key: cord-0801604-hqmwaoxp
authors: Kargar, Mahyar; Lester, Benjamin; Lindsay, David; Liu, Shuo; Weill, Pierre-Olivier; Zúñiga, Diego
title: Corporate Bond Liquidity during the COVID-19 Crisis
date: 2021-05-21
journal: Rev Financ Stud
DOI: 10.1093/rfs/hhab063
sha: 40d6bfdb861597a3650808e105681c5309a4a88e
doc_id: 801604
cord_uid: hqmwaoxp

We study liquidity conditions in the corporate bond market during the COVID-19 pandemic. We document that the cost of trading immediately via risky-principal trades dramatically increased at the height of the sell-off, forcing customers to shift toward slower agency trades. Exploiting eligibility requirements, we show that the Federal Reserve’s corporate credit facilities have had a positive effect on market liquidity. A structural estimation reveals that customers’ willingness to pay for immediacy increased by about 200 bps per dollar of transaction, but quickly subsided after the Fed announced its interventions. Dealers’ marginal cost also increased substantially but did not fully subside.

The COVID-19 pandemic induced an unprecedented shock to the global economy. As the implications of this shock began to crystalize in mid-March 2020, financial markets plummeted, and reports of illiquidity began to surface. One particularly important market "under significant stress" (Bernanke and Yellen, 2020) was the $10 trillion corporate bond market, which a March 18 report from Bank of America deemed "basically broken" (Idzelis, 2020) . In response, the Federal Reserve introduced several facilities designed to bolster liquidity and reduce the costs and risks of intermediating corporate debt, including the Primary Dealer Credit Facility (PDCF) and the Primary and Secondary Market Corporate Credit Facilities (PMCCF and SMCCF, respectively). The latter two facilities represented a particularly bold intervention, in that they allowed the Fed, for the first time, to make outright purchases of investment-grade corporate bonds issued by U.S. companies, along with exchange-traded funds (ETFs) that invested in similar assets.

The purpose of this paper is to study trading conditions in the U.S. corporate bond market in response to the large economic shock induced by COVID-19, as well as the unprecedented interventions that followed. Given the exogenous nature of the pandemic, set against the backdrop of a well-capitalized financial sector, this episode offers a unique opportunity to identify the nature of shocks that precipitate illiquidity in financial markets, the consequences for market participants, and the efficacy of various policy responses designed to restore liquidity in times of distress.

A central feature of our analysis is the distinction between two types of transactions offered by dealers: "risky-principal" trades, in which a dealer offers a customer-seller immediacy by purchasing the asset directly and storing it on his balance sheet until finding a customer-buyer; and "agency" trades, in which the customer-seller retains the asset while waiting for a dealer to find a customerbuyer to take the other side of the trade. This distinction, which has been recently studied using prepandemic data, is crucial in generating several new insights, 1 of which we highlight three.

First, distinguishing between risky-principal and agency trades provides a more complete assessment of market liquidity by accounting for both the cost of trading and the time it takes to trade.

Indeed, we show that focusing on transaction costs alone-ignoring changes in the composition of risky-principal and agency trades-understates the deterioration in liquidity after the COVID-19

shock. Second, studying the cost and quantity of these distinct types of trades in concert with a structural model allows us to disentangle two widely cited (but not mutually exclusive) sources of illiquidity: a large, unexpected increase in customers' demand for immediacy, sometimes called a "dash for cash," and a decrease in dealers' willingness to supply immediacy by absorbing assets onto their balance sheets, either because of rising costs or because of binding regulatory constraints. A key finding is that matching the data requires large shocks to both demand and supply at the onset of the crisis. Finally, studying the evolution of demand and supply factors against the timeline of the Fed's interventions offers new insights into the efficacy of various policies. In particular, we show that the surge in customers' demand for immediacy receded almost immediately, and fully, after the announcement of the Fed's interventions, whereas the negative shock to dealers' supply of immediacy responded more gradually, and only partially.

After providing some background information in Section 1, we begin our analysis in Section 2 by documenting trading conditions in the corporate bond market in response to the panic of mid-March and the Fed's interventions that followed. Using data from the Trade Reporting Compliance Engine (TRACE), we first construct time series to measure the costs of risky-principal and agency trades in the corporate bond market. We find that the cost of risky-principal trades increased significantly during the COVID-induced panic, reaching a peak of more than 250 basis points (bps), while the cost of agency trades increased much more modestly. As the premium paid for risky-principal trades increased, we show that customers substituted toward agency trades: the fraction of total volume executed as agency trades increased by as much as 15% at the height of the sell-off, and remained elevated even months after the initial panic subsided. Hence, the average trade was not only more expensive but also more likely to be slower or of "lower quality."

As trading shifted from risky-principal to agency transactions, we show that the dealer sector as a whole absorbed no inventory, on net, during the most tumultuous period of trading. Therefore, when the demand for transaction services surged, it was customers themselves who ultimately stepped up to provide additional liquidity. In fact, it was only after the announcement of the Federal Reserve's interventions that dealers began to absorb inventory onto their balance sheets, and trading conditions started to improve. Indeed, after the announcement of the Fed's credit facilities, the quantity of corporate debt held by dealers more than doubled relative to pre-COVID levels. At the same time, the cost of risky-principal trades decreased significantly, but remained approximately twice the levels observed before the pandemic.

While these observations establish the coincidence of key interventions and improvements in market liquidity, they do not establish a causal relationship. To further explore the effects of interventions on market liquidity, we exploit restrictions on the types of bonds that could be purchased through the Fed's corporate credit facilities. In particular, using a difference-in-differences approach, we use restrictions on bond ratings and time-to-maturity to identify the change in trading costs induced by the announcement of the SMCCF. We find that, immediately after the announcement of the SMCCF, the cost of trading bonds that were eligible for purchase by the Fed decreased substantially relative to the cost of trading ineligible bonds. Later, the program was expanded in both size and scope, and we show that, following this expansion, the trading costs of all bonds fell.

Hence, our findings suggest that the Fed's interventions had significant effects on transaction costs and trading activity in the corporate bond market. However, the observations described above also lead to several important questions. Why did the Fed's interventions improve trading conditions so quickly, but not fully? Did the announcement and implementation of these policies (at least partially) restore liquidity by easing investors' concerns and halting the "dash for cash"?

Or should the efficacy of these interventions be attributed to easing dealers' balance sheet concerns, thus increasing their willingness to "lean against the wind" (Weill, 2007) ? Given the deterioration of both the cost and quality of intermediation services during the COVID-19 crisis, what was the effect on the surplus of customers in the U.S. corporate bond market during this period?

To confront these questions, and interpret our empirical findings more generally, in Section 3 we construct a parsimonious equilibrium model of a market for vertically differentiated transaction services: low-quality, meant to capture agency trades; and high-quality, meant to capture riskyprincipal trades. We assume that customers prefer high-quality transaction services, but they are more costly for dealers to produce. Within this framework, we characterize the differential impact of two types of shocks-to customers' relative demand for high-quality risky-principal trades and to dealers' cost of supplying these transaction services-on equilibrium prices and allocations.

Then, using our estimates of relative prices and quantities in concert with our theoretical framework, we estimate key parameters of the model, which allows us to identify shocks to customers' demand for immediacy, at the height of the crisis and during the interventions that followed. We confirm that a large, sudden increase in the demand for immediacy was a crucial source of illiquidity early in the crisis. In fact, we estimate that customers' willingness to pay for each inframarginal unit of risky-principal trade (rather than an agency trade) increased by approximately 200 bps at the height of the crisis. However, we also find that this shock alone cannot explain what we observe in the data: to rationalize the observation that customers ultimately substituted toward agency trades, we show that dealers also must have experienced a significant shock to their marginal cost of supplying immediacy. Hence, understanding the market turmoil of March 2020 requires studying both the origins of the "dash for cash" and the factors that dissuaded dealers from absorbing selling pressure onto their balance sheets.

Studying the behavior of shocks to customers' demand for immediacy, and dealers' cost of supplying it, against the timeline of policy announcements and implementation also reveals new insights regarding the channels through which the Fed's interventions operated. In particular, we find that the demand shock receded quickly, and fully, soon after the announcement of the PDCF and SMCCF-that is, the announcement alone seems to have effectively reversed the initial "dash for cash." The increase in dealers' cost of supplying risky-principal trades, however, appears to have lingered even after the Fed began purchasing bonds. While this could be explained multiple ways, we document one plausible candidate: the total volume of customer-dealer transactions remained elevated through June, a factor that-when combined with binding balance sheets constraints-could explain why the relative cost (fraction) of risky-principal trades remained elevated (depressed) months after markets appear to have calmed.

Finally, we leverage our theoretical framework-along with our empirical estimates of preference shocks, prices, and quantities-to construct a measure of customers' well-being. In particular, we define consumers' surplus from immediacy as the net utility per unit of transaction that a customer receives from upgrading from slower, agency trades to faster, risky-principal trades. Relative to the precrisis period, we find that the loss in consumers' surplus from immediacy was less pronounced than the increase in the relative price premium for immediacy, but remained suppressed well after markets had calmed. In fact, we find customers' net utility from upgrading to faster, risky-principal trades per unit of transaction declined by only about 20 bps during the height of the market turmoil, but remained approximately 10 bps below precrisis levels even at the end of June 2020. We argue that these results highlight the importance of accounting for changes in customers' preferences for immediate trades, along with changes in the relative quantities of risky-principal and agency trades, when assessing the effects of shocks and the interventions that follow.

Given the size of the COVID-19 shock, and the historic nature of the Fed's response, it is not surprising that a number of recent papers have emerged to study financial markets since the onset of the pandemic. Our paper belongs to the literature focused on the corporate bond market, which we discuss in more detail below, but shares much in common with studies of other markets, including the market for Treasuries and other government debt (Duffie, 2020; He, Nagel, and Song, 2020; Fleming and Ruela, 2020; Schrimpf, Shin, and Sushko, 2020) , as well as the market for asset-backed securities (Foley-Fisher, Gorton, and Verani, 2020; Chen et al., 2020) .

In the corporate bond market, Falato, Goldstein, and Hortaçsu (2020) study the effect of the pandemic on outflows from bond mutual funds, and the role that the Fed's corporate credit facilities played in reversing these outflows. Ma, Xiao, and Zeng (2020) also explore outflows in fixed-income mutual funds, including those that invest in corporate bonds and Treasuries. They derive a pecking order theory of liquidation, which explains why selling pressure was strongest in the most liquid sectors of these markets. Haddad, Moreira, and Muir (2020) focus primarily on the behavior of credit spreads during the crisis, and attempt to identify the mechanism through which the Fed's interventions improved market conditions. 2 Though different along many dimensions, these three papers all argue that a large, sudden increase in customers' demand for immediacy played a crucial role in the deterioration of market liquidity in March 2020. We, too, identify such a shock, but find that matching the data also requires a significant shock to the dealers' cost of supplying immediacy.

