Skin in the Game and Moral Hazard

What determines securitization levels, and should they be regulated? To address these questions we develop a model where originators can exert unobservable effort to increase expected asset quality, subsequently having private information regarding quality when selling ABS to rational investors. Absent regulation, originators may signal positive information via junior retentions or commonly adopt low retentions if funding value and price informativeness are high. Effort incentives are below first-best absent regulation. Optimal regulation promoting originator effort entails a menu of junior retentions or one junior retention with size decreasing in price informativeness. Zero retentions and opacity are optimal amongst regulations inducing zero effort.

Over the past two decades securitization markets have been an important source of funding for …nancial and non-…nancial corporations. As shown in Table 1, mortgage-related and non-mortgagerelated asset-backed securities (ABS below) accounted for over 30% of U.S. bond market issuance each year from 1996 to 2011, with the percentage exceeding 50% from 2002 to 2005. As shown in Table 2, non-mortgage-related ABS cover a diverse range of assets outside the housing sector: equipment; auto loans and leases; credit card debt; student loans; and trade receivables. Securitization markets collapsed in 2008, with issuance falling by 44% from 2007 levels. The majority of the decline is accounted for by the virtual disappearance of non-agency mortgage-backed securities.
However, it is apparent that weakness extends beyond the housing sector. For example, issuance of credit card and student loan ABS has also fallen signi…cantly in recent years. Gorton (2010) argues that concern over asymmetric information regarding true asset values accounts for the collapse of ABS markets, but disputes the existence of moral hazard, e.g. the alleged failure of originators to carefully screen borrowers. In contrast, Mishkin (2008) and Stiglitz (2010) argue that low originator retentions created moral hazard. In their behavioral narrative, unwary investors had simply overlooked moral hazard pre-crisis. Indeed, implicit in much discussion surrounding the crisis is the notion that ABS featuring low originator retentions are indicative of market irrationality. Moreover, implicit in the recently-passed Dodd-Frank Act is the view that government-mandated retentions will increase social welfare.
Understanding equilibrium in ABS markets and the formulation of optimal regulation have been hindered by the absence of a comprehensive theoretical framework allowing one to answer This paper develops a tractable, yet comprehensive, framework to address the positive and 2 normative questions posed above. Although the primary focus is ABS, the economic setting is more general: Ex ante, an agent ("the originator" below) considers exerting costly unobservable e¤ort to increase the probability of producing a high quality asset. This e¤ort decision is made anticipating subsequent issuance of claims backed by the asset to fund a scalable investment with positive NPV. 1 The issuer privately observes the true asset quality (high or low) but investors do not.
There are three categories of investors: a speculator; competitive uninformed market-makers; and rational uninformed investors with hedging motives. The originator can permit (block) speculator information production by choosing transparency (opacity).
The model delivers a rich set of predictions regarding how issuers will behave in unregulated ABS markets. We …rst investigate what securities will be marketed and retained by privately informed issuers. One possible equilibrium is a separating equilibrium in which high types distinguish themselves from low types by retaining the minimal size junior tranche needed to deter mimicry by low types who fully securitize. In addition to this separating equilibrium, there may exist equilibria in which originators adopt identical structures. Such pooling equilibria exist if both originator types are weakly better o¤ than at the separating equilibrium.
We show that if any pooling equilibrium can be sustained, a pooling equilibrium with full securitization can also be sustained. 2 In this sense, the originate-to-distribute business model (OTD below), which features zero issuer retentions, should not be viewed as an anomaly. However, we also show that pooling at full securitization can only be an equilibrium if prices are su¢ ciently informative and the originator's project NPV is su¢ ciently high. Intuitively, a high type will be willing to pool provided informed speculation drives his issuance price su¢ ciently close to fundamental value.
We also show some observed practices are hard to reconcile with notions of rational equilibrium. For example, a deliberate e¤ort by issuers to preclude speculative information production via opacity is shown to be inconsistent with investor sophistication. Intuitively, issuers with positive information 1 The fact that securities are written on an asset in place, excluding the new investment, departs from some corporate …nance settings and models. 2 Here we refer to the continuation equilibrium. 3 have a strong incentive to deviate from opacity, and sophisticated investors should recognize this.
We next evaluate ex ante e¤ort incentives of originators who anticipate such marketing of securities under asymmetric information. Since e¤ort increases the probability of developing a high quality asset, incentives are increasing in the size of the anticipated wedge between payo¤s accruing to owners of high and low quality assets. Critically, the inability of investors to observe true asset quality at the time of securitization reduces the size of this wedge, lowering e¤ort incentives. In this subtle way, the model shows that the asymmetric information view of Gorton (2010) and the moral hazard view of Mishkin (2008) and Stiglitz (2010) are not necessarily competitors. Rather, if investors are unable to observe true asset quality, then in all possible equilibria e¤ort incentives are lower than under observable types. In the separating equilibrium, incentives are diminished since high types bear signaling costs. In pooling equilibria, incentives are diminished by price noise. In the extreme case of opacity and zero retentions, there is zero e¤ort incentive.
The analysis of unregulated ABS markets reveals three welfare arguments for governmentmandated retentions. First, privately optimal retentions can be socially suboptimal since originators do not internalize e¤ects on investor welfare. When a high type credibly signals via junior retentions he bene…ts directly from his own marketed securities being priced at their fundamental value on the issuance date. But he does not internalize the bene…t accruing to investors who can now e¢ ciently share risks being symmetrically informed. The second argument favoring regulation is that the payo¤ di¤erential between high and low types at the (interim) securitization stage may be insu¢ cient to induce originator e¤ort. In order to encourage e¤ort, low types should get low payo¤s.
But if retentions are not mandated, a low type can always get his symmetric information payo¤ by admitting he is a low type and proceeding to securitize the entire asset. Government-mandated retentions o¤er a commitment device against markets implementing such incentive-reducing equi- A socially optimal mandatory retention scheme for promoting originator e¤ort does so by increasing the spread between payo¤s to high and low types at the securitization stage, while accounting for costs imposed on investors as well as originators. There are two regulatory options. In a separating regulation issuers must choose from a menu of retentions. The menu is designed so that the chosen retention reveals the issuer's private information. In a pooling regulation all issuers must retain the same claim.
In the optimal separating regulation, originators choose from a menu of strictly positive junior tranche retentions of di¤ering size. Although menus featuring other retained claims (e.g. fractions of total cash ‡ow) can also induce truthful revelation of private information, junior tranche retentions minimize the cost of underinvestment by originators. In contrast to the separating equilibrium of unregulated markets, the separating regulation forces even the low type to retain a junior claim. This regulation achieves e¢ cient risk sharing amongst investors since the originator's chosen retention reveals his private information, thus insulating investors from adverse selection.
In the optimal pooling regulation, issuers are forced to hold identical junior tranches. Intuitively, the gap between the interim payo¤s of high and low types is maximized if originators hold a junior claim. The size of the mandated retention is decreasing in price informativeness. This is because junior retentions and market discipline are substitute sources of e¤ort incentives. The disadvantage of the pooling regulation is that it entails costly speculator e¤ort and distortions in risk sharing amongst investors. However, the pooling scheme imposes lower underinvestment costs on originators if prices are su¢ ciently informative.
Our model is most similar to those of Leland and Pyle (1977) and Myers and Majluf (1984) in that we consider equilibrium security issuance by a privately informed originator. We depart from canonical signaling models in three ways. First, we consider that there is an e¤ort decision 5 to be made before the issuance stage, with costly e¤ort increasing the probability of obtaining a high value asset. Second, at the issuance stage, securities are traded by an endogenously informed speculator. Third, rational uninformed investors with hedging needs also trade securities. The …rst model element allows us to address how the anticipation of interim-stage asymmetric information a¤ects ex ante e¤ort incentives. The second element permits assessment of the role of price discipline.
The third element admits a proper analysis of social welfare and the e¢ ciency of risk sharing in light of uninformed investors potentially facing adverse selection.
Dang, Gorton and Holmström (2011) also analyze information production and social welfare, but ignore originator moral hazard. Similar to their analysis, we show opacity combined with full securitization maximizes interim-stage social welfare. However, we show opacity is only socially optimal amongst regulatory schemes failing to induce originator e¤ort. Intuitively, opaque markets fail to provide price discipline. Thus, the choice between mandating opacity versus transparency must weigh interim-e¢ cient risk sharing against ex ante moral hazard.
Rajan, Seru and Vig (2010) analyze a setting most similar to ours in that they too consider a bank that can exert unobservable e¤ort prior to entering into securitization contracts. However, they assume each loan is fully securitized with an exogenous probability. In contrast, we …rst characterize the set of equilibrium ABS structures and then assess the e¤ect of each on e¤ort incentives. Their model does not allow for informed trading and they do not analyze optimal regulation. Gorton and Pennacchi (1995), Parlour and Plantin (2008), and Plantin (2011) consider a di¤erent agency setting in which contracting occurs before a bank chooses e¤ort. The respective agency problems are di¤erent. The pre-contracting e¤ort we consider is akin to screening of loan applicants while the post-contractual e¤ort they consider is akin to monitoring of loan recipients. These papers do not analyze speculative information production or optimal regulation. Plantin (2011) the prediction that securitization rates should be higher if banks place high value on immediate funding.
Hartman-Glaser, Piskorski and Tchistyi (2012) analyze optimal contracting before unobservable e¤ort. Their optimal dynamic contract features a single positive transfer to the agent made only 6 after a su¢ cient time with no defaults. Their privately optimal contract is socially optimal and there is no case for regulation.
The role of price informativeness in alleviating moral hazard has been analyzed in other contexts. Holmström and Tirole (1993), Maug (1998), Kahn and Winton (1998) Each of these papers assumes pure noise trading, precluding welfare analysis. These papers do not analyze socially optimal mandatory retention regulations.
The remainder of the paper is as follows. Section I describes the model. Section II analyzes the …nal continuation game in which market-makers set prices. Section III analyzes the subgame in which the privately informed originator chooses retentions. Section IV analyzes originator e¤ort incentives. Section V contains an analysis of the sources of welfare losses in unregulated market equilibria, followed by an analysis of socially optimal mandatory retentions. The conclusion suggests directions for empirical work.

