The Jumbo-Conforming Spread: A Semiparametric Approach

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Jumbo-Conforming Spread: A Semiparametric Approach Shane M. Sherlund 2008-01 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.

The Jumbo-Conforming Spread: A Semiparametric Approach ∗ Shane M.Sherlund BoardofGovernorsofthe FederalReserveSystem Washington, DC20551 (202)452-3589 Shane.M.Sherlund@frb.gov October23,2007 Allcommentsarewelcome. ∗IthankBrentAmbrose,BrianBucks,KarenDynan,WaynePassmore,KarenPenceandseminarparticipantsattheFederalReserveBoardandthe2007AREUEAAnnualMeetingsforhelpful commentsandsuggestions. Thispaperrepresentstheviewsoftheauthoranddoesnotnecessarily representtheviewsoftheFederalReserveBoard,itsmembers,oritsstaff.

The Jumbo-Conforming Spread: A Semiparametric Approach Abstract This paper estimates the jumbo-conforming spread using data from the Federal HousingFinanceBoard’sMonthlyInterestRateSurveyfromJanuary1993toJune 2007. Importantly, thispaperaugments thetypicalparametric approach byadding state-level foreclosure lawsandZIP-leveldemographic variables tothemodel, estimatingtheeffectsofloansizeandloan-to-value ratioonmortgageratesnonparametrically, andincluding geographic location asacontrolforsomepotentially unobservedborrowerandmarketcharacteristicsthatmightvaryovergeography,such as credit scores, debt-to-income ratios, and house price volatility. A partial locallinearregressionapproachisusedtoestimatethejumbo-conformingspread,onthe premise that loans similar to each other in terms of loan size, loan-to-value ratio, or geographic location might also be similar in other, unobservable borrower and market characteristics. I find estimates of the jumbo-conforming spread of 13 to 24basispoints—50to24percentsmallersinceabout1996,whencreditscoresbecamewidelyusedinmortgageunderwriting,thanestimatesfromacommonlyused parametric model. Itherefore attribute thedifference inestimates tocredit quality and other unobserved characteristics, among other potential explanations, making thesecontrolsanimportantissueinestimating thejumbo-conforming spread. Journal ofEconomicLiteratureclassification numbers: G21,G28. Keywords: Mortgages,jumbo-conforming spread,partial-linear regression, locallinearregression.

1 Introduction The housing government-sponsored enterprises (GSEs), Fannie Mae and Freddie Mac,werecreatedbyCongresstofacilitatetheflowofcapitaltolendersformaking mortgage loans. The GSEs, as well as private-label issuers, purchase mortgages from lenders and package them together as mortgage-backed securities (MBS). The resulting securities can then be sold to investors. This process, known as securitization (orMBSissuance), freeslenders’capital,therebymakingitpossible forlenderstoextendmoremortgageloans. The effect of GSE activities on mortgage rates, in particular, has prompted considerable previous work. Some research argues that the GSEsserve to reduce interest rates on so-called conforming mortgages—those that the housing GSEs are eligible to purchase—by facilitating securitization of these mortgages relative to so-called jumbo mortgages—those that exceed the conforming loan limit and which the GSEsare ineligible to purchase. Other research argues that the jumboconforming spread provides only an upper bound on the effect of the GSEs on mortgagerates. AsshowninFigure1,averagemortgageratesonjumbooriginationshavegenerally exceeded average mortgage rates on conforming originations over the 1993 to 2007 period. The figure also shows the dispersion of mortgage rates across loans atanygivenpointintime, asshownbytherangebetween the10th and90th percentiles for rates on conforming mortgages. Thewide range of mortgage rates presumably reflects the effects of a variety of other factors on mortgage pricing, suchascreditquality. Figure2showsakernel densityestimateandFigure3showstheempiricalcu- 1

mulative distribution function for thirty-year fixed-rate mortgage loan sizes originated during 2006. Over 95 percent of these 30-year fixed-rate mortgage originations had loan sizes at or below the conforming loan limit, most with loan sizes between$100,000 and$200,000. Inaddition, thespikeofloansattheconforming loan limit, and the relative dearth of loans just above the loan limit, suggest that at least some borrowers perceive a difference in rates on jumbo and conforming mortgages,andthereforeselectlower-costconformingmortgages. Someobservers havearguedthattheseempiricalfactssuggestthatGSEsecuritization activitymay reducemortgageratesonconforming mortgages.1 Various studies have provided estimates of the spread between jumbo and conforming mortgages (Hendershott and Shilling (1989), Cotterman and Pearce (1996), Ambrose, Buttimer, and Thibodeau (2001), Naranjo and Toevs (2002), Passmore, Sparks, and Ingpen (2002), U.S. Congressional Budget Office (CBO) (2001),Ambrose,LaCour-Little,andSanders(2004),andPassmore,Sherlund,and Burgess(2005)tonameafew;McKenzie(2002)providesasummary). Thesestudies report estimates of the jumbo-conforming spread (which varies widely across sample periods) as low as a few basis points to as much as 60 basis points. Many of these studies use the Federal Housing Finance Board’s Monthly Interest Rate Survey (MIRS), which contains information on the contract mortgage rate, the loan-to-value (LTV) ratio at origination, the type and term of the mortgage, the loan amount, etc. A key deficiency of the MIRS data, however, is its exclusion ofmeasures ofcreditworthiness (beyond LTV),income, and expected house price volatility—critical variables inunderstanding mortgageunderwriting. 1Using time-series data from 1993 to 2005, Lehnert, Passmore, and Sherlund (2008) find that GSEportfoliopurchaseshavenoeffectonmortgagerates. 2

