An agency problem in the MBS market and the solicited refinancing channel of large-scale asset purchases

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. An agency problem in the MBS market and the solicited refinancing channel of large-scale asset purchases John Kandrac and Bernd Schlusche 2015-027 Please cite this paper as: Kandrac, John and Bernd Schlusche (2015). “An agency problem in the MBS market andthesolicitedrefinancingchanneloflarge-scaleassetpurchases,”FinanceandEconomics DiscussionSeries2015-027. Washington: BoardofGovernorsoftheFederalReserveSystem, http://dx.doi.org/10.17016/FEDS.2015.027. 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.

An agency problem in the MBS market and the solicited refinancing channel of large-scale asset purchases John Kandrac∗ Bernd Schlusche‡ Federal Reserve Board Federal Reserve Board March 31, 2015 ABSTRACT In this paper, we document that mortgage-backed securities (MBS) held by the Federal ReserveexhibitfasterprincipalprepaymentratesthanMBSheldbytherestofthemarket. Next, we show that this stylized fact persists even when controlling for factors that affect prepayment behavior, and thus determine the MBS that are delivered to the Federal Reserve. After rulingoutseveralpotentialexplanationsforthisresult, weprovideevidencethatpointstoan agencyprobleminthesecondarymarketforMBS,whichhasnotpreviouslybeendocumented, as the most likely explanation for the abnormal prepayment behavior of Federal Reserve-held MBS. This agency problem—a key feature of the MBS market—arises when originators of mortgages that underlie the MBS no longer share in the prepayment risk of the securities, thereby increasing incentives to solicit refinancing activity. Therefore, Federal Reserve MBS holdingsacquiredfromoriginatorsasaresultoflarge-scaleassetpurchasescanhelpstimulate economic activity through a so-called “solicited refinancing channel.” Finally, we provide an estimate of the additional refinancing activity resulting from the solicited refinancing channel in the years after the Federal Reserve’s first MBS purchase program, demonstrating that this channel conveyed savings on monthly mortgage payments to homeowners. JEL classification: E52, G01, G21, R38 Keywords: QE, LSAP, mortgage-backed securities, monetary policy, Federal Reserve, mortgage, prepayment rates ∗BoardofGovernorsoftheFederalReserveSystem. E-mail: john.p.kandrac@frb.gov. Tel.: +12029127866. ‡BoardofGovernorsoftheFederalReserveSystem. E-mail: bernd.schlusche@frb.gov. Tel.: +12024522591. We are grateful for helpful comments from Kunal Gooriah, Jeff Huther, Beth Klee, Paul Kupiec, Linsey Molloy, Daniel Newman, Tomasz Piskorski, Roman Shimonov, Zhaogang Song, and Nate Wuerffel, as well as seminar participants at the Board of Governors, the Federal Reserve Bank of New York, and the Federal Reserve Bank of SanFrancisco. WethankJoeKachovecandWeiZhengfortheirexcellentresearchassistance. Theviewsexpressed inthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsofthe Board of Governors of the Federal Reserve System or of anyone else associated with the Federal Reserve System.

1. Introduction The Federal Reserve’s response to the financial crisis that reached a climax in 2008 entailed a number of unconventional policy measures. Initially, various credit and liquidity facilities were implemented in order to ease pressure in financial markets, which put considerable downward pressure on interest rates. As short-term interest rates approached their zero lower bound and the economy remained weak, the Federal Reserve initiated the first of several large-scale asset purchase (LSAP) programs (also known as quantitative easing or QE) in an attempt to spur a more rapid recovery in financial conditions and the economy. Among all of the unconventional policy measures, these LSAP programs that involved purchases of a various mix of Treasury securities, agency debt, and agency mortgage-backed securities (MBS) have garnered the most attention among financial market participants and academics.1 Indeed, the adoption of QE by central banks in response to the recent financial crisis provided the opportunity for researchers to empirically evaluate the effects of these programs and assessthedegreetowhichsuchprogramscanberelieduponbycentralbanksrestrictedbythezero lower bound. A primary goal of LSAPs is to increase the prices of the aforementioned securities and their close substitutes, thereby lowering longer-term interest rates important to economic activity (Bernanke (2010)).2 Consequently, studies evaluating the effects of QE have focused almost exclusively on the effects of central bank securities purchases and holdings on asset prices andyields(e.g.,Gagnonetal.(2011),KrishnamurthyandVissing-Jorgensen(2011),Hancockand Passmore (2011), Neely (2012), D’Amico and King (2013), and Gilchrist and Zakrajˇsek (2013)). In this paper, we analyze the prepayment behavior of MBS held in the Federal Reserve’s System Open Market Account (SOMA) portfolio after the first QE program. We document that MBS held by the Federal Reserve exhibit higher principal prepayment rates than similar 1Throughout the paper, we use the term “MBS” to refer to securities backed by residential mortgages but not those backed by commercial mortgages. 2The theoretical basis for this mechanism is captured in preferred habitat and portfolio balance theories, both of which rest on the presumption that the relative price of an asset is, to a considerable extent, dependent on the amount of the asset that is available to investors as a result of imperfect substitutability. These theories go back to Modigliani and Sutch (1966) and Tobin (1969), but have recently garnered popularity as studies have added rigorousmicrofoundationstothesetheories(see,forexample,Andresetal.(2004)andVayanosandVila(2009)). 1

MBS held by the market and provide several explanations for this result.3 Specifically, we show that the difference in prepayment rates is, to a large extent, explained by the Federal Reserve’s practice of conducting its MBS purchases in the to-be-announced (TBA) market; MBS in the TBA market trade on a “cheapest-to-deliver” basis and, consequently, the Federal Reserve was delivered MBS that carry relatively high prepayment risk.4 According to our results, however, a substantial portion of the difference in prepayment rates of Federal Reserve-held and market-held MBS cannot be attributed to factors that primary dealers would have used to determine which MBS to deliver into TBA contracts. We then investigate several potential explanations that may account for the “unexplained” difference in prepayment rates. Based on our test results, the most likely explanation for the faster prepayment speeds of Federal Reserve-held MBS is that an agency problem arises once the originators of mortgages that underlie the MBS no longer share in the prepayment risk of those MBS once they are sold to the Federal Reserve. A similar agency problem is often cited to explain the otherwise puzzling prepayment behavior exhibited by mortgages that are originatedbythirdparties(LaCour-LittleandChun(1999)). Infact,theincentivesforthirdparty originatorsto“churn”mortgageborrowersinordertoearnrefinancingfeesarestrongenoughthat mortgage lenders include non-solicitation clauses in their agreements with mortgage brokers or loancorrespondentsthatselltheirmortgageproducts. However,sincenon-solicitationagreements areinterpretedverynarrowly,andsincemonitoringandenforceabilitymaybeprohibitivelycostly, mortgagesoriginatedbythirdpartiesexhibitnotablyhigherratesofprepayment. Similarly,when aninvestor(suchastheFederalReserve)purchasesMBS,someofthesecuritieswillbepurchased from the institution that originated the mortgages.5 Importantly, the originating institution no 3Although Krishnamurthy and Vissing-Jorgensen (2013) and Himmelberg et al. (2013) note that mortgage poolsheldbytheFederalReserveprepayfasterthanmatchedpoolsnotheldbytheFederalReserve,neitherstudy empirically investigates whether the difference in prepayment speeds can be fully explained by the characteristics of the securities. 4In fact, the removal of prepayment risk from private portfolios—one of the underlying presumptions of the asset-priceeffectsidentifiedintheaforementionedstudies—wasagoaloftheFederalReserve’sMBSpurchases. As for MBS, the price effect from the Federal Reserve’s purchases comprises a duration effect—that is, a decrease in investors’requiredcompensationforbearinginterestraterisk—andaconvexityeffect,whichdescribesthedecrease in compensation for bearing the prepayment risk associated with holding MBS. 5Sincethefinancialcrisis,themajorityofmortgagesareoriginatedbythefourlargestbanks,whichalsoservice 2

longer shares in the prepayment risk of the MBS or, to the extent that only a portion of the MBS is purchased, bears less of the prepayment risk than prior to the QE program. Consequently, mortgage lenders have a higher incentive to solicit refinancings for previously extended loans that havebeentransferredoffoftheirbalancesheetsalongwithmuchoftheprepaymentrisk. Focusing on Federal Reserve MBS holdings acquired as a result of QE1, we use regression and propensity scorematchingtechniquestodemonstrateeconomicallysignificantabnormalprepaymentactivity of between two and six percentage points in the two years after the end of QE1. An agency problem that generates higher prepayment rates for Federal Reserve MBS holdings highlights a new transmission mechanism by which QE can work, which we refer to as the “solicited refinancing channel.” Because MBS prepayments are overwhelmingly driven by refinancing activity rather than ongoing curtailment payments, more rapid prepayment rates imply savings for homeowners on their monthly mortgage payments. These monthly savings could translate into higher levels of consumption and/or more rapid improvements in household balance sheets, which may have been particularly important in the years since the recession. Thus, if the Federal Reserve purchases MBS that would have otherwise remained on the balance sheets of banks and other originators, QE programs can have stimulative effects that work through channels operating alongside those that affect asset prices and generate reductions in longer-term interest rates. Of course, the potency of this channel depends on the presence of the asset price channels identified in previous work, because the extent of the fall in interest rates will determine the total savings homeowners can realize through refinancing. We present estimates that, as a result of MBS purchases associated with QE1, the solicited refinancing channel can account for at least $16 billion in additional refinancing activity over the following years. Therefore,theliteraturedocumentingtheeffectsoftheFederalReserve’sLSAPsonratesin primary and secondary mortgage markets is most relevant for our study.6 For example, Hancock the majority of the MBS in our sample. Large institutions securitize whole loan mortgages for various reasons, including beneficial liquidity characteristics, credit guarantees provided by the GSEs, and regulatory benefits conveyed by the lower capital risk weights carried by MBS. 6MostotherstudiesoftheFederalReserve’sLSAPsfocusontheireffectsonTreasuryyields. Forexample,using a cross-sectional dataset at the security-level, D’Amico and King (2013) document a statistically significant and economically meaningful impact of the Federal Reserve’s Treasury purchases on yields of Treasuries and of their 3

and Passmore (2011) find that the Federal Reserve’s MBS purchases as part of the first LSAP programsignificantlyloweredmortgagerates. KrishnamurthyandVissing-Jorgensen(2011)study the effects of the first two LSAP programs across several asset classes, and conclude that MBS purchases were indeed effective in lowering MBS yields. In contrast, Stroebel and Taylor (2012) find that after controlling for prepayment and credit risks, only a small portion of the declines in mortgage spreads can be explained by the purchase programs. OurstudyisalsorelatedtoFusterandWillen(2010)whofocusontheeffectsofQE1onthe primary market for MBS. Using event study methodology, Fuster and Willen (2010) document an increase in refinancing activity upon program announcement and show that this increase is attributable to sharp declines in mortgage rates following the program announcement. Our study differs from Fuster and Willen (2010) because we document that Federal Reserve MBS ownership may lead to an increase in refinancing activity for those MBS over and above that caused by a decrease in mortgage rates. That is, even though the potency of our channel depends on the presenceofinterestrateeffectsasaresultofQE1, itsexistenceisexplainedbyanagencyproblem in the secondary market for MBS that is induced by Federal Reserve MBS ownership, as opposed to the asset price effects of QE1. This agency problem represents an interesting and important featureoftheMBSmarketand,tothebestofourknowledge,hasnotpreviouslybeendocumented in the literature. Theremainderofourpaperproceedsasfollows: Section2describespertinentdetailsofthe Federal Reserve’s MBS purchases during QE1, with a focus on the to-be-announced secondary market for MBS. Section 3 describes the data. Section 4 presents the empirical methods and discusses the results. Section 5 discusses possible explanations for the abnormal prepayment speeds of Federal Reserve-held MBS. Section 6 describes the “solicited refinancing channel” and demonstrates the contribution of this channel to additional refinancing activity subsequent to QE1. Section 7 concludes. close substitutes. Other studies, such as Swanson (2011), Gagnon et al. (2011), and Wright (2012), rely on event studiestoprovideevidenceforsignificanteffectsoftheFederalReserve’sTreasurypurchaseprogramsonTreasury yields. Focusingonthe“defaultriskchannel”,GilchristandZakrajˇsek(2013)findthattheLSAPannouncements led to substantial reduction in the cost of insurance against corporate defaults. 4

2. QE1 MBS Purchases and the To-Be-Announced MBS Market On November 25, 2008, the Federal Reserve announced that it would initiate a program to purchase$100billionofdirectgovernment-sponsoredenterprise(GSE)debtandupto$500billion in GSE-guaranteed MBS (also referred to as agency MBS). This program—which came to be known as QE1 as it represented the first of several large-scale asset purchase programs conducted by the Federal Reserve—was undertaken to reduce the cost and increase the availability of credit available to homeowners, which would in turn support housing markets and foster improved conditions in financial markets more generally. Due to the specialized technological and operational requirements associated with MBS purchases, the Federal Reserve retained several investment managers to transact in the agency MBS market. Hiring agents to act on behalf of the Open Market Trading Desk (the Desk) at the Federal Reserve Bank of New York (FRBNY) allowed for a quicker and more efficient implementation of the MBS program, which began on January 5, 2009 and continued thereafter on a daily basis. Although the investment managers worked in close consultation with staff at the Desk, employing outside firms to execute the MBS purchases potentially presented an agency risk. Importantly, in order to accommodate the relatively large purchases under the program, the investment managers conducted transactions in the highly liquid to-be-announced (TBA) market. The TBA market allows for the forward trading of agency MBS based upon a handful of parameters under which mortgage pools can be considered interchangeable. At the time of a trade in the TBA market (which may take place up to three months prior to settlement), only the issuer, maturity, coupon, face value, price, and the settlement date are agreed upon. Thus, buyers in the TBA market agree to purchase MBS at a future date without knowing the CUSIPs that will ultimately be delivered. Two days prior to the contracted settlement date, the seller of the agency MBS will notify the buyer of the identity of the MBS pools that will be delivered to honor the transaction. 5

