Introduction
The article presented by Amihud and Mendelson (2008) which offers an extensive look into the relationship between liquidity costs, as proxied by the bid-ask spread, and the excess monthly stock return, prompted a further look into the subject of corporate liquidity. The authors define liquidity costs as the costs incurred by investors when they partake in the trading of less liquid securities. Although this piece of literature may have been the initial catalyst spurring the birth of this research proposal, Amihud and Mendelson (1986) which offers a model of this liquidity effect on asset pricing, proves to be among one of the seminal works which initiated a vast body of empirical evidence on the subject.
Researchers have invariably reached the same conclusion: the lower the liquidity of a security—after controlling for risk and other relevant characteristics—the higher its expected return or, alternatively, the lower its price or firm value (Amihud & Mendelson, 2008; Amihud, Mendleson, & Pedersen, 2005; Dalvi & Baghi, 2014; Du , Wu , & Liang, 2016; Nguyen, Singh, & Duong, 2014; Noe & Fang, 2009; Sidhu, 2016).
After reviewing the research conducted by the above academics as well as the research listed in the literature review below, it is evident that the relationship between liquidity, as proxied by the bid-ask spread, and firm value, as proxied by Tobin’s Q, has not been researched extensively in a South African context; therefore a gap exists for academic research to be conducted further in this realm.
Aim
This R report aims to run various stationarity tests in order to determine the nature of the raw data gathered from the Bloomberg Terminal. The following steps outline the process followed in order to acheive this goal.
This research aims to investigate the relationship between liquidity, as proxied by both the cash ratioand the bid-ask spread, and firm market value, as proxied by Tobin’s Q. A sample of firms listed on the Johannesburg Stock Exchange (JSE) will be employed, of which monthly time series data will be analysed. This research will be conducted by running stationarity testsas well as a Vector Error Correlation model, VECM, in order to determine the relationship between liquidity and firm market value. In addition. a Granger Causality test will be conducted in order to investigate the causality between liquidity and firm market value in a time series.
Research Objectives
The main research objective outlined in this paper is to determine the relationship between liquidity, as proxied by the bid-ask spread, and firm value, as proxied by Tobin’s Q. Furthermore, the research seeks to:
- determine the causal relationship between liquidity and firm value.
H0: There is no relationship shared between liquidity and firm value
H1: There is a relationship shares between liquidity and firm value.
Methodology
Sampling and Data Collection
The standard approach for time series data analysis will be used. Data will be obtained from the Bloomberg Global Database (BGD). The cash ratios, bid-ask spreads and Tobin’s Q ratio values have been obtained on firms listed on the JSE Top 40 index. Monthly data was collected over the period 2002-2018. A longer sample period could not be used as the necessary data was not available on the BGD.
STEP 1: Firstly, the necessary packages were installed. I hashed out the packages after the intial installation, and called the packages to memory using the library() function. The raw data contained in an excel document was then inputted.This data was collected from the Bloomberg Terminal and contains information on 15 equities from the JSE Top 40 Index. I was unable to find more equities within this index that contained all the necessary data, leaving me with a smaller pool than I’d initially hoped to use. Lastly, I fortified the data into a timeseries dataframe.
# install.packages("backports")
# install.packages("tidyr")
# install.packages("dplyr")
# install.packages("ggplot2")
# install.packages("moments")
# install.packages("forecast")
# install.packages("tseries")
library(moments)
library(ggplot2)
library(dplyr)
library(tidyr)
library(forecast)
library(tseries)
library(knitr)
library(readxl)
CRR <- read_xlsx("Raw Data (Final).xlsx", sheet = "Cash Ratio")
BASR <- read_xlsx("Raw Data (Final).xlsx", sheet = "Bid-Ask Spread")
TQR <- read_xlsx("Raw Data (Final).xlsx", sheet = "Tobin'sQ")
View(CRR)
View(BASR)
View(TQR)
library(zoo)
CRV <- CRR[]
BASV <- BASR[]
TQV <- TQR[]
dataframeall <- data.frame(CRV, BASV, TQV)
CR <- ts(CRV, start = as.yearmon(2002,1), deltat = 1/12, class = c("mts"))
BAS <- ts(BASV, start = as.yearmon(2002,1), deltat = 1/12, class = c("mts"))
TQ <- ts(TQV, start = as.yearmon(2002,1), deltat = 1/12, class = c("mts"))Data Summary Statistics Output
STEP 2: I created a data summary using the summary() function. The summary data output has been surpressed as its relevance is minimal in the context of this assignment.