Our paper is most closely related to contemporaneous work by O'Hara and Zhou (2020) and Boyarchenko, Kovner, and Shachar (2020) , who also investigate liquidity conditions in the corporate bond market during the COVID-19 crisis, and the effects of the Fed's interventions. 3 Despite some overlap, the three papers differ (and complement one another) in several important ways. For example, using the regulatory version of TRACE-which contains dealer identities-O'Hara and Zhou (2020) document the heterogeneous response of different dealers to the Fed's interventions.

This allows them to control for dealer fixed effects and to disentangle the effects of the PDCF and 2 For related work on the behavior of credit risk/spreads throughout the crisis, and the effects of the Fed's interventions, see Qiu (2020) and D'Amico, Kurakula, and Lee (2020) .

3 In more recent work, Gilchrist et al. (2020) quantify the effects of the SMCCF on credit spreads and transaction costs using a regression discontinuity approach. Although they use a different methodology than ours to construct their sample, they find qualitatively similar results for the effects of the SMCCF on transaction costs for eligible and ineligible bonds. However, their quantitative magnitudes differ from ours. We will discuss this further in Section 2. the SMCCF, among other things. Boyarchenko, Kovner, and Shachar (2020) also use the regulatory version of TRACE, along with data on the volume of bonds (or shares of ETFs) purchased by the Fed's corporate credit facilities. This allows them to decompose the effects of the Fed's interventions into direct "purchase effects" and indirect "announcement effects." 4 While our paper makes a number of distinct contributions relative to these contemporaneous studies, we highlight several aspects of our analysis that are particularly important. First, our approach to measuring trading conditions accounts for two channels through which market liquidity can deteriorate-customers can face higher transaction costs or longer waiting times for executing a trade-and hence provides a multidimensional assessment of market conditions during the crisis.

Second, in contrast with the papers cited above, we develop a theoretical framework that, when combined with our empirical estimates, allows us to construct quantitative estimates of the shocks that precipitated the COVID-19 crisis. 5 Finally, we use these estimates of shocks to demand, along with bounds on shocks to supply, to study the efficacy of various policy interventions, and the implications for consumer surplus, at the height of the crisis and beyond.

Despite reports of a potentially lethal virus spreading in China, U.S. equity markets reached alltime highs on February 19, 2020. Just two weeks later, as the scope of the COVID-19 coronavirus and the duration of its effects became apparent, financial markets around the world entered a period of turmoil. For example, between March 5 and March 23, the S&P 500 fell more than 25%. In the corporate bond market, the ICE Bank of America AAA U.S. Corporate Index Option-Adjusted spread increased by about 150 bps over this same period, while the corresponding spread for highyield (HY) corporate debt increased by more than 500 bps. 6 As the price of equities and debt plummeted, reports of illiquidity in key financial markets emerged. Such reports were especially 4 For more on the purchase effects of the SMCCF, see Flanagan and Purnanandam (2020) . 5 Along this dimension, our paper is related to Goldberg and Nozawa (2020) , who use a structural VAR approach to identify demand and supply shocks in the corporate bond market during (and after) the 2007-2009 financial crisis. However, our identification strategy, as well as our focus, is different from theirs. Their primary concern is the asset pricing implications of liquidity supply shocks.

6 See Ebsim, Faria-e Castro, and Kozlowski (2020) for a more comprehensive analysis of credit spreads during this time period. troubling in the corporate bond market, as many large U.S. firms would almost surely need access to capital in light of the impending shocks to their balance sheets. 7

Two complementary factors were cited as the root of the panic in the corporate bond market.

The first was a surge in the demand for immediacy, or so-called "dash for cash," as investors pulled out of corporate bond funds in droves. For example, Falato, Goldstein, and Hortaçsu (2020) report that, between the months of February and March, the average corporate bond fund experienced cumulative outflows of approximately 9% of net asset value-by far the largest outflows in the last decade. At the same time, market participants reported that dealers were either unable or unwilling to supply customers with immediacy by absorbing corporate debt onto their balance sheet. In a Wall Street Journal article, Baer (2020) writes about the experience of Vikram Rao, the head bond trader of Capital Group, after calling senior executives for an explanation on why broker-dealers wouldn't trade:

[T]hey had the same refrain: There was no room to buy bonds and other assets and still remain in compliance with tougher guidelines imposed by regulators after the previous financial crisis [...] One senior bank executive leveled with him: We can't bid on anything that adds to the balance sheet right now."

In response to signs of illiquidity in several key financial markets, the Federal Reserve introduced a number of new facilities designed to bolster liquidity and reduce trading costs. On the evening of March 17, the Federal Reserve revived the aforementioned PDCF, offering collateralized overnight and term lending to primary dealers. By allowing dealers to borrow against a variety of assets on their balance sheets, including investment-grade corporate debt, this facility intended to reduce the costs associated with holding inventory and intermediating transactions between customers. 8 On March 23, the Federal Reserve proposed even more direct interventions in the corporate 7 Indeed, Darmouni and Siani (2020) document that corporate bond issuance reached historic levels in Spring 2020, after the Fed's interventions, despite a relatively healthy banking sector.

8 In addition to the facilities that we highlight in our analysis here, it is also noteworthy that the Federal Reserve temporarily relaxed the supplementary leverage ratio (SLR) rule-first on April 1 and again on May 15, 2020-to ease balance sheet constraints and increase banks' ability to lend to households and businesses. By excluding U.S. Treasury securities and reserves from the calculation of the SLR rule for holding companies, the rule change was primarily intended to increase liquidity in the Treasury market. However, to the extent that it relaxed dealers' balance sheet constraints, the effects could clearly extend to the corporate bond market as well, as we will discuss later in the text. To read more about the rule change, see the press releases on April 1, 2020 (Board of Governors of the Federal Reserve System, 2020a), and May 15, 2020 (Board of Governors of the Federal Reserve System, 2020b). bond market through the PMCCF and SMCCF. These facilities were designed to make outright purchases of corporate bonds issued by investment-grade U.S. companies with remaining maturity of 5 years or less. The facilities were also allowed to purchase shares in U.S.-listed exchange-traded funds (ETFs) that invested in U.S. investment-grade corporate bonds. On April 9, these corporate credit facilities were expanded in size and extended to allow for purchases of ETFs that invested in high-yield corporate bonds. 9 Interestingly, though many of the effects of these corporate credit facilities were observed immediately after they were announced (and expanded), the Federal Reserve did not actually begin purchasing bonds until May 12. We provide a more detailed description of this timeline, and of the Federal Reserve's corporate facilities, in Appendix B.

In this section, we describe how market conditions evolved from the sanguine conditions of mid-February through the freefall of mid-March to the postintervention recovery of April and May. As a first step, we construct time series for several variables of interest: the cost of risky-principal trades, the cost of agency trades, and the fraction of each type of transaction services. We document that, at the height of the selling pressure, the cost of risky-principal trades surged, and the fraction of such trades dropped significantly. Conditions improved immediately after the Fed's announcement of the corporate credit facilities, with dealers providing liquidity directly, via risky-principal trades, at significantly lower prices. To test the causal relationship between the Fed's interventions and market liquidity, we exploit the eligibility requirements for bond purchases by the SMCCF. We find that, after the initial announcement, trading costs for eligible bonds fell substantially more than trading costs for ineligible bonds. Later, after the program was expanded in both size and scope, we document more significant declines in trading costs for all bonds.

We combine the standard TRACE data set (for 2020Q1) with the end-of-day version (for 2020Q2). We first filter the report data following the standard procedure laid out in Dick-Nielsen 9 The April 9 update also allowed the SMCCF to make direct purchases of bonds that had been downgraded from investment-grade to high-yield status (so-called "fallen angels") after March 22. The facility also allowed purchasing of high-yield ETFs.

(2014). We merge the resultant data set with the TRACE master file, which contains bond grade information, and with the Mergent Fixed Income Securities Database (FISD) to obtain bond fundamental characteristics. Following the bulk of the academic literature, we exclude variable-coupon, convertible, exchangeable, and puttable bonds, as well as asset-backed securities, and private placed instruments. We also exclude newly issued and foreign securities.

For most of our analysis, we use the (filtered) data covering the period from January 2 to June 30, 2020, which contains 7.2 million trades and 30,748 unique bonds. Approximately 60% of the transactions are identified as customer-dealer and 40% as interdealer trades. The average trade size is $218,104 across all transactions, with average total daily volumes for customer-dealer and interdealer trades of $7.25 billion and $3.13 billion, respectively. It is worth noting that, in both the standard and end-of-day versions of TRACE, the trade size for investment-grade and high-yield bonds is top-coded at $5 million and $1 million, respectively. 10

In all of our plots below, we include vertical dashed lines to highlight several key dates: February 19, when stock markets reached their all-time peaks; March 5, which marks the beginning of the extended fall in equity prices and rise in corporate credit spreads; March 18, the first day of trading after the announcement of the PDCF; March 23, the day that the PMCCF and SMCCF were announced; April 9, the day that the size and scope of the corporate credit facilities were expanded; May 12, the date that the SMCCF started buying bond ETFs; June 16, the day that the SMCCF began purchasing individual bonds; and June 29, the date the PMCCF began operating.

To capture the average transaction cost for risky-principal trades, we use the measure of bid-ask spreads proposed by Choi and Huh (2018) , CH hereafter. To construct this measure, we first calculate, for each customer trade, the spread

where Q is equal to +1 (−1) when a customer buys from (sells to) a dealer, and the reference price is taken to be the volume-weighted average price of interdealer trades larger than $100,000 in the same bond-day. Importantly, we restrict our sample so that it only includes trades in which the dealer who buys the bond from a customer holds it for more than 15 minutes. In doing so, we leave out those trades where the dealer had prearranged for another party (either a customer or another dealer) to buy the bond immediately. 11 The measure of risky-principal trading costs is aggregated at the bond-day level by taking the volume-weighted average of trade level spreads, and then at the daily level by taking the average in each day across all bonds, weighted by bonds' daily total volume of customer trades where the CH measure is available.

