Financial Markets, the Real Economy, and Self-ful lling Uncertainties

Transcription

1 Financial Markets, the Real Economy, and Self-ful lling Uncertainties Jess Benhabib y Xuewen Liu z Pengfei Wang x This version: September 08 Forthcoming in Journal of Finance Abstract We develop a model of informational interdependence between nancial markets and the real economy, linking economic uncertainty to information production and aggregate economic activities in general equilibrium. The mutual learning between nancial markets and the real economy creates a strategic complementarity in their information production, leading to selfful lling surges in economic uncertainties. In a dynamic setting, our model characterizes selfful lling uncertainty traps with two steady-state equilibria and a two-stage economic crisis in transitional dynamics. We are grateful to the editor and two referees for their detailed comments and suggestions that have signi cantly improved the paper. We thank Russell Cooper, Feng Dong, Gaetano Gaballo, Shiyang Huang, Alexander Kohlhas, Wei Xiong, Liyan Yang, Kathy Yuan, Zhen Zhou, and seminar participants at the FIRS conference 08, Wharton Conference on Liquidity and Financial Fragility 07, Barcelona GSE Summer Forum 07 - Information frictions, HKUST Macro Workshop 07, Tsinghua Finance Workshop 07, AFR Summer Institute of Economics and Finance 07, Ningbo International Finance Conference 06, CUHK-Shenzhen, Tsinghua PBC, CKGSB, Shanghai Jiao Tong University (SAIF), and HKUST for helpful comments. Liu and Wang acknowledge the nancial support from the Hong Kong Research Grants Council (GRF #650485). y Department of Economics, New York University, 9 West 4th Street, New York, NY 00, USA. ess.benhabib@nyu.edu. Tel: () z Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. xuewenliu@ust.hk. Tel: (+85) x Department of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. pfwang@ust.hk. Tel: (+85)

2 Uncertainty in both nancial markets and the real economy rises sharply during recessions. The recent nancial crisis of presented one of the most striking episodes of such heightened uncertainty. The nancial market uncertainty, measured by the VIX index, umped by an astonishing 33% in the Great Recession. The increase in measured real uncertainty was equally astounding. For instance, the macroeconomic uncertainty measured in Jurado et al. (05) almost doubled, and Bloom et al. (0) report a 5% increase in the micro-level real uncertainty measured by the rm-level dispersion of output. What causes such sudden spikes in uncertainty? Why do nancial uncertainty and real uncertainty move together? Why do they rise sharply in recessions? These challenging questions are of central importance for understanding the interaction between nancial markets and the real economy. The purpose of this paper is to provide a theoretical framework to address these questions. We develop a model of informational interdependence between nancial markets and the real economy, linking uncertainty to information production (or acquisition) and aggregate economic activities. As the starting point of our theory, we argue that there exists mutual learning between nancial markets and the real economy. Their oint information productions determine both the real production e ciency in the real sector and the price e ciency in the nancial sector. As an example, oil producing companies scrutinize oil future prices when making their production decisions, while the nancial market studies the nancial reports from these producing companies to learn information when trading on oil futures. This mutual learning creates a strategic complementarity between information production in the nancial sector and that in the real sector. A self-ful lling surge in nancial uncertainty and real uncertainty can naturally arise when both sides produce little information in anticipation of the other producing little information. At the same time, aggregate output falls as the real production e ciency deteriorates. We formalize the idea in an extended Grossman-Stiglitz (980) model. Our key innovation is that we introduce a real sector along the lines of Dixit-Stiglitz (977) in our framework, rms have to make investment decisions under imperfect information about two dimensions of uncertainty: their idiosyncratic productivity and demand shocks. We start with one rm and one nancial market in our baseline partial equilibrium model for a given aggregate output. To reduce uncertainty, the rm can learn about its idiosyncratic productivity shock by incurring a cost, but it has to infer its demand shock from the information provided in the nancial market where speculators (or traders) have a comparative advantage in acquiring information about the demand shock. In this context, the nancial price is ointly determined by the rm s information production and thereby its disclosure and the demand information produced by nancial market speculators. To understand strategic complementarity between these two sources of information, rst suppose that the rm makes more accurate information disclosure about its productivity shock. The reduced uncertainty about the productivity shock attracts more informed traders and induces

