the macroprudential role of stock markets
TRANSCRIPT
The Macroprudential Role of Stock Markets
Kyriakos Chousakos~ Gary Gorton� Guillermo Ordoñez∗
July 2020
Abstract
A financial crisis is an event of sudden information acquisition about collateralbacking short-term debt. When stock market investors see a financial crisis coming,however, they react by more intensively acquiring information about firms, revealingthose that are weaker, which as a result can end up cut off from credit. This cleansingeffect of stock markets’ information on credit markets’ participation discouragesinformation acquisition about the collateral of remaining borrowing firms, slowingdown credit growth and potentially preventing a crisis. Production of informationin stock markets endogenously acts as a macroprudential tool in the economy.
Keywords: Business Cycles, Financial Markets and the Macroeconomy, Financial CrisesJEL Classification: E3, E32, E44, G01
~Bank of America. Email: [email protected] �Yale University and NBER. Email:[email protected] ∗University of Pennsylvania and NBER. Email: [email protected]. Thanks toStefano Lovo, Enrique Mendoza, Ernesto Pasten, Diego Saravia, Yuliy Sannikov and participants inseminars at the Board of Governors, the 2018 Amsterdam Workshop on Safe Assets, the 2018 SEDMeetings at Mexico City, the Cowles Foundation 15th Annual GE Conference, the Stanford Institute forTheoretical Economics 2019 Macroeconomics Conference, the Copenhagen Business School Conferenceon Financial Frictions, the Bank of France, HEC, and INSEAD for comments and suggestions. We alsothank Shah Kahn and Tim Rudner for excellent research assistance and the National Science Foundationfor support. A previous version of this paper was circulated under the title “Aggregate InformationDynamics.”
1 Introduction
In stock markets agents produce information about firms’ projects, which is thenimpounded in prices, improving the allocation of resources in the economy. Stock prices areinformation-sensitive. Credit markets, particularly collateralized credit markets, performbetter when information about firms’ collateral is avoided – when debt is information-insensitive (see Dang et al. (2019)). In a financial crisis, information production about alarge volume of collateral in credit markets cannot be prevented, and credit disappearsfor a large number of borrowers. Output and consumption then fall. How do thesetwo markets interact dynamically, and affect each other, through the cross-incentives toacquire information? We propose a model in which information production – or the lackthereof – in stock markets is about firms’ productivities and determines the allocation ofcredit, while information production – or the lack thereof – in credit markets is about thefirms’ collateral and determines the feasibility of firms’ operations.
Lack of information production about collateral increases the amount of creditavailable in the economy and total output, but decreases the average productivity ofprojects (the more projects are undertaken, the lower is the productivity of the marginalproject). This reduction in the average quality of projects as credit booms evolve eventuallyinduces information acquisition about the quality of firms being traded in stocks markets.When information is produced in stock markets, weak firms (those operating with projectsof relatively lower quality) are identified by lenders through low stock prices, and thenare unable to obtain funds in credit markets without their collateral being investigated.This result does not require that low quality firms also hold in expectation low qualitycollateral, as lenders are still more prone to acquire information about the collateral whenit is more likely that the firm has a bad project and is forced to default.
This cleansing effect of stock markets’ information on credit markets’ compositiondiscourages information acquisition about the collateral of all other firms remaining incredit markets, slowing down credit growth and potentially preventing a crisis. Stockmarkets act as an automatic macroprudential tool – by slowing down credit growth andso stabilizing the economy. This novel dynamic interaction between stock and creditmarkets through information acquisition highlights the delicate balance of their functionin macroeconomics.
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The macroprudential role of stock markets may suggest that it is always optimal toreduce the cost of producing information about firms’ projects, enhancing the precautionaryeffect against crises. There is a cost, however, of too much information in stock markets: itdepresses credit booms and economic activity. When crises are not very likely (say becausethe cost of acquiring information about collateral in credit markets is large enough), stockmarket generated information about which firms operate with low-quality projects (butnot necessarily with inefficient projects) may prevent credit from flowing to those firms,reducing positive productive opportunities. Of course, this last result is just a consequenceof the assumption that all projects, even the worse, are optimal to operate. In case verybad projects have negative net present value, there is an extra, well-studied, positive roleof information in stock markets. In other words, information in stock market alwaysinduce collateral investigation of firms that are relatively weaker. While this reduces creditin normal times, it also relaxes incentives to investigate collateral of relatively strongerfirms, preventing crises.
While information in stock markets displays a credit-crisis trade-off, informationin credit markets is never beneficial in our setting. The losses from information aboutcollateral come from always depriving some, otherwise efficient, firms from operating. Thegains or losses from information about firms in stock markets, however, depends on howthe information affects information acquisition about collateral in credit markets. Whenthere are no risks that collateral will be investigated in credit markets, information aboutwhich firms are weak only induces some to lose credit, which is detrimental for production.When there are risks that collateral will be investigated, information about which firmsare weak relaxes those incentives, avoiding a crisis and a collapse in production.
Based on these results we provide normative insights about the optimal productionof information in both stock and credit markets. If a government could, for instance,affect the cost of information acquisition in both credit and stock markets, it would beoptimal to rise the cost of producing information in both markets. It could allow complexand opaque securities to raise the cost of producing information in credit markets, soas to avoid crises in the midst of a credit boom. It would also want to raise the cost ofproducing information in stock markets to allow firms with lower relative productivity toobtain credit and operate.
But, if the government cannot modify the incentives to acquire information in credit
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markets, and then a crisis is a possibility once the credit boom is large enough, it may beoptimal to encourage information in stock markets. We characterize the optimal cost ofinformation in stock markets. If the cost is too large, stock markets may not be able toprevent a crisis and the government would like to induce more information production, by,for example, loosening reporting standards for public firms so they are more transparentand easier to access by investors. If the cost is too small, stock markets would prevent thecrisis anyway, but it is too stringent for economic activity, then the government wouldlike to induce less information production about firms by, for example, tightening insidertrading restrictions so it is more difficult to exploit information.
The model generates empirical counterparts of information acquisition in stockmarkets, which can be proxied by the evolution of the cross-sectional dispersion of stockreturns. This follows directly from the model, as will be seen. We also obtain the empiricalcounterparts for the average quality of projects from a credit perspective, which can beproxied by the average time-series volatility of stocks – a proxy of default probability andaverage fragility. As we want to capture the relation between stock markets and financialcrises, we implement an empirical analysis exploiting data for many countries over arelatively long period of time, so we can include enough crisis events. For that purpose, weconstruct stock market information measures from daily stock price data for 52 countriesover the period 1973-2012, amounting to approximately 105 million observations.
With these measures of information, credit and quality of projects, we confronttestable implications of our model. In particular, information in stock markets reducesfuture credit growth and tends to precede and predict financial crises. But not for goodbooms, those with relatively high TFP growth that do not end in crises.
Related Literature: In this paper we exploit the informational interpretation offinancial crises in Gorton and Ordonez (2014) and 2020). In contrast to those models,which display the functioning of credit markets in isolation, and study how borrowersreact by reducing the requested loan to discourage information, in this paper we proposea comprehensive model with less structure on credit markets, but more informationdimensions and choices, a stock market with informative prices and rich dynamics. Weuncover a novel role of information in stock markets, besides the well-understood allocativeand redistributive properties: a trade-off in which too much information chokes creditbooms excessively but too little does not allow the prevention of financial crises. Our
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work suggests that in the absence of well-developed stock markets we would have observedmore crises in credit markets around the globe.
Our view of stock markets is consistent with a large literature on stock prices beinginformative and feeding back onto real variables (see, e.g., Dow and Gorton (1997)). Inthis literature, the information content in asset markets direct managers’ investmentsdecisions and allows for a better allocation of resources in the economy. In the work here,however, information in stock markets has another, previously unexplored, positive role inthe economy beyond its pure allocative use – it endogenously acts as a macroprudentialtool to reduce the likelihood of a financial crisis. While information about firms’ collateralcan be counterproductive by reducing aggregate credit in the economy, information instock markets can be beneficial in allocating such credit. Holmström (2015) and Dang etal. (2019) discuss these two markets as separate systems. Here we explore their interaction.
There is also a rich, and more recent, literature considering the conceptual linkbetween information production and economic booms and busts, such as vanNieuwerburghand Veldkamp (2006), Veldkamp (2006), Straub and Ulbricht (2017), Fajgelbaum etal. (2017), Farboodi and Kondor (2019), and Petriconi (2019). Perhaps the closest toour paper is Asriyan et al. (2019), who study a setting in which credit can be backedeither by collateral (with perfect information) or by costly screening of projects, withthis mix affecting macroeconomic dynamics and the probability and recovery from crises.Our setting considers both information about projects for trading in stock marketsand information about collateral in credit markets, the effect of their interaction formacroeconomic dynamics, the likelihood of crises, and the optimal cost of informationacquisition in both markets.
A scarcer literature explores the interaction between stock and credit markets. Onebranch is mostly empirical and focuses on pricing interactions, such as Beck and Levine(2004) and Gilchrist et al. (2009). Another branch is theoretical, such as Dow et al.(2017)), and studies how managers and creditors take actions based on information instock markets, creating feedback effects on the determination of stock prices that magnifyshocks. Our work differs by explicitly defining the concept of a crisis and on highlighting aninformational interaction between these two markets. In our setting stock prices perfectlyreveal information. The complementarity does not come from a feedback between choicesand information about firms, but instead from a feedback between information acquisition
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about firms and about collateral. Furthermore, we explore this interaction through itsimpact on macroeconomics, providing a contribution to most standard macroeconomicmodels. While those models focus on the stock pricing implications of macro, we focus onthe macro implications of the informational content of stock prices.