To capture the average transaction cost of agency trades, we calculate a modified version of the Imputed Roundtrip Cost measure described in Feldhütter (2012) . To construct this modified imputed roundtrip cost (or "MIRC"), we first identify imputed roundtrip trades (IRT) by matching a customer-sell trade with a customer-buy trade of the same size that takes place within 15 minutes of each other. 12 We exclude interdealer trades in constructing IRTs, so that each IRT only includes one customer-buy trade and one customer-sell trade. Then, to compute the MIRC, we calculate

where P max (P min ) is the largest ( 12 In other words, as in earlier papers, we assume that customer-buys and customer-sells that occur in rapid succession are likely to be agency trades. Indeed, in an agency trade, dealers search for counterparties on behalf of customers. When counterparties are found, the two customers are matched by dealers, and two customer-to-dealer trades are recorded in a short time window. J a n -1 9 F e b -1 9 M a r -0 5 M a r -1 8 M a r -2 3 A p r -0 9 M a y -1 2 J u n -1 6 J u n -2 9

Transaction cost (bps)

Risky-Principal (high-quality) Agency (low-quality) difference continues to rise, reaching a peak of more than 250 bps, before beginning a steady decline after the announcement of the SMCCF on March 23. The MIRC measure of agency trading costs, in contrast, increases from a baseline around 8 bps to approximately 28 bps, before receding slightly after the Fed's intervention.

One can see that the cost of risky-principal trades, which we interpret as the cost of trading immediately, was considerably more responsive to both the heightened selling pressure induced by the pandemic in mid-March and the Fed's interventions which followed. Moreover, despite considerable improvement in both metrics during the month of April, the cost of risky-principal trades remained elevated through June, which suggests that liquidity conditions remained somewhat strained well after markets appear to have calmed.

Of course, the change in spreads could be driven by a change in the composition of bonds that were traded during this period of distress. For example, perhaps trading volume was unusually high for retail-size trades of illiquid bonds, which typically involve higher transaction costs. Thus, to further clarify the impact of the crisis and ensuing interventions on the cost of risky-principal and agency trades, we turn to formal regressions that allow us to control for bond-and trade-level fixed effects. We consider the following specification

The dependent variable, y ijt , represents the transaction cost for a type j ∈ {risky-principal, agency} trade of bond i on day t. The dummy variables Crisis t and Intervention t allow us to distinguish between three subperiods: (1) precrisis, which corresponds to dates before March 5, 2020;

(2) crisis, which covers the period March 5-23, 2020; and (3) intervention, which covers the period after March 23. Hence, the coefficients β 1 and β 2 measure transactions costs relative to the precrisis period.

Finally, α i and α s represent bond and trade size fixed effects, respectively. Bond fixed effects capture bond characteristics that are fixed over time, such as industry or par amount. 13 For trade size fixed effects, we consider three categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. We include bond and size category fixed effects and cluster standard errors at the bond and day levels in all regressions to account for correlation over time within a bond and across bonds in a given day. Columns 1 and 3 reveal that, during the crisis period of March 5-23, average bond-level trading costs for risky-principal and agency trades increased by approximately 105 bps and 9 bps, respectively, relative to the precrisis period. After the Fed's interventions on March 23, trading costs for risky-principal trades fell by approximately 64 bps-more than half the initial spike-while transaction costs for agency trades declined much more modestly. These results are consistent with the aggregate results in Figure 1 . Columns 2 and 4 show that the subsample of U.S.-issued bonds exhibits roughly the same behavior as the sample of all bonds, though the cost of agency trades for U.S.-issued bonds increased slightly more during the crisis period. 13 We do not have access to the latest credit rating data for all bonds in our sample, just the binary IG/HY classification provided by TRACE. For the subsample of bonds for which the credit rating is available, we include a credit rating fixed effect in specification (2) to control for the potentially time-invariant nature of bond credit ratings. From Table OA1 in Internet Appendix OA1, we see that controlling for the bond credit rating leads to very similar results to those in Table 1 .

14 One reason we include the results for the U.S. subsample is to demonstrate that the trading cost patterns are similar to the full sample. This is helpful later, in Section 2.5, when we focus on the U.S. subsample exclusively.

This table presents the regression results for the following specification: yijt = αi + αs + β1 × Crisist + β2 × Interventiont + εijt. The dependent variables are our measures of transactions costs for risky-principal and agency trades. Crisist and Interventiont are dummies that take the value of one if day t falls into the Crisis and Intervention subperiods defined above. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. The sample starts on January 3 and ends on June 30, 2020. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Dependent variable: 

We now establish that, as the premium for risky-principal trades increased, customers responded by substituting toward agency trades. Figure 2 plots the proportion of agency trades by number (left axis) and volume (right axis). 15 During the most tumultuous weeks of trading, between

March 5 and March 23, the fraction of agency trades (measured by both number and volume) increased by as much as 15 percentage points, trough to peak, before receding after the March 23rd announcement of the corporate credit facilities. Again, this shift toward agency trades has important implications for assessing market liquidity. In particular, if one were simply to measure trading costs across all trades, they would underestimate the erosion in liquidity as the composition of trades shifted from faster, more expensive risky-principal trades to less costly, but slower agency trades.

To study the substitution from risky-principal to agency trades more carefully, we consider a 15 We discuss in-depth how we identify agency trades in Appendix A. regression with the following specification:

where Agency ijt is an indicator variable that takes the value one if trade j for bond i on day t is an agency trade and zero otherwise. The variables on the right-hand side of specification (3) are the same as in (2). Under this specification, the coefficients β 1 and β 2 measure the change in the probability of an agency trade during the crisis and intervention periods, respectively, relative to the precrisis period. Table 2 presents results using a linear probability model (OLS), along with logit and probit specifications for robustness.

Column 1 reveals that, during the crisis period of March 5-23, the probability of an agency trade for a given bond, on average, rose by 4.3 percentage points relative to the precrisis period.

After the Fed interventions on March 23, this probability decreased from the crisis period (by 160 bps) to 2.7 percentage points higher than the precrisis period. For the sake of completeness, we report marginal effects calculated at the sample means for logit and probit models in columns 2 

The dependent variable, Agency ijt , is an indicator variable that takes the value of one if trade j for bond i on day t is an agency trade and zero otherwise. Columns 1, 2, and 3 report result for the linear probability (OLS), logit, and probit models, respectively. We report marginals effects calculated at the sample means for logit and probit models in columns 2 and 3. Crisist and Interventiont are dummies that take the value of one if day t falls into Crisis and Intervention subperiods defined above. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. In logit and probit specifications, the pseudo-R 2 is defined as 1 − L1/L0, where L0 is the log likelihood for the constant-only model and L1 is the log likelihood for the full model with constant and predictors. The sample starts on January 3 and ends on June 30, 2020. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Probability of agency trade 

As the relative price of risky-principal trades spiked in mid-March, and customers substituted toward agency trades, one might naturally wonder: who was providing liquidity in the corporate bond market? Were dealers "leaning against the wind" and absorbing some of the inventory during the selloff? Or was the shift to agency trades sufficiently large that other customers were ultimately providing liquidity? To answer this question, we construct a measure of the (cumulative) value of bonds that were absorbed over time by the dealer sector. In particular, using the daily Market Sentiment data from FINRA, we subtract the value of bonds that dealers sell to customers from the value of bonds that they buy from customers each day, and then calculate the cumulative sum of Cumulative inventory ($ billion) As a fraction of outstanding supply (%) the net changes. 17 Figure 3 plots the cumulative net change in inventory held in the dealer sector, both in levels (left axis) and as a fraction of precrisis outstanding supply (right axis).

Several aspects of Figure 3 are striking. First, during the most tumultuous period of trading, the dealer sector absorbed, on net, no additional inventory despite the considerable selling pressure from customers. In fact, dealers actually reduced inventory holdings and became net sellers. Hence, during this period, it was indeed other customers that were supplying liquidity to the market. The Market Sentiment data are available through FINRA TRACE Market Aggregate Information from https: //finra-markets.morningstar.com/BondCenter/TRACEMarketAggregateStats.jsp. We use these data, as opposed to the standard or end-of-day TRACE data, because these data are not top-coded and hence allow for a more accurate assessment of the inflow and outflow of bonds in the dealer sector.

18 From table L.130 of the Flow of Funds, at the end of 2019Q4, security brokers and dealers held $54 billion in corporate and foreign bonds on the asset side of their balance sheets.

The results above suggest that the Fed's interventions-in particular, the March 23rd announcement of the SMCCF-had a significant effect on dealers' willingness to absorb inventory onto their balance sheets, and hence on market liquidity. In this section, we exploit the eligibility requirements specified in the SMCCF to test this hypothesis more formally.

According to the original term sheet, a bond is eligible to be purchased through the SMCCF if it has an investment-grade rating on March 23, 2020; if it has a time-to-maturity of 5 years or less;

and if its issuer is domiciled in the United States. 19 However, the Fed has a considerable degree of discretion to determine whether a foreign issuer is domiciled in the United States. Indeed, in the Fed's SMCCF transaction-level disclosures, we found many cases in which the holding firm of the security is a non-U.S. entity. 20 Given this lack of clarity, we chose to focus on U.S. firms exclusively, and classify a bond as eligible based on credit rating and time-to-maturity alone. 21

To start, we repeat the regression specified in (2) with two modifications. First, we separate the sample of bonds into those that were eligible for purchase through the SMCCF and those that were not. Second, we separate the intervention period into two subperiods. The first subperiod, which we call the "SMCCF," covers from March 23 to April 8, 2020. During this period, it appeared that only investment-grade bonds would be eligible for purchase. The second subperiod, which we call the "SMCCF expansion," starts on April 9, when the Fed announced that it was increasing the size of the program and expanding the set of eligible bonds to include high-yield debt. Table 3 reports the results. Column 2 reveals that the initial decline in trading costs was largely driven by bonds that were eligible for the SMCCF: the price of risky-principal trades for ineligible bonds declined much more modestly immediately after the March 23rd announcement, relative to the crisis period, while the price of agency trades for ineligible bonds actually increased during this time period. After the program was expanded on April 9, in both scope and size, the price of risky-principal trades for all bonds declined significantly.

