Logit Estimation

The summary statistics in Table 3.1 show that target firms have a number of characteristics that are different from non-target firms. However, we are not clear about how these variables combine together to predict takeover probabilities. Following Cremers, Nair, and John (2009) and others, I now estimate the probabilities of being taken over in the next period using a logit model. I assume that the marginal probability of becoming a target over the next period follows a logistic distribution and is given by the following equation

P(Tit= 1) =

1

1 +exp(−α−βXit−1)

(3.2)

where Tit is a dummy variable that equals one if the firm is a target in year t, and Xit−1 is a vector of

explanatory variables known at the end of the previous year. The elements ofXit−1includeQ,P P E,Cash,

Size,Leverage, ROA,Industry,Block andOpacity. Detailed definition of those variables are provided in

the data section. All those variables except Opacity have been used by researchers in the prior literature to understand and predict takeover events.10 _{I augment the model by adding Opacity as an additional}

predicting variable since several articles in the literature show that firms’ transparent environment can facilitate takeovers because acquiring firms can bid more effectively and the expected synergies are larger for target firms that are more transparent (see, e.g., Martin and Shalev (2011) or McNichols and Stubben (2011)). Thus transparent firms are more attractive targets and takeover attempts are more likely. All the Compustat variables are industry adjusted by subtracting the median value of the empirical distribution from the data. Year dummy variables are also included in the logit regression to account for the time fixed effect.11

10_{see, for example, Ambrose and Megginson (1992), Cremers, Nair, and John (2009).} 11

The logit model is estimated once using all the observations from 1991 to 200912 _{and the regression}

coefficients are reported in Table 3.2. Model 1 refers to the logit model used in the prior literature and model 2 refers to the new model with all the variables included in model 1 and the additional predicting variable: Opacity. For both models, I report the estimation coefficients for each variable. As is displayed, when using model 1, variablesQ(the market-to-book ratio),Block(more than 5% ownership stake dummy),

Industry(the dummy variable to capture the clustering of takeover activity within industry), andSizehave

larget-statistics and thus are extremely statistically significant.13 _{This shows that target firms tend to have}

low market-to-book ratio, high institutional ownership and small size and it is likely that these firms are in industries with takeover occurance in the previous year. These facts are all consistent with the findings in the prior literature. However, the coefficients onROAandLeverageare significant but with positive sign. This is not expected intuitively because firms with low leverage seem to be easier to be taken over since the deal involves less issue with debt holders and firms with low return on assets seem to be easier to become target because the low return could be the results of bad management. However, this is consistent with the prior literature because others also show positive signs associated with these variables sometimes with different samples. Thus these two variables seem not to have persistant predicting power of takeover probability.14

Model 2 refers to the augmented model with all the variables included in Model 1 and an additional variableOpacity. Notably, using model 2, the coefficient on the variable of interestOpacityis negative and highly statistically significant. Specifically, the coefficient is -7.468 with a t-statistic of 10.21. This shows that transparent firms have higher predicted takeover probability than opaque firms, all else equal. What’s more, adding this additional variable does not diminish the effects of other variables at all and the coefficients on the variables included in model 1 are still highly significant with similar magnitude. For example, the coefficient for the variableIndustryis 0.618 (t-statistic = 5.57) in model 1 and it increases to 0.671 with a t-statistic of 6.05 in model 2. The coefficient for the variable Block is 0.567 (t-statistic = 11.34) in model 1 and it is 0.549 with at-statistic of 10.98 in model 2. The coefficient on the variable Qslightly decreases and the coefficient on the variableSize increases. This might be because there is correlation between the opacity variable and these two variables. Generally speaking, adding the new variable does not have a sig- nificant impact on the effects of the variables in the original model. Thus the results in this table confirm my hypothesis that transparency can facilitate takeovers and hence it should be another dimension that can affect firms’ probability of being taken over in the next time period.

In order to see how well the old and new models fit the takeover data, I also report the Pseudo-R2

for each estimation at the bottom of Table 3.2. It is notable that augmenting the original model with the

Opacity variable raises the level of Pseudo-R2 _{to some extent.}15 _{Specifically, it increases from 3.41% in}

model 1 to 4.20% in model 2. The increase is about 20% of the original value, indicating that the augmented model should fit the data better and have additional predicting power of the takeover likelihood.

12_{Since the estimation of the transparency measure accrual quality has to be constructed using the rolling windows} regression. Reliable values of this measure can only be formed as early as 1991.

13

The unreportedp-value of those coefficients are less than 0.0001.

14_{I also try to use market leverage to replace book leverage, this does flip the sign of leverage from positive to} negative sometimes, but not all the times, thus the predicting power of leverage is not so persistent.

15_{Cremers, Nair, and John (2009) reports a Pseudo-R}2_{of 1.39% using model 1 with a sample of all completed deals} from 1981 to 2004.

To examine whether the results are robust using different measures of transparency, I also run model 2 in Table 3.2 using alternative transparency proxies which are constructed based on analysts’ earnings forecasts. They are termed forecast error and forecast dispersion. Specifically, forecast error is defined as the absolute value of the difference between the actual annual earnings per share (EPS) and the mean of analyst forecasts. Forecast dispersion is defined as the forecast standard deviation across all analysts following the same firm in the same year. Intuitively, higher level of forecast error and forecast dispersion imply lower level of firm transparency because analysts can collect more information about the future performance of the firm if the firm is willing to release more of its true status. 16 The logit estimation results using model 2 over the sample period of 1991 to 2009 are presented in Table 3.3.