Initial Plots
STEP 3: I created a few plots to visualise the data, just to see if there was any sort of initial relationship between the variables.
ggplot(data = dataframeall, aes(x=dataframeall$ANH.SJ.Equity.2, y = dataframeall$ANH.SJ.Equity)) +
geom_jitter() +
geom_smooth(method="loess",
se=F) +
labs(x="Tobin's Q",
y="Cash Ratio",
title = "JSE EQUITY: 2002-2018",
caption="Liquidity v Firm Market Value")
ggplot(data = dataframeall, aes(x= dataframeall$ANH.SJ.Equity.2, y = dataframeall$ANH.SJ.Equity.1)) +
geom_jitter() +
geom_smooth(method="loess",
se=F) +
labs(x="Tobin's Q",
y="Bid-Ask Spread",
title = "JSE EQUITY: 2002-2018",
caption="Liquidity v Firm Market Value")
Description Of Overall Research Design
The methodology of choice has been used throughout the body of research on this topic, dating back from the Amihud and Mendelson (1986) paper up until the recent paper by Ha and Vihn (2017). Firstly, stationarity testing will be conducted in order to assess the characteristics of the sample. Secondly, a VECM will be employed. Finally, a Granger Causality test will be run in order to determine the causal relationship between liquidity and firm market value.
Stationarity Testing
Stationarity of the data employed in the study is required and as such the following tests of stationarity will be run in order to avoid the possibility of a spurious regression, as well as to ensure the reliability of results. An augmented Dickey Fuller test examines the null hypothesis that a unit root is present in a time series sample (Carrion-i-Silvestre, & Sansó, 2006).
The second test that will be used in the testing for stationarity is the Phillips-Perron unit root test (Carrion-i-Silvestre, & Sansó, 2006). Similarly to the above augmented Dickey Fuller test, the Phillips-Perron test examines time series data to test the null hypothesis that a time series is integrated of order one.
The Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test examines if a time series is stationary around a mean or linear trend or is non-stationary due to a unit root (Carrion-i-Silvestre, & Sansó, 2006). The null hypothesis for the test is that the data is stationary.
STEP 4: I ran various stationarity tests using various packages. Most of the functions used below are from the tseries package. I also made use of the tidy and kable packages to easily manipulate the results into neat tables.
ANH Cash Ratio Stationarity Test Results
| statistic | p.value | parameter | method | alternative |
|---|---|---|---|---|
| -2.78015 | 0.2718556 | 3 | Augmented Dickey-Fuller Test | stationary |
