Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 874, September 2006  Screen Reader
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Abstract:
We study the role played by private and public information in the process of price formation in the U.S. Treasury bond market. To guide our analysis, we develop a parsimonious model of speculative trading in the presence of two realistic market frictions  information heterogeneity and imperfect competition among informed traders  and a public signal. We test its equilibrium implications by analyzing the response of twoyear, fiveyear, and tenyear U.S. bond yields to order flow and realtime U.S. macroeconomic news. We find strong evidence of informational effects in the U.S. Treasury bond market: unanticipated order flow has a significant and permanent impact on daily bond yield changes during both announcement and nonannouncement days. Our analysis further shows that, consistent with our stylized model, the contemporaneous correlation between order flow and yield changes is higher when the dispersion of beliefs among market participants is high and public announcements are noisy.
Keywords: Treasury Bond Markets; Macroeconomic News Announcements; Strategic Trading; Market Microstructure; Order Flow; RealTime Data; Expectations; Dispersion of Beliefs
JEL Classification: E44, G14
^{*}Pasquariello is affiliated with the department of Finance at the Ross School of Business at University of Michigan and Vega is affiliated with the Board of Governors of the Federal Reserve System and the University of Rochester Simon School of Business. Please address comments to the authors via email at ppasquar@bus.umich.edu and vega@simon.rochester.edu. We benefitted from the comments of Sreedhar Bharath, Michael Brandt, Michael Fleming, Clifton Green, Nejat Seyhun, Guojun Wu, Kathy Yuan, and other participants in seminars at the 2005 European Finance Association meetings in Moscow, the 2006 Bank of Canada Fixed Income Markets conference in Ottawa, Federal Reserve Board of Governors, George Washington University, the University of Maryland, the University of Michigan, the University of Rochester, and the University of Utah. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Return to text
Identifying the causes of daily asset price movements remains a puzzling issue in finance. In a frictionless market, asset prices should immediately adjust to public news surprises. Hence, we should observe price jumps only during announcement times. However, asset prices fluctuate significantly during nonannouncement days as well. This fact has motivated the introduction of various market frictions to better explain the behavior of asset prices. One possible friction is asymmetric information.^{1} When sophisticated agents trade, their private information is (partially) revealed to the market, via order flow, causing revisions in asset prices even in the absence of public announcements.
The goal of this paper is to theoretically identify and empirically measure the effect of these two complementary mechanisms responsible for daily price changes: aggregation of public news and aggregation of order flow. In particular, we assess the relevance of each mechanism conditional on the dispersion of beliefs among traders and the public signals' noise.
To guide our analysis, we develop a parsimonious model of speculative trading in the spirit of Kyle (1985). The model builds upon two realistic market frictions: information heterogeneity and imperfect competition among informed traders (henceforth, speculators). In this setting, more diverse information among speculators leads to lower equilibrium market liquidity, since their trading activity is more cautious than if they were homogeneously informed, thus making the marketmakers more vulnerable to adverse selection. We then introduce a public signal and derive equilibrium prices and trading strategies on announcement and nonannouncement days. The contribution of the model is twofold. To our knowledge, it provides a novel theoretical analysis of the relationship between the trading activity of heterogeneously informed, imperfectly competitive speculators, the availability and quality of public information, and market liquidity. Furthermore, its analytically tractable closedform solution, in terms of elementary functions, generates several explicit and empirically testable implications on the nature of that relationship.^{2}In particular, we show that the availability of a public signal improves market liquidity (the more so the lower that signal's volatility) since its presence reduces the adverse selection risk for the marketmakers and mitigates the quasimonopolistic behavior of the speculators.
This model is not assetspecific, i.e., it applies to stock, bond, and foreign exchange markets. In this study, we test its implications for the U.S. government bond market for three reasons. First, Treasury market data contains signed trades; thus, we do not need to rely on algorithms (e.g., Lee and Ready, 1991) that add measurement error to our estimates of order flow. Second, government bond markets represent the simplest trading environment to analyze price changes while avoiding omitted variable biases. For example, most theories predict an unambiguous link between macroeconomic fundamentals and bond yield changes, with unexpected increases in real activity and inflation raising bond yields (e.g., Fleming and Remolona, 1997; Balduzzi, Elton, and Green, 2001, among others). In contrast, the link between macroeconomic fundamentals and the stock market is less clear (e.g., Andersen, Bollerslev, Diebold, and Vega, 2004; Boyd, Hu, and Jagannathan, 2005). Third, the market for Treasury securities is interesting in itself since it is among the largest, most liquid U.S. financial markets.
Our empirical results strongly support the main implications of our model. During nonannouncement days, adverse selection costs of unanticipated order flow are higher when the dispersion of beliefs  measured by the standard deviation of professional forecasts of macroeconomic news releases  is high. For instance, we estimate that a one standard deviation shock to abnormal order flow decreases twoyear, fiveyear, and tenyear bond yields by , , and basis points, respectively, on high dispersion days compared to , , and basis points on low dispersion days. These differences are economically and statistically significant. Consistently, these higher adverse selection costs translate into higher contemporaneous correlation between order flow changes and bond yield changes. For example, the adjusted of regressing daily fiveyear Treasury bond yield changes on unanticipated order flow is on high dispersion days compared to on low dispersion days. Intuitively, when information heterogeneity is high, the speculators' quasimonopolistic trading behavior leads to a `` cautious'' equilibrium where changes in unanticipated order flow have a greater impact on bond yields.
The release of a public signal, a tradefree source of information about fundamentals, induces the speculators to trade more aggressively on their private information. Accordingly, we find that the correlation between unanticipated order flow and daytoday bond yield changes is lower during announcement days. For example, comparing nonannouncement days with Nonfarm Payroll Employment release dates, the explanatory power of order flow decreases from to , to , and to for the twoyear, fiveyear, and tenyear bonds, respectively. Yet, when both the dispersion of beliefs and the noise of the public signal  measured as the absolute difference between the actual announcement and its last revision  are high, the importance of order flow in setting bond prices increases. All of the above results are robust to alternative measures of the dispersion of beliefs among market participants, as well as to different regression specifications and the inclusion of different control variables. Lastly, our evidence cannot be attributed to transient inventory or portfolio rebalancing considerations, since the unanticipated government bond order flow has a permanent impact on yield changes during both announcement and nonannouncement days in the sample.
Our paper is most closely related to two recent studies of order flow in the U.S. Treasury market. Brandt and Kavajecz (2004) find that order flow accounts for up to of the variation in yields on days without major macroeconomic announcements. Green (2004) examines the effect of order flow on intraday bond price changes surrounding U.S. macroeconomic news announcements. We extend both studies by identifying a theoretical and empirical link between the price discovery role of order flow and the degree of information heterogeneity among investors and the quality of macroeconomic data releases. In particular, we document important effects of both dispersion of beliefs and public signal noise on the correlation between daily bond yield changes and order flow during announcement and nonannouncement days. This evidence complements the weak effects reported by Green (2004) over thirtyminute intervals around news releases. Since the econometrician does not observe the precise arrival time of private information signals, narrowing the estimation window may lead to underestimating the effect of dispersion of beliefs on market liquidity.^{3}
Our work also belongs to the literature bridging the gap between asset pricing and market microstructure. Evans and Lyons (2003) find that signed order flow is a good predictor of subsequent exchange rate movements; Brandt and Kavajecz (2004) show that this is true for bond market movements; Easley, Hvidkjaer, and O'Hara (2002) argue that the probability of informed trading (PIN), a function of order flow, is a priced firm characteristic in stock returns. These studies enhance our understanding of the determinants of asset price movements, but do not provide any evidence on the determinants of order flow. Evans and Lyons (2004) address this issue by showing that foreign exchange order flow predicts future macroeconomic surprises, i.e., it conveys information about fundamentals. We go a step further in linking the impact of order flow on bond prices to macroeconomic uncertainty (public signal noise) and the heterogeneity of beliefs about real shocks.
We proceed as follows. In Section 2, we construct a stylized model of trading to guide our empirical analysis. In Section 3, we describe the data. In Section 4, we present the empirical results. We conclude in Section 5.
In this section we motivate our investigation of the impact of the dispersion of beliefs among sophisticated market participants and the release of macroeconomic news on the informational role of trading. We first describe a oneshot version of the multiperiod model of trading of Foster and Viswanathan (1996) and derive closedform solutions for the equilibrium market depth and trading volume. Then, we enrich the model by introducing a public signal and consider its implications for the equilibrium price and trading strategies. All proofs are in the Appendix unless otherwise noted.
The basic model is a twodate, oneperiod economy in which a single risky asset is exchanged. Trading occurs only at the end of the period (), after which the asset payoff, a normally distributed random variable with mean zero and variance , is realized. The economy is populated by three types of riskneutral traders: a discrete number () of informed traders (that we label speculators), liquidity traders, and perfectly competitive marketmakers (MMs). All traders know the structure of the economy and the decision process leading to order flow and prices.
At time there is neither information asymmetry about nor trading. Sometime between and , each speculator receives a private and noisy signal of , . We assume that the resulting signal vector is drawn from a multivariate normal distribution (MND) with mean zero and covariance matrix such that and . We also impose that the speculators together know the liquidation value of the risky asset: ; therefore, . This specification makes the total amount of information available to the speculators independent from the correlation of their private signals, albeit still implying the most general information structure up to rescaling by a constant (see Foster and Viswanathan, 1996).
These assumptions imply that and , where is the correlation between any two private information endowments and . As in Foster and Viswanathan (1996), we parametrize the degree of diversity among speculators' signals by requiring that . This restriction ensures that is positive definite. If , then speculators' private information is homogeneous: All speculators receive the same signal such that and . If , then speculators' information is heterogeneous: , , and . Otherwise, speculators' signals are only partially correlated: Indeed, if and if .^{4}
At time , both speculators and liquidity traders submit their orders to the MMs, before the equilibrium price has been set. We define the market order of the speculator to be . Thus, her profit is given by . Liquidity traders generate a random, normally distributed demand , with mean zero and variance . For simplicity, we assume that is independent from all other random variables. MMs do not receive any information, but observe the aggregate order flow from all market participants and set the marketclearing price .
Consistently with Kyle (1985), we define a Bayesian Nash equilibrium as a set of functions , and such that the following two conditions hold:
We restrict our attention to linear equilibria. We first conjecture general linear functions for the pricing rule and speculators' demands. We then solve for their parameters satisfying conditions 1 and 2. Finally, we show that these parameters and those functions represent a rational expectations equilibrium. The following proposition accomplishes this task.
The optimal trading strategy of each speculator depends on the information she receives about the asset payoff () and on the depth of the market ( ). If , Eqs. (1) and (2) reduce to the wellknown equilibrium of Kyle (1985). The speculators, albeit riskneutral, exploit their private information cautiously ( ), to avoid dissipating their informational advantage with their trades. Thus, the equilibrium market liquidity in reflects MMs' attempt to be compensated for the losses they anticipate from trading with speculators, as it affects their profits from liquidity trading.
The intuition behind the parsimonious equilibrium of Eqs. (1) and (2) is similar to that in the multiperiod models of Foster and Viswanathan (1996) and Back et al. (2000). Yet, its closedform solution (in Proposition 1) translates that intuition into unambiguous predictions on the impact of information heterogeneity on market depth.^{5} The optimal market orders depend on the number of speculators () and the correlation among their information endowments (). The intensity of competition among speculators affects their ability to maintain the informativeness of the order flow as low as possible. A greater number of speculators trade more aggressively  i.e., their aggregate amount of trading is higher  since (imperfect) competition among them precludes any collusive trading strategy. For instance, when speculators are homogeneously informed (), then , which implies that the finite difference . This behavior reduces the adverse selection problem for the MMs, thus leading to greater market liquidity (lower ).