3 more aggressive trading. Hence, the amount of information produced on the demand shock in the nancial market increases. Conversely, suppose that the nancial price becomes more informative about the demand shock for some reason. The reduced uncertainty regarding the demand enables the rm to make better investment decisions and hence achieve a higher pro t for every realized supply shock. This implies that the stake is higher for the rm to acquire information about its productivity shock. Hence, the rm has stronger incentives to acquire information about its productivity shock. As the marginal bene t of acquiring information for the rm depends on aggregate output (besides nancial price informativeness), the nature of equilibrium also depends crucially on the level of aggregate output. When the aggregate output is su ciently high, the rm s incentive to acquire information is already strong enough and acquiring information is a dominant strategy for the rm. The resulting equilibrium is hence unique in which the rm produces and discloses more precise information and the nancial market generates a more informative price signal. As a result, both nancial and real uncertainty are low. At the other extreme, when the aggregate output is su ciently low, not acquiring information is a dominant strategy for the rm. Anticipating this, speculators in the nancial market also have little incentive to acquire information about the rm s demand shock. The equilibrium is hence also unique. However, when the aggregate output is in the intermediate range, the economy has two self-ful lling equilibria. The information produced by the rm and the information generated by the nancial market in one equilibrium (the good equilibrium) are much more precise than those in the other equilibrium (the bad equilibrium). Consequently, a surge in uncertainty can suddenly strike as a self-ful lling equilibrium phenomenon. We then extend the baseline model to a macroeconomic general-equilibrium framework with aggregate production to endogenize the aggregate output. The nal consumption good is produced with a continuum of intermediate capital goods as the input according to a Dixit-Stiglitz production function. Each intermediate capital good is produced by one rm located on an island in the spirit of Lucas (97). When information signals on some islands become noisier, the real investment decisions on those islands become less e cient and consequently the aggregate output declines. This causes the aggregate demand faced by other islands to drop. Thus, incentives to acquire information in the real sector on those other islands are also reduced, which decreases information acquisition in their nancial sectors as well. The aggregate output hence declines further, which in turn a ects those islands experiencing the original shock. In short, the complementarity in goods production due to the Dixit-Stiglitz demand externality across islands generates further complementarity in information production across islands. As a result, the complementarity forces for equilibrium multiplicity are strengthened in the general equilibrium. Similar to the partial equilibrium model, the economy may feature multiple (two) equilibria. In particular, in general equilibrium, a selfful lling rise of uncertainty is accompanied by the reduction in investment e ciency and the fall

4 in aggregate output. We derive four key implications of our macroeconomic model. First, an adverse shock originating in either the real sector or the nancial sector that impairs their ability to conduct information acquisition can have a large impact on the aggregate economy due to the compound feedback loops. In fact, both aggregate investment and the endogenous aggregate TFP are decreasing in information precision. Hence, a small shock in information acquisition cost can have a large impact on all three quantities (aggregate investment, endogenous aggregate TFP, and aggregate output) in the same direction, in particular when it triggers a self-ful lling bad equilibrium. Second, our model endogenizes together the three variables nancial uncertainty, real uncertainty, and aggregate economic activities and shows countercyclical uncertainty as observed in the data. Third, our model provides an information contagion channel, where a shock that directly a ects only a small fraction of islands can generate a global recession on all islands through the endogenous information mechanism. Fourth, our model with a production economy sheds light on several puzzling empirical facts on asset price comovement. More information about idiosyncratic shocks results in individual asset prices being more responsive to idiosyncratic shocks and relatively less responsive to the aggregate shock. Hence, a lower degree of comovement of asset prices as well as a higher e ciency of resource allocation is expected to be accompanied by a higher GDP. Finally, we extend the static model into an OLG dynamic framework, deriving several additional economic insights. The OLG model provides a dynamic equilibrium setting to study the process of saving and capital accumulation. The equilibrium, therefore, is dynamically linked across periods through savings. The nature of the equilibrium in each period is path-dependent, depending not only on the realization of the productivity shock in the current period but also on the capital accumulation in past periods. We show that our dynamic model possibly has two steady-state equilibria, meaning that the economy can exhibit self-ful lling uncertainty traps. Interestingly, the transitional dynamics of our OLG model characterizes a two-stage economic crisis. A medium-sized shock to the economy initially generates a mild recession along a unique equilibrium path. But as capital accumulation deteriorates the economy will eventually reach a tipping point, where multiple equilibria start to emerge. Then a self-ful lling uncertainty crisis can suddenly throw the economy into a new bad equilibrium path. Output and capital fall dramatically and uncertainties spike. In contrast, a small shock always generates a unique equilibrium path without the second stage. Empirical studies support our model s key implication on information quality across business Brunnermeier (009) discusses various other ampli cation mechanisms of nancial markets. These implications of our OLG model are qualitatively consistent with some observed patterns of the recent nancial crisis. In fact, the initial recession did not look particularly severe until the third quarter of 008, when full nancial panic broke out after the collapse of Lehman Brothers and aggregate output fell sharply. It is now widely believed that a deterioration in fundamentals and a loss of con dence together drive this type of two-stage crisis (see, e.g., the stamp lecture on January 3, 009 by the Chairman Ben Bernanke). 3