| statistic | p.value | parameter | method | alternative |
|---|---|---|---|---|
| -31.73876 | 0.01 | 2 | Phillips-Perron Unit Root Test | stationary |
| statistic | p.value | parameter | method |
|---|---|---|---|
| 0.4206299 | 0.068263 | 3 | KPSS Test for Level Stationarity |
ANH Bid-Ask Spread Stationarity Test Results
| statistic | p.value | parameter | method | alternative |
|---|---|---|---|---|
| -2.804316 | 0.2625325 | 3 | Augmented Dickey-Fuller Test | stationary |
| statistic | p.value | parameter | method | alternative |
|---|---|---|---|---|
| -30.81761 | 0.01 | 2 | Phillips-Perron Unit Root Test | stationary |
| statistic | p.value | parameter | method |
|---|---|---|---|
| 0.5988933 | 0.022737 | 3 | KPSS Test for Level Stationarity |
ANH Tobin’s Q Stationarity Test Results
| statistic | p.value | parameter | method | alternative |
|---|---|---|---|---|
| -1.753631 | 0.6678892 | 3 | Augmented Dickey-Fuller Test | stationary |
| statistic | p.value | parameter | method | alternative |
|---|---|---|---|---|
| -12.09974 | 0.3480851 | 2 | Phillips-Perron Unit Root Test | stationary |
| statistic | p.value | parameter | method |
|---|---|---|---|
| 0.1838134 | 0.1 | 3 | KPSS Test for Level Stationarity |
STEP 5: Normality tests were run using the tseries package. These were also transposed into tables for ease of viewing. ##### ANH Cash Ratio Normality Test Results
| x |
|---|
| 4.210245 |
| x |
|---|
| 21.62827 |
| statistic | p.value | parameter | method |
|---|---|---|---|
| 557.2226 | 0 | 2 | Jarque Bera Test |
ANH Bid-Ask Spread Normality Test Results
| x |
|---|
| 3.544539 |
| x |
|---|
| 16.67535 |
| statistic | p.value | parameter | method |
|---|---|---|---|
| 316.3604 | 0 | 2 | Jarque Bera Test |
ANH Tobin’s Q Normality Test Results
| x |
|---|
| 0.3248102 |
| x |
|---|
| 2.347 |
| statistic | p.value | parameter | method |
|---|---|---|---|
| 1.131221 | 0.5680134 | 2 | Jarque Bera Test |
STEP 6: GARCH and ARMA tests were conducted making use of the tseries package. The results were manipulated into tables as with the abovementioned tests. ##### ANH GARCH Results
***** ESTIMATION WITH ANALYTICAL GRADIENT *****
I INITIAL X(I) D(I)
1 7.468033e-02 1.000e+00
2 5.000000e-02 1.000e+00
3 5.000000e-02 1.000e+00
IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
0 1 -5.310e+00
1 4 -8.603e+00 3.83e-01 6.09e+00 6.1e-01 9.6e+02 2.3e-01 2.92e+03
2 6 -8.890e+00 3.22e-02 2.49e-02 1.8e-02 3.1e+00 1.2e-02 2.02e+00
3 9 -1.086e+01 1.81e-01 1.70e-01 1.7e-01 1.9e+00 9.3e-02 1.16e+00