The heterogeneity of speculators' signals attenuates their trading aggressiveness. When information is less correlated ( closer to zero), each speculator has some monopoly power on her signal, because at least part of it is known exclusively to her. Hence, as a group, they trade more cautiously  i.e., their aggregate amount of trading is lower  to reveal less of their own information endowments . For example, when speculators are heterogeneously informed (), then , which implies that , i.e., lower than the aggregate amount of trading by homogeneously informed speculators () but identical to the trade of a monopolistic speculator (). This ``quasimonopolistic'' behavior makes the MMs more vulnerable to adverse selection, thus the market less liquid (higher ). The following corollary summarizes the first set of empirical implications of our model.
To gain further insight on this result, we construct a simple numerical example by setting . We then vary the parameter to study the liquidity of this market with respect to a broad range of signal correlations (from very highly negative to very highly positive) when , , and . By construction, both the private signals' variance ( ) and covariance ( ) change with and , yet the total amount of information available to the speculators is unchanged. We plot the resulting in Figure 1A. Multiple, perfectly heterogeneously informed speculators () collectively trade as cautiously as a monopolist speculator. Under these circumstances, adverse selection is at its highest, and market liquidity at its lowest ( ). A greater number of competing speculators improves market depth, but significantly so only if accompanied by more correlated private signals. However, ceteris paribus, the improvement in market liquidity is more pronounced (and informed trading less cautious) when speculators' private signals are negatively correlated. When , each speculator expects her competitors' trades to be negatively correlated to her own (pushing against her signal), hence trading on it to be more profitable.
We now extend the basic model of Section 2.1 by providing each player with an additional, common source of information about the risky asset before trading takes place. According to Kim and Verrecchia (1994, p. 43), ``public disclosure has received little explicit attention in theoretical models whose major focus is understanding market liquidity.''^{6} More specifically, we assume that, sometime between and , both the speculators and the MMs also observe a public and noisy signal of the asset payoff . This signal is normally distributed with mean zero and variance . We can think of as any surprise public announcement (e.g., macroeconomic news) released simultaneously to all market participants. We further impose that , so that the parameter controls for the quality of the public signal and . The private information endowment of each speculator is then given by , where and . Thus, , where .
Again we search for linear equilibria. The following proposition summarizes our results.
The optimal trading strategy of each speculator in Eq. (4) mirrors that of Proposition 1 (Eq. (2)), yet it now depends only on , the truly private  hence less correlated ( )  component of speculator 's original private signal () in the presence of a public signal of . Hence, the MMs' belief update about stemming from makes speculators' private information less valuable. The resulting equilibrium price in Eq. (3) can be rewritten as
Foster and Viswanathan (1993) generalize the trading model of Kyle (1985) to distributions of the elliptically contoured class (ECC) and show that, in the presence of a discrete number of identically informed traders, the unexpected realization of a public signal has no impact on market liquidity regardless of the ECC used. This is the case for the equilibrium of Proposition 2 as well.^{7}Nonetheless, Proposition 2 allows us to study the impact of the availability of noisy public information on equilibrium market depth in the presence of imperfectly competitive and heterogeneously informed speculators. To our knowledge, this analysis is novel to the financial literature. We start with the following result.
The availability of the public signal reduces the adverse selection risk for the MMs, thus increasing the depth of this stylized market, for two reasons. First, the public signal represents an additional, tradefree source of information about . Second, speculators have to trade more aggressively to extract rents from their private information. In Figure 1B we plot the ensuing gain in liquidity, , as a function of private signal correlations when the public signal's noise , i.e., by varying and (so and as well, but not the total amount of information available to the speculators) as in Figure 1A. The increase in market depth is greater when is negative and the number of speculators () is high. In those circumstances, the availability of a public signal reinforces speculators' existing incentives to place market orders on their private signals more aggressively. However, greater , ceteris paribus, increases , since the poorer quality of (lower informationtonoise ratio ) induces the MMs to rely more heavily on to set marketclearing prices, hence the speculators to trade less aggressively.
In the presence of a public signal, information heterogeneity among speculators plays a more ambiguous role on market liquidity. If the volatility of the public signal is low, heterogeneously informed (thus more cautious) speculators put less weight on their private signals (lower in ) and more weight on the public signal (higher in ) when updating their beliefs than homogeneously informed (thus more aggressive) speculators. Hence, the ensuing trading behavior leads to less adverse selection risk for the MMs (lower ). Vice versa, when is high, speculators rely more heavily on their private signals, but more cautiously so if gamma is low, leading to lower equilibrium market depth (higher ), as in Corollary 1.
The volatility of the public signal also affects its direct impact ( ) on the equilibrium price of Eq. (3). Everything else equal, the poorer is the quality of the public signal (higher ), the more the speculators rely on their private signals (see Remark 1) and the MMs rely on the aggregate order flow to infer the asset payoff . Consequently, the MMs put less weight on and more weight on in setting the marketclearing price , toward the benchmark of Eq. (1): and .
We test the implications of the model presented in the previous section using U.S. Treasury bond market data and U.S. macroeconomic announcements. As mentioned in Section 1, this choice is motivated not only by the quality and availability of data on U.S. government bond transactions, but also by the clear theoretical link between macroeconomic fundamentals and bond yield changes.
We use intraday U.S. Treasury bond yields, quotes, transactions, and signed trades for the most recently issued, ``ontherun,'' twoyear, fiveyear, and tenyear Treasury notes. We use these ``ontherun'' notes because, according to Fleming (1997), Brandt and Kavajecz (2004), and Goldreich, Hanke, and Nath (2005), those are the securities with the greatest liquidity and where the majority of informed trading takes place. We are interested in studying the informational role of bond trading related to macroeconomic fundamentals. Therefore, we focus on the intermediate to long maturities, since these are the most responsive to macroeconomic aggregates (e.g., Balduzzi et al., 2001). Consistently, when we perform the analysis that follows on the remaining ``ontherun'' and ``offtherun'' Treasury securities in our database, we find that (i) the resulting inference for the former is weaker than the one described in the paper, and (ii) order flow has no impact on yield changes for the latter. These results are available upon request from the authors.
We obtain the data from GovPX, a firm that collects quote and trade information from six of the seven main interdealer brokers (with the notable exception of Cantor Fitzgerald).^{8} Fleming (1997) argues that these six brokers account for approximately twothirds of the interdealerbroker market, which in turn translates into approximately of the trading volume in the secondary market for Treasury securities. Our sample includes every transaction taking place during ``regular trading hours,'' from 7:30 a.m. to 5:00 p.m. Eastern Standard Time (EST), between January 2, 1992 and December 29, 2000. GovPX stopped recording intraday volume afterward. Strictly speaking, the U.S. Treasury market is open hours a day; yet, of the trading volume occurs during those hours. Thus, to remove fluctuations in bond yields due to illiquidity, we ignore trades outside that narrower interval. Finally, the data contains some interdealer brokers' posting errors not previously filtered out by GovPX. We eliminate these errors following the procedure described in Fleming's (2003) appendix.
We report summary statistics for the daily raw yield and transaction data in Table 1. Bond yields are in percentage, i.e., were multiplied by ; bond yield changes are in basis points, i.e., were multiplied by . Not surprisingly, mean Treasury bond yields are increasing with maturity and display large positive firstorder autocorrelation ( ). Mean daily yield changes are small or zero; yet, their sample variability suggests that economically important fluctuations of the yield curve took place over the sample period. Fiveyear Treasury notes are characterized by the largest mean daily number of transactions (roughly ), hence by the highest liquidity, consistent with the findings of Fleming (2003), among others.
We also compare (but do not report here for economy of space) daily bond yield changes during days when one of the most closely observed U.S. macroeconomic announcement, the Nonfarm Payroll Employment report, is released to daily bond yield changes during nonannouncement days.^{9} Bond yield changes are clearly more volatile on days when the Payroll numbers are announced, but yield changes during nonannouncement days are economically significant as well. These dynamics, together with the poor performance of public macroeconomic surprises in explaining fluctuations in bond yields on nonannouncement days, further motivate our study of the price discovery role of order flow when no public news arrive to the bond market.
We use the International Money Market Services (MMS) Inc. realtime data on the expectations and realizations of of the most relevant U.S. macroeconomic fundamentals to estimate announcement surprises. Table 2 provides a brief description of the most salient characteristics of U.S. economic news announcements in our sample: the total number of observations, the agency reporting each announcement, the time of the announcement release, and whether the standard deviation across professional forecasts is available. Fleming and Remolona (1997) and Andersen, Bollerslev, Diebold, and Vega (2003) discuss the main properties of MMS forecasts; Balduzzi et al. (2001) show that these forecasts are not stale and unbiased.
We define announcement surprises as the difference between announcement realizations and their corresponding expectations. More specifically, since units of measurement vary across macroeconomic variables, we standardize the resulting surprises by dividing each of them by their sample standard deviation. The standardized news associated with the macroeconomic indicator at time is therefore computed as
We use the MMS standard deviation across professional forecasts as a measure of dispersion of beliefs across sophisticated investors. This measure of information heterogeneity is widely adopted in the literature on investors' reaction to information releases in the stock market (e.g., Diether, Malloy, and Scherbina, 2002; Kallberg and Pasquariello, 2004); Green (2004) recently uses it in a bond market context. As indicated in Table 2, this variable is only available for of the macroeconomic news in our sample.
Overall, the dispersion of beliefs is large (e.g., roughly on average of the mean absolute monthly Nonfarm Payroll report), timevarying, and positively correlated across macroeconomic announcements. To conserve space, we do not show the correlation matrix of all the announcements, but only report (in Table 2) the pairwise correlation between each announcement and arguably the most important of them, the Nonfarm Payroll report (e.g., Andersen and Bollerslev, 1998; Andersen et al., 2004; Brenner et al., 2005). This correlation is positive, albeit not statistically significant for most of the announcements. Thus, dispersion of beliefs in Nonfarm Payroll forecasts is not necessarily a good measure of information heterogeneity about the state of the economy, which is ultimately what we are interested in. This motivates us to construct three alternative measures of dispersion of beliefs during announcement and nonannouncement days: one based exclusively on the Payroll announcement, another based on ``influential'' announcements (defined below), and the last one based on the announcements for which the standard deviation of professional forecasts is available (i.e., those italicized in Table 2).
The use of the MMS database to calculate monthly measures of dispersion of beliefs raises two issues: (i) the announcements in Table 2 are released at different frequencies and (ii) the standard deviation of professional forecasts only measures heterogenous beliefs at the time of the announcement. We address these issues by assuming that the dispersion of beliefs remains constant between announcements. This assumption is empirically justified since the first order autocorrelation in the standard deviation of professional forecasts ( in Table 2) is positive and mostly statistically significant. Hence, if the dispersion of beliefs across investors is high in one month (week or quarter), it is likely to remain high in the next month (week or quarter).
To convert weekly and quarterly dispersions to a monthly frequency we use the following procedure. For the single weekly announcement in the sample, Initial Unemployment Claims, we average the dispersion of beliefs across four weeks. For the three quarterly announcements in the sample, GDP Advance, Preliminary, and Final, we assume that the dispersion of beliefs in the first month of the quarter is constant throughout the quarter. The dispersion of beliefs of monthly announcements is instead left unchanged and assumed to be constant between announcements.
We then define our monthly proxy for the aggregate degree of information heterogeneity about macroeconomic fundamentals as a weighted sum of monthly dispersions across announcements,
We use the monthly dispersion estimates from these three methodologies to classify days in which the corresponding monthly variable is above (below) the top (bottom) ( ) percentile of its empirical distribution as days with high (low) information heterogeneity. The resulting time series of high () and low () dispersion days are positively correlated: Their correlations (not reported here) range from (between the Payrollbased series, , and the series constructed with the influential announcements, ) to (between the series using all announcements, , and the one based only on the influential news releases, ).