I. The Model
This section describes the production technology, endowments, investor preferences and the timing of events. Figure 1 provides an overview of the time-line.

A. Production Technology, Endowments and Preferences
There is a single storable consumption good and four periods: 1, 2, 3 and 4. Agents consume in periods 3 and 4 and consumption must be non-negative. The originator (denoted O) has one unit of endowment in period 1 which he can use to fund an observable investment in an asset generating a veri…able cash ‡ow in period 4. O has no other endowment and is risk-neutral with von Neumann-Morgenstern (vNM) utility function C 3 + C 4 : At the time of the initial investment, O has the option to exert unobservable e¤ort which increases expected cash ‡ow. In particular, by exerting e¤ort O increases the probability of the asset being of high quality from to ; where 0 < < < 1. A high quality asset generates cash ‡ow H with probability q and L with probability 1 q: A low quality 7 asset generates H with probability q and L with probability 1 q: It is assumed: 0 < q < q < 1; L 2 (0; H); and qH + (1 q)L > 1: This last assumption implies O …nds it optimal to make the initial investment.
The originator e¤ort cost is denoted c, and this cost is non-pecuniary. We assume the e¤ort cost is less than the expected increase in cash ‡ow that it produces.
Assumption A1 implies the originator would exert e¤ort if he planned to retain all claims to future cash ‡ow.
At the start of period 2, the interim period, Nature draws q and then O privately observes q: The variable q is labeled the asset type.
The …nal set of investors is a measure-one continuum of agents who have no information regarding the asset type, labeled uninformed investors (UI). The UI are identical ex ante aside from idiosyncratic di¤erences in risk-aversion parameters ( ) discussed below. UI are risk-neutral over period 3 consumption and risk-averse over period 4 consumption.
An extant literature treats uninformed trading as exogenous. Although such noise trading frameworks are a bit simpler, they su¤er from two weaknesses in terms of policy analysis. First, noise trading models preclude analysis of total social welfare. Second, by treating uninformed investors as price-insensitive, such models fail to capture deadweight losses arising from portfolio distortions in response to perceived security mispricing. In light of these weaknesses, we depart from the standard noise trading setup. Instead, we model the UI as choosing portfolios optimally given well-de…ned utility functions described below.
Prior to the trading of securities in period 3 each UI privately learns whether he is invulnerable or vulnerable to preference and endowment shocks. The utility function of an arbitrary UI is: 4 U (C 3 ; C 4 ; ; ) C 3 + minfC 4 ; 0g: The idiosyncratic utility function parameters 2 [1; 1) and have density f with cumulative distribution function F . The distribution has no atoms and f is strictly positive. The indicator function in the utility function is equal to 1 if and only if the UI is vulnerable. The term captures an adverse utility shock hitting vulnerable UI, with > 0 representing a higher critical C 4 threshold confronting vulnerable UI. Vulnerable UI face an endowment shock positively correlated with the asset's cash ‡ow. 5 If the cash ‡ow is H; each vulnerable investor's period 4 endowment is equal to their critical consumption threshold : If the cash ‡ow is L; their period 4 endowment is 0. 4 Smooth utility functions could be assumed at the cost of more complex aggregate demands. 5 The characterization of equilibrium securitization structures and originator e¤ort incentives are unchanged if there is negative correlation between UI endowments and cash ‡ow.

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By construction, the preference and endowment shocks of the vulnerable UI give them a motive to purchase units of an Arrow security paying 1 if the realized cash ‡ow is L, and they would do so in the absence of asymmetric information or funding limitations. It is assumed the aggregate period 3 endowment of the UI, denoted y ui 3 , exceeds so vulnerable UI have ample funds to purchase full insurance should they so choose. Finally, the period 4 endowment of the invulnerable UI is : Since these investors su¤er no adverse preference shock, they have no insurance motive and instead desire to transfer resources from period 4 back to period 3.
One may think of the negative endowment shock hitting vulnerable UI in the event of a low cash ‡ow realization as capturing negative externalities arising from distressed or foreclosed properties. The proportion of vulnerable UI is an independent random variable v 2 fv; vg; with each possible v equiprobable and v < v. Whether an agent is vulnerable or not is not observable or veri…able to others, nor is their realized endowment. This prevents writing insurance contracts directly on individual endowments. Further, the realized v is not observable or veri…able. Thus, securities markets are necessarily incomplete.

