4.1 Sample characteristics
Our sample period extends over the 351 trading days from February 2001 to June 2002. The sample is divided into two subperiods: the first period is from February 2001 to September 2001, and the other is from October 2001 to May 2002.
In this paper the period 2, October 2001 to May 2002, be elected the period of high financial distress costs.
Table 1 presents descriptive statistics, such as the mean, median, standard deviation, minimum and maximum of selected variable for pooled data. Pearson correlations coefficients of selected variable for pooled data are given in Table 2. For CP, NT, and MV, there is negative correlation to percentage bid-ask spread. In the other hand, SIG and DLI have positive relation to percentage bid-ask spread.
4.2 Results of cross-sectional regression
Firstly, we inspect that if the percentage bid-ask spread of the sample firms is related to the determinants of spreads, such as CP, NT, SIG and MV, found in Stoll (1978), Welker (1995), Stoll (2000), and Agrawal, et al., (2004). The monthly regression results using ordinary least squares estimation is shown in Table 3. For most months, the coefficients of close price (logCP) and volatility (SIG) are significant at the 0.05 level of significance and the signs of the parameters of the two explanatory variables are both consistent with that we mentioned above. There is negative correlation between logCP and percentage bid-ask spread; otherwise SIG has positive relation to percentage bid-ask spread. Conversely, the coefficients of the
number of trading (logNT) and stock’s market value (logMV) are insignificant for most months.
Moreover the primary variable of interest, DLI, is put in regression equation Eq.
(10). Table 4 presents the monthly regression result of PSP against four control variables and one key variable of interest using generalized least squares estimation under heteroskedastic. Roughly speaking, the coefficients of all explanatory variables are obviously significant with p-value of 0.000 at the 0.05 level for each month. The exceptions are the estimators of logNT and logMV13. Like our prediction, the coefficients of logCP, logNT and logMV are negative and in contrast the coefficients of SIG and DLI are positive. DLI reveals a strongly significant positive relation with PSP in each month, indicating that terrible financial condition increases the percentage bid-ask spread.
4.3 Results of panel data regression
Because the omitted variable may be presence in Eq.(10), ordinary least squares estimation is not expected to consistently estimate any coefficient on independent variables. Unobserved effects panel data model is one of ways to address the problem.
We make an effort to reduce the unobserved effects by panel data regression using fixed effects estimation. Panel data sample is also split up into two periods to demonstrate whether the results are any more significant in the period with high financial distress costs.
In Table 5 is the result of panel data regression. The sign of MV’s parameter is positive unlike the expected direction. The parameter of logPDLI is totally
13 The coefficient of logNT is insignificant in February 2001, January 2002 and June 2002. The coefficient of logMV is insignificant in April 2001, May 2001, October 2001and January 2002.
insignificant. The insignificant results of the effect of DLI and unexpected sign of MV’s parameter in Table 5 might be due to the non-linear relationship between these two variables. Particularly, the model in Table 5 might be mis-specified if a significant threshold effect in DLI exists.
4.4 Results of panel data threshold regression
For avoiding the singular matrix, in Eq.(14) as well as Eq.(15), the regressor logPDLI is introduced to replace DLI in Eq.(10). Table 6 comes out some result for panel threshold regression for each period, including estimators of threshold and
, and the test statistics F. The estimator of threshold is 0.1880 in whole sample period, 0.1627 in period 1 and 0.1073 in period 2. Except for logPDLI of first regime, the coefficients on the other independent variables are extremely significant at 5% or even 1% level. The sign of each parameter is almost coincidence between the estimator and prediction. Three points are noteworthy in the result of Table 6.
The primary estimates claim that there is positive relation between logPDLI and PSP, and “high default risk” regime possesses the enormously significant and higher coefficients than “low default risk” one no matter any period. This indicates that firms in high default risk regime heavy increate more liquidity cost than those in low default risk regime. Secondly, the coefficient of logPDLI for high default risk regime is about 1.5 times bigger in period 2 than in period 1. We demonstrate it is indeed that default risk obviously increases more liquidity cost for the period of expected high financial distress costs. In addition, the sign of MV’s parameter turns positive unlike the unexpected direction in Table 5.
∧
γ1
∧
γ2
For period 2 we find robust evidence of a double threshold effect in Table 7.
There is overwhelming evidence that there are two thresholds in the regression relationship in period 2, =0.1073 and =0.6341. Compare the coefficient of three regimes
∧
γ1 γ∧2
14, the “very high default risk” class gets the highest coefficients, 0.0198, about twice higher than “high default risk” class and 200 times higher than
“low default risk” class. However, Table 5 reports the coefficient of logPDLI without using threshold fails to significant. If we didn’t contemplate threshold effect, the effect of default risk on liquidity would be seriously mis-specified or undervalued. Looking at Table 6 and Table 7, the conventional OLS standard errors and the White-corrected standard errors are almost close, meaning that there is certainty in the estimate. Although in Table 7 the conventional OLS standard errors and the White-corrected standard errors on last two coefficient are considerably different, with the White-corrected ones roughly 1.5 times as big, the t-value with White-corrected standard errors is still large enough to be significant.
14 The table of percentage of firms which fall into the three regimes each month for double threshold model is shown in the appendix, Table A.3.