapturethepotentialeffectsofnewsoffuturetaxchangesin PanelFofTableA.1. Specifically,we“announce”taxincreasestwoandfourquartersbeforetheexogenous shock to taxes occurs. While the timing of the shock will influence real dynamics such as investment and output, the overall effect on the current return is modest. With respect to a tax increase, the current excess return becomes slightly less positive with further lags in implementation due to the sum of real interest rates not falling as much. In response to an expected tax increase, real interest rates rise initially because investmentandlaborrisetoagreaterextent, andthenrealinterestratesdecline alongwithinvestmentand laboroncethetaxincreaseisinplace. Thegreaterthelaginimplementation,themorerealinterestratesrise priortotheactualchange. Thetimingdoesnotsignificantlymatterforthecurrentexcessreturnbecausein themodel,agentsandfirmsareforward-lookingandhaverationalexpectations. Furthermore,ifonewereto calculatetheexcessreturninanyperiodbeyondtheinitialperiodofthisexercise,thecurrentexcessreturn wouldbeveryclosetozero. Investment adjustment costs reduce the volatility of investment, which means investment does not rise as much initially and does not fall as much in the following periods. The short run effect entails a smaller declineindividends(D Y w L I ),whilethemedium-longruneffectimpliesasmallerdeclinein t t t t t D (cid:0) (cid:0) output,sothatdividendsoverallfalllessastheinvestmentadjustmentcostsparameterrises. Withdividends fallingless,thecurrentexcessreturnbecomesmorepositive. 2. ResultsBasedOnEstimatedRule Forthemainresultsofourpaper,welargelyreliedonestimatescomingfromCoibionandGorodnichenko (2015). Coibion and Gorodnichenko (2015) follow Orphanides (2005) and use Greenbook data and least squaresestimationfortwotimeperiods: (1)1969-1978and(2)1983-2002. Fortherobustnessofourtheoreticalresults,were-dotheiranalysisforthetimeperiod1979Q3to2007Q4. EachwindowbetweenFOMC meetingsrepresentsonetimeperiod. Thisprovidesalternativeestimatesforthemonetarypolicyrule,which ismodeledasafunctionofthepreviousperiod’sfederalfundsrate,theGreenbooktimet inflationrate,and theGreenbookoutputgrowthattimet. Wefindvaluesof0.8fortheinertiacoefficient,1.8fortheinflationcoefficient,and1.15fortheoutput growth for the Post-Volcker time period. These values are within confidence intervals of our main results, 4

whichforclaritywere0.9fortheinertiacoefficient,1.58fortheinflationcoefficientand2.21fortheoutput growthcoefficient. SinceGreenbookdataisonlyavailablepost-1969yieldingarelativelyshorttimeseriestoestimateour pre-Volcker policy rule, we supplement this data with forecasts of future inflation and output growth constructedusingalargepanelofmacroeconomicdata. Specifically,weregresstheGreenbookforecastsused inestimatingthemonetarypolicyrulefrom1969to1978onvariablesfromtheFRED-MDdatabaseselected usinganelasticnetwheretheregularizationparametersarechosenusingcrossvalidation. Theseestimates arethenusedtoformforecastsfrom1959to1968.4 TheresultsforthePre-Volckerestimationareincluded inthemaintext. WeshowinFigureA.1theresponsestothesetupwiththeestimatedrule. Wealsoshowresponsesbased on the calibration in the main text but with different values for the output growth coefficient. Specifically, weuseonestandarderrordeviationsfromthepointestimateof2.2,whichis1.4and3. 