The paper proceeds as follows. In Section 2 we present the model. Section 3 analyzesthe dynamic interactions between stock markets and credit markets. In Section 4 weprovide tests of three hypotheses implied by the model. Section 5 concludes.
2 Model
This model highlights the interaction between the incentives to acquire information instock markets (about projects) and in credit markets (about collateral). The challenge isto capture the joint functioning of three markets: of firms (stock markets), of loans (creditmarkets) and of collateral (asset markets) in a dynamic setting that is tractable enoughto characterize business cycles and financial crises, and to map to data counterparts.
2.1 Environment
We present an environment with a set of timing assumptions that allow for mileagein the analysis and testable implications. As we move on with the exposition we will bespecific about the specific role of each assumption.
Agents and Goods: To model who buys, who operates, and who sells firms, weassume an overlapping generation structure, such that in each calendar period t, threeoverlapping generations coexist – young, middle-aged and old – each generation has massone of a continuum of agents. There are two goods in the economy – numeraire, and land.Numeraire, denoted by K, is productive and reproducible (it can be used to produce morenumeraire) but non-storable (it cannot be transferred across periods). Land, on the otherhand, is storable but it is not productive and not -reproducible. Each generation is riskneutral and derives utility from consuming numeraire at the end of the period, withoutdiscounting.1
1No discounting and no concern about when to consume makes credit only useful for facilitatingproduction and not for consumption smoothing.
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Technology: There is the potential for production in the economy. We assume thatmiddle-aged agents are heterogeneous. A third are entrepreneurs, who each come up withan idea for a productive project. They can form a firm by combining the idea with a unitof land. Entrepreneurs cannot operate the firm, but the rest of the middle-aged agentsare managers and can operate firms. An entrepreneur can sell his firm to a manager ina stock market. The assumption that there are two buyers per seller just simplifies themodeling of information acquisition in stock markets later.
Upon becoming old, the manager who bought a firm when middle-aged needs K∗
units of numeraire to operate, in which case produces AK∗ units of numeraire withprobability q, and nothing with probability 1 − q. There are two types of projectsavailable: An exogenous fraction ψ has high probability of success, qH , and the rest havea low probability of success, qL. We assume all projects are efficient, i.e., qHA > qLA > 1,which implies that it is optimal for all firms to operate.
We say a firm is active if it has the chance (based on perceived collateral quality aswe will describe next) to obtain a loan in credit markets. We denote by η the mass ofactive firms, which we will show later is endogenous. We assume that active firms arerandomly assigned to a queue to choose their project quality. When a firm has its turn tochoose according to its position in the queue, an active firm naturally picks the projectwith the highest available quality q of those remaining in the pool.2 This protocol inducesan average productivity of projects among active firms, which we denote by q̂(η), thatdepends on two factors: the exogenous fraction of good projects in the economy, ψ, andthe endogenous fraction of firms operating projects, η, as follows:
q̂(η|ψ) =
qH if η < ψ
ψηqH +
(1− ψ
η
)qL if η ≥ ψ.
(1)
An Agent’s Lifetime: The lifetime of an individual agent is as follows: At thestart of a period, say t, the individual is born young with endowment K̄. The agentcan use this numeraire to lend to a firm against collateral in credit markets. In period
2Notice that the project quality is not a function of an idea, which is just a precondition to have aproject, but instead quality is only determined by the position on the queue. This assumption guaranteesthat, besides the collateral, firms are identical for lenders when providing loans unless stocks marketscommunicate more information through prices.
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t+ 1 the agent becomes middle-aged. At the end of the period, all agents obtain a newendowment K̄ but only a third get an idea.3 These entrepreneurs buy land to combinewith their ideas and to create firms, which are then sold to managers in a stock market.In period t + 2 the agent becomes old, and do not obtain any endowment. Those whoown a firm (managers who bought a firm the previous period) can borrow numeraire K∗
in credit markets to productively operate the project. Firms produce, loan contracts aresettled and land is sold to middle-aged agents at the end the period. Consumption takesplace at the end of each calendar period.
This time line guarantees that resources are in the wrong hands and so there aregains from trade. Entrepreneurs cannot operate firms, so there are gains to sell them tomanagers in stock markets. Managers who owns firms do not have numeraire to operatethe firms when old, so there are gains from borrowing in credit markets. Finally, at theend of the period old agents already used the land in a firm, so there are gains from sellingland in asset markets to entrepreneurs to create new firms. The assumptions about whohas these different roles are just expositional, as they clearly identify who buys and whosells in each of these three markets. We summarize the agent’s lifetime in Figure 1.
Figure 1: An agent’s lifetime
Young Middle-age Old
Born with K.Lends.Consumption.
Get K at end of period.Entrepreneurs buy land, form firms and sell.Managers buy firm in stock market.Consumption.
If owning a firm, borrows.Production.If owning land, sells.Consumption.
Land as Collateral: At the time of production (the start of each calendar period),young agents have numeraire available while firms have a project that needs numeraireto produce. We assume that K > K∗ and since production is efficient, if output wereverifiable it would be possible for firms to borrow the required amount of numeraire K∗
using state-contingent claims. In what follows, however, we assume limited liability anda financial friction – the output of the project is only observable by the borrower andnon-verifiable by the lender. Then firms would never repay their loans and young agents
3The role of having the endowment of numeraire arriving at the end of the period for middle-ageagents, instead of at the beginning of the period as for young agents, is just to assign the role of lendersonly to young agents and the role of land buyers only to middle-aged, so not to confuse who does what.
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would never be willing to lend. The output would be hidden. While we assume thatfirms can hide the numeraire output, we also assume that firms cannot hide land, whichmakes land useful as collateral to relax the financial friction. Firms can credibly promiseto transfer a fraction of land to households in the event of not repaying the loan, whichrelaxes the financing constraint from output non-verifiability.
This particular assumption about the protocol to assign project quality to activefirms is just a way to implement decreasing marginal returns of projects in the economy –the more firms operate, the lower their average quality.
Land comes in two qualities. If land is “good”, it can deliver C units of numeraire,but only once. If land is “bad"’, it is worthless. We assume an exogenous fraction p̂ ofland is good in every period. We denote the perception, or belief, about the quality of aparticular unit of land as p. This belief is critical for the granting of loans. We assumethat C > K∗ so that land that is known to be good can sustain the needed loan size, K∗.But land that is known to be bad is not able to sustain a loan. How many firms are ableto use land as collateral will determine the mass of active firms, η.
The land’s quality is not permanent, which will induce dynamics in our settingabsent any other shock. For now we assume only idiosyncratic (no aggregate) shocks toland, More specifically, after being used in a firm, the quality of each unit of land maybe affected. With probability λ the quality remains unchanged, but with probability(1− λ) it mean reverts and becomes good with a probability p̂, independent of its currenttype. Even when this idiosyncratic shock to land is observable, its realization is not.An implication of this process is that the distribution of beliefs about land quality willhave just a three-point support: 0, p̂, 1, which will simplify the exposition that follows.It is, however, not restrictive. The only relevant assumption to trigger dynamics andinformation depreciation is mean reversion of collateral quality.
Remark on the interpretation of land as collateral: We have called the col-lateral ”land”, but this is a simplification for exposition. In the model there are noexplicit financial intermediaries and no financial collateral. These are also simplifications.However, financial intermediaries and financial collateral can be introduced at the costof more structure. Assume firms need intermediaries to borrow from households andthat debt must be collateralized because households cannot verifiably monitor the bank.The household only knows what firm the bank has lent to, but the household cannot see
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the firm’s output realization. The bank can verifiably monitor the firm, determining theoutput, which is the bank’s function. The bank takes the money deposited by householdsand lends it to the firm. In this extension there is an intermediary and the debt could bea repurchase agreement (“repo") or other money market instruments and the collateralcould be either a specific bond, a portfolio of bonds and loans or a mortgage-backedsecurity (MBS) if the borrower were another household. Other than the specifics of thesecontracts, what is important is that, as “land", collateral does not trade in centralizedmarkets where prices can reveal the information that has been produced.
Stock Market Protocol: In stock markets a middle-aged manager can buy a firmfrom a middle-aged entrepreneur. As there are twice as many buyers as sellers, we modelthe stock market as a random matching of two potential managers to one entrepreneur.Each buyer submits an individual bid in a sealed envelope to the seller, who then sellsthe firm to the highest bidder. Before submitting the bid, a bidder can privately acquireinformation about the firm’s productivity at a cost γq in terms of numeraire. In the caseof acquiring information we assume the bidder not only observes the project’s quality qbut also learns whether his competitor has also acquired information. This last part isnot relevant to the mechanism but greatly simplifies the exposition.
Credit Market Protocol: In credit markets an old manager owning a firm canborrow numeraire to operate from young agents with endowment. We also assume randommatching between a lender and a borrower, and that the borrower has the bargainingpower. Before signing the loan, the lender can privately acquire information about thefirm’s collateral quality at a cost γC in terms of numeraire. We assume this information canbe certified (while the certificate cannot be manipulated, its creation can be absconded),and while the certification is private immediately after being obtained, it becomes publicat the end of the period. Still, the agent can credibly disclose private information (thecertificate) immediately if it is beneficial to do so.
There are, then, two possible collateralized loan contracts. The first, information-sensitive debt (IS), specifies that the lender produces information about the collateralquality before signing the contract. The second, information-insensitive debt (II), specifiesa contract based on the expected value of collateral. This contract is only feasible if thelender does not have incentives to deviate and privately produce information (without theborrower knowing) before signing the contract.