As a result of this information asymmetry, TBA transactions trade on a “cheapest-todeliver” basis because the seller selects the lowest value securities among eligible MBS in their inventory.7 The primary source of differences in agency MBS valuations—and therefore the primary determinant of the cheapest-to-deliver securities—is prepayment risk. Although the GSEs impose standards for the mortgages that underlie securitized mortgage pools eligible for the TBA market, variation in loan sizes, age, geography, and other characteristics can be used to identify MBS that are likely to see higher prepayment rates. Nevertheless, over 90 percent of agency MBS trading takes place in the TBA market (Vickery and Wright (2013)) and, when compared to other U.S. fixed income markets, daily trading volumes are second only to those observed in the market for U.S. Treasuries. Following their meeting on March 18, 2009, the FOMC released a statement that allowed for an additional $750 billion of agency MBS purchases, bringing total authorized purchases to $1.25trillion. Atthesamemeeting,theFOMCalsodecidedtoexpandagencydebtpurchasesand purchase$300billionoflonger-termTreasurysecurities. Asthen-ChairmanBernankewouldlater explain,aprimarygoalofthesepurchaseswastoincreasethepricesofthepurchasedsecuritiesand theirclosesubstitutes, therebyloweringlonger-terminterestratesimportanttoeconomicactivity (Bernanke (2010)). In September of that year, the FOMC committed to purchase the full $1.25 trillion of agency MBS, and explained that the purchase program would be completed in March of 2010. A few weeks prior to the end of QE1, internal staff at the Desk began executing agency MBS purchases, alternating trading days with the sole remaining outside investment manager. However, purchases continued to be conducted in the TBA market, and therefore nearly all MBS settlement associated with QE1 had taken place by June 2010.8 Table 1 contains a summary of the operations conducted as part of QE1. As shown in the table, purchases were concentrated in Fannie Mae and Freddie Mac securities with a 30-year 7ThisfeatureoftheTBAmarketisanalogoustotheTreasuryfuturesmarket,whichalsotradesonacheapestto-deliverbasis. FormoreinformationonthisandothercharacteristicsoftheTBAmarket,seeVickeryandWright (2013). 8As of June 2010, $9.2 billion of Fannie Mae 5.5 percent coupon securities had yet to settle. As a result, the Open Market Trading Desk conducted coupon swap operations in order to acquire agency MBS that were more readily available for settlement. For the purposes of our analysis below, we ignore these securities. 6

original term to maturity. Note that, per TBA guidelines, coupon rates on TBA transactions vary in 1/2 percent increments, reflecting the MBS pools that will be delivered. We now turn to a discussion of our data, which includes a description of the filters and controls that can be used to appropriately compare Federal Reserve holdings with a wider universe of TBA-eligible MBS. 3. Data InordertoevaluatetheeffectofFederalReserveMBSownershiponprepaymentrates, werequire data on Federal Reserve MBS holdings and characteristics for the universe of agency MBS. First, wecompilealistofMBSCUSIPsheldintheFederalReserve’sSOMAportfolio,whichispublished onaregularbasisbytheFRBNYandmadeavailableviatheirwebsite. Inordertoachieveamore homogenous set of MBS, we keep only 30-year MBS that were issued by Fannie Mae and Freddie Mac.9 As summarized in Table 1, these securities were by far the most commonly purchased during QE1. Beginning our sample in June 2010 (three months after the end of the QE1 MBS purchases), the remaining principal balance of these securities held in the SOMA portfolio was about $980 billion. Note that this figure is slightly below the par value of purchases of these securities, which totaled about $1.08 trillion. This difference can be attributed to principal payments received on the purchased securities over the course of QE1. Next, we use data provided by eMBS Inc. (a widely referenced MBS analytics provider) to compile characteristics for the universe of 30-year Fannie Mae- and Freddie Mac-issued MBS that were TBA-eligible as of June 2010. Of these securities, we keep only those securities with fixed-coupons that were purchased by the Federal Reserve during QE1 (shown in the top panel of Table 1). Since Federal Reserve MBS purchases were concentrated in relatively unseasoned MBS, we remove those MBS with production years—also known as “vintages”—that are much older than those held in the SOMA portfolio. More specifically, for each coupon, we identify the production years that compose at least 95 percent of Federal Reserve holdings, and drop all earlier vintages. This results in a sample that contains the following vintages (by coupon): 2009 9Becauseweconductmuchofouranalysisatthecoupon-level,wealsoexcludethe3.5percentcouponsecurities since only 36 CUSIPs were delivered to satisfy less than $250 million in purchases. 7

orlaterforthe4.0percentcoupon, 2005orlaterforthe4.5percentand5.0percentcoupons, 2003 or later for the 5.5 percent coupon, and 2006 or later for the 6.0 percent and 6.5 percent coupons. Additionally, we drop those CUSIPs in each coupon that have prefix identifiers other than those purchased by the Federal Reserve.10 Finally, we remove pools with fewer than 25 loans (though the results below are not sensitive to the precise cutoff). These low-loan pools are dropped since monthly prepayment rates can become outliers when even a single refinancing occurs. In total, these filters reduce the universe of CUSIPs in our sample from 323,836 to 84,535. Figure1displaysthesubstantialdifferencesinmonthlyprepaymentratesbetweensecurities heldinSOMA(thedashedlines)andthoseheldbythemarket(thesolidlines)overthe24months immediatelyfollowingQE1. Comparedwithsecuritiesheldbyprivateinvestors,prepaymentrates are systematically higher for securities purchased during QE1 and held in the SOMA portfolio. The inset tables in each panel of Figure 1 list the total prepayment rates realized from June 2010 through June 2012. Averaging across the coupon stack displayed in 1, prepayment rates on securities held in the SOMA portfolio were about 7 percentage points faster over this two-year period. Weighting by the number of CUSIPs in each coupon reveals that SOMA-held MBS had prepayment rates that were just over 9 percentage points faster than market-held securities. In Table 2, we present selected descriptive statistics for our sample. For each coupon, we distinguish between those CUSIPs that are held by the Federal Reserve (labeled “SOMA”) and those that are not (labeled “Market”). As expected based on the discussion in the previous section, SOMA securities indeed possess some features consistent with faster prepayment rates. For example, SOMA-held MBS have a larger weighted-average loan size and, where differences are large, SOMA securities were more heavily backed by mortgages originated by a third party (TPO share).11 However, systematic differences in other characteristics between SOMA- and 10Pool prefixes are used to identify important characteristics of the mortgages that underlie each CUSIP. For example, pools of adjustable-rate mortgages will have a different prefix identifier than a 30-year fixed rate pool, whichwillinturnhaveadifferentprefixidentifierthana15-yearfixedratepool. Importantly,prefixidentifierscan be used to indicate which securities will command a premium in the specified pool market rather than trading in the TBA market. For more examples of prefix identifiers, see http://www.fanniemae.com/resources/file/mbs/ pdf/pool-prefix-glossary.pdf. The list of prefix identifiers purchased by the Federal Reserve for each coupon is available from the authors upon request. 11Detailed descriptions of the data in Table 2 can be found in the table notes. 8

market-held securities are either smaller than one might naively expect, or nonexistent. This relative similarity is likely due to a combination of two factors. First, our exclusion criteria detailed above likely removed many market-held MBS that would have traded in the specified pool market and would thus not be considered part of the cheapest-to-deliver cohort traded in the TBA market. Second, a reasonable amount of homogeneity is imposed on MBS eligible for TBA trading, as outlined in Vickery and Wright (2013). For example, the securitization process involves a relatively limited number of issuers, is likely to produce geographic diversification, and sets restrictions on interest rates deliverable into a single security. Moreover, loans eligible for agency securitization are subject to constraints on loan size, borrower types, and minimum down payments. A third reason for the relative similarity between the SOMA and market portfolios is that primary dealers, with whom the Federal Reserve transacts, may have not been able to efficiently select among their inventory given the large volume of Federal Reserve purchases. Similarly, the expectation of rising rates during QE1, as implied by the swap curve, may have reducedtheincentiveofinvestorstodeliverfasterprepayingsecurities. Thisisbecauseaprincipal prepayment that is made at par may be attractive to an investor that is holding an MBS that is trading at a discount. 4. Empirical Methods and Results 4.1. Regression Results In order to quantify the extent to which abnormal prepayment rates of SOMA-held MBS are explainedbycheapest-to-delivercharacteristicsofthesesecuritiesversuseffectsrelatedtoFederal Reserve ownership, we begin by running cross-sectional regressions of CUSIP-level prepayment rates on a dummy variable indicating Federal Reserve ownership and a set of control variables. Formally, we estimate the following regression separately for each coupon: TPR = α+βFed ownership +γ(cid:48)x +ε , (1) i i i i 9

where TPR denotes the total prepayment rate of CUSIP i, computed as the amount of prepayi mentsonsecurityifromJune2010throughJune2012dividedbytheremainingprincipalbalance as of June 2010. Importantly, TPR excludes scheduled principal payments. The explanatory i variable of interest, Fed ownership , is a dummy variable that equals one if security i is held i by the Federal Reserve and zero otherwise. The vector x contains control variables that have i previously been shown to affect prepayment speeds (see, for example, Archer et al. (1996) and Green and LaCour-Little (1999)) and are used by dealers to determine which securities to deliver into TBA contracts. The first two control variables are loan age and (loan age)2, which capture the non-linear effectsofagingonasecurity’sprepaymentrisk. Generally,borrowersaredisinclinedtorefinancea recentlyclosedmortgageormovetoadifferenthomeimmediatelyafterpurchasingaproperty. As a result, prepayment rates are normally very low in the months following mortgage closing before ramping up substantially and leveling off. A very seasoned security, however, may be subject to a “burnout” effect. Burnout describes the phenomenon that loan pools become less responsive to refinancing incentives over time. This is because those borrowers that have failed to take advantage of previous refinancing opportunities—perhaps because of higher refinancing costs— are less likely to refinance in the future. In order to account for differential prepayment incentives across pools, we include the weighted-average coupon on the underlying loan pool as a control variable. Furthermore, we include the weighted-average loan size of a pool in our set of controls; securities with small loan sizes are likely to prepay more slowly than securities with larger loan sizesbecauseitismoredifficultforborrowerswithsmallloanstofinanciallyjustifythefixedcosts of refinancing. Moreover, we include the interaction term coupon × loan age as the relationship between the refinancing incentive and prepayment may depend on the age of the loans in a pool. More seasoned pools may respond more slowly to the same refinancing opportunity than less seasoned pools. Factor, which is the fraction of the original principal balance that remains to be repaid, is added as a control variable as it is indicative of the cumulative refinancing a security has experienced. Even though somewhat related to loan age, factor may capture persistence 10

in prepayment speeds. Finally, we include a dummy variable that equals one if a security is Freddie Mac-guaranteed and zero otherwise. This variable allows us to control for differences in prepayment speeds between Freddie Mac and Fannie Mae securities. In some specifications, the weighted-average credit score (FICO), the share of loans originated by a third party (TPO share), and the share of loans in the pool that were originated as a result of a previous refinancing (refi share) are used as additional controls. Our priors for the first two variables are clear: a borrower with a strong credit history is more likely to refinance than a borrower with a lower credit score, and loans originated by a third party generally have increased prepayment risk. The effect of refi share on prepayment speeds is less clear as the variable does not differentiate between “rate refinancing” and “cash-out refinancing,” which tend to have opposite effects on prepayment speeds (see, e.g., Fabozzi (2005)). While rate refinancing may improve a borrower’s credit and therefore lead to an increase in prepayments, cash-out refinancing generally increases a borrower’s leverage and lowers her credit, leading to slower prepayments.12 Finally, vintage and geographic dummy variables are included in some specifications tocapturedifferencesinprepaymentspeedsbetweendifferentproductionyearsaswellasregional differences in prepayment behavior. We estimate equation (1) by coupon using ordinary least squares.13 Table 3 reports the average effects of Fed ownership and various control variables on prepayment rates for the two years following QE1. The first set of columns shows the estimation results for 4.0 percent coupon securities. We report these results for completeness but caution against drawing any conclusions from the estimates as these securities are unseasoned securities with very low prepayment rates that makes reliable inference very difficult.14 Turning to the baseline results for 4.5 percent coupon securities (reported in column (1)), 12During our sample period, rate refinancings are presumably predominant as a high rate of cash-out refinancings tends to occur in periods with solid home price appreciation and loose credit standards, neither of which characterized our sample period. 13Tomoreappropriatelymodelaproportionaloutcome,wealsoestimateafractionalresponsemodelusingGLM and obtain nearly identical results. These results are available from the authors upon request. 14Unlikeothercoupons,recallthatourexclusioncriteriaremovedall4.0percentcouponsthatwereproducedprior to QE1. Refinancings in such unseasoned securities can be driven by highly idiosyncratic factors. Consequently, traditional relationships between prepayments and various explanatory variables may not hold. 11

we obtain statistical significance for fed ownership and various control variables. The positive coefficient on loan age in conjunction with the negative coefficient on (loan age)2 reflect the expected aging-related prepayment path for MBS; prepayments initially increase as a security ages,thenleveloff,andfinallydeclinewhenasecuritybecomeswellaged. Asexpected,thehigher the weighted-average coupon and the larger the weighted-average loan size of the underlying loan pool, the higher the prepayment rate. The negative coefficient on factor suggests that the more has repaid in a pool the higher is the subsequent prepayment rate. This result could be due to persistence in prepayment speeds. Consistent with our prior, we obtain a negative coefficient estimate for the interaction variable coupon × loan age; that is, the more seasoned a security, the weakerprepaymentsforaparticularlevelofrefinancingincentiveasthesavingsfromarefinancing are lower for aged loans all else equal, and may not justify incurring refinancing fees. Moreover, we find that Freddie Mac securities exhibit faster prepayments than otherwise identical Fannie Mae securities. Importantly, even after accounting for cheapest-to-deliver effects by conditioning on various factors that explain prepayment behavior of MBS, securities held by the Federal Reserve prepay more quickly than those securities not held in SOMA, as indicated by the significantly positive coefficient estimate on Fed ownership. As shown in column (2), these results are mostly insensitivetotheinclusionofvintage andgeographic dummy variables, thoughthesedummiesare frequently included in prepayment models and their inclusion increases the explanatory power of the regressions. Similarly, the results are qualitatively the same when adding FICO, TPO share, and refi share as additional controls (see columns (3) and (4)) and, in fact, the coefficient on Fed ownership is the largest in these specifications. Not surprisingly, we find that pools with a higher credit score are more likely to prepay than worse credits, as indicated by the coefficient on FICO. Finally, both TPO share and refi share are positively correlated with prepayment speeds. For the sake of brevity, we focus the discussion for all remaining coupons—that is, 5.0 - 6.5 percent coupons—on the results for the Fed ownership variable. In the baseline specification, the coefficientestimatesonFed ownership rangefrom2.2to5.3andarehighlystatisticallysignificant. 12

The inclusion of additional controls does not render the coefficient estimates insignificant. As before,FederalReserve-heldsecuritiesexhibitsignificantlyfasterprepaymentbehavior,evenafter controllingforfactorsthatdealersusetodeterminewhichsecuritiestodeliverintoTBAcontracts. In economic terms, securities held by the Federal Reserve experienced, on average, abnormal prepayments of up to 5.3 percentage points over the period from June 2010 to June 2012. As was the case for the 4.5 percent coupon, the coefficients on various control variables, in general, carry the expected signs and are highly statistically significant. Although qualitatively the same across coupons, the coefficient estimates on the control variables vary a bit in magnitude. Finally, as indicated by the adjusted R-squared figures in the last row of the table, a significant portion of the variation in prepayment rates is explained by our regression model. Moreover, including the share of the remaining principal balance held by the Federal Reserve, rather than the Fed ownership dummy, yields qualitatively similar results. As shown in Table 4, we obtain statistically positive coefficient estimates for Fed share for all coupons but the 4.0 percent coupon, which suggests that the abnormal prepayment behavior is stronger for those securities that the Federal Reserve holds in larger amounts. In the baseline specification, the estimates range from 2.8 to 6.7. Furthermore, the effect is robust to the inclusion of additional control variables in specifications (2)-(4). Importantly, even though the finding that abnormal prepayments are larger for securities held by the Federal Reserve in large amounts does not rule outthepossibilitythatourresultsareduetoamisspecifiedmodel,itdoesunderminethisconcern and points to a causative effect of Federal Reserve ownership. The estimated effects of various controls are very similar to those in Table 3 when Fed ownership is used as the explanatory variable. As a robustness check, we pool all securities and re-run the regression model specified in equation(1). Forthesepooledregressions,wealsoincludecoupon-vintagedummiesincomespecifications. The first set of columns in Table 5 presents the estimation results when Fed ownership is used as the key independent variable and the second set reports the results when Fed share is used. As before, the estimates for the control variables have the expected sign and, in general, 13

are statistically significant. Importantly, the relationship between Federal Reserve ownership and prepayment rates documented previously holds in the pooled regression framework.15 The coefficient estimates on both Fed ownership and Fed share are highly statistically significant in various regression specifications. The size of the coefficient on Fed ownership in specification (4) implies that securities held by the Federal Reserve show prepayment rates that—after controlling for other factors that determine prepayment speeds—are about 3.4 percentage points higher than they would otherwise be. Comparing the estimates from Table 5 with the prepayments from Figure 1 indicates that a substantial proportion of the total prepayment differences cannot be accounted for by the characteristics used to identify cheapest-to-deliver MBS. Although a prepayment difference of three percentage points over the course of two years may seem relatively small, there are reasons why a more sizable measured effect may not be expected, as we will discuss in more detail below. Nevertheless,thelargeparamountofFederalReserveholdings(approximately$1trillion)implies that Federal Reserve MBS ownership can explain roughly $30 billion of additional refinancings over this period. 4.2. Propensity Score Matching Results According to the results presented above, the effect of Federal Reserve ownership on prepayment rates is robust to different regression specifications. Furthermore, unreported results show that the inclusion of additional interactions and control variables as well as higher powers of the control variables do not materially change the results. Nevertheless, our findings may be the result of model misspecification if we are not controlling accurately for all factors that may affect prepayment behavior. In other words, our observed result could simply reflect the nature of the TBAmarketdiscussedabove,whichimpliesthattheFederalReservewouldreceivesecuritiesthat trade on a cheapest-to-deliver basis. Of course, the finding that prepayment speeds increase in the share of the CUSIP held by the Federal Reserve provides some remedy against this concern. 15The inclusion of the 4.0 percent coupon securities attenuates the magnitude of these coefficients somewhat. 14