B. Securitization Stage
The Securitization Stage takes place in period 2. This stage approximates a shelf registration of securities whereby a prospective issuer of a set of securities registers them in advance and is then free to pull securities "o¤ the shelf" over some time interval without additional …ling requirements.
Shelf registrations are commonly used for ABS. 6 Applying a result of Maskin and Tirole (1992) for 6 Some proposals call for mandatory retentions as a requirement for using the shelf registration procedure. See "SEC signaling games in general, Tirole (2006) shows allowing an issuer to …rst register a set of claims and then choose from his "menu" of registered claims can improve his payo¤ by restricting the set of potential equilibrium outcomes.
The Securitization Stage begins with O registering two securitization structures, ( ; ) with the number of structures equal to the number of possible types. Each structure speci…es the amounts (M L ; M H ) that will paid to outside investors in the respective cash ‡ow states should the originator choose to issue it. Investors are assumed to have limited liability, so payments to them must be non-negative.
Next O, selects one of the registered structures to bring to the market, committing to retain the residual cash ‡ow rights. The payo¤ vector on the retained security is denoted (R L ; R H ): Since the originator has no outside endowment other than the asset, both R L and R H must be non-negative.
The cash ‡ow rights retained by the originator are assumed to be a legally veri…able contractual commitment, consistent with the mandatory disclosure rules of Regulation AB of the Securities Exchange Act. It is worth noting that the owner of a high quality asset stands to bene…t from such a retention commitment as it allows him to credibly signal positive information.
Total state-contingent payo¤s on retained and marketed securities are equal to the cash ‡ow generated by the underlying asset: Notice, the preceding payo¤ identities assume the originator invests all funds raised from investors in the new investment yielding a private bene…t. That is, it is assumed the originator does not place any of the funds raised from investors into risk-free storage. Doing so would simply allow the originator to raise promised payments to investors by one dollar for each additional dollar raised and would be unchanged, while outside investors would be no better or worse o¤ relative to storing the funds on their own accounts.
Voluntary disclosure of additional information is also possible at the Securitization Stage. In particular, the originator has the option to disclose in the prospectus additional information about the underlying asset (transparency) or not (opacity). This additional information can be used by the speculator to acquire a signal of the asset quality.

C. Trading Stage
The Trading Stage of the model takes place in period 3. All securities trading takes place in this period, just after investors observe their private information. There are two securities markets: a market for risk-free bonds and a market for an Arrow security paying 1 if the realized cash ‡ow is L. These two securities span the only two veri…able states (L and H), and the introduction of markets for redundant securities would have no e¤ect on the equilibrium set.
At the start of the Trading Stage, S chooses whether to pay e to acquire a signal of the asset type.
Recall, signal acquisition is only possible if the originator opted for transparency at the Securitization Stage. Next, each UI privately observes whether he is vulnerable to shocks. Next, each agent other than the MM submits his market order. 7  As is standard in the literature on General Equilibrium with Incomplete markets, short-selling is possible in both securities markets, but courts will impose an arbitrarily high utility penalty on any agent who fails to deliver promised payments to securities market counterparties, thus ruling 7 The characterization of equilibrium retentions is unchanged if one instead considers limit orders. 8 Regulations AB and M of the Securities Exchange Act prohibit originators from clandestine trading.
12 out reneging on short sales. 9 The model is solved by backward induction. As in Maskin and Tirole (1992), the equilibrium concept is pure strategy perfect Bayesian equilibrium (PBE).

D. Benchmark: Observable Types
Before characterizing equilibrium under asymmetric information, it is useful to analyze outcomes if the asset type was observable. This benchmark setting is particularly useful in framing our argument that the inability of investors to observe asset quality can be understood as a root cause of originator moral hazard.
If q was observable, O would market all cash ‡ow and receive securitization proceeds equal to the true expected cash ‡ow qH + (1 q)L: Full securitization would occur since > 1 implies there are gains from trade, and these would be fully exploited under symmetric information. Therefore, if types were observable, the maximum e¤ort cost the originator would be willing to incur (b c obq ) is times the expected increase in cash ‡ow arising from e¤ort: Assumption A1 implies that the originator would pay the cost c if the true asset type were commonly observable.
Consider …nally equilibrium risk-bearing with observable types. If q was observable, the speculator would not pay e. The MM would set the price of the L-state Arrow security to 1 q. At that actuarially fair price, all vulnerable UI would fully insure against negative endowment shocks, buying units of the L-state Arrow security.

II. The Trading Stage
This section analyzes UI security demand, speculator e¤ort and price setting by the MM. Given that we con…ne attention to pure strategies, there are two possible information con…gurations at the 9 See Dubey, Geanakoplos and Shubik (2005) for GEI with …nite penalties to reneging and endogenous default.
13 start of the Trading Stage: all agents know the asset's type or all agents other than the originator are uninformed regarding its type. We consider these two cases in turn.

A. Asset Type Common Knowledge
Competition between MM ensures risk-free bonds trade at price 1 per unit of face value. Let P denote the price of the L-state Arrow security. If the type (q) is known to all agents at the start of the Trading Stage, the MM set P = 1 q: With the type known, the speculator has no incentive to incur e¤ort costs, and any trading by the speculator is of no consequence for any agent's expected utility, including her own.
Since securities markets span the veri…able cash ‡ow states, an uninformed investor's portfolio problem can be framed as a choice of state-contingent period 4 portfolio payo¤s, here denoted (x L ; x H ): With common knowledge of type, an optimal UI portfolio solves: As shown in the appendix, one …nds the following optimal UI portfolios under common knowledge of q. Vulnerable UI purchase units of the L-state Arrow security while invulnerable UI sell units of the risk-free bond. The sharing of risks across investors under common knowledge of type is socially e¢ cient ex post, with all vulnerable UI buying from the MM fairly priced insurance against costly consumption shortfalls.

B. Asset Type not Common Knowledge
Consider the remaining case when asset type is not common knowledge at the start of the Trading 14 Stage. Here the optimal period 4 portfolio for an arbitrary UI solves: As shown in the appendix, the solution of the preceding program implies the following optimal portfolios. Invulnerable UI sell units of the risk-free bond. Vulnerable UI buy units of the The remaining vulnerable UI do not trade. Note, the vulnerable UI with b achieve the critical consumption level C 4 = regardless of the realized asset payo¤. In contrast, vulnerable UI with < b consume in state H but only 0 in state L. Intuitively, all vulnerable UI have an incentive to insure against consumption shortfalls by purchasing units of L-state payo¤s. However, if they expect the Arrow security price to exceed its expected payo¤, they forego insurance provided their idiosyncratic loss ( ) from consumption shortfalls is su¢ ciently low.