Finally, we report in Table 3 the differences in the mean daily number of transactions () in the two, five, and tenyear Treasury bond markets across days with high () and low () dispersion of beliefs measured with the three alternative methods described above. The corresponding statistics are computed using NeweyWest standard errors, because Table 1 shows that the number of daily transactions is positively autocorrelated. Consistent with Griffith, Smith, Turnbull, and White (2000) and Ranaldo (2004), among others (but also with the spirit of the model of Section 2), we interpret a big (small) number of daily transactions as a proxy for a high (low) degree of trading aggressiveness. The ensuing differences are economically and statistically significant: fewer transactions take place in high dispersion days than in low dispersion days (i.e., ). Consistently, Spearman correlations between and either , , or (not reported here) are always negative for all maturities and mostly statistically significant. This evidence provides support for the basic intuition of our model and gives us further confidence in the heterogeneity proxies of Eq. (7), since it suggests that, in the government bond market, periods of greater dispersion of beliefs among market participants are accompanied by more cautious speculative trading activity, as argued in Section 2.1.1.
The U.S. government often revises previously released macroeconomic information. Aruoba (2004) identifies these data revisions as either ``informative,'' i.e., due to newly available information, or ``uninformative,'' i.e., due to definitional changes (such as changes in the baseyear or changes in seasonal weights). In this paper, we use the former revisions to measure public signal noise. Specifically, we use the Federal Reserve Bank of Philadelphia ``Real Time Data Set'' (RTDS), which records not only realtime macroeconomic announcements but also their subsequent revisions.^{11} Of the announcements in Table 2 for which MMS forecasts are available, the RDTS contains monthly data on Capacity Utilization, Industrial Production, and Nonfarm Payroll Employment report. The only variable undergoing ``uninformative'' changes over the sample period is Industrial Production, whose baseyear was revised in February 1998. According to extant literature (e.g., Mork, 1987; Faust, Rogers, and Wright, 2003; Aruoba, 2004), (i) the final published revision of each actual announcement represents the most accurate measure for the corresponding macroeconomic variable, and (ii) those revisions should be interpreted as noise, for they are predictable (based on past information).^{12} Hence, we measure public news noise as the difference between each initial announcement and its last revision. Since what matters in our model is the magnitude of the noise ( of Section 2.2), not its direction, we use the absolute value of this difference in our empirical analysis.
Consistent with Aruoba (2004), the resulting time series of simple and absolute macroeconomic data revisions  i.e., the simple and absolute differences between the realtime announcement and the final revision for Capacity Utilization, Industrial Production, and Nonfarm Payroll Employment  display a few spikes and are often negative, revealing a tendency for the government to be overly conservative in its initial announcements. Interestingly, the absolute value of the measurement error tends to be positively correlated with the volatility of the underlying announcement, with correlations (not reported here) varying between a low of (Industrial Production) and a high of (Nonfarm Payroll). This suggests that the measurement error is related to macroeconomic uncertainty. In our theoretical model, arises from either uncertainty about the macroeconomy or the quality of the public signal. In the ensuing empirical analysis, we consider both possibilities.
The model of Section 2 generates several implications that we now test in this section. In the database described in Section 3, we are able to directly observe price changes, , as a proxy for , public news surprises , as a proxy for , and aggregate order flow , as a proxy for . Yet, in our setting, it is only the unexpected portion of aggregate order flow that affects the equilibrium prices of Eqs. (1) and (3).^{13} Furthermore, is assumed to depend only on informed and liquidity trading. Yet, in reality, many additional microstructure imperfections can cause lagged effects in the observed order flow (see Hasbrouck, 2004). Therefore, to implement our model, we estimate , the unanticipated portion of aggregate order flow.
For that purpose, we use the linear autoregressive model of Hasbrouck (1991),
GovPX calculates bond yields using transaction prices, so there is a mechanical inverse relation between the two quantities. To be consistent with the termstructure literature, we estimate the impact of unanticipated order flow and public information arrivals on daily yield changes ( ) rather than on price changes. Nonetheless, our results are robust to either specification. We translate the equilibrium prices of Propositions 1 and 2 into the following estimable equations:
Even in the absence of the information effects of our model, inventory considerations (first formalized by Garman, 1976) may explain, either in full or in part, any significant correlation between price changes and order flow. Yield changes may in fact react to net order flow imbalances, to compensate market participants for providing liquidity, even when the order flow has no information content. To assess the relevance of this alternative hypothesis, we follow Hasbrouck (1991) and include lagged values of unanticipated order flow and yield changes in both Eqs. (9) and (10). As in Hasbrouck (1991), we assume the permanent impact of trades is due to information shocks and the transitory impact is due to noninformation (e.g., liquidity) shocks. Hence, negative and significant estimates for and are driven by transitory inventory control effects when accompanied by a positive and significant impact of lagged unanticipated net order flow on yield changes. In other words, significant contemporaneous order flow effects are transient if they are later reversed. On the other hand, negative and significant estimates for and are driven by permanent information effects (consistent with our model) when accompanied by negative and significant, or statistically insignificant, impact of lagged unanticipated net order flow on yield changes.
We start by estimating Eq. (9) across nonannouncement days and then testing the main implication of Proposition 1, namely that market liquidity ( ) is decreasing in the heterogeneity of speculators' information endowments. First, we define nonannouncement days consistently with our procedures to measure such heterogeneity (in Section 3.2.2). When , we define nonannouncement days as all trading Fridays in the sample in which no Nonfarm Payroll Employment report is released, to control for potential dayoftheweek effects. When or , we define nonannouncement days as all trading days when none of the corresponding announcements (either the influential ones or those italicized in Table 2) take place. We then test Corollary 1 by amending Eq. (9) as follows:
The results in Table 4 provide strong evidence for information effects of order flow on bond yield changes and no evidence for inventory control effects. For all maturities and nearly all measures of dispersion of beliefs, the estimated contemporaneous correlation between unanticipated order flow and yield changes ( ) is negative and significant. The coefficients for oneperiod lagged unanticipated order flow ( ), not reported here, are instead often negative, always statistically insignificant at the level, and about ten times smaller in magnitude than the contemporaneous coefficients . Lastly, the resulting cumulated impact of unanticipated order flow on yield changes ( in Table 4) is mostly statistically significant, albeit more weakly so on nonannouncement days with low heterogeneity of beliefs. In other words, we find no evidence that the impact of unanticipated U.S. Treasury bond order flow on yield changes is reversed in the next five trading days, except in correspondence with low dispersion of beliefs about Nonfarm Payroll announcements ().
The results in Table 4 also provide strong evidence in favor of Corollary 1, especially for the fiveyear bond, the most liquid U.S. Treasury note. Regardless of whether we use only the Nonfarm Payroll announcement to measure dispersion of beliefs or whether we aggregate dispersion of beliefs across macroeconomic announcements, we cannot reject the null hypothesis that . This evidence is consistent with the basic intuition of the benchmark model of Section 2.1: In the absence of a public signal, greater information heterogeneity among investors translates into greater adverse selection risk for the marketmakers, hence into lower market liquidity ( ).
The increase in adverse selection costs in correspondence with high dispersion of beliefs among market participants is not only statistically but also economically significant. For example, when classifying trading days according to (i.e., only with respect to the volatility of Nonfarm Payroll forecasts), we find that a one standard deviation shock to unanticipated order flow in fiveyear bonds decreases their yields by basis points on high dispersion days () and just basis points on low dispersion days (), as compared to a daily yield change one standard deviation from its mean of roughly basis points (in Table 1) over the entire sample. Consistently, the correlation between daily fiveyear bond yield changes and unanticipated daily net order flow (the adjusted of the above regression) is much greater during high dispersion days ( ) than during low dispersion days ( ).
We also find evidence in favor of Corollary 1 in the twoyear bond market, although only when we use the dispersion of analysts' forecasts about Nonfarm Payroll Employment () and Influential announcements () as proxies for information heterogeneity, and in the tenyear bond market when we use the Nonfarm Payroll announcement alone. This may be due to the fact that not all macroeconomic announcements are equally important ex ante, thus making the aggregate dispersion of beliefs across announcements a noisy measure of such heterogeneity. We explore this issue in greater depth in Section 4.2.
In the model of Section 2, equilibrium market liquidity ( and ) is a function of several parameters beyond the one determining the intensity of information heterogeneity among speculators (). For example, in the benchmark equilibrium with no public signal (Proposition 1), also depends on the intensity of noise trading ( ), the number of informed traders (), and the volatility of the intrinsic value of the asset ( ). The regression model of Eq. (11), whose estimates are reported in Table 4, does not explicitly control for any of these parameters. These omissions have the potential to bias our inference.
To begin with, in our model the parameters , , and are unrelated to the dispersion of beliefs. If this were true, the estimation of Eq. (11) would in principle be unbiased. Nevertheless, omitted variable biases may arise from relaxing some of the model's most stringent assumptions. For example, if we allowed for endogenous entry of informed traders, the equilibrium number of market participants might be correlated with their dispersion of beliefs, since the latter would affect investors' potential profits from trading. In addition, misspecification biases may arise from the intertemporal dynamics of either speculators' participation, intensity of noise trading, or fundamental uncertainty. It is difficult to control for these variables. In this section, we do our best to gauge the robustness of the results presented above to their inclusion. The analysis that follows indicates that these results are indeed robust.
Specifically, we conduct several robustness checks. First, the inclusion of lagged unanticipated order flow in Eq. (11) allows us to assess the relevance of any transient, noninformation effect (hence not just inventory control effects but also those due to noise trading, ) on the relationship between trades and price changes (see Hasbrouck, 1991). As previously mentioned, the estimation of Eq. (11) in Table 4 indicates that the impact of unanticipated government bond order flow on yield changes is permanent, i.e., cannot be explained by transitory noise effects. Alternatively, we determine the importance of noise trading by computing order flow and yield changes over disjoint intervals of each day in our sample, as in Brandt and Kavajecz (2004), rather than concurrently. In particular, we aggregate unanticipated order flow in the morning (from 7:30 a.m. to 12:00 p.m.), labeled as time , and average yields from 12:00 p.m. until the end of each trading day (5:00 p.m.), labeled as time . We then regress bond yield changes at time on unanticipated order flow at time . This procedure not only prevents nonsynchronous measurement errors (as argued by Brandt and Kavajecz, 2004) but also allows us to identify the long run or permanent effect of order flow on prices. The resulting estimates of market liquidity, not reported here, are qualitatively similar to those from Eq. (11) presented in Table 4.
We also control for the number of informed traders () and the volatility of the intrinsic value of the asset ( ). We do so by including in Eq. (11) additional variables capturing the interaction between (i.e., the product of): (i) order flow and daily realized volatility,^{16}(ii) order flow and the number of transactions, and (iii) order flow and a weight linearly increasing as the announcement date approaches.^{17} In our model, the degree of information heterogeneity affects both equilibrium price volatility and the aggressiveness of informed trading (proxied by the number of transactions, as in Section 3.2.2). Depending on the strength of these effects, the inclusion of those cross terms in Eq. (11) may reduce the statistical significance of the relation between market liquidity and dispersion of beliefs. Instead, we find no evidence that order flow interacts with either the number of transactions or the proximity to the announcement date. The product of order flow and daily realized volatility is statistically significant only in the fiveyear Treasury bond market.^{18} This is not surprising, since we expect informed investors to be more active in the most liquid trading venues (e.g., Chowdhry and Nanda, 1991), as so the fiveyear bond market is generally deemed (e.g., Fleming, 2003). It is therefore possible that our proxy for realized volatility is successfully capturing the timevarying participation of informed traders only in the market where such participation is probably most important. Nonetheless, neither the economic nor the statistical significance of the dispersion of beliefs dummies in Table 4 are affected by the inclusion of these interaction terms in Eq. (11).
