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Economic Quarterly— Volume 99, Number 4— Fourth Quarter 2013— Pages 251– 285 Evaluating Executive Compensation Packages Arantxa Jarque and John Muth E xecutive compensation is a topic that has received attention both in the media and the academic literature. This article discusses issues relevant to the construction and interpretation of compensation …gures typically reported in both sources. First, it is not clear what precisely should be included within a measure of the chief executive o¢ cer’ (CEO’ income tied to his …rm. Second, the s s) study of executive compensation remains constrained by the availability of data. We discuss the main source of data used in most studies on the topic: Execucomp. We highlight where the lack of data requires a deviation between a theoretical “ideal” measure of compensation and that which the researcher must use as an approximation. In this way, we hope our article will be a useful …rst introduction for those looking to do further research on the topic. We propose a measure of realized annual pay, compare it to other measures used in the literature, and illustrate the di¢ culties in calculating it. Using data in Execucomp, we provide our pay measure for CEOs of large U.S. …rms in the period 1993– 2012 and use it to estimate sensitivity of pay to …rm performance. The main di¢ culties in this exercise lie in the fact that compensation packages of most executives include stock and option grants on their own …rm’ shares, s which typically come with requirements that they be held by the executive for at least three or four years.1 This implies two important We thank the editor, Ned Prescott, and the referees, Kartik Athreya, Zhu Wang, and Peter Debbaut, as well as Huberto Ennis and Todd Keister, for helpful comments. The views expressed in this article are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of Richmond or those of the Federal Reserve System. E-mail: firstname.lastname@example.org. 1 Moreover, it is a fact that most CEOs hold on to stock for which selling restrictions have expired, or to options that are exercisable and in the money. The reasons for these “voluntary” holdings are not entirely clear, since CEOs are risk averse and 252 Federal Reserve Bank of Richmond Economic Quarterly things. First, the compensation …gures that are reported by …rms (and are readily available to the press and researchers) are a combination of both expected value of compensation (for deferred compensation in the form of restricted stock and option grants that are not convertible into cash right away) and realized value (salaries, bonus payments, and perks). Second, a given year’ compensation package provides income s for several years to follow, since the CEO will be able to realize gains from selling and exercising stock and option grants once their vesting restrictions expire. That is, an important part of the annual realized pay of a CEO in any given year comes from his net gains from trading stock that he received in a past grant. Due to the fact that stock price realizations may di¤er from ex-ante expectations of those prices, the ex-post realized gains from those trades will typically di¤er from the valuation made at the time of the grant. A measure of what is sometimes called direct compensation (the sum of salary, bonus, other compensation such as pension plans or perks, and the value of new stock and option grants during the year) is readily available in Execucomp (variable TDC1).2 As we just discussed, grants included in this measure are valued in expectation. Our objective in this article is to provide a measure of realized pay instead. We de…ne realized pay as the sum of salaries, bonuses, and other compensation, plus the gains from trades that the CEO realizes in a given year. We will argue that this measure is close to the one …rst proposed by Antle and Smith (1985) and used later by important contributions such as Hall and Liebman (1998) and Gayle and Miller (2009). Total yearly compensation is de…ned in these studies as the change in the wealth of the CEO that is tied to his employment in the …rm, and it is calculated in practice as direct compensation plus the year-on-year change in the market value of stock and option holdings of the CEO from past grants. This measure is, hence, still a measure of expected pay, although more sophisticated than TDC1. The main departure of our measure of realized pay with respect to this total yearly compensation is that it does not attribute changes in the value of grants that are not yet exercised to the realized pay in the year when they occur; rather, the …nal realized value is captured in gains from trades and attributed to the period of exercise of the grants. This simpli…cation is useful in terms of the calculation of the measure— we need to rely less heavily on assumptions about the unavailable details of grants. standard economic theory would suggest that they would value a diversi…ed portfolio of assets more. Overcon…dence, privileged information, or personal tax considerations have been proposed in the literature as potential explanations (Jin and Kothari 2008). 2 This measure has been studied, for example, in Gabaix and Landier (2008) and Frydman and Saks (2010). A. Jarque and J. Muth: Executive Compensation Packages 253 Figure 1 Median Realized Pay, and Mean Expected Pay as Measured by Execucomp in the Variable TDC1, as well as Measured in Total Yearly Compensation (TYC) Still, only part of the information that we need for our measure (about trades or vesting restrictions and exercise prices of past grants) is available in Execucomp. When approximating the gains from trades, in particular, we follow closely the algorithm used in Clementi and Cooley (2009) to recover the executive’ holdings of stocks and options s of his …rm.3 In the Appendix, we walk the reader through the step-bystep construction of the portfolio, discussing the shortcomings of the available data in Execucomp and how di¤erent assumptions about the unknowns may a¤ect the compensation numbers. We use our measure of realized pay to provide an updated account of CEO compensation through the year 2012. Figure 1 presents a comparison of our measure of realized pay versus two measures of expected pay used in the literature: “direct compensation,” the variable TDC1 in Execucomp, and “total yearly compensation,” as calculated by us following the implementation in Clementi and Cooley (2009) of the 3 For another recent application of the algorithm …rst developed in Antle and Smith (1985), see Gayle and Miller (2009). 254 Federal Reserve Bank of Richmond Economic Quarterly concept introduced by Antle and Smith (1985). Median realized pay is mostly below median direct compensation. The main di¤erence observable with total yearly compensation is that it is a lot more variable than either of the other two measures. This …gure suggests that di¤erent measures of pay present di¤erent pictures of CEO compensation, and it is important to understand what is behind the measurements before using them to evaluate pay practices. We use our realized pay measure to perform a sensitivity analysis of annual realized pay to performance, with a special focus on the …nance sector throughout the recent crisis in 2008. We simplify some of the di¢ culties of the analysis by assuming that the choice of selling and buying stock is invariant to the stock price movements in our counterfactual exercises; i.e., only the pro…ts from the trades change, not the quantities. We …nd that in the aftermath of the crisis the realized pay of CEOs of …nance …rms has decreased in level relative to other industries. Moreover, the sensitivity exercise suggests that, during the whole sample period, mean realized pay for CEOs in …nance …rms changes with the performance of the …rm in similar magnitudes than that of the average CEO. We proceed as follows. In Section 1, we introduce compensation instruments included in most CEO pay packages and discuss data availability and measurement challenges. In Section 2, we present a simpli…ed model of compensation accounting to illustrate the di¤erences between three di¤erent measurement alternatives: the measure of realized pay that we construct in this article, and two measures of expected pay— the simple measure of expected pay readily available in Execucomp, direct compensation, and the one based on the concept of total yearly compensation introduced by Antle and Smith (1985). Section 3 presents the results on the implied measure of realized pay over time, with a special focus on pay sensitivity, as well as a detailed look at the …nancial sector before and after the recent …nancial crises. Section 4 concludes. The Appendix provides the technical details on how we construct our realized pay measure from the data available. 1. UNDERSTANDING COMPENSATION PACKAGES Nowadays, companies pay their top executives mainly through di¤erent combinations of the following instruments: a salary, a bonus program, a signing bonus, stock grants (also referred to as “restricted stock,” since they are usually granted with restrictions on the ability to sell them), grants of options on the stock of the …rm, and perks and longterm incentive plans that specify severance payments, as well as pension plans. A. Jarque and J. Muth: Executive Compensation Packages 255 Table 1 Summary of Annual Compensation Information Available in Execucomp Instrument (Average % of TDC1) Salary (32%) Bonus and Incentive Compensation (23%) Perks and Other Compensation (6%) Restricted Stock Grants (11%) Stock Option Grants (28%) Information in Execucomp Value Value, some details on targets (after 2006) Value Value (stock price times number of shares) Value (Black and Scholes), number of shares underlying options Notes: Information available in Execucomp about the components of CEO compensation packages. For the percent calculations, the sample includes the CEOs of the largest 1,500 public …rms in the United States in the period 1993– 2010. The publicly available information on CEO compensation comes from the compensation tables included by …rms in their annual reports, as mandated by the Securities and Exchange Commission (SEC). This is the same data that Execucomp has compiled since 1992 and has been used in numerous empirical studies of CEO compensation, including this article. When the press publicizes information on CEO pay, it usually reports a summary measure of total or “direct compensation,” which is also readily available in Execucomp as the variable TDC1. Direct compensation is the sum of cash compensation (wage, bonus, and incentive compensation), pension contribution and other perks, plus the expected value of new stock and option grants given to the CEO within a given year. Execucomp also reports separately the di¤erent components of total compensation, and it includes some limited information on stock ownership and the portfolio of unvested restricted stock and option grants of the executives. A brief description of each of the instruments and further details on the information available about them in Execucomp follows. Table 1 presents statistics for their relative importance as a share of total pay using data from 1993 to 2010 and summarizes the information on availability. Salaries are the simplest compensation instrument: They are not contingent on performance and information on their level is readily available on the proxy statements of …rms.4 Bonus plans and incentive pay typically depend on yearly accounting results. Information is available mainly on payouts and more recently on some limited details of 4 The source for the shares of compensation that are reported come from Jarque and Gaines (2012). See the article for details on sample selection. 256 Federal Reserve Bank of Richmond Economic Quarterly Table 2 Classi cation of Compensation Instruments Non-Contingent Contingent Current (within year) Salary, perks, signing bonus Bonus plan Deferred Pension plan Options, stock, severance, future pay the bonus plans. Information on perks and other compensation is also available, although not to a great level of detail. Grants of restricted stock of the …rm make pay depend on the results of the …rm over a longer time horizon, since the CEO is restricted from selling them until their vesting period expires. Execucomp compiles information on their expected value at the time of the grant (number of shares times market price of stock), but it does not have separate information on the number of shares granted. Grants of stock options allow the executive to purchase stock of the …rm at a pre-established price (the “exercise price” and are also typically granted with restrictions as to how soon ) they can be exercised. These also provide incentives for longer-term performance, but they only pay o¤ if the stock price of the …rm is above the exercise price. For option grants, Execucomp has information on both the number and the Black and Scholes value of the total grants during the year. Typically, both stock and option grants come with a clause that forces the executive to forfeit them in the event of employment termination. Information on the vesting periods is not generally available in Execucomp for either stock or option grants.5 It should be apparent that compensation instruments can be classi…ed according to two criteria: whether or not they are contingent on the performance of the …rm, and whether or not they are deferred.6 Table 2 summarizes this classi…cation of the main compensation instruments. Given that executives are risk averse, paying them with contingent instruments, such as bonuses, stocks, and options, comes at a cost, since they will demand higher expected payments to compensate them for the risk. The most accepted explanation for the inclusion of compensation instruments that are contingent on the performance of the …rm is the existence of a moral hazard problem: The separation of ownership and control of the …rm implies the need to provide incentives to the 5 A commonly cited length of this restriction period is four years, with vesting taking place proportionally over this period— see Hall and Liebman (1998). 6 Firm performance is typically proxied by accounting measures such as return on equity, sales, and pro…t, or on market-based measures such as the stock price. A. Jarque and J. Muth: Executive Compensation Packages 257 CEO that align his interests with those of the …rm owners.7;8 Within this context of incentive provision, it is also commonly accepted that expectations over future wages or jobs (career concerns), as well as the threat of dismissal, are also important compensation instruments— although less easy to study due to the lack of hard information on them.9 Deferral of pay also comes at a cost if CEOs are more impatient (i.e., they discount the future more) than the shareholders of the …rms they manage. Several reasons may explain the use of deferred instruments. Perhaps the most accepted one is that, despite the cost of waiting, deferral is valuable— in combination with commitment to long-term contracts— because it allows to smooth incentives over time, making (costly) exposure to risk less necessary.10 Other reasons include retention purposes in the face of lack of commitment to long-term contracts or provision of incentives for hidden actions with long-term e¤ects.11 In most cases, instruments that are “cashed” within the year (labeled “current” in the table) are straightforward to value. In contrast, for contingent deferred instruments an expected value needs to be calculated, which presents some challenges. For example, the actual amount of compensation that the CEO will receive from stock and options granted to him in a given …scal year will depend on the stock price of the …rm at the moment he sells or exercises them. Similarly, the value of future compensation will depend on the performance of the …rm during the tenure of the CEO. The value of pension payments will be contingent on the …rm being solvent once the CEO retires. The value of severance payments is typically pre-set at the time of contracting, but a full list of the contingencies that may lead to termination is not written in the employment contract of the CEO. Hence, in order to calculate the expected value of compensation, one needs to know both the set of contingencies that trigger each payment (for example, the circumstances that trigger …ring of the CEO or the performance targets for granting salary increases), as well as the probability attached to each of these performance contingencies (for example, the probability 7 See Prescott (1999) and Jarque (2010) for an introduction to static and dynamic moral hazard problems, respectively. Classical references in the literature include Grossman and Hart (1983), as well as Spear and Srivastava (1987). 8 Bebchuck and Fried (2004) argue that captive boards may use stock and option grants as a less obvious instrument to transfer excessive amounts of pay to their CEOs. 9 See Jensen and Murphy (1990); Gibbons and Murphy (1992); and Jenter and Kanaan (forthcoming). 10 Wang (1997) ‡eshes out this explanation using a repeated moral hazard model. 11 See Bolton, Sheinkman, and Xiong (2006); Clementi, Cooley, and Wang (2006); and Edmans and Liu (2011). 258 Federal Reserve Bank of Richmond Economic Quarterly distribution over future stock prices of the …rm). These di¢ culties are important when choosing a measure of CEO pay. Measurement of Pay: Expected versus Realized Value There are two main approaches to measuring CEO pay: 1. Expected value of pay: The expected value of compensation granted in a given year, which includes the cash (realized value) he receives in salary and bonus, plus the expected value of the deferred contingent instruments such as stock and options; 2. Realized pay: The actual amount of money received in a given year, which includes the cash he receives in salary and bonus, plus the proceeds from selling past stock and option grants for which selling restrictions have expired (all realized). Any attempt at valuing contingent deferred compensation, either in expectation or its realized value, will be constrained by the availability of data. Table 3 summarizes the data available in proxy statements and compiled by Execucomp about CEO holdings of stock and options of his own …rm, the evolution of which is key to measurements in both categories. For stock holdings, we have the number of shares held by the CEO at the end of the …scal year, as well as the number and value of both stock that remains restricted and of stock that vested during the year. For option holdings, we know the number of options exercised during the year, as well as their value. We also know the number and value of options exercisable (but still unexercised) and those whose vesting restrictions did not yet expire. These values, however, are calculated using the “intrinsic” valuation (stock price at the end of the year minus exercise price, times number of options, if positive), hence ignoring the options that are currently out of the money, and provide a simplistic evaluation (Black and Scholes would be a more accurate choice). We choose our measure of realized pay (presented in the next section) in light of these data availability issues. Our choice tries to minimize the sensitivity of our measurements to assumptions about the unknown details of compensation packages, while still exploiting the information we have available on the portfolio of stock and options of the CEO. Before we present our measure, it is important to note that we view expected and realized measures of pay as complements rather than substitutes when trying to understand incentives for CEOs. Expected A. Jarque and J. Muth: Executive Compensation Packages 259 Table 3 Summary of Information Available in Execucomp about Stock and Option Holdings Stock Holdings Option Holdings Information in Execucomp Number of unrestricted Number of restricted Value of restricted Number vested during the year Value of vested during the year Number exercised during the year Value of exercised during the year Number of all unexercised vested Value of in-the-money unexercised vested (intrinsic) Number of all restricted Value of restricted in-the-money (intrinsic) pay is a forward-looking measure, which gives important information about the value of the current compensation package given to the CEO. However, it is a di¢ cult task to get a realistic valuation of stock or options for the CEO, especially because of selling restrictions and risk aversion considerations. In practice, the data in Execucomp re‡ ects the …rm’ estimate of that value for CEOs. For options, usually a pricing s model based on arbitrage conditions, such as Black and Scholes’option valuation model, is used to provide a value in the company’ report s with the SEC. Ad hoc modi…cations are often used to accommodate the fact that CEOs are risk averse and there are selling restrictions on the option grants.12 Realized pay, instead, is a backward-looking measure: Given past performance, we can calculate how much payo¤ the CEO actually got in the given period. In contract theory terms, we can view this measure as a description of the contract payo¤s on the equilibrium path. That is, we observe what the CEO gets for the actual performance that materialized, but we do not have information on what the payo¤s would have been for better or worse performances. For an estimate of these o¤-the-equilibrium-path payo¤s, in Section 3 we perform sensitivity analyses that exploit the fact that we have some information on the number of stocks and options the executive sold or exercised. 12 See Hall and Murphy (2002) for a quantitative evaluation of the di¤erence between the executive’ value of options and the cost to the …rm in providing them. s 260 Federal Reserve Bank of Richmond Economic Quarterly One advantage of our realized pay measure is that we do not need to take expectations over the value of deferred contingent pay. Hence, we will be able to use the publicly available information on compensation packages without resorting to assumptions about the future value of contingent compensation. Still, even for the purposes of measuring realized pay, we are missing some important information on these deferred contingent instruments. As re‡ ected in Table 3, Execucomp records the value of stock and the value and number of stock underlying options at the time when they are granted to the CEO. The values are approximations to the expected income that the CEO will realize in the future, when their restrictions expire. However, we do not have explicit information on the vesting schedules of these grants, or the exact date when the vested stocks are sold or the options exercised, or the market price of the stock at those times. This information is key to compute the actual cash the CEO receives as a result of the original grant. Our construction of a realized pay measure will necessarily involve assumptions on these unknown characteristics of the compensation, which we discuss in detail in the Appendix. Larcker, McCall, and Tayan (2011) have a short and interesting essay in which they also point out the di¤erences in measuring expected and realized pay.13 The authors include illustrative examples of the di¤erence between expected and realized compensation based on data for a handful of …rms in the year 2010. In this article we will use a larger number of …rms and a longer period of time to illustrate quantitatively the di¤erence between the two measures. 