Consider then Trading Stage outcomes if the originator had chosen opacity in the Securitization
Stage. In this case, the MM know order ‡ow cannot possibly contain any information regarding the asset type. Consequently, regardless of the observed order ‡ow, the MM set the price of the Arrow security equal to 1 q (1 )q: It follows from equation (4)  Consider next Trading Stage outcomes under transparency, conjecturing the speculator will indeed …nd it optimal to acquire the noisy signal of the asset type provided e is su¢ ciently low.
Integrating over uninformed investors' optimal demands (x L ), the aggregate UI demand for the Consider next the speculator's trading strategy in the market for the L-state Arrow security. The speculator cannot make trading gains by shorting, since the MM will justi…ably impute short-selling to the speculator. So she will place buy orders for the L-state Arrow claim when she observes the negative signal s. In order for the speculator to make positive expected trading gains, she must choose a buy order size such that the MM cannot infer s with probability one. This can only be achieved by choosing an order size for the L-state Arrow claim such that MM cannot distinguish between: speculator buying (based upon signal s) cum low UI demand (v) versus speculator not buying (based upon signal s) and high UI demand (v). Using the aggregate demand expression from equation (5), we obtain the following condition pinning down the buy order size (X S L ) that masks the speculator across the states (s; v) and (s; v): For brevity, let: Since each UI has measure zero, any order ‡ow con…guration o¤ the equilibrium path must arise from a deviation by the speculator. O¤ the equilibrium path, MM form worst-case beliefs from the speculator's perspective. An aggregate buy (sell) order o¤ the equilibrium path is imputed to her observing s (s). Given such beliefs, no deviation generates a positive gross trading gain for the speculator.
Having pinned down the speculator's optimal signal-contingent trading strategy, we consider next the conditions under which she will pay the e¤ort cost e. If the speculator acquires the signal, her equilibrium expected gross trading gain G as computed from Table 3 is: It is readily veri…ed that if the speculator were to instead remain uninformed, her optimal strategy is to abstain from trading. 10 Returning to Table 3 we …nd that under transparency vulnerable UI form the following price expectation: The remainder of the analysis assumes the …xed cost of speculator e¤ort satis…es the following technical assumption, which implies the speculator exerts e¤ort in the Trading Stage provided the originator chose transparency at the Securitization Stage.
A2 : And it then follows from equation (9) that risk sharing will be distorted under transparency since a subset of the vulnerable UI fail to insure given that the expected L-state Arrow security price is above its expected payo¤.
The following proposition summarizes the continuation equilibrium at the Trading Stage. (1 )(1 q) and all vulnerable investors insure against shocks. Under transparency: the speculator acquires the costly signal; P is set according to equation (7); and vulnerable investors only insure against shocks if b tran as de…ned in equation (9).

III. The Securitization Stage
Continuing the backward induction, this section describes the set of continuation equilibria at the Securitization Stage. This subgame begins with Nature drawing the type q 2 fq; qg, which is then privately observed by the originator. The other players have a common prior for the probability of the type being q: This -contingent subgame may be of independent interest as it resembles a standard signaling game where the equilibrium set is predicated upon investor priors.
For simplicity, we borrow terminology from Tirole (2006) when possible.
Recall, at the Securitization Stage the originator performs a shelf registration of two securitization structures and then chooses one from the menu. A separating menu contains two di¤erent structures such that each type prefers a di¤erent structure. If such a menu is registered, the subsequent choice of structure reveals the type to all agents, so the type becomes common knowledge at the start of the Trading Stage. A pooling menu contains only one securitization structure so there is no possibility of the type being revealed by the choice of structure.
We …rst characterize the least-cost separating (LCS) allocations which maximize the utility of each originator type within the set of separating menus. We conjecture and then verify the high type will not mimic the low type. The LCS allocations allow the low type to fully securitize his asset since this raises his payo¤ and relaxes the non-mimicry (NM) constraint. The high type's LCS retention solves: 18 subject to the following NM constraint: Solving the above program yields the following lemma. The respective continuation utilities for the low and high type are: In an LCS allocation, the low type receives his symmetric information payo¤. The high type receives his symmetric information payo¤ less the NPV foregone due to signaling via retention of a claim paying zero if the realized cash ‡ow is L: Throughout the analysis we refer to such claims as junior in that their payo¤ is equal to that of a junior claim when there is a senior debt claim with face value between L and H: The next lemma is similar to a more general result from Maskin and Tirole (1992), showing that the LCS payo¤s constitute a lower bound on equilibrium payo¤s. is apparent that any pooling cum transparency makes the UI worse o¤ by exposing them to adverse selection in securities trading (Proposition 1).
Lemma 2 provides a simple algorithm for assessing whether a pooling structure is in the set of PBE. One must simply compute expected utilities for both originator types in a posited pooling equilibrium and compare them with the respective LCSE utilities. Originator utility in the event of pooling is equal to times expected securitization revenues, plus the expected payo¤ on the retained security, with both expectations computed conditional upon the privately known type.
Under opacity, expected securitization revenues are equal across types. Thus, under opacity, the following two inequalities must be satis…ed by any pooling equilibrium: Under transparency, informed trading drives prices closer to fundamentals and securitization revenues vary across originator types. The following two inequalities must be satis…ed by any pooling equilibrium featuring transparency: The endogenous variable z plays a critical role in the model, measuring the informational e¢ ciency of prices. For example, in the purely hypothetical case where z = 1; there is no mispricing. In fact, z is increasing in ; with z 2 ( ; (1 + )=2]: Intuitively, if the speculator has a more precise signal, the expected wedge between price and true value is lower.

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Exploiting equations (12) and (13) Under opacity, a necessary and su¢ cient condition for a pooling equilibrium with full securitization is q q q q : The intuition for Proposition 2 is as follows. In order for a pooling equilibrium to be supported, both types must be weakly better o¤ than at the LCSE. And the low type is able to fully securitize his asset in the LCSE. In order to improve upon this, M H must be su¢ ciently high to ensure the It follows from the …nal two statements of the proposition that if pooling at opacity can be sustained as an equilibrium, then pooling at transparency can also be sustained as an equilibrium.
Intuitively, the high type is more willing to pool if prices are closer to fundamentals as is the case under transparency. Finally, pooling at opacity is easier to sustain as a continuation equilibrium at than under : Intuitively, the high type is more willing to pool at opacity if investors have more favorable prior beliefs, a standard result in signaling models.
Further intuition regarding the set of pooling equilibria is provided by Figures 2A and 2B.
Using equations (12) and (13), each …gure plots pairs of marketed cash ‡ows (M L ; M H ) in pooling equilibria that just pin the two originator types to their respective LCSE payo¤s. The better-than set is the region above the respective indi¤erence curves. Figure 2A depicts transparency and Figure   2B depicts opacity. To isolate the role of price informativeness, model parameters are held …xed across the two …gures. Consider …rst Figure 2A. With transparency, the low type's indi¤erence curve is above that of the high type. Thus, the low type's indi¤erence curve is the relevant boundary for the set of pooling equilibria. Intuitively, the low type is more reluctant to pool than the high type if prices are closer to fundamentals. Consider next Figure 2B. With opacity, the high type's indi¤erence curve is above that of the low type, re ‡ecting his reluctance to pool given that securities will be priced far from fundamentals. Thus, under opacity the high type's indi¤erence curve is the relevant boundary for the set of pooling equilibria. Comparing across the …gures it is apparent that the level of securitization sustainable as a pooling equilibrium is in ‡uenced by price informativeness.
Post-crisis there has been much debate about whether observed securitization levels and the opacity of structures constitute evidence of investor irrationality. Using the perfect Bayesian equilibrium concept, one cannot argue full securitization and/or opacity are inconsistent with rationality.

