Houdou Basse Mama
email: hbassemama@escpeurope.eu.

Rachidi Kotchoni

Investor Relations' Quality and Mispricing

Keywords: Investor relations, Mispricing, Mishkin test, Information asymmetry, Information uncertainty. JEL classication: G12, G14, D82

We investigate the role of corporate investor relations (IR) in the correction process of mispricing. We provide robust evidence of accruals' mispricing for the sub-sample of rms with lower-rated IR. However, mispricing is more pronounced among rms with higher valuation uncertainty. Further analyses show that rms with higher-rated IR on average earn higher returns, and this relation is resilient to known risk/mispricing factors. More important, IR likely has countervailing eects on mispricing. IR may widen the information asymmetry among investors and concomitantly reduce future analyst forecast errors. Overall, high-quality IR appears to facilitate the market's ability to establish ecient stock prices.

Introduction

Stock prices play an important economic role because they convey information that facilitates the ecient allocation of resources (e.g. [START_REF] Goldstein | Manipulation and the Allocational Role of Prices[END_REF][START_REF] Chung | Eects of Disclosure Quality on Market Mispricing: Evidence from Derivative-Related Loss Announcements[END_REF]. However, mispricing might constrain this benecial role of stock prices by distorting corporate investment and nancing decisions (e.g. [START_REF] Warr | Equity mispricing and leverage adjustment costs[END_REF][START_REF] Chang | Pricing deviation, misvaluation comovement, and macroeconomic conditions[END_REF], and creating incentives for corporate misconduct [START_REF] Chi | Overvaluation and earnings management[END_REF][START_REF] Sawicki | Misvaluation and Insider Trading Incentives for Accrual-based and Real Earnings Management[END_REF]. The costs associated with mispricing are potentially large [START_REF] Hau | Real eects of stock underpricing[END_REF] given that investor activists, rating agencies, and regulators often take corrective actions based on information inferred from stock prices [START_REF] Bond | Market-Based Corrective Actions[END_REF]. In this vein, [START_REF] Chang | Pricing deviation, misvaluation comovement, and macroeconomic conditions[END_REF] nd that a faster correction of mispricing is associated with more ecient resource allocation in the real economy. Relatedly, Lev (1992, p. 18) argues that managers have an implicit responsibility to investors to continually maintain market values as close as feasible to intrinsic ones.

Our objective in this study is to examine the role of investor relations (IR) quality in aecting stock mispricing. Following [START_REF] Chang | Pricing deviation, misvaluation comovement, and macroeconomic conditions[END_REF], we dene mispricing as the deviation of a stock price from its predicted intrinsic value. In turn, we construe IR as the functional area dedicated to communications between the rm and the investment community. The IR function thus plays a major role in determining a rm's disclosure policies, and in addressing visibility and investor following concerns [START_REF] Bushee | Investor Relations, Firm Visibility, and Investor Following[END_REF]. In line with this, the U.S. National Investor Relations Institute [START_REF] Niri | NIRI 2013 Annual Report[END_REF] states that IR practitioners can be thought of as chief disclosure ocers who make sure that their rms and board members understand and respond to investors' concerns. By enabling direct access to senior management and providing market participants with more timely, accurate, and complete rm-specic information, the IR function ultimately contributes to a company's securities achieving fair valuation (NIRI, 2013, p. 1).

We hypothesize that shares of rms with higher-rated IR would be priced more eciently than their counterparts with lower-rated IR. A body of literature (biased toward equity undervaluation) provides indirect evidence that mispricing is inversely related to IR quality (heareafter, IRQ; e.g. [START_REF] Kennedy | Are Investor Relations Programs Giving Analysts What They Need?[END_REF][START_REF] Byrd | Finance theory and the new investor relations[END_REF][START_REF] Kirk | Professional investor relations within the rm[END_REF][START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF]. The existing literature also shows that information asymmetry/uncertainty (hereafter, IA/IU) and mispricing are positively associated. While Lev (1992, p. 17) posits that by denition, the source of misvaluations is information asymmetry, [START_REF] Thomas | A test of the market's mispricing of domestic and foreign earnings[END_REF] and [START_REF] Drake | Disclosure quality and the mispricing of accruals and cash ow[END_REF] contend that low-quality disclosures cause investors to misprice earnings information. Moreover, [START_REF] Jiang | Information uncertainty and expected returns[END_REF] show that the correction process of mispricing is more likely to be protracted when the fundamental value is uncertain. Similarly, Zhang (2006a) argues that mispricing eects should be strongest among rms about which there is high uncertainty and poor information. Overall, IRQ seems to be primarily related to mispricing through its impact on IA/IU [START_REF] Agarwal | Investor relations, information asymmetry and market value[END_REF].

To test the impact of IRQ on mispricing, we rely on proprietary analysts' and institutional investors' evaluations of 252 European non-nancial rms' IR over the 2002-2011 period, and make two complementary research design choices. These choices help elucidate (i) what type of mispricing IRQ aects, and (ii) how this inuence works. Specically, following existing research (e.g. [START_REF] Sloan | Flows About Future Earnings?[END_REF][START_REF] Kraft | Regression-Based Tests of the Market Pricing of Accounting Numbers: The Mishkin Test and Ordinary Least Squares[END_REF][START_REF] Drake | Disclosure quality and the mispricing of accruals and cash ow[END_REF], we rst use the [START_REF] Mishkin | A Rational Expectations Approach to Macroeconomics[END_REF] two-stage rational expectations framework to assess whether the earnings expectations embedded in stock prices accurately reect the dierential persistence of accruals and cash ows. We ask: (i) Do stock prices reect the asymmetric persistence of accruals and cash ows resulting from conditional conservatism? (ii) Does IRQ aect investor mispricing of either component of earnings? Second, we employ the pricing deviation-based approach introduced by Rhodes-Kropf et al. (2005, hereafter, RKRV) to test the channels through which IRQ is related to mispricing.

We argue that a high-quality IR function provides an eective way for investor preferences to be communicated to corporate managers and to reduce IA/IU, which ultimately mitigates investor mispricing of rms' stocks. Indeed, high-quality IR programs induce rms to create useful disclosures, and attract more analyst and media coverage (e.g., [START_REF] Bushee | Investor Relations, Firm Visibility, and Investor Following[END_REF][START_REF] Chen | Press coverage and stock price deviation from fundamental value[END_REF][START_REF] Kirk | Professional investor relations within the rm[END_REF], thereby resolving equivocality of communication [START_REF] Weick | Sensemaking in Organizations[END_REF][START_REF] Roberts | In the mirror of the market: The disciplinary eects of company/fund manager meetings[END_REF][START_REF] Barker | Can company-fund manager meetings convey informational benets? Exploring the rationalisation of equity investment decision making by UK fund managers[END_REF], and allowing more precise information to be incorporated into stock prices [START_REF] Bailey | The economic consequences of increased disclosure: Evidence from international cross-listings[END_REF].

However, IA/IU may simultaneously aect IRQ and mispricing. A rm may respond to perceived increases in IA/IU by devoting more eort to improving its IR. Related to this, [START_REF] Anantharaman | Cover me: Managers' responses to changes in analyst coverage in the post-regulation FD period[END_REF] show that managers increase public nancial guidance after exogenous decreases in analyst coverage. Similarly, Green et al. (2014a) nd that greater client demand for management access among hard-to-value rms leads younger, illiquid rms and prospective equity issuers to attend more broker-hosted investor conferences. 1 Thus, rms may strategically choose IRQ levels based on the necessity to reduce IA/IU, and mitigate stock mispricing. The existence of implicit managerial incentives inherent in mispricing supports the view that IRQ and mispricing are endogenously determined. We consider two complementary approaches to tackle this endogeneity concern (see sections 3.2 and 5.3): a linear instrumental variable model (heareafter, two stage least squares or 2SLS) and a piecewise linear Heckman's sample selection model (heareafter, Heckit).

Mishkin tests provide robust evidence of accruals' mispricing for the sub-sample of rms with lower-rated IR. In line with Zhang (2006a), we nd that mispricing is more pronounced among rms with high valuation uncertainty. Surprisingly enough, the dierential persistence of accruals and cash ows is widest in gain states, not in loss states, which refutes the earnings xation hypothesis (EFH) documented in, e.g., [START_REF] Shi | Can the earnings xation hypothesis explain the accrual anomaly?[END_REF].

Besides, portfolio analyses reveal that rms with higher-rated IR on average earn higher stock returns, and this relation is resilient to known risk and mispricing factors. More important, IR appears to play two countervailing roles in its relation with mispricing. Specically, IR quality may widen the information asymmetry among investors (potentially stemming from private meetings with a select group of investors) and concomitantly reduce any future analyst forecast errors. Together, our results suggest that high-quality IR programs are instrumental in facilitating the market's ability to eciently impound accounting information into stock prices. These results are robust to the endogenous nature of IR quality.

Our study makes three main contributions. First, we further the debate on the economic value of IR by showing that IR quality reduces mispricing primarily through its adverse impact on future analyst forecast errors. This attests to the primacy of the accuracy over just the depth of analyst coverage when establishing stock prices [START_REF] Chang | Stock Market Coverage[END_REF].

Second, the Heckit results suggest that IR quality has no direct eect on mispricing when we control for the probability of underpricing in the next period. Indeed, rms appear to endogenously respond to mispricing in an asymmetric manner; they are more concerned about underpricing than about overpricing although either kind of mispricing is harmful for the economy (e.g., [START_REF] Jensen | Agency costs of overvalued equity[END_REF]. Third, unlike [START_REF] Peasnell | The fragile returns to investor relations: evidence from a period of declining market condence[END_REF], we nd robust returns to IR even in periods of declining market condence, thereby supporting the view that IR can add value (e.g., [START_REF] Laskin | How investor relations contributes to the corporate bottom line[END_REF][START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF] by reducing mispricing. 1 Chung et al. (2012) document that absent plans to issue new securities, exercise or grant stock options in the near future, managers would have no strong incentives to correct the mispricing of their stocks in advance of the subsequent release of mandatory disclosures.

The remainder of the paper is organized as follows. Section 2 presents the background and develops testable hypotheses. Section 3 discusses the econometric framework. Section 4 introduces the data. Section 5 shows the empirical results and Section 6 concludes.

2 Background and Hypothesis Development 2.1 Investor Relations IR specialists view their work as managing market expectations and the disclosure process, altering stakeholders' perceptions, institutionalizing shareholder relations, and diversifying the investor base [START_REF] Kennedy | Are Investor Relations Programs Giving Analysts What They Need?[END_REF][START_REF] Rao | Institutional Sources of Boundary-Spanning Structures: The Establishment of Investor Relations Departments in the Fortune 500 Industrials[END_REF]. Although IR departments use various channels for investor outreach non-deal roadshows, broker-hosted investor conferences, and investor visits to rm headquarters are considered as the most signicant ones [START_REF] Gedvila | Investor outreach[END_REF].

Research relates successful IR, inter alia, to reduced costs of acquiring and processing rmspecic information, greater investor recognition, enhanced stock liquidity, and ultimately to improved market valuations [START_REF] Lang | Corporate disclosure policy and analyst behavior[END_REF][START_REF] Brennan | Investor relations, liquidity, and stock prices[END_REF][START_REF] Kirk | Professional investor relations within the rm[END_REF]. The general tenor of that research is that IR activities improve the information environment of the rm, thereby improving the reliability of investors' valuation models and building corporate reputation [START_REF] Metzker | The mystery of valuation[END_REF][START_REF] De Jong | Investor relations, reputational bonding, and corporate governance: The case of Royal Ahold[END_REF]. More importantly, these benets seem to derive primarily from direct access to senior management [START_REF] Barker | Can company-fund manager meetings convey informational benets? Exploring the rationalisation of equity investment decision making by UK fund managers[END_REF][START_REF] Bushee | Investor Relations, Firm Visibility, and Investor Following[END_REF][START_REF] Solomon | What are we meeting for? The consequences of private meetings with investors[END_REF].

A large body of the literature points to the idea that the desired goal of IR is to increase stock market valuations. In line with this, IR professionals often regard IR events as opportunities for stock promotions [START_REF] Chugh | The stock valuation process: The analysts' view[END_REF][START_REF] Solomon | Selective publicity and stock prices[END_REF] or occasions for rms to negotiate favorable identities (Rao and Sivakumar, 1999, p. 36). There is evidence that rms have often used aggressive IR strategies to hype their stocks in the short run (e.g., [START_REF] De Jong | Investor relations, reputational bonding, and corporate governance: The case of Royal Ahold[END_REF][START_REF] Lang | Voluntary disclosure and equity oerings: reducing information asymmetry or hyping the stock?[END_REF]. Doukas et al. (2005, p. 99) note that there is growing suspicion that the wedge between stock prices and fundamental values is likely associated with excessive analyst coverage. Similarly, Chen et al. (2013) nd that abnormal media coverage of rm-generated news creates sentiment among investors, thereby exacerbating stock mispricing. Indeed, increasing sentiment adds to speculative demands, which may contribute to maintaining stock mispricing.

Because overvaluation might induce the illusion of growth and engender managerial malfeasance [START_REF] Jensen | Agency costs of overvalued equity[END_REF], it appears as harmful to shareholders' wealth as undervaluation which might cause losses from potential underinvestment. This is also in the spirit of [START_REF] Lu | Price Shocks, News Disclosures, and Asymmetric Drifts[END_REF], who nd that large short-term price shocks of either sign are followed by negative abnormal returns over the subsequent year. We therefore contend that the ultimate goal of successful IR should be to establish and/or maintain the pricing eciency of a rm's securities. More importantly, rms may attain pricing eciency of their shares by reducing information risk [START_REF] Farragher | Do investor relations make a dierence?[END_REF]. Information risk arises when there are information asymmetries between the rm and outside investors or when investors are uncertain about the quality of information relative to the rm's prospects. [START_REF] Aslan | The characteristics of informed trading: Implications for asset pricing[END_REF] nd that the size of such risk depends on the quality of a rm's information environment.

High-quality IR programs involve direct investor-management interactions that go beyond just providing data; they should additionally deliver information, knowledge, and insight.

The benets associated with these interactions consist in gathering information that is, on its own, non-material to complement the potentially ambiguous signals already in the public domain. [START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF] nd that the business press broadcasts more broadly rm-generated news and adds an editorial content, thus helping mitigate cash ow mispricing. However, neither the information dissemination role of the press nor its information creation role signicantly reduces the accruals' mispricing. We anticipate that, through its impact on IA/IU, IR can aid in mitigating the accruals' mispricing as its major audience, the analyst community, presumably possesses the expertise necessary to fully appreciate the implications of accruals than the press.

IR Quality and Information Asymmetry (IA)

IA exists when players have unequal information sets. Prior studies show that high-quality IR programs attract more information intermediaries (e.g., analysts and the business press).

Beyond increasing the visibility of corporate news, these intermediaries might create private rm-specic information, thus increasing the amount and quality of information available to market participants [START_REF] Lang | Voluntary disclosure and equity oerings: reducing information asymmetry or hyping the stock?[END_REF][START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF]Green et al., 2014a).

The result is a reduction in the information acquisition costs borne by traders and a decrease in the adverse selection component of bid-ask spreads, which fosters a more complete capitalization of the news into stock prices [START_REF] Brennan | Investment analysis and price formation in securities markets[END_REF].

In the context of [START_REF] Merton | A simple model of capital market equilibrium with incomplete information[END_REF] model of incomplete information high-quality IR will induce more trading in the rm's stock by uninformed investors (Brown and Hillegeist, 2007, p. 446). However, intensied trading by the uninformed proportionately attracts more informed trading [START_REF] Kyle | Continuous auctions and insider trading[END_REF]. Yet, to the extent that informed traders are riskaverse and/or capital constrained, one would observe a relative decrease in these agents' propensity to trade as uninformed trading increases. In sum, IRQ reduces the level of IA through the investor recognition channel, thereby lowering stock mispricing (e.g., [START_REF] Lev | Information disclosure strategy[END_REF][START_REF] Collins | Investor sophistication and the mispricing of accruals[END_REF][START_REF] Brown | Conference calls and information asymmetry[END_REF][START_REF] Brown | How disclosure quality aects the level of information asymmetry[END_REF]. Increased analyst and media coverage could additionally mitigate stock mispricing by providing investors with credible and timely editorial content that improves their understanding of the implication of the news for future performance [START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF].