According to Table 3.3, the estimation results are consistent with the previous findings. That is, the coefficients on the transparency proxies are statistically significant for both proxies forecast error and forecast dispersion and adding the new variable does not diminish the effects of other variables at all. Specifically, the coefficient for forecast error is –0.378 and it is statistically significant at 1% level. The coefficient for forecast dispersion is –0.320 with at-statistic of 2.62. Notably, The Pseudo-R2 also increases from model 1 to model 2. For example, the Pseudo-R2_{is 3.41% for the logit estimation using model 1 and it increases to}

4.17% when augmenting the model with the transparency variable forecast error. Similar pattern is shown in the case of another transparency measure forecast dispersion. The Pseudo-R2increases to 4.11% in model 2. Therefore, the test results in Table 3.3 provide another piece of supportive evidence that firms’ transparent environment does have additional predicting power on firms’ future takeover probability.

To further examine the predictability of the new augmented model, I compare the predicted takeover likelihood with the realized takeover event rate. Firms’ predicted takeover likelihood is computed using equation (2) and the logit estimation coefficients from model 2 in Table 3.2. Each year firms are sorted into quintiles or deciles based on the value of the predicted takeover probability. The real takeover event rate is calculated within each quintile or decile every year as the number of takeovers deflated by the total number of firms in that quintile or decile group. Table 3.4 reports the mean value of the predicted takeover likelihood and the realized takeover event rates over the sample period of 1991 to 2009. For comparison, I also perform the same analysis using model 1 to compute the predicted takeover probability and the statistics are reported in the right part of each panel in Table 3.4.

Panel A shows the results for quintile portfolios and Panel B shows the results for decile portfolios. As is shown in the left part of Panel A, when using model 2, the realized takeover rate is increasing monotonically with the predicted takeover likelihood. Specifically, the real takeover rate goes from 0.0117 for quintile 1 to 0.0515 for quintile 5 and the predicted takeover likelihood goes from 0.0152 in quintile 1 to 0.0527 in quintile 5. The correlation between the average predicted takeover likelihood and the realized takeover rate is as high as 0.98. Similar pattern can be found in the left part of Panel B for the decile sorted portfolio. The real takeover rate increases monotonically from 0.0112 in decile 1 to 0.0575 in decile 10 and the predicted takeover probability goes from 0.0077 in decile 1 to 0.0529 in decile 10. The correlation between these two measures is 0.97. Thus the results show that there are actually more takeover activities among firms with higher predicted takeover likelihood and this is an indication of the reasonably good predicting ability of the new logit model.

16

The right part of the table reports the results when calculating the takeover probability using the esti- mation coefficients from the old logit model (Model 1 in Table 3.2). You can see that the predicted takeover likelihood generally follows the trace of the realized takeover event rate from quintile 1 to quintile 5 or from decile 1 to decile 10. For example, the realized takeover rate is 0.0114 in decile 1 and it increases to 0.0469 in decile 10 and the corresponding predicted takeover probability is 0.0149 in decile 1 and 0.0521 in decile 10. However, the correlation of these two measures is 0.67 for the quintile sorted portfolios and it is 0.94 for the decile sorted portfolios. These correlation values are lower than the corresponding values using model 2 as the takeover predicting model. Therefore, the results presented in this table provide supportive evidence that the new augmented model can actually fit the real takeover data slightly better and firm transparency level adds another dimension to the takeover event prediction.

Table 3.4 shows how fit the model is with the predicted takeover likelihood averaged over the sample period. However, an investigation of the relation between the predicted takeover likelihood and the real takeover rate over time would provide more valuable information. Thus in Figure 1, I plot the time-series of the average predicted takeover probability and the real takeover rates17for the top decile group (The decile with the highest level of predicted takeover likelihood) over the sample period of 1991 to 2009.18 _{As is shown}

in the figure, the real takeover activity shows an up-trend in the 90s and then it goes down in early years in the 20th century and goes up again until the start of the financial crisis.19 Although the time-series of the predicted takeover probability is less volatile than that of the actual takeover activity, it generally follows its trace pretty well and the correlation between these two series is as high as 0.86. Thus the predicted takeover probability can capture a reasonably large part of the variations of the realized takeover activity over time. Again for comparison, I also plot the graphs when computing the predicted takeover likelihood using the estimation coefficients from model 1. As is shown in part two of Figure 1, the predicted takeover likelihood curve generally follows the path of the realized takeover rates over time, but it does not capture the details of the real takeover activity as well as the time-series of the predicted takeover probability constructed using model 2. This is also reflected in the correlation between these two series. In this case, the correlation is 0.76, which is lower than the correlation of the two time-series in part one of Figure 1.

In sum, the above test results show that augmenting the old logit model with the additional transparency variable produces better fit of the real takeover activity data. The new model shows better performance than the old one since it produces slightly higher Pseudo-R2 _{for the logit estimation and a larger correlation}

between the time-series of the average predicted takeover probability and the realized takeover rate.