Lastly, we control for variables outside our model that might spuriously affect our results. For example, Treasury auction dates might have a liquidity effect on the secondary bond market. Thus, if our proxies for dispersion of beliefs were spuriously correlated with auction dates, an additional omitted variable bias might arise. We account for this eventuality by including the interaction between order flow and dummies for these dates in Eq. (11).^{19} The liquidity of U.S. Treasury bonds may also be affected by their repurchase agreement (repo) rates, i.e., by their specialness. According to Moulton (2004), the relative repo specialness of ontherun Treasury securities (such as those in our database) generally increases in proximity of auction dates. Hence, the inclusion of auction dummies in Eq. (11) may control for spurious liquidity shocks induced by timevarying specialness as well. Similarly, we include dayoftheweek and annual effects to control for weekly seasonality and temporal trends in the order flow and/or the dispersion of beliefs. None of these effects are statistically significant.
When we introduce a public signal in the model (Proposition 2), market liquidity increases (Corollary 2), because the presence of a tradefree source of information and more aggressive trading by the speculators mitigates the adverse selection risk for the marketmakers. In our empirical analysis, this translates into observing a negative difference (since we work with yields) between (of Eq. (1)) and (of Eq. (3)) in the following regression:
Consistent with Table 4, the evidence in Table 5 indicates that, even during announcement days, both the contemporaneous and cumulative impact of unanticipated order flow on yield changes ( and , respectively) are negative and statistically significant (often at the level). Hence, the correlation between unanticipated order flow and yield changes during announcement days does not appear to be driven by inventory control effects. Table 5 also shows that, in most cases, the difference between and is not statistically significant (except for the fiveyear Treasury notes when or ). Our model suggests that this would be the case if the public news surprises in our sample ( in Eq. (3)) were noisy, since . Yet, our model (Corollary 3) also implies that noisy public signals should have little or no impact on price changes (i.e., as well). This interpretation, although intriguing, is not exhaustive since in unreported analysis we find that seven of the macroeconomic news releases in our sample (the ``influential'' ones) do have a statistically significant impact on daytoday bond yield changes between 1992 and 2000 (i.e., at least some are statistically significant).
An alternative interpretation of the statistically indistinguishable estimates for and in Table 5 is that the release of public macroeconomic signals may increase investors' information heterogeneity (as argued in Kim and Verrecchia, 1994, 1997), hence compensating the reduction in adverse selection costs due to the availability of tradefree sources of information (as in our model). This interpretation is consistent with the evidence reported by Green (2004), who finds that the estimated halfhour price impact of order flow in the Treasury bond market is actually higher during the thirtyminute interval immediately after an announcement than during the thirtyminute interval immediately before the announcement or on nonannouncement days.
However, the analysis of both the estimated correlation between bond yield changes and unanticipated net order flow and the average cumulative impact of the latter on the former provides stronger support for Corollary 2. Indeed, the adjusted of Eq. (12) is always higher for nonannouncement days than for announcement days (i.e., in Table 5), with the sole exception of fiveyear notes when . Furthermore, the impact of unanticipated order flow in either the twoyear or the tenyear Treasury notes on the corresponding yield changes is permanent during nonannouncement days (statistically significant in Table 5), but only transitory during Nonfarm Payroll announcement days (statistically insignificant in Table 5). This suggests that dealers rely more heavily on unanticipated order flow to set bond prices during nonannouncement days than on announcement days, consistent with our model and the findings in Brandt and Kavajecz (2004).
Overall, the evidence reported in Table 5 indicates (albeit not as strongly as in Section 4.1) that the release of public signals does not increase (and occasionally reduces) adverse selection costs and does not impair (and occasionally improves) market liquidity. Nonetheless, both the above discussion and the comparative statics of Figure 1B also indicate that any such liquidity gain may crucially depend on the quality of the public signal ( ) and on the degree of information heterogeneity among market participants (). We explore these issues next, starting with the latter.
In this section, we analyze the effect of information heterogeneity on market liquidity during announcement days. For that purpose, we estimate the following representation of Eq. (10):
According to our model (Remark 2), greater dispersion of beliefs among speculators reduces market liquidity during announcement days (i.e., in Eq. (13)) only when the public signal is noisy, since the latter induces those heterogeneously informed speculators to use cautiously their private signals, thus increasing adverse selection risks for the marketmakers. Vice versa, if the quality of the public signal is high ( is low), more heterogeneously informed speculators display their caution by relying less on their private signals (and more on the public signal) in their trading activity, thus lowering the perceived adverse selections risk for the marketmakers and improving market liquidity (i.e., in Eq. (13)).
Table 6 reveals that the difference between and is always negative and, in most cases, both economically and statistically significant. For instance, when we measure dispersion of beliefs using the Nonfarm Payroll announcement, a one standard deviation shock to unanticipated order flow decreases tenyear bond yields by basis points during high dispersion days, while it increases bond yields by basis points during low dispersion days. This evidence suggests that the dispersion of beliefs among market participants has an important impact on Treasury bond market liquidity, in the direction predicted by our model, even in the presence of public signals of macroeconomic fundamentals. This evidence is also (indirectly) consistent with the conjecture made in Section 4.2 that public signal noise is ``sufficiently'' high in our sample. In Section 4.2.3 below, we gauge more explicitly the potential role of public signal noise on market liquidity.
We now turn to the impact of public signals on yield changes. According to the extended model of Section 2.2, a public signal can induce price (and yield) changes through two channels that, in the spirit of Evans and Lyons (2003), we call direct (through marketmakers' belief updating process) and indirect (through speculators' trades in the order flow). Yet, in the model, the direct channel is always more important than the indirect one. The evidence presented in Table 6 confirms this latter result: The adjusted of the fully specified regressions of Eq. (13), i.e., including both the unanticipated order flow and the public signal(s), , is between and times bigger than the adjusted of the regressions estimated using only unanticipated order flow, .
Many of the results in Section 4.2.1 above are generally weaker in correspondence with the aggregate proxies for information heterogeneity described in Eq. (7). In particular, the relevance of public signals for bond yield changes (i.e., the difference between and in Table 6) is declining in , the number of announcements used in the analysis. This may be explained by a potentially mistaken classification of certain macroeconomic releases as important public announcements. Indeed, both Eq. (7) and the corresponding classification of announcement days implicitly assume that all U.S. macroeconomic news releases listed in Table 2 are equally important. However, the literature (e.g., Fleming and Remolona, 1997) suggests that not all public information may be equally relevant ex ante to participants in the U.S. Treasury bond markets.
This can be due to several factors: The dispersion of beliefs might be higher for certain announcements than for others, some announcements may not reveal any useful information to price bonds (i.e., the days in which they occur are effectively nonannouncement days), or some announcements might be noisier than others. According to our model, the availability of a public signal of higher (lower) quality implies a higher (lower) impact of order flow on equilibrium price changes during announcement days. In this section, we examine the effect of public signal noise directly.
Specifically, Remark 1 and Corollary 3 state that adverse selection costs are higher and the price reaction to public announcement surprises is lower when the public signal noise is high. Intuitively, when the public signal is noisy, the marketmakers rely more heavily on the order flow than on the public signal, thus requiring greater compensation for providing liquidity. The evidence in Table 7 supports this claim. There we report estimates of the following equation:
Table 7 shows that the impact of these public signals on bond yield changes is generally more significant when their noise is lower (columns and ). Accordingly, we also find that (i) the coefficients measuring the contemporaneous and permanent impact of unanticipated order flow on bond yield changes are generally insignificant on announcement days when the public signal noise is low (columns and in Table 7), and (ii) the adjusted of order flow alone is generally higher on days with high public signal noise () than on days with low public signal noise (), i.e., ; yet, these differences are not large. These results suggest that the impact of the release of macroeconomic data on the process of price formation in the U.S. Treasury market is decreasing in the quality of the public signals, as argued in the model of Section 2.2, albeit not importantly so.
Finally, we amend all the regression models specified above to account for the potential omitted variable biases described in Section 4.1.1. Many of these biases are in fact more likely to arise when analyzing the impact of both information heterogeneity and public signal noise on market liquidity during announcement days. For example, the number of informed market participants is likely to be endogenously higher during announcement days regardless of their dispersion of beliefs, if they expect the Treasury bond market to be more liquid then (e.g., Chowdhry and Nanda, 1991). In addition, as observed in Section 3.2.3, public signal noise may stem not only from the signal's intrinsic quality but also from fundamental uncertainty ( in our model), which affects market liquidity directly as well (Proposition 2). Yet, we find that all our conclusions are robust to the inclusion of the same control variables employed for our analysis of nonannouncement days.
The main goal of this paper is to deepen our understanding of the links between daily bond yield movements, news about fundamentals, and order flow conditional on the investors' dispersion of beliefs and the public signals' noise. To that end, we theoretically identify and empirically document important news and order flow effects in the U.S. Treasury bond market. To guide our analysis, we develop a parsimonious model of speculative trading in the presence of asymmetric sharing of information among imperfectly competitive traders and a public signal of the terminal value of the traded asset. We then test its equilibrium implications by studying the relation between daily twoyear, fiveyear, and tenyear U.S. Treasury bond yield changes and unanticipated order flow and realtime U.S. macroeconomic news releases.
Our evidence suggests that announcement and order flow surprises produce conditional, persistent mean jumps, i.e., that the process of price formation in the bond market is linked to information about fundamentals and agents' beliefs. The nature of this linkage is sensitive to the intensity of investors' dispersion of beliefs and the noise of the public announcement (albeit more weakly so). In particular, and consistent with our model, unanticipated order flow is more highly correlated with bond yield changes when the dispersion of beliefs across informed traders is high and the public announcement is noisy.
These findings allow us to draw several implications for future research. Existing term structure models are notorious for their poor outofsample forecast performance (e.g., Duffee, 2002). Recently, Diebold and Li (2003) use a variation of the Nelson and Siegel (1987) exponential components framework to forecast yield curve movements at short and long horizons, finding encouraging results at short horizons. We show here that U.S. Treasury bond order flow is contemporaneously correlated with daily yield changes and that the significance of this relation depends on the degree of information heterogeneity about macroeconomic fundamentals among market participants. In future work, we intend to include order flow information to forecast the term structure.
Our results also indicate that daytoday bond yield changes and order flow are most sensitive to Nonfarm Payroll Employment announcements. Nominal bond yields depend on future inflation and future capital productivity, hence naturally react to employment announcement surprises. Previous studies observe that Nonfarm Payroll Employment is the first news release for a given month (e.g., Fleming and Remolona, 1997; Andersen et al., 2003). However, our analysis implicitly accounts for the timing of the announcements, by focusing exclusively on their surprise content. Hence, the importance of this announcement should depend on its predictive power. Yet, to the best of our knowledge, no study has shown that the Nonfarm Payroll Employment is the best predictor for future activity and inflation out of the macroeconomic announcements in our sample.^{20} Thus, we suspect that its importance goes beyond its predictive power for real activity. Morris and Shin (2002) provide an interesting theoretical explanation for this overreaction to Nonfarm Payroll news. They argue that bond yields will be most reactive to the types of news emphasized by the press. In their model, this overreaction to news is rational and reflects the coordination role of public information. We look forward to future research that further investigates this possibility.
.  (A1) 
,  (A2) 
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In this table we report the mean, standard deviation, maximum, minimum, and firstorder autocorrelation coefficient ( ) for the following variables: Twoyear, fiveyear and tenyear ontherun daily yields (in percentage, i.e., multiplied by 100), daily yield changes (in basis points, i.e., multiplied by 10,000), number of buys, number of sells, daily net order flow (number of buys minus number of sells), daily abnormal order flow, and the daily number of transactions. The daily abnormal, or unanticipated order flow (defined in Section 4 as ) is computed by aggregating over each day all halfhour intraday residuals from the estimation of the linear autoregressive model of Hasbrouck (1991) in Eq. (8). The data source is GovPX. Our sample period starts in January 2, 1992 and ends in December 29, 2000, for a total of 2,246 daily observations.
Mean: TwoYear  Stdev.: TwoYear  Max.: TwoYear  Min.: TwoYear  TwoYear