However, an alternative strategy to account for the likelihood that the Federal Reserve was delivered only those MBS that were cheapest-to-deliver is to use propensity score matching (PSM). Rather than relying on a parametric model that must be correctly specified, the goal of PSM is to non-parametrically balance characteristics of different MBS. In this way, MBS held in the SOMA portfolio can be matched to securities that are very similar across characteristics used to identify cheapest-to-deliver securities. Identifying market-held securities that are also traded on a cheapest-to-deliver basis as of June 2010 allows us to compare the prepayment outcomes of the treated (SOMA-held) MBS with the control (market-held) MBS to achieve an estimate of the causal effect of Federal Reserve ownership. Given conditions outlined in Rosenbaum and Rubin (1983), the propensity score matching estimator can be written as follows: ATTPSM = E(TPR |SOMA = 1,Pr(SOMA = 1|x))−E(TPR |SOMA = 0,Pr(SOMA=1|x)). 1 0 (2) The propensity score matching estimator can be interpreted as the average difference in prepaymentratesbetweensecuritiesheldinSOMA(TPR )andthoseheldbythemarket(TPR ), 1 0 weighted by the propensity score distribution of delivery into the SOMA portfolio (Pr(SOMA = 1|x)). To generate propensity scores for each security, we estimate a probit model using securitylevel characteristics described in Table 2, along with a host of additional variables including indicators of production years, geographic representation, and mortgage servicers. We then use a nearest neighbor matching estimator to identify MBS that were not delivered to the Federal Reserve but would have also been considered cheapest-to-deliver.16 In this way, we are able to estimate the so-called “average treatment effect on the treated” (ATT) securities—that is, the additional prepayments on securities as a result of acquisition by the Federal Reserve—which we report in Table 6. While we do not find discernable treatment effects for the 4.0 percent and 4.5 percent coupon securities, we find highly statistically significant effects that are economically meaningful for other coupons. The strongest treatment effect is documented for the 5.5 percent 16Employing a local linear regression matching estimator produces very similar results. 15

coupon, and indicates that Federal Reserve ownership leads to a prepayment rate that is about 4.6 percentage points faster than it would have otherwise been. Table6alsoreportspseudoR-squaredvaluesoftheprobitmodelbeforeandaftermatching, which demonstrate that adequate balancing was achieved. This is especially true for the higher coupons, which offer a richer set of control (market-held) MBS with which Federal Reserve securities can be matched. Indeed, the relative dearth of market-held MBS in the 4.5 percent coupon may explain the insignificant results achieved for the ATT, though it is also likely that the young age of the loans and the high share of refinancings in these pools (see Table 2) limit the ability to detect differences between SOMA- and market-held securities. Furthermore, we report Rosenbaum bounds to determine how strongly an unmeasured confounding variable must affect selection into treatment in order to undermine the causal effects produced by the matching analysis (Rosenbaum (2002)). In other words, for the 5.5 percent coupon, the observed effect would still be significant even if hidden bias resulted in SOMA-held securitiesbeingmorethantwotimesaslikelytobedeliveredtotheFederalReservethanmatched market-held securities. Since the characteristics provided by eMBS are also those used by market participants to forecast prepayment rates, this degree of hidden bias owing to unobserved variables seems unlikely. Furthermore, in unreported results, we find that extending the comparison window beyond June 2012 increases minimum Rosenbaum bounds for all coupons and shows that SOMA-held 4.5 percent coupon securities eventually began prepaying at a quicker pace than similar market-held CUSIPs. Overall, the PSM results support the previously reported finding that higher-coupon securities held by the Federal Reserve experience substantially faster prepayment rates than comparable securities held by the market, and this difference cannot be explained by characteristics traditionally used to forecast prepayment rates. 16

5. Possible Explanations of the Abnormal Prepayment Rates ThepreviousresultsdemonstratethatMBSpurchasedbytheFederalReserveexhibitabnormally fast prepayment behavior that cannot be explained by the characteristics dealers use to identify cheapest-to-deliver securities. In this section, we discuss several possible explanations for this finding and present empirical evidence that points to a principal-agent problem in the MBS market as the most likely explanation. 5.1. Soft Information One possibility that could explain the results reported above is that banks may deliver securities based at least in part on the “soft” information gathered from their relationships with homeowners. For this to be the case, banks would have to use this information to identify borrowers that are more likely to prepay, and sell the MBS backed by these mortgages disproportionately to the Federal Reserve. Essentially, this would amount to an omitted variable correlated with Federal Reserve ownership. Although this possibility seems rather unlikely, we nevertheless perform a test to rule out this explanation for our results. Specifically, we identify a subset of MBS for which lenders are unlikely to possess soft information that would not be captured by characteristics detailed in eMBS, and run a similar set of regressions. Observing similar results to those reported for the full sample would indicate that the possession of soft information cannot explain the results achieved above. Table 7 presents an identical set of regressions to those included in Table 5, but limits the sample to those MBS for which third party originations compose more than 50 percent of the underlying mortgages. If soft information was used to deliver securities to the Federal Reserve, thecoefficientonFed ownership andFed share shouldbeverysmallorinsignificantforthissubset of MBS. However, as shown in Table 7, Fed ownership and Fed share maintain their explanatory power for TPR. Thus, it seems that soft information acquired through an origination and lending relationship is unable to explain the abnormal prepayment behavior of SOMA-held MBS. 17

5.2. Bundling of Whole Loans Another possible explanation of the anomalous prepayment behavior documented above is that banks selected from their whole loan portfolio to create new MBS that were then delivered to the Federal Reserve. This could have occurred in response to the very high MBS demand engendered byQE1. Ifthenewsecuritiesexhibitedhigherprepaymentratesandourregressionsabovedonot adequately capture drivers of prepayment speeds (perhaps because selection is at the individual loan level), we could incorrectly identify a significant effect of Federal Reserve ownership as a result. In order to test for this possibility, we split our original sample into MBS issued during the course of QE1 (2009 and 2010) and MBS issued prior to QE1. If selection of whole loans for delivery to the Federal Reserve were the cause of the unexplained prepayment differentials, we would expect that MBS issued in 2009 or later drive the results. However, as shown in Table 8, we find significant effects for MBS produced prior to the commencement of QE1. Similarly, Table 9, shows the results for production years 2009 and 2010, while QE1 was ongoing. The effect of Federal Reserve ownership persists for these securities, but is slightly weaker than for the rest of the sample. Thus, we can rule out the possibility that it is the selection from banks’ whole loan portfolios that drives the results reported in Section 4. 5.3. Delinquency Rates There is also the possibility that the abnormal prepayment behavior of MBS held by the Federal Reserve is driven by higher rates of delinquency and default, which may not be fully captured by, for instance, geographic controls, credit scores, and loan-to-value ratios. In this case, higher prepayment rates on securities delivered to the Federal Reserve could merely reflect involuntary prepayment behavior resulting from excessive delinquencies. We note, however, that the results reported above for securities produced in 2009 and 2010 suggest that the higher prepayments on securities held by the Federal Reserve are not due to delinquencies. Given the tight lending standards during this period, the stable house prices, and the relatively short time period used to 18

calculate the total prepayment rate, delinquencies for these securities over our observation period were likely minimal. Consequently, observing an effect for Federal Reserve ownership for this subsample suggests that voluntary prepayments are in fact driving the result. Nevertheless, we are able to account for the effect of delinquency-driven prepayment behavior more directly. Although only available for MBS issued by Freddie Mac, eMBS contains monthly figures for the share of prepayments that are due to agency repurchases of delinquent loans. Thus, we remove these involuntary prepayments from the total prepayment rate, and regress this value on our standard set of controls for Freddie Mac securities. Table 10 presents the results for total prepayment rates that are purged of delinquency repurchases. As evidenced by the positive and statistically significant coefficient estimates for both Fed share and Fed ownership, higher rates of involuntary prepayments cannot explain the abnormally high prepayment behavior of MBS owned by the Federal Reserve. Similarly, in unreported results, we find that including the share of each MBS that is backed by mortgages that are between 30 and 90 days past-due does not affect these results. 5.4. An Agency Problem in the Secondary MBS Market Finally, the above result may be explained by a principal-agent problem that is present in the secondary MBS market more generally. This agency problem can arise when an institution that originated the mortgages underlying an MBS no longer bears the prepayment risk of the security. Having transferred the prepayment risk to an outside investor (the principal), the originating institution (the agent) may wish to refinance mortgages it originated in order to generateincomefromrefinancingfees.17 Infact,asimilaragencyproblemisoftencitedtoexplain the otherwise puzzling prepayment behavior exhibited by mortgages that are originated by third parties (see, for example, LaCour-Little and Chun (1999)). These incentives are so pervasive that non-solicitation agreements are commonly included to protect lenders from the potential agency problem. However,investors(suchastheFederalReserve)simplypurchaseMBSinthesecondary 17Although mortgage originators may continue to be exposed to prepayment risk through a mortgage servicing asset(MSA),arefinancingasaresultofthisbehaviorwouldresultinamorevaluableMSAreplacingtheoriginal. 19

market,andthusnosuchnon-solicitationagreementcouldexist.18 Insulatedfromtheprepayment risk, a bank may face incentives to encourage a higher rate of refinancing activity subsequent to selling MBS. Because banks hold a substantial fraction of MBS outstanding, comparing the Federal Reserve’s MBS portfolio with that of the market, as we have done here, can reveal a significant difference in prepayment rates that would not be explained by the characteristics of the MBS if this mechanism is in operation. Notably, thismechanismwouldrepresentanimportantfeatureofthesecondarymarketfor MBS, because all MBS investors that purchase securities from originators face this agency risk by altering incentives as described above. Indeed, our conversations with staff at large mortgage originators and servicers suggest that this agency issue is widespread. Yet, to the best of the authors’ knowledge, this agency problem has remained undocumented in the literature. If the agency problem mechanism is indeed the cause of the observed prepayment differential between Federal Reserve- and market-held MBS, this mechanism would likely be strongest for large institutions. These institutions originate the majority of the loans and hold a significant amount of the securitized loans on their balance sheets. Therefore, large originators have a greaterincentivetoincurthefixedcostsofidentifyingwhichmortgagesbackwhichMBS,andwill devote resources accordingly. Thus, larger institutions have both the incentives and the ability to preferentially solicit refinancings from borrowers whose prepayment risk has been transferred to the Federal Reserve. Totestfordifferentialeffectsbetweenlargeandsmallinstitutions, wewouldideallyinclude originator information in the pooled regressions. While our dataset contains only limited data on loan originators, it furnishes information about the servicers of the loans. Using the plausible assumption that the four largest banks that originate the overwhelming majority of mortgages in the United States also service many of the originated loans underlying the MBS, we can exploit servicer information to draw inference on differential effects for large and small originators. To 18WewouldnotethatbecauseagoalofQEistoboosteconomicactivity,theFederalReservewouldbeunlikelyto desiresuchanagreementeventhoughitwouldreducetheconvexityriskofitsportfolio. Thisisbecauseincreased refinancingactivityistypicallyassumedtobestimulative(seeFusterandWillen(2010)andthereferencestherein.) 20

that end, we include dummy variables for the four largest U.S. bank holding companies (Bank of America, Citigroup, J.P. Morgan, and Wells Fargo) that equal one if a bank services the plurality of the mortgages in a pool and zero otherwise, as well as interactions of these dummies with Fed ownership and Fed share, respectively. These four banks are the dominant servicers in nearly 60 percent of the MBS in our sample. Table 11 reports the results for various regression specifications using Fed ownership on the left, and the results using Fed share on the right. As before,thecoefficientestimatesonFedownership andFedshare arehighlystatisticallysignificant, indicating that the agency problem mechanism exists in medium- to smaller-sized originators. Inbothsetsofresults, thecoefficientestimatesonthelarge-bankdummyvariablessupport the well-known fact that refinancing activity at Bank of America and Citigroup was more muted over this period; in contrast, J.P. Morgan and Wells Fargo refinanced more mortgages compared to other institutions. Moreover, the stark differences in prepayment rates for different originators underscore the ability of institutions to influence refinancing activity among their borrowers. Finally, in the specifications in which Fed ownership is used, the coefficients on the interaction terms suggest that the abnormal prepayment rates as a result of Federal Reserve ownership is even more pronounced for the four largest banks. This effect is the strongest for pools serviced by Wells Fargo. Interestingly, this result holds even for securities serviced by Bank of America that generally prepaid more slowly. It seems plausible that in light of capacity constraints over this period, any refinancing initiatives may have focused on securities no longer held by the bank. When Fed share is used, this effect remains evident, although the results are slightly weaker for Bank of America and Citigroup. In total, these results suggest that, although the channel is in effect for firms of all sizes, abnormally fast prepayment rates are even more pronounced among larger originators, consistent with an explanation that an agency problem mechanism is at work. Another implication of the mechanism we described above to explain the faster prepayments is that the estimated effect of Federal Reserve ownership on total prepayment rates would not steadily increase over time. Rather, banks would focus first on soliciting refinancings among the set of borrowers that would benefit from such a transaction and whose securitized mortgages 21

it no longer holds. Eventually, though, banks would exhaust this set of borrowers and monthly prepayment rates would be more similar between SOMA-held and bank-held securities (conditional on x ). Potentially, resources may then be used to refinance homeowners whose mortgages i securitize MBS held by the bank, leading to a tapering of the documented effect. In contrast, if the documented effect was the result of model misspecification—that is, if the cheapest-to-deliver featuresofMBSheldbytheFederalReservearenotproperlyaccountedfor—thentheperpetually higher prepayment risk of securities held by the Federal Reserve would imply that, each month, these securities prepay more than market-held securities and, consequently, the size of the observed effect would grow continuously over time.19 Thus, we run the pooled regressions outlined previously for different sample periods that extend beyond our baseline sample. Specifically, we keep the start date for the sample the same but extend the end date in increments of six months until the end of 2013. Figure 2 depicts the leveling-off of the effect over time. As shown in Panel (a), the estimated effect of Fed ownership on prepayment rates increases as the end date of the sample period is extended gradually from the second quarter 2011 to the end of 2012 but then tapers off. Analogously, Panel (b) presents the coefficient estimates on Fed share. The evolution of the effect is the same as that for Fed ownership depicted in Panel (a). Ultimately, this exercise provides additional evidence that the effect of abnormal prepayment behavior of Federal Reserveheld securities is likely due to an agency problem and not the result of improperly accounting for cheapest-to-deliver features of MBS acquired by the Federal Reserve. If this agency problem is indeed the explanation for faster prepayment rates on MBS held by the Federal Reserve, it is understandable that the size of the effect we observe would be relatively modest. First, to the extent that some MBS purchased by the Federal Reserve were not held by the originator shortly before QE1 purchases occurred, we may not expect a causative effect of Federal Reserve MBS ownership since the agency problem arises whenever MBS are transferred to any outside investor. Second, if MBS are held in different business units than the 19It is possible that a burnout effect could lead to a tapering of the measured effect as implied by the agency problem described above. However, the securities held by the Federal Reserve are relatively unseasoned, and the documented effect is therefore unlikely a result of burnout. 22

sales and mortgage origination divisions, it may be more difficult for a bank to identify which mortgages secure MBS held by the bank. Both of these factors could contribute to the modest size of the effect of Federal Reserve ownership on MBS prepayment rates. 6. The Solicited Refinancing Channel of Large-Scale Asset Purchases The existence of the agency problem in the MBS market described in the previous section can generate a “solicited refinancing channel” through which LSAPs may work. If the Federal Reserve’s MBS purchases reduce originators’ holdings of MBS, then these institutions would have a higher incentive to solicit refinancings among the mortgages backing the MBS they no longer hold. As banks respond to these incentives, homeowners realize savings on monthly mortgage paymentsasaresultofrefinancingactivitythatwouldnothaveotherwiseoccurred.20 Thesavings realized by homeowners on their monthly mortgage payments are typically assumed to generate an increase in consumer spending that in turn has stimulative economic effects (see, for example, Canner et al. (2002)). The savings for homeowners as a result of the additional prepayment effect documented in this study are likely a non-negligible factor in providing stimulus for the economy through increased consumer spending or a more rapid improvement in household finances. Of course, the magnitude of the increase in consumption depends on refinancers’ marginal propensity to consume out of monthly savings on mortgage payments and the incidence of cash-out refinancing. We take two approaches to estimate the amount of refinancing activity realized as a result of this channel. In each case, we must first estimate the reduction in banks’ MBS holdings as a consequence of Federal Reserve MBS LSAPs. First, we follow the methodology in Carpenter et al. (2015) and estimate various specifications of the following equation: ∆MBS = θ+φ∆Fed MBS +ψ(cid:48)x +ε , (3) t t t t 20Similarly, savings would be generated even if these incentives simply resulted in refinancings that occurred earlier than they would have if banks continued to hold the MBS on their balance sheets. 23