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After all, one implication of Proposition 2 is that full securitization cum opacity can be sustained as a rational market equilibrium if is su¢ ciently high. However, it can be argued that the PBE concept constitutes a weak test of rationality inasmuch as it can admit o¤-equilibrium beliefs that seem unreasonable. The following proposition identi…es structures satisfying the Intuitive Criterion, which imposes stronger restrictions on o¤-equilibrium beliefs.
Proposition 3 A necessary and su¢ cient condition for a perfect Bayesian equilibrium to satisfy the Intuitive Criterion is that interim type-contingent utilities for the originator (U ; U ) satisfy The Criterion since all originators get paid the same price for marketed securities. A more "sophisticated" market would infer that only low types prefer opacity. Proposition 3 also shows full securitization can satisfy the Intuitive Criterion. However, comparing inequalities across Proposition 2 and Proposition 3 one sees that in order to satisfy the Intuitive Criterion, pooling at full securitization demands a higher degree of price informativeness.

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As the last step in the backward induction, this section considers the originator's e¤ort decision in period 1.

A. Originator Willingness-to-Pay
Let b c denote the maximum cost the originator would be willing to incur in order to increase the high type probability from to : For each pair of type-contingent originator utilities (U ; U ) in the set of Securitization Stage continuation equilibria, the corresponding willingness-to-pay (b c) is: The preceding equation delivers a simple message: originator e¤ort incentives at the ex ante stage are increasing in the wedge between type-contingent interim-state continuation utilities.
Before considering the e¤ort incentive generated by any speci…c continuation equilibrium, we prove that unobservable quality lowers e¤ort incentives in any unregulated market equilibrium. In The …rst inequality in equation (15) follows from the fact that the low type receives at least his perfect information payo¤ in any PBE, as shown in Lemma 2. The last inequality follows from the fact that the high type gets less than his perfect information payo¤ in any PBE. In the LCSE, the high type underinvests in order to signal positive information. And in any pooling equilibrium the high type's securities are underpriced. We have established the following key result.

Proposition 4
In all unregulated market equilibria, originator e¤ ort incentives are less than under perfect information regarding types.
We turn next to a consideration of the e¤ort incentives implied by each continuation equilibrium.
From equation (14) and Lemma 1 it follows that originator willingness-to-pay in the LCSE is b c lcs = [ ( )(q q)(H L)] q q q q : 24 The …rst square bracketed term in the expression for b c lcs is the maximum e¤ort cost the originator would pay under observable types. The second bracketed term is a number less than one. Intuitively, at the LCSE the high type bears the underinvestment cost of signaling while the low type gets his perfect information payo¤. Consequently, there is less incentive to put in e¤ort aimed at becoming a high type.
Consider next e¤ort incentives if the continuation equilibrium entails pooling. Here we must distinguish between pooling cum transparency versus pooling cum opacity. The respective willingnessto-pay expressions are: Notice that under transparency there are two sources of e¤ort incentives: the retained claim and market discipline, with high types expecting a higher price for their marketed security (since Propo- Equation (17) The …rst square-bracketed term in the expression for b c otd tran is the cuto¤ cost that would obtain under perfect information regarding asset type. It can be veri…ed that the second bracketed term is a number less than one half. corresponding willingness-to-pay for the originator using the formulae in the preceding subsection.

B. Equilibrium E¤ort
Next let: Notice, for each of the sets de…ned above, the willingness-to-pay is consistent with the posited continuation path, e.g. b c( ) c if is a continuation equilibrium arising when no e¤ort has been exerted ( = ): b c max max We have the following proposition. The importance of the preceding proposition is to highlight the possibility of multiple equilibrium e¤ort levels. Of course, since continuation payo¤s determine the originator's willingness-to-pay (equation (14)), the possibility of multiple equilibrium e¤ort levels is a natural consequence of the fact that there are potentially multiple Securitization Stage continuation equilibria. To take an example, suppose (q q)=( q q) and [z( ) z( )] 1: The …rst inequality implies full securitization combined with either opacity or transparency falls within the set of continuation equilibria.
And we have seen that if the continuation equilibrium entails opacity cum full securitization, the originator will not exert e¤ort regardless of the required cost c. In contrast, if the continuation equilibrium entails transparency, the second inequality (combined with Assumption A1) implies the originator will exert e¤ort for each possible c. Therefore, in this example, for each possible c value, no-e¤ort and e¤ort can both be sustained as equilibrium decisions at the origination stage.
The preceding proposition o¤ers two alternative interpretations of the apparent decline in lending 27 standards in the run-up to the credit crisis of 2007-2008, with di¤ering implications for regulation.
One interpretation is that no-e¤ort was inevitable in any unregulated market equilibrium. This interpretation corresponds to c > b c max . An alternative interpretation is that unregulated markets were simply trapped in an equilibrium with low e¤ort incentives. This interpretation corresponds to , with unregulated markets happening to implement an equilibrium with a low b c: In this case, a su¢ cient remedy for lender laxity is light-touch regulation selecting an e¤ort-inducing equilibrium from the set of potential unregulated market equilibria, e.g. mandating transparency when opacity was otherwise viable as an equilibrium.
The prior analysis also suggests a potentially critical role for investor sophistication in alleviating originator moral hazard by way of eliminating Securitization Stage continuation equilibria generating low e¤ort incentives. For example, the Intuitive Criterion precludes pooling at full securitization cum opacity, an outcome that destroys e¤ort incentives. More generally, from Proposition 3 it follows the Intuitive Criterion demands that the gap between type-contingent interim utilities be su¢ ciently large, which is precisely what is needed to promote originator e¤ort ex ante, as shown in equation (14).