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Asset Market Protocol: In asset markets a middle-aged entrepreneur can buy aunit of land to combine with an idea and form a firm from an old manager who alreadyproduced. Again we assume random matching between a buyer and a seller, with thebuyer having all the bargaining power. This last assumption immediately implies that thebuyer would never pay more than the expected value of consumption the seller can obtainby extracting the intrinsic value from land, which simplifies its operation and determinesthe price of land as simply pC.
2.2 Timing and Equilibrium
We have discussed the environment, preferences, technologies, markets, and informa-tion structures. Here we discuss the timing in a single period and define the equilibrium.
1. Credit Market: There is random matching between a young agent and an oldagent. If the old agent does not own a firm, this market is irrelevant. If the old agent ownsa firm, both the lender (l) and borrower (b) know the probability p that the land owned bythe borrower is good and observe the price at which the firm was traded in the previousperiod (then making an inference about the project’s quality q). The borrower makesa take-it-or-leave-it offer for a loan K∗, the face value R to be repaid, and the fractionof collateral that should be transferred to the lender in case of default, x. The loancontract also specifies whether the lender acquires information (an information-sensitiveloan contract, denoted IS) or not (an information-insensitive loan contract, denoted II).The lender either accepts or rejects the offer.
2. Firms Production and Land Shocks: Production takes place and all informationgenerated about land at the time of the loan (information privately acquired) gets revealed.Loan contracts are settled. Then, land realizes the mean-reverting idiosyncratic shocks.
3. Asset Market: Middle-aged agents obtain endowment K̄. A third become en-trepreneurs and the rest become managers. Entrepreneurs want land to combine withideas to form firms, so they randomly match with old agents (who have already usedland in their own firms) or with young agents (who have received land as collateral for adefaulted loan).
4. Stock Market: There is a random match between a middle-aged entrepreneur andtwo middle-aged managers. Among these firms, some will hold land with low enough p
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such that they will not be able to obtain credit. The rest, active firms, will draw thequality of the project q, according to the process (1). Two managers are randomly assignedto an entrepreneur and bid for the firm. All agents know p, but the bidders do not knowthe project of quality q, and they can choose to become informed about it at a cost γqbefore submitting the bid.
5. Consumption: Numeraire goods will perish at the end of the period and so areconsumed.
We summarize this timeline of a single period t in Figure 2 are, as we will discuss,periods are only linked by the evolution of beliefs about land quality, p.
Figure 2: Timeline in period t
Credit Market Productionand Shocks
Asset Market Stock Market Consumption
Match: young - old.Info choice about C.Loan contract.
Firm production.Loan settlementsShocks to land type.
Match: old manager- m-a entrepreneurLand traded at pC.
Match: m-a manager- m-a entrepreneurInfo choice about q.Trade at highest bid.
Consumption.
Now we can define the equilibrium. As the asset market is mechanical, with theprice pinned down by the expected value of land and the traded land given by randommatching, we focus on the remaining two markets.
Definition 1. Equilibrium:
• In the credit market borrowers choose the loan contract type (i ∈ {IS, II}, Ri andxi) to maximize expected profits conditional on the lender’s participation constraint;the borrower repays when the project succeeds and defaults when the project fails(truth-telling constraint); and there are no private incentives to acquire informationin the information-insensitive contract (incentive-compatibility constraint).
• In the stock market bidders choose to acquire information or not before submittinga bid for a firm, conditional on knowing collateral type p of a randomly assignedseller, and the mass of active firms (η). The stock price for each firm is determinedby the highest bid.
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2.3 The Credit Market
Here we solve for the optimal short-term collateralized debt contract for a single firmwith a unit of land that is good with probability p and that has a project that is believedto succeed with probability q (this is q̂, qH or qL depending whether stock markets donot reveal q, reveal a good project or a bad project, respectively). There are two possibleloan contracts in terms of their information content.
The first, an information-sensitive (IS) loan contract, implicitly specifies informationproduction about collateral. Lenders are willing to lend K∗ only if they find out that thecollateral is good (with probability p). Then from an ex-ante perspective, the participationconstraint implies p[qRIS+(1−q)xISC−K∗] ≥ γC , where RIS is the payment the borrowerpromises to repay and xIS the fraction of land that goes to the lender if the borrowerdefaults. The truth-telling constraint implies RIS = xISC, otherwise the firm alwaysrepays or defaults. This implies
RIS = K∗ + γCp
and xIS = RIS
C≤ 1.
Hence, this contract is feasible only when p ≥ γC
C−K∗ (the cost of information is low enoughvis-a-vis the expected collateral quality).4
The second, an information-insensitive (II) loan contract, specifies that no informationabout the collateral quality be produced, and then it is just based on the expected valueof collateral. In this case, the lenders’ participation constraint binds when qRII + (1−q)xIIpC = K∗, and subject to the truth-telling constraint, RII = xIIpC. We obtain,
RII = K∗ and xII = RII
pC≤ 1.
Hence, this contract is feasible only when: i) p ≥ K∗
C(the borrower has valuable enough
collateral) and ii) the lender does not have incentives to deviate and check the value ofcollateral privately before signing the contract. Lenders may want to deviate becausethey can lend at beneficial contract terms if the collateral is good, and not lend at all if
4Note that, since the fraction of land posted as collateral does not depend on q, firms cannot signaltheir q by posting a different fraction of land as collateral (or similarly, by offering to pay a different rate).Intuitively, since collateral completely covers the loan value it prevents a loss due to default, so the loancannot be used to signal the probability of default.
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the collateral is bad. Formally, they do not deviate if the expected gains from acquiringinformation, evaluated at xII and RII , are lower than the private loss, γC , this is:
Vcredit = p[qRII + (1− q)xIIC −K∗] < γC ,
or in terms of the belief about the collateral quality, this contract is feasible if and only if
p > p∗ ≡ 1− γC(1− q)K∗ . (2)
It is clear from this expression that the information-insensitive debt region widenswith information costs (p∗ decreases with γC) and shrinks with the project’s expectedprobability of success (p∗ decreases with q). This is the main link between stock marketsand credit markets. When prices in stock markets are informative about q they will creategreater heterogeneity about which firms will be examined in credit markets, and as suchhow much information will be generated in credit markets.
This threshold is depicted in Figure 3.5 When the project is financed, the expected netproduction is (qA−1)K∗. It is clear that an information-insensitive loan is always preferred,as the project is always financed and additionally there is no waste on information costs.Firms that are unlikely to have good land (more specifically with p < p∗), however, cannotobtain information-insensitive loans because the lender has large incentives to deviate. Inthe figure, firms with land that is expected to be good with probability p̂, for instance,can obtain information-insensitive loans. We will show later, when discussing dynamics,that as a credit boom proceeds η increases, expected q (i.e., q̂) declines and p∗ increasesfor an average firm, eventually exceeding p̂. This is a crisis because of the discontinuousdecline in expected production. Some firms that were getting loans suddenly cannot getloans. Output and consumption go down–a crisis.
2.4 The Stock Market
Take a firm with expected project quality q̂ and expected land quality p, the bidders’choice to acquire information about the realized q depends on the expected functioning of
5The figure assumes a relatively high C, so the feasibility constraints of both contracts bind for lowenough p.
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Figure 3: Expected Net Production in Equilibrium
1 / 3
10 K∗
C
↘γC
C−K∗p∗ p̂Beliefs p
ΠII = (qA− 1)K∗
ΠIS = p(qA− 1)K∗ − γC↖
︸ ︷︷ ︸No Loan
︸ ︷︷ ︸IS Loan
︸ ︷︷ ︸II Loan
credit markets (how p maps into credit once the manager tries to raise loans). At thetime, information about the project determines the informativeness of firms’ stock pricesabout q, which is then used in credit markets to determine whether information aboutland will be produced in credit markets. Here we explore this intricate relation. Then westudy its dynamic implications.
Both the seller and potential buyers agree on the belief about the firm’s land quality(p). Buyers also know the fraction of active firms in credit markets (η) and then theprobability of bidding for a firm with a qH-project, which we define as z(η) ≡ Pr(qH) = ψ
η.
A firm’s value is composed of two parts, one is the expected value of its collateral pC andthe other is the expected profit generated by the project according to Figure 3. We defineVH(p) as the value of a firm with a qH-project and VL(p) as the value of a firm with aqL-project.
Define y(p) to be the fraction of uninformed bidders among firms with land of expectedquality p and let PU(p) be the pooling price (i.e., the bid submitted by an uninformed
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bidder for a firm known to have collateral with belief p). These two variables are jointlydetermined in equilibrium by the bidding and information production of potential buyers.
In what follows, and unless there is risk of confusion, we dispense of the explicitreference to the dependence on p. The expected gains of an uninformed bidder are:
ΠU = z[y
2(VH − PU)]
+ (1− z)[(
1− y + y
2
)(VL − PU)
].
In words, an uniformed bidder always bids the pooling price in equilibrium PU . Whenfacing another uninformed bidder, he buys with a probability 1/2, regardless of the firm’sproject quality. When the uninformed bidder faces an informed bidder, he never buys agood firm in equilibrium (as the informed bidder would bid PU + ε for a good firm) andthe uninformed bidder always buys a low quality firm (as the informed bidder would bidless than PU). Similarly, the expected gains of an informed bidder are:
ΠI = z[(y + 1− y
2
)(VH − PU)
].
In words, an informed bidder always bids the value of the firm when facing anotherinformed bidder, a bit above the pooling price when facing an uninformed bidder and thefirm is of high quality, and less than the pooling price when facing an uninformed bidderand the firm is of low quality.
