Benefit Cost Analysis for Financial Regulation AER

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MAY 2013394 AEA PAPERS AND PROCEEDINGS

and Rogoff (2009)document that the economicconsequences of financial crises typically differdramatically from those of other economic cycles.Estimates of the CSC combining the methodolo-gies of these literatures are crucial for BCA.

Research proposing a parameter value willface many of the same problems that the VSLliterature confronted. Despite these, we believethat, by the same logic applied in the use ofVSL, the waste associated with having no com-monly used CSC value is typically greater thanthat associated with having a quite inaccuratenumber. Agreement on a figure in the range150 billion to 3 trillion dollars (viz. a crisis costbetween 1 percent and 20 percent of US GDPof approximately 15 trillion dollars) would

seem relatively easy to reach given the widelyrespected estimates of Reinhart and Rogoff. Wewould advocate a figure in the 12 trillion dollarrange. On its own, implementing such a stan-dard would eliminate many crossed decisionsbetween different agencies and regulators thatlead society to violate transitivity. While deci-sions made outside of this range might seemrare, experience with EHS regulations indicatethat in the absence of a numerical benchmarkextreme waste in both directions is not onlypossible but common (Hahn 2004). The one-and-a-half order-of-magnitude range casuallysuggested here is already only about twice asbroad in logarithmic terms as consensus viewsabout VSL (Viscusi and Aldy 2003)and the nar-rower range we are sympathetic to is no broaderin logarithmic terms.

Agencies will also need to estimate the mag-nitude of risk reduction associated with dif-ferent regulatory options. This will be at leastas challenging as determining a number forCSC; however, if agencies are forced to make

explicit their implicit estimates, it will stimu-late research and criticism, ultimately improv-ing accuracy.

II. The Allocative Value of Price Discovery

Much of the asset pricing literature concernsinformational efficiency of market prices, thatis, the tendency, or not, of financial markets tobring asset prices into line with the risk-adjustedpresent-discounted value of the cash flows the

asset will generate. Many, especially nonbank,financial regulations are either promulgated withthe goal of aiding such informational efficiency

(e.g., limits on automated trading and trans-parency mandates) or criticized by opponentsfor impairing the informational efficiency ofmarkets (e.g., punitive regulation of short-sell-ing and the Tobin tax). Hirshleifer (1971)famously argued that the private supply of infor-mation to prices will typically not agree with thesocially optimal supply.

On the one hand, some of the value of infor-mation is captured by the other side of a tradeas the price moves to its new equilibrium, lead-ing investments in informational trading to beinsufficient. On the other hand, traders have anincentive to be the first to incorporate a piece ofinformation into market prices, even if the socialvalue of this acceleration is small, leading to

excessive investments in accelerating the pace ofadjustments. As Mankiw and Whinston (1986)argue, if an activity is over- (under)rewarded rel-ative to its social value, it will stimulate exces-sive (insufficient) expenditures on entry andinformation acquisition costs.

Yet we know of no quantitative model articu-lating when trading is over- or undersuppliedand to what extent. Suppose that individuals ina market believe, because of a lack of informa-tion or confusion, for a length of time T thatthe value of an asset is p (and, thus, it tradesfor this price) even though the true value ofthe asset isp. What is the social loss from thismispricing?

For a loss to emerge, some decision ofreal economic consequence must depend onthis price signal. While the price theory logicbelow is quite general, we present, for the sakeof definiteness, a simple model here in whichthe quantity of the asset that exists depends onits price. Let q(p)be the quantity of the assetsthat exists when, during the period of length

T, the market price of the asset isp. If supplyis linear,

q(p)= q(1+ T(pp)_

p ),

where qis the equilibrium quantity when priceisp, and Tis the elasticity of the assets sup-ply with respect to a change in price per unittime over the period whenp=p. It seems rea-

sonable to assume this elasticity is proportionalto time if the arrival rate of opportunities to cre-ate or dispose of the assets is close to constant.


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Assuming that the market for producing theasset is efficient and supply is linear, the welfareof asset suppliers over this period is

q

_

p p=0p

p+ T(p p)d p

= q[(1 T)p+ Tp2_

2p ],

while, for simplicity assuming all asset purchas-ers value the asset at its true pricep, their wel-fare is

(p

p)q(p)= q

[p

p

T(p p)2_

p ].Adding these and simplifying, total welfare is

q[p(1 T_

2 ) T

_

2 (p p)2].

This is maximized at p=p, so the loss frommispricing is the Harberger (1964)triangle

(1)

Tq(pp)2__

2 .

While this expression is quite general and inde-pendent of details of the markets operation, theprivate profit to be made from correcting themispricing by buying or shorting the asset untilthe price gap is closed depends on the micro-structure of the market. The more liquid a mar-ket is (the less prices adjust to large purchasesor sales)the greater will be the private profit. Inany case, under a variety of models (monopolis-

tic, competitive with trade limits, etc.), the profitis linearly proportional to the price difference

|pp|and to the size of the market, which if|pp|is not too large, is approximately q.We can therefore represent the private profit as

(2) lq|pp|.