4 11 -1.110e+01 2.16e-02 2.41e-02 4.4e-02 9.7e+00 1.9e-02 1.40e+00
5 12 -1.122e+01 1.08e-02 1.99e-02 9.6e-02 2.2e+00 3.7e-02 6.34e-01
6 14 -1.125e+01 2.45e-03 2.53e-03 1.1e-02 6.5e+00 3.7e-03 5.47e-01
7 16 -1.130e+01 5.15e-03 4.66e-03 3.5e-02 2.0e+00 1.5e-02 5.54e-01
8 18 -1.132e+01 9.48e-04 9.61e-04 8.5e-03 2.2e+01 3.0e-03 5.26e-01
9 20 -1.134e+01 1.77e-03 1.79e-03 1.8e-02 4.7e+00 6.1e-03 2.58e-01
10 22 -1.134e+01 3.39e-04 3.40e-04 3.5e-03 1.2e+02 1.2e-03 9.94e-02
11 24 -1.134e+01 6.70e-05 6.69e-05 7.0e-04 2.7e+02 2.4e-04 1.32e-02
12 27 -1.135e+01 5.26e-04 5.25e-04 5.6e-03 8.9e+00 1.9e-03 1.21e-02
13 31 -1.135e+01 1.03e-06 1.03e-06 1.1e-05 1.4e+04 3.9e-06 1.02e-02
14 33 -1.135e+01 2.06e-06 2.06e-06 2.2e-05 1.6e+03 7.8e-06 9.15e-03
15 35 -1.135e+01 4.13e-06 4.12e-06 4.5e-05 7.9e+02 1.6e-05 9.14e-03
16 38 -1.135e+01 8.25e-08 8.23e-08 9.0e-07 1.6e+05 3.1e-07 9.13e-03
17 40 -1.135e+01 1.65e-07 1.65e-07 1.8e-06 2.0e+04 6.2e-07 9.12e-03
18 42 -1.135e+01 3.30e-08 3.29e-08 3.6e-07 4.0e+05 1.2e-07 9.12e-03
19 44 -1.135e+01 6.60e-08 6.59e-08 7.2e-07 4.9e+04 2.5e-07 9.12e-03
20 46 -1.135e+01 1.32e-08 1.32e-08 1.4e-07 9.9e+05 5.0e-08 9.12e-03
21 48 -1.135e+01 2.64e-08 2.63e-08 2.9e-07 1.2e+05 9.9e-08 9.12e-03
22 50 -1.135e+01 5.28e-09 5.27e-09 5.8e-08 2.5e+06 2.0e-08 9.12e-03
23 52 -1.135e+01 1.06e-08 1.05e-08 1.2e-07 3.1e+05 4.0e-08 9.12e-03
24 54 -1.135e+01 2.11e-08 2.11e-08 2.3e-07 1.5e+05 7.9e-08 9.12e-03
25 57 -1.135e+01 4.23e-10 4.22e-10 4.6e-09 3.1e+07 1.6e-09 9.12e-03
26 59 -1.135e+01 8.45e-10 8.43e-10 9.2e-09 3.9e+06 3.2e-09 9.12e-03
27 61 -1.135e+01 1.69e-10 1.69e-10 1.8e-09 7.7e+07 6.3e-10 9.12e-03
28 63 -1.135e+01 3.38e-10 3.37e-10 3.7e-09 9.7e+06 1.3e-09 9.12e-03
29 65 -1.135e+01 6.76e-11 6.74e-11 7.4e-10 1.9e+08 2.5e-10 9.12e-03
30 67 -1.135e+01 1.35e-10 1.35e-10 1.5e-09 2.4e+07 5.1e-10 9.12e-03
31 69 -1.135e+01 2.70e-11 2.70e-11 2.9e-10 4.8e+08 1.0e-10 9.12e-03
32 71 -1.135e+01 5.41e-12 5.40e-12 5.9e-11 2.4e+09 2.0e-11 9.12e-03
33 73 -1.135e+01 1.08e-11 1.08e-11 1.2e-10 3.0e+08 4.1e-11 9.12e-03
34 75 -1.135e+01 2.16e-12 2.16e-12 2.4e-11 6.0e+09 8.1e-12 9.12e-03
35 77 -1.135e+01 4.33e-12 4.32e-12 4.7e-11 7.5e+08 1.6e-11 9.12e-03
36 79 -1.135e+01 8.65e-12 8.63e-12 9.4e-11 3.8e+08 3.3e-11 9.12e-03
37 82 -1.135e+01 1.73e-13 1.73e-13 1.9e-12 7.5e+10 6.5e-13 9.12e-03
38 84 -1.135e+01 3.43e-14 3.45e-14 3.8e-13 3.8e+11 1.3e-13 9.12e-03
39 86 -1.135e+01 7.20e-15 6.91e-15 7.5e-14 1.9e+12 2.6e-14 9.12e-03
40 88 -1.135e+01 1.57e-15 1.38e-15 1.5e-14 9.4e+12 5.2e-15 9.16e-03
41 90 -1.135e+01 3.13e-16 2.76e-16 3.0e-15 4.7e+13 1.0e-15 9.20e-03