5 cycles. Jiang, Habib and Gong (05) show evidence that management forecast errors, measured by the di erence between forecasted earnings per share (EPS) and actual EPS, increase during economic recessions. Loh and Stulz (07) document that forecast errors of nancial analysts are signi cantly higher during recessions/crises than good times. Related literature. A burgeoning literature in nance studies the informational feedback e ects of nancial markets (see Bond, Edmans and Goldstein (0) for an extensive survey of this literature). This literature argues that rm managers on the real side of the economy learn from nancial prices. Among others, 3 Goldstein, Ozdenoren and Yuan (03) and Sockin and Xiong (05) develop clean model frameworks showing how prices in the secondary nancial market can aggregate the dispersed information of speculators and guide rm managers or investors to make better real investment decisions. The learning in this literature is one way the real sector learns from nancial markets. On the other hand, the accounting literature emphasizes the opposite direction of learning arguing that rm managers typically know more than nancial market participants and focuses on studying how rm managers (i.e., insiders) disclose information to the capital market, based on which nancial speculators trade and security prices are formed. Our paper advances these two bodies of literature by introducing and studying mutual (two-way) learning between the real sector and nancial markets, similar to Sockin (07), Straub and Ulbricht (07), and Wu, Miao and Young (07). The two-way learning mechanism sheds light on important questions, such as how a nancial price is formed, where the information comes from, and how the sources of information interact. The nance literature pioneered by Grossman and Stiglitz (980) and Verrecchia (98) studies information production (or acquisition) in nancial markets. The recent work of Goldstein and Yang (05) analyzes a model where two di erent groups of nancial traders are informed of di erent fundamentals of a security. They show that trading as well as information acquisition by these two groups of nancial traders exhibit strategic complementarities. Ganguli and Yang (009) study a model where traders can obtain private information about the supply of a stock in addition to that about its payo. They show complementarity in information acquisition and the existence of multiple equilibria. Our model introduces the real sector and aggregate production into a Grossman-Stiglitz-type model; information acquisition in our model takes place both in the real sector and in nancial markets. Adding to this literature, our paper shows that complementarity in information production exists between the real sector and the nancial sector. Our model provides a micro-foundation for the two-factor structure of the asset payo in Goldstein and Yang (05). Our paper also adds to the recent literature by showing that the informational interplay between 3 For theoretical work, see, e.g., Fishman and Hagerty (99), Leland (99), Dow and Gorton (997), Subrahmanyam and Titman (999, 03), Hirshleifer, Subrahmanyam, and Titman (006), Foucault and Gehrig (008), Goldstein and Guembel (008), Ozdenoren and Yuan (008), Bond, Goldstein, and Prescott (00), Kurlat and Veldkamp (05), Huang and Zeng (06), Sockin (07), and Foucault and Frésard (06). 4

6 the real sector and the nancial sector can give important macroeconomic implications. 4 A large literature in macroeconomics documents robust evidence of countercyclical uncertainty both real uncertainty and nancial uncertainty increase during recessions. Real uncertainty is often proxied by rm-level dispersion in earnings, productivity and output, and the volatility of aggregate output forecast error, while nancial uncertainty is often measured by nancial market volatility and the VIX index (Bloom (009), Bloom et al. (0), Jurado et al. (05)). An ongoing heated debate in this literature concerns the question of causality, i.e., whether uncertainty is a cause of or merely a response to recessions and where it comes from (see, e.g., Bachmann and Bayer (03, 04)). Our paper contributes to the debate by providing a theoretical framework that is able to address the three variables real uncertainty, nancial uncertainty, and aggregate economic activities simultaneously and show how they are related. 5 Bacchetta, Tille and Wincoop (0) also study the self-ful lling nature of uncertainty. In their model with an endowment economy, if agents believe pure sunspots matter for asset prices, then the perceived risk of future prices will increase. As a result, the current asset prices will indeed be a ected. The uncertainty is self-ful lling because there also exists another equilibrium in which the asset prices are certain and hence bear zero risk. Fagelbaum, Schaal and Taschereau-Dumouchel (06) propose a theory of self-reinforcing episodes of high uncertainty and low activity, through the mechanism of the wait-and-see e ect together with agents learning from the actions of others. In contrast to these contributions, self-ful lling uncertainty in our model comes from the information interdependence between nancial markets and the real economy. This information interplay also allows us to study the impact of uncertainties on real economic activities. Our model is related to a small body of the macroeconomics literature that studies how nancial markets a ect business cycle uctuations through information channels. 6 Angeletos, Lorenzoni and Pavan (00) build a two-stage feedback model where nancial markets in the second stage learn from the volume of asset selling of entrepreneurs in the rst stage, which generates strategic complementarity in investment that ampli es non-fundamental shocks. Benhabib, Liu and Wang (06a) present a self-ful lling business cycle model, where nancial market sentiments a ect the price of capital, which signals the fundamentals of the economy to the real side and consequently leads to real output that con rms the sentiments. David, Hopenhayn and Venkateswaran (06) conduct a quantitative study that links imperfect information and resource misallocation, where 4 Goldstein and Yang (07a) analyze a model where there are multiple dimensions of uncertainty and market prices convey information to real decision-makers. They focus on studying the e ect of disclosing public information on real e ciency. They also study the information acquisition of nancial speculators, but not that of the real sector. 5 Benhabib, Liu and Wang (06b) study endogenous information acquisition of rms that links real uncertainty and economic activities. However, there is no nancial market in the model there and that paper does not touch upon nancial uncertainty. Veldkamp (005) and Van Nieuwerburgh and Veldkamp (006) study learning asymmetries in business cycles, without involving nancial markets. 6 Among others, Reis (006), Angeletos and Pavan (007), Hellwig and Veldkamp (009), Vives (07), Colombo, Femminis and Pavan (04) and Mäkinen and Ohl (05) study information acquisition and e ciency. 5

