An observation which was made during the literature review was the difference in exploring individual firm data sets and exploring panel data sets. The primary difference between the two is how the data is organised, and such also how the unit root tests can utilise the data. When utilising purely the time-series aspect of the firms, that is individual testing, the data will be organised as per table 3.
Time Firm 1
Firm 2
Firm 3
t X1 X2 X3
t+1 Y1 Y2 Y3
t+2 Z1 Z2 Z3
Table 3 - Individual data
Panel data however is organised by individual groups. This requires panel data to both specify the specific group, using subscript i, as well as the time variable, using subscript t, as shown in table 4.
Group Time-period
Notation
1 1 Y11
1 2 Y12
1 T Y1T
⁞ ⁞ ⁞
N 1 YN1
N 2 YN2
N T YNT
Table 4 - Panel data
The primary advantages of utilising panel data in unit root testing is that this specific data format is capable of exploiting both the time dimension as well as the cross-section dimension of the data. This will lead to a greater power when performing unit root tests, as
Page 36 of 86 well as greater efficiency when compared to time series unit root tests (Baltagi, 2005;
Canarella et al., 2014; Levin et al., 2002).
One key issue to address when using panel unit root tests is the assumptions made regarding section independence. Some tests utilising panel data assume cross-sectional independence in the data set, an assumption that seems unrealistic given the focus area of this thesis. There are several reasons why cross-sectional dependence may exist between firms in a given industry. Firms which share an industry are effectively exposed to the same market conditions. When a shock hits the industry, the firms will likely be impacted in much the same way. Even broader, some market factors impact even firms outside of the specific industry, such as the monetary policy employed where the firm is located. If the interest rate is raised, this will increase the cost of borrowing for the firm, which will influence the cost of capital, which might directly influence the firm’s financing decisions (Bokpin, 2009; Frank & Goyal, 2009). Previous studies have also found empirical evidence that observations regarding firms and industries tend to be cross-correlated (Bernier & Mouelhi, 2012; Breitung & Pesaran, 2005; Chan et al., 2001). To handle this specific problem, I will employ what is known as second-generation unit root panel tests, which do allow for cross-sectional dependence by imposing a common factor structure.
These tests still build on the foundational framework of the ADF test, and so still share the null hypothesis of a unit root, and perform, in effect, the same testing, but modified in the way specified above.
Another issue of concern is that of the data structure itself. When discussing panel data, one can group the data into two types: balanced and unbalanced panels. The panel shown in table 4 is a balanced panel, as each group has the same number of observations.
Conversely, an unbalanced panel is one in which some of the groups are missing observations, creating a panel where not every observation is filled in for each and every group. This presents a problem, as certain panel data models only provide valid results when testing on a balanced panel of data. As discussed in the data selection section, I include firms which enter the S&P 500 index later than the 1980s, as not to cherry-pick older and longer-surviving firms. This by default leads to an unbalanced panel of data, as these firms will have no observations to include prior to their entrance into the index.
Therefore, the model for the panel unit root testing also must fulfil the criteria that a balanced panel is not necessary to reach valid results.
Based upon literature regarding the advantages and disadvantages of the different models which fulfil both of the above criteria (Baltagi, 2005; Maddala & Wu, 1999), I have
Page 37 of 86 chosen to perform the Fisher test. The Fisher type ADF test fulfils both criteria in that it allows for cross-sectional dependence and does not require a balanced panel of data.
Additionally, it is the implemented model of testing by both Ahsan et al. (2016) and Canarella et al. (2014), allowing for greater comparability with the results of these two empirical pieces of literature, as differences in testing methodology will not bias the interpretations which can be made from the results presented in this thesis.
Regarding the sorting of the data into panels, the existing literature groups the firms by industrial classification. As mentioned, the tests I will perform are capable of handling the dependency issues these groupings will create, and so I do not consider this issue a particular worry of this data grouping. Therefore, I will also be performing the panel wide tests on groups segmented by industrial classification, utilising the GICS classification.
GICS has been chosen for its greater identification and classification capabilities compared with alternatives such as the SIC system.
Page 38 of 86
4 Empirical Results
In this chapter, I will present the findings of the analysis carried out as described in the methodology section. The chapter will proceed as follows. In section 4.1, I will present the results of the mean reversion testing, with descriptive statistics in section 4.1.1, individual firm testing in section 4.1.2, and panel-level testing in section 4.1.3. Following this, in section 4.2, I will present the results of the testing of the characteristics, with descriptive statistics in section 4.2.1 and testing results in section 4.2.2 and 4.2.3.