Daily Yield100  5.49  0.89  7.73  3.70  0.998  
Daily Yield Change10,000  0.05  6.10  35.10  31.10  0.041  
Number of Buys  202.07  80.00  604  25  0.559  
Number of Sells  170.77  69.89  640  17  0.533  
Order Flow  31.30  37.38  204  89  0.088  
Abnormal Order Flow  0.00  33.74  187.58  102.49  0.032  
Number of Transactions  372.84  145.50  1244  44  0.578 
Mean: FiveYear  Stdev.: FiveYear  Max.: FiveYear  Min.: FiveYear  FiveYear



Daily Yield100  5.97  0.74  7.90  3.98  0.996  
Daily Yield Change10,000  0.01  6.39  35.10  29.30  0.044  
Number of Buys  324.70  127.36  816  34  0.633  
Number of Sells  289.41  114.47  737  33  0.631  
Order Flow  35.29  49.53  278  127  0.128  
Abnormal Order Flow  0.00  47.85  262.72  129.44  0.007  
Number of Transactions  614.11  237.05  1423  88  0.654 
Mean: TenYear  Stdev.: TenYear  Max.: TenYear  Min.: TenYear  TenYear



Daily Yield100  6.26  0.74  8.03  4.16  0.997  
Daily Yield Change10,000  0.04  5.99  33.60  23.00  0.044  
Number of Buys  281.70  109.03  693  34  0.710  
Number of Sells  260.55  102.44  553  22  0.692  
Order Flow  21.14  36.45  153  105  0.160  
Abnormal Order Flow  0.00  40.29  142.98  105.38  0.038  
Number of Transactions  542.25  208.41  1246  73  0.718 
In this table we report the number of observations, source, and release time for the 25 U.S. macroeconomic announcements in our sample. We also report summary statistics for the corresponding standard deviation across professional forecasts, our proxy for dispersion of beliefs among market participants, whenever available. Specifically, we report the mean, standard deviation, Spearman rank correlation with the Nonfarm Payroll standard deviation (Payroll), and the firstorder autocorrelation coefficient () for each series . A "*", "**", or "***" indicate the latter two measures' significance at 10%, 5%, or 1% level, respectively. The release time in the table, in Eastern Standard Time (EST, with Daylight savings time starting on the first Sunday of April and ending on the last Sunday of October), is constant throughout the sample except in the following circumstances: In 01/94, the personal income announcement time moved from 10:00 a.m. to 8:30 a.m.; beginning in 01/96, consumer credit was released regularly at 3:00 p.m. while prior to this date, its release times varied; in 12/93, the personal consumption expenditures announcement time moved from 10:00 a.m. to 8:30 a.m.; whenever GDP is released on the same day as durable goods orders, the durable goods orders announcement is moved to 10:00 a.m.; on 07/96 the durable goods orders announcement was released at 9:00 a.m.; in 01/97, the business inventory announcement was moved from 10:00 a.m. to 8:30 a.m.; beginning in 3/28/94, the fed funds rate was released regularly at 2:15 p.m., while prior to this date, the release times varied. The sources for the MMS data are: Bureau of Labor Statistics (BLS), Bureau of the Census (BC), Bureau of Economic Analysis (BEA), Federal Reserve Board (FRB), National Association of Purchasing Managers (NAPM), Conference Board (CB), Financial Management Office (FMO), and Employment and Training Administration (ETA). The standard deviation across professional forecasts of Capacity Utilization, Personal Income, Consumer Credit, Personal Consumption Expenditures, Business Inventories, Government Budget, and Target Federal Funds Rate (announcements 7, 8, 9, 11, 15, 16, and 24) is not available.
Quarterly Announcements: Obs.  Quarterly Announcements: Source  Quarterly Announcements: Time  Quarterly Announcements: Mean  Quarterly Announcements: Stdev.  Quarterly Announcements: (Payroll) 