This table presents regression results for the following specification: yijt = αi + αs + β1 × Crisist + β2 × SMCCFt + β3 × SMCCF Expansion t + εijt. The dependent variables are measures of transaction costs for risky-principal and agency trades. Crisist is a dummy which takes the value of one if day t falls into the Crisis subperiods defined above. SMCCFt and SMCCF Expansion t are dummies that take the value of one if the trading day t is between March 23 and April 9, and after April 9, 2020, respectively. The SMCCF eligibility criteria were expanded to include fallen angels on April 9, 2020. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. A bond is considered eligible if it has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. The sample begins on January 3 and ends on June 30, 2020. Only U.S. firms are included in the regressions. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Risky-principal Agency To further explore the causal effect of the SMCCF on bond market liquidity during the crisis, we consider a difference-in-differences regression over a subsample of our data from March 6 to April 9, 2020. These dates are chosen to exclude the precrisis period, when spreads were very low, and the postexpansion period, when the set of bonds available for purchase through the SMCCF was widened to include high-yield bonds. In particular, we use the following specification:

where, as before, y ijt represents our measures of transaction costs; Eligible t takes the value of one if the bond in trade j has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020; SMCCF t takes the value of one if the trade occurs between March 23 and April 9, 2020; and α s controls for size fixed effects. 22

22 One potential complication in distinguishing between eligible and ineligible bonds based on maturity is that the criteria for eligibility are determined at the Fed's time of purchase. Therefore, for example, a bond that would be Unlike specification (2), we do not include bond fixed effects in the baseline specification (4), but instead control for industry fixed effects (α k ) and bond-specific characteristics, such as bond age, amount outstanding, and time-to-maturity (X i,t ). However, for robustness, we also include results allowing for bond fixed effects, as well as credit rating fixed effects. To ensure that treatment and control groups do not overlap, we remove all trades in bonds that were downgraded from IG to HY. Finally, we drop all foreign bonds, and we focus on bonds issued by U.S. firms. Table 4 contains our results. As is standard in difference-in-differences regressions, β 1 is the primary coefficient of interest. The first key takeaway is that the SMCCF had a significant effect on the cost of risky-principal trades for eligible bonds relative to ineligible bonds. The quantitative magnitude of this effect is approximately 50 bps, and is robust to a variety of alternative specifications. For example, in column 2, we include a credit rating fixed effect, which allows us to control for differences in average transaction costs using finer definitions of credit rating than IG or HY (e.g., AAA, AA, and so on), but has relatively minor effects on β 1 . In columns 3 and 4, we allow for bond-specific fixed effects, which increases the explanatory power of the regressions (i.e., R 2 ) but does not significantly change the estimates of β 1 .

The second noteworthy result is that, for risky-principal trades, β 2 is not statistically different from zero under any of our specifications. Hence, it appears that the announcement of the initial SMCCF did not have significant spillover effects on the cost of risky-principal trades for ineligible bonds. However, this does not rule out the potential for spillover effects from the actual purchase of eligible bonds, which began May 12, 2020. In particular, by purchasing bonds and relaxing dealers' balance sheet constraints, the SMCCF could potentially increase dealers' willingness to purchase any bond. If this is true, then some of the postexpansion decline in the costs of risky-principle trades for ineligible bonds (reported in Table 3 ) could be attributed to spillover effects from the Fed's bond purchases.

Columns 5-8 indicate that the announcement of the SMCCF on March 23 also reduced the cost of agency trades for eligible bonds. 23 One possible explanation is that, by establishing itself characterized as ineligible when the SMCCF was announced on March 23, 2020, might, in fact, have been purchased by the Fed in November 2020 (since the program remained active until December 31, 2020). To make sure that this complication does not affect our main results, in Tables OA2-OA5 in Internet Appendix OA1.2, we recreate  Tables 1-4 , leaving out all trades involving bonds with maturity 5-6 years on March 23, 2020. Since these bonds represent a small fraction of our transactions, it turns out that our results are largely unaffected. 23 When one looks at the overall effect (β1 + β2 + β3), column 6 indicates that, after controlling for credit rating, the cost of agency trades for eligible bonds decreased after SMCCF announcement. as a buyer of last resort, the Federal Reserve reduced the risk to private investors from purchasing eligible corporate bonds. According to this logic, the announcement of the SMCCF may have made it easier for dealers to locate customer-buyers and hence reduce the spreads they charged on agency trades for eligible bonds. Note that this mechanism could also explain why the cost of agency trades for ineligible bonds went up in the immediate aftermath of the SMCCF announcement: if budgetconstrained customers substituted from ineligible to eligible bonds, it would become more difficult for dealers to locate customer-buyers for ineligible bonds, driving up spreads.

In Appendix C, we provide several additional robustness checks for the results discussed above.

In particular, in Tables A3 and A4, we show that the impact of the SMCCF on the trading cost of eligible bonds is even more pronounced if we limit our sample to those bonds that are just above and below the eligibility thresholds for and credit rating, respectively. In addition, in Tables A5-A7, we

show that small and large trades are responsible for the entire liquidity improvement documented in Table 4 : small trades (with par volume of $100,000 or less) become much more liquid after the SMCCF announcements, while large trades (with volume larger than $1 million) also exhibit a significant decline in trading costs. Odd-lot trades (with volume between $100,000 and $1 million), however, are essentially unaffected by the Fed's intervention.

The empirical analysis above highlights that the U.S. corporate bond market experienced a significant decline in liquidity at the onset of the COVID-19 crisis, which was partially reversed by the Fed's interventions. Though informative, the facts we document leave several key questions unanswered. What was the nature of the shocks that led to a lack of liquidity? Why did the policies that were implemented appear to restore liquidity relatively quickly, but only partially?

And how did these shocks and the ensuing interventions affect the well-being of the customers in this market?

To confront these questions, we now construct a parsimonious equilibrium model of the market for immediacy and use it to conduct a structural analysis of our empirical observations. Our analysis reveals that, at the onset of the crisis, the market was hit by large shocks to both customers' demand for immediacy (the "dash for cash") and dealers' willingness to supply it. After the announcement Table 4 

This table presents regression results for the following difference-in-differences specification from Equation (4)

The dependent variables are measures of transaction costs for risky-principal and agency trades. SMCCFt is a dummy that takes the value of one if day t falls between March 23 and April 9, and zero otherwise. Eligible t takes the value of one if the bond has an investment-grade rating and time-to-maturity of 5 years or on March 23, 2020. Xit controls for log(Amt outstanding), log(Age), and log(Time-to-maturity): log of bond's amount outstanding, years since bond issuance, and years to maturity, respectively. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. The sample begins on March 6 and ends on April 9, 2020. Only U.S. firms are included; we exclude bonds that experience a change in credit grade. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Dependent variable: of the Fed's key policy interventions, the demand shock subsided relatively quickly, and fully, while the supply shock recovered more gradually, and only partially. Relative to the precrisis period, we find that the loss in consumers' surplus from immediacy was less pronounced than the increase in the relative price of immediacy, p ht − p lt , but remained suppressed well after markets had calmed.

In fact, we find customers' net utility from upgrading to faster, risky-principal trades remained approximately 10 basis points below precrisis levels even at the end of June 2020.

There are two types of agents: a measure N of customers and a measure one of dealers, all of whom are price takers. Each customer seeks to trade one share of an asset. We do not distinguish between purchases and sales; this simplification allows us to study the determinants of transaction costs, though it is worth noting that our model is silent on the determinants of the asset's price.

Since there are N customers with unit demand, the aggregate demand for transactions is exogenous and equal to N . However, while the total number of transactions is exogenous, the composition is not. Namely, we assume that customers demand vertically differentiated transaction services supplied by dealers at a convex cost: low-quality (l) transaction services, interpreted as agency trades, and high-quality (h) transaction services, interpreted as risky-principal trades.

Customers have quasi-linear utility for transaction services and for cash. Specifically, the problem of a customer is to choose how much low-and high-quality transaction services to demand from dealers at each time t in order to solve

sub. to x lt + x ht = 1.

We assume that u(x lt , x ht ) is increasing, concave, twice continuously differentiable, and satisfies

where the h and l subscripts denote first partial derivatives with respect to x ht and x lt , respectively. This condition simply means that the customer values highquality transaction services more than low-quality transaction services. The shock θ t in the objective captures time variation in customer's utility for upgrading agency trades into risky-principal trades, or what we call their demand for immediacy. 24

Assuming interior solutions, the first-order optimality conditions can be written

for some multiplier λ t on the constraint x lt + x ht = 1.

On the other side of the market, dealers choose their supply of transaction services, X lt and X ht , in order to maximize profits,

where C(X lt , X ht ) is some continuous, convex, and twice continuously differentiable cost function.

This leads to the first-order optimality conditions

Finally, the market clearing conditions for transaction services are simply

An equilibrium is thus described by a sequence {x lt , x ht , X lt , X ht , p lt , p ht } satisfying equations (6)-(9) at each time t.

Combining the assumption of fixed-size demand, (6), with the customers' first-order optimality conditions in (7), we can express customers' demand for immediacy as a single equation in two unknowns, (p ht − p lt ) and x ht :

This equation defines the inverse demand for immediacy: the relationship between the price premium for risky-principal trades and customers' marginal utility for upgrading from slow, agency trades to fast, risky-principal trades. As anticipated above, θ t is a demand shock that generates a parallel shift of this inverse demand curve.

Exploiting the market clearing conditions in (9), in conjunction with (6) and (8), similar steps reveal an equation that captures the dealers' willingness to supply immediacy:

Hence, the equilibrium characterization reduces to a price premium, p ht − p lt , and a fraction of risky-principal trades, x ht , that lies at the intersection of these demand and supply schedules.

This simple representation offers a parsimonious, transparent framework to analyze the effects of various types of shocks. First, shocks to consumers' relative preference for immediate, riskyprincipal trades, as captured by θ t , shift the demand, but not the supply, for immediacy. As is evident from panel A of Figure 4 , a positive innovation to θ t induces an increase in the relative price of risky-principal trades, along with an increase in the equilibrium fraction of such trades.

Alternatively, under natural conditions, 25 a surge in customer-to-dealer trading volume, as captured by an increase in N t , has no effect on each customer's demand for immediacy, but causes an upward shift in the supply curve, as providing risky-principal transaction services becomes more costly as the total volume of transaction services grows. Of course, any shock to the cost function C(·, ·)-perhaps due to an increase in intermediaries' risk aversion or cost of funding-would engender a similar shift in the supply curve. As is evident from panel B of Figure 4 , an upward shift in dealers' supply curve causes an increase in the price premium paid for risky-principal trades, but a decrease in the equilibrium fraction of such trades.