A. Welfare in Unregulated Markets
This subsection considers the welfare losses implicit in the various unregulated market equilibria.
To understand the source of welfare losses, it is useful to recall outcomes if the asset type was observable. As discussed above, with observable q, the originator would …nd it optimal to exert e¤ort given that the expected output increase exceeds e¤ort costs (Assumption A1). At the Securitization Stage the entire asset would be marketed since the originator's investment has positive NPV. And it was shown in Section II that with known q each vulnerable UI would fully insure against consumption shortfalls by purchasing units of the L-state Arrow security at an actuarially fair price of 1 q.
Invulnerable UI would borrow in period 3 against their future endowment windfall in order to shift consumption forward as desired. Finally, the speculator would not exert costly e¤ort to acquire information and would simply consume his endowment. The implied social welfare with observable types is equal to the sum of the expected utilities of the originator, uninformed investor and speculator: +y ui Appendix B presents formulas for social welfare under each unregulated market equilibrium.
For brevity, we present in this subsection expressions for the welfare gap. Consider …rst the welfare gap if the unregulated market equilibrium entails pooling at opacity cum full securitization of the underlying asset ("OTD"). Such an equilibrium has a number of bene…ts in terms of social welfare.
The speculator does not exert costly e¤ort. And with symmetric ignorance, e¢ cient risk sharing across investors is achieved, with each vulnerable UI buying fairly priced insurance against consumption shortfalls (Proposition 1). Finally, with full securitization, there are no underinvestment costs. In fact, the only social cost of such an equilibrium is that it provides zero e¤ort incentive (b c = 0), as shown in Section IV. So here the welfare gap is equal to the net social value of originator 29 e¤ort. Using the social welfare formulae in Appendix B, the gap between welfare under observable types versus OTD cum opacity is: The right side of the preceding equation measures the net social value of originator e¤ort. The …rst term in the square brackets is the expected increase in the asset's cash ‡ow resulting from originator e¤ort, which is scaled up by the originator's funding value : The second term in square brackets is the expected increase in the endowment of uninformed investors resulting from originator e¤ort.
Recall, a low realized cash ‡ow results in an endowment loss of units for each vulnerable UI, with the aggregate measure of the vulnerable UI being an equiprobable random variable v 2 fv; vg: Essentially, the second term captures the social value of reductions in externalities arising from distressed or foreclosed assets. The failure of lenders to account for such externalities at the time of loan origination is a …rst market failure.
As shown below, the net social value of originator e¤ort is actually a key welfare loss associated with any unregulated market equilibrium failing to induce e¤ort. And at this point it is worth addressing the following question: Why does an unregulated securitization market admit equilibria failing to induce originator e¤ort? Essentially, the unregulated market admits as equilibria securitization structures achieving a su¢ ciently high payo¤ to originators after their e¤ ort decision, as shown in Lemma 2. For example, as shown in Proposition 2, if is very high originators may pool at OTD cum opacity. Such an outcome actually maximizes interim-stage social welfare, but results in zero ex ante e¤ort incentive. Tension between interim-e¢ ciency and moral hazard is common to many agency settings (see e.g. Fudenberg and Tirole (1990)). Anticipating, the tension between ex ante and interim e¢ ciency provides one potential rationale for government intervention.
Regulation can commit issuers not to implement some structures, even some with a high level of interim-e¢ ciency (e.g. opaque OTD), with the goal of restoring e¤ort incentives.
Consider next the welfare gap if the unregulated market equilibrium entails pooling at opacity and partial securitization. In this case, the social welfare gap is increased by an amount equal to the foregone project NPV due to originator retentions. However, the net social value of originator e¤ort is potentially recaptured since the retained claim increases e¤ort incentives provided R H > R L ; as shown in equation (17). We have the following welfare gap.
Consider next the welfare gap if the unregulated market equilibrium entails pooling at transparency. In this case, there are four sources of welfare losses. First, there is a welfare loss equal to the foregone NPV from investment due to originator retentions. Second, the net social value of originator e¤ort is lost if b c tran < c: Third, under transparency the speculator exerts costly e¤ort gathering information. Fourth, as shown in Proposition 1, the existence of an informed speculator distorts risk sharing in that a subset of vulnerable UI forego insurance against consumption shortfalls, fearing adverse selection. As shown in Lemma 2, in their own decisionmaking, originators do not account for the negative externality associated with pooling, a more subtle market failure. The implied total welfare loss under a transparent pooling equilibrium is: Consider …nally the welfare gap arising from the LCSE. The LCSE has a number of bene…ts. In the LCSE the private information of the originator is credibly signaled at the Securitization Stage so there is common knowledge of the asset type at the Trading Stage. As shown in Proposition 1, it follows that the speculator does not exert e¤ort. And with the type revealed, each vulnerable UI purchases a fairly priced Arrow security to insure against consumption shortfalls, so that risk sharing is e¢ cient. Thus, there are only two sources of welfare loss in the LCSE. First, high type retentions result in foregone project NPV. Second, the net social value of originator e¤ort is lost if b c lcs < c: We have the following welfare gap in the LCSE: The next two subsections consider socially optimal mandatory retention schemes that serve to induce speculator e¤ort. Before doing so we recall that opacity and zero retentions generates only one welfare cost, the foregone value of originator e¤ort. This implies the following proposition.

Proposition 6
Mandating opacity and zero originator retentions is socially optimal amongst regulations failing to induce originator e¤ ort.
The preceding proposition illustrates that an optimal regulation need not mandate retentions or transparency. To the contrary, if the regulator is content to tolerate originator moral hazard and forego the net social value of originator e¤ort (equation (22)), then the government should actually mandate zero retentions, with the goal of maximizing originator funding. And if e¤ort incentives are not a concern, there is no need for market discipline, so opacity is optimal. Proposition 6 is consistent with the arguments in Dang, Gorton and Holmström (2011) regarding the bene…ts of opacity. Opacity conserves speculator e¤ort costs and promotes e¢ cient risk sharing. With this in mind, it follows that a high degree of investor sophistication is not necessarily bene…cial in terms of social welfare. In particular, if investor beliefs are "sophisticated" in the sense of satisfying the Intuitive Criterion, then pooling at opacity cannot be sustained as an unregulated market equilibrium (Proposition 3).

B. Motivating E¤ort via Separating Regulations
From Proposition 6 it follows that inducing e¤ort is a necessary condition for some regulation other than mandated opacity and zero retentions to be socially optimal. Therefore, the remainder of the analysis is devoted to determining socially optimal methods for inducing originator e¤ort. This subsection determines the optimal mandatory retention scheme amongst those inducing originators 32 to exert e¤ort, as well as compelling them to credibly reveal the true asset type to investors. From a social perspective, all schemes meeting these two objectives result in the same expected utility for the speculator, who consumes her endowment, and the UI, who fully insure against negative shocks (Proposition 1). Therefore, the socially optimal separating regulation maximizes the expected utility of the originator subject to appropriate incentive constraints.
We begin by noting that if e¤ort is incentive compatible (IC below) in the LCSE, there is no Substituting the right side of IC 0 into the objective function we …nd it is increasing in M L from which it follows the socially optimal separating contract entails: Next, we substitute (M L ; M H ) into the NM constraint to compute the low type's utility under the socially optimal separating contract: Any pair (M L ; M H ) giving the low type the correct utility level su¢ ces. For example, set: We have established the following proposition.

Proposition 7
The socially optimal separating regulation for inducing originator e¤ ort calls for both types to retain junior claims paying zero in state L. In state H, the retained claims of the high and low types have respective payo¤ s: The separating regulation described in Proposition 7 accomplishes two distinct tasks: provision of ex ante e¤ort incentives by increasing the wedge between high and low type Securitization Stage continuation utilities and revelation of the originator's private information. This last e¤ect is socially valuable since it eliminates the speculator's incentive to pay costs to acquire information and also serves to insulate uninformed investors from adverse selection, facilitating e¢ cient risk sharing.
The proposition shows that in order to restore e¤ort incentives the high type is forced to hold a larger junior tranche than in the LCSE. Examination of the low type contract reveals a stark contrast between the LCSE and the socially optimal separating regulation inducing e¤ort. In the LCSE, a low type fully securitizes his asset and achieves his perfect information payo¤. In contrast, the optimal separating regulation mandates that the low type must also retain a junior claim, albeit of smaller size than that of the high type.
It is apparent that in terms of continuation utilities, the proposed regulation leaves both originator types are worse o¤ than at the LCSE. And in fact, Lemma 2 shows an unregulated market would never implement such an outcome since it is interim-ine¢ cient from the perspective of originators.
Thus, the role of the government regulation here is to serve as a commitment device to implement interim-ine¢ cient equilibria that the unregulated market would not, with the goal of increasing ex ante e¤ort incentives.
Finally, it is worth pointing out that the optimality of forcing originators to hold junior claims in the context of the separating regulation is a consequence of the fact that a standard single crossing condition is satis…ed, with high types placing a higher relative valuation on high state payo¤s.
This fact makes the retention of larger junior claim the least-costly signaling device. Mandating the retention of other claims might su¢ ce to separate types and restore e¤ort incentives, but they would generate larger underinvestment costs. This signaling argument is distinct from the traditional moral hazard argument that calls for risk-neutral agents, such as our originator, to be residual claimants (see e.g. Innes (1990)).