42 91 -1.135e+01 -8.81e+08 5.53e-16 6.0e-15 2.4e+13 2.1e-15 1.08e-02
***** FALSE CONVERGENCE *****
FUNCTION -1.134612e+01 RELDX 6.039e-15
FUNC. EVALS 91 GRAD. EVALS 42
PRELDF 5.525e-16 NPRELDF 1.077e-02
I FINAL X(I) D(I) G(I)
1 1.714025e-01 1.000e+00 -2.870e-01
2 2.636656e-16 1.000e+00 2.999e+00
3 2.818011e-02 1.000e+00 -7.533e-02| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| a0 | 0.1714025 | 7.4333675 | 0.0230585 | 0.9816036 |
| a1 | 0.0000000 | 0.3966769 | 0.0000000 | 1.0000000 |
| b1 | 0.0281801 | 42.1574572 | 0.0006684 | 0.9994667 |
***** ESTIMATION WITH ANALYTICAL GRADIENT *****
I INITIAL X(I) D(I)
1 7.696813e+04 1.000e+00
2 5.000000e-02 1.000e+00
3 5.000000e-02 1.000e+00
IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
0 1 2.133e+02
1 2 2.072e+02 2.88e-02 2.71e-01 6.0e-06 5.9e+01 1.0e+00 7.99e+00
2 4 2.057e+02 7.01e-03 7.26e-03 6.3e-07 5.1e+00 1.0e-01 3.21e-01
3 5 2.039e+02 8.87e-03 7.24e-03 1.3e-06 2.3e+00 2.0e-01 7.80e-03
4 7 2.037e+02 6.34e-04 6.25e-04 1.3e-07 1.3e+01 2.0e-02 9.92e-03
5 9 2.035e+02 1.18e-03 1.17e-03 2.6e-07 3.3e+00 4.0e-02 2.69e-02
6 11 2.031e+02 2.15e-03 2.06e-03 5.2e-07 2.4e+00 8.0e-02 3.84e-02
7 14 2.031e+02 4.23e-05 4.23e-05 1.0e-08 1.6e+03 1.6e-03 1.85e-01
8 16 2.030e+02 8.42e-05 8.43e-05 2.0e-08 7.0e+01 3.2e-03 6.83e-02
9 18 2.030e+02 1.66e-04 1.67e-04 4.1e-08 2.5e+01 6.4e-03 3.70e-02
10 21 2.030e+02 3.29e-06 3.29e-06 8.1e-10 2.5e+03 1.3e-04 1.37e-02
11 23 2.030e+02 6.57e-06 6.57e-06 1.6e-09 2.1e+02 2.6e-04 8.36e-03
12 25 2.030e+02 1.31e-06 1.31e-06 3.3e-10 4.1e+03 5.1e-05 8.12e-03
13 28 2.030e+02 1.05e-05 1.05e-05 2.6e-09 1.3e+02 4.1e-04 7.94e-03
14 33 2.030e+02 2.10e-09 2.10e-09 5.2e-13 2.4e+06 8.2e-08 7.66e-03
15 35 2.030e+02 4.20e-09 4.20e-09 1.0e-12 3.0e+05 1.6e-07 7.44e-03
16 37 2.030e+02 8.39e-10 8.39e-10 2.1e-13 5.9e+06 3.3e-08 7.44e-03
17 39 2.030e+02 1.68e-09 1.68e-09 4.2e-13 7.4e+05 6.6e-08 7.44e-03
18 41 2.030e+02 3.36e-10 3.36e-10 8.3e-14 1.5e+07 1.3e-08 7.44e-03
19 43 2.030e+02 6.71e-10 6.71e-10 1.7e-13 1.9e+06 2.6e-08 7.44e-03
20 45 2.030e+02 1.34e-09 1.34e-09 3.3e-13 9.3e+05 5.2e-08 7.44e-03
21 48 2.030e+02 2.69e-11 2.69e-11 6.7e-15 1.9e+08 1.0e-09 7.44e-03
22 50 2.030e+02 5.37e-11 5.37e-11 1.3e-14 2.3e+07 2.1e-09 7.44e-03
23 52 2.030e+02 1.07e-11 1.07e-11 2.7e-15 4.6e+08 4.2e-10 7.44e-03
24 53 2.030e+02 -4.93e+07 2.15e-11 5.3e-15 2.3e+08 8.4e-10 7.44e-03
***** FALSE CONVERGENCE *****
FUNCTION 2.030047e+02 RELDX 5.325e-15
FUNC. EVALS 53 GRAD. EVALS 24
PRELDF 2.148e-11 NPRELDF 7.438e-03
I FINAL X(I) D(I) G(I)
1 7.696813e+04 1.000e+00 1.732e-05