2. CONSTRUCTING A MEASURE OF REALIZED PAY In this section, we provide a framework for comparing di¤erent measures of compensation. For this, we describe the types and timing of the di¤erent components in a typical compensation package. Using this framework, we introduce our proposed measure of realized contingent pay, denoted It ; which is de…ned as the sum of salary, bonus, and gains from selling stock and exercising options in the current year. To construct it, we use information on the several components of pay packages that is publicly available, along with some assumptions. We refer to the model to illustrate the need for these assumptions and to justify 13 Larcker, McCall, and Tayan (2011) also present a third measure that they call earned pay (the value of pay at the moment when all selling restrictions are lifted, which does not necessarily coincide with the value at the time the CEO decides to sell). We do not have enough information in Execucomp to calculate this measure. A. Jarque and J. Muth: Executive Compensation Packages 261 our choices. Then we illustrate in the context of the model what the di¤erences are between our measure and two alternative ones: (1) direct compensation, which is de…ned as the sum of salary, bonus, perks, and other compensation, and the value of stock and options at the time of grant, and (2) total yearly compensation, which is de…ned as direct compensation plus dividends, plus the change in the value of stock and options in the portfolio of the CEO. Consider a CEO who lives for T years. He starts his tenure with a …rm at year t = 1. He receives compensation for all the years he is working, and after he retires he consumes out of his accumulated wealth and pension payments. We assume he has no sources of income other than what he receives as payments for his job as CEO, which we denote as It . The value he attaches to his employment at the beginning of period 1, denoted V0 ; is equal to the expected stream of income that he expects to receive in exchange for his work in each of the periods of his life:14 # " T X It (p1 ; : : : ; pt ) je ; (1) V0 (e ) = E (1 + r)t 1 t=1 where the expectation is with respect to stock price realizations (which summarize the performance of the …rm in this simple model), conditional on the sequence of e¤ort choices by the CEO (denoted e ) given the optimal contract. We denote the market interest as r: In this article, we want to measure the realized value of It : A more ambitious objective, which would relate more directly to theoretical models of CEO compensation based on repeated moral hazard models (Wang 1997), would be to try to measure Vt (e ). We discuss some of the added di¢ culties of this measurement at the end of this section. Realized pay It will not all be delivered directly in cash. Rather, the executive will receive an annual compensation, Ct ; that will consist of two elements: a cash-based portion, or current liquid payment, denoted Lt ; and a grant-based portion, denoted Gt : We assume compensation is received only once per year, at the end of the …scal year. We have that Ct = Lt + Gt 8t; (2) where Lt = Wt + Bt + Dt + Kt 8t: 14 Note that the utility the CEO may get from a given value of employment will also depend on his wealth from sources other than the executive’ employment. There is s typically no information on this outside wealth to be used in empirical studies of CEO compensation. 262 Federal Reserve Bank of Richmond Economic Quarterly That is, Lt is the sum of annual salary Wt ; bonus payment Bt ; which usually will depend on the annual results of the …rm, dividends Dt ; and perks and contributions to pension plans Kt :15 Grants consist of both restricted stock of the …rm, sr ; and options to buy stock, or , and are t t valued at any t0 t as16 0 Gt t = EV (sr ; pt0 ) + EV (or ; xt ; pt0 ) t t r r 0 + EV (o ; xt ; pt0 ) : = st pt t In this expression, EV (sr ; pt0 ) is the estimated value of restricted stock, t i.e., the amount of stock, sr ; valued at the stock price at the time of t valuation, pt0 . The estimated value of options, EV (or ; xt ; pt0 ) ; stands t for some version of the Black and Scholes (1973) option valuation formula and depends both on the market price at the time of valuation, pt0 ; and the exercise price, xt . Our Measure of Realized Pay The stream of realized pay It that the CEO will receive from the …rm while working will be equal to the cash part of his compensation, Lt ; plus whatever net gains from trade he gets from buying and selling unrestricted stock (or vested exercising options). To compute these gains from trade, it will be important to keep track of the accumulated number of stock and option grants that have vested, what we will refer to as the “portfolio” of the CEO.17 Let St 1 denote his holdings of unrestricted stock at the beginning of period t; and Ot 1 denote his holdings of vested options. Let Tt (St 1 ; Ot 1 ) denote the gains from the sales of stock and exercises of options at period t: Then, we can write realized pay as It = Lt + Tt (St 1 ; Ot 1 ) : Tracking the holdings St and Ot involves understanding the law of motion of the quantities of vested stock and options available to the CEO. Under the assumption that the CEO did not own any stock or options of the …rm before his employment as CEO started, we have 15 Note that dividends are not included in Execucomp’ TDC1 (which we will coms pare later to our own proposed measure of income). We include them because they are attached to the grants given to the CEO, and hence they are income that he receives because of his association with the …rm. 16 Here and in the rest of the model description, we use capital letters to denote values and lowercase letters to denote quantities. 17 Note that option grants also come with expiration dates; we are abstracting from those in this discussion, since the information we have on expirations is limited. A. Jarque and J. Muth: Executive Compensation Packages 263 that his holdings in the beginning of year 1 are equal to zero: S0 = 0; O0 = 0: Any subsequent year, the quantities available to trade will change for two main reasons: 1. some of the past grants will have vested, or the CEO may choose to buy unrestricted stock; these actions will increase his holdings; 2. some of the past grants in his holdings will be sold or exercised, decreasing his holdings. It is worth noting here that accurately evaluating the evolution of the holdings of the CEO would necessitate a large amount of information. For example, the CEO may choose to buy or sell stock, or exercise options, at di¤erent times during the year— with di¤erent market prices for each transaction. Also, he may choose to exercise options and hold on to the stock that he obtains with this transaction. Moreover, he may inherit or donate stock at any time. Unfortunately, the only data we have for the holdings of stock and options is their quantities and value at the end of each …scal year (see Table 3), and we are lacking the details on the speci…c transactions that determine their evolution. Hence, we make the following important simplifying assumptions. First, we assume each of the possible trades happens only once in the …scal year. Note that this still accommodates for a given sale of options to include options from di¤erent past grants, which implies di¤erent exercise prices. Second, we assume that the executive never purchases options, and that he exercises options only if he plans to sell the stock immediately. Third, we ignore any inheritances or donations. We can summarize the above discussion in a formal law of motion for the holdings of stock and options by introducing some notation. The vesting restrictions on the stock and option grants determine the available St and Ot in each period. Typically, only a portion of the previous years’restricted stock vests every t. Denoting the vested shares in year t by sv and vested options in year t by ov , the accumulated t t number of shares and options available for selling in year t is St = S t 1 ss sb + sv ; t t t X e v Ot = og og;t + ot ; og 2Ot (3) 1 where we are denoting the three types of trades that can happen at time t as follows: 264 Federal Reserve Bank of Richmond Economic Quarterly 1. selling stock ss of the unrestricted stock available at period t, t St 1 , at price pst ; 2. buying an amount sb of stock from the market, at price pbt ; t 3. buying stock through the exercise of oe of any vested option g;t grant g (with corresponding exercise xg ) at price pet . With this notation, we can write an expression for the gains from trade: X Tt (St 1 ; Ot 1 ) = ss pst sb pbt + max 0; oe (pet xg ) : (4) t t g;t og 2Ot 1 This completes the description of our measure of realized pay, It : Next, before moving on to the estimates of It using data, we use the model in this section to compare our measure of realized pay with alternative measures used in the literature. Alternative Measures: Expected Pay As we discussed in Section 1, the literature has used compensation measures based on the expected value of pay. The theoretical measure of expected pay is described by (1). The employment value, Vt ; is the sum of the expected stream of realized pay. For the measurement of Vt (e ) in the data, however, one would have to make assumptions about the terms of the contract o¤ered to the CEO regarding compensation in future periods (i.e., what would trigger a wage increase, or what is the schedule of future grants contingent on realized performance). One would also need to understand the CEO’ expectations about stock s prices in the future, which will determine his future realized gains from trade. One would also need to understand his expectations regarding his transitions to other …rms and their consequences for his realized pay. Moreover, one would need to model how performance during the CEO’ working life will a¤ect his pension payments. To the best of our s knowledge, no study has provided a reliable measure of Vt . Instead, two di¤erent approximations to Vt have been widely used: “direct compensation” (TDC1) and “total yearly compensation” (TYC). We de…ne each of these using our notation, in turn, and compare them to our measure of realized pay. The Execucomp variable TDC1 can be written in terms of our notation as T DC1t = Wt + Bt + Kt + Gt : t This measure of expected pay does not closely correspond to the theoretical Vt ; since it does not include any estimation of future wages, A. Jarque and J. Muth: Executive Compensation Packages 265 bonuses, and new grants. It includes an estimate of the expected future value of the grants given to the CEO in the current year, Gt = t sr pt + EV (or ; xt ; pt ) ; but it ignores the changes in the value of past t t grants, or the realized gains from exercising them once they are vested, as well as the dividends that correspond to the CEO from holding stock. The main di¤erence between our I measure and TDC1 is that we do not include the value of grants, Gt ; but rather the realized net gains from trade, Tt . Also, dividends are included in It but not in TDC1t : A second alternative measure of expected pay, TYC, has been used in the literature since Antle and Smith (1985) proposed it. The idea behind it is to calculate the expected value that the CEO attaches to working in his …rm, every period, as the current expected value of stock and option holdings plus the expected future compensation; then one can interpret the annual change in this expected value from one period to the next as the TYC of the executive.18 Because the expected value of grants is updated every year, this measure presents a more accurate picture of the incentive value of the CEO’ contract. However, the s measure is not without problems. For example, a common simplifying assumption when computing this measure is to assume that salary and bonus payments remain constant in future years and that the expected value of future grants is zero.19 We follow the description in the Appendix of Clementi and Cooley (2009) to replicate their measure of TYC, assuming wages, bonuses, and perks remain constant throughout the work life of the CEO, and no turnover. We graph it for comparison purposes in Figures 1, 2, and 5. In terms of our notation, TYC can be written as T Y Ct = Wt + Bt + Kt + Dt + t X Gt Gt 1 ; =1 where Gt in this case denotes the updated expected value during period t of stock and (unexpired) option grants that were given at period t 20 and are still unexercised. The measure TYC attributes initial grants as compensation in the year when they are granted, and then subsequent appreciations and 18 Examples of di¤erent implementations of this concept of expected pay include Jensen and Murphy (1990); Garen (1994); Haubrich (1994); Hall and Liebman (1998); Haubrich and Popova (1998); Schaefer (1998); Aggarwal and Samwick (1999); Baker and Hall (2004); Clementi and Cooley (2009); Edmans, Gabaix, and Landier (2009); and Gayle and Miller (2009). 19 See, for example, Clementi and Cooley (2009; 2, 29). 20 Note that Gt 1 = 0 whenever > t: Also, note that this re-evaluation of grants coincides conceptually with our measure of gains from trade, for the portion of the vested portfolio that is converted to cash in period t: That is, if, for example, only grants given at t 4 are exercised at t; then Tt (St 1 ; Ot 1 ) = Gt 4 : t 266 Federal Reserve Bank of Richmond Economic Quarterly depreciations of the grants to the periods when they happen— even if they do not translate into realized pay in that particular period. In comparison, our measure I of realized pay records only the realized value of grants when they get exercised, and it attributes the gains from trade to the particular period when they happen. It is easy to see P P that the simple sum of T It = T T Y Ct ; however, the individual t=1 t=1 year entries will di¤er, and hence the properly discounted sum will di¤er as well. 3. MEASUREMENTS In this section, we present the empirical measurement of pay according to the methodology described above. In the Appendix, we provide the details on how to map the elements of pay described in the previous section to the data available in Execucomp. In this article, we work with the August 2013 release of Execucomp, which includes annual observations through the …scal year 2012. We drop CEOs who own 50 percent or more of the shares of their company, since we want to focus on measuring incentives in relationships for which there is an agency problem. Our …nal sample includes 3,345 di¤erent …rms, for a total 34,497 …rm-CEO-year observations.21;22 Figure 1 presented the median of our measure of realized pay from 1993 to 2012. We compare it to the two measures of expected pay discussed earlier in this article: “total compensation”reported in Execucomp as the variable TDC1 and our own calculation of TYC following Clementi and Cooley (2009).23 Two features emerge from Figure 2. First, averages are much larger than medians. This is well known for the measure TDC1, and it is con…rmed for our measure of realized pay, I. Second, average realized pay is more volatile over time than average total compensation, and it is typically above TDC1t , while it was typically below it when we looked at the medians in Figure 1. However, TYCt is more volatile than either of the other two measures. This is true both when looking at medians, in Figure 1, or when looking at means, here. Our analysis of the 21 The database includes up to …ve executives of a …rm per year, but we restrict our sample to those designated as the CEO by the Execucomp variable CEOANN. 22 We also exclude from our analysis Warren Bu¤ett, the CEO of Berkshire Hathaway, and Larry Ellison, the CEO of Oracle Corporation, because their values of trades are extreme outliers. 23 We replicate Clementi and Cooley’ simpler calculation of TYC, which uses ins trinsic valuations for options when their value is updated with new stock prices at the end of the …scal year. Clementi and Cooley report in their manuscript that their results do not change substantially when they use Black and Scholes to produce those revaluations. A. Jarque and J. Muth: Executive Compensation Packages 267 Figure 2 Mean Realized Pay and Mean Expected Pay as Measured by TDC1 and TYC di¤erent components of pay shows that the estimated gains from trading stock are causing the volatility in realized pay. Also, every year there are a few CEOs who realize very large gains from trading stock, making the averages of the two measures of compensation di¤er more than the medians. Moreover, the large revaluations of the portfolio of the CEOs with changes in the stock price do not seem to translate into gains from trades, causing the large deviation of the measure TYC from the measure I: One potential explanation would be that CEOs have in their portfolios a large fraction of restricted stock and options, so even if their value increases they are not able to realize those gains. However, the information available in Execucomp about restricted stock and options does not seem to support this hypothesis (the restricted grants are a small part of the portfolio of the CEO at any point in time). However, it is still plausible that implicit selling restrictions are in place even after the explicit vesting period expires, presumably with the objective of strengthening the market perception about the con…dence of the CEO in the performance of his own …rm. 268 Federal Reserve Bank of Richmond Economic Quarterly Figure 3 Liquid Portion of Compensation Notes: The blue line presents mean total realized pay, It , and its liquid component, Lt (wage, bonus, perks, and dividends). The di¤erence equals mean trades, Tt : The red line presents mean total expected pay as measured in TDC1t and its liquid component (wage, bonus, and perks). The di¤erence equals grants, Gt . In Figure 3, we display the liquid portion of compensation for mean realized pay, It ; and for mean total expected pay as measured in TDC1t . We see that the higher volatility of mean It compared to that of mean TDC1t is mainly driven by the volatility of trades. Figure 4 plots separately the medians of the di¤erent components of realized pay, Lt and Tt ; and the median of It : (Figure 4 plots also these statistics for …nance …rms, which we will discuss in the next subsection.) Both components, as well as the total It ; are increasing over time. For comparison, the median value of grants, Gt ; is included as well. The value of grants is also increasing over time. As a robustness check, we replicate Figure 2 in Figure 5 for a subsample of the …rms including only the CEOs that own less than 1 percent of the shares of their company.24 The level of TYCt is much 24 This subsample includes 2,169 out of our 3,345 …rms, and 16,302 out of our 34,497 observations. A. Jarque and J. Muth: Executive Compensation Packages 269 Figure 4 All CEOs versus Finance CEOs Notes: A comparison of the medians of liquid compensation, Lt , net gains from trading and stock options, Tt , the expected liquid value of stock and option grants, Gt , and total realized pay, It . Note that although It = Lt + Tt ; the sum of the median of Lt and Tt is not equal to the median of It . lower, and mean realized pay is sometimes above TDC1t . The main di¤erence for this sample continues to be the higher volatility of TYCt . Finance Firms In Figure 4, we include statistics for …rms in the …nance sector with the statistics for …rms in all sectors.25 Note that …rms in the …nance sector are, on average, larger (in the sample, the average size in …nance is between …ve and six times larger than the average size for all …rms, year by year, with a decreasing trend between 2004 and 2009). Because the level of total compensation (TDC1) has been shown to be positively 25 Firms in the …nance sector are those with SIC classi…cation in the 6,000– 6,300 range. There are 144 …rms per year, on average, in our subsample of …nance. We performed the same analysis with a broader category including real estate …rms as well as insurance, and the plots looked qualitatively similar. 270 Federal Reserve Bank of Richmond Economic Quarterly Figure 5 Mean Realized Pay and Expected Pay, as Measured both by TDC1 and TYC, for CEOs Who Own Less Than 1 Percent of the Stock of Their Firm correlated with size, we expect a higher realized pay for CEOs in …nance. This is con…rmed in the data up to the …nancial crisis of 2008. Figure 4 shows that the composition of realized pay is slightly di¤erent among …nance …rms, with higher liquid compensation and higher value of trades (which are also more volatile, although this could be due to the smaller number of …rms). When looking in detail at the period since the 2008 …nancial crisis, it is apparent in the graphs that there has been a steeper decline in median realized pay— both for liquid compensation and trades— for …rms in …nance than for the full sample of …rms. It is worth noting that the median value of grants is, for both groups of …rms, well above the median value of trades. The adjustment pattern of median grants during the crisis is similar to that of realized pay, i.e., we see a steeper decline for …rms in …nance. Sensitivity of Realized Pay to Performance Hall and Liebman (1998) provide a measure of sensitivity of pay to performance by using information on stock holdings to construct A. Jarque and J. Muth: Executive Compensation Packages 271 Figure 6 Stock Returns by Percentile Notes: Evolution of the 5th percentile, median, and 95th percentile stock returns for the largest 1,500 …rms in our sample. For comparison, the same percentiles of returns for all …rms in …nance are included as well. counterfactuals.26 First, they construct a measure of the portfolio of the CEOs, similar to our St and Ot holdings of stock and options. Then, using the realized distribution of performances (stock returns), they evaluate the holdings of each CEO in the data for di¤erent performance scenarios corresponding to di¤erent percentiles of the distribution of returns: We follow this methodology and provide a similar counterfactual for our measure of annual realized pay. An important caveat of this measure is that the quantities of stock traded and of options exercised are assumed to remain constant when stock prices vary in the counterfactual. A model of how these trades would vary in a more realistic setup is beyond the scope of this article. For our performance counterfactuals, we need to propose the support and distribution of stock returns. For this, we use the observed distribution of stock returns in each given year. We denote the annual 26 Given the limited quantitative importance of bonuses in total compensation, we will ignore changes in bonus payments in our sensitivity analyses. 