Ambrose,LaCour-Little,andSanders(2004)useauniquedatasetfromalarge national lender that provides better measures of borrower credit quality and can differentiate directly between conforming and nonconforming mortgages.2 After controlling for borrower characteristics and house price volatility, the authors report an estimated jumbo-conforming spread of about 27 basis points from 1995 to 1997. Moreover, about 9 basis points of the jumbo-conforming spread estimate is attributed to the nonconforming-conforming spread (possibly due to GSE activities), 15 basis points to the jumbo-nonconforming spread (not due to GSE activities), and3basispointstohousepricevolatility. Passmore,Sherlund,andBurgess(2005)showthatthejumbo-conformingspread can vary due to factors outside the GSEs’ control, such as prepayment and credit risks. In particular, they relate the GSE funding advantage, as well as proxies for prepayment, credit, and maturity-mismatch risks, to estimates of the jumboconforming spread. Based on data for 1997-2003, their results suggest that approximately16percentoftheGSEs’fundingadvantageispassedthroughtohomebuyers in the form of lower mortgage rates, implying that as much as 84 percent of the funding advantage is retained by GSE shareholders in the form of profits. Further, the average pass through tohomebuyers accounts forabout 40 percent of the average jumbo-conforming spread, or 6 to 7 basis points, suggesting that the jumbo-conforming spreadalsoarisesbecauseoffactorsoutsidetheGSEs’control. This paper explores a new, comparatively flexible method of estimating the jumbo-conformingspread. Iparticular,Ishowhowtoestimatethejumbo-conforming spread while using geographic information to control for some of the variation in 2Conformingloanshavestricterunderwritingrequirementsthannonconformingloans,whereas jumboloanshaveloansizesabovetheconformingloanlimit. 3

unobserved borrower and market characteristics, such as credit quality, debt-toincome ratios, and house price volatility. It uses a semiparametric approach suggested by Porter (2002), ultimately comparing “similar” mortgage loans in terms ofgeography, loansize,andloan-to-value (LTV)ratio. Intheend,Ifindestimates of the jumbo-conforming spread to be 13 to 24 basis points—50 to 24 percent smallersinceabout1996,whencreditscoresbecamewidelyusedinmortgageunderwriting, than estimates from a commonly used parametric model. I attribute the difference in estimates to credit quality and other unobserved characteristics, among other potential explanations, making these controls an important issue in estimating thejumbo-conforming spread. Theremainderofthepaperisorganizedasfollows. Section2describesthedata whileSection3describesthemethodologyIusetoestimatethejumbo-conforming spread. Section4discusses theresultsandthefinalsection concludes. 2 Data This paper uses the Monthly Interest Rate Survey (MIRS) data from the Federal Housing Finance Board from January 1993 to June 2007. The MIRS collects information on individual mortgages originated during the final five business days ofeachmonth, including nominal andeffectivemortgage rates,loansize, LTVratio, type of loan, loan maturity, loan purpose, and source of loan. It also contains geographic information, including ZIPcode. I use commercially available data to append ZIP-code-level demographic information, basedonthe2000Census,andtogeo-codeZIPcodes(i.e.,convertZIP codes to latitudinal and longitudinal coordinates). Demographic information in- 4

cludesurban/suburban/rural, race,age,andeducationpopulation shares,aswellas average incomeandhousevalues. Inaddition, statelawsmayaffecttheprofitability of lending, and thus may affect the mortgage contracts offered to borrowers. Forexample,foreclosurelawsgovernhowmuchlenderscanrecoverfromdefaulted mortgage borrowers. I add indicator variables for three features of foreclosure laws: whether a state requires a judicial foreclosure process or statutory right of redemptionandwhetherastateprohibitsdeficiencyjudgments. Formoreinformationonthesevariables, seePence(2006). Similar to other studies that estimate the jumbo-conforming spread, I restrict attentionto30-yearfixed-ratemortgageswithLTVratiosbetween20and100percent. Additionally, I exclude mortgages originated in Alaska and Hawaii (these states have higher conforming loan limits and pose an identification problem because they are not contiguous to the continental United States), mortgages with invalidormissingZIPcodes,mortgagessmallerthan1/8thoftheconformingloan limit,aswellasanymortgagewithaninterestratemorethan1.5percentagepoints below the previous month’s average mortgage rate (to eliminate implausibly low mortgagerates;thesamemethodusedbytheFHFBduringthe1990s). Afterthese datafilters,Iamleftwithabout1.9millionmortgagesfortheJanuary1993toJune 2007period.3 3Overthisperiod,theMIRSdatacontainobservationsonover3.4milliontotalmortgageoriginations. Ofthese,908thousandareadjustable-ratemortgages,506thousandhavetermsotherthan 30years, 39thousandhaveinvalidormissingZIPcodes, 11thousandarefromAlaskaorHawaii, 11thousandhaveLTVratioslessthan20percentorgreaterthan100percent,22thousandhaveloan amountssmallerthan1/8ththeconformingloanlimit,andlessthan1thousandviolatedthemortgage ratefilter. 5

