This section gives an overview of analytical tools common for both the earnings response coefficient and the value relevance analysis, as well as describing the reasoning behind adding new variables used in both data sets. The methodology that is not shared by the two methods are separated into the to chapters four and five.
3.1 Quantile – regression
In my models I want to check if there are any interesting conditional quantiles. By this, I am referring to instances where one would expect different coefficient values based on differences in observation values. An interesting conditional quantile in the value relevance model would be to see how the drilling success coefficient changes when looking at firms with low drilling success contra firms with high drilling success. This is interesting because we know that drilling success directly affects whether the asset value of a full cost firm are inflated or not.
To control for this, I plot the quantile coefficient estimates of my final model and display the
results for every variable. I plot quantile coefficients by running regression on the overall
regression on every quantile of every variable, and plotting the results with 0,05 tau
confidence bands. These bands make it easy to see how the coefficient moves over time, and
how accurately it is represented by the current coefficient. An alternative to this is to run
analysis of variance (Anova) regressions to determine which variables that might have
quantile differences. However, with the band plots it is easy illustrate the data and see where
quantile problems may exist, and would require many Anova regressions per variable to
replicate. This is also a technique that has been used in previous research by Machado & Mata
(2005) among others.
After determining whether there are quantile differences, I optimize the model accordingly.
This does not imply that I will always split the variables into quantiles to compensate for the differences, but rather that I will investigate whether including such variables are optimal for the overall regression. To determine if quantiles are needed I use the adjusted R
2and if this measurement is improved by quantiles, the quantiles are included.
3.2 Multicollinearity
Collinearity is when one of the variables is highly correlated with one of the other variables;
multicollinearity is when one of the variables is linearly predicted by a function of the other variables. In a linear model this can create problems such as a too high R
2, and variables becoming significant due to correlations with other variables and not because they contribute to explaining the dependent variable in themselves.
A Variance Inflation Factor-test (VIF-test) is used to check for this, this can be illustrated in the following example:
𝑌 = 𝛼 + 𝛽
!𝑋
!+ 𝛽
!𝑋
!+ 𝛽
!𝑋
!+ 𝜀
(Equation 3.1a)To calculate the VIF number for X
1in this function, one creates another regression where X
1is expressed by the other variables.
𝑋
!= 𝛼 + 𝛾
!𝑋
!+ 𝛾
!𝑋
!+ 𝜀
(Equation 3.1b)Lastly one uses the R
2from equation 3.1b, as input into the final function (3.1c).
𝑉𝐼𝐹 =
!!!! !(Equation 3.1c)To interpret the VIF number it is common to use a rule of thumb where a VIF number higher than 10 indicates departure from the assumptions of the linear regression model, this gives quite a lot of leeway considering this requires an R
2of 0,9 and above. Because of this some researchers (insert reference) argue that a VIF of 5 is enough to be worried (R
2of 0,8). I will therefore comment on any VIF above 5.
3.3 Heteroskedasticity
Heteroskedasticity is simply the absence of homoscedasticity. More precisely
homoscedasticity tells us if variance is uniform across all observations. This means that all
observations are expected to have the same levels of variance. Heteroskedasticity exists when
the variance deviates between different subgroups. This is particularly relevant to thesis. I am
using observations from different periods, therefore there is a chance that some years, or periods have different expected variance than other years. To control for this I run a Breusch–
Pagan test (Breusch and Pagan 1979), which checks whether the variance of the error term is dependent on the values of the independent variables, which would be the case if there is heteroskedasticity.
Starting with the same expression as before,
𝑌 = 𝛼 + 𝛽
!𝑋
!+ 𝛽
!𝑋
!+ 𝛽
!𝑋
!+ 𝜀
(Equation 3.2a)We assume that the OLS conditions are met (insert reference to where OLS is explained), therefore e= 0, The independence of the error term can be verified by through an auxiliary regression.
𝜀 = 𝛼 + 𝛾
!𝑋
!+ 𝛾
!𝑋
!+ 𝛾
!𝑋
!+∈
(Equation 3.2b)Further it uses probability based on Chi-Squared distribution to confirm if the variables are equal to 0
H
0= (γ
1= γ
2= γ
3=0)
If H
0is rejected, there is evidence of heteroskedasticity.
3.4 White Standard Errors
To adjust for heteroskedasticity I am using heteroskedasticity-consistent (HC) errors. More precisely I am using the HC1 model proposed by Mackinnon and White in 1985 (MacKinnon and White 1985). The reason for using these is because it is slightly more complex the simplest HC0 model, and better suited for small samples (Zeileis 2004). While at the same time being fairly common and used as the standard heteroskedasticity-consistent errors in programs such as STATA (Long and Ervin 2000). The function for the HC1 model is as follows.
𝐻𝐶1 = 𝑤
!=
!!!!∗ 𝑢
!!(Equation 3.3)Where 𝑢
!!is the residuals, n is the number of observations and n-k is the degrees of freedom
(White 1980). These standard errors also work as a quick fix for multicollinearity, by binding
the errors the chance for multicollinearity to affect the results is reduced (Aslam 2014).
3.5 New variables
The key differences between full cost and successful efforts accounting, is how they account for drilling cost. In order to analyze this difference as thoroughly as possible several variables based on the drilling success rate are used. The first variable is change in drilling success rate based on average drilling success rate from previous years. This variable is meant to highlight how drilling success rate affects successful efforts companies, because if all else was equal, an increase in drilling success in the current year will make the current year’s bottom line look better, because more of the drilling expenses gets capitalized instead of expensed in the current year. The second variable is a variable based on any diversion from 100% drilling success rate. This is to highlight the differences caused by drilling success rate in full cost accounting. Because all costs of drilling wells is capitalized by full cost companies, the higher diversion from 100% drilling success rate, the more non cash generating assets are placed in the balance sheet. In this thesis lagged variables based on 1-3 previous years are used for both variables. The reason for using 1-3 previous years is decided after considering several arguments, it seems probable that analyst might consider more then just the pervious year when predicting future profits, therefore it is reasonable to include more then one year.
However because of depreciation any historical diversion is decreasing in relevance the older
the accounting data is. Ultimately the data used in this thesis have few companies with more
then 3 years of historical drilling success rate observations. Therefore it is unreasonable to
include more then 3 years of past drilling success rate in this thesis.
In document
Valuation of oil and gas companies
(sider 14-17)