1 GDP Advance  36  BEA  8:30  0.480  0.170  0.162*  0.181 
2 GDP Preliminary  34  BEA  8:30  0.313  0.178  0.014  0.192 
3 GDP Final  35  BEA  8:30  0.128  0.051  0.083  0.250 
Monthly Announcements: Obs.  Monthly Announcements: Source  Monthly Announcements: Time  Monthly Announcements: Mean  Monthly Announcements: Stdev.  Monthly Announcements: (Payroll) 



Real Activity: 4 Nonfarm Payroll  108  BLS  8:30  41.814  14.212  1.000  0.424*** 
Real Activity: 5 Retail Sales  108  BC  8:30  0.302  0.158  0.109  0.047 
Real Activity: 6 Industrial Production  107  FRB  9:15  0.183  0.135  0.236**  0.358*** 
Real Activity: 7 Capacity Utilization  107  FRB  9:15  n.a.  n.a.  n.a.  n.a. 
Real Activity: 8 Personal Income  105  BEA  10:00/8:30  n.a.  n.a.  n.a.  n.a. 
Real Activity: 9 Consumer Credit  108  FRB  15:00  n.a.  n.a.  n.a.  n.a. 
Consumption: 10 New Home Sales  106  BC  10:00  19.270  10.235  0.151  0.099 
Consumption: 11 Pers. Cons. Exp.  107  BEA  10:00/8:30  n.a.  n.a.  n.a.  n.a. 
Investment: 12 Durable Goods Orders  106  BC  8:30/9:00/10:00  1.034  0.333  0.077  0.412*** 
Investment: 13 Factory Orders  105  BC  10:00  0.587  0.577  0.219**  0.015 
Investment: 14 Construction Spending  105  BC  10:00  0.499  0.253  0.176*  0.192*** 
Investment: 15 Business Inventories  106  BC  10:00/8:30  n.a.  n.a.  n.a.  n.a. 
Government Purchases: 16 Government Budget  107  FMO  14:00  n.a.  n.a.  n.a.  n.a. 
Net Exports: 17 Trade Balance  107  BEA  8:30  0.790  0.851  0.122  0.018 
Prices: 18 Producer Price Index  108  BLS  8:30  0.130  0.049  0.186*  0.287*** 
Prices: 19 Consumer Price Index  107  BLS  8:30  0.086  0.051  0.146  0.221** 
ForwardLooking: 20 Consumer Conf. Index  106  CB  10:00  1.646  0.609  0.079  0.230** 
ForwardLooking: 21 NAPM Index  107  NAPM  10:00  0.961  0.303  0.242**  0.382*** 
ForwardLooking: 22 Housing Starts  106  BC  8:30  0.045  0.038  0.160  0.246*** 
ForwardLooking: 23 Index of Leading Ind.  108  CB  8:30  0.202  0.137  0.134  0.480*** 
SixWeek Announcements: Obs.  SixWeek Announcements: Source  SixWeek Announcements: Time  SixWeek Announcements: Mean  SixWeek Announcements: Stdev.  SixWeek Announcements: (Payroll) 



24 Target Fed Funds Rate  71  FRB  14:15  n.a.  n.a.  n.a.  n.a. 
In this table we report estimates of the following equation:
Announcement  TwoYear: b_{h}  TwoYear: b_{m}  TwoYear: b_{l}  TwoYear: b_ {h}b_{l}  TwoYear: 

Nonfarm Payroll Employment  366.687  362.978  374.983  8.296  86.05% 
Nonfarm Payroll Employment: s.e.  5.729  4.811  5.773  8.133  
Influential Announcements  317.836  372.472  409.360  91.524***  86.80% 
Influential Announcements: s.e.  5.596  4.684  5.665  7.963  
All Announcements  321.120  362.468  421.500  100.38***  86.95% 
All Announcements: s.e.  5.543  4.655  5.659  7.921 
Announcement  FiveYear: b_{h}  FiveYear: b_{m}  FiveYear: b_{l}  FiveYear: b_ {h}b_{l}  FiveYear: 

Nonfarm Payroll Employment  603.503  570.535  648.080  44.576***  85.73% 
Nonfarm Payroll Employment: s.e.  9.475  7.958  9.541  13.447  
Influential Announcements  562.774  626.650  599.127  36.353***  85.54% 
Influential Announcements: s.e.  9.617  8.044  9.721  13.675  
All Announcements  534.212  607.237  657.696  123.484***  85.91% 
All Announcements: s.e.  9.459  7.937  9.642  13.507 
Announcement  TenYear: b_{h}  TenYear: b_{m}  TenYear: b_{l}  TenYear: b_ {h}b_{l}  TenYear: 

Nonfarm Payroll Employment  530.563  505.908  570.922  40.359***  85.56% 
Nonfarm Payroll Employment: s.e.  8.353  7.015  8.411  11.854  
Influential Announcements  496.024  554.288  527.157  31.132***  85.55% 
Influential Announcements: s.e.  8.490  7.096  8.576  12.068  
All Announcements  452.617  546.248  584.260  131.643***  86.20% 
All Announcements: s.e.  8.266  6.931  8.420  11.799 
In this table we report estimates of the following regression model (Eq. (11)):
Announcement  _{h0}  _{m0}  _{l0}  _{h0}_{l0}  _{i=0}^{5}_{hi}  _{i=0}^{5} _{mi}  _{i=0}^{5}_{li}  

Nonfarm Payroll  0.213***  0.182***  0.121***  0.092***  0.161**  0.182***  0.072  28.54%  6.66%  21.69% 
Nonfarm Payroll: s.e.  0.033  0.025  0.034  0.048  0.067  0.050  0.056  
Influential  0.140***  0.108***  0.080***  0.060***  0.106***  0.096***  0.049**  14.61%  10.65%  15.52% 
Influential: s.e.  0.016  0.010  0.010  0.019  0.031  0.022  0.022  
All  0.122***  0.093***  0.098***  0.024  0.152***  0.086***  0.086***  15.46%  16.92%  15.83% 
All: s.e.  0.017  0.012  0.014  0.022  0.032  0.024  0.027 
Announcement  _{h0}  _{m0}  _{l0}  _{h0}_{l0}  _{i=0}^{5}_{hi}  _{i=0}^{5} _{mi}  _{i=0}^{5}_{li}  

Nonfarm Payroll  0.210***  0.153***  0.085***  0.125***  0.285***  0.136***  0.019  41.38%  9.65%  23.30% 
Nonfarm Payroll: s.e.  0.029  0.022  0.027  0.040  0.078  0.049  0.062  
Influential  0.151***  0.122***  0.087***  0.064***  0.142***  0.106***  0.050**  19.14%  11.97%  20.31% 
Influential: s.e.  0.014  0.010  0.010  0.018  0.036  0.022  0.025  
All  0.155***  0.097***  0.102***  0.053***  0.167***  0.079***  0.083***  21.37%  18.76%  19.40% 
All: s.e.  0.017  0.012  0.013  0.022  0.041  0.027  0.029 
Announcement  _{h0}  _{m0}  _{l0}  _{h0}_{l0}  _{i=0}^{5}_{hi}  _{i=0}^{5} _{mi}  _{i=0}^{5}_{li}  