In the data, we observed, simultaneously, an increase in the price premium p ht − p lt (Figure 1) and a decrease in the fraction of risky-principal trade x ht (Figure 2) . According to the model, this is indicative of a supply shock. As noted above, a supply shock could have been generated by an increase in the total volume of transaction services which, when combined with binding balance sheet constraints, would make it more costly for dealers to supply risky-principal trades. Indeed, Figure 5 illustrates that customer-to-dealer volume was about 50 percent higher during the crisis, relative to the (average in the) same months in 2016-2019. The figure also shows that the increase in volume was quite persistent, remaining above normal levels through the summer. 25 For the interested reader, we spell out these conditions in Internet Appendix OA2. However, these data do not rule out shocks to the demand for immediacy (θ t ), as it is entirely possible that both the inverse supply and demand curves shifted in the same direction. To separately identify demand from supply shocks, we proceed in two steps. In this section, after imposing a specific functional form on customers' preferences, we estimate the parameter that determines the

post-crisis pre-crisis crisis θ Figure 6 . Identifying relative preference shocks, θ shape of the inverse demand curve by exploiting shifts to the supply curve that occurred during periods outside of the crisis, i.e., in "normal" times. Then, in Section 3.4, we use our estimated inverse demand curve to decompose movements in the price premium and the fraction of riskyprincipal trades during the crisis into movements that occur along the demand curve-caused by shocks to the cost function, including innovations to N t -and movements caused by innovations to θ t , which shift the demand curve.

We plot this basic intuition in Figure 6 . Note that this strategy is, by construction, largely independent of the shape of the supply curve and the nature of the shocks that shift it. However, by separately identifying shocks to the demand for immediacy from shocks to supply, we can study how the two responded differently to policy, and the quantitative implications for consumer surplus from immediacy throughout the pandemic, which we do in Sections 3.4 and 3.5, respectively.

Since x h and x l represent the market shares of high-and low-quality transactions in a vertically differentiated market, respectively, a natural choice for the demand curve is a logit specification. 26

In particular, we assume that, for each dollar of transaction service, the utility function of a consumer is given by

It is well known (see, e.g., Anderson, De Palma, and Thisse, 1992, p. 77 ) that this specification is equivalent to assuming that, for each dollar of transaction services, a consumer chooses between agency and risky-principal trades with net utilities 1 − p lt + ε lt and 1 + θ t − p ht + ε ht , respectively, where ε lt and ε ht are independently and identically distributed (IID) over time and across consumers according to Gumbel distribution with location parameter zero and scale parameter σ. 27

Given this parametric assumption, the inverse demand for immediacy takes a log-linear form:

As one would expect, a larger price premium, p ht − p lt , results in a lower demand for risky-principal

trades, x ht . In addition, one sees that the shape of the demand curve depends on just one semielasticity parameter, σ.

As is well known, a simple OLS regression of the price premium p ht − p lt on log quantities, log(x ht /x lt ), would yield a biased estimate of σ, since relative quantities are, in general, correlated with the relative demand shock θ t . Hence, we use an instrumental variable (IV) approach to estimate the parameter of interest, σ.

To do so, consider an arbitrary instrument Z t for the log relative quantities log(x ht /x lt ). Using the inverse demand specification in (13), one easily sees that

Hence, as is well known, β IV is an unbiased estimator of σ when the instrument Z t is uncorrelated with the demand shock θ t .

Consider observations about prices and relative quantities in two periods: a precrisis period, such as January 2020; and a postcrisis period, such as June 2020. Suppose the instrument Z t takes the value zero in the precrisis period and 1 in the postcrisis period. Since

In other words, as long as the relative demand shock in the postcrisis period has returned to its precrisis average, then it is uncorrelated with the binary instrument, Z t . Of course, we also need the binary instrument to be relevant, that is, correlated with the relative quantities. However, this is verified empirically because, as shown in Figure 2 , relative quantities in the postcrisis period are lower than in the precrisis period. We interpret this observation as follows: as shown in Figure 5 , the trading volume in June remained elevated relative to prepandemic levels, a fact that, in our model, shifts the marginal cost of providing transaction services and creates a supply shock. In equilibrium, the relative quantities demanded by consumers are reduced along a fixed demand curve.

The binary IV approach leads to the following candidate estimate:

where T 0 and T 1 are the lengths of pre-and postcrisis periods in days, respectively. For the estimation, we set the precrisis period to run between January 15, 2020, and February 14, 2020, and the postcrisis period to run between June 1, 2020, and June 30, 2020. We obtain an estimate ofσ = 100.09 with a standard deviation of 15.40. 28 28 Our assumption that θt returned to precrisis levels by June 2020 is supported by a variety of evidence. For example, consistent with our own findings, Haddad, Moreira, and Muir (2020) document that the severe dislocations in the corporate bond market disappeared soon after the Fed's interventions. Falato, Goldstein, and Hortaçsu (2020) and Ma, Xiao, and Zeng (2020) offer further evidence, establishing that bond mutual funds and ETFs experienced record inflows in April and May after massive outflows in March 2020. However, for robustness, we perform a second binary IV estimation that does not rely on the assumption that EJan [θt] = EJun [θt], but rather that θt had settled down to some (arbitrary) level by May 2020. In particular, we assume that the average value of θt in the first half of May is equal to the average value in the second half of June, and repeat a similar estimation procedure to the one described above. We arrive at an estimate ofσ = 80.06, within 1.3 standard deviations of our initial binary IV

An alternative approach to estimating σ is to use high frequency variation in trading conditions that affect prices and quantities but are unlikely to be attributable to aggregate shocks to customers' preferences for risky-principal trades. According to our theory, changes in N t -which could equivalently represent the total volume of trade or the total number of trades (since trade size is fixed)-change the dealers' cost of supplying transaction services, but do not change individual consumers' relative demand for risky-principal trades. 29

Hence, we consider two instruments to measure deviations in the quantity of customer-dealer trading: one based on trading volume and the other based on the number of trades in each day. Importantly, we exclude the crisis period March 1, 2020, to April 15, 2020, as shocks to relative demand during this period are likely significant and correlated with changes in both measures of N t . We seasonally adjust and detrend (by adding month dummies) log(N t ) for both measures, so that shocks represent the residual deviation. After constructing these series, the formal exclusion restriction for the IV estimate to be consistent is Cov (log(N t ), θ t ) = 0. Relative to the first binary IV, this approach has one advantage: it does not assume that the relative demand shock θ t has returned to normal in June. Table 5 presents the estimates of σ that emerge from our high frequency IV. The estimates range from 70 to 73 depending on the instrument, falling near the lower bound of the confidence interval of the binary-IV estimates. 30

In this section, we discuss our model's (qualitative and quantitative) implications for the relative importance of shocks to customers' demand for immediacy and dealers' willingness to supply it over approach. We provide more details about both binary IV estimations in Appendix D.

29 Intuitively, one could imagine that dealers cannot fully adjust the size of their balance sheets or their trading infrastructure in the short term (our time period is a day). Thus, in the short run, an increase in the number of market participants or trading volume could put upward pressure on dealers' cost of providing immediacy, changing the relative prices of risky-principal and agency trades without shifting relative demand. Importantly, note that we are assuming that innovations to Nt are uncorrelated with customers' relative demand for risky-principal trades, and not with customers' aggregate demand for transaction services.

30 As a robustness check, in Appendix D, we combine both our instruments and estimate the overidentified system using two-stage least square (2SLS). We also provide first-stage results for each IV regression verifying that each one is a valid instrument. For our 2SLS, where we use both number and volume as instruments, we provide test statistics for the Sargan-Hansen test of overidentifying restrictions. Table 5 . Estimating the logit demand parameter σ using high-frequency IV approach. This table presents the IV estimates of the logit demand parameter σ. In column 1, the seasonally adjusted log volume of trades is used as an instrument. In column 3, the seasonally adjusted log number of trades is used as an instrument. Standard errors are the maximum of robust and the usual standard errors. The precrisis runs from January 3, 2020, until February 29, 2020. The postcrisis data begin April 15, 2020, and run until July 31, 2020. We exclude holidays, weekends, and half trading days. Our estimates and standard errors are transformed using the delta-method where appropriate. *p <.1; **p <.05; ***p <.01. the course of the COVID-19 crisis and the interventions that followed.

To start, given an estimate of the semielasticity parameter σ, along with the time series for the price premium (p ht − p lt ) and the ratio of agency trades to risky-principal trades (x lt /x ht ), we can infer the sequence of shocks to customers' relative demand for risky-principal trades (θ t ). Using our estimate of σ from the binary IV described above,σ = 100.09, Figure 7 plots the time series relative to a precrisis benchmark, θ t − θ 0 , where θ 0 is the inferred value of θ on January 2, 2020. 31

Not surprisingly, the figure reveals that θ t experiences a dramatic increase during the most tumultuous weeks of March. In fact, our estimates suggest that customers' willingness to pay for each inframarginal unit of risky-principal trade (rather than an agency trade) increased by approximately 200 bps at the height of the crisis, before receding quickly after the announcements of the Fed's interventions. To gain a sense of the effect of this shock, note that we can decompose 31 Our results are largely independent of which estimate we use, as is clear from the error bands in the plots. This is because the estimate ofσ from the high-frequency IV estimation lies within two standard deviations of the estimate from the binary IV and because log quantities vary less than the price premium. F e b -1 9 M a r -0 5 M a r -1 8 M a r -2 3 A p r -0 9 M a y -1 2 J u n -1 6 J u n -2 9 Change in realtive demand shocks, θ t − θ 0 (bps)

This figure plots the time series of the change in the estimated relative demand shocks for risky-principal trades relative to a precrisis benchmark on January 2, 2020, θt − θ0, implied from Equation (13). Plus and minus two standard deviation bands are shown in gray. The shaded areas correspond to the early and late periods used to estimate the semielasticity parameter σ. the change in the price premium if we assume that supply is perfectly inelastic:

In general, this decomposition depends on the relative elasticity of demand and supply. However, we believe that the case of a perfectly inelastic supply is a natural benchmark, for two reasons.

First, it delivers an upper (lower) bound for the contribution of demand (supply) shocks to the price premium. Second, the assumption of an inelastic supply accords with reports of binding balance-sheet constraint at the height of the crisis, and is seemingly confirmed by our evidence on dealers' inventory accumulation from Figure 3 .

According to this decomposition, a large portion of the spike in the cost of risky-principal trades (relative to agency trades) at the height of the crisis can be explained by relative demand shocks. For example, the average value of p ht − p lt over the time period March 5 to April 9 was 75 bps higher than the value on January 2. The portion of this increase in the price premium that can be explained by the demand shifter was 58 bps, or approximately 75%. Hence, our results are consistent with other studies that highlight the "dash for cash" as an important driver of the turmoil in the corporate bond market (see, e.g., Falato, Goldstein, and Hortaçsu, 2020; Ma, Xiao, and Zeng, 2020; Haddad, Moreira, and Muir, 2020) .