3. TimeVaryingParameterVAR Whileweprovideboththeoreticalandstatisticalevidencesupportingafocusonbroadmonetarypolicy regimes,ourchoiceofsampleperiodsmayseemsomewhatadhoc. Inthissection,weestimateaBayesian timevaryingparameterVAR(TVP-VAR)inthespiritofPrimiceri(2005). ThismodelallowsboththeVAR loadings in Equation 21 and the loadings on fiscal policy in Equation 26. Specifically, we estimate the followingVARmodel: Z c A Z (cid:30) FISCAL u ; t 1;:::;T (A.1) t t 1;t t 1 t t t D C (cid:0) C C D whereZ isan 1vectorofendogenousvariables;c isan 1vectoroftime-varyingintercepts;A isa t t 1;t (cid:2) (cid:2) n nmatrixoftime-varyingcoefficientswithlaglength1;phi isan 1vectoroftime-varyingloadings t (cid:2) (cid:2) onfiscalpolicyshocks, andu isan 1vectorofresiduals. Thetime-varyingVARcanthenberewritten t (cid:2) as: Z X A (cid:134) (cid:15) t D t0 Qt C t t (A.2) X I (cid:140)1;Z ;FISCAL (cid:141); t0 t0 1 t D (cid:10) (cid:0) whereA isastackedvectorcontainingallcoefficientsoftherighthandsideofequation21. Var.(cid:15) / I Qt t D n andtheoperator denotestheKroneckerproduct. (cid:10) Thedynamicsofthetime-varyingparameters(A )arefollowingadriftlessrandomwalk: t A A (cid:23) ; (A.3) t t 1 t D (cid:0) C 4Additionaldetailsregardingtheseforecastsareavailablefromtheauthorsuponrequest. 5

The vector of innovations (cid:140)(cid:15) ￿;(cid:23) ￿(cid:141) is assumed to be jointly normally distributed with variance-covariance t t matrix: " I 0 # n Var.(cid:15) ￿;(cid:23) ￿/ ; (A.4) t t D 0 Q whereI isanndimensionalidentitymatrixandQisapositivedefinitematrix. n For evaluating posteriors, prior distributions need to be specified. For the calibration of these priors, we use a training sample that is 25 periods long starting in 1947:Q1and run an OLS estimation on a fixedcoefficient VAR model. The OLS point estimates (B ) and four times their variance specify the mean OLS andthevarianceofB . Thepriorcovariancematrixisspecifiedtobe4 I . Thepriorsfortheinitialstatesof 0 1 (cid:1) n thetime-varyingVAR-parametersB followanormaldistribution. ThehyperparameterQisthecovariance 0 matrixoftheinnovations(seeequations4.5,4.6and4.7). MatrixQisdistributedasanindependentinverse- Wishart. Insummary: B N.B ;4 V.B //; 0 OLS OLS (cid:24) (cid:1) Q IW.k2 (cid:28) V.B /;(cid:28)/; (A.5) (cid:24) 1Q (cid:1) (cid:1) 1OLS (cid:134) IW.I.M/;M 1/ 1 (cid:24) C where(cid:28) hasthesizeofthetrainingsample,thesizeofthetrainingsampledefinesthedegreesoffreedomfor Q. Finally,theparameterk 0:1definespriorbeliefsaboutthedegreeoftimevariationintheparameters, Q D covariancesandvolatilities.5 EstimationforthisreducedformVARiscarriedoutusingBayesianmethodsforthesamplefrom1953:Q1 to2007:Q4. Forapproximatingtheposteriordistribution,50,000iterationsoftheGibbssamplerareusedand wedropthefirst20,000iterationsforconvergence. Forbreakingtheautocorrelationofthedraws,onlyevery 10thiterationiskept. Ourfinalestimatesarethereforebasedon3,000iterations. Thesampleautocorrelation functionsofthedrawsdieoutratherquickly. Furthermore, theconvergencediagnosticsrevealsatisfactory results.6 PanelAofFigureA.2plotstheposteriormedianoftheequityreturnresponsetotheAllShocksseriesof fiscal policy shocks through time. While time-series variation in the response is evident, the broad pattern that fiscal policy’s effect on excess equity returns depending on monetary policy regime remains. During thePre-Volckerregime, stocksrespondnegativelytoexogenousincreasesinthetaxratewiththeposterior medianresponsefallingbelowzeroineachperiod. WiththeonsetofthePost-Volckerregime,theresponse becomespositive. Moreover,theseresponsesdon’tappeartovarysubstantiallyduringNBERrecessionswith the exception of the run-up to early 1990s recession. Panel B plots the posterior median of the combined 5Asasensitivitycheck,wealsoexperimentedwithothervaluecombinationsofthesecoefficients. Theresponsesobtainedare robusttothosepresented. 6Adetailedoverviewcanbeobtaineduponrequest. 6