Alternatively, IRQ might aect IA by altering the incentives to search for private information. High-quality IR programs in form of more timely, consistent, accurate, and complete public disclosures (e.g., [START_REF] Byrd | Finance theory and the new investor relations[END_REF][START_REF] Kirk | Professional investor relations within the rm[END_REF][START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF] might reduce private information search incentives [START_REF] Verrecchia | Information acquisition in a noisy rational expectations economy[END_REF]. By bringing the future forward (Lundholm and Myers, 2002, p. 818), IR reduce the frequency of private information events, i.e. the rate at which informed traders discover and trade on private information [START_REF] Lundholm | Bringing the Future Forward: The Eect of Disclosure on the Returns-Earnings Relation[END_REF].

2

It follows that IRQ reduces IA because (i) it adversely aects the relative amount of informed trading, and/or (ii) it is inversely related to the frequency of private information events. This conclusion is in line with the empirical evidence in [START_REF] Brown | Conference calls and information asymmetry[END_REF] that rms holding more frequent conference calls exhibit lower degrees of IA than their nonholding counterparts (see also [START_REF] Agarwal | Investor relations, information asymmetry and market value[END_REF].

2.3 IR Quality and Information Uncertainty (IU) Jiang et al. (2005, p. 185) dene IU in terms of value ambiguity, or the precision with which a rm's value can be estimated by knowledgeable investors at reasonable cost.

Similarly, Zhang (2006a, p. 105) notes that IU potentially stems from two sources: the volatility of a rm's underlying fundamentals and poor information.

A central result in [START_REF] Jiang | Information uncertainty and expected returns[END_REF] is that market pricing dynamics vary systematically, depending on the degree of IU. Relatedly, Zhang (2006a) nds that uncertainty delays the ow of ambiguous information into stock prices. In turn, [START_REF] Jiang | Information uncertainty and expected returns[END_REF] provide empirical evidence that high IU exacerbates investor psychological biases [START_REF] Hirshleifer | Investor psychology and asset pricing[END_REF] and limits rational arbitrage. 3 Furthermore, [START_REF] Boyarchenko | Ambiguity shifts and the 2007-2008 nancial crisis[END_REF] nds that ambiguity- averse investors assign higher probabilities to lower utility states and charge an ambiguity premium, leading to lower stock prices, when they are faced with doubts about the quality of information and uncertainty about the data-generating process (see also [START_REF] Epstein | Ambiguity, information quality, and asset pricing[END_REF].

IU-induced mispricing may result from two types of sensemaking occasions: ambiguity and uncertainty. Investors engage in sensemaking in the case of ambiguity because they are confused by too many interpretations; in the case of uncertainty, investors do so because they are ignorant of any interpretations [START_REF] Weick | Sensemaking in Organizations[END_REF]. Indeed, under uncertainty, investors suer from imprecision in estimates of future consequences conditional on present actions (March, 1994, p. 174). In turn, investors face ambiguity when information lacks clarity, is highly complex, or when a paradox makes multiple explanations plausible [START_REF] Martin | Cultures in Organizations: Three Perspectives[END_REF].

Firms can remove ignorance by providing a greater quantity of information to investors.

In contrast, Weick (1995, p. 99) argues that the resolution of confusion requires that a dierent kind of information be conveyed to the marketplace, namely, the information that is constructed in face-to-face interaction that provides multiple cues. That is, resolving confusion requires debate, clarications, and enactment more than merely increasing the amount of data [START_REF] Daft | Organizational information requirements, media richness and structural design[END_REF].

To the extent that the IR function manages the rm's disclosure process and institutionalizes rm/investor relationships, high-quality IR can aid in resolving both ignorance (uncertainty) and confusion (ambiguity). [START_REF] Bushee | Investor Relations, Firm Visibility, and Investor Following[END_REF] and [START_REF] Kirk | Professional investor relations within the rm[END_REF], among others, show that U.S. rms initiating professional IR experience increases in public disclosure and in investor awareness. Furthermore, [START_REF] Bushee | Conference presentations and the disclosure milieu[END_REF] demonstrate in a U.S. context that rm/investor private meetings aect the degree to which information intermediaries can update their priors about the rms through direct interactions with senior management and other informed participants. For [START_REF] Roberts | In the mirror of the market: The disciplinary eects of company/fund manager meetings[END_REF], because of the rich sensory data of the shared physical context, IR meetings clearly oer the greatest potential for building reciprocal understanding, thereby reducing mispricing.

Besides, the nancial community also relies heavily on public information, properties of which may be claried during IR private meetings (Green et al., 2014b;[START_REF] Solomon | What are we meeting for? The consequences of private meetings with investors[END_REF]. Notwithstanding the absence of private communication of price-sensitive information, [START_REF] Barker | Can company-fund manager meetings convey informational benets? Exploring the rationalisation of equity investment decision making by UK fund managers[END_REF]) nd that U.K. fund managers paradoxically consider IR meetings as the primary source of information, especially on long-term strategy and prospects, and management capabilities and orientation (see also [START_REF] Marston | Investor relations meetings: evidence from the top 500 UK companies[END_REF][START_REF] Lok | Institutional logics as identity projects[END_REF][START_REF] Hobson | Analyzing speech to detect nancial misreporting[END_REF]. In turn, Roberts et al. (2006, p. 282) report that rms also attach considerable value to IR meetings; this is because such meetings enable rms to alter the the complex and mobile gestalt of company identity that is the basis of investor decision-making.

By expediting the resolution of uncertainty [START_REF] Lang | Corporate disclosure policy and analyst behavior[END_REF] and resolving equivocality of communication [START_REF] Roberts | In the mirror of the market: The disciplinary eects of company/fund manager meetings[END_REF], high-quality IR should fasten the correct capitalization of otherwise ambiguous information into stock prices (Zhang, 2006a).

So far, we have constrained IRQ to aect mispricing through its impact on IA/IU. However, while a direct eect of IR on mispricing is theoretically unclear, we lean on [START_REF] Kirk | Professional investor relations within the rm[END_REF] to hypothesize a direct negative link between IRQ and mispricing. This direct link helps test partial mediation through IA/IU, or test whether IR meetings are organized for 3 While our focus in this study is on IA/IU, we acknowledge that investor cognitive processing biases are another source of mispricing (e.g., [START_REF] Lev | R&D reporting biases and their consequences[END_REF][START_REF] Warr | Equity mispricing and leverage adjustment costs[END_REF]. However, the eects of such biases are found to be strongest in settings characterized by high uncertainty and poor information. Therefore, our tests do, albeit weakly, embody the eect of cognitive biases on mispricing.

reasons other than rm-specic news [START_REF] Soltes | Private Interaction Between Firm Management and Sell-Side Analysts[END_REF], but that aect mispricing. On a view of the above, we form and test three main hypotheses: Hypothesis 1a. The adverse eect of high-quality IR on mispricing runs through its impact on information asymmetry Hypothesis 1b. High-quality IR deters information uncertainty, thereby mitigating mispricing Hypothesis 2. High-quality IR adversely aects mispricing beyond its impact on information asymmetry/uncertainty. Despite the preceding expectations, there are credible reasons that may weaken the ability of IR to mitigate mispricing. In spite of its importance, credibility may sometimes be sacriced by both IR departments and information intermediaries. IR teams may strategically choose to cater to investors' sentiment by just reporting news that conrms investor beliefs while discounting others, thus `catching up' investor intermediaries in the `hype' (e.g., [START_REF] Lang | Voluntary disclosure and equity oerings: reducing information asymmetry or hyping the stock?[END_REF][START_REF] Hong | Talking up liquidity: insider trading and investor relations[END_REF][START_REF] De Jong | Investor relations, reputational bonding, and corporate governance: The case of Royal Ahold[END_REF][START_REF] Solomon | Selective publicity and stock prices[END_REF]. Also, there seems to be an implicit quid pro quo arrangement between information intermediaries and rms' management with respect to favorable coverage and access to senior management (e.g., [START_REF] Ke | The Eect of Issuing Biased Earnings Forecasts on Analysts' Access to Management and Survival[END_REF][START_REF] Chen | Press coverage and stock price deviation from fundamental value[END_REF]. These implicit incentives are likely to momentarily and articially boost stock prices, and cause return reversals around earnings announcements [START_REF] Solomon | Selective publicity and stock prices[END_REF]. In addition, private access to management via IR meetings can exacerbate IA among investors, which runs counter to the notion of level playing eld with regard to information that regulators seek to create [START_REF] Solomon | What are we meeting for? The consequences of private meetings with investors[END_REF]. Whether IRQ mitigates or contributes to mispricing is, therefore, an empirical issue.

3 Econometric Framework [START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF] argue that accruals and cash ows provide an ideal setting to explore the role of an investor intermediary in market pricing dynamics. Therefore, we rst investigate the extent to which IR quality aids in correctly pricing these two primary components of earnings before exploring the possible channels through which this eect can work.

3.1 Tests of Ecient Pricing of Accruals and Cash Flows: The [START_REF] Mishkin | A Rational Expectations Approach to Macroeconomics[END_REF] Test

The Mishkin test (MT) aims at assessing the extent to which investors correctly account for the implication of current earnings' components for future earnings. This procedure can be used to test whether the accruals and cash ow components of earnings are correctly priced by investors. The MT relies on two equations of the following type:

EAR i,t+1 = γ 0 + γ 1 ACC i,t + γ 2 CF i,t + u i,t+1 (1)
RET

i,t+1 = δ (EAR i,t+1 -γ * 0 -γ * 1 ACC i,t -γ * 2 CF i,t ) + v i,t+1 (2)
where EAR i,t , ACC i,t , CF i,t and RET i,t are respectively the earnings, accruals, cash ows and returns on the stock of rm i during year t. In the system above, (1) is a forecasting equation while (2) is a pricing equation. To ease interpretation, it is customary in this literature to convert the variables into terms of their fractional ranks within sectors before proceeding with model estimation [START_REF] Larcker | On the use of instrumental variables in accounting research[END_REF]. For instance, EAR i,t is the fractional rank of rm i's earnings within its sector during year t. This transformation is applied to all variables.

Substituting the expression of EAR i,t+1 into the right hand side of Equation ( 2) yields a reduced-form representation of returns:

RET i,t+1 = δ (γ 0 -γ * 0 ) + δ (γ 1 -γ * 1 ) ACC i,t + δ (γ 2 -γ * 2 ) CF i,t + δu i,t+1 + v i,t+1 (3)
Assuming that the forecasting equation is correctly specied, the accruals and cash ows are correctly priced by the market if γ 1 -γ * 1 = 0 and γ 2 -γ * 2 = 0. See [START_REF] Kraft | Regression-Based Tests of the Market Pricing of Accounting Numbers: The Mishkin Test and Ordinary Least Squares[END_REF] for details. The MT of market eciency is, therefore, equivalent to a likelihood ratio (LR)

test that compares the full model given by ( 1)-( 2) to a constrained model that imposes γ 1 -γ * 1 = 0 and γ 2 -γ * 2 = 0. This LR test is performed within a nonlinear seemingly unrelated regression (NL-SUR) procedure.

Equation (3) suggests that the MT of market eciency may also be conducted via an OLS regression of returns on accruals and cash ows. The theoretical expressions of this regression's coecients are given by

β k = δ (γ k -γ * k ), k = 0, 1, 2.
In principle, this allows us to conduct the MT as simple signicance tests on the coecients β 1 and β 2 . However, the simulations conducted by [START_REF] Kraft | Regression-Based Tests of the Market Pricing of Accounting Numbers: The Mishkin Test and Ordinary Least Squares[END_REF] suggest that a large sample is needed for the OLS regression-based MT to be as powerful as the LR test. This is not surprising given that a test of the null hypothesis β k = 0 tends to be more conservative than a direct test of γ k -γ * k = 0. For that reason, the OLS regression-based MT is not used in this paper. [START_REF] Kraft | Regression-Based Tests of the Market Pricing of Accounting Numbers: The Mishkin Test and Ordinary Least Squares[END_REF] show that excluding relevant earnings' components that are not rationally priced from the model creates an omitted variable bias that can lead to invalid inferences. In an attempt to avoid this kind of bias, we expand Equation (1) as follows:

EAR i,t+1 = γ 0 + γ 1 ACC i,t + γ 2 CF i,t + γ 3 SALGR i,t (
RET i,t+1 = δ(EAR i,t+1 -γ * 0 -γ * 1 ACC i,t -γ * 2 CF i,t -γ * 3 SALGR i,t (5)
-γ * 4 T RV OL i,t -γ * 5 M CAP i,t -γ * 6 P 2B i,t ) + v i,t+1
As previously, a given component of earnings is correctly priced by the market if and only if its coecient satises γ k -γ * k = 0, for k = 1, ..., 6.

With this improved model specication, we can investigate the possible associations between IRQ and the patterns of mispricing. First, we dene a binary variable IRQM i,t that takes the value 1 if rm i's IRQ index is above the median of its industry, and 0 otherwise.

Next, we estimate the system (4)-( 5) and perform the MT separately for the sub-samples identied by IRQM i,t = 1 and IRQM i,t = 0. By considering these sub-samples separately,

we will be able to identify the components of earnings that are likely mispriced for each sub-group.

Recent research (e.g., [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF] suggests that MT should be modied to incorporate both the asymmetric persistence of accruals and the dierential pricing of accruals and cash ows. Failing to account for the eect of timely loss recognition will bias expectations' models, which makes inferences about market eciency sensitive to such bias.

Moreover, while prior research has imposed identical pricing for accruals and cash ows, theory suggests that the pricing of these earnings' components would dier depending on their persistence and ability to predict earnings [START_REF] Barth | Accruals, cash ows, and equity values[END_REF][START_REF] Pope | Earnings components, accounting bias and equity valuation[END_REF]. Indeed, [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF] provide empirical evidence that investors price these components dierently, thereby rejecting rational pricing and the EFH.

To examine the robustness of our inferences based on the system (4)-( 5), we rst investigate whether investors anticipate the lower persistence of accruals in loss years due to timely loss recognition (conditional conservatism). To this end, we determine economic gain states (years) and economic loss states following [START_REF] Ball | The Role of Accruals in Asymmetrically Timely Gain and Loss Recognition[END_REF]. Our proxy for gain and loss states is an indicator variable (D t ) that takes the value 1 if the industry-adjusted cash ows for a rm in year t are negative, and 0 otherwise. Incorporating this indicator permits us to identify the state of the world under which mispricing is found. Under timely loss recognition, one would expect higher mean reversion of accruals in loss states relative to gain states.

In a second step, we relax the restriction, usually imposed in MT, that accruals and cash ows are identically priced (as suggested, e.g., by the coecient δ in the system (4)-( 5)).

Doing so requires estimating a three-equation system, including two predictive regressions for future earnings (one for accruals and one for cash ows) and a regression that articulates how unexpected earnings' components map into future stock returns. Accounting for asymmetry across states and dierential pricing of cash ows and accruals surprises allows more direct tests of the naive EFH. Under conditional conservatism, EFH would require that the accruals anomaly be more pronounced among loss rms relative to prot rms [START_REF] Patatoukas | Asymmetrically Timely Loss Recognition and the Accrual Anomaly[END_REF]. For expository purposes, we rely on a parsimonious model that allows a valid test for market eciency (see also [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF].

ACC i,t+1 = γ 0 + γ 01 D t + γ 1 ACC i,t + γ 2 CF i,t + γ 3 ACC i,t D t + γ 4 CF i,t D t + u 1i,t+1 (6) CF i,t+1 = ω 0 + ω 01 D t + ω 1 ACC i,t + ω 2 CF i,t + ω 3 ACC i,t D t + ω 4 CF i,t D t + u 2i,t+1 (7)
RET

i,t+1 = δ 1 (ACC i,t+1 -γ * 0 -γ * 01 D t -γ * 1 ACC i,t -γ * 2 CF i,t -γ * 3 ACC i,t D t -γ * 4 CF i,t D t ) +δ 2 (CF i,t+1 -ω * 0 -ω * 01 D t -ω * 1 ACC i,t -ω * 2 CF i,t -ω * 3 ACC i,t D t -ω * 4 CF i,t D t ) +v i,t+1 (8)
where the parameters γ 3 , γ 4 , ω 3 , and ω 4 are incremental coecients pertaining to loss states in the predictive equations. In contrast to the parameters in the predictive equations, the pricing parameters (γ * k and ω * k ) are collectively underidentied, which prompts us to re- write Equation (8) for the purpose of our empirical tests of rationality conditions:

RET i,t+1 = δ 1 ACC i,t+1 + δ 2 CF i,t+1 -(κ * 0 -κ * 01 D t -κ * 1 ACC i,t -κ * 2 CF i,t -κ * 3 ACC i,t D t -κ * 4 CF i,t D t ) +v i,t+1 (9)
where κ * k = δ 1 γ * k + δ 2 ω * k , with k = 0, 1, 2, 3, 4.