Nonfarm Payroll  0.170***  0.129***  0.071  0.099  0.192**  0.269***  0.017  15.10%  1.02%  10.29% 
Nonfarm Payroll: s.e.  0.043  0.032  0.043  0.061  0.093  0.058  0.079  
Influential  0.081***  0.093***  0.079***  0.002  0.075**  0.109***  0.053  2.83%  4.72%  6.05% 
Influential: s.e.  0.018  0.013  0.013  0.025  0.035  0.027  0.042  
All  0.075***  0.086***  0.071***  0.004  0.109**  0.119***  0.097**  3.82%  4.43%  6.16% 
All: s.e.  0.023  0.017  0.019  0.029  0.053  0.033  0.038 
In this table we report estimates of the following regression model (Eq. (12)):
Announcement  _{0}  _{p0}  _{0}_{p0}  _{i=0}^{5}_{i}  _{i=0}^{5}_{pi}  

Nonfarm Payroll  0.108***  0.087***  0.021  0.131***  0.013  15.31%  6.47%  14.72% 
Nonfarm Payroll: s.e.  0.021  0.027  0.034  0.041  0.064  
Influential  0.103***  0.112***  0.009  0.075***  0.059***  15.34%  12.29%  13.98% 
Influential: s.e.  0.008  0.008  0.011  0.016  0.019  
All  0.102***  0.109***  0.007  0.096***  0.059***  16.00%  13.24%  13.99% 
All: s.e.  0.011  0.006  0.013  0.023  0.015 
Announcement  _{0}  _{p0}  _{0}_{p0}  _{i=0}^{5}_{i}  _{i=0}^{5}_{pi}  

Nonfarm Payroll  0.124***  0.168***  0.044**  0.121***  0.242***  21.03%  19.61%  21.37% 
Nonfarm Payroll: s.e.  0.017  0.025  0.019  0.043  0.062  
Influential  0.117***  0.137***  0.020*  0.095***  0.137***  19.88%  20.88%  20.76% 
Influential: s.e.  0.007  0.008  0.011  0.017  0.020  
All  0.115***  0.131***  0.016  0.107***  0.115***  20.29%  20.48%  20.70% 
All: s.e.  0.011  0.006  0.012  0.024  0.016 
Announcement  _{0}  _{p0}  _{0}_{p0}  _{i=0}^{5}_{i}  _{i=0}^{5}_{pi}  

Nonfarm Payroll  0.087***  0.053*  0.034  0.181***  0.020  6.74%  3.59%  7.07% 
s.e.  0.025  0.030  0.048  0.049  0.088  
Influential  0.086***  0.086***  0.000  0.083***  0.086***  6.73%  5.73%  6.52% 
Influential: s.e.  0.010  0.011  0.015  0.021  0.026  
All  0.077***  0.090***  0.013  0.103***  0.076***  7.08%  5.99%  6.49% 
All: s.e.  0.014  0.009  0.017  0.030  0.019 
In this table we report estimates of the following regression model (Eq. (14)):
, 
Announcement  _{ph0}  _{pm0}  _{pl0}  _{ph0} _{pl0}  _{i=0}^{5}_{phi}  _{i=0}^{5}_{pmi}  _{i=0}^{5}_{pli}  

Nonfarm Pay.  6.279***  0.141**  0.117**  0.116  0.025*  0.087  0.301***  0.055  7.81%  8.04%  8.51%  40.87% 
Nonfarm Pay: s.e.  0.883  0.060  0.047  0.092  0.014  0.151  0.113  0.176  
Influential  2.805***  0.179***  0.08***  0.106***  0.073***  0.152***  0.063**  0.040  15.86%  9.57%  13.54%  30.27% 
Influential: s.e.  0.322  0.019  0.012  0.016  0.024  0.047  0.031  0.036  
All  1.490***  0.165***  0.092***  0.093***  0.072***  0.130***  0.030  0.055**  16.65%  14.50%  13.79%  26.70% 
All: s.e.  0.196  0.015  0.010  0.012  0.020  0.034  0.026  0.027 
Announcement  _{ph0}  _{pm0}  _{pl0}  _{ph0} _{pl0}  _{i=0}^{5}_{phi}  _{i=0}^{5}_{pmi}  _{i=0}^{5}_{pli}  

Nonfarm Pay.  6.028***  0.220***  0.179***  0.117**  0.103***  0.209  0.253***  0.087  11.45%  4.37%  14.46%  46.68% 
Nonfarm Pay: s.e.  0.855  0.065  0.042  0.049  0.034  0.161  0.097  0.138  
Influential  2.670***  0.184***  0.111***  0.124***  0.060***  0.202***  0.129***  0.083**  24.16%  15.27%  21.45%  34.00% 
Influential: s.e.  0.318  0.017  0.012  0.015  0.023  0.048  0.030  0.038  
All  1.259***  0.183***  0.111***  0.124***  0.059***  0.192***  0.100***  0.083***  23.94%  24.78%  21.83%  31.27% 
All: s.e.  0.194  0.014  0.010  0.012  0.019  0.039  0.025  0.027 
Announcement  _{ph0}  _{pm0}  _{pl0}  _{ph0} _{pl0}  _{i=0}^{5}_{phi}  _{i=0}^{5}_{pmi}  _{i=0}^{5}_{pli}  

Nonfarm Pay.  4.195***  0.239**  0.017  0.076  0.315**  0.157  0.040  0.109  10.27%  3.53%  0.26%  22.81% 
Nonfarm Pay: s.e.  0.815  0.097  0.081  0.105  0.143  0.206  0.178  0.224  
Influential  2.445***  0.103***  0.068***  0.072***  0.031  0.130**  0.064*  0.038  3.55%  5.33%  5.58%  16.95% 
Influential: s.e.  0.329  0.024  0.018  0.023  0.033  0.062  0.039  0.057  
All  1.329***  0.117***  0.079***  0.068***  0.049**  0.120**  0.070**  0.014  4.26%  6.71%  6.31%  15.04% 
All: s.e.  0.199  0.021  0.014  0.018  0.021  0.051  0.032  0.037 
In this table we report estimates of the following regression model (Eq. (14)):
, 
Ann.  _{snh}  _{snm}  _ {snl}  _{pnh0}  _{pnm0}  _{pnl0}  _{i=0}^{5}_{pnhi}  _{i=0}^{5}_{pnmi}  _{i=0}^{5}_{pnli}  

Non. P.  6.861***  7.569***  5.205***  0.132*  0.164***  0.108*  0.105  0.378***  0.041  32.67%  39.24%  39.00%  46.88% 
Non. P: s.e.  1.678  1.288  1.609  0.067  0.050  0.062  0.191  0.140  0.152  
In. P.  1.672*  1.468  0.820  0.075*  0.106***  0.130**  0.037  0.154*  0.008  2.38%  10.93%  9.50%  23.40% 
In. P: s.e.  0.916  1.035  1.337  0.043  0.034  0.058  0.092  0.090  0.116  
Cap. U.  1.643  1.399  2.123  0.072  0.092***  0.097  0.113  0.075  0.052  9.01%  18.20%  18.80%  25.73% 
Cap. U: s.e.  1.011  0.866  1.521  0.045  0.030  0.069  0.105  0.070  0.114 
Ann.  _{snh}  _{snm}  _ {snl}  _{pnh0}  _{pnm0}  _{pnl0}  _{i=0}^{5}_{pnhi}  _{i=0}^{5}_{pnmi}  _{i=0}^{5}_{pnli}  

Non. P.  5.959***  5.513***  4.267***  0.196***  0.212***  0.210***  0.411**  0.343***  0.290***  26.77%  39.16%  38.21%  51.06% 
Non. P: s.e.  1.580  1.202  1.546  0.052  0.053  0.052  0.158  0.131  0.111  
Ind P.  1.251  0.233  0.916  0.099**  0.157***  0.122*  0.035  0.048  0.096  2.44%  22.80%  20.82%  23.05% 
In. P: s.e.  0.963  1.125  1.597  0.043  0.034  0.067  0.113  0.094  0.138  
Cap. U.  1.466  0.152  1.956  0.128**  0.152***  0.085  0.053  0.065  0.135  7.66%  27.80%  24.85%  28.06% 
Cap. U: s.e.  0.904  0.962  1.588  0.053  0.031  0.063  0.106  0.085  0.163 
Ann.  _{snh}  _{snm}  _ {snl}  _{pnh0}  _{pnm0}  _{pnl0}  _{i=0}^{5}_{pnhi}  _{i=0}^{5}_{pnmi}  _{i=0}^{5}_{pnli}  

