PIN Model Used Our Research Design 1 New Quarterly Reporting Regulations in Japan

318 parameter vector with tick data we numerically maximize this likelihood function without constraints using a standard computing procedure. 44 s b PIN       ˆ ˆ ˆ ˆ ˆ ˆ    1 This PIN variable, based on Bayes‘s theorem, represents the ex post probability that the trades are triggered by private information among all tick-by-tick trades. In 1 the numerator denotes the number of orders which is composed of the information- based order arrival rate times the occurrence of the information event, and the denominator is the total sum of the information-based trade and the sell and buy trades for the non-information event case. In estimating the necessary parameters as shown in Appendix A‘s equation A-2, we use tick-by-tick records for all the stocks and classify each transaction as either a buy or a sell order without ambiguity with the following method. 45 That is, all previous and current bid and ask quotes are recorded in our dataset, and based on these quotes, we classify all transactions as either buy or sell depending on whether each market-cleared transaction is determined either above or below the middle point of the most recent bid and ask price. We impose further conditions, in that at least 45 days of trading data are available to compute the quarterly PIN for each firm.

3. Definition of the Variables Used and the PIN Estimates

The data we use for this study is as follows. First, the sample is firms listed in the first and the second section of the Tokyo Stock Exchange from 1996 through the third quarter of 2008. To estimate the PIN variable we use tick-by-tick quote and transaction data provided by Nikkei Media Marketing Co., Ltd. For financial data, the source is again Nikkei Media Marketing Co., Ltd. Two variables we use are: lnMV, which is a natural logarithm of market value of equity in million yen, and BM, which is the book-to-market ratio of the firm in percent. These financial attributes of the firm, lnMV and BM, are computed from the Nikkei Portfolio-Master Database. As for the record of quarterly disclosure by firms listed in the Tokyo Stock Exchange, we use the ―eol‖ on-line database provided by eol, Inc. This data is originally constructed by the TD-Net of the TSE, and the data is automatically transmitted to eol, who construct their database from HTML and PDF files of quarterly financial statements from the TSE. We conduct the c ontent search using eol‘s search engine to collect necessary data. 44 We estimate the parameters by using the function min_uncon_mulvar in the IMSL CMATH Library. This function uses a quasi-Newton method to minimize the multivariate function and the details of our algorithm as explained in Dennis and Schnabel 1983. The resulting estimates of the PIN variable belong to a class of asymptotically efficient estimators Amemiya, 1985. 45 Hence, we do not have to use the conventional ―tick test‖ which is the case for markets with specialists. 319 Based on the collected records from eol, we construct a dummy variable called the ―QDDummy‖ variable and this variable is assigned value 1 if we find quarterly financial statements, and it assigned value 0 otherwise. As for the number of analysts following the firm, which we call ―NAnalysts,‖ this figure is computed based on the IBES International Summary History File provided by Thomson Reuters Markets KK. To construct the liquidity measures, we compute two alternatives: ILLIQ by Amihud 2002 and the turnover ratio. The data source is the Nikkei Portfolio-Master Database. The definition of these measures is as follows. First, let NSTD j,t denote the number of shares of firm j traded in month t, and NS j,t denote the number of shares outstanding for firm j at the end of month t . Then the ‗Turn j,t ‘, turnover ratio of firm j in month t is defined as t j t j t j NS NSTD Turn , , ,  2 This variable measures the degree of liquidity by looking at the trading volume, which is a standard measure used in microstructure studies. Next, the ―illiquidity‖ measure proposed by Amihud β00β is defined as the average ratio of the daily absolute return to the trading volume on that day. Let D j,t denote the number of days in which trading volume of firm j is strictly positive, r j,d,t denote the daily return of stock, and v j,d,t denote the trading volume in million yen. Then, ILLIQ j,t , the illiquidity measure by Amihud 2002 for firm j in month t is defined as follows.    t j D d t d j t d j t j t j r D ILLIQ , 1 , , , , , , | | 1  3 This measure is widely used in asset pricing theory tests in financial economics for example, Avramov et al. 2006 for U.S. data and Kubota and Takehara 2009b for Japanese, and we choose to use this measure. The a dditional two variables that we use as control variables in our regression analysis are the number of analysts following each firm and the number of outstanding series of corporate bonds. The first variable is directly taken from the IBES data and we count the number of earnings‘ forecasts at the end of each quarter for each firm. The second variable is from the Nikkei NEEDS Database and the counts the number of series of outstanding bonds. These are to control for the general inflow of firm-related public information. Analysts contribute to increased information about firms‘ future profitability and thus, on stock returns, and the new issuance of corporate bonds needs new credit ratings each time by credit rating agencies. Next, we report the basic PIN estimation results in Table 2, Figures 1, and Figure 2. TABLE 2 ABOUT HERE FIGURE 1 ABOUT HERE FIGURE 2 ABOUT HERE