response of discount rates (both real interest rates and the future equity returns) to fiscal policy shocks. Again, responses are volatile around the 1987 crash and the early 1990s recession, but overall results are consistentwithourpreviousfindings. TableA.3presentstheposteriormediansforallequityresponsechannelsbymonetarypolicyregimefor eachofourexogenoustaxshockseries. Formanyoftheestimates,the68percentcoverageintervalsarequite wideanddonotallowustorejectthenullofzeroresponse. HoweverforboththeAllShocksandSurprise Shocksseries,thecoverageintervalforoverallequityresponseinthePost-Volckerperiodispositivewiththe rangecoveringthefixed-loadingresponsesreportedinTable3. Resultsaresimilarforthedifferenceinthe overall response across the two monetary policy regimes as well. The overall equity response to increases withtheonsetofthePost-Volckerregime,andthesizeoftheestimateddifferenceintheTVP-VARisinline withthosereportedinthemainresultsofthepaper. 7

FigureA.1: Post-VolckerResponsesBasedonEstimationandRobustness ThisfigureshowstheeconomicresponsesforthePostVolckerregime(basedonestimatedparameters and the main framework at different values for the output growth coefficient) in response to aonestandarddeviationincometaxrateincrease(0.22%). Theonlydifferenceacrossthetwocalibrationsisthedefinitionofthemonetarypolicyrule. ForthePost-Volckerbasedontheestimated rule,(cid:11) 1:8,(cid:11) 1:15,(cid:11) 0:8. ForthePost-Volckerbasedonthemainresults,(cid:11) 1:58, (cid:25) (cid:129)y R (cid:25) D D D D (cid:11) 1:4 or (cid:11) 3, and (cid:11) 0:9. We use the values of 1.4 and 3 because these are -/+ 1 (cid:129)y (cid:129)y R D D D standard error (0.8) based on the estimates in Coibion and Gorodnichenko (2011). The results are similartowhatarepresentedinthemaintext: inresponsetoataxincrease,thediscountratenews dominatesthecashflownewssothattheoveralleffectispositive. Excess Equity Return Investment Percent (deviation from steady state) Percent (deviation from steady state) 0.15 1 0.1 0.5 0.05 0 0 −0.05 −0.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters (t) Quarters (t) Dividends Output Percent (deviation from steady state) Percent (deviation from steady state) 0 0.2 −0.2 0.1 −0.4 0 −0.6 −0.1 −0.8 −0.2 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters (t) Quarters (t) Real Interest Rate Consumption x 10−3 Percent (deviation from steady state) Percent (deviation from steady state) 5 0 −0.05 0 −0.1 NK: Post−Volcker (Main): αΔy = 1.4 −5 NK: Post−Volcker (Main): αΔy = 3.0 −0.15 NK: Post−Volcker Estimated −10 −0.2 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters (t) Quarters (t) 8

FigureA.2: TVP-VARresponsetotaxshocks Thisfigurepresentsthetime-varyingeffectofapositivetaxshockonthecurrentexcessreturnand discount rate news. Tax shocks are the All Shocks series described in Section 4.2. The estimation follows Primiceri (2005) and is described in Section 3. The posterior median of the responses is plotted. TheshadedareascoincidewithNBERrecessions. PanelA:CurrentExcessReturn PanelB:DiscountRateNews 9