A first pass at quantifying the distortions of pri-vate incentives obtains from taking the ratio ofexpressions (1)and (2):

(3)T|pp|

2l .

A few qualitative results emerge immediatelyfrom this analysis. First, corrections to smallmispricings will be socially overincentivizedand, thus, oversupplied relative to correctionsof large mispricings. Second, mispricings thatpersist for a long period will go undercorrectedrelative to those that are short-lived. Third,mispricing of assets whose supply respondselastically to market prices are undercorrectedrelative to assets in fairly fixed supply.1Finally,arbitrage of mispricings in liquid markets willbe oversupplied relative to those in less liquidmarkets.

The first two points provide a simple quan-tification of the common intuition that whileexpenditures on the acceleration of high-speed

trading on many small bets is largely waste,arbitrage activity to close long-standing bubblesis likely to be undersupplied relative to the socialoptimum. The third point expresses a differentcommon intuition that improving the pricing ofmarkets whose prices have little impact on realeconomic activity (e.g., certain derivative secu-rities)has little value. The fourth point is per-haps best seen as a corrective to the first three:if policy interventions are being considered thatimpact the liquidity of markets they will be ben-eficial or harmful to the extent that they targetliquidity at markets where otherwise correctionof mispricing would be undersupplied or over-supplied, respectively. This logic highlights theattractiveness of some commonly advocatedpolicies, such as a small Tobin tax on transac-tions that would filter out small arbitrages, aswell as proposals to reduce the frequency withwhich trades can be made, while cautioningagainst others, such as high collateral require-ments for long-term short positions that mightreduce the incentive of market participants to

pop bubbles.By the same logic as in the derivation above,

the social loss from failing to correctly incentiv-ize the correction of mispricing is proportionalto the square of the difference between expres-sions (1)and (2)and to the elasticity of arbitrage

1 This result is, perhaps, a bit overstated, as is the tempo-ral dimension, because the more elastic is economic activityover a period the easier it will be to profit on the differencesin prices. However, we follow most of the finance literature

(Kyle 1985)in believing that real economic activity elastic-ity is a small part of the total liquidity of an asset, and, thus,that this dampens our result only slightly.
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MAY 2013396 AEA PAPERS AND PROCEEDINGS

activity itself with respect to the profit it yields.Thus, the costs and benefits of policies affectingmarket liquidity or any other factor facilitatingor inhibiting price discovery may be quanti-fied by measuring the parameters above and theelasticity of arbitrage activity with respect to itsrewards.

III. Gambling versus Insurance

Along with their informational role, perhapsthe most commonly touted virtue of finan-cial markets is the efficiency with which theyallocate risks to those most able to bear them,providing insurance against shocks individualsface. On the other hand, if different investors

have, or act as if they have, different priors overrisks in the economy but have similar wealth,risk-aversion and exposure to risks, they willtend to engage in bets against one another thatincrease risk (or allocate it less efficiently underany of their priors) but allow both to believethey are benefiting at the others expense (Weyl2007). To the extent that financial interventionsor regulations aid (e.g., position limits or assetpurchases that prevent market collapse)or limit(e.g., prohibitions or high capital charges forinnovative assets)market completion, regulatorsmust account for the benefits and costs accom-panying such new assets.

The simplest, though controversial, case inwhich market completing may be harmful iswhen different individuals simply have differentbeliefs. In this case, Brunnermeier, Simsek, andXiong (2012)propose a criterion for determin-ing if one or more transactions is beneficial orharmful. They argue that a transaction should bedeemed inefficient if under any single belief thatis a convex combination of the beliefs held by

the agents engaged in the tradesthe transactionis Pareto-dominated by the transaction not tak-ing place and instead some transfers being madeamong the agents. That is, all agents or anyonewith a belief between theirs agree that the trans-action is wealth-destroying in aggregate.

One natural way to make this principle quan-titative is to adopt the least interventionist evalu-ation of transactions possible. This would countthe social cost associated with a transactionthat agents desire to take place as the smallest

outside subsidy that would have to be given sothat, under some convex-combination belief,the transaction would not be dominated by any

set of transfers. Similarly, beneficial privatelydesired trades could be treated in an equallygenerous way, as generating gains equal to thelargest tax that could be imposed on the tradesuch that there is some convex-combinationbelief under which it is not dominated by someset of transfers. Essentially this asks what is themost libertarian belief-consistent interpretationof welfare from the trades consistent with theactions of the agents and other available infor-mation. An alternative standard would be to esti-mate the true distribution of outcomes (viz. truebelief) from available evidence, including thebehavior of agents, and take the average welfareloss or gain from the trade.