Investigating the Causal Links between IR Quality and Mispricing

In Section 2, we have suggested that IR quality (I RQ i,t ) may have a direct eect on mispricing (MSV). However, IRQ may also aect MSV via the channels of IA and IU. We have also argued that rms may select IRQ strategically in response to undesirable levels of IU, IA, and MSV. Therefore, the latter variables potentially have a causal eect on IRQ as well.

Our main objective is to investigate the causal eects of IRQ, IU, and IA on MSV. To this end, we operationalize the IU and IA using six variables (see Section 4.2): the bidask spread (BASP i,t ), [START_REF] Amihud | Illiquidity and stock returns: cross-section and time-series eects[END_REF] illiquidity ratio (AM IH i,t ), the trading volume (T RV OL i,t ), analyst forecast errors (ERR i,t ), the number of analysts following a rm (N OEST i,t ) and the dispersion of analyst forecasts (DI SP i,t ). Six other variables that potentially reect various aspects of IU and IA are also considered for control purposes. These are the relative systematic risk as measured by the realized beta (RBET A i,t ), the realized idiosyncratic volatility (RI V OL i,t ), the realized idiosyncratic skewness (RSK EW i,t ), the use of public capital markets (U P CM i,t ), the cross-listing on either the NYSE or the LSE (C LIST i,t ) and the leverage ratio (LEV i,t ). Our regressions control for three other rm characteristics used in the MT, namely the price-to-book ratio (P 2B i,t ), the market capitalization (M CAP i,t ) and sales growth (SALGR i,t ).

First, we seek to understand whether MSV can be predicted using lagged information. For that purpose, we specify the following regression model:

M SV i,t = β 0,0 + β 0,1 IRQ i,t-1 + β 0,2 AM IH i,t-1 + β 0,3 BASP i,t-1 + β 0,4 T RV OL i,t-1 (10) +β 0,5 ERR i,t-1 + β 0,6 DISP i,t-1 + β 0,7 N OEST i,t-1 + β 0,8 M SV i,t-1 +β 0,9 RBET A i,t-1 + β 0,10 RIV OL i,t-1 + β 0,11 RSKEW i,t-1 + β 0,12 U P CM i,t-1 +β 0,13 CLIST i,t-1 + β 0,14 LEV i,t-1 + β 0,15 P 2B i,t-1 + β 0,16 M CAP i,t-1 +β 0,17 SALGR i,t-1 + ε 0,i,t
The inclusion of the lagged value of MSV in the RHS of the regression above allows us to control for the persistence of misvaluation so that the coecients of the other regressors basically capture their eects on the increments of MSV over time.

Second, we perform a regression of MSV onto contemporaneous information controlling for lagged MSV in order to explore the directions in which the coecients of IRQ, IA and IU would change. The model estimated is:

M SV i,t = β 1,0 + β 1,1 IRQ i,t + β 1,2 AM IH i,t + β 1,3 BASP i,t + β 1,4 T RV OL i,t (11)
+β 1,5 ERR i,t + β 1,6 DISP i,t + β 1,7 N OEST i,t + β 1,8 M SV i,t-1 +β 1,9 RBET A i,t + β 1,10 RIV OL i,t + β 1,11 RSKEW i,t + β 1,12 U P CM i,t +β 1,13 CLIST i,t + β 1,14 LEV i,t + β 1,15 P 2B i,t + β 1,16 M CAP i,t +β 1,17 SALGR i,t + ε 1,i,t
It can be shown that the dierences between the coecients of the regressors across both models is mainly driven by the increments of the regressors between periods t-1 and t and their correlations with the error term ε 1,i,t . For instance, if the coecient of IRQ in the second regression (θ 1,1 ) is very dierent from its coecient in the rst (θ 0,1 ), this would suggest that the incremental eort devoted by rms to attaining or maintaining a certain level of IRQ between periods t -1 and t is non-random (endogenous). In this context, endogeneity means that rms strategically choose their IRQ level in order to control the magnitude of mispricing.

As we shall see in the sequel, the empirical results support the intuition that the increments of IRQ are endogenous. This suggests that the other regressors operationalizing IA and IU are possibly endogenous as well. We consider two complementary approaches to tackle this endogeneity problem: a linear instrumental variable model (heareafter, 2SLS) and a piecewise linear Heckman's sample selection model (heareafter, Heckit). In both approaches, lagged regressors are used as instruments.

In the rst-step of the 2SLS procedure, we regress each of the variables IRQ i,t , BASP i,t , AM IH i,t , T RV OL i,t , ERR i,t , N OEST i,t , and DISP i,t onto past information. For instance, our rst instrumental regression is given by:

IRQ i,t = θ 0 + θ 1 IRQ i,t-1 + θ 2 AM IH i,t-1 + θ 3 BASP i,t-1 + θ 4 T RV OL i,t-1 (12) +θ 5 ERR i,t-1 + θ 6 DISP i,t-1 + θ 7 N OEST i,t-1 + θ 8 M SV i,t-1 +θ 9 RBET A i,t-1 + θ 10 RIV OL i,t-1 + θ 11 RSKEW i,t-1 + θ 12 U P CM i,t-1 +θ 13 CLIST i,t-1 + θ 14 LEV i,t-1 + θ 15 P 2B i,t-1 + θ 16 M CAP i,t-1 +θ 17 SALGR i,t-1 + ε 2,i,t .
Likewise, each of the variables BASP i,t , AM IH i,t , T RV OL i,t , ERR i,t , N OEST i,t , and DISP i,t is regressed onto the same set of regressors as on the RHS above. The results of these seven instrumental regressions will shed light on the complexity of the interactions that may exist between IR quality and mispricing. For instance, if θ 8 turns out to be positive and signicant in Equation ( 12), this would lead us to infer that higher past misvaluation is associated with higher future IRQ.

The second-step estimating equation of the 2SLS procedure is given by:

M SV i,t = β 1,0 + β 1,1 IRQ i,t + β 1,2 AM IH i,t + β 1,3 BASP i,t + β 1,4 T RV OL i,t (13)
+β 1,5 ERR i,t + β 1,6 DISP i,t + β 1,7 N OEST i,t + β 1,8 M SV i,t-1 +β 1,9 RBET A i,t + β 1,10 RIV OL i,t + β 1,11 RSKEW i,t + β 1,12 U P CM i,t +β 1,13 CLIST i,t + β 1,14 LEV i,t + β 1,15 P 2B i,t + β 1,16 M CAP i,t +β 1,17 SALGR i,t + ε1,i,t
where the regressors with a hat symbol denote their tted values obtained from the rststep instrumental regressions. Note that we are advocating that the regressors without a hat symbol are exogenous.

Considering the Heckit approach, we split our original sample into two sub-samples: a sub-sample where pricing errors are negative and another sub-sample with positive pricing errors. A negative pricing error means that the underlying company's stock is undervalued, and vice versa (RKRV, 2005). Also, recall that observations consist of rm-years such that a given rm may migrate across both sub-samples over time.

We rst ask: Can past information be used to predict the probability of a rm being overvalued or undervalued in the next period? To answer this question, we dene a binary variable U N DER i,t that takes the value 1 if rm i is undervalued at period t, and 0 otherwise. Next, we estimate a Probit model where past information conditions the probability of U N DER i,t = 1. This amounts to assuming the existence of a lead indicator Z i,t taking the form:

Z i,t = γ 0 + γ 1 IRQ i,t-1 + γ 2 AM IH i,t-1 + γ 3 BASP i,t-1 + γ 4 T RV OL i,t-1 (14) +γ 5 ERR i,t-1 + γ 6 DISP i,t-1 + γ 7 N OEST i,t-1 + γ 8 M SV i,t-1 +γ 9 RBET A i,t-1 + γ 10 RIV OL i,t-1 + γ 11 RSKEW i,t-1 + γ 12 U P CM i,t-1 +γ 13 CLIST i,t-1 + γ 14 LEV i,t-1 + γ 15 P 2B i,t-1 + γ 16 M CAP i,t-1 +γ 17 SALGR i,t-1 + ε 3,i,t
where ε 3,i,t ∼ N (0, 1) and U N DER i,t = 1 if and only if Z i,t >0. Hence,

P rob (U N DER i,t = 1|X i,t-1 ) = Φ Ẑi,t
where X i,t-1 is the vector of lagged regressors and Ẑi,t is the tted value of Z i,t .

Next, we ask whether the determinants of mispricing are the same when U N DER i,t = 1 and when U N DER i,t = 0. A naive approach to answer this question would be to estimate Equation ( 11) separately for the sub-samples identied by U N DER i,t = 1 and U N DER i,t = 0. However, we need to control for biases stemming from the correlation between the error term of the equation governing the truncation (ε 3,i,t ) and the error term of the equation of MSV (ε 1,i,t ). Therefore, the equations that we consider are:

M SV i,t = β 2,0 + β 2,1 IRQ i,t + β 2,2 AM IH i,t + β 2,3 BASP i,t + β 2,4 T RV OL i,t (15)
+β 2,5 ERR i,t + β 2,6 DISP i,t + β 2,7 N OEST i,t + β 2,8 M SV i,t-1 +β 2,9 RBET A i,t + β 2,10 RIV OL i,t + β 2,11 RSKEW i,t + β 2,12 U P CM i,t +β 2,13 CLIST i,t + β 2,14 LEV i,t + β 2,15 P 2B i,t + β 2,16 M CAP i,t +β 2,17 SALGR i,t + λ 1 IM R 1,i,t + η 1,i,t and M SV i,t = β 3,0 + β 3,1 IRQ i,t + β 3,2 AM IH i,t + β 3,3 BASP i,t + β 3,4 T RV OL i,t (16)
+β 3,5 ERR i,t + β 3,6 DISP i,t + β 3,7 N OEST i,t + β 3,8 M SV i,t-1 +β 3,9 RBET A i,t + β 3,10 RIV OL i,t + β 3,11 RSKEW i,t + β 3,12 U P CM i,t +β 3,13 CLIST i,t + β 3,14 LEV i,t + β 3,15 P 2B i,t + β 3,16 M CAP i,t +β 3,17 SALGR i,t + λ 0 IM R 0,i,t + η 0,i,t where IM R 1,i,t = φ( Ẑi,t) Φ( Ẑi,t) is proportional to the expectation of ε 1,i,t conditional on U N DER i,t = 1 and IM R 0,i,t = - φ( Ẑi,t) 1-Φ( Ẑi,t)
is proportional to the expectation of ε 1,i,t conditional on U N DER i,t = 0. Accordingly, Equation ( 15) is restricted to the sub-sample U N DER i,t = 1 while Equation ( 16) is restricted to the sub-sample U N DER i,t = 0.

If either of the coecients λ 1 or λ 0 in Equations ( 15) and ( 16) is signicant, this would imply that the truncation biases matter. Moreover, the signs of these coecients coincide with the sign of the linear correlation coecient of ε 0,i,t (in Equation ( 10)) and ε 3,i,t on each sub-sample. If λ 1 is negative, for instance, this would suggest that a perceived higher probability of undervaluation ex ante is associated with a lower magnitude of undervaluation ex post.

Main Variables

We discuss the construction of the main variables and relegate the denition of all variables used in the empirical analysis to Appendix 1.

Earnings' components. EAR is income before extraordinary items and dividends; CF is cash ows from operations; ACC is accruals dened as EAR minus CF . These variables are then deated by one-year lagged total assets. Stock returns. RET is the log buy and hold return on a given stock over a 12-month period beginning three months after the scal year-end (see [START_REF] Drake | Disclosure quality and the mispricing of accruals and cash ow[END_REF]. An alternative measure used in the MT is SIZERET which denotes the dierence between a rm's buy and hold return and a return on a corresponding size decile-matched portfolio. Although these four components capture dierent aspects of IR, they are highly correlated.

Therefore, subsequent analyses use only the aggregate measure.

Information Asymmetry (IA). We use three proxies for IA: bid-ask spreads, trading volume and price impact. The bid-ask spread (BASP ) is commonly thought to measure information asymmetry explicitly [START_REF] Leuz | The economic consequences of increased disclosure (digest summary)[END_REF]. This pertains to the adverse selection arising from having asymmetrically informed investors trading in the same security. The more severe the IA, the wider the spread necessary for market makers to recoup losses from trading with potentially informed traders. We calculate BASP as: (ask-bid)/((ask+bid)/2). The trading volume (T RV OL) captures investors' willingness to transact in a stock which, in turn, is inversely related to the existence of IA [START_REF] Leuz | The economic consequences of increased disclosure (digest summary)[END_REF]. Yet, T RV OL is noisy as it might reect such factors unrelated to IA as portfolio rebalancing needs. The [START_REF] Amihud | Illiquidity and stock returns: cross-section and time-series eects[END_REF] illiquidity ratio (AM IH), computed as the ratio of daily absolute returns over euro trading volume is intended to capture the ability of an investor to trade in a stock without moving its price. As in [START_REF] Daske | Mandatory IFRS reporting around the world: Early evidence on the economic consequences[END_REF], we use the annual median of AM IH in our empirical analyses.

Information Uncertainty (IU). We rely on three proxies for IU. The rst proxy is the number of analysts who cover a rm (N OEST ). A rm with deeper analyst following is theoretically more transparent in its future prospects and intended actions, and is therefore less uncertain in its valuation (Zhang, 2006a;[START_REF] Lu | Information uncertainty, information asymmetry and corporate bond yield spreads[END_REF]. The second proxy for IU is the dispersion in analyst earnings forecasts (DI SP ). Widely used in the literature (e.g. [START_REF] Barron | Dispersion in analysts' earnings forecasts as a measure of uncertainty[END_REF][START_REF] Bissessur | Analyst information precision and small earnings surprises[END_REF], DISP reects the uncertainty about the future prospects of a rm by capturing the degree of consensus among analysts.

We measure DISP as the standard deviation of analyst forecasts scaled by the prior yearend stock price to mitigate heteroskedasticity. Our last measure for IU is analyst forecast error (hereafter ERR; [START_REF] Farragher | Do investor relations make a dierence?[END_REF][START_REF] Gu | Governance and equity prices: Does transparency matter?[END_REF]. We calculate ERR as the natural log of one plus the dierence between analysts' earnings per share (EPS) forecasts and actual EPS scaled by the absolute value of median. ERR can thus be considered a measure for the accuracy of analyst forecasts.

Summary Statistics

Table 1 provides descriptive statistics for the full sample and for sub-samples of rms with higher-rated IR (H_IRQ) and those with lower-rated IR (L_IRQ). The mean (median) rm has a market value of ¿12.3 billion (¿1.7 billion) and the standard deviation is ¿22.1 billion. In turn, the average rm reports total earnings, cash ows, and accruals (each in percent of lagged total assets) of 4.8%, 10%, and -5.2%, respectively. M SV is statistically signicant (t = 3.46), suggesting that market participants and rm managers rely on dierent sets of information about the prospects of the rms in our sample.

7

We nd that both groups of rms are relatively overpriced; however, higher-rated rms tend to be more overvalued. More importantly, the dierences in mispricing turn out to stem from the rm-specic component of M SV , which shows that lower-rated rms are generally underpriced while higher-rated rms on average are overvalued. The average rms in the two sub-samples are of similar size. Interestingly, our proxies for IA are collectively higher for the sub-sample of rms with lower-rated IR. By contrast, IU measures provide no clear picture. Indeed, we nd no dierence in analyst forecast errors; at the same time, better-rated rms have deeper analyst following and less dispersed analyst forecasts.

Finally, we observe that lower-rated rms exhibit higher idiosyncratic risk and leverage, while they are associated with lower values of EAR, CF , ACC, and returns.

[Table 1 about here] 5 Results

Mishkin Tests

Primary results

In Table 2, we use the system (4)-( 5) to perform the MT via a NL-SUR. Column 1 corroborates the ndings in [START_REF] Sloan | Flows About Future Earnings?[END_REF] that accruals are signicantly less persistent than cash ows (γ 1 -γ 2 = -0.174). However, these results do not support the null hypothesis that investors rationally anticipate and price the dierential persistence of accruals and cash ows with respect to their implications for future earnings. The LR test for the null hypothesis of market eciency recommends rejection at the 1% level. We, therefore, explore potential sources of the apparent market ineciencies. Parameter tests based on column 1 of Table 2 reveal that investors appear to systematically overweight accruals' surprises (γ * 1 > γ 1 ) 7 Because mispricing is rather transient in nature [START_REF] Baker | Multinationals as arbitrageurs: The eect of stock market valuations on foreign direct investment[END_REF], we examine the adequacy of M SV by testing whether high M SV rms earn subsequently lower returns. Our results are consistent with this prediction (Online Appendix Part B). Therefore, mispricing persists long enough to allow managers to respond.

while they tend to correctly price information conveyed in cash ows' surprises (γ * 2 ≈ γ 2 ).