7 rms learn from both internal sources and stock market prices about one dimension of fundamental uncertainty. The information is exogenous in their paper, and they conclude that rms turn primarily to internal sources for information, rather than to nancial markets. 7 Compared with the aforementioned studies, ours shows that the amount of information in the economy is endogenous, and that there is feedback between the level of economic activity and the amount of information, ampli ed through the mutual learning between rms and nancial markets. Our model s cross-sectional implication on asset pricing comovements is closely related to and motivated by the study of Peng and Xiong (006), who show that limited investor attention leads to category-learning behavior, i.e., investors tend to process more market- and sector-factor information than rm-speci c information. As a consequence, return correlations between rms can be higher than their fundamental correlations and sectors with a higher average return correlation across rms will exhibit less informative stock prices. Similarly, Veldkamp (006) argues that investors endogenously purchasing same information results in comovement of asset prices. Unlike us, these works study pricing comovements in an exchange economy and hence they do not link the pricing comovements to uctuations in the business cycle and investment e ciency as we do. Finally, equilibrium multiplicity due to strategic complementarity in information production in our model also adds to the large literature on coordination failures and multiple equilibria. Multiple equilibria exist in these models because each individual agent would like to do what others do. So if there is enough heterogeneity to reduce their incentives to act like others, multiple equilibria can disappear. For example, Ball and Romer (99) show that if the xed menu cost is heterogeneous, equilibrium multiplicity is still possible but depends crucially on the shape of the distribution function of the xed menu cost. Morris and Shin (998) show that heterogeneity in information can lead to a unique equilibrium in an otherwise multiple-equilibria model of currency attacks. Schaal and Taschereau-Dumouchel (05) apply the global games approach developed by Morris and Shin (998) to remove multiple equilibria in a model in which rms coordinate on capacity utilization. Interestingly, we nd that heterogeneity across rms in productivity or the information acquisition cost can actually increase, rather than reduce, the possibility of multiple equilibria in our model. This result is in sharp contrast to the types of coordination failure in other models. The paper is organized as follows. In Section I, we present the simple baseline model. In Section II, we extend our baseline model to study endogenous information. In Section III, we further extend the model to a macroeconomic framework. In Section IV, we extend the static model to an OLG dynamic framework. Section V provides numerical illustrations of our model. Section VI concludes. 7 Because David, Hopenhayn and Venkateswaran (06) consider neither endogenous information acquisition nor the feedback on information production between the real side and nancial markets, incorporating our mechanism in their quantitative study may bring new results; see our numerical calibration in Section V. 6

8 I. The Baseline Model In this section, we present a simple baseline model with one rm, one nancial market, and with exogenous information. The rm faces two uncertainties: demand shock and supply (or productivity) shock. The rm has some information about the supply shock while the nancial market has some information about the demand shock. We show that there exists two-way learning between the rm and the nancial market. A. Setup There are two types of agents: rm and a group of nancial market traders (speculators). There are two types of goods: an intermediate capital good and a nal good. The price of the nal good is normalized as the numeraire, P. Intermediate Goods Firm Firm is an intermediate goods rm. It produces the intermediate capital good Y using the nal good as input according to the production function Y = ZA K for 0 < < ; () where Z is the common productivity shock to the whole economy (regarded as a constant in the baseline model), A is rm s productivity, and K is the investment input of the nal good. 8 The input K fully depreciates after production. We will show that rm borrows the investment input at interest rate R f. The market demand function of the intermediate capital good Y is assumed to be Y = Y, () P where P is the price of the capital good (in terms of the nal good), and measures the idiosyncratic demand shock to good. Moreover, in the baseline model Y is an exogenous constant, which corresponds to the aggregate output (real GDP) (denote y log Y ), whereas parameter measures the price elasticity of demand. Financial Market and Traders (Speculators) A nancial market exists, where speculators trade a nancial asset (a derivative) contingent on the rm s asset value or rm value (also its total income): V = Y P. (3) 8 The label nal here only means that this good is a di erent good from the intermediate good. In our static model, the input K (the nal good) comes from endowment. In the extended dynamic model, the input K in the current period is the savings after consumption (i.e., the nal consumption good) from the last period. 7

9 Speci cally, we assume that the payo of the nancial derivative contract takes the form of v = log V. Note that the log form is for tractability. 9 Denote by q the market trading price of the nancial derivative contract. That is, the long position of one unit of the nancial asset (derivative) incurs an initial outlay of q and entitles to having the risky payo v later. The utility function of speculators is assumed to be U(W i ) = exp W i ; where W i is the end-of-period wealth for speculator i [0; ], and is the risk-aversion (CARA) coe cient. The initial wealth for a speculator is assumed to be W 0 and the risk-free (gross) interest rate is R f. This means that if a speculator takes a position of m units of the nancial asset, his end-of-period wealth would be W i = (W 0 mq ) R f + mv = W 0 + m(v q ). The assumption that speculators trade a derivative contract contingent on the rm s asset value, V, is made for tractability. This is along the line of the assumption in the literature that a rm s asset value or sales revenue follows a geometric Brownian motion (see, e.g., Merton (973) and He and Xiong (0)). The nancial derivative can also be contingent on the rm s product price, P (that is, v takes the form of v = log P ). In the latter case, the nancial market can be interpreted as a commodity nancial futures market that specializes in trading nancial futures regarding the intermediate capital good Y, in the spirit of Sockin and Xiong (05). Assuming that the underlying asset of the derivative is either V or P is to ensure that the payo of the underlying asset follows a log-normal distribution and thus to achieve tractability. This parallels the modeling device that assumes a speci c function form of noisy trading (or asset supply) as in Goldstein, Ozdenoren and Yuan (03), Sockin and Xiong (05), and Goldstein and Yang (07a). The net aggregate supply of the nancial asset (i.e., derivative) is assumed to be 0. The demand of noise/liquidity traders in the nancial market is n, where n follows distribution n N(0; n ). Uncertainties and Information The rm faces two uncertainties: productivity (or supply) shock A and demand shock. Their prior distributions are log A a N ( a ; a ) and log " N ( " ; " ). And a and " are independent. The common productivity shock Z is public information (denote z = log Z). 9 Goldstein and Yang (07a) study the nancial asset s payo being nonlinear with a log-normal distribution. They show numerically without analytical solutions that being more informative about one factor motivates speculators to acquire more information about the other factor. 8