TableA.1: Robustnessofsimulatedresultstochangesinmodelparameters This table reports the impact of a positive exogenous tax shock on the current excess equity return, and the discounted sums of future excess equity returns, current and future real interest rates, and current and future cash flows. Data are the solutions to the DSGE model described in Section 3. In the first column of each panel, the results from our preferred calibration is presented for reference. PanelA:MonetaryPolicyRuleParameters OutputGrowth InertiaCoefficient InflationCoefficient Coefficient ((cid:11) 0:90) ((cid:11) 1:58) ((cid:11) 2:2) (cid:26) (cid:25) (cid:129)y D D D Baseline 0.00 0.95 1.25 2 1.2 2.4 CurrentExcessReturn 0:0515 0:0419 0:0534 0:0600 0:0565 0:0286 0:0434 FutureExcessReturn 0:0030 0:0081 0:0002 0:0135 0:0053 0:0646 0:0030 (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2588 0:2489 0:2624 0:3009 0:2475 0:2815 0:2704 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:2103 0:2151 0:2088 0:2274 0:1963 0:1883 0:2239 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelB:NewKeynesianParameters Priceadjustment Elast. subs. ofgoods costs( 35) ((cid:17) 7) D D Baseline 10 100 4 10 CurrentExcessReturn 0:0515 0:0524 0:0492 0:0274 0:0735 FutureExcessReturn 0:0030 0:0031 0:0044 0:0030 0:0031 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2588 0:2581 0:2570 0:2633 0:2565 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:2103 0:2088 0:2123 0:2389 0:1861 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelC:UtilityParameters SubjectiveDiscount IntertemporalElasticity RiskAversion Factor ofSubstitution ((cid:13) 5) ((cid:12) 0:9990) ( 0:2) D D D Baseline 2 10 0.99 0.9999 0.15 0.25 CurrentExcessReturn 0:0515 0:0496 0:0554 0:0508 0:0486 0:0895 0:0160 FutureExcessReturn 0:0030 0:0011 0:0091 0:0060 0:0017 0:0026 0:0057 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2588 0:2657 0:2446 0:2535 0:2528 0:2776 0:2437 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:2103 0:2150 0:1983 0:2086 0:2059 0:1907 0:2221 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 10

TableA.1: Robustnessofsimulatedresultstochangesinmodelparameters(cont.) PanelD:Production&TaxRateParameters CapitalShare Depreciation TaxRatePersistence MarginalTaxRate ((cid:18) 0:3) ((cid:14) 0:10) ((cid:26)(cid:28) 0:9999) ((cid:28)SS 0:17) D D D D Baseline 0.25 0.35 0.06 0.14 0.99 0.9 0.10 0.25 CurrentExcessReturn 0:0515 0:0309 0:0716 0:0627 0:0434 0:0515 0:0044 0:0494 0:0530 FutureExcessReturn 0:0030 0:0045 0:0015 0:0022 0:0029 0:0030 0:0001 0:0029 0:0027 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2588 0:2511 0:2664 0:2586 0:2574 0:2588 0:0174 0:2388 0:2820 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:2103 0:2246 0:1963 0:1982 0:2169 0:2103 0:0129 0:1924 0:2317 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelE:WageParameters Wageadjustment Asym. wageadjustment LaborHours MarketPowerofWorkers costs((cid:30) 1000) costs( 3800) ((cid:19) 0:25) ((cid:18) 1:4) W D D D D Baseline 500 1500 0 5000 0.2 0.3 1.2 1.6 CurrentExcessReturn 0:0515 0:0262 0:0599 0:0630 0:0453 0:0243 0:0872 0:0734 0:0299 FutureExcessReturn 0:0030 0:0072 0:0043 0:0064 0:0003 0:0045 0:0014 0:0041 0:0027 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2588 0:2762 0:2377 0:2400 0:2667 0:2517 0:2571 0:2278 0:2624 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:2103 0:2429 0:1821 0:1834 0:2217 0:2228 0:1713 0:1586 0:2298 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelF:Misc. Parameterizations OutputGrowthCoefficient TaxShockattime InvestmentAdj. Costs (when(cid:11) 0:91,(cid:11) 1:32)(Pre-Volcker) (t 0) ((cid:137) 0) R (cid:25) D D D D Baseline 0.94 1.50 2.00 2 4 1 5 CurrentExcessReturn 0:0515 0:0502 0:0381 0:0556 0:0516 0:0498 0:0603 0:0624 (cid:0) FutureExcessReturn 0:0030 0:0513 0:0092 0:0034 0:0030 0:0030 0:0006 0:0016 (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2588 0:2272 0:2784 0:2712 0:2569 0:2526 0:2607 0:2573 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:2103 0:3287 0:2312 0:2121 0:2083 0:2057 0:1998 0:1933 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 11