272 Federal Reserve Bank of Richmond Economic Quarterly stock price return as rt = pt pt pt 1 : (5) 1 This measure has the advantage of being comparable across …rms, as opposed to the stock price itself. In Figure 6, we summarize the evolution of these distributions of returns rt of the 1,500 largest …rms in our sample over time by plotting the return value for the median, and the 5th and 95th percentiles. Each realization of returns in the support of the distribution can be translated into a stock price for each individual …rm using (5). That is, when calculating the counterfactual value of Tt for an individual executive working for …rm j; we will construct a counterfactual stock price for various percentiles of the return distribution. We use a hat to denote a variable’ counterfactual value, and a superscript nth to s indicate the percentile to which we are setting the performance of the …rm. For the nth percentile, the counterfactual price for …rm j at time t is nth pnth = 1 + rt ^j;t pj;t 1: With this price pnth , a new valuation of Tj;t can be produced, assuming ^j;t nth the return of the …rm was equal to the nth percentile return, rt . Recall that we approximate the gains from trade coming from stock purchases and sales as max[0; pt qt ]; where pt is the average price within the year. We will set the counterfactual for this average price to pt d pnth = pnth ; ^ t pt t (6) that is, we assume that the proportionality between the average price and the end-of-the-year price is maintained in the counterfactual. For the portion of the gains from trade that comes from exercising options, we will need several pieces of information. First, in order to compute the net bene…t per option exercised, (^et xg ), we would p need to construct the counterfactual for the stock price at the time of exercise, pet ; possibly using pet ; and we would need to know the exercise ^ price, xg , corresponding to each option exercised. Unfortunately, as discussed earlier, we do not know pet or xg (we do not know which particular past grant g was used to purchase the shares). The value of exercised options is recorded in Execucomp: X oe (pet xg ) OP T _EXER_V ALt 8t: g;t og 2O0 A. Jarque and J. Muth: Executive Compensation Packages 273 Figure 7 Mean Counterfactual Income Notes: Average percentage change in income for three di¤erent performance counterfactuals, for all …rms and for …rms in …nance only. We also have the number of options exercised within the year: X oe = oe OP T _EXER_N U Mt 8t: t g;t og 2O0 To produce an estimate for the counterfactual value of exercising options, we assume pet = p; the average price during the year, and we solve for an “e¤ective” exercise price x using e X oe (p x) = e oe (pet xg ) : t g;t og 2O0 Finally, we also assume that CEOs do not exercise options in the d counterfactual if they are “out of the money” (that is, if pnth < x): e t With these assumptions, we have that our counterfactual for gains of trade is h d d ^nth Tj;t (Sj;t ; Oj;t ) = max[0; pnth qt ] + max 0; oe pnth t t t x e i : 274 Federal Reserve Bank of Richmond Economic Quarterly This, together with the actual liquid compensation for the executive in the data, Lt ; which is not contingent on stock price realizations, ^nth amounts to a calculation of a counterfactual Ij;t : The numerical results are listed in Tables 4 (levels) and 5 (percentage changes). We display the percentage changes for the 5th, median, and 95th percentile counterfactuals graphically in Figure 7. Keeping in mind that percentage changes are bounded below by 100 percent, we see that there is an obvious asymmetry in changes when the …rm performs better rather than worse. This responds to the uncontingent nature of the wage and the bonus in our calculations. Also, we see in Figure 7 that the gains for the 95th percentile (i.e., outstanding stock return performance) is very extreme in particular years. Two things can lead to high net gains from trade: particularly good stock returns in the given year (i.e., the 95th percentile stock return is an outlier when compared to the other 95th percentile returns in other years) or particularly generous past grants that imply a large number of stock or options are available for trade. We can use the distribution of stock returns, plotted in Figure 5, to track which of the two explanations seems more plausible. The years 2000, 2003, and 2009 represent examples of outlier stock return performance in the 95th percentile; however, only in the year 2000 does this translate into a very large counterfactual mean realized pay in the 95th percentile. The spikes in income for the years 2005 and, to a lesser extent, 2008– may correspond instead to 09 particularly large net quantities traded, as computed by us from the portfolios of the CEOs. Sensitivity for Finance Firms We observed a sharper decrease in median realized pay for …rms in …nance during the recent …nancial crisis (see Figure 4). However, this does not seem to correspond to a very di¤erent sensitivity of realized pay to performance for …nancial …rms during the crisis. Tables 5 and 7 replicate the sensitivity analysis of Tables 4 and 6 for …rms in …nance. That is, using the stock and option holdings of …nancial …rms, we feed in the same percentile stock returns used in Tables 4 and 6 (i.e., those from the distribution of stock for the overall population of …rms) to calculate their counterfactual realized pays. We …nd that the sensitivity estimates align with those of the general sample for the whole sample period.27 It is worth referring back to Figure 4 and noting that the median liquid (uncontingent) compensation of CEOs in …nance is 27 Given the way we construct the counterfactuals, any di¤erences in level between Tables 1 and 3 is due to the original di¤erences in the level of actual compensation between the average …nance …rm and the average …rm in the sample. Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 5th 4,301 3,438 3,694 5,291 5,246 4,775 10,618 6,859 4,439 9,840 7,917 10,266 8,883 6,991 5,076 8,078 6,899 6,443 7,996 25th 5,630 4,296 4,923 7,231 9,150 7,060 27,698 11,909 6,956 12,994 11,463 14,414 11,849 10,090 8,934 11,230 8,447 8,809 10,718 Median 6,378 4,926 5,734 9,083 12,397 8,668 41,383 14,968 8,910 14,718 13,211 17,072 13,802 12,326 12,177 13,450 9,459 10,325 12,080 75th 7,203 5,562 6,554 10,809 15,911 11,217 55,636 18,089 10,472 17,314 15,242 20,330 15,503 14,769 15,324 17,288 10,749 11,913 13,623 95th 8,821 6,832 8,157 14,289 24,021 20,479 87,588 27,074 13,455 26,321 20,491 26,911 19,754 19,817 20,812 28,866 13,825 15,215 18,149 Actual 6,182 4,659 5,286 8,243 9,364 8,460 11,268 11,022 7,448 14,156 13,023 16,382 13,200 12,531 9,636 14,474 9,640 11,270 12,747 A. Jarque and J. Muth: Executive Compensation Packages Table 4 Counterfactual Income: Mean Level of Income if Certain Percentile Stock Return Had Been Achieved|All Firms 275 276 Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 5th 3,687 5,256 6,515 6,656 5,664 6,341 6,189 8,507 6,345 8,898 8,933 11,591 9,153 10,455 4,957 5,600 5,291 4,314 5,535 25th 3,987 5,700 9,468 8,323 8,173 8,800 10,105 13,528 9,544 11,051 13,099 15,828 12,596 14,958 8,523 7,378 6,322 5,350 7,174 Median 4,190 6,072 11,628 11,956 10,442 10,453 16,523 16,610 12,237 12,293 15,118 18,226 14,916 18,105 11,570 8,645 7,025 6,024 8,023 75th 4,414 6,488 13,792 15,389 12,902 12,996 24,242 19,757 14,405 14,159 17,452 21,159 16,925 21,476 14,561 10,847 7,910 6,719 8,983 95th 4,851 7,679 18,017 22,304 18,538 22,127 41,568 28,852 18,536 20,626 23,474 27,077 21,937 28,427 19,803 17,502 10,125 8,152 11,791 Actual 4,228 7,047 9,881 12,473 9,452 9,485 12,604 14,333 10,947 12,467 13,744 17,473 13,284 14,184 7,918 8,275 6,621 8,980 7,594 Federal Reserve Bank of Richmond Economic Quarterly Table 5 Counterfactual Income: Mean Level of Income if Certain Percentile Stock Return Had Been Achieved|Finance Firms Only A. Jarque and J. Muth: Executive Compensation Packages 277 Table 6 Counterfactual Income: Mean Percent Change in Income if Certain Percentile Stock Return Had Been Achieved|All Firms Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 5th 9.2 11.5 12.1 15.0 16.4 16.6 16.5 17.6 17.2 13.8 18.6 18.7 18.4 20.8 19.7 15.3 14.8 18.6 18.2 25th 2.2 3.5 1.6 3.7 1.7 5.0 13.7 1.4 1.5 4.3 3.7 4.3 6.4 8.2 1.9 6.1 6.2 5.8 2.8 Median 2.1 2.7 5.4 6.6 11.2 3.4 38.8 13.7 11.5 1.1 4.2 31.8 1.7 1.3 14.0 0.8 0.4 2.8 5.5 75th 6.8 9.0 12.5 16.3 25.5 16.8 65.3 26.5 22.1 9.4 13.4 65.6 8.9 11.8 29.9 13.1 7.1 12.0 14.8 95th 16.4 21.4 26.5 35.9 62.6 66.1 125.3 63.6 42.4 38.3 37.5 133.9 26.9 33.5 57.8 50.8 25.2 31.3 42.1 particularly large compared to the entire sample, up until the recent crisis. This, together with the fact that sensitivity estimates are similar to those of the overall sample, suggests that the quantities of stock and options held by …nance CEOs are larger than those in other industries, hence implementing a similar risk in their realized pay in spite of larger uncontingent compensation levels. 4. CONCLUSION Information on CEO pay is typically obtained from the mandatory disclosure of compensation required by the SEC for large public …rms. A good measure of realized pay for CEOs, which includes the actual gains from trading stock rather than their expected value at the time when the …rm awards them to the CEO, is not readily in this source. This article discusses how to construct an approximation to the value of realized pay using the partial information compiled in the database Execucomp on the stock owned, bought, and sold by CEOs each year. We present our estimates for the period 1993– 2012 and compare them to two alternative measures of expected annual total compensation that are frequently used in the media and the academic literature: direct compensation (the sum of salary, bonus, other compensation, and the 278 Federal Reserve Bank of Richmond Economic Quarterly Table 7 Counterfactual Income: Mean Percent Change in Income if Certain Percentile Stock Return Had Been Achieved|Finance Firms Only Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 5th 7.7 13.3 17.8 22.1 21.9 16.0 21.0 20.4 21.8 13.7 18.3 13.6 18.9 13.7 12.7 7.8 10.2 13.5 11.1 25th 2.6 8.9 8.2 11.9 1.6 0.5 3.2 0.6 8.1 5.0 1.1 1.9 7.8 0.2 6.8 2.6 3.4 4.9 0.9 Median 0.9 5.2 1.2 2.2 15.6 10.1 13.5 14.4 5.7 0.1 7.9 5.4 0.2 10.0 24.3 10.4 1.2 1.1 7.6 75th 4.8 1.1 6.3 7.2 34.2 26.6 31.6 29.0 17.0 7.9 18.3 14.5 6.4 20.9 42.5 24.1 7.1 7.3 15.2 95th 12.5 7.5 21.0 26.1 76.9 85.6 72.8 71.9 38.5 34.8 45.1 32.9 22.8 43.4 75.4 65.5 23.8 20.2 37.5 market value of new grants) and total yearly compensation (which includes the year-on-year change in the value of the stock holdings of the CEO). Our measure of realized pay tends to be more volatile over time than direct compensation, mainly due to the volatility of the gains that CEOs realize from trading stock. However, total yearly compensation is markedly more volatile than the other two measures. We …nd that, while the average realized pay level has historically been at or above that of direct compensation, its median has consistently been lower. We provide descriptive statistics of realized pay for …rms in the …nance sector. In the aftermath of the crisis the realized pay of CEOs of …nance …rms seems to have decreased in level relative to the realized pay of CEOs in all industries. Our calculations suggest, however, that realized pay of …nance CEOs changes with the performance of their …rm in similar magnitudes to that of the average CEO for the whole 1993– 2012 period. A. Jarque and J. Muth: Executive Compensation Packages 279 APPENDIX In this Appendix, we show how to map the variables de…ned in Section 2 to the Execucomp database. We discuss the elements of our ideal measure of compensation that are missing in the data, and what assumptions we make to go around these di¢ culties. As we list the objects needed to calculate It ; we will note how the change in reporting requirements of the SEC in 2006 changes the availability of data (or, sometimes, simply the name of the Execucomp variable that corresponds to a given concept). For this purpose, we will refer to the reporting period before 2006 as P1 ; and the one after as P2 : Measuring Liquid Compensation, Lt Our measure of liquid or cash-based compensation, Lt ; is the sum of the executives’annual salary, bonus, dividends, and any perks received within the year, such as contributions to pension plans. Data on annual salary Wt is directly available in Execucomp: Wt SALARYt ; 8t: Our measure of bonus, Bt ; is the sum of the Execucomp variable BONUS and two variables that capture payments received from hitting “objective” performance targets such as sales growth or stock price performance:28 Bt BON U St + LT IPt BON U St + N ON EQ_IN CEN Tt if t 2 P1 if t 2 P2 : We also have information in the data about the dividend yield (dividends per share, divided by pt ; times 100) that the executive receives from his stock ownership of the company. We back out the total dividend payments as follows: DIV _Y IELDt P RCCFt SHROW N _EXCL_OP T St 8t; Dt 100 28 Speci…cally, after 2005 Execucomp’ BONUS variable was modi…ed to only s include discretionary or guaranteed bonuses. So to include payments from objective targets, we sum BONUS with NONEQ_INCENT, the amount of income received in the year pursuant to non-equity incentive plans being satis…ed. Whenever NONEQ_INCENT is missing (i.e., prior to 2006), we add BONUS with LTIP, the amount of income received in the year pursuant to long-term incentive plans that measure performance over more than one year. 280 Federal Reserve Bank of Richmond Economic Quarterly where P RCCFt is Execucomp’ record of the stock price at the closing s of the …scal year: pt = P RCCFt 8t: Finally, our measure of perks and pension payments Kt is the sum of Execucomp variables related to “other compensation” : Kt ALLOT HT OTt + OT HAN Nt if t 2 P1 DEF ER_RP T _AS_COM Pt + OT HCOM Pt if t 2 P2 : Tracking Grants, Gt Our measure of grant-based compensation Gt is the sum of the value of restricted stock grants and options in the period. We have data on the value of the stock component of that sum, EV (sr ; pt ), with the t following variables:29 EV (sr ; pt ) t RST KGRN Tt if t 2 P1 ST OCK_AW ARDS_F Vt if t 2 P2 : In reality, there may be N grants within the year, each with a quantity st;n and a market price at the time of granting of pt;n ; for n = 1 : N: The variables above that we observe in Execucomp will not have the disaggregated information grant by grant, but rather they correspond to EV (sr ; pt ) = t N P st;n pt;n : n=1 The value of options awarded in the period is recorded in the data as follows:30 EV (or ; xt ; pt ) t OP T ION _AW ARDS_BLK_V ALU Et if t 2 P1 OP T ION _AW ARDS_F Vt if t 2 P2 : 29 Both variables measure the value of stock awards as of the grant date. RSTKGRNT was reported by the companies themselves in the Summary Compensation Table, while STOCK_AWARDS_FV is calculated by Execucomp. Strictly speaking, each also contains restricted stock units and phantom stocks. 30 OPTION_AWARDS_BLK_VALUE is calculated by Compustat, during that period of time when— prior to FAS 123R— companies typically expensed options using the “instrinsic value” method, i.e., the di¤erence between grant date stock price and exercise price of the option, which nearly always led to no expensing of options. OPTION_AWARDS_FV is the grant date fair value of option awards in the year, reported by the company per FAS 123R using some version of Black and Scholes (1973) or a similarly accepted calculation. A. Jarque and J. Muth: Executive Compensation Packages 281 Again, these variables aggregate all grants within a year, so e¤ectively we will set M P EV (or ; xt ; pt ) = EV or ; xtg; ; pg;t ; t g;t g=1 where M is the total number of option grants in the year. There is some partial information in Execucomp about the date and exercise price of the di¤erent grants for an executive in a given year. However, we do not have their vesting schedule or the date of their exercise (that is, we do not know what the stock market price was at the time when the executive exercised the options). See the related discussion in the realized pay sensitivity analysis in Section 3. Computing Net Gains from Trading Stock, Tt We will now de…ne the components of our net gains from trade measure, Tt . To begin, recall that we assume each of these trades happens only once in the …scal year, and if the executive exercises options, he sells the acquired shares immediately. The portion of Tt that comes from exercising options is captured by the Execucomp variable OPT_EXER_VAL:31 X oe (pe;t xg ) OP T _EXER_V ALt ; 8t: g;t oe 2Ot g;t 1 The portion of Tt that comes instead from buying and selling stock on the open market, ss ps1 sb pb1 ; must be estimated, because we cannot 1 1 observe in the data the quantities ss or sb (and, correspondingly, the t t prices ps or pb ). We use an algorithm similar to Clementi and Cooley t t (2009) to estimate this di¤erence, with slightly di¤erent assumptions that we discuss later in this section. From the law of motion for vested stock in (3), we have that the di¤erence between last year’ unrestricted s stock holdings and this year’ is either coming from the newly vested s stock this year, sv ; or net purchases. We denote the net quantity of t shares sold in t as qt ss sb : Rearranging (3) and substituting qt , we t t have qt = St 1 St + sv ; 8t: (7) t Typically, qt will be positive in the data, i.e., the CEO will sell more shares than he buys in a given year. Occasionally, however, qt 31 OPT_EXER_VAL is the total value realized from option exercises in the year, and is measured (for each g award, in our notation) as the di¤erence between the exercise price and stock price on the date of exercise. 282 Federal Reserve Bank of Richmond Economic Quarterly calculated as in (7) will be negative. This could be due to violations of our assumption that the CEO immediately sells stock acquired through the exercise of options.32 Because we would rather bias our measure of realized pay upward, we set qt in our calculations equal to the maximum of qt from (7) and 0. To calculate qt using (7) we need St 1 and St ; which correspond to the CEO’ holdings of unrestricted stock. We observe this variable s directly in Execucomp:33 St SHROW N _EXCL_OP T St ; 8t: We also need the variable sv ; the stock vested within the year. This t variable maps directly into Execucomp’ SHRS_VEST_NUM in the s reporting period P2 : For observations in P1 ; when it is missing, we estimate it by examining annual changes in aggregate restricted stock holdings and annual grants. Speci…cally: 8 ST OCK_U N V EST _N U Mt 1 < if t 2 P1 ; ST OCK_U N V EST _N U Mt + sr sv ; t t : SHRS_V EST _N U Mt if t 2 P2 : where our measurement of the number of stocks granted within the year, sr ; is an approximation to the real total number of stock (unt available in the data) that we recover from EV (sr ) by assuming all t grants are valued at the average price within the year, denoted pt :34 EV (sr ) t sr = : t pt Note that pt is not in Execucomp. We match the …rms in Execucomp to a di¤erent database from the Center for Research in Security Prices (CRSP) containing daily stock prices, and we construct the average price ourselves. For this, we take the 12-month window of each …rm’ s …scal year. To summarize, in our notation, our estimate for the amount of stock vested within t is r sv = St t 1 r St + sr : t Once we get qt from (7), we estimate the value ss ps1 sb pb1 by t t assuming the qt shares were traded at the average market price over 32 In addition to what we have described, there are two other types of transactions that will change CEO holdings: stock inheritances and stock donations. We abstract from them, as these transactions will typically be small, if non-zero. However, these could also be behind some of the negative qt in the data. 33 SHROWN_EXCL_OPTS reports shares of the …rm owned by the CEO, excluding options that are exercisable or will become so within 60 days. This amount is reported as of some date between the …scal year-end and proxy publication. 34 Clementi and Cooley (2009) use the end-of-the-…scal-year price for this calculation. We choose average price hoping to avoid some of the idiosyncrasy of pt due to volatility of stocks. A. Jarque and J. Muth: Executive Compensation Packages 283 the year, i.e., ps1 = pb1 = pt . Given our assumption of non-negative net quantities traded, this amounts to stating ss ps;t t sb pb;t t max[0; pt qt ]: Thus, adding the stock and option portions of Tt , we get Tt (St 1 ; Ot 1 ) max[0; pt qt ] + OP T _EXER_V ALt ; 8t: Note that there are two di¤erences between our estimation of net revenue from trade and the calculations in Clementi and Cooley (2009). First, we use average instead of end-of-year prices to recover the quantity of shares granted in a given year, sr ; from the value of the grants; t this in‡ uences our estimate of the net quantities traded, qt : Second, we use OPT_EXER_VAL directly to account for the proceeds of options sales during the year: This variable is the true value of option exercises collected in Execucomp and hence uses actual exercise prices and actual stock prices on date of exercise. Clementi and Cooley (2009) instead choose to lump the stock purchases resulting from option exercises in with other stock sales, and they assume that they are acquired at the average price. REFERENCES Aggarwal, Rajesh K., and Andrew A. Samwick. 1999. “The Other Side of the Trade-o¤: The Impact of Risk on Executive Compensation.” Journal of Political Economy 107 (February): 65– 105. Antle, Rick, and Abbie Smith. 1985. “Measuring Executive Compensation: Methods and an Application.” Journal of Accounting Research 23 (Spring): 296– 325. Baker, George P., and Brian J. Hall. 2004. “CEO Incentives and Firm Size.” Journal of Labor Economics 22 (October): 767– 98. Black, Fischer, and Myron S. Scholes. 1973. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81 (May/June): 637– 54. Bebchuk, Lucian, and Jesse Fried. 2004. Pay without Performance: The Unful…lled Promise of Executive Compensation. Cambridge, Mass.: Harvard University Press. 284 Federal Reserve Bank of Richmond Economic Quarterly Bolton, Patrick, Jose Sheinkman, and Wei Xiong. 2006. “Executive Compensation and Short-termist Behaviour in Speculative Markets.” Review of Economic Studies 73 (July): 577– 610. Clementi, Gian Luca, and Thomas F. Cooley. 