3 Methodology The typical starting point for estimating the jumbo-conforming spread (HendershottandShilling(1989))istoestimatearelationship oftheform: ′ ′ (1) r = αJ +βln(Size )+LTV γ +x λ+ε , i i i i i i wherer isthemortgagerate(orspread)onloani,J = 1indicatesthatloaniisa i i jumboloan(J = 0isnon-jumbo),ln(Size )isafunctionofloansize(presumably i i capturingtheamortizationoffixedandoriginationcosts),LTV isavectorofLTVi ratioindicator variables4 (capturing onedimensionofcreditrisk),x isavectorof i other observable features (such as type of originator, new or existing home, and whetherornotfeeswerepaidatclosing), andε isanerrorterm. Thecoefficientα i thenrepresents theeffectofjumbostatus onthemortgagerate—typically referred toasthejumbo-conforming spread. This paper augments this parametric model by (1) adding state-level foreclosure laws and ZIP-level demographic variables to x , (2) estimating nonparameti rically the effect of loan size and LTV ratio on mortgage rates, and (3) including geographic location as a control for some unobserved borrower and market characteristics that might vary over geography, such as credit scores, debt-to-income ratios, orhouse pricevolatility. Morespecifically, thesemiparametric modeltakes theform: ∗ ∗′ ∗ ∗ (2) r = α J +f(Size ,LTV ,ZIP )+x λ +ε . i i i i i i i 4Classificationsinclude LTV ≤ 75, 75 < LTV ≤ 80 (excluded), 80 < LTV ≤ 90, and i i i 90<LTV . i 6

Thefirstcontributionofthispaperisstraightforward. Ifdemographicvariables influence mortgage rates and the probability of having a jumbo mortgage, but are excluded from equations 1 or 2, then estimates of the jumbo-conforming spread will be biased. By including ZIP-level demographic variables, I hope to avoid at leastpartofthispotential bias. The second contribution of this paper is to allow the data to determine the shape of f(Size ,LTV ,ZIP ), using nonparametric regression techniques. This i i i contrasts withtheparametric approach ofspecifying ′ (3) f(Size ,LTV ,ZIP )= βln(Size )+LTV γ i i i i i apriori, asin1. Anincorrectly specified functional form forf( )canalso lead ··· tobiasedestimatesofthejumbo-conforming spread. The third contribution of this paper is the inclusion of geographic location (ZIP )asacontrol forsomeunobservable borrowerormarketcharacteristics that i mightvaryovergeography. Thatis,householdsneareachothermighthavesimilar unobservable borrower or market characteristics, such as credit quality, debt-toincomeratios,orhousepricevolatility. Several conditions for consistent estimation are necessary. First, some degree ′ of smoothness of f(z ) in z = (Size ,LTV ,ZIP ) is required. The primary i i i i i discontinuities to be modeled explicitly in the model are at the conforming loan limit (the effect of jumbo status on mortgage rates) and at state boundaries (via the foreclosure indicator variables).5 Second, the familiar exogeneity condition, 5Additional discontinuities include loan-to-value ratio, whether the mortgage had fees paid at closing, whetherthemortgagewasoriginatedbyamortgagecompany, andwhetherthehomewas new. 7

E[ε ∗ x ∗ ,z ]= 0,isrequired.6 i| i i The trick, then, is how to identify the effect of jumbo status on the mortgage ∗ rate, α . Hahn, Todd, and Van der Klaauw (2001) suggest estimating separately: (i)thelimitofE[r z ]astheloansizeapproaches theconforming loan limitfrom i i | below, denoted E[r z ] − , using data only on conforming mortgages, and (ii) the i i | limitofE[r z ]fromabove,denotedE[r z ]+,estimatedusingdataonlyonjumbo i i i i | | mortgages. An estimate of the effect of jumbo status on the mortgage rate is then the difference in the limits of E[r z ] at the conforming loan limit: E[r z ]+ i i i i | | − E[r z ] − . i i | An alternative approach, suggested by Porter (2002) and implemented in this ∗ paper, istomoveα J overtotheleft-hand side ofequation 2,andthen minimize i ∗ ∗ the sum of squared residuals with respect to the choice of α . That is, choose α suchthat n 2 ∗ ∗ ∗′ ∗ (4) αˆ = argmin α∗ X(cid:16) r i − α J i − f(z i ) − x i λ (cid:17) . i=1 Each of these two approaches has advantages and disadvantages. The former methodiseasytocompute,butsuffersfromtheeffectsofsmallsamples,especially giventhesizeofsomeofthemonthlyjumbomortgagesamples. Ithastheadditional disadvantage that the jumbo-conforming spread is identified at the boundary of twosubsamples, raising questions aboutboundary bias. Thelatterapproach, however, is computationally expensive, as it estimates local-linear regressions on the entire sample for each step of the optimization process. It does, however, reduce problemsassociated withsmallsamplesizesandboundary bias. 6Irelaxthisconditioninsection4.1. 8