Hence, there is no information acquisition in stock markets for firms p as long as
Vstock = ΠI(p)− ΠU(p) < γq.
Notice that bidding competition across uninformed bidders implies that ΠU = 0,otherwise there are incentives to marginally increase the bid PU and discretely raise theprobability of buying the firm. This implies that PU should be such that, for a given y,the pooling price PU balances the gains of buying a good firm and the losses of buying abad one. Hence
PU = ωVH + (1− ω)VL with ω(z, y) = zy
zy + (1− z)(2− y) . (3)
The fraction of uninformed bidders y affects the price that uninformed bidders bid for afirm. When no bidder is informed (i.e., when y = 1), PU = zVH + (1− z)VL, the ex-ante
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value of the firm. When all bidders are informed (i.e., when y = 0), then PU = VL, as theonly firms that are available for the uninformed to buy are those of low quality.
All bidders for a firm p acquire information (this is, y = 0) when Vstock > γq. Wheny = 0, ω = 0 and PU = VL. This implies that ΠU(y = 0) = 0 and ΠI(y = 0) =z2(VH − VL) > 0, and then we can express the condition for all bidders being informed asγq≡ 2
2(VH − VL) > γq. In words, when the cost of information production is very smallall bidders acquire information and all firms are traded either at a price VH if the firmhas a qH-project or at a price VL if the firm has a qL-project. This situation is the mostinformative one, in which all prices determined for traded firms with land of expectedquality p reveal projects’ qualities.
At the other extreme, no bidder acquires information (this is, y = 1) when Vstock < γq.When y = 1, ω = z and PU = zVH + (1 − z)VL. This implies that ΠU(y = 1) = 0 andΠI(y = 1) = z(1− z)(VH − VL) > 0, and then we can express the condition for no bidderbeing informed as γq ≡ z(1− z)(VH − VL) < γq. In words, when the cost of informationis very large no bidder has incentives to deviate and become informed. This is the case inwhich the stock market is the least informative as all firms with land of expected qualityp are traded at the same price, PU .
Hence, there is an intermediate range of the cost γq ∈ (γq, γq) in which the equilibrium
is given by Vstock = γq, with an interior y that has to be consistent with equilibrium pricesPU . In this case y∗ is the solution to the following equation
zy∗(1− z)(2− y∗)zy∗ + (1− z)(2− y∗)(VH − VL) = γq. (4)
and P ∗U is determined by equation (3) evaluated at y∗.
The first panel of Figure 4 shows how the fraction of informed investors (1− y(p))depends on the fraction of active firms with qH-projects (this is z = ψ/η, on the x-axis).This has an inverted-U shape. When all firms have qH-projects, bidders do not acquireinformation. As there are more and more active firms (during a credit boom, for instance)eventually more of the projects will be qL firms and will attract information in stockmarkets. The incentives to acquire information are maximized when there is relativelylarge uncertainty about the composition of projects in the market.
The second panel shows the pooling price, PU(p), also as a function of the fraction
16
of active firms with qH-projects. Not surprisingly, as the composition of projects in themarket worsens, PU (p) declines. As more informed bidders participate in the market theyforce a faster decline in the pooling price because those bidders “cream skim" the market.Note that the two kinks in the second panel correspond to the points at which no bidderbecomes informed, because either almost all the projects are qH (RHS) or qL (LHS) so itdoes not pay to produce information.
Figure 4: Fraction of Informed Bidders and Pooling Price
2 / 3
10 Fraction of qH-projects (z)
Fraction of informed buyers, (1− y(p))
3 / 3
10 Fraction of qH-projects (z)
Pooling firm price, PU(p)
Notice that the solution y∗ determines the information content of the stock market.The distribution of observed prices in the economy determines beliefs about q. A fractionz(1 − y∗)2 of firms with land p trades at price VH , which reveals that the firm has aqH-project, a fraction (1 − z)(1 − y∗)2 trade at price VL, which reveals that the firmhas a qL-project, and a fraction 1 − (1 − y∗)2 trades at the pooling price PU , which isuninformative about q. As can be seen, the higher is the fraction of informed bidders (thelower is y∗), the more information about q is revealed in stock markets, which affects thefraction of firms that are able to raise funds with information-insensitive loans in creditmarkets.
3 Credit and Stock Markets - Dynamic Interactions
In this section we show how information about collateral in credit markets andinformation about projects in stock markets interact dynamically.
17
3.1 Credit Booms, Busts and the Evolution of Beliefs
The idiosyncratic shock process for collateral generates depreciation of credit marketcollateral information. Given our assumed mean reverting process, a unit of land fallsinto one of three possible categories: it is either known to be good (p = 1), known to bebad (p = 0) or of uncertain quality (p = p̂). We denote the mass of land in each categoryp ∈ {0, p̂, 1} after period t production (i.e., after idiosyncratic shocks to land but beforethe stock market opens) as m(p)t. As the mass of active firms is given by all firms thatmay have good collateral. Formally,
ηt = m(p̂)t +m(1)t. (5)
In what follows we assume that p̂ < p∗(qL) (there is information production aboutcollateral of unknown quality for firms known to operate with qL-projects) and thatp̂ > p∗(qH) (there is no information production about collateral of unknown quality forfirms known to operate with qH-projects). These parametric assumptions allow us tofocus attention on an environment in which information about firms’ projects affectstheir performance in credit markets. Otherwise, information about collateral in the creditmarket does not depend on the availability of information about projects in the stockmarket, muting any interaction between stock and credit markets.
In credit markets at t+ 1, a fraction vt+1 of land of unknown quality (this is, of p̂)will be investigated. The mass of land in each belief category after credit markets (whichwe denote by (t+ 1)′) changes to:
m(p̂)(t+1)′ = (1− vt+1)m(p̂)tm(1)(t+1)′ = m(1)t + vt+1p̂m(p̂)tm(0)(t+1)′ = m(0)t + vt+1(1− p̂)m(p̂)t.
After production at t+ 1, the mass of land in each belief category (after idiosyncratic
18
shocks), which determines the collateral belief distribution in the next period, are:
m(p̂)t+1 = λm(p̂)(t+1)′ + (1− λ)
m(1)t+1 = λm(1)(t+1)′
m(0)t+1 = λm(0)(t+1)′ .
Putting these elements together, the mass of active firms in period t+ 1 is
ηt+1 = m(p̂)t+1 +m(1)t+1
= λ[1− vt+1(1− p̂)]m(p̂)t + λm(1)t + (1− λ). (6)
The first term corresponds to land p̂ that has not suffered an idiosyncratic shock, andeither was not examined during the credit market or was examined and was found to begood. The second term corresponds to land known to be good (i.e., p = 1) that has notsuffered an idiosyncratic shock. The last term corresponds to all land that has sufferedan idiosyncratic shock.
Combining equations (5) and (6) a credit boom is defined as the change in the massof firms that are actively participating in credit markets,
ηt+1 − ηt = (1− λ)(1−m(1)t)− [1− λ(1− vt+1(1− p̂))]m(p̂)t= (1− λ)m(0)t − λvt+1(1− p̂)m(p̂)t. (7)
The credit boom is given by the old collateral known to be of bad quality that suffered anidiosyncratic shock and started in the pool of unknown collateral, minus the unknowncollateral that was investigated and found to be bad collateral.
Now, we can put structure on the fraction of collateral vt+1 that is investigated inperiod t+1. First, the mass of active firms ηt reduces the fraction zt = ψ
ηtof qH-projects in
the economy. This fraction reduces the average quality of projects, q̂t = ztqH + (1− zt)qLand, as depicted in Figure 4, determines information acquisition in the stock market,(1− yt). Among firms with collateral p̂, a fraction (1− zt)(1− yt)2 is identified in the stockmarket as qL-firms, a fraction zt(1− yt)2 as qH-firms, and the rest are not explored in thestock market. If p∗(q̂t) ≤ p̂ there is no information production about the third group, justabout the first group. If in contrast, p∗(q̂t) > p̂ there is also information production about
19
the third group, which we denote a crisis. Denoting by IC,t+1 a crisis indicator functionin period t+ 1, with IC,t+1 = 1 in case of a crisis and 0 otherwise,
vt+1 = (1− zt)(1− yt)2 + IC,t+1[1− (1− yt)2
](8)
In short, when IC,t+1 = 0 and there is no information production about collateral ofunknown quality of a firm with unknown project quality, vt+1 = (1− zt)(1− yt)2 (only thecollateral of qL-projects are investigated). In contrast, during a crisis (this is IC,t+1 = 1)only the collateral of known qH-projects is not investigated, and then vt+1 = 1−zt(1−yt)2.
The fraction of collateral that is examined in credit markets in t+1, vt+1, is a functionof the mass of active firms in the economy, ηt and changes in the following way.
∂vt+1
∂ηt=
ψ(1−yt)η2
t
[(1− yt) + 2(1− zt)∂yt
∂zt
]if IC = 0 (i.e., ηt < η∗)
ψ(1−yt)η2
t
[(1− yt)− 2zt ∂yt
∂zt
]if IC = 1 (i.e., ηt > η∗)
(9)
where η∗ is the mass of active firms for which p∗(q̂t(η∗)) = p̂.
This derivative shows that information in credit markets changes with the volumeof credit in the economy (the mass of active firms) through two channels. The first isby triggering a a financial crisis, in which vt+1 increases discontinuously after a certainvolume of credit requests. From equation (2), p∗(q̂t) decreases with q̂t (which increaseswith ηt), and then the indicator IC,t+1 switches from 0 to 1 when ηt gets large enough.