2010. “Executive Compensation: Facts.” Working Paper 15426. Cambridge, Mass.: National Bureau of Economic Research (October). Clementi, Gian Luca, Thomas F. Cooley, and Cheng Wang. 2006. “Stock Grants as a Commitment Device.” Journal or Economic Dynamics and Control 30 (November): 2,191– 216. Edmans, Alex, and Qi Liu. 2011. “Inside Debt.”Review of Finance 15 (1): 75– 102. Edmans, Alex, Xavier Gabaix, and Augustin Landier. 2009. “A Multiplicative Model of Optimal CEO Incentives in Market Equilibrium.” Review of Financial Studies 22 (December): 4,881– 917. Frydman, Carola, and Raven E. Saks. 2010. “Executive Compensation: A New View from a Long-Term Perspective, 1936– 2005.” Review of Financial Studies 23 (May): 2,099– 138. Gabaix, Xavier, and Augustin Landier. 2008. “Why Has CEO Pay Increased So Much?” The Quarterly Journal of Economics 123 (1): 49– 100. Garen, John E. 1994. “Executive Compensation and Principal-Agent Theory.” Journal of Political Economy 102 (December): 1,175– 99. Gayle, George-Levi, and Robert A. Miller. 2009. “Has Moral Hazard Become a More Important Factor in Managerial Compensation?” American Economic Review 99 (December): 1,740– 69. Gibbons, Robert, and Kevin J. Murphy. 1992. “Optimal Incentive Contracts in the Presence of Career Concerns: Theory and Evidence.” Journal of Political Economy 100 (June): 468– 505. Grossman, Sanford J., and Oliver D. Hart. 1983. “An Analysis of the Principal-Agent Problem.” Econometrica 51 (January): 7– 45. Hall, Brian J., and Je¤rey B. Liebman. 1998. “Are CEOs Really Paid Like Bureaucrats?” The Quarterly Journal of Economics 113 (August): 653– 91. Hall, Brian J., and Kevin J. Murphy. “Stock Options for Undiversi…ed Executives.” Journal of Accounting & Economics 33 (February): 3– 42. A. Jarque and J. Muth: Executive Compensation Packages 285 Haubrich, Joseph G. 1994. “Risk Aversion, Performance Pay, and the Principal-Agent Problem.” Journal of Political Economy 102 (April): 258– 76. Haubrich, Joseph G., and Ivilina Popova. 1998. “Executive Compensation: A Calibration Approach.” Economic Theory 12 (3): 561– 81. Jarque, Arantxa. 2010. “Hidden E¤ort, Learning by Doing, and Wage Dynamics.” Federal Reserve Bank of Richmond Economic Quarterly 96 (4): 339– 72. Jarque, Arantxa, and Brian Gaines. 2012. “Regulation and the Composition of CEO Pay.” Federal Reserve Bank of Richmond Economic Quarterly 98 (4): 309– 48. Jensen, Michael C., and Kevin J. Murphy. 1990. “Performance Pay and Top-Management Incentives.” Journal of Political Economy 98 (April): 225– 64. Jenter, Dirk, and Fadi Kanaan. Forthcoming. “CEO Turnover and Relative Performance Evaluation.” Journal of Finance. Jin, Li, and S. P. Kothari. 2008. “E¤ect of Personal Taxes on Managers’Decisions to Sell Their Stock.” Journal of Accounting and Economics 46 (September): 23– 46. Larcker, David F., Allan L. McCall, and Brian Tayan. 2011. “What Does it Mean for an Executive to ‘ Make’$1 Million?” Stanford Closer Look Series No. CGRP-22 (December 14). Prescott, Edward S. 1999. “A Primer on Moral-Hazard Models.” Federal Reserve Bank of Richmond Economic Quarterly 85 (Winter): 47– 77. Schaefer, Scott. 1998. “The Dependence of Pay-Performance Sensitivity on the Size of the Firm.” The Review of Economics and Statistics 80 (August): 436– 43. Spear, Stephen E., and Sanjay Srivastava. 1987. “On Repeated Moral Hazard with Discounting.” Review of Economic Studies 54 (October): 599– 617. Wang, Cheng. 1997. “Incentives, CEO Compensation, and Shareholder Wealth in a Dynamic Agency Model.” Journal of Economic Theory 76 (September): 72– 105. Economic Quarterly— Volume 99, Number 4— Fourth Quarter 2013— Pages 287– 303 The Business Cycle Behavior of Working Capital Felipe Schwartzman F irms require short-term assets or liabilities in order to facilitate production and sales. Those “working capital”requirements are often incorporated in macroeconomic models designed to study the impact of monetary or …nancial shocks.1 They are important for the propagation of those shocks since they a¤ect the marginal cost of funds faced by some set of agents in the economy. If …rms require working capital in order to acquire variable inputs, a change in the cost of funds faced by …rms translates into immediate changes in macroeconomic activity.2 This article investigates the cyclical properties of the three main components of working capital— inventories (raw materials, workin-process, and …nished goods), cash and short-term investments, and trade credit— aggregated across all …rms and with special attention to their correlations across time with output. The key objective is to obtain stylized facts. While theory informs what kind of facts are worth examining, the uncovering of stylized facts also serves as an input for the development of new theories. The discussion above provides a couple of examples of existing theoretical models that motivate the exploration that follows, but the results stand on their own as useful The views expressed in this article are those of the author and do not necessarily represent the views of the Federal Reserve Bank of Richmond or those of the Federal Reserve System. E-mail: email@example.com. 1 Technically, the accounting de…nition of working capital is the di¤erence between the sum of short-term assets and the sum of short-term liabilities. In the article, as in the literature, I use the term more broadly to refer to the collection of short-term assets and short-term liabilities rather than the aggregate accounting concept. 2 Examples of articles that model working capital requirements explicitly are Christiano and Eichenbaum (1992) and Fuerst (1992), who develop the canonical model of working capital in monetary economics, and Jermann and Quadrini (2012), who advance working capital as a key part of the transmission mechanism for …nancial shocks. Working capital also plays a prominent role in the emerging markets business cycles literature, much of which emphasizes the aggregate impact of shocks a¤ecting the supply of foreign funds. Neumeyer and Perri (2004) is a primary example of the latter. 288 Federal Reserve Bank of Richmond Economic Quarterly for potentially any theory in which working capital plays a signi…cant role. In the simplest models, working capital is needed in advance of production. This requirement implies that, so long as data is available at a high enough frequency, the relevant components of working capital ought to be more strongly correlated with future values of cash ‡ ows than with current values. This, however, need not be generally the case. In an environment with credit frictions, working capital could also lag production. Credit frictions commonly imply that …rms have a borrowing capacity that is increasing in the size of their balance sheet. In particular, interest rates can increase with leverage, as in Bernanke and Gertler (1989), or there might be outright leverage limits, as in Kiyotaki and Moore (1997).3 Models with credit frictions generate endogenous propagation, since pro…ts retained in a given period increase the size of …rms’ balance sheets, which in turn allow …rms to subsequently expand their borrowing and their acquisition of working capital. To evaluate the lead-lag relationships, I use data from the Financial Accounts of the United States.4 The data set is put together by the Federal Reserve Board and distributed online four times per year. The accounts are constructed based on a variety of data sources to provide a comprehensive view of how di¤erent sectors of the economy (households and di¤erent types of corporations) interact with one another, as well as providing a breakdown of the assets and liabilities held in each one of those sectors. The time series span most of the post-WWII period, from 1952 onward, and I use all of the data in my analysis. The advantage of using this data set over …rm-level data, such as COMPUSTAT, is that it provides a comprehensive view of the economy, including noncorporate businesses, whereas COMPUSTAT data only include the largest …rms. For all the time series, I compare correlations before and after 1984. This marks the end of the 1981 recession and the beginning of the “Great Moderation.”The motivation for splitting the sample follows Lubik, Sarte, and Schwartzman (2014), who …nd that around the same time as the onset of the Great Moderation there was a marked change in key business cycle properties of the U.S. economy. Strikingly, these changes in correlations survive the end of the Great Moderation after 2008. Since the focus of the article is on correlations 3 These two articles also correspond to the two most widely used microfoundations for credit frictions, which are costly state veri…cation and imperfect commitment, respectively 4 These data were previously called the “Flow of Funds Accounts of the United States.” Schwartzman: The Business Cycle Behavior of Working Capital 289 and not on volatilities, I treat the whole period from 1984 onward as a single one. The …ndings are as follows: First, inventories lag business cycles in the years before 1984 by about three quarters but by only one or two quarters in the more recent period. This is consistent with the view that before 1984 inventory accumulation was determined by previous cash ‡ accumulation by …rms but less so afterward. The second …nding ow is that cash holdings broadly de…ned to include short-term investments commonly lead the business cycle, consistent with the cash-in-advance model for short-term production decisions. This echoes classic results by Sims (1972) and updated in Stock and Watson (1999) showing that monetary aggregates are a good leading indicator of output. However, and in contrast to monetary aggregates, the lead-lag relationship between cash holdings and output is considerably more robust, remaining in place in the past 30 years, a period in which the relationship between conventional monetary aggregates and output has broken down. Finally, I …nd that trade credit lags output, although less markedly than inventories. This article has a very simple structure. I …rst discuss in more detail how decisions made by a …rm over time can give rise to the various components of working capital. The following three sections examine in turn each of the three major components of working capital (inventories, cash and short-term investments, and trade credit). I provide for each component additional background information about existing theories explaining why …rms are willing to hold them, as well as some broad descriptive statistics about how relevant those components are on …rms’balance sheets, the long-run trends in those holdings, if any, and the cyclical properties of those di¤erent components. The last section concludes. 1. WORKING CAPITAL DEMAND In models, working capital requirements often arise out of timing restrictions. As an example of such restrictions, consider a …rm whose production and sales process follows a seasonal ‡ ow, so that cash ‡ ows are only realized every four periods f:::; t 4; t; t + 4; :::g. As an example of a real activity, one could think of this as a Christmas decorations producer that only sells its products in the last quarter of the year. However, in order to receive a cash ‡ at t, the …rm needs to perow form several activities throughout the year that result in accumulating working capital between t 3 and t. If one were to look at the balance sheet of this …rm, one would see working capital peaking in the quarters 290 Federal Reserve Bank of Richmond Economic Quarterly Figure 1 Timeline between cash ‡ accumulation periods and the cash ‡ ow ows peaking in periods f:::; t 4; t; t + 4; :::g. Figure 1 shows a detailed breakdown of the production cycle, depicting the di¤erent components of working capital. The ‡ ows are depicted by the vertical lines and stocks are described by the arrows. In the example, the …rm starts the year with some cash ‡ that it ow receives in t 4. It may choose to distribute some of this cash ‡ ow to shareholders as dividends, to use it to pay outstanding debts or to dedicate it to long-term investments. It may also choose to retain some of the cash for future use, an option that is attractive if external funds are costly to acquire. The production cycle starts in the spring, in t 3, with the acquisition and use of inputs, including materials and labor. These can be paid for using the cash that the …rm has on its balance sheet or with credit. The typical “cash-in-advance” assumption is that a subset of the inputs that …rms acquire in t 3 require it to have cash available from the previous period, t 4, onward. The required cash may be a leftover of period t 4 cash ‡ ows that were not put to alternative uses, raised through …nancial intermediaries, or acquired by issuing new shares. Alternatively, the …rm might choose to defer payment for inputs to which the cash-in-advance constraint does not apply, acquiring an account payable. In the example, those accounts payable remain on the …rm’ balance sheet until it receives new cash ‡ s ows in t and uses those to pay the accounts payable out. The raw materials that the …rm purchases in the spring, in t 3, are incorporated into raw materials inventories. Some part of it is processed right away, and the combination of the cost of those materials with Schwartzman: The Business Cycle Behavior of Working Capital 291 labor and overhead costs involved in the processing are incorporated into work-in-process inventories. Raw materials and work-in-process inventories remain on the …rm’ balance sheet until production is …nals ized in the summer, in t 2. At that point, all the inventories become …nished goods inventories, which remain on the balance sheet until the fall in t 1, when the Christmas decorations producer sells the goods to wholesalers. However, since wholesalers will only sell those goods to …nal customers in the last quarter of the year, the producer may agree to let them delay the payment, acquiring an account receivable, which is canceled at t. Firms can then use the associated cash ‡ ows to cancel outstanding accounts payable and restart the production cycle. The assumption of a seasonal pattern may be appropriate for certain …rms and industries but not for others. Some models of working capital requirements such as in Christiano and Eichenbaum (1992) incorporate a seasonal-like pattern. However, instead of taking place over the year, the seasonality takes place within each period, with working capital being required in the beginning of the period so that cash ‡ ows can be realized in the end of the period. Since model periods are chosen to correspond to periods in the data, the seasonality is not observable to an econometrician. A perhaps more natural case (although not usually explicitly modeled in the literature) is for …rms to run multiple production processes simultaneously, with working capital being accumulated in any point in time for the sake of production in the following period. The di¤erent forms of working capital assets require the …rm to commit funds ahead of cash ‡ ows. The marginal cost of those funds can be determined in di¤erent ways depending on the details of the environment in which the …rms …nd themselves. In the simplest case in which there are no credit market frictions, the marginal cost of funds dedicated to working capital assets is given simply by the interest rate on …nancial assets of similar maturity. If, however, credit frictions impose a wedge between the interest rate on borrowing and the return on …nancial assets, the marginal cost of funds will depend on whether the …rm is a borrower. More generally, if the …rm faces credit rationing, the marginal cost of funds is given by the return on alternative uses of those funds, for example in illiquid, long-term investment projects. Finally, note that the demand for di¤erent components of working capital emerges for very di¤erent reasons. The demand for inventories arises because of a discrepancy between the timing of purchase and use of inputs, production, and sales that is likely to arise largely for technological reasons. However, the demand for cash and trade credit is largely a function of the type of access that the …rm and its trading 292 Federal Reserve Bank of Richmond Economic Quarterly partners have to payment and credit institutions. We will examine each component of working capital in the following sections. 2. INVENTORIES There is a large literature on inventories, some of it summarized in Ramey and West (1999), but it is still evolving. Hornstein (1998) also provides a detailed overview of stylized facts associated with inventory investment. Holding inventories is inherently costly, because by dedicating funds to the purchase of inputs that will only result in cash ‡ ows in the future, …rms forgo the return on …nancial investments. Furthermore, they might have to incur storage costs. Given those costs, there are two dominant views of why …rms hold inventories. One emphasizes …rms’desire to avoid stockouts, i.e., situations in which customers desire to purchase some good or the …rm desires to use some input but cannot because it is not available at that moment.5;6 The second view points to …xed costs of moving goods between locations, which leads …rms to purchase inputs or deliver output to retailers in batches.7 In both views, inventories are a pre-condition for sales and, to the extent that these theories also explain the holding of raw materials inventories, they are a pre-condition for production. Given either stockout avoidance or …xed delivery costs, …rms choose the inventory/sales ratio to balance out the costs associated with very low inventories against the opportunity cost of funds and storage costs associated with holding those inventories. For a given target inventory/sales ratio, changes in the economic environment that lead …rms to increase their prospective sales are, therefore, likely to be accompanied by a prior buildup of inventories. Likewise, changes in the opportunity cost of holding inventories due to less expensive bank credit or lower return on …nancial investments might also lead …rms to build up inventories and, subsequently, increase their cash ‡ ow. In both cases, a buildup in inventories precedes increases in cash ‡ ows. Alternatively, to the extent that reduced cash holdings are associated with a higher 5 For a recent article analyzing the implications of this view for the macroeconomy, see Wen (2011). 6 A closely related view is that …rms hold inventories in order to smooth production in the face of erratic demand shocks. While still an important building block of inventory models, production smoothing is, by itself, at odds with the fact that production is generally more volatile than sales (Ramey and West 1999). 7 See Khan and Thomas (2007) for an analysis of the implications of this view for macroeconomic dynamics. Schwartzman: The Business Cycle Behavior of Working Capital 293 Figure 2 Components of Working Capital/GDP Notes: Share of GDP averages are in parentheses. opportunity cost of funds for the …rm, a reduction in output or sales may precede reductions in inventories holdings.8 Figure 2 shows the evolution of the di¤erent components of working capital, as calculated using the Financial Accounts of the United States all normalized by gross domestic product (GDP). The normalization is chosen to control for underlying trends, and to give a sense of the importance of inventories in production. In the speci…c case of inventories, we can see that between 1952 and 2013 non…nancial businesses have held an amount of inventories equal to around 19 percent of GDP. Furthermore, from the early 1980s onward there is a welldocumented secular decline in the inventories/GDP ratio (Ramey and West 1999).9 Figure 3 shows the cyclical component of inventories together with the cyclical component of GDP, where both GDP and inventories were 8 More complicated dynamics are certainly possible. For example, if demand for products increases unexpectedly and …rms need time to ramp up production, …nal goods inventories might decline momentarily with an increase in output and sales following that decline. 9 When calculating ratios, I use nominal values in both the numerator and the denominator. 294 Federal Reserve Bank of Richmond Economic Quarterly Figure 3 Cyclical Components of GDP and Inventories de‡ ated using the GDP de‡ ator. The cyclical component of the de‡ ated series is extracted using the band-pass …lter to isolate variation in the data corresponding to cycles with amplitude between four and 32 quarters. Thus, it excludes seasonal variation (which have an amplitude of four quarters) and ‡ uctuations at lower than what is typically considered business cycle frequencies (which have amplitudes of eight years or fewer), including long-run trends. From the …gure, it is almost immediate that inventories have lagged business cycles before the mid1980s, but that the lead-lag relationship becomes less salient afterward. Table 1 con…rms the visual impression. For each column, the …rst line of the table shows the correlation of the cyclical component of GDP at t with the cyclical component of inventories in some t + k; with each column corresponding to a di¤erent value of k. We say that inventories lead output if the peak correlation occurs for k < 0 and that it lags output if it occurs for k > 0. The table omits standard errors for simplicity, but as a rule of thumb correlations above 0.2 in absolute value are statistically signi…cant. The table shows that before 1984 GDP correlated most with inventories three quarters in the future. After 1984, the peak of the lead-lag di¤erence shortens from three quarters to one quarter, and the di¤erence between the peak and the contemporaneous correlation becomes less salient. The result provides a di¤erent perspective on the stylized facts pointed out by Lubik, Sarte, and Schwartzman (2014), who show that inventory/sales Schwartzman: The Business Cycle Behavior of Working Capital 295 Table 1 Correlations Between Inventories and Measures of Economic Activity t 4 t 3 t 2 t GDP Final Sales Cash Flow 1 Cash Flow 2 0.48 0.50 0.56 0.52 0.31 0.32 0.53 0.43 0.11 0.11 0.44 0.29 1 t t+1 1952– 1983 0.13 0.39 0.61 0.13 0.38 0.61 0.29 0.09 0.15 0.11 0.11 0.35 GDP Final Sales Cash Flow 1 Cash Flow 2 0.06 0.23 0.36 0.11 0.22 0.40 0.23 0.05 0.40 0.55 0.09 0.23 1984– 2013 0.57 0.70 0.67 0.73 0.03 0.11 0.38 0.47 0.78 0.77 0.21 0.51 t+2 t+3 t+4 0.76 0.78 0.37 0.55 0.81 0.84 0.53 0.66 0.77 0.82 0.60 0.66 0.77 0.75 0.36 0.54 0.63 0.60 0.50 0.52 0.40 0.37 0.58 0.48 ratios were strongly countercyclical prior to 1984 but became acyclical or even somewhat pro-cyclical afterward. As Figure 1 suggests, production begets inventories, thus implying mechanically the possibility of a lead-lag relationship. The bottom rows of each of the panels in Table 1 examine this possibility by investigating whether the lead-lag relationship uncovered for GDP is also present for …nal sales and cash ‡ ows. Final sales are de…ned as being equal to GDP with inventory investment excluded from it. For cash ‡ ow, I use two alternative de…nitions. The …rst one de…nes cash ‡ ows to be equal to net income plus the consumption of capital of both corporate and noncorporate …rms. Adding the consumption of capital back to net income is necessary in order to obtain a sensible measure of cash ‡ since the consumption of capital (which is closely related ow to depreciation) does not reduce …rm cash ‡ ows even if it reduces the economic income. The second one adds interest payments, thus separating the ability of the …rm to generate cash ‡ from the …nancial ow position of the …rm and the timing of interest payments. These de…nitions of cash ‡ are imperfect in that net income is recognized at ow the time of sale, not at the time in which trade receivables are paid out. Thus, in terms of the diagram in Figure 1, the measured cash ‡ ow might be recognized closer to time t 1 than to t. In all cases, inventories lag the particular ‡ ows considered, demonstrating that the lead-lag relationship with output is not an artifact of timing restrictions. 