Our data do not support the EFH, which would require that both accruals and cash ows be jointly mispriced [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF]. Indeed, in unreported analyses we nd that the average persistence parameter obtained from regressing one-year ahead earnings on current earnings is 0.63, clearly indicating that γ 1 < γ 2 < 0.63. In this setting, for investors to naively xate on reported total earnings both accruals and cash ows would have to be overweighted in the pricing equation such that γ * 1 = γ * 2 = 0.63. 8

[Table 2 about here]

The rejection of rational pricing for accruals surprises suggests that accruals are a far too more complex accounting disclosure than cash ows, the interpretation of which requires high levels of sophistication. Recall that the most important audience of IR departments is composed of sophisticated delegated information intermediaries of investors [START_REF] Collins | Investor sophistication and the mispricing of accruals[END_REF][START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF]: sell-side analysts. This constituency is reportedly more sophisticated than individual investors and the business press [START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF], and, as with institutional investors (especially hedge funds), continues to hold private meetings with companies' senior management even after Reg FD in the U.S. [START_REF] Solomon | What are we meeting for? The consequences of private meetings with investors[END_REF]. In spite of the absence of privately communicating material information, IR meetings do increase the accessibility and clarity of information provided to investors [START_REF] Kalay | Investor sophistication and disclosure clienteles[END_REF], thereby reducing IA/IU [START_REF] Agarwal | Investor relations, information asymmetry and market value[END_REF]; see also Section 2).

Therefore, we anticipate that high-quality IR programs would aid in reducing the documented mispricing of the accruals component of earnings. To explore this conjecture, we rst group rms into two sub-samples on a year-by-year basis using the industry-specic median of IRQ: higher-quality IR rms (see column 2 of Table 2) vs. lower-quality IR rms (column 3 of Table 2). As our proxy of IRQ might systematically vary across industries and years, this procedure ensures that the median rm in each industry gets a ranking of 0.5.

As expected, we could not reject the null hypothesis of rational pricing of both components of earnings on the sub-sample of higher-quality IR rms (χ 2 2 = 0.19, p = 0.91). In contrast, we nd that pricing ineciency is restricted to the sub-sample of rms with lower-quality IR programs. There, the LR test of rational pricing of both components of earnings is rejected at the 1% level (χ 2 2 = 10.88, p = 0.0043). What is more, cash ows continue to be rationally priced even in this latter sub-sample (p = 0.42). As in column 1 of Table 2, accruals remain the mispriced component of total earnings (p = 0.003). Together, the evidence in columns 13 indicates that IRQ is instrumental in providing guidance on the valuation implications of a harder-to-value component of earnings (accruals). 9 In Section 5.3, we elaborate on the possible channels through which this eect might operate.

Notwithstanding, prior research suggests that nancial analysts can inuence the information content of stock prices. By translating a mixture of public and private information (gleaned from private meetings with senior management and applying the mosaic approach) into earnings forecasts, sell-side analysts likely facilitate the process of valuing rms.

For example, [START_REF] Lee | Did Regulation Fair Disclosure, SOX, and Other Analyst Regulations Reduce Security Mispricing?[END_REF] document a signicant reduction in return continuation following analyst forecast revisions and earnings announcements. In a similar vein, Karolyi 8 The results remain qualitatively unaltered when we cluster standard errors by year to account for cross-sectional correlations of residuals in dierent years in the MT. We refrain from clustering standard errors on two dimensions (by rm and by year), relying on [START_REF] Petersen | Estimating standard errors in nance panel data sets: Comparing approaches[END_REF] and [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF], who provide evidence that rm eects are likely negligible when returns are the dependent variable. 9 Although the results discussed here use raw returns calculated in the interval starting at the beginning of April t and ending at the end of March t + 1 (similar to [START_REF] Drake | Disclosure quality and the mispricing of accruals and cash ow[END_REF], the inferences hitherto are resilient to the use of alternative measures of returns. Specically, we employ size-adjusted returns (i.e. the dierence between a rm's raw returns and the contemporaneous returns on a size-matched portfolio). The conclusions remain qualitatively unaltered. Details are available upon request from the authors.

and [START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF] show that the positive impact of IR on rm market value runs essentially through greater analyst following, improved analyst forecast accuracy, and lower forecast dispersion. Consistent with this, we nd, in unreported tests, that rms with higher-quality IR exhibit subsequently deeper coverage by sell-side analysts (t = 9.42, p < 0.001), more accurate analyst forecasts (t = 3.04, p = 0.002), and lower forecast dispersion (t = 3.86, p < 0.001) than their counterparts with lower-rated IR. While not denitive, these univariate results are in line with [START_REF] Bushee | Conference presentations and the disclosure milieu[END_REF], who argue that IR meetings in a well-dened physical and social milieu aect the degree to which the audience can update their priors about the rm through direct interactions with management and other informed participants.

Debate is ongoing about what causes the accruals anomaly [START_REF] Shi | Can the earnings xation hypothesis explain the accrual anomaly?[END_REF]. 10 To provide exploratory evidence, we nd (see columns 47 of Table 2), however, that the irrational pricing of accruals tends to be concentrated in rms with high realized idiosyncratic risk, high trading volume, low quoted bid-ask spreads, and low realized market beta. This evidence partially supports the notion that risk-averse arbitrageurs might shy away from fully exploiting the accruals anomaly in the presence of excessive idiosyncratic risk. At the same time, it runs counter to the transaction costs argument advanced by [START_REF] Mashruwala | Why is the accrual anomaly not arbitraged away? The role of idiosyncratic risk and transaction costs[END_REF], because investors appear to correctly price the two earnings' components of rms for which they are more likely to bear higher transaction costs that is, rms with low trading volume and high quoted bid-ask spreads. However, while puzzling at rst sight, Hirshleifer et al. ( 2013) interpret rms with higher turnover (i.e. ratio of trading volume over outstanding shares) as having higher valuation uncertainty. Firms with lower trading volume can thus be seen as rms with lower valuation uncertainty, hence the ability of investors to rationally price such stocks. Unlike [START_REF] Shi | Can the earnings xation hypothesis explain the accrual anomaly?[END_REF], who dismiss the arbitrage explanation of the accruals anomaly, we tentatively conclude that the apparent mispricing of accruals is driven, not necessarily by prohibitive transaction costs, but by arbitrage risk potentially due to the absence of close substitutes [START_REF] Mashruwala | Why is the accrual anomaly not arbitraged away? The role of idiosyncratic risk and transaction costs[END_REF]. The results suggest that accruals and cash ows show dierential persistence in gain and loss states when forecasting future cash ows. The earnings response coecients for accruals and cash ows range from 0.18 to 0.20 and from 0.51 to 0.54, respectively (see Table 3). Therefore, one would expect rational investors to price these two earnings' components as well as their surprises dierently. It turns out that investors value cash ow surprises much higher than accruals surprises. Indeed, the dierential earnings response coecient (δ 1 -δ 2 ) is signicantly negative and amounts to -0.33. As a result, investors tend to distinguish between news related to cash ows and that related to accruals. This is strong evidence against the naive earnings xation explanation for the accruals anomaly (see also [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF]. 10 Providing a comprehensive review of this debate goes beyond the scope of this study; please, refer to, e.g., [START_REF] Richardson | Accounting anomalies and fundamental analysis: A review of recent research advances[END_REF], for an excellent review.

In the predictive equation for future accruals, current accruals and cash ows exhibit similar persistence. The picture is reversed when forecasting future cash ows, where we note a dierential persistence in both gain states (χ 2 2 = 48.15, p < 0.001) and loss years (χ 2 2 = 64.95, p < 0.001). However, unlike [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF], our results indicate that the related dierential persistence between accruals and cash ows is seemingly greatest, not in loss states, but in gain years. Also, the dierential persistence resides in the magnitude, not in the sign. Specically, the incremental coecient on cash ows during loss states (-0.168) is signicantly lower than that on accruals (-0.063) when predicting cash ows (χ 2 2 = 11.09, p = 0.004). The signicant negative incremental coecient on accruals is suggestive of the transitory nature of accruals in loss years under timely loss recognition. Thus, our nding is not supportive of the evidence by [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF] that cash ows are more persistent in loss states when forecasting cash ows and using industry-adjusted cash ows as the conditioning variable to identify the economic states.

We next use Equation ( 9) to test rational pricing conditions in dierent economic states via non-linear combinations of estimators. In gain states, the null hypothesis of rational pricing of both accruals and cash ows surprises is rejected at the 1% level. However, investors appear to rationally price cash ows in loss years. Opposed to this evidence, we provide that investors irrationally process information related to accruals surprises in loss years. We further test whether accruals and cash ows surprises are indeed dierently priced in gain years and loss years. The aim is to identify potential sources of apparent mispricing by revealing the mispriced component of earnings and the economic states under which mispricing is observed. To this end, we test the restrictions κ * 3 = δ 1 γ 3 + δ 2 ω 3 for accruals, and κ * 4 = δ 1 γ 4 + δ 2 ω 4 for cash ows. Results from these tests reveal that (see column 2 of Table 3) the dierential coecient on cash ows surprises in gain and loss states is negative but statistically insignicant (p = 0.39). The corresponding dierential coecient for accruals is insignicant (p = 0.73).

In sum, we nd evidence of asymmetric persistence of both accruals and cash ows only when forecasting future cash ows. Surprisingly enough, the dierential persistence of accruals and cash ows is widest in gain states, not in loss states. Moreover, our parsimonious specications indicate that the accruals anomaly in gain states is signicant at the 5% level or better (see columns 14 of Table 3) while it is signicant only at the 10% level in loss states; it even becomes insignicant in loss states when we use size-adjusted returns as the dependent variable in the pricing equation and standard errors are clustered by year. Despite these contrasts, we nd no evidence conducive to asymmetric persistence of accruals across gain and loss years (the related p-values range from 0.39 to 0.73, see

Table 3). Finally, there is limited, if any, evidence that investors tend to misprice cash ows only in gain years (see the bottom lines in Table 3). Similarly to accruals, we nd no evidence that investors are more likely to misprice the cash ows of loss rms relative to gain rms. These results thus refute the naive EFH.

5.1.3

Does the role of IR in mitigating mispricing vary across economic states?

Table 3 uses parsimonious specications and does not account for the role of IR in mitigating the market ineciencies observed in pricing accruals in gain and loss states, and to a lesser extent, in pricing cash ows in gain states. We re-run the system (6)(8) above while re-writing (8) as shown in ( 9) and including all the controls used in Table 2 in order to avoid the omitted variable bias and strengthen our ability to make clear inferences about the sources of ineciencies. The standard errors are clustered by year, and the results are summarized in Table 4. Column 1 shows the full sample, which is contrasted in column 2 with the estimates from column 2 of Table 3. Columns 3 and 4 contain the results relative to rms with higher-quality IR and rms with lower-quality IR, respectively.

[Table 4 about here]

On the one hand, using the full sample in column 1 of Table 4, we nd strong evidence of accruals' mispricing in both gain and loss states. In addition, we nd no evidence that the mispricing of accruals systematically diers in loss and gain states. On the other hand, if anything, we can reject the null hypothesis of rational pricing of cash ows only in gain years at the 10% level (p = 0.06). Together, the evidence in column 1 of Table 4 suggests that investor mispricing of earnings' components is more likely for accruals and less so for the cash ow component and, if anything, it should be limited to gain years. These results contradict partly the conclusions attained from Table ,2 where we reported that cash ows are generally rationally priced but accruals are not. To that extent, one may conclude that allowing for asymmetric persistence, dierential pricing and standard errors clustered by year may matter for inferences drawn from the MT. However, using size-adjusted returns as the dependent variable in the pricing equation (untabulated), cash ows appear to be rationally priced in both gain and loss years. What is more, the mispricing of accruals is now restricted to gain years.

Firms with higher-rated IR exhibit a rather interesting picture, in that investors tend to systematically overvalue their cash ows in gain states (p = 0.003) while this item is fairly rationally priced in loss states. Remarkably though, investors seem to correctly understand the valuation implications conveyed in the accruals' disclosures of these rms. This seems at rst sight to contradict the ability of IR to improve the accessibility and clarity of information provided to investors. For the sub-sample of rms with lower-rated IR, accruals are consistently mispriced in gain and loss states, and the incremental mispricing in loss years (-0.07) is insignicant (p = 0.66). We interpret this result to mean that there is no asymmetry across states in the mispricing of accruals for rms with lower-rated IR. In rebuttal, the null hypothesis of rational pricing of cash ows in gain years is rejected only at the 10% level (p = 0.076). 11

If investor mispricing is driven by the naive earnings xation, IR may have no explanatory power or could exacerbate the mispricing [START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF]. At odds with this prediction, the results hitherto suggest that higher-quality IR improve investors' ability to eciently impound accounting information into stock prices. If anything, cash ows tend to be mispriced only in gain states, but the evidence is not resilient to alternative measures for returns in the pricing equation. [START_REF] Barone | An examination of the eects of investor sophistication on the pricing of accruals and cash ows[END_REF] nd that cash ow mispricing is reduced by the trading activity of sophisticated investors. In a similar vein, [START_REF] Call | Analysts' cash ow forecasts and the predictive ability and pricing of operating cash ows[END_REF] shows that analysts' cash ow forecasts correct underpricing of operating cash ows while [START_REF] Mohanram | Analysts' cash ow forecasts and the decline of the accruals anomaly[END_REF] reports that analysts' cash ow forecasts mitigate accruals' mispricing because earnings forecasts and cash ow forecasts jointly provide investors with implicit accrual forecasts [START_REF] Drake | The media and mispricing: The role of the business press in the pricing of accounting information[END_REF]. These studies suggest potential channels through which IR may aect (mis)pricing of earnings' components: the analyst forecasts and trading activity of sophisticated investors.

A subtle but remarkable outcome of superior IR programs is the subsequent shift of the investor base away from more sophisticated investors toward more concentration of less sophisticated investors. This conjecture relies on [START_REF] Merton | A simple model of capital market equilibrium with incomplete information[END_REF] investor recognition hypothesis (hereafter, IRH), which predicts decreasing information acquisition and processing costs as a result of heightened investor cognizance of a company's brand. Consistent with this prediction, [START_REF] Kalay | Investor sophistication and disclosure clienteles[END_REF] nds that there is a higher concentration of less sophisticated investors in rms with superior IR (top decile). In contrast, Karolyi and Liao 11 When we use size-adjusted stock returns in lieu of raw returns in the pricing equation ( 14), higherquality IR appear pivotal in facilitating the market's ability to eciently impound accruals and cash ows information into stock prices irrespective of the economic state. In contrast, investors tend to misprice the accruals of rms with lower-rated IR indierently in gain and loss states; only is the mispricing in gain years signicantly larger in magnitude than in loss states (0.33 > 0.20).

(2015) report that rms with more active IR are associated with higher institutional and hedge fund ownership; they, however, add that the economic magnitude of these relations are smaller relative to analyst variables. Therefore, the relationship between superior IR and subsequent concentration of sophisticated investors is an empirical issue.

To address this empirical issue, we investigate whether our data support the widening investor base argument for rms with superior IR programs. We crudely project our oneyear-ahead measure of institutional ownership onto current-period levels of IR fractional ranks and control for year and sector xed eects. We nd that rms with higher-quality IR exhibit a decrease in institutional ownership in magnitude of up to 5.1% 12 (t = -2.68, p = 0.007) relative to rms with lower-quality IR in the subsequent year. While we have no ne-grained data to distinguish between the dierent types of institutional investors, it seems likely that IR benets more individual investors.