I use local-linear regression to estimate f(z ) in this paper. Under this api proach, the expected value of a variable will be a weighted average of the values forobservations whichare“nearby”inthesenseofhavingsimilarvaluesofconditioning variables z . The kernel weights place more weight on observations close i by than on those farther away. Here, Iuse a normal (Gaussian) product kernel, so that (5) K(u) = φ(u )φ(u )φ(u ), Size LTV ZIP where φ() is the standard normal density function. The kernel bandwidth, b , n · controls how much weight each observation receives in the weighted average. It is effectively a scaling variable, so that with a small bandwidth, only very close observations are included, while with a larger bandwidth, more observations are included. Thebandwidth entersthekernelviau = (z z)/b .7,8 i i n − As opposed to Nadaraya-Watson regression, which essentially fits a constant to the data close to a specific observation using data near that observation (yˆ = w y wherew = K / K ),local-linearregressionfitsastraightlinethrough Pi i i i i Pj j ∗ ∗ aspecific observation using datanearthatobservation (yˆ= w y wherew = Pi i i i e ′ 1 ( Pj z j K j z j ′ ) −1z i K i and e1 is a selection vector with 1 in its first element and zeroselsewhere). Asitturnsout,local-linearregressionisequivalenttoaweighted ′ 1/2 leastsquaresregression ofy on(1,(z z)) withweightsK . i i − i 7DistancesbetweenZIPcodecentroidsarecomputedusingtheHaversineformulaforgreatcircle distances. 8Ideally,onewouldcross-validatethebandwidthparameters,butthisprovestobecomputationallyprohibitiveinthisapplication. Ithereforeusearule-of-thumbbandwidthsuggestedbySilverman (1986),b = cσ n−1/(d+4),wherec = d1/(d+4)( 4 )1/(d+4),σ isthestandarddeviationofz, n z 2d+1 z andd = dim(z ). Bandwidthsrangefrom0.15to0.22forln(Size ),from4.4to6.5percentage i i pointsforLTV ,andfrom28to44milesovergeography. i 9

∗ Robinson(1988)showshowtoestimateλ fromequation2—similartopartial linear regression in the linear regression context. First, take conditional expecta- ∗ tionsofequation 2(withα J subtracted frombothsides): i (6) E[r α ∗ J z ] = E[f(z )z ]+E[x ∗ z ] ′ λ ∗ +E[ε ∗ z ]. i − i | i i | i i| i i| i Thenletyˆ = E[r α ∗ J z ]andxˆ ∗ = E[x ∗ z ],sothat i i − i | i i i| i ∗′ ∗ (7) yˆ = f(z )+xˆ λ i i i (note that E[f(z )z ] = f(z ) and E[ε ∗ z ] = 0). Now subtract equation 7 from i | i i i| i equation 2toobtain ∗ ∗ ′ ∗ ∗ (8) y yˆ = (x xˆ )λ +ε . i − i i − i i ∗ ∗ So to estimate λ , first perform local-linear regressions of y = r α J on z i i i i − ∗ ∗ ∗ and x on z , then regress the residuals y yˆ on the residuals x xˆ . In our i i i − i i − i ∗ ∗ optimization algorithm, λ is computed for each trial α in the Newton-Raphson iterations. AsnotedbyPaganandUllah(1999), local-linear regression reduces boundary bias relative to the usual Nadaraya-Watson regression. Note that boundary bias could be a particular problem with the approach suggested by Hahn, Todd, and VanderKlaauw(2001),inthatthetreatmenteffectisidentifiedattheboundariesof thejumboandconforming subsamples. Theapproach suggested byPorter(2002), ∗ however, identifies α in the interior of the data span. Further, Robinson (1988) and Porter (2002) show that λˆ∗ λ ∗ at semiparametric rates (slower than √n- → 10

convergence).9 4 Results For each month of the MIRS data, I estimate the benchmark parametric model and the semiparametric partial local-linear regression model.10 Figure 4 shows the 12-month moving averages for the two estimated time series of the jumboconforming spread as well as the unconditional jumbo-conforming spread, while Table1showssomesamplestatistics. Asshown,theestimatedjumbo-conforming spread series vary considerably during the January 1993 to June 2007 period. On average, the estimated jumbo-conforming spread under the parametric approach (27 basis points) is nearly 20 percent higher than under the semiparametric approach (22 basis points), and about 24 percent higher since 1996. This difference rises to asmuchas 75percent in2004. Bothsets ofestimates consistently exceed theunconditional difference betweenjumboandconforming mortgagerates. Of particular note is how the 12-month moving averages tend to track each otherclosely upuntilabout1996. Thenthetwoseries appeartodriftapartpermanently. One possible explanation for this is the widespread introduction of credit scoring in mortgage underwriting. In particular, the inclusion of credit scores in mortgage underwriting processes started around the end of 1995. Because the jumbo-conforming spread is estimated to be smaller when geography is includ- 9Aswithcross-validationofthebandwidthparameters,bootstrappingthestandarderrorsofthe parameterestimatesistoocomputationallyburdensome,althoughIshowbootstrappedstandarderrorsforonemonth,inparticular,asanexample. 10Ialsoestimateaparametricmodelthatexcludesthestate-levelforeclosureandZIP-leveldemographicvariablestoshowhowmuchpowerthenonparametriccomponentsaddtotheestimation,as opposedtothestate-andZIP-levelvariables.Theseestimatesaresimilartothebenchmarkparametricmodel’sandthusarelargelyomitted. 11