Inequation(3), ∆MBS denotesthechangeinbanks’MBSholdingsformontht, and∆Fed MBS t t captures the monthly change in Federal Reserve MBS holdings. Thus, the parameter φ measures the sensitivity of banks’ MBS holdings to Federal Reserve MBS holdings. The vector x denotes t control variables, which include the lagged difference of the stock of outstanding 30-year Fannie Mae and Freddie Mac MBS and one lag of the dependent variable. In other specifications, x t additionally includes three controls for changes within the banking sector—the lagged differences ofsystem-wideassets,capital,andrealestateloans—aswellasthreecontrolsforbroadereconomic and financial market conditions—the lagged value of the St. Louis Fed financial stress index, lagged industrial production growth, and the change in Treasury notes and bonds outstanding net of Federal Reserve holdings. To capture the potential for calendar-related changes in MBS holdings due to financial reporting requirements or other factors generating seasonality in the series, we also include monthly fixed effects in x .21 t Table12reportstheresultsfromtheestimationofequation(3). InTable12, thefirstthree columns report the results using the full sample period of January 1997 through June 2014. In the first column, the coefficient on Federal Reserve MBS holdings indicates an additional dollar of Federal Reserve MBS holdings is associated with a contemporaneous 8 cent decline in banks’ MBS holdings. However, the absolute value of this coefficient could be biased down for several reasons. For instance, banks could respond to the higher demand for MBS by securitizing more of their whole loans, or Federal Reserve MBS purchases could improve financial conditions more broadly, increasing banks’ willingness to expand their MBS portfolios. In order to control for such effects, columns (2) and (3) include the additional covariates outlined previously. In these specifications,theresponseofbanks’MBSholdingstoFederalReservepurchasesisabouttwiceas strong. Though the banking-system controls exhibit no statistically significant association with changes in MBS holdings, the economic and financial market controls are generally significant. 21Banks’ MBS holdings correspond to the data series published in the Federal Reserve’s statistical release H.8. Note that for the period prior to July 2009, the series is not publicly available. The stock of outstanding MBS is obtainedfromeMBSandthestockofoutstandingTreasurynotesandbondsheldbythepublicispublishedinthe U.S.Treasury’s“MonthlyStatementofthePublicDebtoftheUnitedStates.” Allotherseriesaremadeavailable by the Federal Reserve Bank of St. Louis through the Federal Reserve Economic Data (FRED) repository. 24

Of course, the Federal Reserve did not maintain MBS holdings until the beginning of LSAP1 in early 2009. Thus, the second set of specifications in Table 12 limits the sample to the months after the start of Federal Reserve MBS purchases and settlements in January 2009. In these specifications, we observe a similar downward bias of φ in the most basic specification. The coefficient of -0.31 reported in the richest specification (the final column of Table 12), implies that the Federal Reserve’s $1.25 trillion of MBS purchases in QE1 reduced banks’ MBS holdings by approximately $390 billion.22 Using the estimate from Table 5 that total prepayment rates on SOMA-held MBS were approximately four percentage points higher suggests that LSAP1 generated about $16 billion in additional refinancing activity over a two-year period. As a second approach to estimate the amount of refinancing activity realized as a result of the QE1 solicited refinancing channel, we gauge the reduction in banks’ MBS holdings by summing out-of-sample forecast errors during QE1. Below, we report coefficient estimates and robust standard errors (in parentheses) from a bank MBS holdings prediction equation estimated for the ten years from January 1997 to December 2006: ∆MBS = 0.13 ·∆MBS + 0.03 ·∆assets + 0.33 ·∆capital + 0.01 ·∆RE loans t t−1 t−1 t−1 t−1 (0.08) (0.04) (0.22) (0.18) +8.01 ·stress + 8.41 ·IP growth + 0.13 ·∆Treas outstanding t−1 t−1 t (4.11) (2.91) (0.06) +0.49 ·∆MBS outstanding +γ(cid:48)M +ε . (4) t−1 1−12 t (0.21) N = 120; R-squared = 0.24; DW stat = 1.98. Equation 4 corresponds to the final specification from the previous exercise, with the exception of the variable ∆Fed MBS , as Federal Reserve MBS holdings simply equal zero for all months t prior to 2009. Next, we use equation (4) to predict MBS holdings for the 18-month period during which QE1 MBS were delivered to the Federal Reserve. Figure 3 plots actual changes in banks’ MBS holdings versus the predicted values for the QE1 period of January 2009 through June 2010. The predicted change in banks’ MBS holdings was frequently greater than the actual change during QE1, though this pattern dissipated somewhat toward the end of the program 22We ignore the lagged dependent variable for this calculation as it is not statistically different from zero. 25

as the Desk gradually reduced MBS purchase amounts. Nevertheless, actual increases in banks’ MBS holdings were greater than predicted in only two months during QE1, and in total, banks’ actual MBS holdings were approximately $425 billion lower than predicted. Assuming that the Federal Reserve’s MBS purchases caused this deviation in MBS holdings, and again using the result that prepayment rates attributable to solicited refinancings were four percentage points higher implies that LSAP1 generated about $17 billion in additional refinancing activity over a two-year period—very close to the previous estimate of $16 billion. However, the $16-$17 billion estimate likely understates total refinancing activity as a result of this channel, since the difference in prepayment rates reported in Table 5 is achieved by comparing SOMA-held securities to all other similar CUSIPs rather than just the subset held by banks. Including the holdings of other MBS investors (such as asset managers or foreign central banks) in the comparison cohort produces a downward bias of the estimated effect of Federal Reserve ownership, since these securities are subject to the same agency problem as those held by the Federal Reserve. In addition, subsequent Federal Reserve MBS purchases—such as those associated with the MBS purchases of QE3—would have generated additional refinancings and savings for homeowners as a result of this channel. We note that, since 2009, the Federal Reserve has purchased over $3 trillion of MBS. Importantly, the refinancings that are produced by the solicited refinancing channel are in addition to those that occur simply as a result of the decline in interest rates per se, which could follow a QE-induced fall in interest rates regardless of the type of assets purchased under the program. Rather, the solicited refinancing channel arises because originators act as agents of MBSinvestorssuchastheFederalReserve, andcaninfluenceprepaymentratesthroughborrower outreach. Indeed, because there can be potentially important differences in the effects of central bank purchases depending on the type of asset purchased, many economists refer to these programs as LSAPs rather than QE, since QE has traditionally been used to describe an expansion of a central bank’s liabilities with little consideration for the composition of purchased assets (Bernanke (2009)). 26

7. Conclusion In this paper, we show that Federal Reserve-held MBS prepay significantly faster than MBS not held by the Federal Reserve. We then show that much of the prepayment differences cannot be explained by factors that are used by dealers to determine the cheapest-to-deliver securities sold to the Federal Reserve. Weassessfourpossibleexplanationsthatmayexplaintheshareofthedifferenceinprepayment rates between SOMA- and market-held MBS that is not explained by “cheapest-to-deliver” characteristics of the securities: 1) dealers may determine which securities to deliver based, in part, on soft information obtained through their business relationships with the borrowers; 2) banks may have selected from their whole loan portfolio loans with very high prepayment risk to create new MBS that they then delivered to the Federal Reserve; 3) dealers may have delivered securities that suffered from higher rates of delinquency and involuntary prepayments; and 4) an agency problem that arises because institutions that originated the mortgages backing a security no longer share in the prepayment risk of that security after it is purchased by the Federal Reserve, which can incentivize institutions to refinance mortgages that underlie MBS they no longer hold. Our test results point to the agency problem mechanism as the most likely explanation for the abnormal prepayment behavior of Federal Reserve-held MBS. Under this mechanism, originators are more likely to solicit refinancings from borrowers when the prepayment risk of the MBS has been transferred off of their balance sheets. Although this agency problem is an important feature of the secondary market for MBS, it has hitherto gone undocumented in the literature. We explain that the presence of this agency problem can generate a so-called “solicited refinancing channel” of large-scale MBS purchases by the Federal Reserve that can result in substantial refinancing activity. Higher prepayment rates as a result of Federal Reserve MBS ownership, in conjunction with a QE1-induced decrease in mortgage rates, lead to savings for borrowers on their monthly mortgage payments, which can improve household finances by 27

reducingdebt-serviceburdensforhouseholds. Althoughmodestcomparedwithotherdocumented channelsofQE,withlargeenoughMBSpurchases,thesolicitedrefinancingchannelcanhavenonnegligible stimulative effects for the economy. 28

References Abadie, Alberto, and Guido W. Imbens, 2006, Large sample properties of matching estimators for average treatment effects, Econometrica 74, 235–267. Andres, Javier, J. David L´opez-Salido, and Edward Nelson, 2004, Tobin’s imperfect asset substitution in optimizing general equilibrium, Journal of Money, Credit and Banking 36, 665–690. Archer, Wayne R., David C. Ling, and Gary A. McGill, 1996, The effect of income and collateral constraints on residential mortgage terminations, Regional Science and Urban Economics 26, 235–261. Bernanke, Ben S., 2009, The crisis and the policy response, Remarks at the Stamp Lecture, London School of Economics, London, England, January 13, http://www.federalreserve. gov/newsevents/speech/bernanke20090113a.htm. Bernanke, Ben S., 2010, The economic outlook and monetary policy, Remarks at the Federal Reserve Bank of Kansas City Economic Symposium, Jackson Hole, Wyoming, August 27, http://www.federalreserve.gov/newsevents/speech/bernanke20100827a.pdf. Canner, Glenn, Karen Dynan, and Wayne Passmore, 2002, Mortgage refinancing in 2001 and early 2002, Federal Reserve Bulletin 88, 469–481. Carpenter,Seth,SelvaDemiralp,JaneIhrig,andElizabethKlee,2015,AnalyzingFederalReserve asset purchases: From whom does the Fed buy?, Journal of Banking & Finance 52, 230–244. D’Amico, Stefania, and Thomas B. King, 2013, Flow and stock effects of large-scale Treasury purchases: Evidence on the importance of local supply, Journal of Financial Economics 108, 425–448. Fabozzi, FrankJ., 2005, The Handbook of Mortgage-Backed Securities, 6thedition(McGraw-Hill, New York). 29

Fuster, Andreas, and Paul S. Willen, 2010, $1.25 trillion is still real money: Some facts about the effects of the Federal Reserve’s mortgage market investments, Federal Reserve Bank of Boston, Public Policy Discussion Paper 10-4. Gagnon, Joseph, Matthew Raskin, Julie Remache, and Brian Sack, 2011, The financial market effects of the Federal Reserve’s large-scale asset purchases, International Journal of Central Banking 7, 3–43. Gilchrist, Simon, andEgonZakrajˇsek, 2013, TheimpactoftheFederalReserve’slarge-scaleasset purchase programs on corporate credit risk, Journal of Money, Credit and Banking 45, 29–57. Green, Richard K., and Michael LaCour-Little, 1999, Some truths about ostriches: Who never refinances their mortgage and why they don’t, Journal of Housing Economics 8, 233–248. Hancock, Diana, and Wayne Passmore, 2011, Did the Federal Reserve’s MBS purchase program lower mortgage rates?, Journal of Monetary Economics 58, 498–514. Himmelberg, Charles, Marty Young, Hui Shan, and Chris Henson, 2013, The impact of Fed MBS purchases on TBA pool quality, Goldman Sachs Credit Strategy Research, June 20. Krishnamurthy, Arvind, and Annette Vissing-Jorgensen, 2011, The effects of quantitative easing on interest rates: channels and implications for policy, Brookings Papers on Economic Activity 43, 215–287. Krishnamurthy, Arvind, andAnnetteVissing-Jorgensen, 2013, TheinsandoutsofLSAPs, Working paper presented at the Kansas City Federal Reserve Symposium on Global Dimensions of Unconventional Monetary Policy. LaCour-Little, Michael, and Gregory H. Chun, 1999, Third party originators and mortgage prepayment risk: an agency problem?, Journal of Real Estate Research 17, 55–70. Modigliani, Franco, and Richard Sutch, 1966, Innovations in interest rate policy, American Economic Review 56, 178–197. 30

Neely,ChristopherJ.,2012,Thelarge-scaleassetpurchaseshadlargeinternationaleffects,Federal Reserve Bank of St. Louis Working Paper Series. Rosenbaum, Paul R., 2002, Observational Studies, second edition (Springer, New York). Rosenbaum, Paul R., and Donald B. Rubin, 1983, The central role of the propensity score in observational studies for causal effects, Biometrika 70, 41–55. Stroebel, Johannes, and John B. Taylor, 2012, Estimated impact of the Federal Reserve’s mortgage-backed securities purchase program, International Journal of Central Banking 8, 1–42. Swanson, Eric T., 2011, Let’s twist again: A high-frequency event-study analysis of Operation Twist and its implications for QE2, Brookings Papers on Economic Activity 42, 151–207. Tobin, James, 1969, A general equilibrium approach to monetary theory, Journal of Money, Credit and Banking 1, 15–29. Vayanos, Dimitri, and Jean-Luc Vila, 2009, A preferred-habitat model of the term structure of interest rates, NBER Working Paper Series, Working Paper 15487. Vickery, James, and Joshua Wright, 2013, TBA trading and liquidity in the agency MBS market, Federal Reserve Bank of New York Economic Policy Review, May. Wright, Jonathan H., 2012, What does monetary policy do to long-term interest rates at the zero lower bound?, Economic Journal 122, F447–F466. 31

