130 The Basics of financial economeTrics
tAble 6.2 (continued)
Issue # Residuals Residuals Dummy 1 Residuals Dummy 2
196 –42.709500 –33.855500 –50.285700
197 257.550200 34.224540 70.337910
198 90.307160 102.727000 89.148700
199 –61.373800 –35.037300 –37.531400
200 –30.310400 –29.889500 –32.034600
Notes:
Residuals: residuals from the pooled regression without dummy variables for
investment grade.
Residuals Dummy 1: inclusion of dummy variable for investment grade.
Residuals Dummy 2: inclusion of dummy variable to test for regime shift.
Let’s now analyze whether we obtain a better fit if we consider the two
categories of investment-grade and below-investment-grade bonds. It should
be emphasized that this is only an exercise to show the application of regres-
sion analysis. The conclusions we reach are not meaningful from an econo-
metric point of view given the small size of the database. The new equation
is written as follows:
Spreadi = β 0 + β 1 D (^1) i + β 2 Couponi + β 3 D (^1) iCouponi + β 4 CoverageRatioi
- β 5 D (^1) iCoverageRatioi + β 6 LoggedEBITi
- β 7 D (^1) iLoggedEBITi + εi
There are now seven variables and eight parameters to estimate. The
estimated model coefficients and the t-statistics are shown as follows:
Coefficient
Estimated
Coefficient
Standard
Error t-Statistic p-Value
β 0 284.52 73.63 3.86 0.00
β 1 597.88 478.74 1.25 0.21
β 2 37.12 7.07 5.25 3.96E-07
β 3 –45.54 38.77 –1.17 0.24
β 4 –10.33 1.84 –5.60 7.24E-08
β 5 50.13 40.42 1.24 0.22
β 6 –83.76 13.63 –6.15 4.52E-09
β 7 –0.24 62.50 –0.00 1.00