ed in the conditioning set, homeowners right at the conforming loan limit might have better credit quality than homeowners just above the conforming loan limit. For instance, a borrower who has the resources available to lower his or her loan size or LTV (perhaps as a signal on his or her credit worthiness) might have better credit quality than a borrower who does not have the resources available to lower his or her loan size or LTV. It could also be the case that jumbo borrowers no longer need to signal their credit quality through their loan-to-value ratios and jumbo-conforming status; now they can signal their credit quality through their creditscores. Ineithercase,controllingfor(unobserved) creditqualitywouldtend to lower estimates of the jumbo-conforming spread, relative to an approach without such a control, as the effect would be separately identified from the jumboconforming spread. Table2showstheaverageparameterestimatesacrosstimeforeachoftheestimatedmodels. Notethattheaverageestimatedeffectofjumbostatusonmortgage rates is positive (22 basis points), as are the effects of fees paid at closing (7 basis pints), whether the mortgage was originated by a mortgage company (9 basis points),whetherthehomewasnew(7basispoints),aswellasstatelawspertaining to whether judicial foreclosure is required (2 basis points) and whether deficiency judgments are prohibited (6 basis points). In the parametric specifications, loan sizeandtheLTVratioalso havefairlysubstantial effects onmortgage rates(these effectsareimplicitinthesemiparametric estimates). Ofparticular notearetheaverageR-squared values. Thebenchmark parametric modelexplains onlyabout11 percent ofthevariation inmortgagerates,onaverage. Withoutstate-level foreclosure and ZIP-level demographic variables, the average R-squared falls to around 8 percent. But for the semiparametric model the average R-squared increases to 12

over61percent,presumablyreflectingnonlinearities off(z )inz andunobserved i i borrowerandmarketcharacteristics thatvaryovergeographic location. Table 3 shows the parameter estimates for July 2005, as a particular example. The estimated effect of jumbo status on mortgage rates is statistically significant and positive (24 basis points), as are the effects of mortgage company origination (11 basis points), fees paid at closing (8 basis points), and new homes (20 basis points). In the parametric specifications, loan size and the LTV ratio again have statistically significant effects on mortgage rates. The same pattern also emerges withrespecttothemeasureoffit: Thesemiparametricmodeldominatesthebenchmarkparametricmodel. Atthispoint,severalextensionsdeserveadditionalconsideration. First,outside of Ambrose, LaCour-Little, and Sanders (2004), the literature has largely ignored thepotentialendogeneityofloansizeandLTV(andthussampleselectioninjumbo status). Intheparametric setting atleast, procedures already existtoaddress these issues. The following subsections take a first pass at exploring these issues in the semiparametric context. Finally, estimates ofthejumbo-conforming spread might vary across geographic locations. Thus, estimating the jumbo-conforming spread forspecificgeographies couldprovetobeaninteresting exercise. 4.1 Endogeneity Asnotedabove,estimatesofthejumbo-conformingspreadtothispointhavelargely ignored the potential endogeneity of loan size and the loan-to-value ratio—i.e., the ability of certain borrowers to choose loan sizes and LTV ratios in order to secure conforming mortgage status (be it due to perceived price differences or to signalinggoodcreditquality)—andtheresultingsampleselectionofjumbostatus. 13

Thus, this section considers a semiparametric model that conditions only on geo- ′ graphic location (i.e., z = (ZIP ) inequation 2). Now loans are compared only i i onthebasisofhowphysically closetheyareandnotonhowtheycompareinloan sizeandloan-to-value ratio. Inaddition, Iestimateanonparametric sampleselection equation usingjumbo ′ mortgage status as the dependent variable and z = (ZIP ) as the conditioning i i set. Thisessentiallyestimatestheproportionofjumbomortgagesforanyparticular ZIPcodeandassumesthatoneborrower’sjumbo-conformingstatusdependsonhis or her neighbors’ jumbo-conforming status. Then, inserting the estimated inverse Mills ratio as an additional regressor in equation 2, we can evaluate the estimated effectofsampleselection onmortgagerates. As shown in Figure 5, controlling for the potential endogeneity of loan size andLTVand sampleselection injumbostatus reduces theaverage estimate ofthe jumbo-conforming spread to about 13 basis points—a difference of over 40 percentfromtheoriginal semiparametric modelandadifference ofnearly50percent fromthebenchmark parametric model. However,thisestimateisnotaslowasthe unconditional difference between jumbo and conforming mortgage rates, which averages 7basis points overthe1993-2007 period. Further, contrary totheresults reported inAmbrose,LaCour-Little, andSanders(2004), theestimated coefficient ontheinverse Millsratioisconsistently smallandstatistically insignificant across timeusingthesedataandthesemethods.11 11Estimatesareavailableuponrequest. 14