Non. P.  3.702**  3.165**  4.225**  0.139  0.078  0.036  0.566**  0.267  0.116  20.88%  21.29%  19.84%  27.62% 
Non. P: s.e.  1.648  1.209  1.615  0.101  0.087  0.085  0.220  0.182  0.183  
Ind. P.  0.281  2.025*  1.940  0.059  0.117  0.131*  0.020  0.071  0.036  3.70%  5.47%  7.69%  0.96% 
In. P: s.e.  0.991  1.084  1.538  0.077  0.073  0.078  0.142  0.11  0.143  
Cap. U.  1.365  1.174  2.456*  0.013  0.057  0.148**  0.013  0.022  0.09  8.15%  7.44%  10.64%  6.03% 
Cap. U: s.e.  0.994  1.008  1.443  0.089  0.058  0.074  0.137  0.103  0.135 
In this figure we plot the market liquidity parameter defined in Proposition 1, in Figure 1A, and the difference between the sensitivity of the equilibrium price to the order flow in the absence and in the presence of a public signal in Figure 1B, as a function of the degree of correlation of the speculators' signals, , in the presence of M = 1, 2, or 4 speculators, when . According to Proposition 1, , while in Proposition 2, where and . Since , , and , the range of correlations compatible with a positive definite is obtained by varying the parameter within the interval [0, 10] when M = 2, and the interval [0, 5] when M = 4.
In this figure we plot the market liquidity parameter defined in Proposition 1, . We construct a simple numerical example by setting . We then vary the range of signal correlations (from very highly negative to very highly positive) when the number of informed traders, , , and . Multiple, perfectly heterogeneously informed speculators () collectively trade as cautiously as a monopolist speculator. Under these circumstances, adverse selection is at its highest, and market liquidity at its lowest ( ). A greater number of competing speculators improves market depth, but significantly so only if accompanied by more correlated private signals. However, ceteris paribus, the improvement in market liquidity is more pronounced (and informed trading less cautious) when speculators' private signals are negatively correlated. When , each speculator expects her competitors' trades to be negatively correlated to her own (pushing against her signal), hence trading on it to be more profitable.
More detail. Figure 1A plots lambda on the vertical axis with range [0.2, 0.55] and gamma on the horizontal axis with range [1,+1]. For M=1, lambda is constant at 0.5 for all values of gamma. For M=2, lambda starts at about 0.28 for gamma=0.9, with lambda increasing rapidly to 0.5 at gamma=0, then dropping off slowly to about 0.48 at gamma=1. For M=4, lambda starts at about 0.23 for gamma=0.3, with lambda increasing rapidly to 0.5 at gamma=0, then dropping off to about 0.4 at gamma=1.
In Figure 1B we plot the difference between the sensitivity of the equilibrium price to the order flow in the absence and in the presence of a public signal , , as a function of the degree of correlation of the speculators' signals, , in the presence of , , or speculators, when and the public signal's noise . The increase in market depth is greater when is negative and the number of speculators () is high. In those circumstances, the availability of a public signal reinforces speculators' existing incentives to place market orders on their private signals more aggressively. However, greater , ceteris paribus, increases , since the poorer quality of (lower informationtonoise ratio ) induces the market makers to rely more heavily on to set marketclearing prices, hence the speculators to trade less aggressively.
More detail. Figure 1B plots lambdalambda_p on the vertical axis with range [0.14, 0.26] and gamma on the horizontal axis with range [1,+1]. For M=1, lambdalambda_p is constant at 0.2 for all values of gamma. For M=2, lambdalambda_p starts at about 0.17 for gamma=0.9, with lambdalambda_p increasing rapidly to about 0.24 at gamma about 0.6, then dropping off slowly to about 0.19 at gamma=0.75, and increasing slightly to gamma=1. For M=4, lambdalambda_p starts at about 0.15 for gamma=0.3, with lambdalambda_p increasing rapidly to about 0.25 at gamma about 0.2, then dropping off to about 0.15 at gamma=0.75, and increasing slightly to gamma=1.
1. According to Goodhart and O'Hara (1997, p. 102), ``one puzzle in the study of asset markets, either nationally or internationally, is that so little of the movements in such markets can be ascribed to identified public `news'. In domestic (equity) markets this finding is often attributed to private information being revealed.'' This friction has been recently studied by Brandt and Kavajecz (2004) and Green (2004) in the U.S. Treasury bond market, by Andersen and Bollerslev (1998) and Evans and Lyons (2002, 2003, 2004) in the foreign exchange market, by Berry and Howe (1994) in the U.S. stock market, and by Brenner, Pasquariello, and Subrahmanyam (2005) in the U.S. corporate bond market, among others. Return to text
2. Foster and Viswanathan (1996) and Back, Cao, and Willard (2000) extend Kyle (1985) to analyze the impact of competition among heterogeneously informed traders on market liquidity and price volatility in discretetime and continuoustime models of intraday trading, respectively. Foster and Viswanathan (1993) show that, when the beliefs of perfectly informed traders are represented by elliptically contoured distributions, price volatility and trading volume depend on the surprise component of public information. Yet, neither model's equilibrium is in closedform, except the (analytically intractable) inverse incomplete gamma function in Back et al. (2000). Hence, their implications are sensitive to the chosen calibration parameters. Further, neither model, by its dynamic nature, generates unambiguous comparative statics for the impact of information heterogeneity or the availability of public information on market liquidity. Finally, neither model can be easily generalized to allow for both a public signal of the traded asset's payoff and less than perfectly correlated private information. Return to text
3. For instance, heterogeneously informed investors may not trade immediately after public news are released but instead wait to preserve (and exploit) their informational advantage as long (and as much) as possible, as in Foster and Viswanathan (1996). Return to text
4. The assumption that the total amount of information available to speculators is fixed ( ) implies that and , hence . Further, the absolute bound to the largest negative private signal correlation compatible with a positive definite , , is a decreasing function of . Return to text
5. This contrasts with the numerical examples of the dynamics of market depth reported in Foster and Viswanathan (1996, Figure 1C) and Back et al. (2000, Figure 3A). Return to text
6. Admati and Pfleiderer (1988) and Foster and Viswanathan (1990) consider dynamic models of intraday trading in which the private information of either perfectly competitive insiders or a monopolistic insider is either fully or partially revealed by the end of the trading period. McKelvey and Page (1990) provide experimental evidence that individuals make inferences from publicly available information using Bayesian updating. Diamond and Verrecchia (1991) argue that the disclosure of public information may reduce the volatility of the order flow, leading some market makers to exit. Kim and Verrecchia (1994) show that, in the absence of better informed agents but in the presence of better information processors with homogeneous priors, the arrival of a public signal leads to greater information asymmetry and lower market liquidity. Return to text
7. Specifically, it can be shown that the oneshot equilibrium in Foster and Viswanathan (1993, Proposition 1) is a special case of our Proposition 2 when private signal correlations for any ECC. Return to text
8. In our sample period (1992 to 2000), the major interdealer brokers in the U.S. Treasury market are Cantor Fitzgerald Inc., Garban Ltd., Hilliard Farber & Co. Inc., Liberty Brokerage Inc., RMJ Securities Corp., and Tullet and Tokyo Securities Inc. Cantor Fitzgerald's share of the interdealer Treasury market is about over our sample period (Goldreich et al., 2005). Nevertheless, Cantor Fitzgerald is a dominant player only in the ``long end'' of the Treasury yield curve, which we do not study in depth in this paper. Return to text
9. Andersen and Bollerslev (1998), among others, refer to the Nonfarm Payroll report as the ``king'' of announcements because of the significant sensitivity of most asset markets to its release. Return to text
10. In unreported analysis, we show that these announcements represent the most important information events in the U.S. Treasury Market, i.e., the only ones having a statistically significant impact on daytoday bond yield changes, consistent with Fleming and Remolona (1997), among others. Return to text
11. See Croushore and Stark (1999, 2001) for details of this database and examples of empirical applications. The database is publicly available on the internet at http://www.phil.frb.org/econ/forecast/reaindex.html. Return to text
12. Much of this evidence stems from the analysis of either GDP or the RTDS variables listed above. The evidence is more controversial for money stock announcements. For instance, Mankiw, Runkle, and Shapiro (1984) and Mork (1990) find that the preliminary growth rates of several Federal Reserve's money aggregates are not efficient predictors of the growth rates of finallyrevised data. Yet, according to Kavajecz and Collins (1995), the bias in preliminary monetary data may be attributed either to the specific seasonal adjustment procedure used by the Federal Reserve or to a different temporal aggregation than for finallyrevised, notseasonally adjusted data. Monetary aggregates are not included in our database. Return to text
13. Indeed, the distributional assumptions in Section 2.1 imply that in both Propositions 1 and 2. Return to text
14. Our results are also robust to different specifications of Eq. (8). For example, we sample bond yields each time there is a transaction, rather than at thirtyminute intervals. We also sample bond yields at an `` optimal'' frequency determined according to the procedure of Bandi and Russell (2005). The evidence presented below is qualitatively and quantitatively similar to that obtained using these alternative sampling procedures, as well as using the aggregate raw (rather than unanticipated) order flow, . The robustness of our results reflects the fact that aggregate unanticipated order flow, , is very closely related to . Indeed, regardless of the selected specification, the resulting from Eq. (8) are lower than . Return to text
15. Nonetheless, the inference that follows is robust to smaller or bigger values for . Return to text
16. We estimate realized volatility applying the procedure of Andersen, Bollerslev, Diebold, and Labys (2003) to yield midquotes sampled at an ``optimal'' frequency determined according to Bandi and Russel (2005). Return to text
17. Presumably, the number of informed traders might increase as the public announcement date approaches. We do not include this product term when measuring dispersion of beliefs only with forecasts of Nonfarm Payroll announcements (i.e., ), since then we only use the Fridays before the announcement dates to control for potential dayoftheweek effects. Return to text
18. The resulting adjusted from the introduction of this cross term in Eq. (8) for fiveyear bond yield differentials increases from , , and (i.e., of Table 4) to , , and when measuring the dispersion of beliefs with the standard deviation of professional forecasts of Nonfarm Payroll (), ``influential'' (), and all available macroeconomic news announcements (), respectively. Return to text
19. The history of auction dates we use in the analysis is available on the U.S. Treasury website, at http://www.publicdebt.treas.gov/of/ofaicqry.htm. Return to text
20. The NBER's Business Cycle Dating Committee mentions that no single macroeconomic variable is the most important predictor of recessions and expansions (e.g., see http://www.nber.org/cycles/recessions.html). The committee takes into account real GDP, real income, employment, industrial production, and wholesale and retail sales to determine whether the U.S. is in a recession or in an expansion. When running a horse race between macroeconomic variables and financial variables to predict the business cycle, Estrella and Mishkin (1998) do not even consider Nonfarm Payroll announcements. Return to text
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