3. CASH AND SHORT-TERM INVESTMENTS Cash and short-term investments represent cash and all securities readily transferable to cash. This includes, apart from cash on hand, 296 Federal Reserve Bank of Richmond Economic Quarterly certi…cates of deposits, commercial paper, government and other marketable securities, demand deposits, etc. Firms hold cash and shortterm investments for many reasons, including to facilitate day-to-day payments of variable inputs (Christiano and Eichenbaum 1992), to serve as cushions to allow …rms to insure against negative cash ‡ shocks ow (Bates, Kahle, and Stulz 2009), to help …rms take advantage of ‡ eeting investment opportunities (Kiyotaki and Moore 2012), or to help them with their tax management (Foley et al. 2007). Of those motives, business cycle models in which …rms demand cash typically focus on the …rst, which is the payments for variable inputs. These models are normally posited as “cash-in-advance” models, in which …rms need to have cash at hand for a nontrivial period of time before the time in which they use the cash. For cash-in-advance constraints to play a meaningful economic role, it must be the case that cash pays a rate of return below the opportunity cost of funds for …rms. This is trivially the case if cash is understood to include only currency, which pays no interest rate and the value of which declines with in‡ ation. In that case, the opportunity cost of holding cash is given by the nominal rate of interest on bonds. However, …rms also hold a variety of assets that are “as good as cash,”in the sense that they either mature very quickly or can be converted into cash at very short notice. The opportunity cost of holding these “short-term” investments is given by their liquidity premia, that is, by the di¤erence between the rate of return on those securities and the rate of return on alternative, illiquid investments. Using the Financial Accounts of the United States data, I calculate cash and short-term investments for both corporate and noncorporate non…nancial businesses. For noncorporate businesses, these are the sum of checkable deposits and currency, time and savings deposits, money market fund shares, Treasury securities, and municipal securities. For non…nancial corporate businesses, cash includes, in addition to those just listed, foreign deposits and agency and GSE-backed securities. From Figure 2, we can see that between 1952 and 2013 corporate businesses have held on average 11 percent worth of GDP in cash. Furthermore, in the last few decades there has been a secular increase in the shares of cash and short-term investments, a fact pointed out in articles by Foley et al. (2007) and Bates, Kahle, and Stulz (2009), among others, who have found …rms holding increasing amounts of cash in the last three decades. Figure 4 shows the cyclical component of cash and short-term investments held by corporate businesses together with the cyclical component of GDP, with both series de‡ ated by the GDP de‡ ator, and Schwartzman: The Business Cycle Behavior of Working Capital 297 Figure 4 Cyclical Components of GDP and Cash and Short-Term Investments …ltered using the band-pass …lter for variations at cycles with amplitudes between four and 32 quarters. As Table 2 makes clear, cash leads business cycles throughout the period under analysis, although the relationship weakens after 1984. The relationship is only hard to discern when cash ‡ 1 (incoming pro…ts plus depreciation, net of interest ow expenses) is used as a measure of economic activity, but it is again apparent with cash ‡ 2 (incoming pro…ts plus depreciation, gross of ow interest expenses). Such a lead-lag relationship echoes the old monetarist view that money is a good leading indicator for business conditions, as well as formal analysis by Sims (1972), updated by Stock and Watson (1999). Table 3 revisits these results by showing the lead-lag relationship between M2 (which includes currency, demand deposits, money market mutual funds, and other time deposits) and GDP, both de‡ ated by the GDP de‡ ator and band-pass …ltered, for the whole sample and broken down before and after 1984. The lead-lag relationship of M2 with GDP is very strong before 1984, but disappears afterward. Given the comparison with the behavior of M2, it is remarkable that the lead-lag relationship between cash and short-term investments held by …rms with output is as robust as it is. The …nding goes along with the assertion by Lucas and Nicolini (2013) and Belongia and Ireland (2014) that traditional monetary aggregates do not measure adequately the amount of liquidity in the economy, and that more carefully constructed measures of aggregate 298 Federal Reserve Bank of Richmond Economic Quarterly Table 2 Correlations Between Cash and Short-Term Investments and Measures of Economic Activity t 4 t 3 t 2 t GDP Final Sales Cash Flow 1 Cash Flow 2 0.46 0.47 0.17 0.35 0.60 0.60 0.34 0.48 0.69 0.68 0.48 0.55 1 t t+1 1952– 1983 0.70 0.61 0.42 0.70 0.62 0.44 0.57 0.61 0.56 0.59 0.56 0.44 GDP Final Sales Cash Flow 1 Cash Flow 2 0.25 0.33 0.08 0.20 0.41 0.42 0.08 0.26 0.54 0.48 0.07 0.28 1984– 2013 0.57 0.51 0.49 0.46 0.08 0.12 0.24 0.20 0.43 0.41 0.20 0.18 t+2 t+3 t+4 0.18 0.21 0.40 0.24 0.09 0.04 0.19 0.02 0.32 0.28 0.01 0.17 0.31 0.33 0.28 0.17 0.19 0.22 0.33 0.16 0.09 0.11 0.34 0.17 liquidity have retained the ability to forecast output. Of course, a measure of liquidity based on cash and short-term investments held by …rms is distinct from measures such as M2 or others in that it does not include cash held by households. A closer investigation of whether liquid assets held by …rms are specially correlated with future output as compared to those held by households is an interesting avenue for future work. 4. TRADE CREDIT The third major component of working capital is trade credit, with trade receivables as part of the assets and trade payables as part of the liabilities. Trade receivables represent amounts owed by customers for goods and services sold in the ordinary course of business. Conversely, trade payables represent trade obligations due within one year, or the normal operating cycle of the company. Trade credit is an active area of research in corporate …nance, with an abundant theoretical and empirical literature. To a large degree, theories of trade credit emphasize the fact that, relative to …nancial institutions, suppliers often have advantages in securing repayment from their customers. Among other reasons for that advantage, the literature mentions information advantages for suppliers (Mian and Smith 1992), incentives for customers to preserve their relationship with suppliers (Cuñat 2007), and the fact that, since goods are harder to divert than cash, borrowers have less incentive to default (Burkart and Ellingsen 2004). The opportunity cost of holding trade receivables is given by the di¤erence between the rate of return on alternative investments and Schwartzman: The Business Cycle Behavior of Working Capital 299 Table 3 Correlations Between M2 and Short-Term Investments and Measures of Economic Activity t 4 t 3 t 2 t GDP Final Sales Cash Flow 1 Cash Flow 2 0.66 0.66 0.24 0.45 0.77 0.76 0.44 0.60 0.82 0.80 0.62 0.71 1 t 1952– 1983 0.78 0.65 0.78 0.67 0.75 0.80 0.77 0.74 GDP Final Sales Cash Flow 1 Cash Flow 2 0.02 0.14 0.06 0.07 0.08 0.20 0.01 0.13 0.14 0.23 0.08 0.21 1984– 2013 0.22 0.29 0.26 0.29 0.19 0.31 0.31 0.38 t+1 t+2 t+3 t+4 0.46 0.47 0.74 0.62 0.23 0.22 0.61 0.43 0.01 0.02 0.43 0.22 0.22 0.23 0.23 0.02 0.32 0.30 0.42 0.41 0.27 0.25 0.49 0.38 0.15 0.14 0.52 0.30 0.01 0.01 0.50 0.20 the interest rate paid by customers. If the latter is smaller than the former, it will be costly for …rms to hold trade receivables. Conversely, there is a cost associated with issuing trade payables if the interest rate on trade payables is higher than the rate of return on real or …nancial investments. When analyzing trade credit, I focus on trade receivables, which I de…ne to include consumer credit held by corporate and noncorporate non…nancial …rms. Including consumer credit follows the spirit of including in trade receivables all short-term credit conceded by the …rm to other parties in order to facilitate production and sales. I focus only on receivables rather than payables since, in a closed economy, whenever a …rm issues a trade payable, the counterpart acquires a trade receivable. Because the U.S. economy is not closed, the two numbers do not exactly coincide. Furthermore, even after accounting for foreign holdings and issuance of trade credit, the di¢ culties in collecting accurate data are signi…cant enough that there exists a nontrivial discrepancy between aggregate trade payables and aggregate trade receivables. Finally, trade payables do not include consumer credit. In spite of those di¤erences, both measures of trade credit behave very similarly, so that for brevity I will only discuss trade receivables. From Figure 2 we can see that between 1952 and 2013 corporate businesses hold a value of trade receivables equal to 19 percent of GDP. Furthermore, unlike inventories and cash, there is no clear trend in the ratio of trade receivables to GDP. Figure 5 shows the cyclical component of receivables together with the cyclical component of GDP, both de‡ ated using the GDP de‡ ator and extracted using a band-pass …lter for frequencies between four and 32 quarters. Table 4 presents the cross-time correlation. Trade receivables lag output by a quarter both 300 Federal Reserve Bank of Richmond Economic Quarterly Figure 5 Cyclical Components of GDP and Trade Receivables before and after 1984. This is in line with the diagram depicted in Figure 1, which predicts that …rms accumulate trade receivables after production and sales have taken place. A comparison with …nal sales and the di¤erent measures of cash ‡ shows a similar pattern. This ow is still in line with the diagram, since net income is recognized at the time of sale, not at the time in which …nal payment is received. Thus, to the extent that …rms tend to provide …nancing for their customers, one would expect trade receivables to lag cash ‡ ows de…ned using data from income. 5. CONCLUSION Working capital is an important part of many macroeconomic models that emphasize the impact of ‡ uctuations in the cost of capital on …rm decisions. I …nd that the cyclical properties of the di¤erent components are quite di¤erent. In particular, cash holdings consistently lead the business cycle, whereas inventories and trade receivables are lagging. Interestingly, the lead-lag relationships for inventories appear to weaken after 1984. To the extent that those relationships are indicators of payment and …nancial frictions, the reductions in the lead-lag relationships between inventories and economic activity are consistent with the view, argued by Jermann and Quadrini (2006), that …nancial markets became more e¢ cient after the early 1980s. A second set of interesting facts concerns cash holdings, which are particularly Schwartzman: The Business Cycle Behavior of Working Capital 301 Table 4 Correlation of Trade Receivables with Di erent Measures of Economic Activity t 4 t 3 t 2 t GDP Final Sales Cash Flow 1 Cash Flow 2 0.25 0.22 0.55 0.40 0.03 0.03 0.49 0.29 0.25 0.23 0.32 0.08 1 t 1952– 1983 0.53 0.73 0.50 0.73 0.04 0.25 0.18 0.45 GDP Final Sales Cash Flow 1 Cash Flow 2 0.04 0.08 0.47 0.14 0.13 0.25 0.35 0.04 0.32 0.41 0.22 0.19 1984– 2013 0.50 0.64 0.56 0.67 0.07 0.09 0.31 0.40 t+1 t+2 t+3 t+4 0.81 0.84 0.47 0.64 0.78 0.83 0.59 0.70 0.68 0.74 0.63 0.62 0.52 0.58 0.60 0.48 0.71 0.72 0.25 0.45 0.71 0.71 0.38 0.47 0.64 0.65 0.47 0.47 0.54 0.53 0.50 0.45 noteworthy because the facts are robust over time. This is in contrast to the lead-lag relationship between M2 and GDP, which broke down after the 1980s. The results suggest that availability of cash is an important precursor of economic activity, giving some credence to models that emphasize cash-in-advance type constraints. REFERENCES Bates, Thomas W., Kathleen M. Kahle, and René M. Stulz. 2009. “Why Do U.S. Firms Hold So Much More Cash Than They Used To?” The Journal of Finance 64 (October): 1,985– 2,021. Belongia, Michael T., and Peter N. Ireland. 2014. “Interest Rates and Money in the Measurement of Monetary Policy.” Working Paper 20134. Cambridge, Mass.: National Bureau of Economic Research (May). Bernanke, Ben, and Mark Gertler. 1989. “Agency Costs, Net Worth, and Business Fluctuations.” The American Economic Review 79 (March): 14– 31. Burkart, Mike, and Tore Ellingsen. 2004. “In-Kind Finance: A Theory of Trade Credit.” The American Economic Review 94 (June): 569– 90. 302 Federal Reserve Bank of Richmond Economic Quarterly Christiano, Lawrence J., and Martin Eichenbaum. 1992. “Liquidity E¤ects and the Monetary Transmission Mechanism.” Working Paper 3974. Cambridge, Mass.: National Bureau of Economic Research (January). Cuñat, Vicente. 2007. “Trade Credit: Suppliers as Debt Collectors and Insurance Providers.” Review of Financial Studies 20 (March): 491– 527. Foley, C. Fritz, Jay C. Hartzell, Sheridan Titman, and Garry Twite. 2007. “Why Do Firms Hold So Much Cash? A Tax-Based Explanation.” Journal of Financial Economics 86 (December): 579– 607. Fuerst, Timothy S. 1992. “Liquidity, Loanable Funds, and Real Activity.” Journal of Monetary Economics 29 (February): 3– 24. Hornstein, Andreas. 1998. “Inventory Investment and the Business Cycle.” Federal Reserve Bank of Richmond Economic Quarterly 84 (Spring): 49– 72. Jermann, Urban, and Vincenzo Quadrini. 2006. “Financial Innovations and Macroeconomic Volatility.”Working Paper 12308. Cambridge, Mass.: National Bureau of Economic Research (June). Jermann, Urban, and Vincenzo Quadrini. 2012. “Macroeconomic E¤ects of Financial Shocks.” The American Economic Review 102 (February): 238– 71. Khan, Aubhik, and Julia K. Thomas. 2007. “Inventories and the Business Cycle: An Equilibrium Analysis of (S; s) Policies.” The American Economic Review 97 (September): 1,165– 88. Kiyotaki, Nobuhiro, and John Moore. 1997. “Credit Cycles.” The Journal of Political Economy 105 (April): 211– 48. Kiyotaki, Nobuhiro, and John Moore. 2012. “Liquidity, Business Cycles, and Monetary Policy.” Working Paper 17934. Cambridge, Mass.: National Bureau of Economic Research (March). Lubik, Thomas, Pierre-Daniel Sarte, and Felipe Schwartzman. 2014. “What Inventories Tell Us About How Business Cycles Have Changed.” Manuscript. Lucas, Jr., Robert E., and Juan Pablo Nicolini. 2013. “On the Stability of Money Demand.” Manuscript, University of Chicago. Mian, Shehzad L., and Cli¤ord W. Smith, Jr. 1992. “Accounts Receivable Management Policy: Theory and Evidence.” The Journal of Finance 47 (March): 169– 200. Schwartzman: The Business Cycle Behavior of Working Capital 303 Neumeyer, Pablo A., and Fabrizio Perri. 2005. “Business Cycles in Emerging Economies: The Role of Interest Rates.” Journal of Monetary Economics 52 (March): 345– 80. Ramey, Valerie A., and Kenneth D. West. 1999. “Inventories.” In Handbook of Macroeconomics, Vol. 1, edited by J. B. Taylor and M. Woodford. Philadelphia: Elsevier, 863– 923. Sims, Christopher A. 1972. “Money, Income, and Causality.” The American Economic Review 62 (September): 540– 52. Stock, James H., and Mark W. Watson. 1999. “Business Cycle Fluctuations in U.S. Macroeconomic Time Series.” In Handbook of Macroeconomics, Vol. 1, edited by J. B. Taylor and M. Woodford. Philadelphia: Elsevier, 3– 64. Wen, Yi. 2011. “Input and Output Inventory Dynamics.” American Economic Journal: Macroeconomics 3 (October): 181– 212. Economic Quarterly— Volume 99, Number 4— Fourth Quarter 2013— Pages 305– 340 Pecuniary Externalities, Segregated Exchanges, and Market Liquidity in a Diamond-Dybvig Economy with Retrade Borys Grochulski P rice changes a¤ect economic agents primarily by altering their budget constraints. In many economic environments, however, price changes additionally impact the agents by altering other constraints agents face. Those additional ways in which prices a¤ect agents, other than through budget constraints, are known as pecuniary externalities.1 Examples of the additional constraints that can be a¤ected by prices include incentive compatibility, participation, and collateral constraints. Numerous recent macroeconomic studies have shown that pecuniary externalities can lead to market failure.2 The intuition behind this failure is as follows. In standard Arrow-Debreu economies, where The author would like to thank Tee Kilenthong, Sam Marshall, Wendy Morrison, Pierre Sarte, Felipe Schwartzman, and Ned Prescott for their helpful comments. The views expressed in this article are those of the author and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System. E-mail: firstname.lastname@example.org. 1 The term pecuniary externality has been used more broadly than this de…nition. Viner (1932) uses it to describe the impact of a change in the price of an input on the production cost curve of a …rm. Greenwald and Stiglitz (1986) and, more recently, Bianchi (2011) and Dávila et al. (2012) among others, use it in reference to the generic constrained-ine¢ ciency of competitive equilibria in economies with exogenously imposed market incompleteness (studied in, e.g., Stiglitz  and Geanakoplos and Polemarchakis ). In the language of Prescott and Townsend (1984), the de…nition we use corresponds to prices having a direct impact on the agents’ consumption possibility set, in addition to the budget constraint. 2 See, e.g., Kehoe and Levine (1993), Golosov and Tsyvinski (2007), Lorenzoni (2008), and Di Tella (2014). 306 Federal Reserve Bank of Richmond Economic Quarterly prices only a¤ect budget constraints, equilibrium allocations are e¢ cient. It is therefore impossible to alter equilibrium prices (perhaps by imposing taxes) and obtain a Pareto improvement (i.e., make an agent better o¤ without making someone else worse o¤). An increase in the price of good x, for example, will relax budget constraints of some agents, loosely speaking the sellers of x, making them better o¤, but it will tighten budget constraints of others, the buyers of x, making this group worse o¤. The equilibrium price of good x cannot therefore be improved upon in Pareto sense. The same may no longer hold true when prices a¤ect not only budget but also some other constraints that can be tightened or relaxed for all agents simultaneously. If an increase in the price of x relaxes everyone’ incentive compatibility constraint, for example, then not s only the sellers of x but also the buyers of x can bene…t from a higher price of x, as long as the relaxed incentive constraint helps them more than the tightened budget constraint hurts them. The benevolent social planner— a stand-in concept we use to calculate optimal allocations— will take this e¤ect into account. In a market economy, however, agents take prices as independent of their individual actions. By ignoring the general equilibrium impact of their actions on prices, agents also ignore the indirect e¤ect they have on how tight their own incentive constraints are. The planner’ and the agents’ costs-bene…t calculus s are thus di¤erent, which leads to suboptimal equilibrium outcomes. By relaxing a constraint that all agents face, a high price of good x has in the preceding example a positive “external”e¤ect similar to, e.g., a clean environment or a good public highway system. Agents’inability to coordinate on a su¢ ciently high price for good x in equilibrium is therefore similar to the failure to internalize an external e¤ect, which has led to the name pecuniary externality. In this article, we discuss the pecuniary externality that leads to underprovision of liquidity in the banking model of Diamond and Dybvig (1983) (hereafter, DD). We introduce the DD economy in Section 1. In this economy, agents have access to two assets: a short-term, liquid asset with net return normalized to zero and a long-term, illiquid ^ asset with positive net return R 1 > 0. Agents face random liquidity shocks: They may become impatient, i.e., …nd themselves having to consume before the illiquid asset matures, or remain patient, in which case they can postpone consumption until the illiquid asset pays o¤. By investing a part of their initial endowment/wealth in the low-yielding liquid asset, agents purchase insurance against the liquidity shock. In Section 2, we derive the e¢ cient allocation of liquidity in this economy, i.e., the optimal levels of investment in the two assets along with the resulting amounts of consumption for the agents who do and B. Grochulski: Pecuniary Externalities and Segregated Exchanges 307 do not experience the need for liquidity. At the optimum, the liquidity shock is partially insured: The impatient agents are able to capture a part of the return on the long-term asset despite the fact that they have to consume before this asset matures. There are several variants of the DD model in the literature. The variant we consider follows closely Jacklin (1987) and Farhi, Golosov, and Tsyvinski (2009). It has been designed to focus on market provision of liquidity and not on the possibility of bank runs.3 In particular, we assume that liquidity shocks are agents’ private information, but we do not assume a sequential service constraint: Trade can be organized after all agents have received their realizations of the liquidity shock. To study pecuniary externalities, we follow Farhi, Golosov, and Tsyvinski (2009) in giving the agents access to an anonymous, hidden market in which they can borrow and lend at the market-determined gross rate of return R. As this rate of return (the price of credit) a¤ects incentive compatibility constraints, it gives rise to a pecuniary externality. This pecuniary externality makes competitive equilibria ine¢ cient. To show this ine¢ ciency, we analyze in Section 3 a simple model of trade with incomplete markets. In this model, agents invest directly in the two assets ex ante and trade the long-term asset for cash ex post, i.e., after they …nd out their liquidity needs. Diamond and Dybvig (1983) showed that competitive equilibrium in this simple, incompletemarkets model is ine¢ cient. In this model, a no-arbitrage condition determines how the return on the long-term asset is allocated in equi^ librium: The whole net return R 1 is captured by the patient agents, leaving the impatient agents with zero net return on their investment, which is too low relative to the optimal allocation. In this incompletemarkets equilibrium, thus, agents do not obtain su¢ cient liquidity insurance. This ine¢ ciency prevails even when markets for state-contingent contracts are introduced. Jacklin (1987) and Farhi, Golosov, and Tsyvinski (2009) show that when agents can borrow and lend privately in a hidden retrade market, liquidity is underprovided in competitive equilibrium with complete markets and fully state-contingent contracts (or banks). The ine¢ ciency is caused by a pecuniary externality that, as we mentioned, enters the model through the agents’incentive compatibility constraints that depend on the retrade interest rate R. In equilibrium, this interest rate is too high, which, by arbitrage, forces the secondary-market price for the long-term asset to be too low. The impatient agents, thus, re-sell their holdings of the long-term asset 3 See Ennis and Keister (2010) for a review of the literature on bank runs in the DD model. 