C. Motivating E¤ort via Pooling Regulations
regulation such that all originators are forced to retain the same claim. A pooling regulation can be used in combination with either mandated transparency or opacity.
Consider …rst the optimal pooling regulation combined with mandated transparency. The socially optimal regulation maximizes the weighted average of originator utilities subject to the appropriate IC constraint, since the expected utility of all other agents is the same across all transparent pooling regulations. The social planner's program is: subject to If the IC constraint is slack then the solution to the above program is full securitization. Consider then the remaining case in which the IC constraint binds (c > b c otd tran ). Substituting the IC constraint into the objective function it follows that the optimal pooling contract cum transparency calls for the originator to market the following bundle of cash ‡ows: Consider next the optimal pooling regulation when combined with mandated opacity. Again, the socially optimal regulation maximizes the weighted average of originator utilities. The social planner's program is: Here the IC constraint must bind since otherwise the optimum would entail full securitization, but this would necessarily violate the IC constraint. Substituting the IC constraint into the objective 36 function it follows that the optimal pooling regulation cum opacity calls for the originator to market the following bundle of cash ‡ows: We have established the following proposition.
Proposition 8 Socially optimal pooling regulations for inducing e¤ ort call for originators to retain junior claims paying zero in state L. If the regulation mandates transparency, the retained claim has state H payo¤ equal to: If the regulation mandates opacity, the retained claim has state H payo¤ equal to: Proposition 8 shows that if the regulatory intent is for originators to pool at a common structure, the socially optimal means of providing e¤ort incentives is for the originator to retain a junior claim such that R L = 0. Intuitively, reductions in R L serve to relax the respective IC constraints as well as increasing the level of originator fundraising. The proposition also shows that originators must be forced to hold larger junior claims if the regulation mandates opacity. After all, under opacity market discipline is absent at the time of securitization, so all e¤ort incentives must come from the retained claim. Finally, it is readily veri…ed that R tpool H decreases with the informational e¢ ciency of markets, as measured by z z: Intuitively, under the pooling regulation, originator retentions and market discipline are substitute mechanisms for providing e¤ort incentives. Thus, the optimal pooling regulation cum transparency requires making a judgement about informational e¢ ciency.

D. Welfare Comparisons Across Regulations
Having characterized the optimal regulations within each category in the preceding two subsections, we can now determine the optimal e¤ort-inducing regulation. Appendix B contains the social welfare equations. For brevity, this section compares social welfare losses across the alternatives.
Consider …rst a comparison of social welfare under the separating regulation versus the opaque pooling regulation. Both regulatory schemes have the bene…t of conserving speculator e¤ort costs and achieving …rst-best risk sharing (Proposition 1). In the separating regulation, symmetric infor- Essentially, the opaque pooling regulation imposes the same high level of retentions that the separating regulation reserves for the high type, with low types being permitted to retain smaller claims.
Comparing the respective welfare losses under the separating regulation and the opaque pooling regulation we have: Since the opaque pooling regulation is dominated, the optimal e¤ort-inducing regulation is either the separating regulation or a pooling regulation with mandatory transparency. Qualitatively, the two regulations di¤er along the following lines. The separating scheme conserves speculator e¤ort costs and achieves …rst-best risk sharing. Again, this is due to the fact that the separating scheme The …rst term on either side of the preceding inequality measures expected underinvestment costs under the two regulatory schemes. The analysis reveals that determination of the optimal regulation for inducing e¤ort requires policymakers to answer some di¢ cult questions. Moreover, the correct answer may di¤er across markets. For example, we have seen that the optimal regulation for e¤ort-inducement varies with the perceived informational e¢ ciency of the market. If informational e¢ ciency is low, the separating regulation dominates in terms of risk sharing and expected originator investment. However, if informational e¢ ciency is high, the pooling regulation may be preferred since in this case it has low underinvestment costs. Similarly, a view must be taken on the relative importance of achieving e¢ cient risk sharing versus increasing originator investment.
It should also be stressed that despite e¤ort-inducement sounding like a reasonable goal, it is not obvious that this goal should be pursued across all ABS markets. After all, e¤ort-inducement generates welfare losses in the form of lower originator investment and/or distortions in risk sharing.
Therefore, once the optimal e¤ort-inducing regulation has been determined, its respective social welfare loss should be compared with the social value of originator e¤ort (equation (22)). If it is smaller, then the optimal regulation induces e¤ort. Otherwise, it is optimal to forego e¤ort incentives and instead mandate opacity and full securitization (Proposition 6). Here it is apparent that the right policy call hinges upon good estimates of the magnitude of negative externalities associated with distressed assets ex post. Moreover, the magnitude of such externalities surely varies across ABS asset classes. For example, distressed residential real estate is likely to impose higher external costs than distressed auto loans. Therefore, one might argue that mandated retentions is appropriate for the former ABS class, but not the latter.