The second channel is more continuous and comes from changes in information instock markets. When there is no crisis, there is more collateral examination when there ismore information in the stock market and there are more qL-projects identified. If a crisisis triggered, there is more collateral examination when there is less information in thestock market, but more qL-projects. Given these relations, the next Lemma characterizesthe evolution of credit in the economy.Lemma 1. The mass of active firms follows the following first-order difference equation.
ηt+1 = 1− λ+ λ[vt+1(ηt)p̂+ (1− vt+1(ηt))ηt] (10)
and then∂ηt+1
∂ηt= λ(1− vt+1(ηt))− λ(ηt − p̂)
∂vt+1
∂ηt(11)
20
with ∂vt+1∂ηt
given by equation (9).
Proof Among collateral with known quality (i.e., 1−m(p̂)t), a fraction p̂ is of goodquality. Then, m(1)t = p̂(1−m(p̂)t). Substituting into equation (5), we can express m(p̂)tas a function of ηt. This is,
ηt = p̂+ (1− p̂)m(p̂)t =⇒ m(p̂)t = ηt − p̂1− p̂ ,
and we can rewrite equation (6) as
ηt+1 = (1− λ) + λ(m(p̂)t +m(1)t)− λvt+1(1− p̂)m(p̂)t= (1− λ) + ληt − λvt+1(1− p̂)m(p̂)t
Replacing m(p̂)t in this equation we obtain the equation (10) in the Lemma. q.e.d.
3.2 Benchmark Without Information in Stock Markets
We use the equations in Lemma 1 to characterize the stationary equilibria in theeconomy. We start with a benchmark case without information production in the stockmarket. This is the same as assuming γq = ∞, and then no incentives to acquireinformation about the project in the stock market (i.e., yt = 1 in all t).
In the next Proposition we show the economy can be in a stationary good boomequilibrium (in which all firms receive credit), a stationary no boom equilibrium (in whichonly a fraction of firms receive credit) and a stationary cyclical bad boom equilibrium,with a deterministic sequence of booms and busts.
Proposition 1. Assuming γq =∞, yt = 1 for all t. From equation (8), vt = IC in all t.Then
ηt+1 = 1− λ+ λ[IC p̂+ (1− IC)ηt]
where IC = 1 for all ηt > η∗ and 0 otherwise, with η∗ given by p∗(q̂(η∗)) = p̂. Definingη ≡ 1−λ+λp̂ the lowest possible mass of active firms (all firms that suffer an idiosyncraticshock and all firms with good quality collateral that do not face an idiosyncratic shock),the stationary equilibria are:
21
1. No Boom: If η∗ ≤ η, information is replenished every period and ηSS = η.
2. Good Booms: If η∗ ≥ 1, information is never generated and ηSS = 1.
3. Cycles of Bad Booms: If η∗ ∈ (η, 1), information is generated only when ηt > η∗.
The proof follows directly from the dynamics in equations (10) and (11). When thereis no crisis, (this is IC = 0), ∂ηt+1
∂ηt= λ and when there is a crisis, (this is IC = 1), ∂ηt+1
∂ηt= 0.
We show this next using a phase diagram. The first panel of Figure 5 shows the first caseof the proposition, in which the mass of active firms is constant and at the minimum, asinformation is replenished every period. The second panel shows the second case of theproposition, in which an economy with information transits to a steady state withoutinformation about any collateral and all firms are active (a good boom). The third panelshows the last case of the proposition, in which the economy cycles between booms thatend in crises once the mass of active firms (η∗) is high enough, just to restart the processagain from η.
Figure 5: No Information in the Stock Market
1 / 7
ηt1η0
η
ηt+1
ηt+1 = 1− λ+ λp̂
(a) No Boom2 / 7
ηt1η0
1− λ
1
ηt+1
ηt+1 = 1− λ+ ληt
(b) Good Booms3 / 7
ηt1η∗η0
1− λ
ηt+1
ηt+1 = 1−λ+λ[IC p̂+(1−IC)ηt]
(c) Bad Booms
3.3 The Stock Market as a Macroprudential Mechanism
In this section we obtain three results. First, we study an extreme situation in whichstock markets reveal full information about the quality of all firms’ projects. Here we showthe economy just has one stationary equilibrium with an intermediate level of active firms,and there is never a crisis. Second we assume that information in stock markets is constantand we point out that a lot of information prevents crises, but even if the information
22
produced is not enough to avoid a crisis, still it reduces the crisis magnitude. Finally, weconsider the more general setting in which information in stock markets is endogenousto the credit boom. This case, with a two-way interaction between stock and creditmarkets, shows that information in stock markets endogenously builds up when a crisisbecomes more likely, then serving as a market-generated, automatic, macroprudentialtool. Furthermore, even though avoiding a financial crisis, endogenous information mayinduce deterministic non-crisis cycles.
First, assume full information in stock markets (this is, γq = 0 and yt = 0 in all t).The economy just has one stationary equilibrium with an intermediate level of activefirms, and there is never a crisis.
Proposition 2. Assuming γq = 0, yt = 0 in all t. From equation (8), vt+1 = 1− zt in allt. Then
ηt+1 = 1− λ+ λ[(1− zt)p̂+ ztηt] with zt = min{ψ
ηt, 1}
There is a unique steady state in which ηSS ∈ (η, 1).
The proof follows directly from the dynamics in equations (10) and (11). Whenthere is perfect information in the stock market, only collateral of unknown quality isinvestigated if it is backing qL-projects. This is why there are no crises, as there areonly two possible thresholds for information acquisition, p∗(qL) > p̂ and p∗(qH) < p̂. Thecredit boom is continuous, strictly increasing at a decreasing rate, as there are moreqL-firms operating in the economy. Formally, from equation (11), ∂ηt+1
∂ηt= λp̂ψ
η2t
(positiveand decreasing in η). Figure 6 shows this result graphically.
This result is a first indication of the role of stock markets in preventing crises. Whenthe stock market reveals which firms are very likely to repay and which are more likelyto default, this informs the credit market about which collateral to investigate. When,during a credit boom, there are more and more firms that are less likely to repay thereis more information acquisition in credit markets, but no sudden change in that process– no crisis. Information in the stock market generates a stationary equilibrium that ismediocre (i.e., low consumption because fewer firms get credit), but stable.
Now we assume information in the stock market is constant over time (this is,yt = y ∈ (0, 1)) for all t. The next proposition shows that, even when information in the
23
Figure 6: Full Information in the Stock Market
4 / 7
ηt1η∗η0
1− λ
ηt+1
ηt+1 = 1−λ+λ[(1−zt)p̂+ztηt]↗
1− λ(1− p̂)(1− ψ)
stock market is not enough to prevent a crisis (y is relatively high), the crisis is smallerthan in an alternative scenario without information in stock markets.
Proposition 3. Assume bad booms in the absence of information in stock markets.Information in the stock market prevents crises and, if not, it reduces their magnitude.
Proof When there is some information in stock markets, this result follows froma credit boom that grows at a slower rate than without information when there is nocrisis, and that the mass of active firms is larger than without information when there iscrisis. Formally, the first condition implies ∂ηt+1
∂ηt|IC=0,yt=y <
∂ηt+1∂ηt|IC=0,yt=1 from equation
(11). This is the case because ∂ηt+1∂ηt|IC=0,yt=y = λ[1− (1− zt)(1− y)2]− λ(ηt − p̂) ψη2
t< λ,
and because 1 − (1 − zt)(1 − y)2 < 1 and ηt > η > p̂. The second condition impliesηt+1|IC=1,yt=y > ηt+1|IC=1,yt=1 from equation (10). This is the case because ηt+1|IC=1,yt=y =1− λ+ λp̂+ λzt(1− y)2(ηt − p̂) > η, and because η = 1− λ+ λp̂.
q.e.d.
Figure 7 is based on the parametric combination that generates bad booms in theabsence of information in the stock market (third panel of Figure 5). The first paneldisplays the case with relatively high information production in the stock market (that is,
24
Figure 7: Some Information in the Stock Market
5 / 7
ηt1η∗η0
1− λ
ηt+1
↘Case: y = 0
↗Case: y = 1
(a) High Info (Low y)6 / 7
ηt1η∗η0
1− λ
ηt+1
↘Case: y = 0
↗Case: y = 1
(b) Low Info (High y)
relatively low y). This information slows down the credit boom so much that the economycomes to a steady state without triggering a crisis. The second panel displays the casewith relatively low information in the stock market (that is, relatively high y). Thisinformation slows down the credit boom, but not so much to prevent a crisis. However,the information acquired in the stock market allows some qH-projects to avoid collateralexamination and decreases the magnitude of the crisis relative to the situation withoutinformation in the stock market. In other words, information acquisition in stock marketsmay prevent crises, and if not, it reduces the volatility of deterministic boom-bust cycles.
Finally, we take the general setting with endogenous information in stock markets(this is, y is endogenous to the credit boom, as in Figure 4). The next Proposition showsthat information in stock markets reacts endogenously at the peak of the credit boom,when more in need given the proximity of a crisis. Even though this reaction most likelyprevents a crisis, it also has the possibility to induce non-crisis cycles.
Proposition 4. When information in the stock market is endogenous, it may preventcrises but create non-crisis cycles.
Proof From the proof of Proposition 3, ∂ηt+1∂ηt|IC=0,yt=y > 0 . Combining equation
(11) from Lemma 1 with equation (9), ∂ηt+1∂ηt|IC=0,y∗ can be negative. The reason is that, as
credit booms increase ∂zt
∂ηt< 0, and from equation (9), ∂yt
∂zt> 0. If this derivative is large
enough the derivative is negative and can generate a cyclical steady state with a cyclethat does not involve a crisis. q.e.d.