The observed decrease in relative institutional holdings in rms with higher-quality IR is potentially consistent with [START_REF] Merton | A simple model of capital market equilibrium with incomplete information[END_REF] investor recognition hypothesis. It attests to high-quality IR inducing more trading in the rm's stock by uninformed investors [START_REF] Collins | Investor sophistication and the mispricing of accruals[END_REF]. To the extent that more uninformed trading would prompt proportionate informed trading [START_REF] Kyle | Continuous auctions and insider trading[END_REF], the signicant relative decrease in institutional holdings for the sub-sample of rms with higher-rated IR is strong evidence that IR likely aects the investor mispricing of accounting information through its adverse impact on IA. In addition, the documented dwindling institutional ownership is potentially attributable to perceived decreased incentives to search for private information as more assertive IR programs are associated with more forthcoming disclosures [START_REF] Lundholm | Bringing the Future Forward: The Eect of Disclosure on the Returns-Earnings Relation[END_REF] and thus lower frequency of private information events. Our results corroborate the nding in [START_REF] Brown | How disclosure quality aects the level of information asymmetry[END_REF] that IA is negatively associated with IR activities (see Section 2.2). It is, however, unclear whether our weak evidence of cash ow mispricing in gain states for rms with higher-rated IR can be associated with the signicant reduction in institutional ownership [START_REF] Barone | An examination of the eects of investor sophistication on the pricing of accruals and cash ows[END_REF]. This evidence interests managers, investors, and market regulators as well. Companies' senior management should recognize the potential for the existence of disclosure clientele [START_REF] Kalay | Investor sophistication and disclosure clienteles[END_REF]; that is, there is possibly heterogeneity in the demand for information across investors, which is a function of an investor's ability to parse information. IR can bring about changes in the shareholder mix [START_REF] Brennan | Investor relations, liquidity, and stock prices[END_REF]. Thus, IR programs appear as a device of choice to eectively get rid of cumbrous investor types and achieve fair valuation. However, there has to be a warning of caveat emptor for managers here. Basse Mama and Bassen (2016) show that higher-quality IR programs subtly instill managerial discipline in the form of reduced agency costs. Indeed, heightened visibility improves rm transparency, making possible processes of managerial subjection to investor rights. To that extent, market regulators motivated by investor protection and ecient allocation of capital should pursue measures to improve IR. Using a sample of publicly listed rms in China, [START_REF] Firth | Corporate Accessibility, Private Communications and Stock Price Crash Risk[END_REF] observe that corporate accessibility, as measured by the amount and the quality of private communications between rms and investors, complements public information sources in reducing future stock price crash risk.

Portfolio Analysis on the Role of IR

The MT provide robust evidence of accruals' mispricing for the sub-sample of rms with lower-rated IR. Therefore, we focus on the accruals' mispricing to validate the results from the MT. We investigate whether, conditionally on the level of accruals and the quality of a rm's IR, the stock is systematically mispriced. We rst independently classify the sample rms into deciles based on their accruals and IRQ in each year. For either conditioning variable (accruals and IRQ), we dene rms in the top 30% (bottom 30%) as high (low), and consider the middle 40% as neutral. As a result, we pursue our analyses only with rms in the top 30% and bottom 30% of the distribution of accruals. We then re-sort the two accruals-based portfolio stocks by the quality of their IR programs to obtain 4 doublesorted long-only accruals/IR portfolios: [1] low accruals/low IR, [2] high accruals/low IR,

[3] low accruals/high IR, and [4] high accruals/high IR. 13

Next, we compute yearly value-weighted average one-year-ahead returns on each portfolio.

The holding period spans from 1 July 2002 to 30 June 2012. We construct the portfolios at the end of June of year t because the IR awards forming the basis of our proxy for IR quality are typically bestowed in mid-June of each year (see Section 4.2). The awards' ceremony and the results are largely publicized by the business press.

Theory suggests that high accruals are associated with overvaluation, thus leading to lower future returns. If high-quality IR programs play a major role in mitigating accruals' mispricing, [4] would outperform [2], and [1] would under-perform [3]. We, therefore, construct two hedge portfolios that we refer to as Hedge_high (HH, a portfolio that is long in high accruals/high IR rms [4] and short in high accruals/low IR rms [2]) and Hedge_low (HL, a portfolio that is long in low accruals/high IR rms [3] and short in low accruals/low IR rms [1]). The idea is to explore the role of IR quality for each level of accruals (low vs. high). Toward this end, we obtain the widely used [START_REF] Fama | Common risk factors in the returns on stocks and bonds[END_REF] monthly factors (MKTRF, SMB, HML) and the monthly series of Carhart (1997) WML factor from Wharton Research Data Services. 14 Finally, to capture potential commonality in the mispricing of IR quality we augment the [START_REF] Carhart | On persistence in mutual fund performance[END_REF] model by the mispricing factor Undervalued Minus Overvalued (UMO; [START_REF] Hirshleifer | A nancing-based misvaluation factor and the crosssection of expected returns[END_REF] 15 .

Because the returns on these pricing factors are collectively dollar-denominated, we rst convert them into euro terms (see [START_REF] Solnik | Global Investments[END_REF]) before using them in the regressions.

We subsequently regress the monthly returns pertaining to each of the long-only portfolios from [1] through [4] and the two hedge portfolios on euro denominated Fama-French factors augmented by the factors WML and UMO over the period from 1 July 2002 through 30 June 2012 in a SUR framework.

[Table 5 about here] A general result from Table 5 is that risk-adjusted returns increase monotonically in IR quality. Indeed, a portfolio that is long in rms with high accruals levels and higher-rated IR [4] outperforms a portfolio of rms with comparable accruals levels but which have lowerrated IR programs [2] when we use the augmented Carhart model as benchmark returngenerating process. Similarly, in the sub-group of rms with lower levels of accruals ([1] and [3]), we nd that the portfolio comprising of rms with lower-rated IR [1] is dominated by the portfolio of rms with higher-rated IR [3]. Specically, the annualized dierential riskadjusted return between [4] and [2], HH, levels out at 8.2% and is statistically signicant and economically meaningful. Correspondingly, the annualized dierential risk-adjusted return between [3] and [1], HL, amounts to 8.9% and is both statistically and substantively signicant. 16 To appreciate the economic meaning of the documented dierential return 13 This mode of portfolio construction is widely used in the nance literature. Also, we do not distinguish between gain and loss states because we nd no asymmetry in the mispricing of accruals.

14 MKTRF: market risk premium; SMB: small minus big; HML: high minus low; WML: winners minus losers. SMB, HML, and WML are hedge portfolios and are widely used in nance. 15 We collected data relative to this factor from Danling Jiang's website: https://sites.google.com/site/danlingjiang/data-library.

We adjusted the series the same way as with the factors in the [START_REF] Carhart | On persistence in mutual fund performance[END_REF] model. In a slight abuse of language, we refer to the resulting model as the augmented Carhart model. 16 The alphas estimated from the Fama and French three-factor models and Fama and French ve-factor models are qualitatively similar to the ones shown in this section (available upon request).

estimates, suce it to observe that the average annualized returns on the various pricing factors used in our augmented Carhart model range from 0.36% (HML) to 4.62% (UMO) over the sample period; the corresponding market risk premium is 2.39%. 17

Table 5 shows that high-quality IR rms have, on average, smaller loadings than low-quality IR rms on the market factor, suggesting that high-quality IR rms are less risky than lowquality IR rms. In addition, we evaluate the weights allocated to the two hedge portfolios (HH and HL) and the four factors used in the [START_REF] Carhart | On persistence in mutual fund performance[END_REF] model in the ex post tangency portfolio. The weights level out at 52.82% (HH), 37.4% (HL), 19.72% (MKTRF), 8.31% (SMB), -58.7% (HML), -56.74% (WML), and 97.2% (UMO), respectively. By according high weights to portfolios of rms with higher-rated IR, the stock market recognizes the value of high-quality IR. At the same time, the market does not seem to fully reect the eect of high-quality IR. Consistent with [START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF], our results indicate that rms with higher-rated IR do not merely manipulate IR-induced media coverage [START_REF] Solomon | Selective publicity and stock prices[END_REF], or choreograph earnings conference calls [START_REF] Cohen | Playing favorites: How rms prevent the revelation of bad news[END_REF]. Instead, our results suggest that high-quality IR programs can be used as value-relevant signals by investors.

At the same time, these results seem to cast doubt on the rational factor risk explanation of the accruals anomaly (see [START_REF] Hirshleifer | The accrual anomaly: risk or mispricing?[END_REF]. We hark back to the results from the MT in Section 5.1 to recall that the accruals anomaly tends to be limited to rms with high realized idiosyncratic risk, low realized market beta, and high trading volume. Such rm-level attributes can be considered as capturing a higher valuation uncertainty that places a greater burden on investor attention (e.g. [START_REF] Hirshleifer | Innovative eciency and stock returns[END_REF]. Taking this evidence from the MT and controlling for well-known risk-based or mispricing factors in our portfolio analysis, we conclude that the IR eect on future returns potentially comes from mispricing (see Hirshleifer et al., 2013, for similar conclusions). Inconsistent with ndings in recent studies (e.g. [START_REF] Green | Going, going, gone? The apparent demise of the accruals anomaly[END_REF][START_REF] Shi | Can the earnings xation hypothesis explain the accrual anomaly?[END_REF][START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF] it seems that the accruals anomaly is still alive but is less pronounced in rms with stronger information environments. The results in this study provide valuable insights to investors interested in trading on the accruals anomaly. We propose that investors might be better o when they take long positions in rms with higher-rated IR programs or alternatively design long/short positions conditional on the quality of the underlying rms. Managers and regulators may also be interested in our results because we nd no evidence that rms assertively engage in IR to choreograph earnings conference calls or to manipulate media coverage, all actions that are associated with subsequent lower returns.

Causal Links between MSV, IRQ, IA and IU

This section presents the results of the investigations on the potential channels through which IR quality and mispricing (as per RKRV, 2005) inuence each other. Below, the rst subsection presents preliminary results which suggest that IRQ is endogenously determined.

The second subsection presents the results of the 2SLS estimation and the third subsection presents the Heckit regressions. In all regressions, standard errors are clustered by year and by rm [START_REF] Petersen | Estimating standard errors in nance panel data sets: Comparing approaches[END_REF].

Preliminary results

Column 1 of Table 6 contains the regression of MSV onto lagged information. Surprisingly enough, the results suggest that the past IRQ is positively associated with current pricing 17 The German stock market, as measured by the Composite DAX index, earns an annual average raw return of only 4.43% with a standard deviation of 25.34% over the holding period. We use the German stock market as a potential benchmark as the sample is dominated by German rms (see Online Appendix Part A).

errors while the past bid-ask spread is negatively associated with current pricing errors. A plausible explanation of the sign of the coecient of lagged IRQ in this regression is that pricing errors respond in real time to rms' eort to improve their IRQ. Also, the sign of the coecient of the lagged bid-ask spread suggest that rms facing large IA in the past devote more eort to mitigating it, thereby reducing their current pricing errors. The coecient of lagged MSV is positive and signicant as well, which suggests that pricing errors are quite persistent over time. Past realized idiosyncratic volatility increases current pricing errors while prior cross-listing of the rm on either the NYSE or the LSE decreases them.

Column 2 of Table 6 shows the regression of MSV onto contemporaneous information.

Interestingly, the results suggest that IRQ is negatively associated with contemporaneous mispricing. Amihud's illiquidity ratio, analysts' forecast errors, and market capitalization are all positively related to contemporaneous pricing errors. The realized idiosyncratic volatility has a positive and signicant eect on contemporaneous MSV while contemporaneous cross-listing has no signicant eect. The signs of the coecient of IRQ, Amihud's illiquidity ratio and the analysts' forecast errors are rather intuitive. Indeed, pricing errors are expected to be higher when IRQ is lower and when investors face greater IA/IU (e.g. [START_REF] Lev | Information disclosure strategy[END_REF]Zhang, 2006aZhang, , 2006b)). The fact that IRQ is negatively associated with contemporaneous pricing errors but positively associated with future pricing errors conrms that MSV responds in real time to the eort devoted by rms to maintaining good IRQ [START_REF] Anantharaman | Cover me: Managers' responses to changes in analyst coverage in the post-regulation FD period[END_REF]. Moreover, the changes in the eects of the variables operationalizing IA and IU, depending on whether they are lagged or not suggest that these regressors are endogenous in the second regression (Table 6).

[Table 6 about here]

In order to test the robustness of the results above, we consider a third regression where MSV is regressed onto an information set containing contemporaneous and lagged regressors. More precisely, we take the second regression and add the rst lags of the seven variables operationalizing IRQ, IU, and IA. Column 3 of Table 6 presents the results of this regression which are largely consistent with the two previous ones. Indeed, the eects of lagged and contemporaneous IRQ are more pronounced than in the separate regressions (shown in Columns 1 and 2 of Table 6). The eect of market capitalization is not signicant here, while cross-listing appears to reduce mispricing again. Otherwise, the other coecients that were found signicant in the separate regressions are signicant here as well.

Given our claim that some contemporaneous regressors are endogenous, the last two regressions may be providing biased coecients. We therefore address this endogeneity issue in the ensuing subsections.

5.3.2

The Two-Stage Least Square Approach

First-stage instrumental regression

The seven regressors suspected of endogeneity are IR quality (I RQ i,t ), bid-ask spread (BASP i,t ), Amihud's illiquidity ratio (AM IH i,t ), trading volume (T RV OL i,t ), analyst forecast errors (ERR i,t ), the number of analysts following a rm (N OEST i,t ) and dispersion of analysts' forecast (DI SP i,t ). Each of these variables is regressed onto their own rst lags and the rst lags of the other control variables.

The rst regression is of particular interest as it allows us to identify the determinants of IRQ and assessing its predictability. First, we note that IRQ is quite persistent as the coecient of the lagged IRQ is approximately equal to 0.43. Second, past MSV has no signicant eect on current IRQ. Third, we note that IRQ is quite predictable. The variables that positively aect current IRQ are the lagged bid-ask spread, number of analysts, realized idiosyncratic skewness, market capitalization and sales growth. Hence, a large bid-ask spread in the past compels rms to take actions directed at increasing current IRQ and reducing current MSV (cf. the previous subsection). On the contrary, current IRQ is negatively associated with lagged Amihud's illiquidity ratio, trading volume and analysts' forecast errors. The sign of the eect of trading volume on IRQ possibly mirrors the one of the bid-ask spread. Indeed, larger bid-ask spreads are associated with lower trading volume and higher illiquidity levels, ceteris paribus.

This relation is conrmed by the second instrumental regression, where a high trading volume and market capitalization at the previous period predict a lower level for the current Amihud's illiquidity ratio. The illiquidity ratio is quite persistent, as shown by the sign and signicance of the coecient of its lag. More important, past MSV is positively associated with current illiquidity ratio, indicating that perceived mispricing in the previous period deters investors from transacting in a stock.

The third instrumental regression suggests that higher past IRQ, illiquidity ratio, bid-ask spread, and analyst forecast errors all predict a higher bid-ask spread for the current period.

In contrast, the lagged number of analysts, the lagged realized idiosyncratic skewness, the lagged market capitalization and the use of public capital markets at the previous period are all negatively associated with current bid-ask spreads. The results also suggest that past pricing errors are unrelated to current bid-ask spreads.

The fourth instrumental regression documents that the current trading volume is positively related to the lagged trading volume (high persistence), lagged dispersion of analyst forecasts, lagged cross-listing and lagged leverage. However, current trading volume is negatively associated with lagged Amihud's illiquidity ratio and lagged realized idiosyncratic skewness. The positive association of trading volume with the dispersion of analyst forecasts supports the view that the trading volume is an appropriate measure of IA. Indeed, IA contributes to divergence of opinions among investors, which in turn is necessary for (information-based) trades to take place. In another vein, [START_REF] Polk | The stock market and corporate investment: A test of catering theory[END_REF] hold that rms with higher share turnover are rms with shorter shareholder horizons. Finally, we note that current trading volume is unrelated to past pricing errors.

Our fth instrumental regression shows that analyst forecast errors are persistent over time, but less so than the remaining endogenous regressors. In addition, current analysts forecast errors respond positively to the lagged dispersion of analyst forecasts, lagged realized idiosyncratic volatility and lagged use of public capital markets. This evidence corroborates the nding by [START_REF] Bissessur | Analyst information precision and small earnings surprises[END_REF] that greater forecast uncertainty is associated with larger absolute forecast errors. On the contrary, current analyst forecast errors are negatively related to lagged IRQ, lagged number of analysts, and lagged sales growth. Because analysts collect, process, and distribute information about the prospects of the rm they cover, the activity of nancial analysts contributes to increasing the amount of information available about the rm, thereby reducing uncertainty. Markedly, however, past pricing errors have no eect on current analyst forecast errors.

The sixth instrumental regression suggests that the dispersion of analyst forecasts is quite persistent over time. In addition, the dispersion of analyst forecasts responds positively to the lagged analyst forecast errors, the lagged number of analyst estimates and the realized idiosyncratic volatility. On the contrary, it responds negatively to the price to book ratio.

Past pricing errors have no eect on the current dispersion of analyst forecasts.

The seventh and last instrumental regression concerns the number of analysts following a rm, which is found to be quite persistent over time. Moreover, the number of analysts following a rm is positively associated with the lagged market capitalization, lagged sales growth, and lagged cross-listing. In rebuttal, the depth of analyst coverage is negatively associated with lagged analyst forecast errors and lagged pricing errors.