4.2 State-Level Estimates Figure 6 shows how the concentration of jumbo mortgages varies from state to stateduringJuneandJuly2005. Ingeneral,fewerjumbomortgageswereoriginated in the middle of the country with the vast majority of jumbo mortgages being originated in coastal states. Within these data, the highest concentration of jumbo mortgage originations occurred in Washington DC, California, Maryland, Rhode Island, Virginia, Massachusetts, and New Jersey, while no jumbo mortgages were originated in Arkansas, Iowa, Mississippi, Nebraska, North Dakota, and Vermont duringthisperiod. Withthisinmind,howdoesthejumbo-conformingspreadvary acrossstates? To answer this, I estimate the models for each state.12 As shown in Figure 7, semiparametric estimates of the jumbo-conforming spread were close to zero in 15 states and in excess of 33 basis points in 6 states. The national average was 24 basis points. Parametric estimates of the jumbo-conforming spread, in contrast,werenearzeroin8statesandexceeded33basispointsin20states. Here, the national average was 33 basis points. So the jumbo-conforming does indeed appear to vary by state, possibly reflecting further unobserved borrower or local market characteristics. Interestingly, there is no obvious correlation between the concentrationofjumbomortgagesoriginatedandtheestimatedjumbo-conforming spreadacrossstates. 12Becausemanycitiesspanstatelines,Iincludeout-of-stateobservationswithin100milesofstate boundariesineachstate’sindividualestimation. 15

5 Conclusion This paper estimates the jumbo-conforming spread using data from the Federal HousingFinanceBoard’sMonthlyInterestRateSurveyfromJanuary1993toJune 2007. Importantly, thispaperaugments thetypicalparametric approach byadding state-level foreclosure lawsandZIP-leveldemographic variables tothemodel, estimatingtheeffectsofloansizeandloan-to-value ratioonmortgageratesnonparametrically, andincluding geographic location asacontrolforsomepotentially unobservedborrowerandmarketcharacteristicsthatmightvaryovergeography,such as credit scores, debt-to-income ratios, and house price volatility. A partial locallinearregressionapproachisusedtoestimatethejumbo-conformingspread,onthe premise that loans similar to each other in terms of loan size, loan-to-value ratio, or geographic location might also be similar in other, unobservable borrower and marketcharacteristics. Ifindestimatesofthejumbo-conforming spreadtobe13to 24basispoints—50to24percentsmallersinceabout1996,whencreditscoresbecamewidelyusedinmortgageunderwriting,thanestimatesfromacommonlyused parametric model. Itherefore attribute thedifference inestimates tocredit quality and other unobserved characteristics, among other potential explanations, making thesecontrolsanimportantissueinestimating thejumbo-conforming spread. References Ambrose, B.,M.LaCour-Little, andA.Sanders(2004). Theeffectofconformingloanstatusonmortgageyieldspreads: Aloanlevelanalysis.RealEstate Economics32,541–69. Ambrose, B. W., R. Buttimer, and T. Thibodeau (2001). A new spin on the jumbo/conformingloanratedifferential.JournalofRealEstateFinanceand 16

Economics23,309–35. Cotterman,R.F.andJ.E.Pearce(1996).StudiesonPrivatizingFannieMaeand Freddie Mac, Chapter The Effects of the Federal National Mortgage AssociationandtheFederalHomeLoanMortgageCorporation onConventional Fixed-Rate Mortgage Yields, pp. 97–168. U.S.Department ofHousing and UrbanDevelopment,OfficeofPolicyDevelopmentandResearch. Hahn, J., P. Todd, and W. Van der Klaauw (2001). Identification and estimation of treatment effects with a regression-discontinuity design. Econometrica69,201–9. Hendershott, P. H. and J. D. Shilling (1989). The impact of the agencies on conventionalfixed-ratemortgageyields.JournalofRealEstateFinanceand Economics2,101–15. Lehnert, A., W. Passmore, and S. M. Sherlund (2008). GSEs, mortgage rates, and secondary market activities. Forthcoming in Journal of Real Estate FinanceandEconomics. McKenzie, J.(2002). Areconsideration ofthejumbo/non-jumbo mortgage rate differential. JournalofRealEstateFinanceandEconomics25,197–214. Naranjo,A.andA.Toevs(2002).Theeffectsofpurchasesofmortgagesandsecuritizationbygovernmentsponsoredenterprisesonmortgageyieldspreads andvolatility. JournalofRealEstateFinanceandEconomics25,173–96. Pagan,A.andA.Ullah(1999). Nonparametric Econometrics. Cambridge, UK: CambridgeUniversityPress. Passmore, W., S. M. Sherlund, and G. Burgess (2005). The effect of housing government-sponsored enterprises on mortgage rates. Real Estate Economics33,427–63. Passmore, W., R. Sparks, and J. Ingpen (2002). GSEs, mortgage rates, and the long-run effects of mortgage securitization. Journal of RealEstate Finance andEconomics25,215–42. Pence,K.M.(2006).Foreclosingonopportunity: Statelawsandmortgagecredit.ReviewofEconomicsandStatistics 88,177–82. Porter, J. R. (2002). Asymptotic bias and optimal convergence rates for semiparametric kernel estimation inthe regression discontinuity model. DiscussionPaperNo.1989,HarvardInstituteofEconomicResearch,HarvardUniversity,CambridgeMA. Robinson, P.M. (1988). Root-N-consistent semiparametric regression. Econometrica56,931–54. 17