TableA.2: Robustnessofsimulatedresultstoestimatedmonetarypolicyrule This table reports the impact of a positive exogenous tax shock on the current excess equity return, and the discounted sums of future excess equity returns, current and future real interest rates, and current and future cash flows. Data are the solutions to the DSGEmodeldescribedinSection3. Inthefirstcolumnofeachpanel,theresultsfromourpreferredcalibrationwiththealternative monetarypolicyruleispresentedforreference. PanelA:MonetaryPolicyRuleParameters OutputGrowth InertiaCoefficient InflationCoefficient Coefficient ((cid:11) 0:80) ((cid:11) 1:8) ((cid:11) 1:15) (cid:26) (cid:25) (cid:129)y D D D Baseline 0.00 0.9 1.5 2.5 1.05 2 CurrentExcessReturn 0:0765 0:0730 0:0414 0:1589 0:0207 0:1377 0:0620 FutureExcessReturn 0:0079 0:0278 0:0498 0:0238 0:0173 0:0867 0:0045 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2299 0:2217 0:2573 0:2050 0:2325 0:1892 0:2458 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1613 0:1766 0:1660 0:0699 0:1945 0:1382 0:1884 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelB:NewKeynesianParameters Priceadjustment Elast. subs. ofgoods costs( 35) ((cid:17) 7) D D Baseline 10 200 5 10 CurrentExcessReturn 0:0765 0:0762 0:0821 0:0813 0:0847 FutureExcessReturn 0:0079 0:0095 0:0100 0:0437 0:0138 (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2299 0:2289 0:2241 0:2167 0:2368 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1613 0:1622 0:1520 0:1791 0:1383 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelC:UtilityParameters SubjectiveDiscount IntertemporalElasticity RiskAversion Factor ofSubstitution ((cid:13) 5) ((cid:12) 0:9990) ( 0:2) D D D Baseline 2 10 0.99 0.9999 0.15 0.25 CurrentExcessReturn 0:0765 0:0734 0:0817 0:1469 0:0638 0:1463 0:0374 FutureExcessReturn 0:0079 0:0053 0:0129 0:0764 0:0022 0:0678 0:0149 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2299 0:2345 0:2218 0:2351 0:2255 0:2121 0:2331 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1613 0:1664 0:1530 0:1646 0:1595 0:1336 0:1808 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 12

TableA.2: Robustnessofsimulatedresultstoestimatedmonetarypolicyrule(cont.) PanelD:Production&TaxRateParameters CapitalShare Depreciation TaxRatePersistence MarginalTaxRate ((cid:18) 0:3) ((cid:14) 0:10) ((cid:26)(cid:28) 0:9999) ((cid:28)SS 0:17) D D D D Baseline 0.25 0.35 0.08 0.12 0.999 0.995 0.10 0.24 CurrentExcessReturn 0:0765 0:0837 0:0772 0:0693 0:0915 0:0590 0:0151 0:0833 0:0696 FutureExcessReturn 0:0079 0:0207 0:0003 0:0047 0:0262 0:0001 0:0212 0:0269 0:0103 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2299 0:2209 0:2376 0:2375 0:2203 0:2194 0:1783 0:2025 0:2607 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1613 0:1580 0:1607 0:1635 0:1550 0:1602 0:1420 0:1461 0:1808 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelE:WageParameters Wageadjustment Asym. wageadjustment LaborHours MarketPowerofWorkers costs((cid:30) 1000) costs( 3800) ((cid:19) 0:25) ((cid:18) 1:4) W D D D D Baseline 750 1250 0 5000 0.2 0.3 1.3 1.5 CurrentExcessReturn 0:0765 0:0459 0:1090 0:0470 0:0826 0:0156 0:1807 0:1573 0:0400 