10 In the baseline model, we assume that the rm and the nancial market have some exogenous (imperfect) information about a and ", respectively. Speci cally, the rm possesses or is endowed with a noisy signal about its own productivity: s = a + e, where e N(0; s ). Firm will disclose its signal s to the nancial market. 0 For simplicity, we assume that the rm has no private information about the demand shock, ". In the nancial market, as in Grossman and Stiglitz (980), there is a continuum of traders with unit mass. The traders are of two types: informed and uninformed. An informed trader i has a noisy private signal x i = " + % i, where % i N(0; x ) and % i is independent across di erent informed traders i. An uninformed trader has no private signal regarding ". The proportion of informed traders is, which is exogenous in the baseline model. Timeline The sequence of events (within the one period) in the baseline model is as follows: T : Firm discloses its signal s to the nancial market. T : Financial market trading takes place, and nancial price q is realized. T 3 : Firm makes its investment decision, K, based on information fs ; q g. T 4 : The income or asset value, V, is realized. The payo of the nancial contract is delivered. The timeline captures the two-way informational learning and production in a simple way. B. Equilibrium The equilibrium consists of a nancial market equilibrium at T and the rm s investment decision at T 3. We conduct analysis by backward induction. Firm s Investment Decision at T 3 Firm maximizes its expected pro t: K K(s ; q ) = arg max K E [P Y R f K s ; q ] (4) with constraints () and (). Here E(s ; q ) is the conditional expectation operator over a and ". It is well understood that a rm s obective is not always well de ned in an asymmetric-information environment. For simplicity and convenience, we assume that rms maximize their expected pro t. 0 As will become clear later, a rm has incentives to disclose its information to the nancial market because the disclosure can attract more information from the nancial market, which can guide the rm to make better investment decisions. Goldstein and Yang (07a) show that rms always have incentives to disclose their information orthogonal to traders (see also Bond and Goldstein (05)). We will relax this assumption in Section II.C to allow the rm to have information on the demand shock as well. 9

11 Alternatively, we can assume that rms are run by risk-neutral entrepreneurs. Financial Market Trading at T In the nancial market, the information set of informed n o speculators is s ; q ; x i while that of uninformed speculators is fs ; q g. An informed speculator chooses his risky asset holdings, m Ii, to maximize his utility: m Ii (s ; q ; x i ) = arg max E U(W Ii )s ; q ; x i m Ii, (5) where W Ii = (W 0 c) + m Ii (v q ) and c denotes a constant expense, to be explained later. An uninformed speculator chooses his risky asset holdings, m Ui, to maximize his utility: m Ui (s ; q ) = arg max m Ui E U(W Ui )s ; q, (6) where W Ui = W 0 + m Ui (v q ). In (5) and (6), E() is the expectation operator over v. De nition An equilibrium consists of the nancial price function q rm s investment decision function K = K(s ; q ), such that = q (s ; " ; n ) and the. Price q (s ; " ; n ) clears the nancial market at T : Z 0 m Ii di + ( ) Z 0 m Ui di + n = 0, (7) where, for given K = K(s ; q ), m Ii and m Ui solve (5) and (6), respectively;. Given price q (s ; " ; n ), investment decision K(s ; q ) solves the rm s problem (4). C. Characterization of Equilibrium First, we characterize the nancial market equilibrium. We conecture that log K k = k(s ; q ) is a linear function in De nition. We also conecture a linear price function: q = 0 + (" + s + 3 n ), (8) where 0,, and 3 are coe cients. When combined with s, price q can be converted into another piece of public information about " : ~q (q ; s ) = q 0 s = " + 3 n " + % q, (9) where % q N(0; q ) with q = 3 n. Information set fs ; q g is a one-to-one mapping to fs ; ~q g. We have Lemma. Lemma In the equilibrium of the nancial market, for a given, q is an increasing function of s, s > 0. 0