25
The first panel of Figure 4 shows how yt changes with zt and then with ηt. Thatinformation in the stock market reacts to availability of credit changes the nature of thestationary equilibrium. If stocks markets attract information acquisition before crisesdevelop, then not only does information production in the stock market prevent a crisisbut it may also generate non-crisis cycles. Figure 8 shows this possibility: the evolutionof ηt bends as information acquisition in the stock market changes. If at some pointinformation starts being acquired in the stock market, the difference equation transitionsgradually from the case without information (y = 1) to the case of full information (y = 0).Once the credit moves back to a situation with low information acquisition in the stockmarket, the difference equation transitions back to the case y = 1.
The shape of the difference equation critically depends on the shape of the first panelof Figure 4. In the case depicted, the economy cycles before suffering a crisis. The cyclestill displays less volatility than the one involving crises. More in general, however, thephase diagram is contained between the benchmarks of y = 0 and y = 1 depending on howinformation in stock markets reacts to the credit boom. The shape of the phase diagramdetermines whether the crisis is avoided with a non-crisis cycle, with a non-cyclical steadystate or not avoided at all.
Figure 8: No-Crisis Cycles
7 / 7
ηt1η∗η0
1− λ
ηt+1
↘Case: y = 0
↗Case: y = 1
26
3.4 Normative Insights
Our setting offers a clear characterization of the unconstrained first best: since wehave assumed that all firms have a positive net present value project and their financingis feasible, the first best specifies that all firms operate in all periods, which would beachieved in the absence of financial frictions. Then, what makes our economy depart fromthe first best is the reliance on collateral with heterogeneous quality and the possibility ofprivate information acquisition in both markets. While information in stock markets doesnot affect allocations directly, it does so by affecting information production in creditmarkets.
The first best is implemented in equilibrium in the situation we denoted as “goodbooms" in Proposition 1 (depicted in the second panel of Figure 5). In all other steadystates the equilibrium implements lower welfare than in the first best, either becauseit displays recurrent crises (as in the case of bad booms) or because it displays lessproduction than optimal (as in the case with full information in stock markets).
What can a government do in those situations to bring the economy near to the firstbest? The answer depends on the available policy tools. Here we assume the governmentcan implement a set of policies (regulations, restrictions, controls, etc) that induce shadowtaxes and subsidies to the cost of information production and processing, both aboutprojects in stock markets (which we denote by τq in proportion to the private cost) andabout collateral in credit markets (which we denote by τC).
Policies that induce a shadow tax on information acquisition in credit markets includeall interventions that make it more difficult for a lender to obtain information aboutcollateral, for instance deregulating opaque over-the-counter markets, facilitating the useof complex structured products and rehypothecation or relaxing regulatory constraintsthat punish the use of non-standard contracts such as those specified in the Dodd-FrankReform. Policies that induce a shadow tax to information acquisition in stock marketsinclude all interventions that make it more difficult for an investor to obtain informationabout firms, for instance relaxing accounting guidelines and restrictions of reportingpractices such as those specified in the Sarbanes-Oxley Act.
If the government could intervene in both markets, it would like to discourageinformation in credit markets to a point in which there is no crisis even if all firms operate,
27
(η∗ = 1) and also in stock markets, which would lose their macroprudential role and onlyinduce an inefficient reduction of credit in the economy.
Proposition 5. If the government can intervene in both markets, it would like to discour-age information in both. To implement the first best allocation with stable high production,the set of policies should induce a “shadow tax" to the cost of information in credit markets(about collateral) such that τC ≥ (1−p̂)(1−q̂t(1))K∗
γC− 1 and in stock markets (about projects)
such that τq ≥ ψ(1− ψ)(qH − qL)AK∗ − 1.
Proof The government would like to implement all firms operating (η∗ = 1) butwithout crises. This implies p∗(q̂t(η∗ = 1)) < p̂, or using equation (2), 1− γC(1+τC)
(1−q̂t(1))K∗ < p̂,where τC captures the shadow cost of restrictive policies and regulations. The condition inthe proposition follows, with q̂(1) = ψqH+(1−ψ)qL. To avoid information in stock markets,from equation (4) evaluated at y∗ = 1 and at η∗ = 1 (which implies z(η∗ = 1) = ψ), thecondition to prevent information is ψ(1− ψ)(VH − VL) < γq(1 + τq). Since, evaluated atthe situation in which all firms get credit, VH − VL = (qH − qL)AK∗, the equation in theproposition follows. q.e.d.
The desirability of discouraging information production in stock markets arises fromthe possibility of discouraging information production in credit markets so to avoid crises,and then eliminating the macroprudential benefit of information in stock markets. Ifdirect interventions in credit markets were not feasible, intervening in stock markets wouldstill help. The next proposition shows the optimal level of difficulty to obtain informationthat can be implemented in stock markets when facing the possibility of a crisis.
Proposition 6. If the government cannot intervene in credit markets and there is a crisisat a credit boom η∗, the optimal amount of information in stock markets is given by,
(1− y∗) =[
(1− λ)(1− η∗)η∗(1− ψ)(η∗ − p̂)
]0.5
,
which can be induced by policies that implement a “shadow tax/subsidy" such that equation(4) holds.
Proof If there is a mass of active firms η∗ that triggers a crisis, it implies that thefraction of informed bidders in stock markets for firms with collateral p̂ is low enough toprevent it (as in the second panel of Figure 7). The maximum amount of production that
28
is stable is η∗. This credit volume is maintained in steady state when equation (10) inLemma 1 holds when evaluated at η∗ (which implies evaluating vt+1 as (1− ψ
η∗)(1− y∗),
from equation (8). The equation in the proposition follows. The fraction (1−y∗) representsthe minimum fraction of informed bidders that prevent a crisis. It can be implementedby reducing the cost of information to γq in equation (4) evaluated at the target y∗ forz = ψ
η∗and VH − VL = (qH − qL)AK∗. q.e.d.
Intuitively, there is a crisis once the credit boom reaches a mass η∗ of active firms andthere is not enough information in stock markets to prevent it (as in the second panel ofFigure 7). The proposition shows the minimum amount of information in stock marketsthat prevent a crisis exactly at that point. The government would not like to have moreinformation than the volume characterized in the Proposition because it would just reduceproduction without further gains in terms of stability (as in the first panel of Figure7). In other words, if the government cannot directly discourage information in creditmarkets it may want to encourage information in stock markets to indirectly discourageinformation in credit markets and avoid a crisis. Still discouraging information directly incredit market is superior as it can avoid a crisis while at the same time increasing thefeasible magnitude of the credit boom.
4 Testing Aggregate Information Dynamics
In this section, we test a number of implications of the model. First, we explainthe empirical measures that we use in our analysis. Motivated by our setting, we usestock market price data to construct an empirical proxy of information produced in theeconomy and a measure of economy-wide fragility that captures the probability of defaultin credit markets. We then discuss our dataset. Finally, we turn to the hypotheses tests.
4.1 Measures of Information and Fragility
Corresponding to the model we examine two measures that capture informationencoded in stock markets and a stock-based measure of fragility or default probability incredit markets.
29
The first is a stock price-based measure of information in the economy. If informationis produced in stock markets, firms are distinguished by the quality of their project,which gets embedded in firms’ stock prices. Our empirical counterpart is a cross-sectioncharacterization, more specifically the cross-section of firms’ average stock returns. Inparticular we look at the standard deviation of firms’ average returns: CsAvg.6 We labelthis variable Information.
The second measure also comes from the model and corresponds to default probabilityin credit markets, which has implications for the likelihood of information acquisitionabout collateral, and then credit. It is is a stock price-based measure of economy-widefragility. When ψ is low, eventually there are more qL firms in the economy and thesefirms are more likely to default because qL < qH . We measure fragility (the extent oflow-quality projects operating in the economy) with the inverse of the time-series volatilityof a stock, which we denote by 1/V ol and label as Fragility.7
This definition of fragility is from Atkeson et al. (2013). Based on Leland’s (Leland(1994)) and Merton’s (Merton (1974)) structural models these authors develop twoconcepts of default: Distance-to-Insolvency and Distance-to-Default. They then showthat the variable one over the firm’s equity volatility (1/V ol) is bounded between thesetwo measures. Intuitively, when a firm’s equity volatility is high, the firm is more likelyto default (for given leverage). The fragility of an economy moves over time and spikessignificantly during a crisis. Based on 1/V ol, Atkeson et al. (2013) study the U.S. over1926-2012 and show that 1932-1933, 1937 and 2008 stand out as especially fragile periods.8
6This variable is related to the cross-section of firms’ stock return volatility: CsV ol, and are highlycorrelated, 0.96. Hence, we will restrict attention to CsAvg in the remaining of the paper.
7Fragility is essentially a measure of economy-wide bankruptcy risk. There is a history of researchthat shows that firms are increasingly prone to bankruptcy leading up to a recession. Burns and Mitchell(1946) show that the liabilities of failed non-financial firms is a leading indicator of recession. Also seeZarnowitz and Lerner (1961). As mentioned above, Gorton (1988) shows that when the unexpectedcomponent of this variable spikes there was a banking panic during the U.S. National Banking Era,1863-1914. There was never a panic without the threshold being exceeded; and the threshold was neverexceeded without a panic. See the discussion in Gorton (2012), p. 75-77.
8Vassalou and Xing (2004) use the Merton (1974) model measure of default risk to show that defaultrisk is a systematic risk and that the Fama-French asset pricing factors partially reflect default risk.