However, an increase in the demand for immediacy alone would generate an increase in x h , as in Figure 4 , which is opposite of what we observe in the data. Therefore, a second key takeaway from our analysis is that the onset of the pandemic must have also induced a negative shock to dealers' willingness to use their balance sheet space to accommodate the surge in selling pressure. Indeed, within the context of Figure 6 , our results suggest that the relative supply of risky-principal trades would have to experience a significant shift to the left in order to induce a drop in x h . Thus, in addition to a surge in customers' demand for immediacy, our analysis reveals an equally important shock to dealers' costs of supplying immediacy; simply put, matching the data on prices and quantities requires an increase in the expected cost of dealers adding inventory to their balance sheets, as documented in the Treasury market by He, Nagel, and Song (2020) . 32

Finally, studying the behavior of the series {θ t , p ht −p lt , x ht } against the timeline of the Fed's interventions reveals important, new insights into the channels through which various policies affected market liquidity. First, the time path of relative preference shocks suggests that the announcement of the Fed's interventions was enough to halt and reverse the "dash for cash" that began in the second week of March. To explore the relationship between customers' preferences and the Fed's interventions in greater depth, we can estimate the time path of θ t separately for those bonds that were eligible versus ineligible for purchase according to the March 23rd announcement of the corporate credit facilities; Figure 8 plots the results. 33 The figure reveals that the Fed's announcement had a more immediate impact on the relative demand for risky-principal trades of eligible bonds, relative to ineligible bonds. Taken together with the results in Table 4 , it appears that the expectation of price support from the Fed played an important role in halting the rush among customers to liquidate corporate debt immediately, and thus helped to reduce bid-ask spreads for risky-principal trades.

32 Studying the market for mortgage-backed securities (MBS), Chen et al. (2020) also find that the combined liquidity constraints of customers and dealers are responsible for the severe price dislocations observed during the COVID-19 pandemic. 33 We provide more details about estimated preference shocks for eligible and ineligible bonds in Appendix E. 200 J a n -1 9 J a n -1 9 F e b -1 9 M a r -0 5 M a r -1 8 M a r -2 3 A p r -0 9 M a y -1 2 J u n -1 6 J u n -2 9 Change in relative demand shocks, θ t − θ 0 (bps) eligible bonds ineligible bonds

This figure plots the time series of the change in the estimated relative demand shocks for risky-principal trades relative to a precrisis benchmark on January 2, 2020, θt − θ0, implied from Equation (13), for eligible and ineligible bonds. The shaded areas correspond to the early and late periods used to estimate the semielasticity parameter σ.

After the dash for cash subsided, and the demand curve shifted down, we observe that x h does not decrease, but rather increases slightly. Hence, it must be that the announced interventions also reduced dealers' perceived cost of supplying risky-principal trades, shifting their supply curve to the right and inducing them to absorb inventory onto their balance sheet, as documented in Figure   3 . However, the fact that the price premium and the fraction of agency trades remained elevated, even months after the initial shock appears to have passed, suggests that the supply curve did not return to its original location, i.e., that balance sheet costs remained higher than precrisis levels despite calmer markets and the Fed's interventions. These costs could derive from persistently high trading volume (as documented in Figure 5 ), from expectations of future price declines or volatility, or from losses incurred on other parts of the dealers' balance sheets.

The analysis above highlights the important distinction between risky-principal and agency trades during the COVID-19 crisis: we have shown that customers' demand for immediacy increased drastically at the height of the crisis, while dealers' willingness to supply immediacy by accumulating inventory on their balance sheets simultaneously declined. In this section, we attempt to quantify the effects of these pandemic-induced shocks-and the interventions that followed-on the net utility that customers derived from immediacy. 34

Given equilibrium prices and allocations, we define the consumer surplus from immediacy, per dollar of transaction, as

For each dollar of transaction, s ht measures the customers' extra value of upgrading a fraction x ht of agency trades into risky-principal trades, at a cost (p ht − p lt ) x ht . 35

Namely, based on (6) and (10), one obtains

34 Note that we are intentionally not making any statements about optimal policy interventions or design. As we will describe in greater detail below, our definition of consumer surplus from immediacy does not account for possible aggregate shocks to customers' demand for transaction services, nor does it capture any effects of prices and allocations in the corporate bond market on real investment decisions, possible linkages between corporate bond market liquidity and other funding markets, and so on. While certainly interesting, these extensions are beyond the scope of the current paper. 35 We could also study the total surplus from all transaction, s ht − p lt . However, this measure could be biased, since our analysis of customer demand only identifies shocks to the demand for upgrading from risky-principal to agency trades, and not shocks to the overall demand for transaction services. There are at least two reasons to analyze the surplus from immediacy, as opposed to the total surplus. First, the bulk of the variation in transaction costs during the crisis, p lt x lt + p ht x ht , is accounted for by the cost of immediacy, (p ht − p lt )x ht . Second, much of the policy discussion surrounding the crisis was focused on the demand and supply for immediacy: customers' need to trade quickly and dealers' willingness to accommodate their demand with risky-principal trades that would have used their balance sheet space.

where the final equality follows from integration by parts. The term − [u hh − 2u lh + u ll ] in the integral represents the slope of the inverse demand curve. Hence, the integral measures the area between the price premium and the inverse demand curve and so captures the surplus from upgrading from low-quality to high-quality transaction services.

Notice that the demand shock θ t does not appear in the surplus from immediacy (16). Indeed, for any fixed x ht , the surplus from immediacy is the same regardless of the location of demand. This is because a parallel shift to the inverse demand curve increases the willingness to pay for all infra-marginal units by the same amount, θ t . Put differently, when θ t increases but x ht stays the same, customers derive more utility from immediacy but pay more for it, with zero net effect on their surplus. Of course, in equilibrium, x ht does not stay the same: hence the change in surplus from immediacy between time zero and time t is the consequence of customers substituting from risky-principal to agency trades:

In other words, what ultimately makes consumers worse or better off is the net effect that the supply and demand shocks have on the quantity of risky-principal trades consumed in equilibrium.

With the logit specification, − (u hh − 2u lh + u ll ) = 1/[y(1 − y)] and so we obtain a simple, closed-form expression for the change in the surplus from immediacy between time zero and time t:

Using Equation (17), together with our estimate of σ, Figure 9 plots the change in consumer surplus from immediacy, per unit of transaction, over time. The figure reveals, not surprisingly, that there was a sharp, significant decline at the height of the market turmoil in mid-March 2020.

However, the figure also reveals that this decline was persistent: consumer surplus from immediacy per unit of transaction remained approximately 10 bps below precrisis levels even at the end June.

Comparing the dynamics of the surplus from immediacy to the expenditures on immediacy, (p ht − p lt )x ht , reveals two important differences. First, one can easily confirm that the decline in the surplus from immediacy is much smaller than the increase in expenditures. Second, the recovery takes longer to materialize and is less dramatic. As explained above, these differences arise because the surplus from immediacy accounts for two additional effects that matter for evaluating consumer well-being. First, customers' preference for immediacy change: this implies that the surplus loss induced by the increase in immediacy expenditure is partly offset by the additional value derived from immediacy. Second, the composition of transaction services changes as well: consumers substitute toward agency trades, so that the average quality of transaction services they enjoy falls.

We believe these observations serve as an important reminder that changes in consumers' well-being is often not well-approximated by changes in prices.

It often takes a bad shock to discover whether or not a market is liquid, and to expose any sources of illiquidity. Unfortunately, many shocks to financial markets originate inside financial intermediaries, and hence the aggregate shock is a liquidity shock. In this sense, the COVID-19 pandemic-a truly exogenous, large shock that did not originate in the banking sector-offers a unique opportunity to study market conditions, the shocks that precipitate episodes of illiquidity, and the implications for transaction costs, policy, and consumer surplus.

In this paper, we study trading conditions in the U.S. corporate bond market from many angles as the COVID-19 pandemic unraveled. However, a key insight is that distinguishing between riskyprincipal and agency trades offers not only a more complete assessment of market conditions but also a unique window into the sources of illiquidity and the efficacy of policy interventions in this large, important market. In particular, we find that the initial panic was caused by shocks to both customers' demand for immediacy and dealers' willingness to supply it. The former shock receded quickly, and almost fully, after the mere announcement of the Fed's intention to enter the market and purchase bonds. The latter shock, however, lingered months after markets appeared to calm, indicating that elevated trading volume in conjunction with balance sheet constraints remain a risk in times of crisis.

While this is an important first step, much work remains to be done. Perhaps most importantly, further examination of dealers' balance sheets and changes (or heterogeneity) in regulatory requirements could allow us to pinpoint the precise source of dealers' unwillingness to "lean against the wind" during times of crisis. Identifying and understanding these constraints would allow us to design better policies to balance the crucial trade-off between risk-taking and liquidity provision often at the heart of liquidity provision in financial markets. We leave this work for the future.

We use data from the Trade Reporting Compliance Engine (TRACE) made available by the Financial Industry Regulation Authority (FINRA). The raw TRACE data provides detailed information on all secondary market transactions self-reported by FINRA member dealers. These include bond's CUSIP, trade execution time and date, transaction price ($100 = par), the volume traded (in dollars of par), a buy/sell indicator, and flags for dealer-to-customer and inter-dealer trades.

To construct our sample, we combine two versions of TRACE: the standard version (2020Q1), and the end-of-day version (2020Q2).

We first filter the report data following the procedure laid out in Dick-Nielsen (2014). We merge the resultant data set with the TRACE master file, which contains bond grade information, and with the Mergent Fixed Income Securities Database (FISD) to obtain bond fundamental characteristics.

Following the bulk of the academic literature, we exclude bonds with optional characteristics, such as variable coupon, convertible, exchangeable, and puttable, as well as asset-backed securities and private placed instruments. Table A1 provides summary statistics for our sample.

In our empirical specifications, we exclude newly issued securities (with age less than 90 days), as on-the-run bonds tend to trade differently than off-the-run securities. Since our sample only contains about 130 days, the age and time-to-maturity of a particular bond will vary little over time. Thus, we do not include the standard cross-sectional controls related to the bond's age or time-to-maturity. Furthermore, since we exclude newly issued bonds, over time, the age (maturity) of any bond will increase (decrease) by one day each day. Thus, the average age (maturity) of our bonds will increase (decrease) monotonically over time, meaning these controls will also correlate with the time trends we are documenting.