12 Lemma states that when the precision of the rm s disclosed information about a increases, the informativeness of the nancial price about " also increases. The intuition is as follows. The total uncertainty over v is the sum of uncertainties over a and ". When uncertainty over a decreases under a higher precision s, informed traders have incentives to trade more aggressively, which overwhelms the trading of noise/liquidity traders, thus increasing the informativeness of the nancial price. Lemma shows the nancial price comes partially from information disclosure in the real sector and partially from price discovery in the nancial market. These two sources of information interact. Next, we move to characterize rm s investment decision at T 3. The FOC of (4) implies k = k(s ; ~q ) = ( s ) s + a + s q " + q ~q ; (0) where = ( ) (; ) and the constant coe cient 0 0 is provided in Appendix. Because ~q is a linear function of s and q by (9), (0) implies that k is also a linear function of s and q. Lemma The rm s investment decision at T 3, K(s ; q ), is given by (0) (together with (9)). The realized pro t for rm at T 4 is (a ; " ; s ; ~q ) = P (" ; Y ) Y (a ; K ) K (s ; ~q ). Hence, the expected pro t perceived at the stage of investment at T 3 is E [(a ; " ; s ; ~q )s ; ~q ]. Exploiting the law of iterated expectations, we nd the ex ante expected pro t of rm perceived at T 0 : ( s ; q ; Y; Z) = EE [(a ; " ; s ; ~q )s ; ~q ] = Y Z E E A! s ; ~q ; where E E A! s ; ~q 8 < = exp : n o ( ) h a + h a+ s + i " i "+ q by noting that the outer E() is the unconditional expectation operator over s and ~q. 9 = ;, () It is easy to s > q > 0: () The intuition behind the above comparative statics is easy to understand. When the rm has a more precise signal about a or ", it makes a better investment decision because its investment can be more closely aligned with the realized productivity or demand q > 0, (3)

13 which means that the precisions of signals a and " are complementary in a ecting the rm s ex ante pro t. In other words, the informational value of knowing about one shock increases with the information precision of the other shock. The intuition is as follows. When q is higher, the rm has more accurate information about its demand. This enables the rm to make a better investment decision that is more closely aligned with the true demand shock and increases its pro t multiplicatively for every realized productivity shock. Therefore, the incremental pro t of knowing the realization of the productivity shock (versus not) is also higher for a higher q. This means that the rm has a higher stake to acquire information about a when q is > > 0. A key insight of the baseline model is that the learning between the nancial market and the real economy occurs both ways. The nancial market learns information from a rm s disclosure in trading, and conversely, the rm learns information from the nancial price in making its real (investment) decision. II. The Model with Endogenous Information In this section, we study the model with acquisition of endogenous information. The purpose is to understand the information acquisition of the rm and that of the nancial market, and how they interact. A. Setup We add T 0 to the timeline. At T 0, after the common productivity shock Z is realized (which becomes public information), the rm and the nancial market simultaneously make their information acquisition decisions. By paying an information acquisition cost b > 0 (in terms of the nal good), the rm receives a signal s = a + e with e N(0; s ); otherwise, it receives a less precise signal s = a + e with e N(0; s ), where s > s. And s = 0 corresponds to the extreme case where the rm receives a useless signal. In short, s f s ; s g. In addition, in the spirit of the classic moral hazard problem (concerning hidden actions), we assume that a rm s choice of information precision s is private information (i.e., unobservable to outsiders including nancial market participants). In other words, the rm s choice of information precision has no strategic e ect on nancial market participants. In the nancial market, a trader can choose to be informed or uninformed. By paying an information acquisition cost c > 0 (in terms of the nal good), a trader receives a private signal x i = " + % i with %i N(0; x ), as speci ed in the baseline model; otherwise, it receives no signal (or equivalently a useless signal). The proportion of informed speculators,, is endogenous.

14 Our assumption that the rm and nancial markets have comparative advantages in acquiring information about di erent types of uncertainties is realistic. On the one hand, the rm has advantage over outsiders including nancial analysts in obtaining information about its own productivity shock. On the other hand, nancial analysts in maor investment banks specializing in di erent regional or sectoral submarkets could, on aggregate, be better informed about the demand for the rm s product than the rm itself. Furthermore, in Section.C, we will relax the assumption to allow the rm to obtain information on the demand shock as well. B. Equilibrium Information Acquisition Decision of Speculators an uninformed speculator and an informed one have the same expected utility: where EV (W i ) E U(W i )s ; q. We have the following result. Proportion is determined such that EV (W Ii ) EV (W Ui =, (4) ) Proposition In the equilibrium of the nancial market with endogenous, q is a function of s and c, written as q = q ( s ; c). We have the comparative s > 0 < 0. Proposition states that with taking the endogenous into account, the informativeness of the nancial price about " increases as the precision of the rm s information about a increases. The intuition behind the comparative statics is as follows. There are two driving forces under the comparative s > 0. First, as in the earlier discussion of Lemma, when uncertainty over a decreases, informed traders trade more aggressively, increasing the informativeness of the nancial r price. Second, in the spirit of Grossman and Stiglitz (980), (4) implies e c = that is, e c = s V ar[v s ;q ] V ar[v s ;q ;x i ]; V ar a s + V ar( " s ; q ) V ar a s + V ar( " s ; q ; x i (5) ), the right-hand side (RHS) of which is the gain in information advantage for an informed speculator over an uninformed one. When one dimension of uncertainty (the term V ar a s ) is reduced, the information advantage on the other dimension of uncertainty (the term V ar( " )) becomes more valuable. For example, in the extreme case when V ar a s is very large, being informed has little advantage over being uninformed. Hence, when the precision of signal s increases and thus V ar (a s ) decreases, an uninformed speculator has incentives to switch to being informed by paying a cost c. also improves. As for the comparative When more speculators acquire information, price informativeness < 0, a lower c induces more traders to become Of course, there is a third force, which is the classic free-rider problem in Grossman and Stiglitz (980). A more informative price reduces the incentive for a trader to acquire information. 3