))ttnneeccrreepp(( MMMMSS 44 33 22 11 00 Total prepayment rate: SOMA: 25.97 % Market: 22.01 % 01 nuJ 01 guA 01 tcO 01 ceD 11 beF 11 rpA 11 nuJ 11 guA 11 tcO 11 ceD 21 beF 21 rpA 21 nuJ SOMA Market (a) 4.0% Coupon ))ttnneeccrreepp(( MMMMSS 44 33 22 11 00 Total prepayment rate: SOMA: 37.14 % Market: 28.08 % 01 nuJ 01 guA 01 tcO 01 ceD 11 beF 11 rpA 11 nuJ 11 guA 11 tcO 11 ceD 21 beF 21 rpA 21 nuJ SOMA Market (b) 4.5% Coupon ))ttnneeccrreepp(( MMMMSS 44 33 22 11 00 Total prepayment rate: SOMA: 43.73 % Market: 40.08 % 01 nuJ 01 guA 01 tcO 01 ceD 11 beF 11 rpA 11 nuJ 11 guA 11 tcO 11 ceD 21 beF 21 rpA 21 nuJ SOMA Market (c) 5.0% Coupon ))ttnneeccrreepp(( MMMMSS 44 33 22 11 00 Total prepayment rate: SOMA: 50.37 % Market: 40.9 % 01 nuJ 01 guA 01 tcO 01 ceD 11 beF 11 rpA 11 nuJ 11 guA 11 tcO 11 ceD 21 beF 21 rpA 21 nuJ SOMA Market (d) 5.5% Coupon ))ttnneeccrreepp(( MMMMSS 44 33 22 11 00 Total prepayment rate: SOMA: 50.58 % Market: 43.19 % 01 nuJ 01 guA 01 tcO 01 ceD 11 beF 11 rpA 11 nuJ 11 guA 11 tcO 11 ceD 21 beF 21 rpA 21 nuJ SOMA Market (e) 6.0% Coupon ))ttnneeccrreepp(( MMMMSS 44 33 22 11 00 Total prepayment rate: SOMA: 47.83 % Market: 40.17 % 01 nuJ 01 guA 01 tcO 01 ceD 11 beF 11 rpA 11 nuJ 11 guA 11 tcO 11 ceD 21 beF 21 rpA 21 nuJ SOMA Market (f) 6.5% Coupon Figure 1. Prepayment Rates of Fannie Mae and Freddie Mac 30-Year MBS. Thisfigure plotsmonthlyprepaymentrates(singlemonthlymortalityrates)foreachcoupon. Thebluedashedlinerepresents averageprepaymentratesacrossallFannieMaeandFreddieMac30-yearsecuritiesheldbytheFederalReservein the System Open Market Account (SOMA). The red solid line represents the analogous prepayment rates across securities that are not held by the Federal Reserve. The total prepayment rates—computed as the amount of prepayments over the period 06/2010-06/2012 divided by the remaining principal balance as of 06/2010— for the twosetsofsecuritiesarereportedinthebottomrightofeachpanel. OldervintagesandMBSwithprefixidentifiers notpurchasedbytheFederalReservehavebeendroppedinordertoremovesecuritieslikelytotradeinthespecified pool market. Source: eMBS Inc. and Federal Reserve Bank of New York.

Coefficient estimate 5 4 3 2 1 0 2011:H1 2011 2012:H1 2012 2013:H1 2013 (a) Federal Reserve ownership Coefficient estimate 5 4 3 2 1 0 2011:H1 2011 2012:H1 2012 2013:H1 2013 (b) Federal Reserve share Figure 2. Coefficient Estimates for Different Subsamples. This figure plots OLS coefficient estimates of Fed ownership and Fed share in Panels (a) and (b), respectively. Each bar represents the coefficient estimate over the sample from 06/2010 to the date indicated on the x-axis. Fed ownership is a dummy variable that equals one if security i is held by the Federal Reserve and Fed share denotes the share of security i that the Federal Reserve holds.

srallod fo snoilliB 0088 0066 0044 0022 00 0022−− 90 naJ 90 beF 90 raM 90 rpA 90 yaM 90 nuJ 90 luJ 90 guA 90 peS 90 tcO 90 voN 90 ceD 01 naJ 01 beF 01 raM 01 rpA 01 yaM 01 nuJ Predicted change in MBS holdings Actual change in MBS holdings Figure 3. MBS Holdings Predictions. This figure plots actual changes in bank MBS holdings versus the predicted values for the QE1 period of January 2009 through June 2010.

Table 1 Operations Summary Coupon distribution 3.5 0.03% 4.0 15.23% 4.5 46.30% 5.0 24.09% 5.5 12.33% 6.0 - 6.5 2.02% Agency distribution Fannie Mae 56.15% Freddie Mac 34.72% Ginnie Mae I 6.86% Ginnie Mae II 2.28% Term distribution 15-year 3.42% 30-year 96.42% Note: This table provides a summary of the MBS operations conducted over the period 1/5/2009- 3/31/2010aspartofLSAP1. Source: FederalReserve Bank of New York.

2 elbaT )0102 enuJ fo sa( scitsitatS evitpircseD nopuoC%5.6 nopuoC%0.6 nopuoC%5.5 nopuoC%0.5 nopuoC%5.4 nopuoC%0.4 tekraM AMOS tekraM AMOS tekraM AMOS tekraM AMOS tekraM AMOS tekraM AMOS 673,7 765 570,51 986,2 780,92 978,5 744,8 655,5 596,2 521,5 633 307,1 SPISUCfo# — 31.0 — 81.0 — 53.0 — 55.0 — 18.0 — 48.0 erahsdeF — )42.0( — )62.0( — )63.0( — )04.0( — )23.0( — )92.0( 20.73 †82.43 81.73 †65.23 88.95 †54.73 32.04 †57.32 25.81 †99.21 88.8 †40.21 eganaoL )93.9( )49.8( )89.9( )10.9( )27.12( )95.71( )88.22( )16.71( )02.02( )12.11( )06.4( )11.3( 20.7 †50.7 45.6 †65.6 99.5 †70.6 85.5 †65.5 20.5 †99.4 55.4 65.4 nopuoC )91.0( )12.0( )51.0( )61.0( )51.0( )61.0( )71.0( )81.0( )71.0( )41.0( )31.0( )51.0( 23.596 67.396 36.807 99.707 65.517 †84.917 36.927 †72.337 77.557 43.557 02.567 82.567 OCIF )23.82( )39.03( )00.32( )96.52( )73.12( )65.12( )86.02( )57.81( )87.51( )21.31( )81.01( )12.9( 28.97 †29.87 72.67 †08.67 53.37 †01.47 18.17 †85.37 77.76 †72.17 94.56 †97.66 eulav-ot-naoL )30.8( )13.7( )52.8( )86.7( )93.7( )30.7( )86.6( )89.6( )97.6( )16.5( )85.6( )74.5( 521 †661 241 †691 631 †881 751 †702 731 †232 002 †132 ezisnaoL )16( )27( )96( )06( )26( )17( )86( )56( )17( )06( )47( )35( )sdnasuoht$( 35.0 †54.0 65.0 †15.0 94.0 †65.0 07.0 †97.0 19.0 †49.0 89.0 †79.0 rotcaF )51.0( )21.0( )31.0( )11.0( )81.0( )41.0( )81.0( )61.0( )21.0( )80.0( )20.0( )20.0( 23 †421 94 †321 94 †481 65 †521 46 †521 28 801 tnuomaeussI )97( )054( )221( )844( )761( )417( )091( )025( )182( )424( )402( )303( )snoillim$( 719,2 †754,11 359,6 †961,11 054,11 †473,44 187,21 568,51 583,2 †693,1 649 †944 snaolfo# )876,22( )456,44( )482,55( )720,87( )950,29( )157,291( )384,38( )718,69( )606,21( )698,8( )245,4( )213,1( 94.24 25.04 83.34 †81.73 14.61 †15.13 71.52 †61.63 03.73 †43.04 05.54 †61.93 erahsOPT )19.83( )10.83( )65.63( )61.83( )14.03( )80.63( )91.33( )08.43( )86.13( )99.53( )65.23( )23.33( 452 †054 082 †754 772 †074 243 †794 862 †935 564 †925 ezisnaol .xaM )771( )651( )091( )731( )071( )951( )491( )671( )512( )671( )032( )171( )sdnasuoht$( 40.44 †93.84 34.64 †24.74 13.65 †22.25 27.55 †54.16 26.46 †34.37 99.47 †30.28 erahsfieR )98.81( )24.81( )19.81( )96.02( )51.02( )43.02( )64.81( )84.02( )46.91( )89.91( )88.81( )72.51( 34.0 †42.0 45.0 †60.0 64.0 †51.0 55.0 †62.0 15.0 †43.0 15.0 †63.0 rotacidnieidderF snmuloc ni detroper scitsitats evitpircsed ehT .elpmas ruo ni scitsiretcarahc SBM suoirav fo noitaived dradnats eht ,sesehtnerap ni ,dna egareva eht nopuoc hcae rof sedivorp elbat sihT :etoN tahtseitirucesllassorcadetupmoceratekraMdelebalsnmulocehtniesehtdnatnuoccAtekraMnepOmetsySehtnievreseRlaredeFehtybdlehseitirucesllassorcadetupmoceraAMOSdelebal si rotcaf ;loop egagtrom gniylrednu eht no nopuoc egareva-dethgiew eht si nopuoc ;sdloh evreseR laredeF eht taht i ytiruces fo erahs eht setoned erahs deF .evreseR laredeF eht yb dleh ton era sadetanigiroerewtahtloopanisnaolfoerahsehtsi erahsfier;ytrapdrihtaybdetanigirosnaolfoerahsehtsi erahsOPT;diaperebotsniamertahtecnalablapicnirplanigiroehtfonoitcarfeht naolselbairavehT .seitiruceseaMeinnaFdnacaMeidderFforebmunehtfomusehtybdedividseitirucescaMeidderFforebmunehtsi rotacidni eidderFdna ;gnicnanfiersuoiverpafotlusera .cnISBMe :ecruoS .seitirucestekraMmorf)50.0<p(tnereffidyllacitsitatssinaemelpmas’seitirucesAMOStahtsetacidni † .segarevadethgiewera ezis naoldna,eulav-ot-naol,erocs tiderc,ega .kroYweNfoknaBevreseRlaredeFdna

3 elbaT setaR tnemyaperP rof setamitsE noissergeR snopuoC %0.5 - %0.4 :A lenaP )4( )3( )2( )1( )4( )3( )2( )1( )4( )3( )2( )1( selbairaV nopuoC%0.5 nopuoC%5.4 nopuoC%0.4 ***317.3 ***744.3 ***574.3 ***081.3 ***457.3 ***167.3 ***365.3 ***326.3 981.0- 303.0- 724.0- 186.0pihsrenwodeF )812.0( )122.0( )812.0( )122.0( )923.0( )033.0( )233.0( )633.0( )295.0( )506.0( )885.0( )895.0( ***517.2 ***317.3 ***936.2 ***587.3 ***516.4 ***271.4 ***443.4 ***568.3 ***831.9- ***42.11- ***368.7- ***35.01eganaoL )781.0( )571.0( )091.0( )771.0( )033.0( )933.0( )423.0( )633.0( )414.2( )004.2( )274.2( )774.2( ***110.0- ***210.0- ***110.0- ***310.0- ***010.0- ***600.0- ***010.0- ***010.0- ***151.0 ***151.0 ***231.0 ***241.0 2)eganaoL( )100.0( )000.0( )100.0( )000.0( )100.0( )100.0( )100.0( )100.0( )810.0( )410.0( )810.0( )410.0( ***02.6 ***90.21 ***13.5 ***67.01 ***93.44 ***83.54 ***32.04 ***41.93 **32.51 81.7 ***91.81 13.9 nopuoC )126.1( )336.1( )626.1( )946.1( )969.1( )159.1( )859.1( )519.1( )918.6( )178.6( )599.6( )240.7( ***250.0 ***250.0 ***050.0 ***050.0 ***170.0 ***270.0 ***270.0 ***470.0 ***160.0 ***260.0 ***460.0 ***860.0 )0001/1×(ezisnaoL )200.0( )200.0( )200.0( )200.0( )200.0( )200.0( )200.0( )200.0( )500.0( )400.0( )500.0( )400.0( ***513.0- ***915.0- ***813.0- ***525.0- ***586.0- ***117.0- ***806.0- ***426.0- ***535.1 ***889.1 ***863.1 ***688.1 eganaol×nopuoC )530.0( )430.0( )630.0( )530.0( )660.0( )960.0( )560.0( )960.0( )815.0( )035.0( )035.0( )745.0( ***283.0- ***734.0- ***983.0- ***844.0- ***613.0- ***224.0- ***323.0- ***354.0- ***155.0- ***527.0- ***135.0- ***796.0- )001×(rotcaF )610.0( )610.0( )610.0( )610.0( )240.0( )240.0( )340.0( )440.0( )071.0( )171.0( )271.0( )371.0( ***639.1 ***768.1 ***150.2 ***250.2 ***711.1 ***011.1 ***483.1 ***715.1 292.0 672.0 954.0 723.0 eidderF )091.0( )981.0( )781.0( )781.0( )332.0( )522.0( )432.0( )722.0( )124.0( )314.0( )224.0( )314.0( ***960.0 ***180.0 ***560.0 ***860.0 410.0 330.0- OCIF )500.0( )500.0( )210.0( )210.0( )620.0( )520.0( ***610.0 ***020.0 ***810.0 ***030.0 ***620.0 ***330.0 erahsOPT )300.0( )300.0( )400.0( )400.0( )600.0( )600.0( ***130.0- ***510.0- ***440.0 ***670.0 ***940.0 ***240.0 erahsfieR )600.0( )600.0( )900.0( )800.0( )310.0( )310.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG 199,31 199,31 310,41 310,41 918,7 918,7 028,7 028,7 930,2 930,2 930,2 930,2 SPISUCfo# 445.0 615.0 435.0 505.0 295.0 165.0 685.0 645.0 165.0 415.0 455.0 405.0 derauqs-RdetsujdA 2102/60-0102/60 morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc fo stluser noitamitse SLO eht stneserp elbat sihT :etoN i ytiruces fi eno slauqe taht elbairav ymmud a si pihsrenwo deF .selbairav yrotanalpxe rehto dna pihsrenwo deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid eb ot sniamer taht ecnalab lapicnirp lanigiro eht fo noitcarf eht si rotcaf ;loop egagtrom gniylrednu eht no nopuoc egareva-dethgiew eht si caw ;evreseR laredeF eht yb dleh si drihtaybdetanigirosnaolfoerahsehtsi erahs OPT;erocstidercOCIFehtsi OCIF;ytirucescaMeidderFasiiytirucesfienoslauqetahtelbairavymmudasi eidderF;diaper .segareva-dethgiewera OCIFdna,ezis naol,ega naolselbairavehT .gnicnanfiersuoiverpafotluserasadetanigiroerewtahtloopanisnaolfoerahsehtsi erahs fierdna;ytrap .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .nopuochcaerofyletarapesdetamitseerasnoitacfiicepsnoissergerruoF .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗ :ecnacfiingislacitsitatS