In many cases, transactions that appear to

be driven by differences in beliefs rather thanin their utility functions or endowments do notoriginate, fundamentally, in belief differencesbut instead in the informational setting in whichthey operate. For example, suppose an individ-ual invests her money with an active managerbut is unaware of the full set of vehicles in whichthat manager is able to invest. If she observesonly a subset of the dimensions of the productsin which the investor places her money (e.g.,average annual return and a coarse summary risksuch as a credit rating), her manager will havean incentive to invest in products that performwell along these dimensions even at the cost ofperforming poorly along the dimensions that areunobservable to the investor (Holmstrm andMilgrom 1991). The agent, combined with hermanager, will thus act as if they are optimisticabout their performance of products that do wellalong these observable dimensions but poorlyalong dimensions unobservable to the investor.If different agents are observable to differentinvestors, who have different managers, opening

markets between these investors may be harmfulas it leads each investors manager to exploit herimperfect information more effectively. Similararguments apply for imperfectly informed prin-cipals of other sorts, such as tax authorities orcapital regulators.

The welfare analytics of this more indirectchannel for gambling are similar to those whenthere are real differences in prior beliefs. In bothcases, different reduced-form investors act as ifthey had different beliefs and engage in trades

that are wealth-destroying under any convexcombination of their perceived beliefs. The onlysignificant difference is that the principal-agent


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scenario might call for stronger interventionboth because the libertarian arguments are lesscompelling in this case and because it might beeven more appropriate to ignore the beliefs ofthe two investors as these are clearly distorted bythe imperfections in their information. In bothcases, of course, the standard insurance benefitsof market completion must be weighed againstthe harms from gambling in judging the netvalue of market completion. In Posner and Weyl(forthcoming)we provide informal examples ofthis calculus as applied to a range of new assetscreated over the past two centuries.

IV. Conclusion

In this paper we propose three principles forthe quantitative evaluations of normative trade-offs in the regulation of financial markets. Whilewe anticipate that in the near future such analy-sis will be used primarily to evaluate the costsand benefits of restrictions on the operations ofmarkets, in Posner and Weyl (forthcoming)weadvocate an alternative baseline for new deriva-tive securities. In particular, we argue that a BCAshould be applied to the introduction of newproducts into markets by private participants.Whether this more precautionary approach(products or practices are disallowed until theypass a BCA) or the more traditional, libertar-ian approach (regulations restricting productsor practices must pass a BCA) is appropriatedepends on the circumstances and should, itself,likely be subject to a BCA.

The importance of developing methods forbenefit-cost analysis for financial regulation canscarcely be overstated. In recent years, courtshave awakened to the fact that many such regu-lations lack a sound economic basis and have

started blocking them (Trindle 2012). Agenciesare scrambling to develop reliable methods; wehope future research will come to their aid.

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Chauvin, Kyle, David Laibson, and JohannaMollerstrom. 2011. Asset Bubbles and the

Cost of Economic Fluctuations. Journal ofMoney, Credit, and Banking43 (S1): 23360.

Hahn, Robert W. 2004. The Economic Analysisof Regulation: A Response to the Critics. Uni-versity of Chicago Law Review71 (3): 102154.

Harberger, Arnold C. 1964. The Measurementof Waste.American Economic Review54 (3):5876.

Harberger, Arnold C. 1971. Three Basic Postu-lates for Applied Welfare Economics: An Inter-pretive Essay.Journal of Economic Literature9 (3): 78597.

Hirshleifer, Jack. 1971. The Private and SocialValue of Information and the Reward to Inven-tive Activity.American Economic Review61

(4): 56174.Holmstrom, Bengt, and Paul Milgrom. 1991.

Multitask Principal-Agent Analyses: Incen-tive Contracts, Asset Ownership, and JobDesign. Journal of Law, Economics, andOrganization7 (S): 2452.

Kyle, Albert S. 1985. Continuous Auctions andInsider Trading.Econometrica53 (6): 131535.

Lucas, Robert E., Jr. 1987. Models of BusinessCycles. New York: Blackwell.

Mankiw, N. Gregory, and Michael D. Whinston.

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Posner, Eric, and E. Glen Weyl. Forthcoming.An FDA for Financial Innovation: Applyingthe Insurable Interest Doctrine to 21st CenturyFinancial Markets. Northwestern University

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2009. This Time Is Different: Eight Centuriesof Financial Folly. Princeton, NJ: PrincetonUniversity Press.

Trindle, Jamila. 2012. Another Scalia VexesRegulators. Wall Street Journal, October 2.

Viscusi, W. Kip, and Joseph E. Aldy. 2003. TheValue of a Statistical Life: A Critical Review ofMarket Estimates throughout the World.Jour-nal of Risk and Uncertainty27 (1): 576.

Weyl, E. Glen. 2007. Is Arbitrage Socially Ben-eficial? http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1324423.

Whitehead, Charles K. 2012. The Goldi-locks Approach: Financial Risk and Staged

Regulation. Cornell Law Review 97 (5):12671308.
http://scholar.princeton.edu/markus/files/welfare10.pdfhttp://scholar.princeton.edu/markus/files/welfare10.pdfhttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=1324423http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1324423.http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1324423.http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1324423http://scholar.princeton.edu/markus/files/welfare10.pdfhttp://scholar.princeton.edu/markus/files/welfare10.pdf


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Benefit Cost Analysis for Financial Regulation AER

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