These instrumental regressions shed light on the complexity of the relations between MSV, IRQ, IU, and IA. From the last instrumental regression, for instance, one could imagine that large pricing errors at year t -1 leads rms to take actions that draw more attention from analysts as a means to reducing future pricing errors. Besides, all the variables used to operationalize IRQ, IU, IA, and MSV are persistent over time.

Our third and fth instrumental regressions suggest that lagged IRQ potentially plays two countervailing roles in that it is positively associated with BASP (a measure for IA) while it is inversely related to analyst forecast errors (a measure of IU). The induced increase in IA potentially stems from corporate selective disclosure. This evidence points to the possibility that rms either provide material information to a select group of investors during private meetings (in violation of the EU Market Abuse Directive) or that such private meetings exacerbate IA among investors due to heterogenous abilities to process information. In turn, the negative relation between IRQ and IU is reminiscent of the nding by [START_REF] Solomon | What are we meeting for? The consequences of private meetings with investors[END_REF] that investors who have access to management exhibit better timing ability when they meet with the rm; however, the increase in timing ability is restricted to the group of hedge funds that are reportedly more sophisticated than pension or mutual funds.

In line with the evidence in this subsection, [START_REF] Bissessur | Analyst information precision and small earnings surprises[END_REF] nd that private access to management enhances the precision of analysts' estimates and thereby reduces expected forecast errors. Because investors systematically overweight analyst forecasts when they face poor information environments [START_REF] So | A new approach to predicting analyst forecast errors: Do investors overweight analyst forecasts?[END_REF], IRQ might mitigate mispricing through its adverse impact on IU. However, our ndings are inconsistent with the evidence in [START_REF] Farragher | Do investor relations make a dierence?[END_REF] who report a signicant inverse relation between IR quality and the dispersion of analyst forecasts while they fail to document a signicant impact of IR quality on the accuracy of analyst forecasts.

[Table 7 about here]

Second-stage regression

We now consider the estimating Equation ( 13) for MSV, where all the regressors suspected of endogeneity are replaced by their tted values obtained from the previous rst-step regressions. Table 8 presents the estimation results. Counter-intuitively, the estimated eect of IRQ is positive, and more pronounced than in the preliminary regression of MSV onto lagged information (see previous sub-subsection). Equally surprising is the eect of the bid-ask spread, which is negative, signicant and more pronounced than previously. The coecient of Amihud's illiquidity ratio is positive but not signicant. The other regressors with signicant coecients are the lagged MSV (which indicates a positive persistence), the realized idiosyncratic volatility (positive eect) and cross-listing on either the NYSE or the LSE (negative eect). Overall, the results of the 2SLS estimation are qualitatively similar to those obtained by regressing MSV onto lagged information. However, the coefcients stemming from the 2SLS have the interpretation of contemporaneous eects that are corrected for endogeneity.

The fact that the 2SLS yields similar results as the regression of MSV onto lagged information is not completely absurd, since our instruments consist of lagged regressors. If we decide to trust these instruments, then we shall interpret the regression of MSV onto lagged information as predictive and the 2SLS regression as causal. Both models predict that the IRQ (lagged in the predictive model and contemporaneous in the 2SLS) is positively associated with mispricing while the bid-ask spread is negatively associated with mispricing. The signs of these coecients are rationalized by noting that the pricing errors of year t can be aected by the actions taken by rms between year t -1 and year t. Such actions are not reected in the lagged regressors used as instruments. This explains why the contemporaneous association of IRQ and MSV is negative as expected (see Table 6) while the eect of IRQ measured by 2SLS is counter-intuitively positive. In order to reconcile the two approaches, we need to construct instruments that are forward-looking, that is, instruments that can be measured at time t -1 while incorporating rms' anticipations about time t. This is what we attempt to do in the next sub-subsection.

[Table 8 about here]

The Heckit Approach

Unlike in the 2SLS, where linear relationships are assumed between MSV and the instruments, we now consider constructing instruments that capture rms' anticipation on the level of their future pricing errors. For simplicity, we ask whether rms can predict the probability that their stocks will be underpriced at the next period. To answer this question, we t a Probit model to the binary variable U N DER i,t which takes 1 when rm i is underpriced at year t, and 0 otherwise. The latent variable underlying this Probit model is given by Equation ( 14), which contains lagged regressors on the RHS. Panel A of Table 9 shows the estimation results.

The results suggest that only four variables have an eect on the probability of underpricing at the next period. The number of analysts following a rm has a positive eect on undervaluation, which suggests that analyst coverage does not always contribute to reducing IA and IU as one would expect. This evidence attests to the importance of the accuracy of stock coverage as opposed to just the depth of coverage for determining stock prices [START_REF] Chang | Stock Market Coverage[END_REF]. Indeed, analysts produce public signals about rm earnings of heterogenous precision, and prior research provides evidence consistent with what [START_REF] Chang | Stock Market Coverage[END_REF] label the positive assortative matching in the labor market for analysts. That is, more talented analysts are paid signicantly more than their peers with lower ability, and are assigned to cover larger rms [START_REF] Hong | Analyzing the analysts: Career concerns and biased earnings forecasts[END_REF]. In turn, market capitalization and price-to-book ratio are negatively related to the probability of underpricing at the next period, while a high leverage at the current period predicts a higher probability of underpricing at the next period.

[Table 9 about here]

Next, we generate the inverse Mills ratios IM R 0,i,t and IM R 1,i,t and estimate the models described by Equations ( 15) and ( 16). Equation ( 15) is the regression of MSV onto contemporaneous information and IM R 1,i,t using the sub-sample U N DER i,t = 1 (underpriced sub-sample). Equation ( 16) is the regression of MSV onto contemporaneous information and IM R 0,i,t using the sub-sample U N DER i,t = 0 (overpriced sub-sample). Panel B of Table 9 presents the estimation results. First, we note that the coecient of IRQ is not signicant in either regression. This suggests that IRQ has no direct eect on MSV once we control for the probability of underpricing at the next period.

Second, the truncation bias captured by the coecients of the inverse Mills ratios is signicant only in the undervalued sub-sample. Indeed, the coecients of IM R 0,i,t and IM R 1,i,t are both negative, but only that of IM R 1,i,t is signicant. This indicates that the error term on the latent variable underlying the Probit model is negatively correlated with the error term of Equation ( 15). Concretely, this means that in the set of underpriced rms, a higher ex-ante probability of underpricing at the next period is associated with a lower level of ex-post mispricing. Undervalued rms that perceive ex-ante that they have a high probability of being undervalued again at the next period take specic actions to reduce IA/IU and improve their IRQ so that their ex-post mispricing is mitigated. In the subset of overvalued rms, there is no visible correlation between the ex-ante probability of underpricing and the ex-post mispricing. Note that the non-linear mechanism that links past information to future mispricing through the anticipations of the probability of undervaluation cannot be detected within a linear instrumental variable framework. Overall, rms are averse to underpricing but not to overpricing.

Some asymmetries can also be noted in the eects of the regressors. Indeed, the bid-ask spread is negatively associated with mispricing in the set of undervalued rms but has no eect in the set of overvalued rms. The dispersion of analysts' forecasts is positively associated with mispricing in the set of undervalued rms but has no eect in the set of overvalued rm. The idiosyncratic realized volatility, the price-to-book ratio, and the market capitalization are positively associated with mispricing in the set of overvalued rms but have no eect in the set of undervalued rms. Analysts forecast errors are positively associated with mispricing in both sub-samples. Recall that column 5 of Table 7 suggests that IRQ is negatively related to ERR, but not to DISP. Combining this evidence with the results in Panel B of Table 9, we argue that IRQ might aect mispricing through its adverse impact on analyst forecast errors. Finally, mispricing is signicantly persistent on both sub-samples.

Conclusion

Despite the diusion of IR departments among public rms, we know remarkably little about the contribution of IR to shareholder value [START_REF] Laskin | How investor relations contributes to the corporate bottom line[END_REF][START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF].

That the IR function plays an information role in determining security prices is better known. What is less clear relates to the channels through which IR activity is related to mispricing. This question is important because shareholder value and resource allocation could be substantially enhanced due to reduced pricing errors [START_REF] Lu | Price Shocks, News Disclosures, and Asymmetric Drifts[END_REF].

Our paper combines the [START_REF] Mishkin | A Rational Expectations Approach to Macroeconomics[END_REF] Allowing for asymmetric persistence and dierential pricing of accruals and cash ows surprises, our Mishkin tests suggest that there is robust evidence of accruals' mispricing for the sub-sample of rms with lower-rated IR. However, accruals' mispricing tends to be concentrated among rms with high realized idiosyncratic risk, high trading volume, low quoted bid-ask spreads, and low realized market beta. By contrast, evidence of cash ows mispricing is weak. Surprisingly enough, the dierential persistence of accruals and cash ows is widest in gain states, not in loss states, thereby refuting the EFH. High-quality IR thus foster the market's ability to eciently impound accounting information into stock prices.

Further, portfolio analyses reveal that rms with higher-rated IR on average earn higher risk-adjusted stock returns. We show that the positive relationship between IRQ with subsequent stock returns cannot be fully explained by known risk and mispricing factors.

Because accruals' mispricing tends to be more pronounced in rms with greater valuation uncertainty, our evidence of a positive IRQ-return relation is, therefore, likely driven by psychological biases or constraints [START_REF] Hirshleifer | Innovative eciency and stock returns[END_REF].

We nd that IR potentially plays two countervailing roles in its relation with mispricing.

IRQ may widen IA among investors (potentially stemming from private meetings with a select group of investors), while it is inversely related to future analyst forecast errors.

This result is important on three grounds. First, although analyst forecast errors may dierentially aect the welfare of retail and institutional investors, a matter of greater concern is the impact on the ecient allocation of capital in the economy. [START_REF] So | A new approach to predicting analyst forecast errors: Do investors overweight analyst forecasts?[END_REF] shows that investors systematically overweight analyst forecasts when facing IA/IU. It results that over-reliance on analyst forecasts (of poor precision) could result in substantial valuation errors. Thus, [START_REF] So | A new approach to predicting analyst forecast errors: Do investors overweight analyst forecasts?[END_REF] recommends that regulators pursue measures to improve analyst forecasts. We contribute to this debate by documenting that high-quality IR can reduce mispricing through their adverse impact on analyst forecast errors.

Second, the empirical literature on stock coverage has largely focused on the number of analysts following a rm. However, the evidence in this paper highlights the importance of the accuracy of analyst coverage as opposed to just the depth of coverage for determining stock prices [START_REF] Chang | Stock Market Coverage[END_REF]. [START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF] nd that greater IR activity is associated with higher Tobin's q valuations. The latter authors add that this eect runs substantially via increased analyst following and forecast accuracy, and reduced analyst forecast dispersion. Indeed, analysts and managers of rms with more active IR programs consume a signicant amount of time interacting privately and oer the investing community a unique window into a rm's operations [START_REF] Soltes | Private Interaction Between Firm Management and Sell-Side Analysts[END_REF][START_REF] Solomon | What are we meeting for? The consequences of private meetings with investors[END_REF].

Third, our results indicate that rms do not engage in IR activity to manipulate media coverage [START_REF] Solomon | Selective publicity and stock prices[END_REF], or choreograph earnings conference calls [START_REF] Cohen | Playing favorites: How rms prevent the revelation of bad news[END_REF]. In contrast, our results suggest that high-quality IR programs may be used as value-relevant signals by investors. Therefore, inconsistent with the reasoning in [START_REF] Karolyi | The economic consequences of investor relations: A global perspective[END_REF], our results suggest that externally-observable proxies such as IR Magazine ratings are not the root cause of some studies relating IR to negative outcomes.

Finally, we nd that rms exhibit a preference for overvaluation and abhor undervaluation.

Indeed, in the set of underpriced rms, a higher ex-ante probability of underpricing at the next period is associated with a lower level of ex-post mispricing. Undervalued rms that perceive ex-ante that they have a high probability of being undervalued again at the next period take specic actions to reduce IA/IU and improve their IRQ such that their ex-post mispricing is mitigated. In contrast, there is no visible correlation between the ex-ante probability of underpricing and the ex-post mispricing in the subset of overvalued rms. Such asymmetric behavior toward either type of mispricing unveils potential implicit managerial incentives that is, managers may exploit IR as a launching pad for oensive operations directed at securing their own interests via short-lived overvaluations. A.1.2 Realized Measures Let r i,n,t be the log-return on the stock of rm i on week n of year t, and r M,n,t the corresponding market log-return. The realized beta, RBET A, of rm i is:

βi,t = N n=1 r M,n,t r i,n,t N n=1 r 2 M,n,t
,

where N is the number of opening weeks during year t. The numerator of β is the realized covariance and the denominator is the realized market volatility.

The weekly residuals of the regression are r i,n,t -βi,t r M,n,t . The realized idiosyncratic volatility, RIV OL, of rm i's stock is:

σi,t = N n=1 (r i,n,t -βi,t r M,n,t ) 2 .
Finally, the realized idiosyncratic skewness, RSKEW , is: Note. Table 4 reports the results obtained from estimating the three-equation system ( 6)-( 8), whereby Equation ( 8) is re-written as in Equation ( 9). Unlike Table 3, this table controls for SALGR, TRVOL, MCAP , and P2B , thereby allowing us not only to test rational pricing but also to explore sources of potential ineciency [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF]. The dependent variable in the forecasting equations are CF and ACC , respectively. In this table, RET is the dependent variable in the pricing equation. Standard errors are adjusted for clusters in year as proposed in [START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF]. δ1 is the response coecient relative to accruals while δ2 denotes the response coecient of cash ows. N is the number of observations used in a given estimation Column 1 shows the full sample results that are contrasted with those reported in column 2 of Table 3. Columns 3 and 4 contain the corresponding results for the sub-samples of rms with higher-rated and lower-rated IR, respectively. Dt is an indicator that captures an economic loss state. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively. [START_REF] Petersen | Estimating standard errors in nance panel data sets: Comparing approaches[END_REF]. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively. [START_REF] Petersen | Estimating standard errors in nance panel data sets: Comparing approaches[END_REF]. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively. [START_REF] Petersen | Estimating standard errors in nance panel data sets: Comparing approaches[END_REF]. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively. 9 ts a Probit model to the binary variable U N DERi,t which takes 1 when rm i is underpriced at year t, and 0 otherwise; the latent variable governing this Probit regression is given in Equation ( 14). In turn, Column (1) of Panel B is the regression of MSV onto contemporaneous information and IM R1,i,t using the subsample U N DERi,t = 1 (underpriced subsample). The second equation is the regression of MSV onto contemporaneous information and IM R0,i,t using the subsample U N DERi,t = 0 (overpriced subsample). The variables are as dened in Appendix 1. Standard errors are clustered by rm and year [START_REF] Petersen | Estimating standard errors in nance panel data sets: Comparing approaches[END_REF]. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively.

Ŝi,t = N 1/2 σ3 i,t N n=1 r i,n,t -βi,t

  of stocks included in the European index EURO STOXX 50, and in the German indices DAX (large-caps), MDAX (mid-caps in classical sectors), TecDAX (technology mid-and small-caps) and SDAX (small-caps in classical sectors).

4

  We require observations to have non-negative values on the total assets, sales, leverage, and book value of equity. The nal sample includes 252 non-nancial European rms, and spans the period from 2002 to 2011. Our measure of IR quality is derived from the proprietary ratings of rm IR programs by analysts and institutional investors compiled by the Society of Investment Professionals in Germany (DVFA) on behalf of the magazine Capital. Capital market and accounting data are obtained from Datastream, while the data on analyst forecasts are collected from I/B/E/S. 4 See Online Appendix Part A for more details about the sample.