308 Federal Reserve Bank of Richmond Economic Quarterly in the secondary market for too little. As in the incomplete-markets model, they are unable to capture any part of the long-run net return ^ R 1, which again is ine¢ cient. We review this result in detail in Section 4. As is the case with standard externalities like pollution, the market failure caused by the pecuniary externality creates a role for government intervention. Farhi, Golosov, and Tsyvinski (2009) consider direct government intervention imposing a minimum requirement on the level of liquid investment. They show that this intervention decreases the retrade interest rate R and increases the return on the initial investment in the liquid asset. This allows the impatient agents to capture a part ^ of R and eliminates the e¤ect of the pecuniary externality.4 If the extent of an externality can be costlessly and veri…ably quanti…ed, the problem of excessive externality can also be addressed with a more decentralized approach that can be implemented through the so-called cap-and-trade mechanism. An explicit assignment of property rights over the extent of the externality lets markets for these rights emerge. In these markets, agents face prices for generating the externality, which makes them take into account the full impact of the externality and thus restores the e¢ ciency of the equilibrium outcome.5 Pollution is a textbook example of a negative external e¤ect. Currently, emission of greenhouse gasses is regulated through the cap-and-trade mechanism in many countries.6 In a recent article, Kilenthong and Townsend (2011) (hereafter, KT) study a market solution to the pecuniary externality problem analogous to cap-and-trade.7 In addition to a class of moral hazard environments, they consider a DD economy with retrade.8 In their model, the impact of one’ liquidity demand on the retrade interest s rate is priced, which results in e¢ cient ex ante investment, su¢ cient liquidity, and an optimal amount of retrade in competitive equilibrium. Clearly, this approach is interesting because it implies no need for direct government intervention into markets. Similar to the cap-and-trade 4 In this article, we do not present details of the implementation of this intervention. The interested reader is referred directly to Farhi, Golosov, and Tsyvinski (2009). 5 See Chapter 11 of Mas-Colell, Whinston, and Green (1995). 6 The …rst and to-date largest implementation of this mechanism is the European Union Emission Trading Scheme; see Ellerman and Buchner (2007). 7 Bisin and Gottardi (2006) use a similar approach in the Rothschild-Stiglitz adverse selection economy. 8 Kilenthong and Townsend (2014a) study the model with segregated exchanges in a class of environments with collateral constraints. Kilenthong and Townsend (2014b) extend the analysis of segregated exchanges to a generalized framework nesting collateral and liquidity constraints, incentive constraints with retrade, and exogenously incomplete markets. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 309 mechanism, this approach requires that agents’ activities generating the externality— in this case retrade— be observable. We discuss the KT model in Section 5. In the KT market model, retrade is allowed but only within accesscontrolled ex-post markets called segregated exchanges. Agents are admitted to membership in an exchange upon payment of an entry fee. The size of the entry fee depends on the composition of the agent’ s investment portfolio. The de…ning characteristic of a segregated exchange is the price at which agents expect to be able to (re)trade the long-term asset ex post. In equilibrium, these expectations must be correct. This market structure is free of pecuniary externalities because agents can no longer take retrade prices as independent of their actions. The portfolio-contingent exchange entry fee, similar to the price for greenhouse gas emissions in the cap-and-trade mechanism, creates an explicit connection between the investment decisions an agent makes ex ante and the price at which he is able to trade ex post. Consequently, equilibrium with segregated exchanges does not su¤er from the problem of underprovision of liquidity, and the market outcome is e¢ cient. Our exposition of the KT mechanism in Section 5 extends the exposition in Kilenthong and Townsend (2011). We explicitly solve for equilibrium entry fees associated with each segregated exchange and show how with these prices the agent’ ex ante utility maximization s problem becomes aligned with the planner’ problem of maximization s of ex ante welfare. In Section 6, we conclude the article with a discussion of the question of whether the possibility of retrade in the DD model implies the need for government intervention. The literature we review makes it clear that the answer depends on the agents’ability to commit themselves to restrict retrade to access-controlled venues with priced entry. This means that retrade itself does not imply the existence of a pecuniary externality requiring government intervention, only hidden retrade without commitment does. Which of these two kinds of retrade possibilities …nancial …rms face in reality is an important empirical question. The Appendix contains proofs of two auxiliary results and a precise de…nition of the incomplete-markets equilibrium studied in Section 3. Table 1 summarizes the frictions and outcomes associated with all allocation mechanisms we discuss in this article. 310 1. Federal Reserve Bank of Richmond Economic Quarterly A DIAMOND-DYBVIG ECONOMY WITH RETRADE The version of the Diamond-Dybvig economy that we consider here is close to those studied in Jacklin (1987); Allen and Gale (2004); Farhi, Golosov, and Tsyvinski (2009); and Kilenthong and Townsend (2011). There is a continuum of ex ante identical agents. There are three dates: t = 0; 1; 2. There is a single consumption good at each date. Each agent is endowed with resources e at date 0. These resources can be invested in two available technologies/assets. The short-term asset pays the return of 1 unit of the consumption good at date 1 per unit of resources invested at date 0. We will often refer to this asset as the ^ cash asset. The long-term asset pays nothing at date 1 and R > 1 at date 2 per unit invested at date 0. Note that the long-term asset is technologically illiquid at date 1, i.e., it cannot be physically turned into the consumption good. Agents do not consume at date 0. Their preferences over consumption at dates 1 and 2 are represented by a DD utility function u(c1 + c2 ); where 2 f0; 1g is an idiosyncratic shock with Prf = 0g = > 0. Note that if = 0, the agent is extremely impatient: He only values consumption at date 1. The standard interpretation of this shock is that with = 0 the agent experiences at date 1 a critical need for liquidity. If = 1, however, the agent is extremely patient: He is in fact indi¤erent to the timing of consumption between dates 1 and 2.9 We follow DD in assuming that relative risk aversion is larger than 1, i.e., cu00 (c)=u0 (c) > 1 for all c. As we will see, this assumption implies that the impatient agents will be allocated consumption with present value larger than the value of their initial endowment e. A consumption allocation c consists of fc1 (0); c2 (0); c1 (1); c2 (1)g; where ct ( ) 0 denotes date-t consumption for an agent with shock . Associated with allocation c are initial asset investment s 0 in the liquid asset and x 0 in the illiquid asset. To ensure that resources at date 1 and 2 are su¢ cient to provide consumption as speci…ed in c, initial investment (s; x) associated with allocation c must satisfy s c1 (0) + (1 )c1 (1); (1) 9 Note that with these preferences the DD economy violates standard smoothness and convexity assumptions. In particular, the shadow interest rate (i.e., the rate at which an agent is willing to refrain from borrowing or saving) is plus in…nity for the impatient type and one for the patient type regardless of the allocation of consumption. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 311 and ^ Rx c2 (0) + (1 )c2 (1): (2) The amounts s and x that can be invested in the two technologies are constrained by the amount e of resources available at date 0: s+x e: (3) Substituting (1) and (2) into (3), we can express the economy’ aggres gate resource constraint in terms of just the consumption allocation c: c1 (0) + c2 (0) ^ R + (1 ) c1 (1) + c2 (1) ^ R e: (4) Allocation c gives an agent an expected utility value of E[u(c1 + c2 )] = u(c1 (0)) + (1 )u(c1 (1) + c2 (1)): (5) Since all agents are ex ante identical, the expected utility of the representative agent measures total utility, or social welfare, attained in this economy. We follow DD in assuming that realizations of are private information. That is, given an allocation c = fc1 (0); c2 (0); c1 (1); c2 (1)g; an agent can obtain either fc1 (0); c2 (0)g or fc1 (1); c2 (1)g depending on what realization of he reports. In addition, we follow Farhi, Golosov, and Tsyvinski (2009) and Kilenthong and Townsend (2011) in assuming that individual …nal consumption is also private and that agents have access to a hidden retrade market where they can lend and borrow from one another “behind the back” of the planner, i.e., with all trades in this market being hidden from everyone but the parties directly involved. More precisely, at date 1 agents have access to a perfectly competitive market for one-period IOUs. Given an allocation c = fc1 (0); c2 (0); c1 (1); c2 (1)g, an agent reporting shock realization ~ obtains the bundle (c1 (~); c2 (~)). But this bundle does not have to be his actual consumption. Rather, this bundle becomes his endowment of goods in the hidden retrade market. The agent’ …nal consumption is determined by his retrade activity. s At the hidden-market interest rate R, the agent can either save some of his c1 (~) for consumption at date 2, or borrow against c2 (~) for consumption at date 1. Speci…cally, given an allocation c and a gross interest rate R in the hidden retrade market, an agent of type selects a report ~ 2 f0; 1g, IOU purchases b, and a …nal consumption bundle 312 Federal Reserve Bank of Richmond Economic Quarterly (~1 ; c2 ) c ~ (0; 0) that solve ~ V (c; R; ) = c ~ max u(~1 + c2 ) ~;~1 ;~2 ;b c c s:t: c1 + b c1 (~); ~ c2 Rb + c2 (~): ~ (6) ~ The value V (c; R; ), thus, is determined by the agent’ best strategy s with respect to reporting his realization of the shock as well as saving/borrowing in the hidden market. Allocation c is incentive compatible (IC) if agents prefer to reveal their type truthfully and not use the retrade market. That is, c is IC if it satis…es ~ u(c1 ( ) + c2 ( )) V (c; R; ) (7) for both , with R being an equilibrium gross interest rate in the hidden retrade market. 2. OPTIMAL ALLOCATION In this section, we …rst provide a result of DD characterizing the best allocation with no frictions (i.e., without private information or hidden retrade), which is often referred to as the …rst-best allocation. This allocation provides the highest social welfare among all allocations that are resource feasible, i.e., it maximizes (5) subject to (4). Next, we present a result of Farhi, Golosov, and Tsyvinski (2009) showing that the …rstbest allocation remains feasible even with the frictions of private and hidden retrade. The …rst-best allocation thus remains optimal in this environment, even with these two frictions present. Optimal Allocation with no Frictions Let us start out by noting that given the in…nite impatience of the agents of type = 0, it is never e¢ cient in this economy to have the impatient types consume a positive amount at date 2. Likewise, given ^ the complete patience of type = 1 and R > 1, it is never e¢ cient to have the patient types consume a positive amount at date 1. Lemma 1 If c = fc1 (0); c2 (0); c1 (1); c2 (1)g maximizes (5) subject to (4), then c2 (0) = c1 (1) = 0. Proof. In the Appendix. Below, we will often write c1 for c1 (0) and c2 for c2 (1), silently assuming c2 (0) = c1 (1) = 0, and refer to (c1 ; c2 ) as an allocation. With B. Grochulski: Pecuniary Externalities and Segregated Exchanges 313 these notational shortcuts, the social welfare function (5) can be written simply as u(c1 ) + (1 )u(c2 ); the aggregate resource constraint (4) as c2 c1 + (1 ) ^ R (8) e; (9) and …rst-best allocation can be de…ned as a maximizer of (8) subject to just (3), i.e., ignoring the incentive constraint (7). Further, from (1) ^ and (2) we have c1 = s and c2 = 1 x R. If no initial wealth is to be wasted, we must have x = e s. We can thus express any resourcefeasible allocation (c1 ; c2 ) as a function of the initial liquid investment s alone: s e ; 1 (c1 ; c2 ) = s ^ R with s 2 [0; e]. The social welfare function (8) can thus be written as u s + (1 )u e 1 s ^ R : (10) Denote this function by W (s). The …rst-best planning problem is reduced here to …nding a level of liquid investment s in [0; e] that maximizes W (s). Denote such a level by s . The corresponding level of illiquid investment is x = e s and the …rst-best optimal allocation ^ is (c1 ; c2 ) = s ; e s R . 1 Proposition 1 (Diamond and Dybvig) The social welfare function W (s) has a unique maximizer s in [0; e]. The maximizer satis…es ^ R e<s < ^ R+1 e: (11) Proof. In the Appendix. The two inequalities in (11) imply that the …rst-best consumption allocation (c1 ; c2 ) satis…es e < c1 < ^ Re > c2 > ^ Re ^ R+1 ^ Re ; (12) : (13) ^ R+1 The right inequalities above show that the …rst-best allocation does ^ not provide full insurance, c1 < ^ Re < c2 . The reason for this is R+1 314 Federal Reserve Bank of Richmond Economic Quarterly that …rst-period consumption is more expensive to provide than secondperiod consumption. At the full-insurance allocation c1 = c2 = ^ Re ^ R+1 ; (14) marginal utility of consumption is the same at both dates, but by giving ^ up " > 0 units of consumption at date 1 the planner can deliver R" > " units of consumption at date 2. Such a reallocation would therefore increase overall expected welfare, and so full insurance is not optimal. The left inequality in (11) implies that the …rst-best allocation gives a larger present value of consumption to impatient agents than to patient ones. Indeed, discounting consumption at date 1 and 2 at, respectively, the rate of return of the short- and long-term asset, and using the left inequalities in (12) and (13), shows c1 c > e > 2: ^ 1 R (15) The optimality of this unequal allocation of the present value of consumption follows because relative risk aversion of the utility function u(c) larger than 1 means that as consumption c increases, marginal utility of consumption u0 (c) drops fast (faster than 1=c). Liquid in^ vestment s = e gives a …nal consumption allocation (c1 ; c2 ) = (e; Re), where the present value of both types’consumption is the same (and equal to the per capita initial endowment): c2 c1 =e= : ^ 1 R (16) ^ At this allocation, however, c2 = Re > e = c1 , so the marginal utility of c2 is low and the marginal utility of c1 is high. By increasing the liquid investment s at date 0 above s = e, say by " > 0, the planner gives up ^ the return R" but is able to increase consumption in the high marginal utility state, i.e., at date 1. On balance, this is an improvement because ^ u0 (c1 ) is su¢ ciently high relative to u0 (c2 ) and R [that is, "u0 (e) > 0 (Re)]. ^ R"u ^ Alternatively, we can express this intuition using the elasticity of substitution of the utility function u. With zero elasticity of substitution (Leontief preferences), the full insurance allocation (14) would be optimal. With unit elasticity of substitution (logarithmic preferences), the allocation (16) spending the same amount on each good would be optimal. Under the DD assumption of the elasticity of substitution larger than zero but smaller than one, it is optimal to make c1 and c2 closer to one another than under logarithmic preferences, but not go all the way to full insurance. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 315 Optimal Allocation with Private Shocks and Retrade Having characterized the optimal allocation in the …rst-best version of the DD environment, we now ask what the optimal allocation is with private information and a hidden retrade market, i.e., with the addition of the IC constraint (7). With realizations of being private information and with agents having access to retrade, Farhi, Golosov, and Tsyvinski (2009) show that the …rst-best allocation is incentive compatible, i.e., remains feasible and thus optimal. This result is obtained as follows. The retrade interest rate R associated with the optimum (i.e., the shadow interest rate at the …rst-best), denoted by R , is R = c2 : c1 (17) First, let us check that with “endowments” (c1 ; c2 ), the interest rate R = R is an equilibrium interest rate in the hidden market. c1 c2 Note that from c2 > c1 we get R > 1 and from 1 > e > ^ we get R ^ ^ R < R, so 1 < R < R. Suppose the impatient types enter the hidden market with an endowment vector (c1 ; 0) and patient types enter with (0; c2 ). The impatient agent has no income at t = 2, so he cannot borrow in this hidden market (for there is nothing he could pay back with). Also, this agent wants to consume his income c1 irrespective of the interest rate. Thus, the impatient type’ utility is maximized s with the quantity of zero traded at the interest rate R . A patient agent could borrow against his date-2 endowment c2 and consume at date 1, but R > 1 implies he would not want to do it, as his marginal utility of consumption is the same at either date and he can consume c only R2 < c2 if he decides to use the hidden market and consume at date 1. This con…rms that consumption (c1 ; c2 ) and interest rate R are an equilibrium in the retrade market (with zero quantity traded in equilibrium). Now consider potential deviations in the revelation of combined with retrade. The …rst-best allocation is immune to these deviations because at the interest rate R the present value of each type’ endows ment is the same. Indeed, the impatient types could claim endowment (0; c2 ) and borrow against c2 in order to consume at date 1, but doing c so would give them R2 = c1 units of consumption, so there is no gain for them from doing so. As well, the patient types could claim endowment (c1 ; 0) and save at the market interest rate R . But doing so gives them …nal consumption R c1 = c2 so, again, no gain. This con…rms 316 Federal Reserve Bank of Richmond Economic Quarterly that the …rst-best allocation is incentive compatible in the model with private information and hidden retrade. Note that although the possibility of hidden retrade does not change the optimal allocation, it does change the IC constraint. With just private information about the liquidity shock (without retrade), the IC constraint would be c2 c1 . The …rst-best allocation satis…es this constraint as a strict inequality simply because c2 > c1 . With the hidden retrade market, however, the IC constraint holds only as an c equality because R2 = c1 . Next, we move on to discuss market provision of liquidity in this environment. 3. COMPETITIVE EQUILIBRIUM WITH INCOMPLETE MARKETS The remainder of this article is devoted to studying competitive equilibrium outcomes under three di¤erent market arrangements, and comparing these outcomes with the optimal allocation (c1 ; c2 ). In this section, we discuss a simple incomplete-markets model of trade, in which agents invest directly in the two assets and subsequently trade them (i.e., there are no intermediaries, no state-contingent contracts). This natural model of trade is a point of departure for Diamond and Dybvig (1983). DD start their analysis of market provision of liquidity by considering this incomplete market structure. They conclude that the equilibrium level of liquidity is too low, i.e., there is a market failure. We brie‡ review this result in this section and move on y to showing in the next section that with hidden retrade this conclusion generalizes to any market structure (even when state-contingent contracts and/or intermediaries are taken into consideration). The simple market structure is as follows. At date 0, each agent invests directly in the two assets subject to s + x e. At date 1, after agents …nd out their type , they trade the long-term asset for cash at a market-determined price p. In addition to the market for the long-term asset, agents have access at date 1 to a market for one-period IOUs.10 A formal statement of the agents’optimization problem and competitive equilibrium in this economy is given in the Appendix. Note that this market structure is incomplete: There are no contracts for provision of consumption conditional on . A simple arbitrage argument shows that in any equilibrium of this trading arrangement the date-1 cash price p of a unit of the long-term 10 As we will see, however, the (hidden) IOU market will not be active here, nor imposing any binding constraints on the equilibrium allocation. