Manager‟s investment Equilibrium analysis

995 Lemma 2. In the perfect information case in which means that v P   , the manager‘s optimal investment is given by 2   r v FB  . Proof. See Appendix A. This obviously suggests that the manager‘s investment increases with the mean of the investment return and decreases with both the variance of the investment return and the magnitude of the manager‘s risk aversion.

3.2.2 Imperfect information case second-best scenario

Now, we consider the imperfect information case in which the stock price is set by the market maker who only observes the public earnings information e~ and the total order x u Y ~ ~ ~   as a two-signal version of the model in Kyle 1985. In other words, the stock price is informationally imperfect in the sense that the market maker sets the stock price without kn owing the informed trader‘s private information s~ and the value of the firm v~  , as well as without separating the informed trader‘s order flow x ~ from the uninformed trader‘s order flow u~ . More specifically, the manager faces the following problem when she makes her choice of the investment level:      P Var r P E 2 max   subject to e Y 2 1       v P . The following proposition provides some characterizations of the optimal investment policy undertaken by the manager. Proposition 1 a In the imperfect information case, the manager‘s investment policy is given by: 996                 2 2 2 2 1 2 Ve se se Ve Vs SB r v        . 1 b The manager overinvests in the sense that FB SB    if      2 2 2 1 1 2 - se Ve se Ve Vs - ρ - ρ     and underinvests in the sense that FB SB    if      2 2 2 1 1 2 - se Ve se Ve Vs - ρ - ρ     . If      2 2 2 1 1 2 - se Ve se Ve Vs - ρ - ρ     , the manager invests optimally in the sense that SB  is equal to FB  . Proof. See Appendix A. The main issue of interest in this paper is the relationship between information quality and corporate investment efficiency. In other words, would information quality, particularly the quality of public earnings information, improve corporate investment efficiency? To investigate this problem, let us first observe how the optimal investment level in the imperfect information case SB  depends on the correlation among the value of the firm v~  , the public earnings signal e~ and the private signal s~ . The following proposition provides some comparative static results of the managers‘ investment policy in equilibrium. Here, it is natural that the quality of the information is described by the correlation coefficient between the value of the firm and each signal. Proposition 2 a If the private signal s~ and public earnings signal e~ are independent  se  , hereafter ―the independent case‖, the optimal investment level SB  decreases as the quality of the private signal Vs  andor the public earnings signal Ve  become better higher. Further, the effect of Ve  on the reduction in investment is larger relative to Vs  the magnitude of the effect of Ve  is double. 997 b The optimal investment level decreases as the quality of the private signal becomes higher. c The optimal investment level decreases when the quality of public earnings information is high 2 1  Ve  . d The optimal investment level increases with a higher correlation coefficient between the private signal and the public earnings signal if   -  se Vs Ve    and decreases with a higher correlation coefficient between the private signal and the public earnings signal if   -  se Vs Ve    . If   -  se Vs Ve    , the optimal investment level is unchanged. Proof. See Appendix A.

3.2.3 The quality of the signals and investment efficiency

It is now possible to consider how the information quality affects corporate investment efficiency. In dealing with this problem, we note the quality of the public earnings information Ve  , as Ve  captures an aspect of the characterization of the accounting information. We define the following threshold function   Ve  Z based on Proposition 1b to specifically identify the overinvestment and the underinvestment region respectively in terms of Ve  :        2 2 2 1 1 2 Ve se Vs Ve se Ve ρ ρ ρ ρ Z   － － － －  . 2 Clearly,       Ve ρ Z represents the manager‘s overinvestment underinvestment in the imperfect information case relative to the first-best investment level in the perfect information case, and    Ve ρ Z means that the manager‘s investment level SB  is equivalent to the first-best case FB  . If we assume the public earnings signal 998 e~ fully reflects the value of the firm in the sense that 1  Ve  , we provide the following proposition. Proposition 3. The quality of public earnings information would enhance the manager‘s investment efficiency in the sense that the manager undertakes the first-best investment if the public earnings signal was informationally perfect 1  Ve  . Proof. se Vs    in the case of 1  Ve  . Inserting into eq. 2,    Ve ρ Z .

4. Concluding Remarks

This paper investigates how the quality of accounting information improves a firm‘s investment efficiency using a stock market model t hat incorporates the manager‘s investment decisions. In particular, we focus on the role of public disclosure in forming more efficient security prices and thereby improving firm investment. Recent empirical research suggests that higher quality financial reporting Our results indicate that higher quality accounting information generally improves investment efficiency by reducing information asymmetries, and this is consistent with the empirical findings in Biddle and Hilary 2006 and Biddle et al. 2008. Appendix A Proof of Lemma 1 Given any vector of normal random variables 1 X and any vector of normal random variables 2 X , 999       2 1 X X ~N    ,  , where        2 1    and             22 21 12 11 , then,     2 2 1 22 12 1 2 1 X  - μ X X E -     , and   21 1 22 12 11 2 1      - X X V － . Proof of Lemma 2 The manager faces the following problem in maximizing her utility in the perfect information case,      P Var r P E 2 max   subject to ] ~ [ v E P   . Taking the first-order condition with respect to  and equating it to 0, we have 2    r v－ and, therefore, 2   r v FB  . Proof of Proposition 1a From Lemma 1,   v P E   and                 2 2 2 2 2 1 2 Ve se se Ve Vs ρ - ρ ρ - ρ ρ σ α P Var . Taking the first- order condition with respect to  and equating it to 0, we then have SB  , as in Proposition 1a. Proof of Proposition 1b It is obvious from a comparison of the amounts invested in the imperfect information case SB  and the perfect information case FB  , specifically from comparing     2 2 2 - 1 2 - Ve se se Ve Vs       in the former with 1 in the latter.