We also distinguish between bonds that are eligible for the SMCCF and ineligible bonds. In Appendix B, we present a detailed description of eligibility criteria for the SMCCF. We define a bond as eligible if it has investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020, when the SMCCF was first announced. The eligibility criteria also state that the firm must be a U.S.-domiciled corporation. Specifically, the Fed restricts its purchases to bonds where The issuer is a business that is created or organized in the United States or under the laws of the United States with significant operations in and a majority of its employees based in the United States.

This criterion leaves the Fed with a considerable degree of discretion. For instance, if a foreigndomiciled corporation uses a U.S. subsidiary to issue dollar-dominated debt, our firm-level data identify the firm as a non-U.S. firm. We would then classify its bonds as foreign, making them ineligible for the SMCCF. However, under the Fed's definition of a U.S. issuer, the bonds may be Table A1. Summary statistics  This table provides the mean, standard deviation, median, 5th and 95th percentiles of the average daily number of trades and volume by counterparty type, proportion of agency trades, proportion of trades on IG bonds, proportion of trades on the bonds eligible for SMCCF, and daily average trading cost for risky-principal (CH) and agency trades (MIRC) for eligible and ineligible bonds respectively. "Num" refers to number of trades, and the "vol" refers to volume of trades in par value. A bond is considered eligible for the SMCCF if it has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. The sample starts on January 3 and ends on June 30, 2020. Sources: TRACE and FISD. eligible for purchase. Using the Fed's SMCCF transaction-level disclosures, we find that in many cases, the holding firm of the security is a non-U.S. entity. 36 One such example is British American Tobacco (BAT), a firm listed on the London Stock Exchange and domiciled in the UK. Our firmlevel data correctly identifies this firm as foreign; however, its bonds were purchased by the Fed. 37

These bonds were issued by a U.S. wholly-owned subsidiary of BAT, BAT Capital Corporation.

Since this subsidiary is guaranteed and wholly-owned by BAT, correctly classifying these bonds as U.S. domiciled is a very challenging task. We, therefore, will not use U.S. versus non-U.S. as an SMCCF eligibility criterion in our regressions discussed below, and we focus on U.S. firms.

Moreover, we do not have access to the latest credit rating data for all bonds in our sample.

For the subsample of bonds for which the credit rating is available, we include a credit rating fixed 36 SMCCF transaction-specific disclosures are provided by the Federal Reserve and are available at https://www. federalreserve.gov/monetarypolicy/smccf.htm. 37 On July 10, 2020, the Fed reported that BAT's bonds were purchased as part of the SMCCF (CUSIP 05526DAZ8). effect to control for potentially time-invariant nature of bond credit ratings.

We choose the following dates to highlight in the figures with vertical, dashed lines: January 19: beginning of the series, chosen to start the sample period one month before the stock market peak.

March 5: beginning of extended fall in equity prices and rise in corporate credit spreads.

March 18: first day of trading after announcement of Primary Dealer Credit Facility (announced evening of March 17).

April 9: expansion of PMCCF and SMCCF (in both size and scope).

May 12: the SMCCF began purchasing eligible ETFs.

June 29: the PMCCF began operating.

We define agency trades as two trades in a given bond with the same trade size that take place within 15 minutes of each other. For each bond, we divide its trading sample into three groups: customer-sell-to-dealer (C2D), dealer-sell-to-customer (D2C), and interdealer (D2D) trades. Our identification of agency trades includes the following steps:

1. We match each trade X in group C2D with a trade Y in group D2C that has the same trade size and happens within 15 minutes of X. If several trades in D2C satisfy these conditions, we choose the trade that takes place closest in time to X. The identified pair of agency trades is then (X, Y ). After this step, we denote the collection of unmatched trades in C2D as u-C2D and that in D2C as u-D2C.

2. We match each trade in u-C2D with a trade in group D2D by the same algorithm. We then obtain a collection of unmatched trades in D2D, denoted by u-D2D.

3. We match each trade in u-D2D with one in u-D2C following the same algorithm. 4. We repeat steps 1-3 using all remaining unmatched trades in the three groups while relaxing the matching criteria. In each agency trade pair, we require the second trade to happen within 15 minutes of the first trade, but it can have a smaller trade size than the first one.

By doing so, we consider the situation in which dealers split the trade volumes when they behave as matchmakers.

5. Finally, within all the remaining unmatched trades after steps 1-4, we identify trades with field remuneration == "C" in TRACE (commission is included in the price) as agency trades, because, by FINRA's definition, broker-dealers receive commissions only when they intermediate agency trades. 2. The issuer was rated at least BBB−/Baa3 as of March 22, 2020, by a major nationally recognized statistical rating organization ("NRSRO"). If rated by multiple major NRSROs, the issuer must be rated at least BBB−/Baa3 by two or more NRSROs as of March 22, 2020.

38 For more details, see the Frequently Asked Questions for PMCCF and SMCCF from the New York Fed, available at https://www.newyorkfed.org/markets/primary-and-secondary-market-faq/corporate-credit-facility-faq.

39 Source: Secondary Market Corporate Credit Facility Term Sheet available from https://www.federalreserve. gov/newsevents/pressreleases/files/monetary20200728a1.pdf, last updated on July 28, 2020.

(a) An issuer that was rated at least BBB−/Baa3 as of March 22, 2020, but was subsequently downgraded, must be rated at least BB−/Ba3 as of the date on which the Facility makes a purchase. If rated by multiple major NRSROs, such an issuer must be rated at least BB−/Ba3 by two or more NRSROs at the time the Facility makes a purchase.

(b) In every case, issuer ratings are subject to review by the Federal Reserve.

3. The issuer is not an insured depository institution, depository institution holding company, or subsidiary of a depository institution holding company, as such terms are defined in the Dodd-Frank Act.

4. The issuer has not received specific support pursuant to the CARES Act or any subsequent federal legislation.

5. The issuer must satisfy the conflicts of interest requirements of section 4019 of the CARES Act.

In Table A2 , we repeat the OLS regression in column 1 of Table 2 but focusing only on bonds issued by U.S. firms. In columns 2 and 3, we repeat the regression in column 1 restricting the sample to eligible and ineligible bonds, respectively. As before, a bond is considered eligible if it has an IG credit rating and remaining time-to-maturity of 5 years or less.

Results in column 1, for U.S. bonds, are very similar to what shown in column 1 of Table A2 for all bonds. From columns 2 and 3, we observe that the shift toward agency trades was much more pronounced among bonds that were eligible for the Fed's purchasing program. The probability of an agency trade for a given eligible bond, on average, rose by approximately seven percentage points relative to the precrisis period. After the Fed interventions on March 23, this probability decreased from the crisis period (by 200 bps) to five percentage points higher than the precrisis period. For ineligible bonds, in contrast, the probability of an agency trade rose by only 1.9 percentage points relative to the precrisis period and remained relatively unchanged after the Fed intervention.

In this subsection, we present several robustness checks for the difference-in-differences (DID) results in Section 2.5.

First, in Table A3 , we repeat the regressions in Table 4 but focusing only on bonds just above and below the SMCCF eligibility threshold for time-to-maturity (TTM): bonds with four to six years left to maturity. 

This table presents regression results for the following specification from: Agency ijt = αi + αs + β1 × Crisist + β2 × Interventiont + εijt. The dependent variable, Agency ijt , is an indicator variable that takes the value of one if trade j for bond i on day t is an agency trade and zero otherwise. Only U.S. firms are included in the regression. Crisist and Interventiont are dummies that take the value of one if day t falls into Crisis and Intervention subperiods defined above. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. A bond is considered eligible if it has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. The sample starts on January 3 and ends on June 30, 2020. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01. Next, in Table A4 , we repeat the regressions in Table A3 but adding the extra restriction that the bonds should be close to the IG-HY threshold. In particular, we only include bonds that in addition to having TTM of four, five and six years, are also rated at the bottom tier of investment-grade (BBB+/Baa1, BBB/Baa2, and BBB−/Baa3) or the top tier of high-yield (BB+/Ba1, BB/Ba2, and BB−/Ba3).

Here we run the regressions in (4) but with the trades of a particular size category in a different regression. In Tables A5-A7, we show that small and large trades are responsible for the entire liquidity improvement documented in Table 4 : small trades (with par volume of $100,000 or less) become much more liquid after the Fed's CCF announcements followed by large trades (with volume larger than $1 million). Liquidity of odd-lot trades (with volume between $100,000 and $1 million) seem to be unaffected by the Fed's intervention. Curiously we fail to find an affect for Odd-lot trades. Some evidence, for example, Feldhütter (2012) , suggests that trades with different sizes are affected differently by market turmoil. (4): yijt = αs + α k + β1 × SMCCFt × Eligible t + β2 × SMCCFt + β3 × Eligible t + γ × Xi,t + εijt. The dependent variables are measures of transactions costs for risky-principal and agency trades. SMCCFt is a dummy that takes the value of one if day t falls between March 23 and April 9, and zero otherwise. Eligible t takes the value of one if the bond has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. Xit controls for log(Amt outstanding), log(Age), and log(Time-to-maturity): logs of bond's amount outstanding, years since bond issuance, and years to maturity, respectively. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. The sample begins on March 6 and ends on April 9, 2020. Only U.S. firms, bonds with 4, 5, or 6 years left to maturity on the intervention date are included. We exclude bonds that experience a change in credit grade. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Risky-principal Agency (4): yijt = αs + α k + β1 × SMCCFt × Eligible t + β2 × SMCCFt + β3 × Eligible t + γ × Xi,t + εijt. The dependent variables are measures of transactions costs for risky-principal and agency trades. SMCCFt is a dummy that takes the value of one if day t falls between March 23 and April 9, and zero otherwise. Eligible t takes the value of one if the bond has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. Xit controls for log(Amt outstanding), log(Age), and log(Time-to-maturity): logs of bond's amount outstanding, years since bond issuance, and years to maturity, respectively. There are three trade size categories: less than $100,000, between $100,000 and $1 million, and larger than $1 million. The sample begins on March 6 and ends on April 9, 2020. Only U.S. firms, bonds with 4, 5, or 6 years left to maturity that are rated at the bottom tier of IG (BBB+/Baa1, BBB/Baa2, and BBB−/Baa3) or the top tier of HY (BB+/Ba1, BB/Ba2, and BB−/Ba3) are included. We exclude bonds that experience a change in credit grade. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01. where, with some abuse of notation, θ τ is the average relative demand shifter in period τ ∈ {A, B}, and ε t is a mean zero shock. The supply equation is assumed to have the following form

where η t is a mean zero supply shock, and N t is the customer-to-dealer volume. Consistent with our model, N t enters in the supply equation because it increases the marginal cost of providing transaction services. It does not enter the demand equation because the total utility for transaction (4): yijt = αs + α k + β1 × SMCCFt × Eligible t + β2 × SMCCFt + β3 × Eligible t + γ × Xi,t + εijt. The dependent variables are measures of transactions costs for risky-principal and agency trades. SMCCFt is a dummy that takes the value of one if day t falls between March 23 and April 9, and zero otherwise. Eligible t takes the value of one if the bond has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. Xit controls for log(Amt outstanding), log(Age), and log(Time-to-maturity): logs of bond's amount outstanding, years since bond issuance, and years to maturity, respectively. The sample begins on March 6 and ends on April 9, 2020. Only trades that are less than $100,000 in par volume, that is, micro trades, are included. We exclude bonds that experience a change in credit grade. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Risky-principal Agency services is linearly homogeneous: the utility of a given bundle of transaction service is the same for each dollar of transaction. We assume, moreover, that volume is smaller in the earlier period (A) than in the later period (B). 40 Formally, this can be written log(N t ) = log(N τ ) + ξ t , where ξ t is a mean zero shock, τ ∈ {A, B} and N A > N B .