FutureExcessReturn 0:0079 0:0117 0:0326 0:0036 0:0339 0:0233 0:1036 0:0773 0:0154 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2299 0:2432 0:2127 0:2888 0:2152 0:2344 0:1983 0:1906 0:2417 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1613 0:1857 0:1363 0:2453 0:1665 0:1955 0:1211 0:1106 0:1863 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) PanelF:Misc. Parameterizations OutputGrowthCoefficient TaxShockattime InvestmentAdj. Costs (when(cid:11) 0:91,(cid:11) 1:32)(Pre-Volcker) (t 0) ((cid:137) 0) R (cid:25) D D D D Baseline 0.94 1.50 2.00 2 4 1 5 CurrentExcessReturn 0:0765 0:0502 0:0381 0:0556 0:0776 0:0779 0:0849 0:0950 (cid:0) FutureExcessReturn 0:0079 0:0513 0:0092 0:0034 0:0087 0:0102 0:0131 0:0369 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RealInterestRateNews 0:2299 0:2272 0:2784 0:2712 0:2279 0:2234 0:2248 0:1815 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) CashFlowNews 0:1613 0:3287 0:2312 0:2121 0:1590 0:1557 0:1531 0:1234 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 13

TableA.3: TheimpactofexogenoustaxshocksonequityreturnsinaTVP-VARframework This table reports the impact of exogenous tax shocks on the current excess equity return, and the discounted sums of future excess equity returns, current and future real interest rates, and current and future dividends (cash flows) in a Bayesian time varying parameter VAR (TVP-VAR) framework. Thesix-variableVAR(1)usedtoconstructexcessequityreturnandrealinterestrateforecasts is estimated over the sample 1947Q1 to 2007Q4. The VAR state variables are defined in the text. TaxshocksaredescribedinSection4.2. TheestimationfollowsPrimiceri(2005)andisdescribed in Section 3. The posterior median of the responses over the Pre- and Post-Volcker periods are reportedinPanelAandB,respectively. Posteriormediansinbolddonotcontain0.0inthe68percentcoverageoftheposteriordistribution. Theintervalofthe68percentcoverageoftheposterior distributionispresentedinparenthesesbelowtheposteriormedian. Surprise SurpriseSVAR AllShocks SVARShocks Shocks Shocks PanelA:1980Q3-2007Q4 CurrentExcessReturn 0.3110 0.0033 0.2981 -0.0270 (0.0424,0.5868) (-0.0918,0.0971) (0.0478,0.5553) (-0.1055,0.0521) FutureExcessReturn -0.2499 -0.0244 -0.2225 0.0089 (-1.3769,0.8440) (-0.5451,0.4969) (-1.2253,0.7590) (-0.5097,0.5118) RealInterestRateNews 0.0259 0.0006 0.0398 0.0064 (-0.8289,0.8646) (-0.4073,0.4143) (-0.7565,0.8204) (-0.3993,0.4166) CashFlowNews 0.0741 -0.0211 0.1015 -0.0144 (-1.1955,1.3372) (-0.6189,0.5838) (-1.0361,1.2216) (-0.6159,0.5979) PanelB:1947Q1-1980Q2 CurrentExcessReturn -0.2648 -0.0435 -0.0765 -0.0182 (-0.5262,-0.0094) (-0.1068,0.0198) (-0.2531,0.1036) (-0.0809,0.0432) FutureExcessReturn 0.1177 0.0074 -0.0144 -0.0134 (-0.9181,1.1469) (-0.5184,0.5078) (-0.8871,0.8412) (-0.5239,0.4972) RealInterestRateNews 0.0250 0.0062 0.0428 0.0165 (-0.7664,0.8109) (-0.4165,0.4340) (-0.6581,0.7221) (-0.4081,0.4432) CashFlowNews -0.1270 -0.0311 -0.0528 -0.0145 (-1.3229,1.0612) (-0.6500,0.5721) (-1.0891,0.9729) (-0.6511,0.6059) PanelC:Difference CurrentExcessReturn -0.5785 -0.0463 -0.3719 0.0085 (-0.9299,-0.2331) (-0.1567,0.0645) (-0.6674,-0.0824) (-0.0902,0.1069) FutureExcessReturn 0.3650 0.0290 0.2036 -0.0174 (-1.7058,2.4682) (-1.0017,1.0337) (-1.6167,2.0137) (-1.0431,0.9750) RealInterestRateNews -0.0055 0.0069 0.0008 0.0149 (-1.6301,1.6337) (-0.8343,0.8318) (-1.4614,1.4856) (-0.8023,0.8296) CashFlowNews -0.1913 -0.0126 -0.1563 -0.0053 (-2.6187,2.1942) (-1.2052,1.1919) (-2.3146,1.9879) (-1.2540,1.2397) 14