  Mispricing. Our measure of mispricing, MSV, is widely used in nance and is derived from the RKRV(2005) model that decomposes the market-to-book ratio (MBR) into mispricing eects and growth options. Indeed, the non-fundamental component of the MBR, MSV, is assumed to be positively related to investor sentiment in the stock market and involves a rm-specic component and a sector-wide component. For brevity, we have relegated the extraction of MSV to Online Appendix Part B. 5 IR quality (IRQ). IRQ consists of four components and relies on the `DVFA principles for eective capital market communication'. 6 The target group orientation component measures how well IR departments provide information to the investment community on a proactive basis. This component likely measures private disclosure activities and access to management. The transparency component probably tracks management credibility and the quality of corporate governance. The track record component pertains to the accuracy and precision of a rm's communications over time. Finally, the sustainability reporting component measures the extent to which rms disclose non-nancial information; this component helps gauge a rm's commitment to social and environmental issues.

  the results from our three-equation MT conditional on loss and gain states. It contains the coecient estimates of four specications. Columns 12 show the results relative to the specication that uses raw stock returns as the dependent variable in Equation (8) while columns 34 pertain to specications in which size-adjusted dierential returns are the dependent variable. Standard errors in columns 2 and 4 are clustered by year. The sample size in each panel remains the same for each specication.

  two-stage rational expectations framework with the RKRV (2005) pricing deviation-based approach to test whether and what type of mispricing IRQ aects, and examine specic mechanisms through which IRQ is related to mispricing. To capture the quality of IR investments and actions, we rely on the proprietary ratings of rm IR programs by analysts and institutional investors compiled by the Society of Investment Professionals in Germany (DVFA) on behalf of the magazine Capital. Our sample includes 252 non-nancial European rms, and spans the period from 2002 to 2011.

  IR quality measure (This measure aggregates the components target group orientation, transparency, track record and sustainability reporting using the average ex post weights allocated by survey respondents.IRQ is used in its industry-year fractional rank version which is dened as:(rank -1)/(number of rms in the industry -1), with values ranging from 0 (the lowest-rated IR) to 1 (the highest-rated IR).)[DVFA] MSV Aggregate non-fundamental component of the market-to-book ratio obtained from the Rhodes-Kropf et al. (RKRV, 2005) decomposition technique. This item is used to proxy for stock mispricing in this study. [Datastream] MSVS Measure for sector-wide mispricing derived from the RKRV (2005) model. See Online Appendix Part B. [Datastream] MSVF Measure for rm-specic mispricing derived from the RKRV (2005) model. See Online Appendix Part B. [Datastream] BASP Bid-ask spread calculated as the ratio of the dierence between the Ask and the Bid quote over the midpoint. [Datastream] 18 [...] is the data source. AMIH Annual median of the Amihud (2002) illiquidity ratio calculated as the ratio of daily absolute returns over euro trading volume. See Online Appendix 2. [Datastream] TRVOL Median of weekly trading volume. [Datastream] ERR Analyst forecast errors, calculated as the natural log of one plus the dierence between analysts' earnings per share (EPS) forecasts and actual EPS, scaled by the absolute value of median. [I/B/E/S] NOEST Number of analysts covering a rm over the year. [I/B/E/S] INST Percentage of outstanding shares owned by institutional investors such as investment banks and pension funds. [Datastream] DISP Dispersion in analyst earnings forecasts calculated as the standard deviation of analyst forecasts, scaled by the prior year-end stock price. [I/B/E/S] EAR Income before extraordinary items and dividends, deated by one-year lagged total assets. This item is used as our proxy for net income. [Datastream] CF Cash ows from operations, deated by one-year lagged total assets. [Datastream] ACC Accruals calculated as EAR minus CF, deated by one-year lagged total assets. [Datastream] RET Log buy and hold return on a given stock over a 12-month period beginning three months after the scal year-end (see Drake et al., 2009). [Datastream] MCAP Market capitalization (as of end of March of year t) used as a proxy for rm size. the ratio of total debt over total assets. [Datastream] UPCM Use of public capital markets in subsequent periods; it as construed as an indicator variable that takes a value of 1 if the rm issues public debt or equity in the next two scal years, and 0 otherwise. [Datastream] CLIST Cross-listing on either the New York Stock Exchange (NYSE) or on the London Stock Exchange (LSE). [Datastream]

  Note. Table1reports the summary statistics of the sample characteristics. The sample covers 252 non-nancial European rms and spans the period 20022011. All variables are dened in Appendix 1 above.Variables of primary interest are the measure for IR quality (IRQ) and the aggregate measure of mispricing (MSV ). MCAP is in millions of ¿. Except for the last three columns, the summary statistics in this table refer to the full sample of 252 rms. In contrast, the columns headed H_IRQ and L_IRQ relate to sub-samples of rms with higher-rated IR programs and those with lower-rated IR programs, respectively. The last column compares the means of these two sub-samples. MSVF and MSVS, in turn, stand for the rm-specic component and the sector-wide component of mispricing, respectively (Please, refer to Online Appendix Part B, for more details on these two variables.) ***, **, * denote signicance at the 1%, 5%, and 5% level, respectively.

			r M,n,t	3	.
			Table 1: Summary statistics
		mean	SD		Q1	median	Q3	H_IRQ	L_IRQ	t-test
	IRQ	0.4994	0.3079	0.2300	0.5000	0.7670	0.7746	0.2414	-66.58***
	MSV	0.0703	0.7105	-0.3496	0.0793	0.4908	0.1300	0.0113	-2.94***
	MSVF	-0.0046	0.8665	-0.3583	0.0367	0.4077	0.0837	-0.0913	-3.57***
	MSVS	0.0480	0.6333	-0.2297	0.0781	0.3019	0.0409	0.0550	0.39
	SALGR	0.0759	0.2516	-0.0160	0.0609	0.1436	0.0855	0.0666	-1.42
	MCAP	12300	22100		440	1700	14000	13000	11600	-1.17
	P2B	2.4531	1.9248	1.2781	1.9078	2.8865	2.6369	2.2753	-3.50***
	BASP	0.0088	0.0082	0.0025	0.007	0.0125	0.0077	0.0098	5.10***
	AMIH	0.0643	0.2183	0.0022	0.0185	0.0577	0.0460	0.0814	3.20***
	TRVOL	11233	46698		16	59	309	7088	15164	3.34***
	ERR	-0.0138	0.6666	-0.0566	0.0751	0.2516	-0.0361	0.0091	1.23
	DISP	0.0566	0.1326	0.0119	0.0240	0.0482	0.0416	0.0710	4.28***
	NOEST	17.5565	10.9603			9	16	26	19.8069	15.4200	-7.71***
	INST	0.3435	0.2611		0.1	0.31	0.55	0.3301	0.3560	1.89*
	UPCM	0.5031	0.5002			0	1	1	0.4972	0.5086	0.44
	CLIST	0.1653	0.3716			0	0	0	0.1597	0.1706	0.57
	RBETA	0.1438	0.3657	-0.0700	0.1242	0.3229	0.1419	0.1455	0.19
	RIVOL	0.3838	0.2144	0.2493	0.3279	0.4564	0.3562	0.4097	4.85***
	RSKEW	-0.0039	0.1246	-0.0739	0.0003	0.0711	-0.0058	-0.0021	0.58
	LEV	0.2331	0.1634	0.1081	0.2177	0.3329	0.2109	0.2543	5.06***
	EAR	0.0476	0.1043	0.0171	0.0432	0.0833	0.0652	0.0308	-6.33***
	CF	0.0998	0.0987	0.0559	0.0909	0.1345	0.1111	0.0889	-4.24***
	ACC	-0.0519	0.1038	-0.0834	-0.0489	-0.0155	-0.0455	-0.0580	-2.27**
	RET	0.0330	0.5373	-0.2140	0.1022	0.3400	0.1026	-0.0354	-4.76***
	SIZERET 0.0075 0.3969 -0.1784 0.0010 0.1727 0.0756 -0.0595 -6.35***

Table 2 :

 2 Primary results of the Mishkin tests Table2reports the results obtained from estimating the system (4)-(5). The dependent variable in the forecasting equation is EAR as dened above, while the pricing equation uses RET as the dependent variable. In all specications shown in this table, we follow[START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF] and adjust standard errors for clusters in year. Coecients without a star as superscript stem from the forecasting equation while estimates with a star derive from the pricing equation. δ is the earnings response coecient and N is the number of observations used in a given estimation. Column 1 shows the results of the MT using the full the full sample of 252 non-nancial rms; columns 2 and 3 show the MT for the sub-samples of rms with higher-rated IR and rms with lower-rated IR programs, respectively. Columns 4-5, exhibit MT results for rms with high idiosyncratic volatility and rms with low idiosyncratic volatility, respectively. Finally, columns 6-7 contain MT results pertaining to rms with high trading volume and those with low trading volume, respectively.

		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	γ 0 -0.1590*** -0.1837*** -0.1184** -0.1596*** -0.1117*** -0.2594*** -0.1343**
		(0.0000)	(0.0000)	(0.0349)	(0.0010)	(0.0002)	(0.0000)	(0.0197)
	γ 1 0.3411*** 0.3962*** 0.2762*** 0.3534*** 0.3145*** 0.3251*** 0.3307***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	γ 2 0.5153*** 0.5234*** 0.4893*** 0.5181*** 0.4916*** 0.5265*** 0.4524***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	γ 3 0.1755*** 0.1779*** 0.1650*** 0.1994*** 0.1625*** 0.1401*** 0.2289***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	γ 4 -0.0443**	0.0166	-0.0592*	-0.0638*	-0.0272	0.0919	-0.0232
		(0.0237)	(0.5199)	(0.0502)	(0.0588)	(0.4755)	(0.1493)	(0.7637)
	γ 5 0.0466***	-0.0175	0.0710**	0.0048	0.0355	0.0835***	-0.0234
		(0.0065)	(0.5762)	(0.0387)	(0.8910)	(0.4678)	(0.0081)	(0.4551)
	γ 6 0.2744*** 0.3074*** 0.2425*** 0.2543*** 0.2719*** 0.2450*** 0.3207***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	δ	0.3242***	0.2489***	0.3178***	0.3666***	0.2927***	0.2964***	0.3844***
		(0.0000)	(0.0052)	(0.0000)	(0.0000)	(0.0012)	(0.0000)	(0.0000)
	γ * 0	-1.9307***	-2.6909***	-1.9290***	-1.7916***	-2.0276***	-2.1922***	-1.5183***
		(0.0000)	(0.0058)	(0.0001)	(0.0000)	(0.0027)	(0.0030)	(0.0000)
	γ * 1	0.6143***	0.3247*	0.9392***	0.6384***	0.5443***	0.7617***	0.4350***
		(0.0000)	(0.0694)	(0.0000)	(0.0000)	(0.0020)	(0.0001)	(0.0022)
	γ * 2	0.5484***	0.5188**	0.6669***	0.5127***	0.5577***	0.7499***	0.2910
		(0.0000)	(0.0213)	(0.0002)	(0.0054)	(0.0020)	(0.0000)	(0.1950)
	γ * 3	-0.2345	-0.2460	-0.2605	-0.3055***	-0.1207	-0.5112***	0.0957
		(0.1188)	(0.3425)	(0.2538)	(0.0068)	(0.5635)	(0.0058)	(0.5044)
	γ * 4	0.4032***	0.1709	0.3996*	0.3868*	0.4682***	0.7673**	-0.1684
		(0.0099)	(0.4698)	(0.0749)	(0.0846)	(0.0061)	(0.0257)	(0.3527)
	γ * 5	-0.1048	0.3575	-0.2217	-0.0084	-0.2713	-0.3236	0.0035
		(0.6032)	(0.2251)	(0.4092)	(0.9635)	(0.2881)	(0.2482)	(0.9803)
	γ * 6	0.4186**	0.6099**	0.3483*	0.4537**	0.4170***	0.3658	0.4754***
		(0.0106)	(0.0314)	(0.0631)	(0.0257)	(0.0006)	(0.1770)	(0.0024)
	N	1096	561	535	467	629	580	516
	Note.

p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively.

Table 3 :

 3 Mishkin tests under asymmetry and dierential pricing of earnings' components

		(1)	(2)	(3)	(4)
		Forecasting cash ows [Equation (7)]
	D t	-0.3102***	-0.3102***	-0.3102***	-0.3102***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	CF	0.2939***	0.2939***	0.2939***	0.2939***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	ACC	0.0815***	0.0815***	0.0815***	0.0815***
		(0.0002)	(0.0021)	(0.0002)	(0.0021)
	CF.D t	-0.1678***	-0.1678***	-0.1678***	-0.1678***
		(0.0000)	(0.0012)	(0.0000)	(0.0012)
	ACC.D t -0.0635**	-0.0635*	-0.0635**	-0.0635*
		(0.0485)	(0.0774)	(0.0485)	(0.0774)
		Forecasting accruals [Equation (6)]
	D t	0.2221***	0.2221***	0.2221***	0.2221***
		(0.0000)	(0.0040)	(0.0000)	(0.0040)
	CF	0.2965***	0.2965***	0.2965***	0.2965***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	ACC	0.3734***	0.3734***	0.3734***	0.3734***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	CF.D t	0.0883	0.0883	0.0883	0.0883
		(0.1592)	(0.2304)	(0.1592)	(0.2304)
	ACC.D t 0.0299	0.0299	0.0299	0.0299
		(0.5933)	(0.7367)	(0.5933)	(0.7367)
		Pricing Equation [Equation (9)]
	δ 1	0.1765***	0.1765***	0.2047***	0.2047***
		(0.0000)	(0.0079)	(0.0000)	(0.0005)
	δ 2	0.5100***	0.5100***	0.5424***	0.5424***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	D t	0.0318	0.0318	-0.0005	-0.0005
		(0.7423)	(0.8364)	(0.9953)	(0.9968)
	CF	0.4507***	0.4507***	0.4043***	0.4043***
		(0.0000)	(0.0001)	(0.0000)	(0.0002)
	ACC	0.3098***	0.3098***	0.3231***	0.3231***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	CF.D t	-0.2244**	-0.2244	-0.1174	-0.1174
		(0.0397)	(0.1588)	(0.2410)	(0.4035)
	ACC.D t -0.0667	-0.0667	-0.1072	-0.1072
		(0.4870)	(0.5467)	(0.2307)	(0.2789)

Note.

  Table3reports the results obtained from estimating the parsimonious three-equation system (6)-(8), whereby Equation (8) is re-written as in Equation (9). The dependent variable in the forecasting equations are CF and ACC , respectively. In this table, columns 1 and 2 use in the pricing equation RET as the dependent variable while the dependent variable in columns 3 and 4 is a size-decile adjusted return, SIZERET . In turn, only in columns 2 and 4 do we adjust standard errors for cluster in year as proposed in[START_REF] Konstantinidi | Asymmetric Persistence and the Market Pricing of Accruals and Cash Flows: Asymmetric Persistence and the Accrual Anomaly[END_REF]. δ1 is the response coecient relative to accruals while δ2 denotes the response coecient of cash ows.

N is the number of observations used in the estimation and equals 1,105 for each of the four estimations shown in this table. The estimations therefore pertain to the full sample of 252 non-nancial rms. Dt is an indicator that captures an economic loss state. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively.

Table 4 :

 4 Role of IR in the correction process of mispricing across economic gain/loss states

		(1)	(2)	(3)	(4)
		Forecasting cash ows
	D t	-0.3150***	-0.3102***	-0.2835***	-0.3439***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)
	CF	0.2413***	0.2939***	0.2709***	0.2001***
		(0.0000)	(0.0000)	(0.0000)	(0.0015)
	ACC	0.0436**	0.0815***	0.0671***	0.0124
		(0.0282)	(0.0021)	(0.0071)	(0.7402)
	CF.D t	-0.1572***	-0.1678***	-0.2122***	-0.1043
		(0.0018)	(0.0012)	(0.0001)	(0.2470)
	ACC.D t	-0.0494	-0.0635*	-0.0687***	-0.0292
		(0.1187)	(0.0774)	(0.0048)	(0.5365)
			Forecasting accruals
	D t	0.2269**	0.2221***	0.2883***	0.1852
		(0.0109)	(0.0040)	(0.0007)	(0.1389)
	CF	0.2012***	0.2965***	0.2104**	0.1934*
		(0.0026)	(0.0000)	(0.0114)	(0.0524)
	ACC	0.3291***	0.3734***	0.3714***	0.2797***
		(0.0000)	(0.0000)	(0.0000)	(0.0078)
	CF.D t	0.1066	0.0883	0.0892	0.0900
		(0.2268)	(0.2304)	(0.3394)	(0.4093)
	ACC.D t	0.0316	0.0299	-0.0149	0.0694
		(0.7399)	(0.7367)	(0.8906)	(0.6228)
			Pricing Equation
	δ 1	0.2000***	0.1765***	0.1154**	0.2169***
		(0.0003)	(0.0079)	(0.0430)	(0.0013)
	δ 2	0.5259***	0.5100***	0.3616***	0.5512***
		(0.0000)	(0.0000)	(0.0091)	(0.0000)
	D t	0.0219	0.0318	0.0107	0.0683
		(0.8804)	(0.8364)	(0.9341)	(0.7229)
	CF	0.3893***	0.4507***	0.3897***	0.4754***
		(0.0000)	(0.0001)	(0.0003)	(0.0006)
	ACC	0.2669***	0.3098***	0.1395	0.4061***
		(0.0002)	(0.0000)	(0.2499)	(0.0003)
	CF.D t	-0.1969	-0.2244	-0.0096	-0.3446*
		(0.1801)	(0.1588)	(0.9641)	(0.0660)
	ACC.D t	-0.0395	-0.0667	-0.0227	-0.0714
		(0.7257)	(0.5467)	(0.8243)	(0.6640)
	N	1096	1105	561	535

Table 5 :

 5 Portfolio analysis on the role of IR . Panel A reports the summary statistics relative to four two-sorted portfolios based on annualized excess returns over the period from 1 July 2002 to 30 June 2012. [1] low accruals/low IR, [2] high accruals/low IR, [3] low accruals/high IR, and [4] high accruals/high IR. HH is a portfolio that is long in high accruals/high IR rms [4] and short in high accruals/low IR rms [2]); HL is a portfolio that is long in low accruals/high IR rms [3] and short in low accruals/low IR rms[1]. In contrast, Panel B reports the results from estimating the alphas using the augmented[START_REF] Carhart | On persistence in mutual fund performance[END_REF] model. The pricing factors MKTRF, SMB, HML, and WML are taken from Wharton Research Data Services (WRDS) while we download the factor UMO from Jiang's website (https://sites.google.com/site/danlingjiang/datalibrary). All estimations are in euro terms. p -values are in parentheses. ***, **, and * denote signicant at the 1%, 5%, and 10% level, respectively.