Solving the system of simultaneous equations gives

Using an unpaired two-sample t-test, we test whether that the volume is smaller in the earlier period (A) than in the later one (B). We first check whether the variance of log volume is similar in the two periods using an F -test. The null hypothesis is that the variance of log volume is the same in both period. The value of the test statistic is 0.32, corresponding to a p-value of .012. Hence, we fail to reject the equality of variances for log volume (in level variances seem different, which is why we did it in logs). Next, we do a one-sided t-test. The null hypothesis is that volume is smaller in the period A than in period B. The value of the test statistic is −0.97 corresponding to a p-value of .83. Again, we fail to reject the null that volume is smaller in period A than in period B. (4): yijt = αs + α k + β1 × SMCCFt × Eligible t + β2 × SMCCFt + β3 × Eligible t + γ × Xi,t + εijt. The dependent variables are measures of transactions costs for risky-principal and agency trades. SMCCFt is a dummy that takes the value of one if day t falls between March 23 and April 9, and zero otherwise. Eligible t takes the value of one if the bond has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. Xit controls for log(Amt outstanding), log(Age), and log(Time-to-maturity): logs of bond's amount outstanding, years since bond issuance, and years to maturity, respectively. The sample begins on March 6 and ends on April 9, 2020. Only trades greater than $100,000 and less than $1 million in par volume, that is, odd-lot trades, are included. We exclude bonds that experience a change in credit grade. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Risky-principal Agency and (4): yijt = αs + α k + β1 × SMCCFt × Eligible t + β2 × SMCCFt + β3 × Eligible t + γ × Xi,t + εijt. The dependent variables are measures of transactions costs for risky-principal and agency trades. SMCCFt is a dummy that takes the value of one if day t falls between March 23 and April 9, and zero otherwise. Eligible t takes the value of one if the bond has an investment-grade rating and time-to-maturity of 5 years or less on March 23, 2020. Xit controls for log(Amt outstanding), log(Age), and log(Time-to-maturity): logs of bond's amount outstanding, years since bond issuance, and years to maturity, respectively. The sample begins on March 6 and ends on April 9, 2020. Only trades greater than or equal to $1 million in par volume, that is, large trades, are included. We exclude bonds that experience a change in credit grade. Clustered standard errors at the day and bond levels are shown in parentheses. *p <.1; **p <.05; ***p <.01.

Risky-principal Agency It thus follows that, if θ A = θ B :

Thus, an estimator of σ is obtained by replacing the conditional expectations by sample averages.

To be more precise, we let Y t = p ht − p lt log(x ht /x lt ) denote the vector of observations at time t. Assume for now that all the vector of disturbances, (u t , v t , w t ) are IID over time with finite covariance matrices. The estimate of the mean vector over periods A and B are:

where T τ denotes the number of observations in period τ . Then, the weak Law of Large Numbers implies that sample means converge in probability to their population counterpart, Y τ , as T τ goes to infinity. The Central Limit Theorem implies that √ T τ Ŷ τ − Y τ is asymptotically normally distributed with mean zero and covariance matrix S. Moreover, these two random variables are also independent. Since Y t − Y τ , τ ∈ {A, B} are IID, an unbiased and consistent estimator of S isŜ

The estimate of σ can be written aŝ

where the 1 and 2 subscripts denote the first and second coordinates of the Y vector. By standard delta method, we thus have that

By symmetry it is clear that

have the same asymptotically normal distribution, with mean 0 and variance

It thus follows that the estimateσ is asymptotically normal with mean σ and standard deviation

A consistent estimate of the standard deviation is found by replacing S byŜ, and the population means in ∂f /∂Y A by their sample counterparts.

For the estimation we set the early period A to run between 2020-01-15 and 2020-02-14, and the late period B to run between 2020-06-01 and 2020-06-30. We use the raw series for x h and x l , not their moving average, so as not to artificially reduce standard errors. We obtain an estimate ofσ = 100.09 with a standard deviation of 15.4.

One may argue that the assumption underlying our IV estimation, E Jan [θ t ] = E Jun [θ t ], is too strong. A key concern is that, by May 2020, θ t has not returned to its precrisis level. Instead, it has stabilized to a "new normal": it is lower than at the height of the crisis, but higher than before the crisis.

To address this concern, we reestimate σ under this "new normal" assumption. We take the initial period T A to be from May 1 to May 15, 2020 and the final period T B to be from June 15 to June 30, 2020. Our assumption is that the average level of θ t is the same in both periods. Figure   5 suggests that the volume of customer-to-dealer trades declined significantly between periods T A and T B : following the same logic as in Section 3.3.2, we argue that this decline in volume shifted the supply curve for risky-principal trade, leading to the estimatê

This calculation leads to an estimate ofσ = 80.06 which is close to our other estimates. Given this value of the semielasticity of demand, we can infer a new series for the demand shock as we did in Section 3.4.

θ t − θ 0 =σ [log (x lt /x ht ) − log (x l0 /x h0 )] − (p ht − p lt − (p h0 − p l0 )) .

As before, we take t = 0 to be January 2, 2020.

In Figure A1 , we plot the implied demand shocks from the four different estimates of the semielasticity parameter σ: two binary IVs (solid blue and dashed red line) and two high-frequency IVs (green dotted and orange dashed-dotted lines). As we can see from Figure A1 , the demand shock is at a stable level between early May and late June. Notice that the "new normal" assumption only implies that the average level in those subperiods would be the same and does not imply stability in between those periods. More importantly, we do not make an assumption on the level at which the demand shock would stabilize, yet we find that it is remarkably close to the precrisis level.

The figure reveals that our estimates are quite robust: despite the fact that these estimation procedures derive from significantly different identification assumptions and strategies, the implications for our estimate of θ t -and hence the discussion in Section 3.4-is essentially unchanged. J a n -1 9 J a n -1 9 F e b -1 9 M a r -0 5 M a r -1 8 M a r -2 3 A p r -0 9 M a y -1 2 J u n -1 6 J u n -2 9 Change in realtive demand shocks, θ t − θ 0 (bps) σ = 100.09σ = 80.06σ = 70.17σ = 73.31 Figure A1 . The change in the estimated relative demand shocks for risky-principal trades for different estimates of the semielasticity parameter σ This figure plots the time series of the change in the estimated relative demand shocks for risky-principal trades relative to a precrisis benchmark on January 2, 2020, θt − θ0, implied from the logit demand, p ht − p lt = −σ log (x ht /x lt ) + θt, for four values for parameter σ.

In this section, we provide additional details and robustness results for the high-frequency IV method discussed in Section 3.3.3. 41 Table A8 presents our estimates for σ from an overidentified IV. All specifications contain a postcrisis dummy variable allowing for a one-time shift in the demand curve. This method gives us an estimate of σ of 73.10, that lies between the two individual IV estimates in columns 1 and 2 from Table 5 . The weak instrument test statistic is 11.172. Here, we have an overidentified system, so we obtain the Sargan J-test statistics. The value of the test statistic is 0.057, and the p-value of .81. So we fail to reject the validity of the overidentification restrictions.

In Table A9 , we present the first stage of our IV regressions for each instrument. We find that both log number and volume of trades are valid instruments for log (x h /x l ). The F -stat for the weak instruments test is 16.731 in the case of volume and 22.509 for the number of trades. In both cases, we therefore reject the null that the instruments are weak at the 1% level. Both instruments have a correlation of 0.88. 41 In Internet Appendix OA4 we provide IV estimation results for the full sample from January to July, 2020. 

To explore the relationship between customers' preferences and the Fed's interventions in greater depth, we can estimate the time path of θ t separately for those bonds that were eligible versus ineligible for purchase according to the March 23rd announcement of the corporate credit facilities.

According to the eligibility requirements specified in the March 23, 2020, announcement of the SMCCF, we divide the whole sample of transactions into two subsamples, one for eligible bonds and the other for ineligible bonds. We identify eligible bonds as the ones with an investment-grade rating on March 23, a time-to-maturity of five years or less by March 23, and its issuer domiciled in the U.S. In particular, we calculate each bond's time-to-maturity by March 23 as the gap in days between its maturity date and the date of March 23. We set all the other bonds as ineligible ones. Then we use the two subsamples of transactions to correspondingly generate two samples of observations on prices and relative quantities, and separately estimate the time path of θ t for each sample.

Then given the estimate of the semielasticity parameter σ for all bonds, using the time series of the price premium and the ratio of the risky-principal trades for eligible and ineligible bonds, we can infer the sequence of shocks to customers' relative demand shock for eligible and ineligible risky-principal trades:

, j ∈ {eligible, ineligible}. Table A9 . The first stage of the IV regressions for estimating the logit demand parameter σ We regress the log ratio of fraction of risky-principal and agency trades on the log of the seasonally adjusted daily aggregate number and volume of trades in columns 1 and 2, respectively. The precrisis period runs from January 3, 2020, until February 29, 2020. The postcrisis data begin April 15, 2020, and run until July 31, 2020. We exclude holidays, weekends, and half trading days. Standard errors are given by the maximum of robust and the usual standard errors. *p <.1; **p <.05; ***p <.01.

log(x h /x l )

(1) Using the estimateσ = 100.09 from our binary IV approach, Figure 8 plots the time series of the change in θ relative to a precrisis benchmark (on January 2, 2020) for eligible (solid blue line) and

ineligible bonds (dashed red line).

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