15 informed, causing price informativeness to improve. Information Acquisition Decision of the Firm Considering that pro t function ( s ; q ; Y; Z) given in () has the s > s@ q > 0 shown in () and (3), we can obtain rm s optimal information acquisition decision at T 0 : s = ( s if q ^ q (Y; Z; b) s otherwise where threshold ^ q ^ q (Y; Z; b) is de ned as the unique root to the equation ; (6) It is easy to show that ( s = s ; ^ q ; Y; Z) ( s = s ; ^ q ; Y; Z) = b. < < 0, > 0. In other words, the rm s information acquisition decision given by (6) is a step function, written as s ( q ; Y; Z; b). Proposition The optimal information acquisition decision of the rm at T 0, s ( q ; Y; Z; b), is given by (6). We have q s s 0, 0. Proposition states that if and only if the rm expects the nancial e ciency q to exceed the threshold value ^ q (Y; Z; b) would it choose a high precision s = s. This is because precisions of signals a and " are complementary in a ecting the rm s ex ante pro t. Intuitively, when the uncertainty over " is reduced, information about a becomes more valuable in maximizing the rm s expected pro t. The equilibrium s also depends on Y and Z; that is, when Y or Z is higher, the marginal bene t of increasing the signal precision s is also higher, and so the rm is more likely to acquire information about a. Proposition is a novel result of our model. Earlier work in the literature such as Goldstein and Yang (05) has shown information production complementarity within the nancial market. Our paper shows information production complementarity between the real side of the economy and the nancial side. Full Equilibrium Proposition gives the reaction function q ( s ; c) while Proposition gives the reaction function s ( q ; Y; Z; b). Let q q ( s = s ; c) and q q ( s = s ; c); clearly q > q by Proposition. Proposition 3 follows. Proposition 3 The rational expectations equilibrium, characterized by the pair ( s ; q ) for given 4

16 (Y; Z; b; c), solves the system of equations q ( s ; c) (given in Proposition ) and s ( q ; Y; Z; b) (given in Proposition ). There are three possible equilibrium cases: i) Case : ^ q > q The equilibrium is unique: ( s ; q ) = s ; q ; ii) Case : ^ q q; q There are multiple (two) equilibria: ( s ; q ) = s ; q or s ; q ; iii) Case 3: ^ q < q The equilibrium is unique: ( s ; q ) = s ; q, where threshold ^ q = ^ q (Y; Z; b) is given by (7). The intuition behind Proposition 3 is as follows. The two-way feedback in information production between the nancial sector and the real sector can generate a unique equilibrium or multiple equilibria, depending on parameters Y, Z, b and c. For illustration, let us change Y while keeping Z, b and c constant. Recall that when aggregate output Y is su ciently low (high), the rm s incentive to acquire information is already weak (strong) enough. Speci cally, if Y is so low (and hence threshold ^ q (Y; Z; b) is so high) such that not acquiring information is a dominant strategy for the rm (regardless of whether nancial price informativeness q = q or q ), then a unique equilibrium exists in which the real side does not acquire information and the nancial e ciency is also at a lower level. This is case. Conversely, if aggregate output Y is so high (and hence threshold ^ q (Y; Z; b) is so low) such that acquiring information is a dominant strategy for the rm, then a unique equilibrium exists in which the real side acquires information and the nancial e - ciency is also at a higher level. This is case 3. Between these two extreme cases, there are multiple self-ful lling equilibria, which is case. Figure (with three panels) illustrates the three equilibrium cases, corresponding to di erent levels of aggregate output (i.e., Y L < Y M < Y H ). The two curves in each panel are the two reaction functions (i.e., q ( s ; c) and s ( q ; Y; Z; b)) and their intersection(s) represent the equilibrium. 3 It is easy to see that when Y is kept constant, a change in b or c or Z (where a change in c corresponds to a horizontal shift of curve q ( s ; c) in Figure ) also leads to di erent cases of equilibrium. 3 Typically, q( s; c) is a curve and not a straight line. But when x = +, it is a straight line. 5

17 Figure : Three cases of equilibrium with Y L < Y M < Y H (Case : top; Case : middle; Case 3: bottom) C. Discussions We discuss two simpli ed assumptions of our model. First, for tractability and to obtain closedform solutions, we have assumed the binary choice of information acquisition of the rm. We can instead assume that the rm s information acquisition is a continuous choice, and our model results 6