Silverman,B.(1986).DensityEstimationforStatisticsandDataAnalysis.New York,NY:ChapmanandHall. U.S. Congressional Budget Office (CBO) (2001). Interest rate differentials betweenjumboandconformingmortgages. http://www.cbo.gov. 18

FIGURE 1: 30-YearFixed-RateMortgageRates 10 9 8 7 6 5 4 1994 1996 1998 2000 2002 2004 2006 Average conforming mortgage rate Average jumbo mortgage rate Conforming 10th and 90th percentiles )tnecrep( etar egagtroM NOTE. January1993toJune2007. 19

FIGURE 2: 2006LoanSizeDistribution 0 100000 200000 300000 400000 500000 600000 Loan size ($) ytisned lenreK Conforming Loan Limit ($417,000) NOTE. Normal(Gaussian)kerneldensitywithbandwidthof$5000. 20

FIGURE 3: 2006LoanSizeDistribution 1.0 0.8 0.6 0.4 0.2 0.0 0 100000 200000 300000 400000 500000 600000 Loan size ($) ytilibaborp evitalumuC Conforming Loan Limit ($417,000) NOTE. Empiricalcumulativedistribution function. 21

FIGURE 4: Jumbo-Conforming SpreadEstimates 50 40 30 20 10 0 -10 -20 1994 1996 1998 2000 2002 2004 2006 Semiparametric Parametric Unconditional stniop sisaB NOTE. 12-monthmovingaverage. 22

FIGURE 5: Jumbo-Conforming SpreadEstimates 50 40 30 20 10 0 -10 -20 1994 1996 1998 2000 2002 2004 2006 Semiparametric Geography only Parametric Unconditional stniop sisaB NOTE. 12-monthmovingaverage. 23

FIGURE 6: JumboMortgageOriginations byState Jumbo Proportion (percent) 9.7 to 22.2 (7) 5.2 to 9.7 (6) 3.3 to 5.2 (6) 2.6 to 3.3 (5) 2.1 to 2.6 (4) 1.4 to 2.1 (7) 0.5 to 1.4 (6) 0 to 0.5 (8) NOTE. June-July 2005. 24

FIGURE 7: Jumbo-Conforming SpreadEstimatesbyState Semiparametric Estimates Jumbo-Conforming Spread (basis points) 32.8 to 41.2 (6) 24.6 to 32.8 (13) 16.4 to 24.6 (6) 8.2 to 16.4 (9) 0 to 8.2 (15) Parametric Estimates Jumbo-Conforming Spread (basis points) 67.2 to 83.8 (4) 50.4 to 67.2 (1) 33.6 to 50.4 (15) 16.8 to 33.6 (21) 0 to 16.8 (8) NOTE. June-July 2005. 25

TABLE 1: Jumbo-Conforming Spread Mean Median Std.Dev. Minimum Maximum Correlation Total Semiparametric 22.23 22.83 13.49 -30.74 57.93 .7291 Parametric 26.53 27.53 12.76 -44.77 62.26 1993 Semiparametric 19.64 17.88 11.47 -5.41 35.76 .3099 Parametric 22.60 24.08 10.14 9.71 36.52 1994 Semiparametric 7.24 7.87 18.79 -30.74 32.94 .7415 Parametric -0.25 5.95 20.69 -44.77 23.95 1995 Semiparametric 22.26 23.55 17.45 -14.89 55.28 .8130 Parametric 24.53 27.03 15.00 -3.85 41.49 1996 Semiparametric 27.51 27.27 12.45 6.40 50.12 .7360 Parametric 24.83 21.54 8.68 15.17 39.71 1997 Semiparametric 16.71 16.03 8.15 2.53 29.34 .8453 Parametric 21.55 22.64 6.30 11.80 31.59 1998 Semiparametric 30.06 30.93 7.03 11.66 38.76 .5107 Parametric 35.20 34.68 3.42 30.36 41.15 1999 Semiparametric 23.60 24.16 8.98 9.25 38.55 .7478 Parametric 27.40 25.50 6.47 18.42 38.19 2000 Semiparametric 22.35 22.02 14.14 -5.64 43.96 .5880 Parametric 33.95 34.63 7.13 24.56 47.65 continued onnextpage 26

TABLE 1: continued Mean Median Std.Dev. Minimum Maximum Correlation 2001 Semiparametric 34.18 31.83 15.55 5.27 57.93 .9546 Parametric 38.79 34.72 12.72 18.50 62.26 2002 Semiparametric 19.13 17.87 7.93 9.82 30.85 .5376 Parametric 27.10 28.19 5.59 18.47 32.88 2003 Semiparametric 27.53 24.97 12.47 10.19 56.73 .7550 Parametric 31.74 29.79 9.72 17.77 47.55 2004 Semiparametric 14.59 15.39 6.55 2.71 23.77 .4686 Parametric 25.49 24.83 2.35 22.14 28.96 2005 Semiparametric 16.10 19.30 9.37 -3.36 25.94 .4607 Parametric 26.33 26.03 5.27 16.60 37.62 2006 Semiparametric 29.47 33.62 11.75 9.44 51.53 .6501 Parametric 31.85 31.09 6.16 22.38 41.66 2007 Semiparametric 23.90 21.06 10.11 15.88 43.83 .9439 Parametric 27.04 24.24 7.19 22.64 41.54 27