30
4.2 Data
The measures of Information and Fragility are constructed using daily stock price datafrom Thomson/Reuters DataStream. We use daily stock price data from 52 countries over1973-2012, which amounts to approximately 105 million observations.9 Online AppendixFigure 9 shows the evolution of the number of countries included in the sample and Tables6 and 7 summarize our quarterly and annual data respectively. Online Appendix Tables4 and 5 show the countries and the time period covered for each country. The panel isunbalanced. We follow Valencia and Laeven (2012) for the dating of financial crises.
We proceed as follows. To measure CsAvg in each country we compute the cross-sectional standard deviation of average of firms’ monthly stock returns in the stock marketof that country. For 1/V ol, we compute the average of firms’ monthly stock returnvolatilities in each country. For stability of these figures, we take these two monthly seriesand average them across months to create quarterly series. The annual series that westudy next are formed using the last quarter observation of the quarterly series.
4.3 Three Tests
In this subsection we test three hypotheses that follow from the model.
1) Information and Fragility predict financial crises: As the credit boomgoes on, the economy is becoming increasingly fragile. This is because the marginalproject is of lower quality and higher fragility that the average (in the model, more qLprojects are under taken and they are more likely to default than qH projects). As thisoccurs, information is increasingly produced in the stock market, leading up to the crisis.Table 1 below addresses this hypothesis. The left-hand side variable is a dummy variableindicating that there was a crisis in a specific country that year when equal to 1, as perValencia and Laeven (2012). We provide results from Linear Probability and LOGITspecifications (controlled by GDP, credit and productivity, as well as clustering). Weconfirm the hypothesis, as an increase in Information (this is, an increase in CsAvg andan increase in Fragility (this is, a decline in 1/V ol), both tend to precede and predict
9We drop stock price data when there are less than 100 listed stocks.
31
financial crises.10
Table 1: Information Measures, Macroeconomic Variables, and FinancialCrises. The table summarizes the predictive power of information measures (1/V ol,CsAvg, ∆(1/V ol), ∆CsAvg) and macroeconomic variables (∆rGDP , ∆Credit, ∆TFP ,∆Labor Productivity) on the occurrence of financial crises. The linear probabil-ity model regression specification is: 1n,t(Crisis) = αn + β′Xn,t−1 + εn,t and thelogit regression specification is: 1n,t(Crisis) = αn + β′Xn,t−1 + εn,t, where Xn,t−1 =(1/V oln,t−1, CsAvgn,t−1,∆V oln,t−1,∆CsAvgn,t−1,∆rGDPn,t−1,∆Creditn,t−1,∆TFPn,t−1,∆LPn,t−1)′.The data are annually and span a period from 1973 until 2012. All regression specificationstake into account country fixed effects and standard errors are clustered both at a countryand time level.
(1) (2)LPM LOGIT
1/V olt−2 -0.052 -0.796+
(-1.48) (-1.65)
CsAvgt−2 0.743+ 7.555∗
(1.80) (2.18)
∆(1/V ol)t−1 -0.087∗∗ -1.337∗∗∗
(-2.82) (-6.21)
∆CsAvgt−1 0.551+ 4.983+
(1.84) (1.87)
∆rGDPt−1 -4.052∗∗∗ -45.629∗∗∗
(-4.35) (-3.65)
∆Creditt−1 -0.000 -0.275(-0.02) (-0.59)
∆T F Pt−1 0.780 14.046(0.99) (1.45)
∆LPt−1 0.789 7.469(0.87) (0.76)
Constant 0.267+ 0.208(1.66) (0.13)
N 674 575R2 0.22 .F 3.79 .Cluster (Time) YES YESCluster (Country) YES YESFE (Country) YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
2) Information and Fragility do not predict financial crises when preced-ing credit boom happens jointly with high productivity growth: The theoreticalanalysis showed that the relative abundance of qH-projects, ψ, is important to drive creditbooms and to determine the dynamic interaction between stock and credit markets. More
10Table 8 in the internet Appendix confirms the result using quarterly data, but without the macrovariables which are only available annually. Also, Table 9 in the internet Appendix shows that thepredictive power of the Information measure extends up to four quarters prior to the crisis, whereas thatof the Fragility measure extends up to eight quarters (two years) prior to a crisis.
32
specifically, when ψ is high, the probability of default in the q̂(η) is lower for all η andthe condition p∗(q̂(η∗)) = p̂ at which a crisis happens implies η∗ is larger and that crisesare less likely, regardless of information in stock markets. Indeed, Gorton and Ordoñez(2020) show that good booms (those that do not end in a crisis) are indeed characterizedby high total factor productivity (TFP) growth while bad booms (those that do end in acrisis) display a TFP growth path that starts to decline leading up the crisis.
Similar to Gorton and Ordoñez (2020), we define a credit boom as follows. Thebeginning of a credit boom is marked by three consecutive years of credit growth greater orequal to 3% and the end by two consecutive years of negative credit growth. Empirically,we distinguish between high-TFP and low-TFP credit booms by dividing the boomsaround the mean growth in TFP across all the identified booms. Since low and high-TFP are indeed interpreted as low and high Fragility, we dispense from Fragility in theregression. Table 2 shows that indeed Information predicts financial crises during low-TFPbooms, but not in high-TFP booms.
Table 2: Information Production during Low and High Productivity CreditBooms.The table summarizes the predictive power of ∆CsAvg interacted with dummyvariables indicating years into the credit boom on future ∆Credit. The regressionspecification is: 1n,t(Crisis) = αn + β∆CsAvgn,t−1 + γCsAvgt−2 + δ′Xn,t−1 + εn,t, whereXn,t−1 = (∆rGDPn,t−1,∆TFPn,t−1,∆LPn,t−1,∆INVn,t−1)′. The data are annual andspan a period from 1973 until 2012. All regression specifications take into account countryfixed effects and standard errors are clustered both at a country and time level.
(1) (2) (3)All Booms Low T F P High T F P
∆CsAvgt−1 0.691∗ 0.741∗ 0.367(2.13) (2.22) (0.56)
CsAvgt−2 0.829∗ 0.811∗ 0.583(2.54) (2.36) (0.61)
∆LPt -1.404 -2.578 0.074(-0.89) (-1.16) (0.04)
∆GDPt−1 -0.648+ -1.245 -0.265(-1.74) (-1.33) (-1.19)
∆T F Pt−1 0.647 0.684 0.490(0.91) (1.31) (0.39)
∆INVt−1 -0.771∗ -0.649 -0.799+
(-2.51) (-1.22) (-1.96)
N 382 235 147R2 0.34 0.33 0.31F 4.19 5.87 0.87Cluster (Boom) YES YES YESCluster (time) YES YES YESFE (Boom) YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
33
3: Information production in stock markets negatively predicts futurecredit during credit booms. As highlighted when comparing the two panels in Figure7, information in stock markets delays credit growth during a credit boom (the first panelshows a faster decline in the growth rate of credit than the second). In words, moreinformation production in stock markets reduce the amount of future credit because alarger fraction of weak firms are revealed as such, their collateral is examined and theyare cut out of the credit market when found out with bad collateral.
To test this hypothesis and to track the role of information in different phases of thecredit boom, we interact the change in the measure of Information, ∆CsAvg with theyear of the credit boom, e.g., first year, second year, and so on. Table 3 shows the results.For boom years one, two, and three the coefficients on the interaction terms are negativeand significant, implying that indeed, when there is more information generated in stockmarkets during a credit boom there is a decline in subsequent credit growth.
5 Conclusion
A financial crisis occurs when information-insensitive debt becomes sensitive, affectingall collateral that, because it was previously information-insensitive, looks alike. Thisis more likely to happen after long credit booms, as the quality of projects undertakendecreases with the boom (this is, marginal projects are of lower quality) and comes a(Minsky) moment when it is suddenly profitable to produce information about all firms’unknown collateral. In a financial crisis information production about all firms’ collateralcannot be prevented and a large mass of firms loose credit and cannot operate.
In this paper we explore the interaction of credit markets subject to crises, and theother main financial market, stock markets, unveiling a novel macroprudential role forstock markets. We endow participants in both markets to acquire information about theirrespective objects of interest, firms’ projects in stock markets and firms’ collateral in creditmarkets. As credit booms evolve and average projects’ quality decline, not only thereare more incentives to acquire information about collateral but also about firms in stockmarkets. Once weaker firms are discovered and stop participating in credit markets, thereis a relaxation of the incentives to acquire information about the collateral of participatingfirms, potentially preventing a crisis.
34
Table 3: Future Credit in Relation to Information Production Dur-ing Credit Booms. The table summarizes the predictive power of ∆CsAvginteracted with dummy variables indicating years into the credit boom onfuture ∆Credit. The regression specification is: ∆Creditt+1 = αn +β′∑5k=1 ∆CsAvgk,t−1 × 1n,t(Boom-year = k) + γ′Xn,t−1 + εn,t, where Xn,t =
(∆Creditt−1,∆(1/V ol)t,∆CsAvgt,∆rGDPn,t,∆Creditn,t,∆TFPn,t,∆LPn,t). The dataare annually and span a period from 1973 until 2012. All regression specifications take intoaccount country and year fixed effects, and standard errors are clustered at the countryand year level.