3 elbaT deunitnoc snopuoC %5.6 - %5.5 :B lenaP )4( )3( )2( )1( )4( )3( )2( )1( )4( )3( )2( )1( selbairaV nopuoC%5.6 nopuoC%0.6 nopuoC%5.5 ***767.1 ***603.2 ***266.1 ***402.2 ***942.2 ***583.2 ***161.2 ***052.2 ***697.3 ***142.5 ***926.3 ***792.5 pihsrenwodeF )444.0( )054.0( )054.0( )554.0( )532.0( )732.0( )732.0( )832.0( )971.0( )181.0( )081.0( )681.0( ***995.1 ***476.1 **702.1 **413.1 *127.0 ***730.1 762.0 365.0 ***023.1 ***761.3 ***651.1 ***653.3 eganaoL )795.0( )855.0( )395.0( )845.0( )024.0( )483.0( )814.0( )583.0( )531.0( )711.0( )631.0( )021.0( 100.0- 000.0 100.0- 000.0 100.0- 100.0- 000.0 000.0 ***300.0 ***200.0- ***400.0 ***200.0- 2)eganaoL( )300.0( )100.0( )300.0( )100.0( )200.0( )100.0( )200.0( )100.0( )000.0( )000.0( )000.0( )000.0( **63.6 **99.5 22.4 24.3 66.1- 44.0 *86.3- 67.2- ***87.5 ***47.12 ***75.4 ***27.32 nopuoC )269.2( )219.2( )178.2( )718.2( )191.2( )851.2( )741.2( )721.2( )822.1( )251.1( )422.1( )481.1( ***950.0 ***760.0 ***060.0 ***760.0 ***540.0 ***050.0 ***640.0 ***940.0 ***650.0 ***060.0 ***650.0 ***950.0 )0001/1×(ezisnaoL )300.0( )300.0( )300.0( )300.0( )200.0( )100.0( )200.0( )100.0( )100.0( )100.0( )100.0( )100.0( ***972.0- ***482.0- ***532.0- ***332.0- ***161.0- ***891.0- **611.0- **231.0- ***392.0- ***515.0- ***082.0- ***565.0eganaol×nopuoC )970.0( )870.0( )870.0( )770.0( )950.0( )750.0( )950.0( )750.0( )020.0( )020.0( )020.0( )020.0( ***252.0- ***003.0- ***152.0- ***982.0- ***973.0- ***124.0- ***283.0- ***124.0- ***352.0- ***423.0- ***542.0- ***823.0- )001×(rotcaF )410.0( )410.0( )410.0( )310.0( )010.0( )900.0( )010.0( )900.0( )800.0( )800.0( )800.0( )900.0( ***507.1 ***666.1 ***776.1 ***506.1 ***538.2 ***906.2 ***284.2 ***662.2 ***182.2 ***252.2 ***806.2 ***851.3 eidderF )182.0( )182.0( )832.0( )732.0( )791.0( )691.0( )661.0( )561.0( )131.0( )231.0( )421.0( )621.0( 300.0- 700.0 300.0 ***510.0 ***530.0 ***560.0 OCIF )500.0( )500.0( )400.0( )400.0( )300.0( )300.0( 500.0 100.0 *500.0- **600.0- ***030.0 ***750.0 erahsOPT )400.0( )400.0( )300.0( )300.0( )300.0( )300.0( ***860.0- ***340.0- ***560.0- ***250.0- ***830.0- ***310.0erahsfieR )600.0( )600.0( )500.0( )400.0( )400.0( )300.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG 249,7 249,7 349,7 349,7 857,71 857,71 467,71 467,71 657,43 657,43 179,43 179,43 SPISUCfo# 173.0 343.0 263.0 833.0 193.0 763.0 383.0 063.0 883.0 243.0 973.0 913.0 derauqs-RdetsujdA 2102/60-0102/60 morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc fo stluser noitamitse SLO eht stneserp elbat sihT :etoN i ytiruces fi eno slauqe taht elbairav ymmud a si pihsrenwo deF .selbairav yrotanalpxe rehto dna pihsrenwo deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid eb ot sniamer taht ecnalab lapicnirp lanigiro eht fo noitcarf eht si rotcaf ;loop egagtrom gniylrednu eht no nopuoc egareva-dethgiew eht si caw ;evreseR laredeF eht yb dleh si a yb detanigiro snaol fo erahs eht si erahs OPT ;erocs tiderc OCIF eht si OCIF ;ytiruces caM eidderF a si i ytiruces fi eno slauqe taht elbairav ymmud a si eidderF ;diaper .segareva-dethgiew era scaow dna ,slaw ,alaw selbairav ehT .gnicnanfier suoiverp a fo tluser a sa detanigiro erew taht loop a ni snaol fo erahs eht si erahs fier dna ;ytrap driht .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .nopuochcaerofyletarapesdetamitseerasnoitacfiicepsnoissergerruoF .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗ :ecnacfiingislacitsitatS

4 elbaT setaR tnemyaperP rof setamitsE noissergeR snopuoC %0.5 - %0.4 :A lenaP )4( )3( )2( )1( )4( )3( )2( )1( )4( )3( )2( )1( selbairaV nopuoC%0.5 nopuoC%5.4 nopuoC%0.4 ∗∗∗700.4 ∗∗∗217.3 ∗∗∗846.3 ∗∗∗233.3 ∗∗∗676.2 ∗∗∗686.2 ∗∗∗225.2 ∗∗∗238.2 127.0- 568.0- ∗849.0- ∗∗181.1erahsdeF )892.0( )592.0( )003.0( )892.0( )633.0( )233.0( )143.0( )833.0( )965.0( )195.0( )565.0( )485.0( ∗∗∗228.2 ∗∗∗877.3 ∗∗∗437.2 ∗∗∗348.3 ∗∗∗495.4 ∗∗∗761.4 ∗∗∗333.4 ∗∗∗388.3 ∗∗∗438.8- ∗∗∗99.01- ∗∗∗925.7- ∗∗∗52.01eganaoL )881.0( )571.0( )191.0( )871.0( )733.0( )343.0( )133.0( )143.0( )704.2( )883.2( )564.2( )564.2( ∗∗∗210.0- ∗∗∗310.0- ∗∗∗110.0- ∗∗∗410.0- ∗∗∗010.0- ∗∗∗700.0- ∗∗∗110.0- ∗∗∗010.0- ∗∗∗841.0 ∗∗∗051.0 ∗∗∗031.0 ∗∗∗341.0 2)eganaoL( )100.0( )000.0( )100.0( )000.0( )100.0( )100.0( )100.0( )100.0( )810.0( )410.0( )810.0( )310.0( ∗∗∗082.6 ∗∗∗50.21 ∗∗∗553.5 ∗∗∗86.01 ∗∗∗65.44 ∗∗∗26.54 ∗∗∗64.04 ∗∗∗46.93 ∗∗97.51 746.7 ∗∗∗18.81 ∗∗∗058.9 nopuoC )526.1( )636.1( )036.1( )356.1( )889.1( )869.1( )089.1( )239.1( )408.6( )348.6( )879.6( )210.7( ∗∗∗250.0 ∗∗∗350.0 ∗∗∗050.0 ∗∗∗150.0 ∗∗∗570.0 ∗∗∗770.0 ∗∗∗670.0 ∗∗∗870.0 ∗∗∗260.0 ∗∗∗460.0 ∗∗∗560.0 ∗∗∗960.0 )0001/1×(ezisnaoL )200.0( )200.0( )200.0( )200.0( )200.0( )200.0( )200.0( )200.0( )500.0( )400.0( )500.0( )400.0( ∗∗∗523.0- ∗∗∗225.0- ∗∗∗823.0- ∗∗∗825.0- ∗∗∗876.0- ∗∗∗407.0- ∗∗∗306.0- ∗∗∗326.0- ∗∗∗884.1 ∗∗∗549.1 ∗∗∗313.1 ∗∗∗338.1 eganaol×nopuoC )530.0( )430.0( )630.0( )530.0( )760.0( )070.0( )760.0( )070.0( )615.0( )825.0( )925.0( )545.0( ∗∗∗004.0- ∗∗∗554.0- ∗∗∗504.0- ∗∗∗564.0- ∗∗∗323.0- ∗∗∗924.0- ∗∗∗923.0- ∗∗∗064.0- ∗∗755.0- ∗∗∗237.0- ∗∗935.0- ∗∗∗507.0- )001×(rotcaF )610.0( )610.0( )710.0( )610.0( )240.0( )340.0( )340.0( )540.0( )071.0( )071.0( )271.0( )371.0( ∗∗∗335.1 ∗∗∗484.1 ∗∗∗246.1 ∗∗∗876.1 ∗∗∗320.1 ∗∗∗520.1 ∗∗∗082.1 ∗∗∗934.1 572.0 062.0 654.0 833.0 eidderF )881.0( )781.0( )481.0( )381.0( )632.0( )722.0( )632.0( )922.0( )614.0( )804.0( )714.0( )804.0( ∗∗∗070.0 ∗∗∗180.0 ∗∗∗616.0 ∗∗∗046.0 610.0 030.0erocstiderC )500.0( )500.0( )210.0( )210.0( )620.0( )520.0( ∗∗∗510.0 ∗∗∗020.0 ∗∗∗710.0 ∗∗∗920.0 ∗∗∗620.0 ∗∗∗330.0 erahsOPT )300.0( )300.0( )400.0( )400.0( )600.0( )600.0( ∗∗∗130.0- ∗∗310.0- ∗∗∗540.0 ∗∗∗570.0 ∗∗∗840.0 ∗∗∗140.0 erahsfieR )600.0( )600.0( )900.0( )800.0( )310.0( )310.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG 199,31 199,31 310,41 310,41 918,7 918,7 028,7 438,7 930,2 930,2 930,2 040,2 SPISUCfo# 045.0 315.0 135.0 205.0 785.0 655.0 285.0 245.0 165.0 515.0 455.0 505.0 derauqs-RdetsujdA 2102/60-0102/60 morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc fo stluser noitamitse SLO eht stneserp elbat sihT :etoN evreseR laredeF eht taht i ytiruces fo erahs eht setoned erahs deF .selbairav yrotanalpxe rehto dna erahs deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid ymmudasi eidderF;diaperebotsniamertahtecnalablapicnirplanigiroehtfonoitcarfehtsi rotcaf;loopegagtromgniylrednuehtnonopuocegareva-dethgiewehtsi caw;sdloh si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs eht si erahs OPT ;erocs tiderc OCIF eht si OCIF ;ytiruces caM eidderF a si i ytiruces fi eno slauqe taht elbairav snoitacfiicepsnoissergerruoF .segareva-dethgiewera scaowdna,slaw,alawselbairavehT .gnicnanfiersuoiverpafotluserasadetanigiroerewtahtloopanisnaolfoerahseht :ecnacfiingis lacitsitatS .sesehtnerap ni detroper era srorre dradnats tsuboR .)detroper ton( tnatsnoc a edulcni snoitacfiiceps llA .nopuoc hcae rof yletarapes detamitse era .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗

4 elbaT deunitnoc snopuoC %5.6 - %5.5 :B lenaP )4( )3( )2( )1( )4( )3( )2( )1( )4( )3( )2( )1( selbairaV nopuoC%5.6 nopuoC%0.6 nopuoC%5.5 ∗∗∗245.4 ∗∗∗007.5 ∗∗∗695.4 ∗∗∗597.5 ∗∗∗264.4 ∗∗∗418.4 ∗∗∗513.4 ∗∗∗017.4 ∗∗∗765.4 ∗∗∗660.6 ∗∗∗307.4 ∗∗∗386.6 erahsdeF )976.1( )327.1( )096.1( )227.1( )037.0( )637.0( )227.0( )727.0( )143.0( )053.0( )443.0( )363.0( ∗∗∗455.1 ∗∗∗616.1 ∗∗761.1 ∗∗062.1 ∗527.0 ∗∗∗230.1 862.0 755.0 ∗∗∗743.1 ∗∗∗192.3 ∗∗∗691.1 ∗∗∗074.3 eganaoL )995.0( )855.0( )495.0( )845.0( )424.0( )383.0( )124.0( )383.0( )631.0( )811.0( )631.0( )121.0( 100.0- 000.0 100.0- 000.0 200.0- 100.0- 000.0- 100.0- ∗∗∗300.0 ∗∗∗200.0- ∗∗∗300.0 ∗∗∗200.0- 2)eganaoL( )300.0( )100.0( )300.0( )100.0( )200.0( )100.0( )200.0( )100.0( )000.0( )000.0( )000.0( )000.0( ∗∗430.6 ∗395.5 309.3 450.3 549.1- 780.0 ∗879.3- 711.3- ∗∗∗648.5 ∗∗∗54.32 ∗∗∗966.4 ∗∗∗12.52 nopuoC )169.2( )909.2( )078.2( )418.2( )091.2( )151.2( )741.2( )221.2( )032.1( )751.1( )522.1( )091.1( ∗∗∗950.0 ∗∗∗760.0 ∗∗∗060.0 ∗∗∗760.0 ∗∗∗540.0 ∗∗∗150.0 ∗∗∗640.0 ∗∗∗050.0 ∗∗∗750.0 ∗∗∗260.0 ∗∗∗750.0 ∗∗∗060.0 )0001/1×(ezisnaoL )300.0( )300.0( )300.0( )300.0( )200.0( )100.0( )200.0( )100.0( )100.0( )100.0( )100.0( )100.0( ∗∗∗272.0- ∗∗∗672.0- ∗∗∗822.0- ∗∗∗522.0- ∗∗∗651.0- ∗∗∗191.0- ∗111.0- ∗∗621.0- ∗∗∗492.0- ∗∗∗535.0- ∗∗∗282.0- ∗∗∗285.0eganaol×nopuoC )970.0( )870.0( )870.0( )770.0( )950.0( )750.0( )950.0( )750.0( )020.0( )020.0( )020.0( )020.0( ∗∗∗272.0- ∗∗∗672.0- ∗∗∗552.0- ∗∗∗692.0- ∗∗∗783.0- ∗∗∗034.0- ∗∗∗983.0- ∗∗∗924.0- ∗∗∗162.0- ∗∗∗243.0- ∗∗∗352.0- ∗∗∗643.0- )001×(rotcaF )970.0( )870.0( )870.0( )770.0( )010.0( )900.0( )010.0( )010.0( )800.0( )800.0( )800.0( )900.0( ∗∗∗726.1 ∗∗∗465.1 ∗∗∗706.1 ∗∗∗805.1 ∗∗∗005.2 ∗∗∗852.2 ∗∗∗251.2 ∗∗∗239.1 ∗∗∗089.1 ∗∗∗067.1 ∗∗∗482.2 ∗∗∗676.2 eidderF )082.0( )182.0( )732.0( )632.0( )191.0( )091.0( )951.0( )751.0( )131.0( )131.0( )321.0( )521.0( 300.0- 800.0 300.0 ∗∗∗510.0 ∗∗∗530.0 ∗∗∗760.0 erocstiderC )500.0( )500.0( )400.0( )400.0( )300.0( )300.0( 500.0 100.0 ∗500.0- ∗∗600.0- ∗∗∗520.0 ∗∗∗450.0 erahsOPT )400.0( )400.0( )300.0( )300.0( )300.0( )300.0( ∗∗∗760.0- ∗∗∗240.0- ∗∗∗560.0- ∗∗∗050.0- ∗∗∗830.0- ∗∗∗010.0erahsfieR )600.0( )600.0( )500.0( )400.0( )400.0( )300.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG 249,7 249,7 349,7 349,7 857,71 857,71 467,71 467,71 657,43 657,43 179,43 179,43 SPISUCfo# 173.0 143.0 163.0 733.0 093.0 663.0 183.0 853.0 383.0 333.0 673.0 013.0 derauqs-RdetsujdA 2102/60-0102/60 morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc fo stluser noitamitse SLO eht stneserp elbat sihT :etoN evreseR laredeF eht taht i ytiruces fo erahs eht setoned erahs deF .selbairav yrotanalpxe rehto dna erahs deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid ymmudasi eidderF;diaperebotsniamertahtecnalablapicnirplanigiroehtfonoitcarfehtsi rotcaf;loopegagtromgniylrednuehtnonopuocegareva-dethgiewehtsi caw;sdloh si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs eht si erahs OPT ;erocs tiderc OCIF eht si OCIF ;ytiruces caM eidderF a si i ytiruces fi eno slauqe taht elbairav snoitacfiicepsnoissergerruoF .segareva-dethgiewera scaowdna,slaw,alawselbairavehT .gnicnanfiersuoiverpafotluserasadetanigiroerewtahtloopanisnaolfoerahseht :ecnacfiingis lacitsitatS .sesehtnerap ni detroper era srorre dradnats tsuboR .)detroper ton( tnatsnoc a edulcni snoitacfiiceps llA .nopuoc hcae rof yletarapes detamitse era .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗

5 elbaT setaR tnemyaperP rof setamitsE noissergeR delooP )4( )3( )2( )1( selbairaV )4( )3( )2( )1( selbairaV erahs deF :elbairaVtnednepednI pihsrenwo deF :elbairaVtnednepednI ***099.3 ***188.4 ***509.3 ***169.4 erahsdeF ***144.3 ***005.4 ***033.3 ***505.4 pihsrenwodeF )261.0( )261.0( )361.0( )461.0( )501.0( )501.0( )601.0( )701.0( ***285.3 ***816.2 ***794.3 ***426.2 eganaoL ***185.3 ***305.2 ***894.3 ***015.2 eganaoL )570.0( )620.0( )570.0( )620.0( )570.0( )620.0( )570.0( )620.0( ***300.0- ***400.0- ***300.0- ***400.0- 2)eganaoL( ***300.0- ***400.0- ***300.0- ***400.0- 2)eganaoL( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( ***15.91 ***78.11 ***05.81 ***10.11 nopuoC ***45.91 ***07.11 ***75.81 ***78.01 nopuoC )375.0( )681.0( )965.0( )571.0( )175.0( )481.0( )865.0( )271.0( ***750.0 ***060.0 ***750.0 ***950.0 )0001/1×(ezisnaoL ***750.0 ***950.0 ***750.0 ***850.0 )0001/1×(ezisnaoL )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( ***355.0- ***304.0- ***455.0- ***314.0eganaol×nopuoC ***255.0- ***583.0- ***455.0- ***593.0eganaol×nopuoC )210.0( )500.0( )210.0( )500.0( )210.0( )500.0( )210.0( )500.0( ***013.0- ***873.0- ***503.0- ***183.0- )001×(rotcaF ***692.0- ***653.0- ***292.0- ***953.0- )001×(rotcaF )500.0( )500.0( )500.0( )500.0( )500.0( )500.0( )500.0( )500.0( ***317.1 ***763.1 ***859.1 ***789.1 eidderF ***830.2 ***458.1 ***103.2 ***484.2 eidderF )280.0( )280.0( )570.0( )770.0( )280.0( )380.0( )770.0( )870.0( ***630.0 ***060.0 OCIF ***630.0 ***950.0 OCIF )200.0( )200.0( )200.0( )200.0( ***510.0 ***820.0 erahsOPT ***710.0 ***030.0 erahsOPT )100.0( )100.0( )100.0( )100.0( ***530.0- ***700.0erahsfieR ***530.0- ***900.0erahsfieR )200.0( )200.0( )200.0( )200.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniv-nopuoC 503,48 503,48 565,48 565,48 503,48 503,48 565,48 565,48 SPISUCfo# 954.0 014.0 354.0 893.0 264.0 614.0 654.0 404.0 derauqs-RdetsujdA morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc deloop fo stluser noitamitse SLO eht stneserp elbat sihT :etoN fo tes dnoces eht ni( erahs deF ro ))4(-)1( snmuloc fo tes tsrfi eht ni( pihsrenwo deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid 2102/60-0102/60 setoned erahsdeF;evreseRlaredeFehtybdlehsiiytirucesfienoslauqetahtelbairavymmudasi pihsrenwodeF .selbairavyrotanalpxerehtosallewsa))4(-)1(snmuloc lapicnirplanigiroehtfonoitcarfehtsi rotcaf;loopegagtromgniylrednuehtnonopuocegareva-dethgiewehtsicaw;sdlohevreseRlaredeFehttahtiytirucesfoerahseht ehtsi erahsOPT;erocstidercOCIFehtsi OCIF;ytirucescaMeidderFasiiytirucesfienoslauqetahtelbairavymmudasi eidderF;diaperebotsniamertahtecnalab ,alaw selbairav ehT .gnicnanfier suoiverp a fo tluser a sa detanigiro erew taht loop a ni snaol fo erahs eht si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs :ecnacfiingislacitsitatS .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .segareva-dethgiewera scaowdna,slaw .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗

Table 6 Propensity Score Matching Results 4.0% Coupon 4.5% Coupon 5.0% Coupon ATT (%) 0.47 0.16 3.43∗∗∗ (1.17) (0.66) (0.43) Min. Rosenbaum Bound 1.00 1.00 1.50 Pseudo R-squared for Entire Sample 0.247 0.367 0.341 Pseudo R-squared for Matched Sample 0.027 0.033 0.008 5.5% Coupon 6.0% Coupon 6.5% Coupon ATT (%) 4.59∗∗∗ 2.86∗∗∗ 3.01∗∗∗ (0.35) (0.35) (0.59) Min. Rosenbaum Bound 2.00 1.50 1.40 Pseudo R-squared for Entire Sample 0.396 0.319 0.131 Pseudo R-squared for Matched Sample 0.011 0.003 0.004 Note: This table presents the average treatment effect for the treated (ATT) securities held by the Federal Reserve. Values for the ATT reported using a local linear regression matching estimator. Abadie and Imbens (2006) heteroskedasticity-consistent analytical standard errors are reported in parentheses. The minimum Rosenbaum bound reports the minimum level of hidden bias that produces a confidence interval that includes zero(seeRosenbaum(2002)). PseudoR-squaredvaluesofthematchingregressionsarereportedtodemonstrate that an appropriately balanced sample was achieved. Statistical significance: ∗∗∗ p < 0.01,∗∗ p < 0.05,∗ p < 0.10.

7 elbaT )05.0 > noitanigirO ytraP drihT fo erahS( setaR tnemyaperP rof setamitsE noissergeR delooP )4( )3( )2( )1( selbairaV )4( )3( )2( )1( selbairaV erahs deF :elbairaVtnednepednI pihsrenwo deF :elbairaVtnednepednI ***135.5 ***662.6 ***042.5 ***729.5 erahsdeF ***312.4 ***471.5 ***630.4 ***600.5 pihsrenwodeF )242.0( )932.0( )042.0( )732.0( )961.0( )071.0( )961.0( )171.0( ***746.4 ***144.3 ***506.4 ***705.3 eganaoL ***276.4 ***652.3 ***926.4 ***433.3 eganaoL )451.0( )350.0( )451.0( )350.0( )351.0( )125.0( )451.0( )250.0( ***500.0- ***300.0- ***300.0- ***300.0- 2)eganaoL( ***500.0- ***300.0- ***300.0- ***300.0- 2)eganaoL( )100.0( )000.0( )100.0( )000.0( )100.0( )000.0( )100.0( )000.0( ***99.91 ***49.01 ***97.91 ***95.01 nopuoC ***04.02 ***66.01 ***51.02 ***43.01 nopuoC )249.0( )133.0( )549.0( )303.0( )249.0( )823.0( )549.0( )892.0( ***040.0 ***540.0 ***730.0 ***040.0 )0001/1×(ezisnaoL ***140.0 ***640.0 ***830.0 ***140.0 )0001/1×(ezisnaoL )100.0( )100.0( )100.0( )100.0( )100.0( )100.0( )100.0( )100.0( ***807.0- ***835.0- ***747.0- ***165.0eganaol×nopuoC ***117.0- ***605.0- **057.0- ***135.0eganaol×nopuoC )300.0( )010.0( )720.0( )010.0( )620.0( )010.0( )720.0( )010.0( ***193.0- ***724.0- ***893.0- ***144.0- )001×(rotcaF ***763.0- ***493.0- ***573.0- ***904.0- )001×(rotcaF )800.0( )800.0( )800.0( )800.0( )800.0( )800.0( )800.0( )800.0( ***518.0 *672.0- ***446.0 **303.0eidderF ***381.1 **692.0 ***600.1 *972.0 eidderF )441.0( )341.0( )541.0( )441.0( )741.0( )741.0( )841.0( )841.0( ***820.0 ***140.0 OCIF ***820.0 ***340.0 OCIF )400.0( )400.0( )400.0( )400.0( ***240.0- ***360.0erahsOPT ***040.0- ***060.0erahsOPT )400.0( )400.0( )400.0( )400.0( ***580.0- ***050.0erahsfieR ***480.0- ***940.0erahsfieR )500.0( )400.0( )500.0( )400.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniv-nopuoC 077,72 077,72 518,72 518,72 077,72 077,72 518,72 518,72 SPISUCfo# 805.0 754.0 694.0 544.0 905.0 164.0 794.0 054.0 derauqs-RdetsujdA morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc deloop fo stluser noitamitse SLO eht stneserp elbat sihT :etoN fo tes dnoces eht ni( erahs deF ro ))4(-)1( snmuloc fo tes tsrfi eht ni( pihsrenwo deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid 2102/60-0102/60 setoned erahsdeF;evreseRlaredeFehtybdlehsiiytirucesfienoslauqetahtelbairavymmudasi pihsrenwodeF .selbairavyrotanalpxerehtosallewsa))4(-)1(snmuloc lapicnirplanigiroehtfonoitcarfehtsi rotcaf;loopegagtromgniylrednuehtnonopuocegareva-dethgiewehtsicaw;sdlohevreseRlaredeFehttahtiytirucesfoerahseht ehtsi erahsOPT;erocstidercOCIFehtsi OCIF;ytirucescaMeidderFasiiytirucesfienoslauqetahtelbairavymmudasi eidderF;diaperebotsniamertahtecnalab ,alaw selbairav ehT .gnicnanfier suoiverp a fo tluser a sa detanigiro erew taht loop a ni snaol fo erahs eht si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs :ecnacfiingislacitsitatS .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .segareva-dethgiewera scaowdna,slaw .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗

8 elbaT )9002 erofeb sraeY noitcudorP( setaR tnemyaperP rof setamitsE noissergeR delooP )4( )3( )2( )1( selbairaV )4( )3( )2( )1( selbairaV erahs deF :elbairaVtnednepednI pihsrenwo deF :elbairaVtnednepednI ***555.3 ***380.4 ***466.3 ***290.4 erahsdeF ***588.2 ***734.3 ***558.2 ***353.3 pihsrenwodeF )472.0( )172.0( )472.0( )272.0( )321.0( )221.0( )321.0( )321.0( ***065.0 **921.0 ***192.0 420.0 eganaoL ***755.0 **631.0 ***382.0 030.0 eganaoL )401.0( )550.0( )201.0( )350.0( )301.0( )350.0( )101.0( )250.0( ***500.0 ***100.0 ***500.0 ***100.0 2)eganaoL( ***500.0 ***100.0 ***600.0 ***100.0 2)eganaoL( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( *581.1 ***509.2- 185.0- ***888.3nopuoC *772.1 ***804.2- 784.0- ***793.3nopuoC )917.0( )953.0( )996.0( )343.0( )717.0( )453.0( )796.0( )933.0( ***050.0 ***750.0 ***150.0 ***750.0 )0001/1×(ezisnaoL ***050.0 ***650.0 ***150.0 ***650.0 )0001/1×(ezisnaoL )100.0( )100.0( )100.0( )100.0( )000.0( )000.0( )000.0( )000.0( ***212.0- ***280.0- ***781.0- ***470.0eganaol×nopuoC ***112.0- 380.0- ***781.0- ***470.0eganaol×nopuoC )410.0( )800.0( )410.0( )800.0( )410.0( )800.0( )410.0( )800.0( ***992.0- ***633.0- ***492.0- ***923.0- )001×(rotcaF ***982.0- ***223.0- ***482.0- ***613.0- )001×(rotcaF )500.0( )500.0( )500.0( )500.0(( )500.0( )500.0( )500.0( )500.0( ***998.1 ***158.1 ***960.2 ***581.2 eidderF ***612.2 ***172.2 ***404.2 ***206.2 eidderF )590.0( )590.0( )580.0( )580.0( )690.0( )690.0( )780.0( )780.0( ***020.0 ***530.0 OCIF ***020.0 ***530.0 OCIF )200.0( )200.0( )200.0( )200.0( ***010.0 ***410.0 erahsOPT ***210.0 ***510.0 erahsOPT )200.0( )200.0( )200.0( )200.0( ***540.0- ***320.0erahsfieR ***540.0- ***520.0erahsfieR )200.0( )200.0( )200.0( )200.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniv-nopuoC 191,96 191,96 714,96 714,96 191,96 191,96 714,96 714,96 SPISUCfo# 053.0 513.0 443.0 903.0 353.0 023.0 743.0 713.0 derauqs-RdetsujdA morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc deloop fo stluser noitamitse SLO eht stneserp elbat sihT :etoN fo tes dnoces eht ni( erahs deF ro ))4(-)1( snmuloc fo tes tsrfi eht ni( pihsrenwo deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid 2102/60-0102/60 setoned erahsdeF;evreseRlaredeFehtybdlehsiiytirucesfienoslauqetahtelbairavymmudasi pihsrenwodeF .selbairavyrotanalpxerehtosallewsa))4(-)1(snmuloc lapicnirplanigiroehtfonoitcarfehtsi rotcaf;loopegagtromgniylrednuehtnonopuocegareva-dethgiewehtsicaw;sdlohevreseRlaredeFehttahtiytirucesfoerahseht ehtsi erahsOPT;erocstidercOCIFehtsi OCIF;ytirucescaMeidderFasiiytirucesfienoslauqetahtelbairavymmudasi eidderF;diaperebotsniamertahtecnalab ,alaw selbairav ehT .gnicnanfier suoiverp a fo tluser a sa detanigiro erew taht loop a ni snaol fo erahs eht si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs :ecnacfiingislacitsitatS .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .segareva-dethgiewera scaowdna,slaw .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗

9 elbaT )0102 dna 9002 sraeY noitcudorP( setaR tnemyaperP rof setamitsE noissergeR delooP )4( )3( )2( )1( selbairaV )4( )3( )2( )1( selbairaV erahs deF :elbairaVtnednepednI pihsrenwo deF :elbairaVtnednepednI ***882.2 ***501.3 ***161.2 ***930.3 erahsdeF ***248.2 ***925.3 ***166.2 ***733.3 pihsrenwodeF )712.0( )322.0( )712.0( )422.0( )512.0( )812.0( )512.0( )022.0( ***863.1 ***925.1- ***643.1 ***059.1eganaoL ***945.1 ***653.1- ***415.1 ***797.1eganaoL )843.0( )392.0( )833.0( )472.0( )243.0( )982.0( )433.0( )072.0( ***101.0 ***001.0 ***101.0 ***201.0 2)eganaoL( ***101.0 ***001.0 ***101.0 ***201.0 2)eganaoL( )500.0( )400.0( )500.0( )400.0( )500.0( )400.0( )500.0( )400.0( ***17.42 ***49.7 ***94.22 ***32.3 nopuoC ***80.52 ***55.8 ***08.22 ***76.3 nopuoC )542.1( )495.0( )632.1( )994.0( )532.1( )295.0( )822.1( )894.0( ***380.0 ***770.0 ***280.0 ***570.0 )0001/1×(ezisnaoL ***180.0 ***470.0 ***080.0 ***370.0 )0001/1×(ezisnaoL )200.0( )100.0( )200.0( )100.0( )200.0( )100.0( )200.0( )100.0( ***684.0- *590.0 ***674.0- ***081.0 eganaol×nopuoC ***915.0- 260.0 ***705.0- ***151.0 eganaol×nopuoC )560.0( )650.0( )460.0( )250.0( )460.0( )550.0( )360.0( )250.0( ***094.0- ***284.0- ***294.0- ***874.0- )001×(rotcaF ***774.0- ***464.0- ***184.0- ***164.0- )001×(rotcaF )420.0( )720.0( )420.0( )720.0( )420.0( )720.0( )420.0( )720.0( ***468.0 ***969.0 ***300.1 **002.1 eidderF ***739.0 ***630.1 ***870.1 ***462.1 eidderF )651.0( )951.0( )751.0( )061.0( )651.0( )951.0( )751.0( )061.0( ***270.0 ***001.0 OCIF ***470.0 ***301.0 OCIF )600.0( )600.0( )600.0( )600.0( ***800.0 ***110.0 erahsOPT ***900.0 ***210.0 erahsOPT )300.0( )300.0( )300.0( )300.0( ***220.0 ***130.0 erahsfieR ***220.0 ***230.0 erahsfieR )600.0( )600.0( )600.0( )600.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniv-nopuoC 411,51 411,51 841,51 841,51 411,51 411,51 841,51 841,51 SPISUCfo# 195.0 715.0 685.0 605.0 395.0 915.0 785.0 705.0 derauqs-RdetsujdA morf stnemyaperp fo tnuoma eht sa detupmoc—setar tnemyaperp latot fo snoisserger lanoitces-ssorc deloop fo stluser noitamitse SLO eht stneserp elbat sihT :etoN fo tes dnoces eht ni( erahs deF ro ))4(-)1( snmuloc fo tes tsrfi eht ni( pihsrenwo deF no—0102/60 fo sa ecnalab lapicnirp gniniamer eht yb dedivid 2102/60-0102/60 setoned erahsdeF;evreseRlaredeFehtybdlehsiiytirucesfienoslauqetahtelbairavymmudasi pihsrenwodeF .selbairavyrotanalpxerehtosallewsa))4(-)1(snmuloc lapicnirplanigiroehtfonoitcarfehtsi rotcaf;loopegagtromgniylrednuehtnonopuocegareva-dethgiewehtsicaw;sdlohevreseRlaredeFehttahtiytirucesfoerahseht ehtsi erahsOPT;erocstidercOCIFehtsi OCIF;ytirucescaMeidderFasiiytirucesfienoslauqetahtelbairavymmudasi eidderF;diaperebotsniamertahtecnalab ,alaw selbairav ehT .gnicnanfier suoiverp a fo tluser a sa detanigiro erew taht loop a ni snaol fo erahs eht si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs :ecnacfiingislacitsitatS .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .segareva-dethgiewera scaowdna,slaw .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗

01 elbaT )sesahcrupeR ycneuqnileD gnidulcxE( setaR tnemyaperP rof setamitsE noissergeR delooP )4( )3( )2( )1( selbairaV )4( )3( )2( )1( selbairaV erahs deF :elbairaVtnednepednI pihsrenwo deF :elbairaVtnednepednI ***529.5 ***344.4 ***958.5 ***551.4 erahsdeF ***854.4 ***907.4 ***094.4 ***446.4 pihsrenwodeF )592.0( )203.0( )003.0( )703.0( )191.0( )791.0( )491.0( )102.0( ***920.3 ***145.2 ***498.2 ***805.2 eganaoL ***270.3 ***005.2 ***939.2 ***184.2 eganaoL )511.0( )440.0( )811.0( )440.0( )411.0( )340.0( )611.0( )340.0( ***300.0- ***300.0- ***200.0- ***300.0- 2)eganaoL( ***300.0- ***300.0- ***200.0- ***300.0- 2)eganaoL( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( ***38.31 ***65.8 ***27.11 ***69.5 nopuoC ***20.41 ***67.8 ***09.11 ***62.6 nopuoC )538.0( )003.0( )638.0( )482.0( )928.0( )892.0( )038.0( )182.0( ***830.0 ***240.0 ***630.0 ***830.0 )0001/1×(ezisnaoL ***040.0 ***240.0 ***830.0 ***830.0 )0001/1×(ezisnaoL )100.0( )100.0( )100.0( )100.0( )100.0( )100.0( )100.0( )100.0( ***274.0- ***214.0- ***774.0- ***014.0eganaol×nopuoC ***474.0- ***304.0- **874.0- ***404.0eganaol×nopuoC )810.0( )800.0( )810.0( )800.0( )810.0( )800.0( )810.0( )800.0( ***973.0- ***244.0- ***673.0- ***644.0- )001×(rotcaF ***663.0- ***924.0- ***263.0- ***434.0- )001×(rotcaF )800.0( )800.0( )800.0( )800.0( )800.0( )800.0( )800.0( )800.0( ***470.0 ***301.0 OCIF ***047.0 ***201.0 OCIF )300.0( )300.0( )300.0( )300.0( ***410.0- 000.0 erahsOPT ***410.0- 100.0erahsOPT )200.0( )200.0( )200.0( )200.0( ***350.0- ***920.0erahsfieR ***150.0- ***920.0erahsfieR )400.0( )400.0( )400.0( )400.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniv-nopuoC 947,53 947,53 667,53 667,53 947,53 947,53 667,53 667,53 SPISUCfo# 204.0 433.0 583.0 803.0 404.0 933.0 783.0 413.0 derauqs-RdetsujdA gnidulcxestnemyaperpfotnuomaehtsadetupmoc—setartnemyaperplatotfosnoissergerlanoitces-ssorcdeloopfostlusernoitamitseSLOehtstneserpelbatsihT :etoN deFro))4(-)1(snmulocfotestsrfiehtni( pihsrenwo deFno—0102/60fosaecnalablapicnirpgniniamerehtybdedivid2102/60-0102/60morfsesahcruperycneuqniled laredeFehtybdlehsiiytirucesfienoslauqetahtelbairavymmudasi pihsrenwodeF .selbairavyrotanalpxerehtosallewsa))4(-)1(snmulocfotesdnocesehtni( erahs eht si rotcaf ;loop egagtrom gniylrednu eht no nopuoc egareva-dethgiew eht si caw ;sdloh evreseR laredeF eht taht i ytiruces fo erahs eht setoned erahs deF ;evreseR eht si OCIF ;ytiruces caM eidderF a si i ytiruces fi eno slauqe taht elbairav ymmud a si eidderF ;diaper eb ot sniamer taht ecnalab lapicnirp lanigiro eht fo noitcarf suoiverpafotluserasadetanigiroerewtahtloopanisnaolfoerahsehtsi erahsfierdna;ytrapdrihtaybdetanigirosnaolfoerahsehtsi erahsOPT;erocstidercOCIF eidderF ylno ,snoitatimil atad ot euD .)detroper ton( tnatsnoc a edulcni snoitacfiiceps llA .segareva-dethgiew era scaow dna ,slaw ,alaw selbairav ehT .gnicnanfier .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗ :ecnacfiingislacitsitatS .sesehtnerapnidetropererasrorredradnatstsuboR .elbatsihtnidedulcnieraseitirucesdeetnaraug-caM

11 elbaT srecivreS egraL :setaR tnemyaperP rof setamitsE noissergeR delooP )4( )3( )2( )1( selbairaV )4( )3( )2( )1( selbairaV erahsdeF :elbairaVtnednepednI pihsrenwodeF :elbairaVtnednepednI ***768.2 ***921.4 ***586.2 ***761.4 erahsdeF ***463.2 ***907.3 ***321.2 ***736.3 pihsrenwodeF )681.0( )871.0( )881.0( )181.0( )031.0( )921.0( )231.0( )131.0( ***432.3 ***064.2 ***951.3 ***764.2 eganaoL ***332.3 ***743.2 ***161.3 ***353.2 eganaoL )760.0( )420.0( )760.0( )420.0( )760.0( )420.0( )760.0( )420.0( ***300.0- ***400.0- ***300.0- ***400.0- 2)eganaoL( ***300.0- ***400.0- ***300.0- ***400.0- 2)eganaoL( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( ***80.91 ***00.11 ***73.81 ***62.01 nopuoC ***11.91 ***58.01 ***54.81 ***31.01 nopuoC )505.0( )171.0( )205.0( )261.0( )405.0( )961.0( )105.0( )061.0( ***450.0 ***750.0 ***350.0 ***750.0 )0001/1×(ezisnaoL ***450.0 ***650.0 ***450.0 ***650.0 )0001/1×(ezisnaoL )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( )000.0( ***105.0- ***673.0- ***405.0- ***683.0eganaol×nopuoC ***005.0- ***853.0- ***405.0- ***863.0eganaol×nopuoC )110.0( )400.0( )110.0( )400.0( )110.0( )400.0( )110.0( )400.0( ***892.0- ***473.0- ***292.0- ***773.0- )001×(rotcaF ***682.0- ***353.0- ***082.0- ***653.0- )001×(rotcaF )500.0( )500.0( )500.0( )500.0( )500.0( )500.0( )500.0( )500.0( ***466.0 ***684.0 ***358.0 ***090.1 eidderF ***029.0 ***359.0 ***321.1 ***665.1 eidderF )570.0( )770.0( )960.0( )270.0( )670.0( )870.0( )170.0( )370.0( ***330.0 ***650.0 OCIF ***330.0 ***550.0 OCIF )200.0( )200.0( )200.0( )200.0( ***310.0 ***920.0 erahsOPT ***510.0 ***030.0 erahsOPT )100.0( )100.0( )100.0( )100.0( ***040.0- ***700.0erahsfieR ***040.0- ***900.0erahsfieR )200.0( )200.0( )200.0( )200.0( ***909.5- ***043.4- ***863.5- ***913.4aciremAfoknaB ***958.5- ***394.4- ***233.5- ***784.4aciremAfoknaB )092.0( )880.0( )092.0( )980.0( )882.0( )390.0( )882.0( )490.0( ***801.2- ***457.0- ***398.1- ***995.0puorgitiC ***171.2- ***679.0- ***379.1- ***338.0puorgitiC )123.0( )421.0( )713.0( )521.0( )023.0( )231.0( )713.0( )331.0( ***081.9 ***53.11 ***532.9 ***83.11 nagroM.P.J ***761.9 ***81.11 ***902.9 ***71.11 nagroM.P.J )633.0( )321.0( )433.0( )421.0( )633.0( )131.0( )533.0( )331.0( ***954.4 ***808.3 ***546.4 ***900.4 ograFslleW ***193.4 ***695.3 ***855.4 ***977.3 ograFslleW )773.0( )711.0( )373.0( )611.0( )773.0( )321.0( )273.0( )221.0( 270.0- **017.0 870.0 **365.0 erahsdeF×aciremAfoknaB *163.0 ***877.0 ***775.0 ***767.0 pihsrenwodeF×aciremAfoknaB )913.0( )672.0( )023.0( )282.0( )391.0( )481.0( )591.0( )781.0( 976.0 ***260.1 *678.0 ***118.1 erahsdeF×puorgitiC ***348.0 ***571.1 ***070.1 ***736.1 pihsrenwodeF×puorgitiC )744.0( )573.0( )054.0( )973.0( )072.0( )252.0( )172.0( )652.0( ***935.2 104.0- ***796.2 342.0erahsdeF×nagroM.P.J ***887.0 882.0 ***650.1 **925.0 pihsrenwodeF×nagroM.P.J )074.0( )534.0( )074.0( )144.0( )362.0( )562.0( )362.0( )962.0( ***408.2 ***268.3 ***791.3 ***586.3 erahsdeF×ograFslleW ***577.1 ***581.2 ***160.2 ***232.2 pihsrenwodeF×ograFslleW )755.0( )375.0( )455.0( )475.0( )672.0( )192.0( )772.0( )192.0( (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniV (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudcihpargoeG (cid:88) — (cid:88) — (cid:88) — (cid:88) — seimmudegatniv-nopuoC (cid:88) — (cid:88) — (cid:88) — (cid:88) — snoitcaretniegatniv-recivresegraL 503,48 503,48 565,48 565,48 503,48 503,48 565,48 565,48 SPISUCfo# 685.0 925.0 085.0 815.0 885.0 435.0 185.0 325.0 derauqs-RdetsujdA ybdedivid2102/60-0102/60morfstnemyaperpfotnuomaehtsadetupmoc—setartnemyaperplatotfosnoissergerlanoitces-ssorcdeloopfostlusernoitamitseSLOehtstneserpelbatsihT :etoN deF .selbairavyrotanalpxerehtosallewsa))4(-)1(snmulocfotesdnocesehtni(erahsdeFro))4(-)1(snmulocfotestsrfiehtni(pihsrenwodeFno—0102/60fosaecnalablapicnirpgniniamereht egareva-dethgiewehtsi caw ;sdlohevreseRlaredeFehttahtiytirucesfoerahsehtsetoned erahsdeF ;evreseRlaredeFehtybdlehsiiytirucesfienoslauqetahtelbairavymmudasi pihsrenwo eidderFasiiytirucesfienoslauqetahtelbairavymmudasi eidderF ;diaperebotsniamertahtecnalablapicnirplanigiroehtfonoitcarfehtsi rotcaf ;loopegagtromgniylrednuehtnonopuoc a fo tluser a sa detanigiro erew taht loop a ni snaol fo erahs eht si erahs fier dna ;ytrap driht a yb detanigiro snaol fo erahs eht si erahs OPT ;erocs tiderc OCIF eht si OCIF ;ytiruces caM lacitsitatS .sesehtnerapnidetropererasrorredradnatstsuboR .)detroperton(tnatsnocaedulcnisnoitacfiicepsllA .segareva-dethgiewerascaowdna,slaw,alawselbairavehT .gnicnanfiersuoiverp .01.0<p ∗,50.0<p ∗∗,10.0<p∗∗∗ :ecnacfiingis

21 elbaT sgnidloh SBM ’sknaB rof setamitsE noissergeR )3( )2( )1( )3( )2( )1( selbairaV 4102/60-9002/10 :doirep elpmaS 4102/60-7991/10 :doirep elpmaS 271.0- 790.0- 380.0- 370.0 760.0 280.0 SBM∆ 1−t )511.0( )711.0( )990.0( )560.0( )660.0( )660.0( ***013.0- ***092.0- ***322.0- ***871.0- ***461.0- **980.0- SBM deF∆ t )480.0( )370.0( )770.0( )050.0( )940.0( )340.0( **952.0 ***342.0 **832.0 621.0 121.0 950.0 gnidnatstuo SBM∆ 1−t )511.0( )480.0( )101.0( )780.0( )380.0( )270.0( 210.0 400.0 010.0- 110.0stessA∆ 1−t )230.0( )030.0( )510.0( )510.0( 660.0 450.0 902.0 651.0 latipaC∆ 1−t )591.0( )561.0( )831.0( )531.0( 040.0 350.0 360.0- 930.0snaol etatse laeR∆ 1−t )301.0( )090.0( )150.0( )050.0( ***516.5 ***650.5 *334.2 *822.2 xedni sserts laicnaniF 1−t )348.1( )737.1( )813.1( )703.1( **642.8 **980.8 **720.4 780.3 htworg PI 1−t )302.3( )901.3( )959.1( )229.1( 020.0 910.0 **350.0 ***150.0 gnidnatstuo sdnob dna seton yrusaerT∆ t )520.0( )420.0( )120.0( )020.0( (cid:88) — — (cid:88) — — seimmud htnoM 66 66 66 012 012 012 snoitavresbo fo # 171.0 322.0 851.0 170.0 430.0 010.0 derauqs-R detsujdA tnedneped deggal eht no sgnidloh SBM ’sknab ni segnahc fo stluser noitamitse SLO eht stneserp elbat sihT :etoN raey-03 gnidnatstuo fo kcots eht fo egnahc deggal eht dna ,sgnidloh SBM evreseR laredeF ni egnahc eht ,elbairav ,stessa ediw-metsys fo secnereffid deggal eht edulcni osla snoitacfiiceps emoS .SBM caM eidderF dna eaM einnaF eht ,htworg noitcudorp lairtsudni deggal ,sserts laicnanfi fo xedni deggal a sa llew sa ,snaol etatse laer dna ,latipac si elpmas noitamitse ehT .seimmud htnom dna ,)AMOS-xe( gnidnatstuo sdnob dna seton yrusaerT ni ecnereffid llA .)3(-)1( snmuloc fo tes dnoces eht rof 4102/60-9002/10 dna )3(-)1( snmuloc fo tes tsrfi eht rof 4102/60-7991/10 lacitsitatS .sesehtnerap ni detroper era srorre dradnats tsuboR .)detroper ton( tnatsnoc a edulcni snoitacfiiceps .01.0<p ∗,50.0<p ∗∗,10.0<p ∗∗∗ :ecnacfiingis