TABLE 2: AverageParameterEstimatesfor1993-2007 Semiparametric Parametric Parametric Constant -0.0019 9.0605 8.6741 Jumbomortgage 0.2223 0.2695 0.2653 ln(Size ) — -0.1652 -0.1644 i LTV 75 — -0.0069 -0.0121 i ≤ 80 < LTV 90 — 0.1164 0.1127 i ≤ LTV > 90 — 0.0567 0.0575 i Mortgagecompany 0.0888 0.0763 0.0904 Feespaid 0.0700 0.0647 0.0649 Newhome 0.0674 0.0509 0.0512 Urbanpop. share -0.0004 — -0.0005 Suburban pop. share -0.0002 — -0.0001 Blackpop. share 0.0008 — 0.0003 Asianpop. share -0.0001 — 0.0011 Hisp. pop. share 0.0004 — 0.0020 Age0-9pop. share 0.0004 — 0.0002 Age10-17pop. share 0.0012 — 0.0008 Age18-21pop. share 0.0002 — -0.0029 Age22-29pop. share 0.0017 — 0.0000 Age40-49pop. share 0.0014 — -0.0004 Age50-59pop. share 0.0022 — -0.0002 Age60-69pop. share 0.0021 — 0.0021 Age70-79pop. share 0.0000 — 0.0004 Age80+pop. share 0.0005 — 0.0020 Edu. <9pop. share -0.0007 — -0.0047 Edu. 9-12pop. share -0.0002 — 0.0011 Edu. coll. pop. share 0.0010 — 0.0030 Edu. Assoc. pop. share -0.0039 — 0.0011 Edu. Bach. pop. share -0.0010 — -0.0055 Edu. Prof. pop. share -0.0014 — 0.0018 ln(Income) 0.0012 — -0.0288 ln(House value) 0.0033 — 0.0576 Judicial foreclosure 0.0152 — 0.0211 Rightofredemption 0.0040 — 0.0017 Deficiencyjudgment 0.0584 — 0.0110 R-squared 0.6144 0.0824 0.1110 28

TABLE 3: ParameterEstimatesforJuly2005 Semiparametric Parametric Parametric Constant -0.0033 * 8.3491 * 8.3885 * (.0011) (.2066) (.7236) Jumbomortgage 0.2387 * 0.3896 * 0.3762 * (.0566) (.0331) (.0305) ln(Size ) — -0.2220 * -0.2037 * i (.0170) (.0180) LTV 75 — -0.0618 * -0.0617 * i ≤ (.0155) (.0149) 80 <LTV 90 — 0.3299 * 0.3061 * i ≤ (.0344) (.0329) LTV > 90 — 0.0527 * 0.0366 i (.0215) (.0208) Mortgagecompany 0.1062 * 0.1206 * 0.1327 * (.0174) (.0172) (.0137) Feespaid 0.0825 * 0.0664 * 0.0704 * (.0122) (.0171) (.0143) Newhome 0.1987 * 0.2321 * 0.2314 * (.0189) (.0236) (.0215) Urbanpop. share 0.0003 — 0.0000 (.0003) (.0003) Suburban pop. share 0.0013 * — 0.0012 * (.0004) (.0004) Blackpop. share 0.0004 — 0.0012 (.0008) (.0007) Asianpop. share -0.0024 — 0.0000 (.0014) (.0019) Hisp. pop. share 0.0009 — 0.0032 * (.0012) (.0010) Age0-9pop. share -0.0053 — -0.0086 (.0065) (.0056) Age10-17pop. share -0.0001 — -0.0001 (.0058) (.0046) Age18-21pop. share -0.0001 — -0.0050 (.0041) (.0039) Age22-29pop. share -0.0049 — -0.0066 continued onnextpage 29

TABLE 3: continued Semiparametric Parametric Parametric (.0068) (.0050) Age40-49pop. share 0.0030 — 0.0010 (.0052) (.0050) Age50-59pop. share -0.0077 — -0.0096 * (.0055) (.0047) Age60-69pop. share 0.0091 — 0.0064 (.0065) (.0067) Age70-79pop. share -0.0107 * — -0.0040 (.0053) (.0062) Age80+pop. share 0.0032 — 0.0005 (.0065) (.0059) Edu. <9pop. share 0.0064 — -0.0060 (.0055) (.0052) Edu. 9-12pop. share -0.0013 — 0.0102 * (.0057) (.0042) Edu. coll. pop. share 0.0013 — 0.0038 (.0041) (.0034) Edu. Assoc. pop. share 0.0004 — -0.0050 (.0068) (.0051) Edu. Bach. pop. share -0.0046 — -0.0009 (.0031) (.0032) Edu. Prof. pop. share 0.0007 — 0.0048 (.0033) (.0031) ln(Income) 0.0347 — 0.0116 (.0779) (.0590) ln(House value) -0.0049 — -0.0231 (.0380) (.0312) Judicial foreclosure -0.0116 — 0.0237 (.0346) (.0174) Rightofredemption 0.2287 * — -0.0928 * (.0593) (.0319) Deficiencyjudgment -0.1123 — -0.0321 * (.1163) (.0191) R-squared 0.6636 0.1213 0.1404 Bootstrap standarderrorsinparentheses. *=statistically significant at95percentconfidence level. 30