	Panel A: Summary statistics of the dierent portfolios
	Portfolio	[1]	[2]	[3]	[4]		HH	HL
	mean	0.0112	0.0629	0.0831	0.0819	0.0190	0.0719
	median	0.1094	0.0415	0.1068	0.1304	0.0617	0.0316
	SD	0.3379	0.3227	0.2635	0.2972	0.1676	0.1225
	Panel B: Estimating the alphas using monthly returns
		[1]		[2]		[3]		[4]	HH	HL
	MKTRF	1.4146***	1.2629***		1.1503***	1.1085***	-0.1545***	-0.2644***
		(0.0000)	(0.0000)		(0.0000)		(0.0000)	(0.0000)	(0.0000)
	SMB	-1.5068***	-0.6754***	-1.0870***	-1.1655***	-0.4902***	0.4198***
		(0.0000)	(0.0000)		(0.0000)		(0.0000)	(0.0000)	(0.0003)
	HML	-0.5192**	-0.7720***	0.1910		-0.1997	0.5723***	0.7101***
		(0.041)	(0.0000)		(0.414)		(0.380)	(0.0000)	(0.0000)
	WML	-0.2104**	-0.5721***	-0.0623		0.3478***	0.9199***	0.1481***
		(0.020)	(0.0000)		(0.454)		(0.0000)	(0.0000)	(0.0065)
	UMO	0.3440***	0.6571***		-0.0384		-0.7766***	-1.4337***	-0.3825***
		(0.006)	(0.0000)		(0.737)		(0.0000)	(0.0000)	(0.0000)
	Intercept	-0.0020*	0.0012		0.0052***	0.0077***	0.0066***	0.0071***
		(0.053)	(0.1216)		(0.0000)		(0.0000)	(0.0000)	(0.0000)
	N	120		120		120		120	120	120
	Adj. R-sq	87%		91%		81%		86%	89%	64%

Note

Table 6 :

 6 Preliminary results of the causal link between IRQ, IA/IU, and MSV . The sample in Table6includes 252 European non-nancial rms and spans the period from 2002 to 2011. The dependent variable is the absoluted value of our mispricing measure, MSV. Column 1 contains the regression of MSV onto lagged information. Colum 2 shows the regression of MSV onto contemporaneous information, and column 3 regresses MSV onto an information set containing contemporaneous and lagged regressors. While not shown here for expository purposes, the full set of controls inlcude RBETA, RIVOL, RSKEW, MCAP, P2B, SALGR, UPCM, CLIST, and LEV. Standard errors are clustered by rm and year

		(1)	(2)	(3)
	IRQ t-1	0.0560*		0.0851**
		(0.0579)		(0.0299)
	AM IH t-1	0.0619		-0.1119
		(0.5259)		(0.3664)
	BASP t-1	-0.1090*		-0.1398***
		(0.0655)		(0.0003)
	T RV OL t-1	-0.0484		-0.0194
		(0.5168)		(0.8347)
	|ERR t-1 |	-0.0074		-0.0517
		(0.8789)		(0.3184)
	DISP t-1	-0.0010		-0.0059
		(0.9763)		(0.8584)
	N OEST t-1	-0.0756		0.0224
		(0.3077)		(0.7864)
	|M SV t-1 |	0.3969***	0.3568***	0.4022***
		(0.0000)	(0.0000)	(0.0000)
	RIV OL t-1	0.0995**
		(0.0416)
	CLIST t-1	-0.0528**
		(0.0421)
	IRQ		-0.0731***	-0.1034***
			(0.0001)	(0.0000)
	AM IH		0.2026***	0.2157**
			(0.0079)	(0.0132)
	BASP		-0.0566	0.1297
			(0.3691)	(0.2535)
	T RV OL		0.0093	-0.0121
			(0.8230)	(0.8633)
	|ERR|		0.0781***	0.1197***
			(0.0006)	(0.0000)
	DISP		-0.0049	0.0230
			(0.9083)	(0.5701)
	N OEST		-0.0910	-0.0325
			(0.2309)	(0.7278)
	RIV OL		0.0907***	0.0844**
			(0.0021)	(0.0185)
	M CAP		0.2106*	0.1186
			(0.0514)	(0.4113)
	CRSLIST		-0.0286	-0.0441***
			(0.1228)	(0.0056)
	LEV		0.0383	0.0435
			(0.2347)	(0.2592)
	N	899	1020	802
	R -sq	0.19	0.20	0.24

Note

Table 7 :

 7 First-stage regressions under the 2SLS approach . The sample in Table7includes 252 European non-nancial rms and spans the period from 2002 to 2011. In this table, we regress seven regressors suspected of endogeneity onto their own rst lags and the rst lags of the other control variables including the proxy for mispricing, MSV. The variables are as dened in Appendix 1. Standard errors are clustered by rm and year

		IRQ	AM IH	BASP	T RV OL	|ERR|	DISP	N OEST
	IRQ t-1	0.4288***	0.0024	0.0387***	-0.0194	-0.0515*	-0.0051	0.0198
		(0.0000)	(0.8495)	(0.0000)	(0.1736)	(0.0637)	(0.7418)	(0.1452)
	AM IH t-1	-0.1891*	0.6291***	0.1706***	-0.0522*	-0.0321	-0.0634	-0.0050
		(0.0755)	(0.0000)	(0.0013)	(0.0736)	(0.7985)	(0.4547)	(0.8713)
	BASP t-1	0.2814***	0.0344	0.4770***	0.0028	0.0260	-0.0286	0.0100
		(0.0009)	(0.4488)	(0.0000)	(0.9044)	(0.7521)	(0.7981)	(0.7104)
	T RV OL t-1	-0.1936**	-0.1599***	-0.0073	0.8937***	0.0925	-0.0207	0.0413
		(0.0369)	(0.0000)	(0.8266)	(0.0000)	(0.3114)	(0.6189)	(0.1729)
	|ERR t-1 |	-0.0279*	0.0128	0.0312***	-0.0014	0.1758***	0.0722***	-0.0342**
		(0.0852)	(0.1847)	(0.0043)	(0.8955)	(0.0000)	(0.0031)	(0.0114)
	DISP t-1	-0.0262	0.0076	0.0156	0.0341**	0.2107***	0.4667***	0.0049
		(0.5381)	(0.4369)	(0.1916)	(0.0208)	(0.0000)	(0.0000)	(0.8122)
	N OEST t-1	0.1449*	-0.0203	-0.0823***	0.0123	-0.0836**	0.1889***	0.7044***
		(0.0581)	(0.1364)	(0.0000)	(0.3722)	(0.0346)	(0.0000)	(0.0000)
	|M SV t-1 |	-0.0381	0.0232**	0.0112	-0.0064	0.0141	0.0092	-0.0249*
		(0.2798)	(0.0148)	(0.3458)	(0.3928)	(0.5882)	(0.6397)	(0.0518)
	RBET A t-1	-0.0429	-0.0049	-0.0067	0.0079	-0.0068	-0.0080	-0.0075
		(0.1392)	(0.6543)	(0.5951)	(0.6695)	(0.8882)	(0.7265)	(0.6637)
	RIV OL t-1	-0.0264	-0.0015	0.0100	0.0026	0.1388***	0.1517***	-0.0075
		(0.5432)	(0.9218)	(0.5710)	(0.8441)	(0.0001)	(0.0000)	(0.6365)
	RSKEW t-1 0.0980***	-0.0071	-0.0215*	-0.0324***	-0.0145	-0.0320	-0.0215
		(0.0001)	(0.5166)	(0.0890)	(0.0047)	(0.7145)	(0.2876)	(0.1909)
	M CAP t-1	0.1972**	-0.1553***	-0.2526***	0.0009	-0.0108	-0.0887	0.1733***
		(0.0131)	(0.0000)	(0.0000)	(0.9556)	(0.9092)	(0.1717)	(0.0000)
	P 2B t-1	-0.0315	-0.0002	-0.0001	-0.0033	-0.0442	-0.1051***	-0.0118
		(0.2918)	(0.9712)	(0.9932)	(0.8247)	(0.3873)	(0.0000)	(0.3464)
	SALGR t-1	0.0612*	-0.0151	0.0056	0.0022	-0.0788**	0.0149	0.0408***
		(0.0783)	(0.1542)	(0.6025)	(0.7652)	(0.0186)	(0.6422)	(0.0009)
	U P CM t-1	-0.0170	-0.0019	-0.0195***	0.0051	0.0350	-0.0069	-0.0035
		(0.3254)	(0.6131)	(0.0020)	(0.2174)	(0.1084)	(0.6706)	(0.7430)
	CLIST t-1	0.0148	-0.0050	-0.0011	0.0131	-0.0205	0.0099	0.0153*
		(0.7825)	(0.5344)	(0.8724)	(0.1114)	(0.5087)	(0.4818)	(0.0882)
	LEV t-1	-0.0353	-0.0135	-0.0113	0.0247***	-0.0190	0.0344	-0.0030
		(0.1817)	(0.2237)	(0.4786)	(0.0018)	(0.4842)	(0.2700)	(0.8171)
	Intercept	0.2053**	0.3333***	0.3155***	0.0530	0.3310**	0.2161***	0.0781
		(0.0121)	(0.0000)	(0.0000)	(0.1025)	(0.0190)	(0.0001)	(0.1148)
	N	861	1023	1023	1023	949	1018	1023
	R -sq	0.33	0.88	0.84	0.91	0.18	0.40	0.77

Note

Table 8 :

 8 Second-step regression of the linear instrumental variable model (2SLS) .Table 8 reports the results from the second-stage of our linear instrumental variable model. The sample includes 252 European non-nancial rms and spans the period from 2002 to 2011. In this table, the seven regressors suspected of endogeneity are replaced by their tted values obtained from Table 7. The variables are as dened in Appendix 1. Standard errors are clustered by rm and year

		(1)
	IRQ	0.1258**
		(0.0363)
	AM IH	0.2166
		(0.3390)
	BASP	-0.2797*
		(0.0928)
	T RV OL	0.0384
		(0.7934)
	|ERR|	-0.0618
		(0.8175)
	DISP	0.1347
		(0.4631)
	N OEST	-0.1708
		(0.1475)
	|M SV t-1 | 0.3931***
		(0.0000)
	RBET A	-0.0251
		(0.2134)
	RIV OL	0.0803*
		(0.0879)
	RSKEW	-0.0086
		(0.7551)
	M CAP	0.0202
		(0.8802)
	P 2B	0.0648
		(0.2969)
	SALGR	-0.0043
		(0.8826)
	U P CM	0.0040
		(0.7801)
	CLIST	-0.0487**
		(0.0179)
	LEV	0.0264
		(0.5030)
	Intercept	0.2174*
		(0.0797)
	N	899
	R -sq	0.19

Note

Table 9 :

 9 Results of the Heckit model . Table 9 reports the results of the piecewise linear Heckman's sample selection model (Heckit). The sample includes 252 European non-nancial rms and spans the period from 2002 to 2011. Panel A of Table

	Panel A: First-stage	Panel B: Second-stage
		U N DER		(1)	(2)
	IRQ t-1	-0.0919	IRQ	-0.0322	-0.0513
		(0.5485)		(0.4305)	(0.2226)
	AM IH t-1	0.1135	AM IH	0.1504	0.1402
		(0.8038)		(0.2245)	(0.3526)
	BASP t-1	-0.1710	BASP	-0.2291***	0.0955
		(0.6373)		(0.0013)	(0.4239)
	T RV OL t-1	-0.0579	T RV OL	-0.0869	0.0159
		(0.8463)		(0.3471)	(0.8639)
	|ERR t-1 |	0.0724	|ERR|	0.0885***	0.1018***
		(0.6413)		(0.0094)	(0.0000)
	DISP t-1	0.2231	DISP	0.0981*	-0.0477
		(0.2320)		(0.0983)	(0.3623)
	N OEST t-1	0.5549**	N OEST	0.1519	-0.1087
		(0.0482)		(0.2669)	(0.2817)
	|M SV t-1 |	0.0425	|M SV |	0.2580*	0.3444***
		(0.7804)		(0.0980)	(0.0000)
	RBET A t-1	0.1536	RBET A	-0.0265	-0.0212
		(0.3036)		(0.6048)	(0.5911)
	RIV OL t-1	0.2486	RIV OL	0.0843	0.0933*
		(0.1824)		(0.3424)	(0.0609)
	RSKEW t-1	0.0226	RSKEW	-0.0218	0.0228
		(0.8836)		(0.7054)	(0.4462)
	M CAP t-1	-0.8914***	M CAP	-0.2021	0.4231***
		(0.0088)		(0.1897)	(0.0002)
	P 2B t-1	-1.3563***	P 2B	-0.0520	0.2934***
		(0.0000)		(0.4732)	(0.0010)
	SALGR t-1	-0.0009	SALGR	0.0330	-0.0231
		(0.9955)		(0.4045)	(0.4471)
	U P CM t-1	0.1186	U P CM	-0.0135	0.0180
		(0.1848)		(0.6690)	(0.2768)
	CLIST t-1	0.0408	CLIST	-0.0177	-0.0542***
		(0.7562)		(0.6070)	(0.0024)
	LEV t-1	0.4400***	LEV	0.0116	0.0327
		(0.0038)		(0.8452)	(0.5324)
			IM R 1	-0.2512***
				(0.0059)
			IM R 0		-0.0403
					(0.6423)
	Intercept	-0.0350	Intercept 0.5525***	-0.2010
		(0.9424)		(0.0000)	(0.1735)
	N	1023	N	333	463
	P seudo -R -sq 0.1020	R -sq	0.30	0.34

Note

[START_REF] Verrecchia | Essays on disclosure[END_REF] points out, this conclusion relies on the assumption that investors' private information is exogenously endowed. It is possible that more frequent disclosures increase the incentives of sophisticated investors to acquire and trade on private information[START_REF] Fu | Financial reporting frequency, information asymmetry, and the cost of equity[END_REF]. Moreover, increasing the frequency of mandatory disclosures may reduce rms' voluntary disclosures[START_REF] Gigler | Conservatism, optimal disclosure policy, and the timeliness of nancial reports[END_REF], and encourage or discourage the production of information by information intermediaries.

To obtain reliable estimates, we use a much larger sample of 30,446 observations for 2,312 European rms (except for nancials and utilities) collected from Datastream from 1991 to 2011.

URL: www.dvfa.de/verband/publikationen/eektive-nanzkommunikation/(accessed

July 2015). On behalf of the Magazine Capital, the DVFA administers annual web-based questionnaires to over 400 institutional investors and analysts, and commissions an independent researcher to compute normalized overall realizations of IRQ, ranging from 0 to 500. The list is published in Capital magazine each year and thus highly visible to investors. The publication date was typically in mid-June. These realizations form the basis of IRQ.

This estimate is similar to the subsequent decrease of institutional ownership by 4% reported by Kalay (2015) in a U.S. context. He uses IR scores published by IR Magazine from 2002 to 2007.

study, as well as participants at the 2016 meeting of the Summer Institute for Economic Research (SIER) in Abomey-Calavi. We would like to thank Professor Alexander Bassen and the Deutsche Vereinigung für Finanzanalyse und Asset Management e.V.