Conclusions
This paper revisits a canonical problem in corporate …nance, security issuance and retention when the issuer has private information. The model departs from prior literature in three ways. We consider …rst potential equilibria in unregulated securitization markets. One possible equilibrium is a separating equilibrium in which high types separate from low types by retaining the minimum junior tranche needed deter mimicry by low types who fully securitize. In addition, issuers may pool at a common securitization structure. We show that it is easier to sustain pooling at transparent structures than opaque structures. Moreover, if any pooling equilibrium can be sustained, a pooling equilibrium with full securitization can also be sustained. In this sense, full securitization 40 should not be viewed as an anomaly. However, full securitization is only an equilibrium outcome if originators place high value on funding and/or prices are su¢ ciently informative.
Unobservability of types at the (interim) securitization stage reduces ex ante e¤ort incentives in all unregulated market equilibria. Intuitively, originators recognize that asymmetric information at the time of security issuance will reduce the payo¤ di¤erential between owners of high and low quality assets. Transparency and sophisticated investor beliefs were shown to increase originator e¤ort incentives. Finally, there can be multiple equilibrium originator e¤ort levels in unregulated markets. With multiple equilibria, low originator e¤ort can be a self-ful…lling prophecy.
We identify three market failures. First, privately optimal retentions can be socially suboptimal since originators do not internalize e¤ects on investor welfare. In particular, when an issuer credibly signals positive information via large junior retentions he bene…ts directly from his own marketed securities being priced at fundamentals at the time of issuance. But he does not internalize the bene…t accruing to investors who can now e¢ ciently share risks being symmetrically informed.
Second, the anticipation of asymmetric information, in the form of uninformed investors, at the time of securitization reduces originator e¤ort incentives prior to securitization. Essentially, signaling costs and/or security mispricing reduce the payo¤ di¤erential between owners of high and low quality assets, which discourages e¤ort aimed at producing a high quality asset. Finally, there is a social bene…t to originator e¤ort at the time of loan origination inasmuch as screening out weak borrowers reduces ex post externalities associated with distressed assets.
In light of these three market failures, mandated retentions have the potential to raise social welfare by increasing originator e¤ort incentives in an e¢ cient way, accounting for investor-level externalities. The …rst direct policy implication to emerge from the model is that originators should be required to hold junior tranches. The underlying logic for this prescription depends on the nature of the regulation. In a pooling regulation, retention of a junior claim increases the spread between payo¤s accruing to high and low types. In a separating regulation, retention of a junior claim allows issuers to signal with minimal reduction in their investment. Second, in contrast to standard signaling model results, it is optimal to impose mandatory retentions on even the low type, since this increases e¤ort incentives e¢ ciently. Third, in the optimal pooling regulation, the size of the mandated junior retention is decreasing in informational e¢ ciency. Fourth, a necessary condition for the pooling regulation to dominate is su¢ cient informational e¢ ciency. Fifth, the separating (pooling) regulation generally maximizes welfare if e¢ cient risk sharing (originator investment) is the dominant concern. Finally, if the net social value of originator e¤ort is low, then it is optimal to forego e¤ort incentives altogether and instead maximize investment and the e¢ ciency of risk sharing. This is achieved by mandating opacity and zero retentions.
We close by brie ‡y suggesting potential directions for future empirical work based on the model.
A key prediction of the model is that common adoption of low retentions should only be observed if ABS price informativeness and originator funding values are su¢ ciently high. Otherwise one should observe dispersion of retention policies as the result of signaling. A potentially surprising implication of the model is that, for a given level of retentions, ABS sold by more constrained issuers should actually perform better on average, since even owners of high quality assets will be willing to fully securitize if they attach high value to immediate funding.
A central argument is that originator retentions and price informativeness are substitute mechanisms for generating e¤ort incentives. We are unaware of any systematic analysis of ABS price informativeness nor its link to lending standards. At …rst glance there appears to be contradictory evidence regarding the relationship between retention rates and ABS performance. Many argue that low originator retentions were a prime causal factor in deteriorating lending standards. However, the notion that banks sold-o¤ all risk exposure is contradicted by the fact that many took very large losses during the crisis.
How then does one reconcile the apparent conjunction of large risk exposure and apparent moral hazard? The conjunction of bank risk exposure and moral hazard is best understood as arising from banks holding the wrong type of risk. As we argued, moral hazard is most e¢ ciently curbed via retention of junior tranches. However, Acharya and Schnabl (2009) …nd that many banks held look to two frictions outside our model. First, one can reasonably argue that banks were engaged in regulatory arbitrage, holding AAA rated super-senior CDO tranches in order to capture their small spread above AAA rated Treasuries. Second, and relatedly, too-big-to-fail institutions might have been the natural holders of such assets since they were more likely than other investors to receive transfers from the government in the event that an economic catastrophe caused the super-senior tranches to become impaired.

43
Appendix A: Proofs

Uninformed Investor Portfolios
Consider …rst portfolio choice under common knowledge of type. Each vulnerable UI solves the following program: Utility is increasing in x L for all x L 2 (0; ) and is decreasing in x L for all For an invulnerable UI utility is decreasing in x L and x H on the relevant interval so their optimal portfolio payo¤ is ( ; ).
Consider next UI portfolio choice when the type is not common knowledge. A vulnerable UI solves the following program: We conjecture (and verify): Under the stated conjecture, utility is increasing in x L for all x L 2 (0; ) i¤ b , and is otherwise decreasing. Utility is decreasing in x L for all x L : Utility is decreasing in x H for all x H 0 and increasing in x H for all x H 2 ( ; 0): The optimal portfolio for an invulnerable UI solves: For an invulnerable UI utility is decreasing in x L and x H on the relevant interval so their optimal portfolio payo¤ is ( ; ).

Lemma 1: LCS Allocations
The program can be written as Each type can guarantee himself at least his LCS payo¤ (in any sequential equilibrium) by proposing the LCS retention scheme. It follows that no other separating contract is in the equilibrium set since such a contract would lower at least one type's payo¤. Further, it follows a necessary condition for a pooling menu to be in the equilibrium set is that both types are weakly better o¤ than at the LCS. We next establish su¢ ciency. To this end, consider any conjectured equilibrium in which both types receive at least their LCS payo¤. Deviations to a separating contract cannot be pro…table for either type since no separating contract improves upon the LCS payo¤s. Consider next deviations to a pooling menu. We need only identify and stipulate o¤-equilibrium beliefs su¢ cient to deter deviation.
Consider …rst deviations with total marketed cash ‡ows such that M H M L : Such deviations are assumed to be imputed to the low type. The low type payo¤ to such a deviation is: And the high type payo¤ to deviating is: For brevity, we express the constraints on pooling equilibria as follows. The case of opacity is subsumed in the prior equations by setting z = z = : We begin by proving a few useful lemmas.
Finally, to establish the existence of a pooling equilibrium at full securitization we need only check the condition under which the high type is better o¤ than at the LCS (since the low type is necessarily better o¤). We have: K L (q; z)L + K H (q; z)H + qH + (1 q)L (A25) [qH + (1 q)L] ( 1)q (q q)(H L) ( q q) m z (q q)=( q q): (A26)

Proposition 3: The Intuitive Criterion
We begin by recalling that with two types (t; t 0 ), a PBE fails to satisfy the Intuitive Criterion if there exists: an unsent menu proposal m 0 ; a type t 0 who is strictly better o¤ than at the posited PBE by proposing m 0 for all best responses with beliefs focused on t 0 ; and a type t who is strictly better at the posited PBE than at m 0 for all best responses for all beliefs in response to m 0 .
With this de…nition in mind a few lemmas are immediate. First, a PBE will never be pruned via a low type deviation (imputed to him) since the associated payo¤ is weakly less than his LCS payo¤.
Second, no separating menu can prune the PBE set since any separating contract yields either type weakly less than his LCS payo¤. Third, any pruning high type pooling contract deviation must    indifference curves pinning each type to their LCSE payoff in a candidate pooling equilibrium. The better-than set for each type is due north. In any pooling equilibrium, both types must be better off than at the LCSE. The set of pooling equilibria is therefore the shaded region. The figure assumes: L=1; H=2; sigma=.99; rho=0.5; q-upper=.9; and q-lower=.3. indifference curves pinning each type to their LCSE payoff in a candidate pooling equilibrium. The better-than set for each type is due north. In any pooling equilibrium, both types must be better off than at the LCSE. The set of pooling equilibria is therefore the shaded region. The figure assumes: L=1; H=2; sigma=.5; rho=0.5; q-upper=.9; and q-lower=.3.