18 would not change qualitatively. In fact, in this case, the reaction curve s ( q ; Y; Z; b) in Figure is smoothed and becomes an S -shaped curve, so the nature of equilibrium (i.e., the number of the intersections of the two reaction curves) is the same as in Figure. Second, for simplicity, in Section I we have assumed that the rm has no private information about the demand shock ". We can relax this assumption, and our model results would be robust. To save space here, we provide the details in our working paper version of Benhabib, Liu and Wang (08). III. The Macroeconomic Model In this section, we extend the model to a macroeconomic framework. The extended model provides a macroeconomic background for the baseline model and endogenizes various exogenous speci cations and variables of the baseline model. In particular, the aggregate output (i.e., real GDP), Y, is endogenized, which gives a number of novel implications. A. Setup Final goods rms The nal (consumption) good is produced with a continuum of capital goods as input according to a Dixit-Stiglitz production function Z Y = Y d, (8) where [0; ], > is the elasticity of substitution between intermediate capital goods, and measures the demand shock to intermediate good. The representative competitive nal goods rm maximizes its pro ts: Z max P Y d Z P Y d, (9) where P is the price of intermediate good. The price of the nal good, P, is normalized as the numeraire price, i.e., P. The rst-order condition of (9) with respect to Y gives the demand schedule for good : Y = Y; P which endogenizes the demand function of (). Intermediate Goods Firms There is a continuum of intermediate (capital) goods rms with a unit measure, indexed by. The setup for a typical rm, rm, is presented in Section I.A. We may think of each intermediate good as being produced by one rm that is located on an island in the spirit of Lucas (97). Both a and " are i.i.d. across rms (or islands). Financial markets In the nancial market(s), there is a continuum of nancial assets. Financial asset (derivative) is contingent on intermediate goods rm s asset value, V = Y P. 7

19 The payo of nancial derivative contract is v = log V. The demand from noise/liquidity traders for nancial asset is n N(0; n ), and n is independent across nancial assets. It might be the case that each island has one nancial market with nancial asset being traded in the nancial market on island or the case that there is only one nancial market (exchange) where all the nancial assets are traded. In the current framework of the aggregate economy, we may interpret noise trading as: ) foreign capital ow, or ) liquidity trading by some investors who must trade (for exogenous reasons such as balancing portfolios, endowment shocks, and so on). 4 The setup for information acquisition for a rm and on a nancial asset is the same as that in Section II. Investors The economy consists of a continuum of [0; ] [0; ] investors. Each investor is endowed with W 0 units of the nal good at T 0. 5 Each investor has three identities: capital supplier (i.e., lender), rm owner (i.e., shareholder), and nancial market trader. The economy is decentralized, analogous to the Robinson Crusoe economy. The decisions of an investor made under di erent identities are independent. We assume that W 0 is su ciently high and a storage technology exists, so that in equilibrium R f =. 6 An investor maximizes utility U(C i ) = exp C i (0) with constraint C i = W 0 + ( ) + D i ; () where C i is the end-of-period wealth at T 4 for investor i. The term is the aggregate pro t of rms; that is, = R (P Y The term R f K ) d, which corresponds to () by the law of large numbers. is the aggregate net pro t of the rms distributed to an investor (as an owner of rms), where f0; bg is the aggregate information acquisition cost to the rms. 7 The term D i is his payo in nancial market trading. If he is an informed trader in nancial market, then D i = c + m Ii (v q ); if he is an uninformed trader, then D i = m Ui (v q ). Notice that for simplicity and expositional clarity, we have assumed here that an investor can trade only in one nancial market (asset). In Section III.D., we will provide a robustness analysis and show that our model insight is intact if investors are allowed to access all nancial assets and hold a portfolio. It is easy to show that the trading (asset holding) and information acquisition decision of an 4 David, Hopenhayn and Venkateswaran (06) also use the general equilibrium framework with noise traders. 5 Clearly now, by calling the nal good, we do not only mean the good produced with the intermediate inputs under Dixit-Stiglitz aggregation but also the endowment which can be used for either consumption or capital. The point is that the endowment good and the good produced under Dixit-Stiglitz aggregation are the same good. 6 More speci cally, W 0 is greater than the aggregate investment given in (4) later. 7 We will consider the symmetric equilibrium, in which either all rms or none of them acquires information. 8

20 investor (as a nancial market trader) is exactly the same as that in Sections I and II. B. Equilibrium Within each island, the equilibrium is given by Propositions -3. Now we study the equilibrium of the aggregate economy, endogenizing Y. We consider the symmetric equilibrium, in which all intermediate goods rms have the same level of information precision. To nd the symmetric equilibrium, we proceed in two steps. First, suppose that the equilibrium information precision on the representative island (or equivalently all islands 6= ) is given by ( s ; q ), and work out the aggregate output Y. Second, given this Y, characterize the partial equilibrium on island as studied in Section II.B. We take the rst step and nd that the aggregate output is given by Y = ZAK ; () where A = A ( s ; q ) is the endogenous aggregate TFP and K = K ( s ; q ; Z) is the aggregate investment in the economy, with ( " A = A ( s ; q ) = E E A #) s ; ~q (3) and " and the term E E A expressed as K = K ( s ; q ; Z) = Y = Y (A; Z) = Z A ( s ; q ), (4) # s ; ~q is calculated in (). The aggregate output can also be [Z A ( s ; q )]. (5) Equation () implies that despite heterogeneity among rms caused by idiosyncratic productivity shocks and demand shocks, our economy works as if there existed a representative rm with productivity A and aggregate investment K. Proposition 4 follows. Proposition 4 Both the endogenous aggregate TFP, A, and the aggregate investment, K, are increasing in s and q (given by (3) and (4), respectively). Hence, the aggregate output Y is increasing in s and q (given by ()). Proposition 4 highlights two e ects of information frictions. First, given K, the aggregate TFP, A, measuring the e ciency of resource allocation, has the properties s > q > 0. E cient allocation requires more resources to be allocated to rms with higher realized 9