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 317 asset must be 1. This argument is as follows. The fact that a market for the long-term asset exists at date 1 makes the long-term asset de facto liquid and thus a perfect substitute, at date 0, for the short-term asset. The return from holding the long-term asset for one period, therefore, must be the same as the return from investing in the short-term asset. The date-1 price of the long-term asset must therefore be p = 1, or else there is an arbitrage. Indeed, if p > 1, all agents want to invest their initial resources in the long-term asset only, as investing a unit of resources in that asset and selling it at date 1 yields p, while investing in the shortterm asset yields 1. In this case, however, nobody has cash at date 1 and thus aggregate demand for the long-term asset is zero. This level of demand is inconsistent with the equilibrium price p being positive. Similarly, if p < 1, all agents want to invest exclusively in the shortterm asset at date 0, as investing a unit of resources in the long-term asset is dominated by investing this unit in the short-term asset and then buying the long-term asset at date 1 at price p < 1. This, however, means that supply of the long-term asset at date 1 is zero while demand is positive, as the patient types are willing to buy at p < 1. Thus, p < 1 cannot be an equilibrium price, either.11 The only price p consistent with equilibrium, therefore, is p = 1. At this price, the return from holding the short- and the long-term asset from date 0 to date 1 is the same, so agents are indi¤erent between investments s and x. At date 1, the impatient agents want to sell their holdings x of the illiquid asset. With p = 1, the patient agents want to hold on to their x and spend their cash s to purchase additional ^ ^ units of the long-term asset, as the return on this investment, R = R, p exceeds their required rate of return, 1. Aggregate supply of the longterm asset to the market at date 1 is therefore x and the supply of cash is (1 )s. The market-clearing condition, thus, is xp = (1 )s; where, by the arbitrage argument given above, p = 1. The date-0 budget constraint implies x=e s: Solving the above two conditions, we obtain s = e; x = (1 11 )e: (18) Strictly speaking, these corner investment strategies are not arbitrages because they are not self-…nancing. But they could be turned into arbitrages if agents could short the expensive asset at date 0. 318 Federal Reserve Bank of Richmond Economic Quarterly This solution is unique, so there exists only one equilibrium. In equilibrium, consumption of the impatient types is c1 = s + px = e + s ^ 1(1 )e = e; while the patient types consume c2 = x + p R = ^ ^ (1 )e + 1e R = eR. Let us denote the unique equilibrium consumption bundle by (^1 ; c2 ). We have just shown that c ^ ^ (^1 ; c2 ) = (e; Re): c ^ (19) In the hidden retrade market, there is no active trade. The equi^ librium retrade interest rate is R = R. At this rate, agents choose not to alter their consumption allocation (^1 ; c2 ) by either borrowing or c ^ lending. The hidden retrade market has no impact on the equilibrium outcome here because the (regular, “non-hidden” date-1 market for ) ^ ^ the long-term asset already o¤ers a riskless return R = R = R. The p hidden IOU retrade market is thus redundant. A key property of the DD environment is that the equilibrium allocation of consumption, (^1 ; c2 ), is ine¢ cient. That is, this allocation c ^ yields lower ex ante welfare than the optimal allocation c . Clearly, ^ ^ the right inequalities in (12) and (13) tell us that c1 > c1 and c2 < c2 . Since, by Proposition 1, the optimum (c1 ; c2 ) is a unique welfare maximizer, equilibrium allocation (^1 ; c2 ) is indeed ine¢ cient. c ^ As we saw in Section 2, optimal allocation calls for a present-value transfer from the patient types to the impatient types. In equilibrium with incomplete markets, however, each agent consumes the worth of his own initial endowment, e, i.e., there are no present value transfers between types, and insurance markets are missing. Moreover, it is easy to see that an intervention by a benevolent planner/government can improve welfare without introducing any new markets. If the planner forces each agent to invest (s; x) = (s ; x ) at date 0 and allows free trade at date 1, the market price for the long-term asset will be p = p , the retrade market rate will be R = R , and the equilibrium consumption allocation will be (c1 ; c2 ).12 In sum, the equilibrium investment in the liquid asset is too low relative to the optimum, s = e < s , i.e., free trade leads to underprovision of liquidity. 12 In the language of the incomplete-markets literature, equilibrium (^1 ; c2 ) is c ^ constrained-ine¢ cient. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 319 4. COMPETITIVE EQUILIBRIUM WITH CONTINGENT CONTRACTS In this section, we allow for state-contingent contracts. We review the following important result. Jacklin (1987) points out that when retrade is allowed, an arbitrage argument similar to the one used in the previous section implies that markets will underprovide liquidity, even when fully state-contingent contracts are allowed. With retrade, thus, the market failure shown in the previous section for the simple incomplete-markets model continues to hold for all feasible models of trade in the DD environment, including the intermediation economy of Diamond and Dybvig (1983). Consider the following general model of trade with fully statecontingent contracts, direct investment, and retrade.13 In addition to directly investing in the two assets, agents can contract with intermediaries and access the hidden IOU market. Intermediaries, or banks, make available to agents at date 0 a state-contingent contract ( 1 ; 2 ). Under this contract, which can be thought of as a deposit contract, the agent can obtain from the intermediary, at the agent’ discretion, s either 1 at date 1 or 2 at date 2 (but not both). Let us normalize the price of this contract to e, i.e., an agent who accepts a contract deposits his whole initial wealth with a bank. Also, as before, agents can borrow from and lend to each other privately in the hidden retrade market at date 1. Under this market structure, an agent has the following choices to make. At date 0, he decides whether to deposit his wealth e with a bank or to invest directly in assets s and x. If he deposits, after he learns his type , he chooses whether to withdraw at date 1 or 2, and how much, if at all, to borrow or lend in the hidden retrade market at the market rate R. If the agent chooses not to deposit at date 0 but rather to invest directly, he selects a portfolio (s; x). At date 1, after he learns his type and his cash investment s matures, the agent decides how much to borrow or lend in the retrade market at the market rate R. Competition among banks (existing or potential entrants) drives banks’ pro…ts to zero and forces each active bank to o¤er the same contract (namely, the contract that maximizes the ex ante expected utility of the representative agent, for otherwise agents would deposit with a di¤erent bank). Since intermediation is an activity with constant returns to scale in this model, it is without loss of generality to assume 13 For a formal statement a version of this economy see Section 3.1 of Farhi, Golosov, and Tsyvinski (2009) or Allen and Gale (2004). 320 Federal Reserve Bank of Richmond Economic Quarterly that a single large bank operates in equilibrium (the market, however, is perfectly contestable). The bank’ contract design problem is similar to the social planning s problem in that in both cases the objective is to maximize the agent’ s expected utility. There is, however, a key di¤erence. The planner can control date-0 investment, which enables her to have an (indirect) impact on the retrade market interest rate R. The bank cannot force the agents to deposit, which means it must act competitively, i.e., take prices as given. In particular, the bank takes as given the retrade market interest rate R. Given this di¤erence, it is not hard to see that the optimal allocation (c1 ; c2 ) cannot be an equilibrium allocation. If (c1 ; c2 ) were to be an equilibrium allocation, the interest rate R in the hidden retrade market would have to be equal to the shadow rate R given in (17), for otherwise agents would use that market to trade away from this allocation. But R cannot be an equilibrium retrade interest rate be^ cause the fact that R is strictly smaller than R creates an arbitrage opportunity. This arbitrage opportunity is similar to the one that in the incomplete-markets model discussed in the previous section pinned down the secondary-market asset price p at 1. The arbitrage strategy, described in Jacklin (1987), calls for investment x = e at date 0. If the agent executing this arbitrage is patient, ^ i.e., his = 1, he consumes nothing at date 1 and Re > c2 at date 2. If he turns out impatient, i.e., his = 0, he can access the retrade market ^ Re and borrow at rate R , which gives him date-1 consumption R > c1 . In either case, thus, he consumes more than (c1 ; c2 ), which shows that (c1 ; c2 ), with its shadow interest rate R , cannot be an equilibrium allocation of consumption. What allocation can be a market equilibrium allocation in this model? The Jacklin arbitrage strategy pins down the interest rate ^ in the retrade market at R = R. With this interest rate, it is easy to check (or consult Allen and Gale  or Farhi, Golosov, and Tsyvinski ) that the equilibrium allocation (19) from the incomplete-markets model discussed in the previous section is a unique equilibrium allocation, also here in the richer model with fully statecontingent contracts.14 Why is the planner able to do better than the market in this model? The planner makes the Jacklin arbitrage strategy infeasible for the 14 This conclusion applies to all conceivable market structures in which the Jacklin arbitrage strategy remains feasible. In particular, when the hidden retrade market is included, it applies to the general competitive private information model of Prescott and Townsend (1984) in which agents trade lotteries over allocations subject to incentive compatibility constraints. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 321 agent by controlling initial investment (s; x). In the planning problem, although the agent has unfettered access to the retrade market, the agent does not have private control over his initial investment. The initial investment choice is publicly observable and therefore can be controlled by the planner/government. The Jacklin arbitrage strategy calls for the all-long investment (s; x) = (0; e) at date 0. By forcing/choosing investment (s; x) = (s ; e s ), the planner eliminates this arbitrage. Moreover, this choice of date-0 investment pins down the amount of resources available at dates 1 and 2 and, thus, also the interest rate in the hidden retrade market, which with liquid investment s is R = R . In a competitive market economy, by contrast, …rms have to respect the agents’freedom to not contract with them but instead to invest directly (or set up another …rm that will do the investing for them, as in Farhi, Golosov, and Tsyvinski ). Intermediaries thus cannot make the Jacklin arbitrage strategy infeasible for the agents. Having to respect this arbitrage condition, the best allocation they can ^ provide is (^1 ; c2 ) = (e; Re) with the associated retrade market interest c ^ ^ rate R = R. To recap, the planner internalizes the fact that her control of the initial investment changes the price in the equilibrium of the retrade market. Firms, in contrast, take all prices as given, including those in the retrade market. The discrepancy constitutes a pecuniary externality in this model and the equilibrium allocation is ine¢ cient. E ciency Without Retrade The Jacklin arbitrage strategy is clearly impossible to execute if arbitrageurs do not have access to the hidden retrade market. Absent retrade, competitive equilibrium with state-contingent contracts would be e¢ cient. Indeed, if the retrade market is shut down, the value func~ ~ tion V (c; R; ) de…ned in (6) reduces to V (c; R; ) = max~ u(c1 (~) + ~)), which no longer depends on R. The incentive constraint (7), c2 ( therefore, no longer depends on a price.15 This means that there is no pecuniary externality. The welfare theorems of Prescott and Townsend (1984) apply, and competitive equilibrium is e¢ cient. In particular, it can be implemented as a banking equilibrium of Diamond and Dybvig (1983) with the equilibrium deposit contract ( 1 ; 2 ) = (c1 ; c2 ). The theoretical results we reviewed in this section suggest that retrade generates a pecuniary externality and leads to equilibrium 15 In particular, given Lemma 1, the impatient types will never misrepresent their type and the patient types’ incentive constraint reduces to c2 c1 . 322 Federal Reserve Bank of Richmond Economic Quarterly underprovision of liquidity. In practice, banks and other …nancial intermediaries have ample access to various retrade markets. Therefore, one might be tempted to take as an implication of this theory the prediction that markets will fail to provide su¢ cient liquidity. In the next section, we present a simple version of the analysis of Kilenthong and Townsend (2011) showing that this conclusion would be premature: If harnessed inside appropriate venues, retrade can be consistent with e¢ cient functioning of markets in the provision of liquidity. 5. COMPETITIVE EQUILIBRIUM WITH SEGREGATED EXCHANGES In this section, we consider the model of Kilenthong and Townsend (2011), in which a market-maker eliminates the Jacklin arbitrage by segmenting the retrade market and pricing entry into market segments as a function of the investment portfolio held by agents entering a given segment. With the Jacklin arbitrage eliminated, the pecuniary externality causing market failure is eliminated as well. The resulting equilibrium is e¢ cient. We supplement the analysis of Kilenthong and Townsend (2011) by characterizing explicitly how the equilibrium exchange entry fees depend on the fundamentals of the exchange and on the portfolio of the agent (equation  and Figure 2). We conclude with a discussion of an important di¤erence between the environment with pecuniary externality studied in the previous sections and the environment without it that we study here. The segregated-exchanges equilibrium is e¢ cient, but, e¤ectively, it requires that agents commit ex ante to not using the hidden retrade market ex post. Whether or not retrade leads to a pecuniary externality and ine¢ ciency of market outcomes, therefore, depends on the practical feasibility of such a commitment. Trade Inside Segregated Exchanges at Date 1 Before we de…ne the general equilibrium concept with segregated exchanges proposed by KT, we describe in this subsection segregated exchanges, their fundamentals, and internal prices. A segregated exchange is a competitive market for the long-term asset that opens at date 1 after types are realized. A de…ning characteristic of such an exchange is a set of fundamentals determining the market price p at which the long-term assets will be traded. The fundamentals and the price must be consistent: Given the fundamentals in an exchange, the price p must indeed be a competitive equilibrium price in that exchange. In the DD economy at hand, the level of the B. Grochulski: Pecuniary Externalities and Segregated Exchanges 323 cash asset investment s held by each member of an exchange is a suf…cient description of the fundamentals in the exchange. Thus, we will index exchanges by S 2 [0; e], where S represents the level of liquid investment held by each agent entering the exchange. Note that this de…nition assumes identical asset holdings by all exchange members. We will see later that this assumption is without loss of generality in the present environment. Equilibrium price in exchange S Let us derive an equilibrium consistency condition between fundamentals S and price p in the exchange S 2 [0; e]. It is a simple equilibrium pricing condition in a competitive market with all agents holding the same portfolio of assets (s; x) = (S; e S) and experiencing shocks drawn from the same distribution. We will denote the equilibrium price in exchange S by p(S). The equilibrium condition for consistency between S and p is (1 (e p(S) = min )S ^ ;R : S) (20) This condition is derived as follows. The equilibrium price of the illiquid asset is determined by supply and demand in exchange S in the same way as it was determined in the incomplete-markets model of Section 3. At date 1, the impatient agents want to sell their long-term asset in the market at any price. They supply (e S) units of the long-term asset to the market. The behavior of the patient agents depends on the price ^ p. If p > R, a short position in the asset gives them a positive return, so patient agents want to sell their holdings of the asset, just like the impatient ones. This cannot be an equilibrium, as demand for the asset ^ is zero and supply is positive. Thus, in any equilibrium, p R. With ^ a long position in the asset gives patient agents a non-negative p R, ^ return (strictly positive if p < R). With any such price, the patient agents are willing to buy the long-term asset. They demand (1 )S p S units. Thus, the equilibrium price p(S) solves (e S) = (1 ) p(S) , which gives us (1 (e )S ; S) (21) ^ ^ R. Solving R = (1 )S (e S) for S, we get a threshold p(S) = provided that p(S) S= ^ Re ^ R+1 : (22) 324 Federal Reserve Bank of Richmond Economic Quarterly Figure 1 Equilibrium Asset Price p in Exchange S ^ For all S S, the equilibrium price is ‡ at R.16 Combining this at restriction with (21) gives us the consistency condition (20). Figure 1 illustrates the derivation of the consistency condition (20) graphically. When S is small and e S is large, there is a large quantity of the illiquid asset in the market, supplied by the impatient agents, and very few units of the consumption good (cash), supplied by the patient agents, and so the price of the asset is low.17 In exchanges with higher S, the proportion of cash to units of the asset in the market is higher, so the price p(S) is higher. This is true up to the threshold S. ^ In exchanges with S larger than S, the price p(S) remains ‡ at R and at the patient types are indi¤erent between buying and selling the asset. ^ ^ The price of the asset cannot exceed R, as at a price higher than R the patient agents would switch from buying to selling the asset. As we see, the range of prices that can be consistent with some fundamentals S 2 (0; e] is 0<p ^ R: (23) 16 Note that S is the same threshold that in Proposition 1 results with the fullinsurance allocation (an upper bound on s ). 17 We will exclude the exchange S = 0 from our analysis. In this exchange, the supply of resources at date 1 would be zero and thus welfare of the impatient agents would be extremely low. No agent would want to enter this exchange at date 0. B. Grochulski: Pecuniary Externalities and Segregated Exchanges 325 Markets at Date 0 and Equilibrium De nition In this subsection, we use the segregated exchanges to de…ne the KT notion of competitive equilibrium with segregated retrade. At date 0, agents choose their investments s and x and join segregated exchanges. Each agent can physically join one exchange. Exchanges are de…ned by their fundamental level of liquid investment S. Associated with each exchange is an entry fee pricing any deviations of the investment portfolio of an agent wishing to join a given exchange from that exchange’ fundamentals. If an agent joins an exchange S s with liquid investment s, the amount of shortage of his liquid asset relative to the exchange fundamentals is S s. Upon entry, the agent is charged a fee proportional to the amount of shortage of liquid investment in his portfolio. The price per unit of shortage in exchange S is (S). Thus, an agent entering exchange S with liquid investment s is charged an entry fee of (S)(S s). This charge is assessed by the exchange as of the time of entry, i.e., at date 0. The unit price (S) can be positive or negative. Note that if (S) > 0 and an agent joins exchange S with liquid investment s > S, the entry fee is negative, so the exchange makes a payment to the agent. In sum, at date 0 agents choose investment portfolios (s; x) and exchange membership S subject to the budget constraint s + x + (S)(S s) e: (24) If, for example, an agent decides to join exchange S and go all-long, i.e., invest s = 0 and x = e, then the price for this shortage would be (S)S. Clearly, public observability of the agent’ portfolio is important for the s assessment of fees. In particular, agents cannot avoid fees by “window dressing” or changing the composition of their portfolio after the fees are assessed but before the shock is realized and exchanges open for business. What if an agent chooses not to join an exchange? The decision not to join is equivalent to joining an exchange in which the price of any “deviation”or “shortage”relative to the “fundamentals”is zero. Thus, not joining a segregated exchange is equivalent to maintaining access to the free exchange in which = 0. As we will see shortly, the exchange S = e will have = 0. This exchange corresponds to the incompletemarkets model of Section 3, where, as we saw earlier, all agents choose investment s = e at date 0. It is natural to default all agents who do not join a di¤erent exchange into this one. The model with segregated exchanges, therefore, nests the simple incomplete-markets model as a special case in which there is only one secondary market for the longterm asset, and access to this market is free. 326 Federal Reserve Bank of Richmond Economic Quarterly Let us now discuss the agents’ objective function as of date 0. Agents maximize E[V1 (s; x; S; )]; (25) where V1 (s; x; S; ) is the indirect utility function as of date 1, i.e., the value the agent can get in exchange S with an asset portfolio (s; x) and a liquidity shock realization . The indirect utility function V (s; x; S; ) = max u(c1 + c2 ); s:t: c1 + p(S)n s; n x; ^ c2 (x + n)R; (26) where n is the agent’ net demand at date 1 in the market for the s illiquid asset inside exchange S. Next, we de…ne competitive equilibrium with segregated exchanges. De…nition 1 (Kilenthong and Townsend) A price system (p( ); ( )), ex ante investment and exchange membership choices s, x, S, value functions V1 ( ; ; ; ) for 2 f0; 1g, and a consumption allocation (c1 ; c2 ) are an equilibrium with segregated exchanges if 1. expectations are correct: For each S, price p(S) satis…es the consistency condition (20) and value functions V1 ( ; ; ; ) solve (26); 2. agents optimize ex ante: Taking prices ( ( ); p( )) and value functions V1 ( ; ; ; ) as given, agents’choices s, x, S maximize their ex ante utility (25) subject to the budget constraint (24); 3. market clearing: Consumption allocation (c1 ; c2 ) is an equilibrium allocation of consumption in the exchange S. Note that this de…nition does not allow for mixed strategies. In general, mixed strategies may be useful, as agents face a discrete choice of exchange membership. As the theorem presented next makes clear, in the environment at hand it is without loss of generality to restrict attention to equilibria in pure strategies, where all agents, being ex ante identical, join the same exchange.18 18 In excluding random exchange assignments, this de…nition follows De…nition 4 in Kilenthong and Townsend (2014a). B. Grochulski: Pecuniary Externalities and Segregated Exchanges 327 E cient Equilibrium with Segregated Exchanges Theorem 1 Prices p(S) as in (20) and (S) = min 1 1 e S ^ R 1 ;1 1 ; (27) ex ante investment and membership choices s = s , x = e s , S = s , and consumption allocation (c1 ; c2 ) = (c1 ; c2 ) are a competitive equilibrium with segregated exchanges. The rest of this subsection is devoted to proving this theorem. We need to check the three equilibrium conditions in De…nition 1. We start by characterizing value functions (26). For = 0, the optimized value of (26) is V1 (s; x; S; 0) = u (s + p(S)x) : (28) Clearly, the impatient agents want to sell their holdings x of the longterm asset at any price p(S) and consume all their wealth at date 1, as they have no use for consumption at date 2. At price p(S), an impatient agent can a¤ord consumption c1 = s + p(S)x, which gives us (28). The patient type’ value as of date 1 is s V1 (s; x; S; 1) = u x+ s p(S) ^ R : (29) To see that this is the case, note that in each exchange S patient agents are happy to buy the long-term asset at date 1 because, by (23), ^ p(S) R in all exchanges S. This means that the rate of return on ^ R this investment, p(S) , exceeds the patient type’ rate of time preference, s s which is 1. A patient agent’ demand for the long-term asset is n = p(S) , s his consumption at date 1 is c1 = 0, and consumption at date 2 is s ^ c2 = (x + p(S) )R. These quantities substituted to (26) with = 1 give us (29). We can now con…rm that with value functions (28) and (29) the …rst equilibrium condition (correct expectations) is satis…ed, as these value functions and prices p(S) de…ned in (20) are consistent with agents’ optimization at date 1. Note that the general pattern of behavior at date 1 is the same in all exchanges. The impatient types sell and the patient types buy the long-term asset. The exchanges are di¤erent only in the composition of demand and supply, which gives rise to di¤erent equilibrium prices at which the asset is traded in each exchange. In order to check the second equilibrium condition (agents’ optimization ex ante), we now study the agents’ behavior at date 0. Substituting the indirect utility functions (28) and (29) into the objective (25), we express the ex ante expected utility function of the 328 Federal Reserve Bank of Richmond Economic Quarterly Figure 2 Unit Liquidity Shortage Price in Exchange S representative agent as u (s + p(S)x) + (1 )u x+ s p(S) ^ R : This expression gives the agent’ expected value of being in exchange s S with assets s and x. The representative agent chooses investment portfolio (s; x) and exchange membership S to maximize this value subject to the date-0 budget constraint (24). The structure of the portfolio fees (S) charged upon exchange entry is a key part of the budget constraint. Figure 2 graphs against S the unit liquid asset shortage price (S) given in (27). As we argue, these prices support the e¢ cient equilibrium. e ^ It is easy to check directly in (27) that 1 1 <1 R 1 1 S for all S < S, where S is, as before, given in (22). Thus, (S) = 1 1 1 e S 1 ^ R 1 for S for S S; S: Note that (S) is increasing. This means that the portfolio charge per unit of liquidity shortage is higher in exchanges with higher fundamental liquidity S. Substituting in (27) S = e < S, we check that ( e) = 0. Thus, the exchange with S = e is a (unique) free-entry exchange, where portfolio charges are zero for all portfolios (s; x). In exchanges with S > e, (S) > 0, i.e., agents are subject to a positive charge for shortage of liquidity in their portfolio. For all S < e, B. Grochulski: Pecuniary Externalities and Segregated Exchanges 329 (S) < 0, i.e., portfolio charges are positive if the long-term investment x is less than e S. We now can study the agents’ date-0 problem of choice of investment (s; x) and exchange membership S. For each exchange S, we need to determine the investment portfolio (s; x) the agent will choose conditional on joining S and the consumption pair (c1 ; c2 ) he will be able to a¤ord inside S. This will give us the ex ante expected value of joining S, which we will then use to determine the agent’ most s preferred exchange membership decision and thus the solution to his utility maximization problem. We start by examining the exchanges with S S. What ex ante value can the representative agent obtain if he plans on joining one of these exchanges? All exchanges S S have the same entry fees and long-term asset prices: ^ (S) = 1 R ^ p(S) = R: 1 ; (30) Given a portfolio (s; x), an agent in exchange S consumption S can a¤ord ^ c1 = s + Rx if impatient, or c2 = x+ s ^ R ^ ^ R = s + Rx if patient. As we see, the agent is fully insured against the liquidity shock in any exchange S S, as his optimal consumption in any such exchange is independent of the realization of the liquidity shock . His ex ante expected utility is therefore simply ^ u s + Rx : (31) ^ With the entry fee of (S) = 1 R 1 per unit of liquidity shortage, the agent’ ex ante budget constraint (24) can be written as s ^ s + Rx ^ Re ^ (R 1)S: (32) Comparing the agent’ objective (31) and his budget constraint (32), s we see that the agent is indi¤erent between all portfolios (s; x) on the ^ ^ ^ budget line s + Rx = Re (R 1)S. This is because any such portfolio ^ ^ gives the agent the same ex ante utility of u Re (R 1)S . Since ^ R > 1, this value is decreasing in S. Thus, among all exchanges S S, exchange S is the best one for the agent. 330 Federal Reserve Bank of Richmond Economic Quarterly Next, let us consider the choices of an agent who plans on joining one of the exchanges with S S. The prices this agent faces are (S) = 1 p(S) = e S 1 (1 (e 1 ; )S : S) (33) Thus, given a portfolio (s; x), in exchange S the agent can a¤ord consumption c1 = s + if impatient, or 0 c2 = @x + s (1 )S (e S) 1 ^ AR = (1 (e s+ )S x S) (1 (e )S x S) (e (1 S) ^ R )S if patient. Unlike in the previous case, these consumptions are not )S identical. They are, however, directly proportional to s + (1 S) x. (e Substituting these consumption values into the ex ante expected utility function, we have S) ^ R : )S (34) With the entry fee (S) given in (33), the agent’ ex ante budget cons straint (24) can be rewritten, after some algebra, as u s+ (1 (e )S x + (1 S) )u s+ (1 (e s+ (1 (e S )S x S) )S x S) (e (1 : Comparing this budget constraint and the agent’ objective (34) we s see that here, as in the previous case, the agent is indi¤erent between )S all portfolios (s; x) on the budget line s + (1 S) x = S as any such (e portfolio gives him the same expected utility value of u S + (1 )u e 1 S^ R : Finally, we observe that this objective function, representing the agent’ s utility from joining exchange S, is mathematically the same as the objective function (10) in the social welfare maximization problem studied in Proposition 1. As we saw there, this objective is maximized by a unique s < S. Thus, exchange S = s is a unique maximizer in the B. Grochulski: Pecuniary Externalities and Segregated Exchanges 331 agent’ utility maximization problem we study here.19 To simplify the s notation, we will use S to denote the exchange S = s . The last equilibrium condition that we need to check is to con…rm that (c1 ; c2 ) is an equilibrium allocation of consumption in exchange S with the asset price p(S ). For the pair (c1 ; c2 ) to be resource-feasible in exchange S , agents must enter this exchange carrying the investment portfolio (s ; e s ). Portfolio (s ; e s ) is (weakly) optimal for an agent joining exchange S because, as we saw earlier, conditional on joining an exchange, agents are indi¤erent among all portfolios (s; x) on the budget line. Finally, since the asset price p(S ) satis…es the consistency condition (20), the market for the long-term asset inside the exchange S does clear. We conclude that the prices and quantities speci…ed in Theorem 1 are indeed a competitive equilibrium with segregated exchanges. This equilibrium is e¢ cient, as the equilibrium consumption bundle is exactly the optimal consumption bundle (c1 ; c2 ). Discussion In the two equilibrium concepts without segregated exchanges that we discussed in Sections 3 and 4, arbitrage pinned at p = 1 the equilibrium price in the secondary market for the long-term asset or, equivalently, ^ the retrade market interest rate at R = R. In the model with segregated exchanges, agents trade the long-term asset in the secondary market inside the exchange S at the equilibrium price ^ (1 ) c1 R (1 )s ^c =R 1 = = > 1: p(S ) = c (e s ) c2 R (1 ) 2 ^ R Why does arbitrage not force p(S ) down to 1 in the segregated exchanges model? The Jacklin arbitrage strategy is infeasible in the segregated exchange model because of the entry fees ex ante and the separation of agents in di¤erent exchanges ex post. The Jacklin arbitrage strategy calls for the all-long initial investment (s; x) = (0; e) and a subsequent sale of the long-term asset, or borrowing against it, in case the agent attempting arbitrage turns out needing funds at date 1. But which exchange should the arbitrageur join at date 0? If he defaults to the entry-fee-free market S = e, he does not receive the favorable asset price p(S ) > 1 but only the arbitrage-free price p( e) = 1, so no arbitrage pro…t can be made in this exchange. If the arbitrageur joins 19 Note in particular that the right inequality in (11) implies that exchange S = s dominates the exchange S = S and thus also all exchanges S S. 332 Federal Reserve Bank of Richmond Economic Quarterly exchange S , he must pay the entry fee of (S )S . This fee o¤sets exactly the pro…t he makes selling the long-term asset at the high price p(S ); thus eliminating the overall pro…tability of this attempt at arbitrage. The entry fee o¤sets exactly the asset sale pro…t because, conditional on joining an exchange, agents are indi¤erent between all feasible portfolio choices. In particular, the arbitrageur joining exchange S with the all-long portfolio (0; e) does no better than an agent entering this exchange with the equilibrium portfolio (s ; e s ). Similarly, if the arbitrageur with portfolio (0; e) joins any other exchange S, he is exactly as well o¤ as an agent joining S with the fundamentals-consistent portfolio (S; e S). Thus, the arbitrageur joining S obtains the ex ante expected utility value of W (S). As we saw in Proposition 1, this value is maximized at S = S . No arbitrage attempt therefore can be successful. The agents’ ability to commit to not trading across exchanges ex post is key in eliminating the Jacklin arbitrage. The segregated exchanges mechanism lets each agent join only one exchange. In addition, it requires that agents sign o¤ their right to trade freely with the counterparty of their choice. Instead, it requires that agents commit to trading only with other members of the exchange they belong to. If agents do not have the ability to contractually give away their freedom to trade without counterparty restrictions, an impatient arbitrageur residing in the entry-fee-free exchange S = e can easily convince a patient agent in exchange S to buy the long-term asset from him rather than in exchange S because he can sell for less than p(S ) and still make a pro…t. As agents anticipate this at date 0, price expectations embedded in p(S) are not credible and the equilibrium breaks down. Thus, the restriction of participation to one exchange only and the assumption of the agents’ ability to commit to not step out of their exchanges ex post are crucial. In the KT equilibrium, segregated exchanges can therefore be thought of as a commitment device allowing the agents to promise credibly to not access the hidden IOU market. Clearly, if in the KT model agents could access the hidden IOU retrade market after they trade in segregated exchanges, the equilibrium with segregated exchanges supporting the optimal asset price p(S ) would collapse. The argument for it is the same as in Section 4. The optimal allocation (c1 ; c2 ) is consistent with free access to the retrade market only if the interest rate in this market equals R = c2 =c1 . But with this interest rate, the Jacklin arbitrage can again be executed by investing all long, joining the entry-fee-free exchange S = e, and not trading in this exchange B. Grochulski: Pecuniary Externalities and Segregated Exchanges 333 but rather borrowing in the IOU market if liquidity is needed at date 1.20 In the banking model discussed in Section 4, the intermediary designing the state-contingent deposit contract cannot put any restrictions on retrade between depositors and non-depositors. The marketmaking …rm in the segregated exchanges model, in contrast, can. In particular, an agent who did not join exchange S and subject his portfolio to the entry fee (S) cannot retrade with agents who did join exchange S. This additional power given to the market-maker in the segregated exchanges model makes her equally as e¤ective as the social planner in Section 4 in controlling agents’ investment at date 0. Unlike the planner, the market-maker does not control this investment directly but rather sets up prices (i.e., exchange entry fees) to induce e¢ cient investment. As we see, the model with segregated exchanges, where retrade does not lead to a pecuniary externality, requires a di¤erent economic environment than the models in Sections 3 and 4, where access to hidden retrade causes an externality. The segregated exchanges model requires that agents have the ability to commit themselves to refrain from trading in the hidden retrade market, which e¤ectively makes this model equivalent to the model with observable trades that we discussed in Section 4.21 If such commitment can be made credible, e.g., by physically separating agents ex post, then all agents would choose to extend it ex ante. If, however, it is a feature of the environment that such a commitment cannot be made credible, as in Farhi, Golosov, and Tsyvinski (2009), access to hidden retrade makes the Jacklin arbitrage strategy feasible, the pecuniary externality exists, and markets fail to provide su¢ cient liquidity in equilibrium. Clearly, the cap-and-trade mechanism will not be successful at limiting greenhouse gas emissions if …rms can emit completely privately/anonymously, i.e., without anyone observing it. If they can, the price of the right to emit one tonne of CO2 will be zero. In the KT model, retrade is analogous to observable emissions that can be priced. In the pecuniary externality model, hidden retrade is analogous to anonymous emissions that cannot be priced or internalized with a cap-and-trade scheme. Are then segregated exchanges a solution to the pecuniary externality problem caused by retrade? Segregated exchanges do not solve 20 Better yet, the arbitrageur could join one of the exchanges S < e, where (S) < 0, which means with s = 0 he would get a payment from the exchange upon entry. 21 That the segregated exchanges model requires a di¤erent environment than the unfettered hidden retrade model is clear from Table 1 on page 1,046 in Kilenthong and Townsend (2011). 334 Federal Reserve Bank of Richmond Economic Quarterly the pecuniary externality problem, but they show that retrade does not have to lead to one. The literature on pecuniary externalities with complete markets and retrade assumes that agents have unfettered access to an anonymous, hidden retrade market and cannot do anything to make credible an ex ante promise to refrain from accessing this market ex post. The segregated exchanges model assumes that such a commitment is possible. The segregated exchanges model, therefore, does not solve the pecuniary externality problem associated with anonymous, hidden retrade. Instead, it points out that retrade by itself does not imply the existence of a pecuniary externality. The model shows that retrade can be accounted for within the competitive market framework without violating e¢ ciency, provided that a su¢ ciently rich market structure, including markets for exchange membership, is allowed for. In addition, the KT model shows that exclusivity and ex post trade restrictions can be socially valuable. Their role can be to serve as a commitment device that agents may be able to use to help them refrain from the “harmful,”hidden retrade activity and still be able to engage in e¢ cient, priced retrade. 6. CONCLUSION The literature we review makes it clear that in the Diamond-Dybvig economy, the agents’access to retrade is key in understanding whether markets are e¢ cient or require government intervention. The theory makes a distinction between two kinds of retrade: the “priced” kind and the “hidden” kind. Hidden, anonymous retrade leads to a pecuniary externality and market failure. Priced retrade, harnessed into access-controlled segregated exchanges with exchange- and portfoliodependent entry fees does not cause market failure. The observation of retrade itself in present-day …nancial markets does not therefore imply that markets are ine¢ cient or e¢ cient in providing liquidity. To answer the question of e¢ ciency, one must assess which of the two kinds of retrade discussed in the model is a better re‡ ection of reality. Kilenthong and Townsend (2014a) suggest that the assumption of restricted retrade is a good one in …nancial markets. In other applications, for example in the problem studied in Kehoe and Levine (1993) where pecuniary externalities result from workers’ unrestricted access to spot labor markets, this assumption may be more problematic, as …rms may lack the commitment to deny employment to workers who have defaulted on some …nancial obligations in the past. Given these theoretical predictions and their implications for the e¢ cacy of government intervention, empirical research identifying B. Grochulski: Pecuniary Externalities and Segregated Exchanges 335 the nature of retrade and the existence or nonexistence of pecuniary externalities is needed. APPENDIX Proof of Lemma 1 Suppose allocation c is optimal with c2 (0) > 0 and de…ne an allocation c = f^1 (0); c2 (0); c1 (1); c2 (1)g as follows: ^ c ^ ^ ^ c1 (0) = c1 (0); c1 (1) = c1 (1); ^ ^ c2 (0) = 0; ^ c2 (1) = c2 (1) + ^ 1 c2 (0): Allocation c is feasible because at each date t = 1; 2 it uses the same ^ amount of resources as allocation c. Indeed: c2 (1) ^ c2 (0) ^ + (1 ) c1 (1) + ^ c1 (0) + ^ ^ ^ R R c2 (1) + 1 c2 (0) = c1 (0) + (1 ) ^ R c2 (0) c2 (1) = c1 (0) + + (1 ) c1 (1) + ^ ^ R R e: Allocation c, however, attains a higher value of the objective (5) be^ cause it provides the same utility u(c1 (0)) to the impatient type and a higher utility u(c1 (1) + c2 (1) + 1 c2 (0)) > u(c1 (1) + c2 (1)) to the patient type. This contradicts the supposed optimality of c. To prove that c1 (1) = 0, suppose that c is optimal with c1 (1) > 0 and de…ne an allocation c = f^1 (0); c2 (0); c1 (1); c2 (1)g as follows: ^ c ^ ^ ^ c1 (0) = c1 (0); c1 (1) = 0; ^ ^ ^ c2 (0) = c2 (0); c2 (1) = c2 (1) + Rc1 (1): ^ ^ Allocation c is feasible because it costs the same in present value terms ^ as the feasible allocation c. Indeed: c2 (0) ^ c2 (1) ^ c1 (0) + ^ + (1 ) c1 (1) + ^ ^ ^ R R ^ c2 (0) c2 (1) + Rc1 (1) = c1 (0) + + (1 ) ^ ^ R R c2 (0) c2 (1) = c1 (0) + + (1 ) c1 (1) + ^ ^ R R e: 336 Table 1 Allocation Mechanisms, Frictions, and Outcomes Allocation Mechanism Hidden IOU Retrade Market Market Structure Allocation Page First-best planning problem Absent Absent No markets– planner chooses allocation (c1 ; c2 ) 313 Planning problem with private Present Absent No markets– planner chooses allocation (c1 ; c2 ) 321 Planning problem with private and hidden retrade Present Present No markets– planner chooses allocation (c1 ; c2 ) 315 Incomplete markets model Present Present Ex ante: direct investment (s; x) Ex post: market for the long-term asset and the hidden IOU market Market model with statecontingent contracts, no hidden IOU retrade markets Present Market model with statecontingent contracts and hidden IOU retrade markets Present Market model with segregated exchanges Present Absent Present Absent Ex ante: deposit contract ( 1 ; 2 ) with price e Ex post: no markets Ex ante: deposit contract ( 1 ; 2 ) with price e Ex post: hidden IOU retrade market Ex ante: continuum of segregated exchanges Ex post: retrade inside exchanges, but not across 316 (^1 ; c2 ) c ^ 321 (c1 ; c2 ) 319 (^1 ; c2 ) c ^ (c1 ; c2 ) 322 Federal Reserve Bank of Richmond Economic Quarterly Private Shocks B. Grochulski: Pecuniary Externalities and Segregated Exchanges 337 Allocation c , however, attains a higher value of the objective (5) ^ than c, because it provides the same utility u(c1 (0)) to the impatient ^ type and a higher utility u(c2 (1) + Rc1 (1)) > u(c1 (1) + c2 (1)) to the patient type. This contradicts the supposed optimality of c. QED Proof of Proposition 1 Since W 00 (s) = 1 u00 u0 s ^ Ru0 s e s ^ R 1 ^ + 1 1 R2 u00 e s ^ R 1 < 0, we have that W 0 (s) = is continuous and strictly decreasing. The exis- tence of a unique solution to W 0 (s) = 0 in (0; e) thus follows from the fact that lims!0 W 0 (s) ! 1 and lims!e W 0 (s) ! 1. For the two bounds on s , it is su¢ cient to show that W 0 ( e) > 0 ^ < 0. We …rst note that relative risk aversion and W 0 e ^ R R+1 everywhere strictly greater than one implies that the function f ( ) = u0 ( e) is strictly decreasing. Indeed, with f 0 ( ) = u0 ( e) + eu00 ( e) 00 ( we have that f 0 ( ) < 0 follows from 1 < ueu e) e) . Now, evaluating 0( ^ ^ ^ W 0 at s = e, we have W 0 ( e) = u0 (e) Ru0 (eR) = f (1) f (R) > 0, ^ where the strict inequality follows from f strictly decreasing and R > 1. To show W 0 s e s ^ R 1 = W 0 = ^ R ^ R+1 ^ Re . ^ R+1 ^ Re ^ R+1 ! ^ Re ^ R+1 < 0; note that with s = e we have Therefore, = u = 0 1 ^ Re ^ R+1 ^ R u0 ! ^ Re ^ R+1 ^ Re ^ Ru0 ! ^ R+1 ! < 0; ^ where the inequality follows from u0 > 0 and R > 1. QED Formal De nition of Incomplete-Markets Equilibrium in Section 3 At date 0, each agent chooses an investment portfolio (s; x). Agents solve max (s;x) (0;0) s:t: s+x E[V1 (s; x; )] e; (35) 338 Federal Reserve Bank of Richmond Economic Quarterly where V1 (s; x; ) is the indirect utility function representing the value the agent can obtain at date 1 if he holds investments (s; x) and receives realization of the liquidity shock. 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