(1) (2) (3)∆CsAvgt -0.128+ -0.177
(-1.72) (-0.97)
1t(Boom) 0.034 0.037 0.033+
(1.63) (1.29) (1.77)
∆CsAvgt × 1t(Boom = 1) -0.021 -0.150(-0.07) (-0.36)
1t(Boom = 1) 0.057∗ 0.054+ 0.059∗∗
(2.49) (1.79) (2.82)
∆CsAvgt × 1t(Boom = 2) -0.006 -0.012(-0.03) (-0.04)
1t(Boom = 2) 0.046∗∗∗ 0.032 0.048∗∗∗
(3.39) (1.28) (3.35)
∆CsAvgt × 1t(Boom = 3) -0.281∗ -0.280+
(-2.42) (-1.93)
1t(Boom = 3) 0.003 -0.022 0.003(0.20) (-1.10) (0.21)
∆CsAvgt × 1t(Boom = 4) 0.214 0.136(1.30) (0.28)
1t(Boom = 4) -0.014 -0.014 -0.010(-1.17) (-1.55) (-0.86)
∆CsAvgt × 1t(Boom = 5) -0.069 0.030(-1.22) (0.12)
1t(Boom = 5) 0.005 0.001 0.006(0.25) (0.04) (0.27)
∆Creditt -0.101 -0.137∗ -0.085(-1.62) (-2.24) (-1.39)
∆CsAvgt−1 -0.187∗ -0.367+
(-2.47) (-1.90)
∆LPt -0.003(-0.01)
∆rGDPt 0.186(0.87)
∆T F Pt -0.168(-0.38)
∆INVt 0.174(1.30)
N 891 583 930R2 0.13 0.13 0.12F 3.69 2.35 4.36Cluster (country) YES YES YESCluster (time) YES YES YESFE (country) YES YES YESFE (time) YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
35
In few words, by play an unexplored positive macroprudential role in the economy,stock markets become an automatic stabilizer of credit markets. This cleansing effectof stock markets’ information on credit markets’ composition prevent crises. On theone hand, when stock markets do not convey too much information we may observemore crises. on the other hand, when stock markets convey too much information, creditmarkets may not function at full potential. Weighting on this credit-crisis trade-off ofstock markets, we discuss normative implications that guide policy restrictions that mayhave effects on information incentives in both markets.
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38
A Online Appendix (Not for Publication)
Figure 9: Number of countries. The figure summarizes the evolution of the numberof countries in the equity data sample. The data are quarterly from Thomson/Reuters(DataStream) and span a period from 1973 until 2012.
15
20
25
30
35
40
# o
f C
ountr
ies
1973−Q1 1978−Q3 1984−Q1 1989−Q3 1995−Q1 2000−Q3 2006−Q1 2011−Q3
date
39
Tab
le4:
Equ
ityda
ta-pa
rt1.
The
tablesummarizes
thenu
mbe
rof
firmsforagivencoun
tryan
dyear
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return
data
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frequ
ency
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tais
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.Datais
from
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mson/
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DataS
tream.
Co
un
try
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
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91
19
92
19
93
Arg
enti
na
1314
1618
2878
Au
stra
lia
7374
7779
8282
8284
8680
9099
100
112
127
250
336
330
370
407
484
Au
stri
a15
1310
912
915
1112
1615
1427
2430
2749
6769
7885
Bel
giu
m34
4039
4036
3739
3940
4141
4448
8092
8688
8985
8893
Bra
zil
1016
2440
Bu
lgar
iaC
hil
e83
101
109
120
138
Co
lom
bia
3432
Cro
atia
Cze
chR
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bli
c94
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mar
k22
2914
916
1516
1918
3539
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4543
137
151
156
181
191
209
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Est
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3246
5654
6368
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6570
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313
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109
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2833
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318
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6461
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222
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227
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832
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738
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9110
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119
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8312
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106
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143
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7210
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9191
121
126
114
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216
213
213
215
231
215
217
213
Bu
lgar
ia29
2731
3341
3831
3038
4448
5149
5553
5455
Ch
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139
143
129
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140
132
122
119
110
114
118
119
122
113
116
123
120
123
116
109
108
Co
lom
bia
5243
4849
3625
3036
3233
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3743
3041
4234
3133
29C
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4232
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6797
138
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105
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Cze
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522
423
415
714
812
393
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4428
3030
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820
821
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021
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917
215
316
216
816
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420
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416
115
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86
117
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2019
1718
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3236
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105
110
128
138
150
166
169
164
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153
148
141
149
146
142
134
136
131
130
129
137
Fra
nce
638
655
793
880
892
891
937
924
870
828
799
805
853
871
820
811
756
707
666
669
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Ger
man
y46
647
453
859
678
611
2713
8314
6214
1814
0714
5715
6617
9819
4419
5818
1418
2816
0015
3813
7213
84G
reec
e20
622
223
024
226
329
233
633
633
833
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1636
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3326
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4646
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1513
1724
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192
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41
Table 6: Summary Statistics (Quarterly). The table reports summary statistics for∆rGDP , α, 1/V ol, CsV ol, ∆(1/V ol), ∆CsV ol. The data are from the OECD iLibraryand Thomson/Reuters (DataStream), and span a period from 1973 until 2012. “Count”label refers to country-quarters.
count mean sd min max1/V ol 3963 3.226 0.977 0.888 6.796CsAvg 3963 0.134 0.095 0.023 1.138∆(1/V ol) 3952 0.002 0.533 -2.721 3.316∆CsAvg 3952 0 0.077 -0.654 0.640No. of Countries 169 25.633 8.809 15 42
Table 7: Summary Statistics (Annual). The table reports summary statisticsfor real GDP in bn. $, TFP , Credit/rGDP , Labor Productivity in hours, ∆rGDP ,∆TFP , ∆Credit/rGDP , ∆Labor Productivity, 1/V ol, CsAvg, ∆(1/V ol), and ∆CsAvg.The data are from the Penn World Tables (PWT), WIPO statistics database, World Devel-opment Indicators, Total Economy Database (TED), and Thomson/Reuters (DataStream),and span a period from 1973 until 2012. “Count” label refers to country-years.
Count Mean StDev Min Maxreal GDP in bn $ 2787 383.466 939.771 3.096 10228.909T F P 1895 451.679 175.543 104.050 823.585Credit/rGDP 2730 57.454 46.122 1.385 232.097Labor P roductivity in hours 1903 15.171 8.738 1.586 41.145∆rGDP 2726 0.035 0.042 -0.321 0.308∆T F P 1857 0.007 0.038 -0.180 0.236∆Credit/rGDP 2674 0.036 0.168 -0.863 2.881∆Labor P roductivity 1858 0.026 0.033 -0.179 0.1961/V ol 998 3.191 0.999 0.921 6.680CsAvg 998 0.135 0.092 0.023 0.854∆(1/V ol) 959 0.007 0.850 -2.867 3.403∆CsAvg 959 0.002 0.080 -0.429 0.536
42
Table 8: Information Measures and Financial Crises - Quarterly Observa-tions. The table summarizes the predictive power of information measures (1/V ol,CsAvg, ∆(1/V ol), ∆CsAvg) on the occurrence of financial crises. The regressionspecification is: 1n,t(Crisis) = αn + β′Xn,t−1 + εn,t for linear probability models andPr(1n,t(Crisis) = 1|Xn,t−1) = Φ(αn + β′Xn,t−1) for LOGIT models, where Xn,t−1 =(1/V oln,t−1, CsAvgn,t−1,∆V oln,t−1,∆CsAvgn,t−1)′. The data are quarterly and span aperiod from 1973 until 2012. All regression specifications take into account country fixedeffects and standard errors are clustered both at a country and time level.
(1) (2)Linear Logit
1/V olt−2 -0.098∗∗∗ -1.761∗∗∗
(-3.88) (-6.54)
CsAvgt−2 0.491+ 4.104∗
(1.95) (2.22)
∆(1/V ol)t−1 -0.059∗∗ -1.068∗∗∗
(-2.89) (-3.88)
∆CsAvgt−1 0.327∗ 2.792∗∗
(2.33) (2.71)
Constant 0.180 2.465∗∗
(1.52) (3.01)
N 3920 3220R2 0.16 .F 14.64 .Cluster (Time) YES YESCluster (Country) YES YESFE (Country) YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Table 9: Information Measures and Financial Crises - lagged regressions(LOGIT). The table summarizes the predictive power of information measures (1/V ol,CsAvg, ∆(1/V ol), ∆CsAvg) on the occurrence of recession with crises events. Theregression specification is: Pr(1n,t(Crisis) = 1|Xt−q) = Φ(αn + β′Xt−q), whereXn,t−q = (1/V oln,t−q, CsAvgn,t−q,∆V oln,t−q,∆CsAvgn,t−q)′. The data are quarterly andspan a period from 1973 until 2012. All regression specifications take into account countryfixed effects and standard errors are clustered both at a country and time level.
(1) (2) (3) (4) (5) (6)q=0 q=1 q=2 q=3 q=4 q=8
1/V olt−q−1 -1.808∗∗∗ -1.761∗∗∗ -1.578∗∗∗ -1.346∗∗∗ -1.105∗∗∗ -0.500+
(-6.58) (-6.54) (-5.77) (-4.76) (-4.03) (-1.95)
CsAvgt−q−1 4.976∗∗ 4.104∗ 3.173+ 2.436 2.026 1.243(2.65) (2.22) (1.74) (1.45) (1.25) (0.82)
∆(1/V ol)t−q -0.955∗∗ -1.068∗∗∗ -1.179∗∗∗ -0.969∗∗ -1.015∗∗∗ -0.491+
(-3.20) (-3.88) (-4.45) (-3.18) (-3.53) (-1.94)
∆CsAvgt−q 3.011∗∗ 2.792∗∗ 2.525∗∗ 1.818+ 1.578+ 0.711(3.00) (2.71) (2.68) (1.72) (1.79) (0.88)
N 3201 3220 3196 3116 3093 3001Cluster (Time) YES YES YES YES YES YESCluster (Country) YES YES YES YES YES YESFE (Country) YES YES YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
43