2 8.874647e-01 1.000e+00 -1.104e+00
3 4.156519e-10 1.000e+00 5.080e+00| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| a0 | 7.696813e+04 | 1.445565e+05 | 0.5324431 | 0.5944191 |
| a1 | 8.874647e-01 | 8.691116e-01 | 1.0211171 | 0.3071990 |
| b1 | 0.000000e+00 | 2.515097e-01 | 0.0000000 | 1.0000000 |
***** ESTIMATION WITH ANALYTICAL GRADIENT *****
I INITIAL X(I) D(I)
1 6.031197e-02 1.000e+00
2 5.000000e-02 1.000e+00
3 5.000000e-02 1.000e+00
IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
0 1 1.750e+02
1 2 3.101e+01 8.23e-01 1.53e+01 9.0e-01 2.7e+03 1.0e+00 2.04e+04
2 4 3.082e+01 6.02e-03 6.44e-03 2.6e-02 1.9e+00 5.0e-02 2.61e-01
3 6 3.078e+01 1.36e-03 1.16e-03 3.9e-03 3.9e+00 1.0e-02 8.65e-03
4 8 3.055e+01 7.46e-03 7.56e-03 3.2e-02 2.8e+00 8.0e-02 9.53e-03
5 10 3.053e+01 4.94e-04 4.97e-04 3.8e-03 6.6e+00 1.0e-02 1.64e-03
6 12 3.053e+01 8.65e-05 8.65e-05 7.5e-04 2.3e+01 2.0e-03 1.09e-03
7 14 3.053e+01 1.61e-04 1.61e-04 1.5e-03 3.6e+00 4.0e-03 1.00e-03
8 16 3.052e+01 2.71e-04 2.72e-04 3.1e-03 2.2e+00 8.0e-03 8.37e-04
9 18 3.052e+01 4.63e-05 4.63e-05 6.4e-04 1.9e+01 1.6e-03 5.61e-04
10 20 3.052e+01 8.93e-06 8.93e-06 1.3e-04 8.5e+01 3.2e-04 5.16e-04
11 22 3.052e+01 1.77e-06 1.77e-06 2.6e-05 4.2e+02 6.4e-05 5.08e-04
12 24 3.052e+01 3.53e-06 3.53e-06 5.2e-05 5.3e+01 1.3e-04 5.06e-04
13 26 3.052e+01 7.02e-06 7.02e-06 1.0e-04 2.7e+01 2.6e-04 5.03e-04
14 29 3.052e+01 1.40e-07 1.40e-07 2.1e-06 5.1e+03 5.1e-06 4.96e-04
15 31 3.052e+01 2.79e-07 2.79e-07 4.2e-06 6.4e+02 1.0e-05 4.96e-04
16 33 3.052e+01 5.58e-08 5.58e-08 8.4e-07 1.3e+04 2.0e-06 4.95e-04
17 35 3.052e+01 1.12e-08 1.12e-08 1.7e-07 6.4e+04 4.1e-07 4.95e-04
18 37 3.052e+01 2.23e-08 2.23e-08 3.4e-07 8.0e+03 8.2e-07 4.95e-04
19 39 3.052e+01 4.47e-09 4.47e-09 6.7e-08 1.6e+05 1.6e-07 4.95e-04
20 41 3.052e+01 8.93e-09 8.93e-09 1.3e-07 2.0e+04 3.3e-07 4.95e-04
21 43 3.052e+01 1.79e-09 1.79e-09 2.7e-08 4.0e+05 6.6e-08 4.95e-04
22 45 3.052e+01 3.57e-10 3.57e-10 5.4e-09 2.0e+06 1.3e-08 4.95e-04
23 47 3.052e+01 7.15e-10 7.15e-10 1.1e-08 2.5e+05 2.6e-08 4.95e-04
24 49 3.052e+01 1.43e-09 1.43e-09 2.1e-08 1.2e+05 5.2e-08 4.95e-04
25 51 3.052e+01 2.86e-10 2.86e-10 4.3e-09 2.5e+06 1.0e-08 4.95e-04
26 54 3.052e+01 5.72e-12 5.72e-12 8.6e-11 1.2e+08 2.1e-10 4.95e-04
27 56 3.052e+01 1.14e-12 1.14e-12 1.7e-11 6.2e+08 4.2e-11 4.95e-04
28 59 3.052e+01 9.15e-12 9.15e-12 1.4e-10 1.9e+07 3.4e-10 4.95e-04
29 62 3.052e+01 1.83e-13 1.83e-13 2.7e-12 3.9e+09 6.7e-12 4.95e-04
30 64 3.052e+01 3.66e-13 3.66e-13 5.5e-12 4.9e+08 1.3e-11 4.95e-04
31 66 3.052e+01 7.32e-14 7.32e-14 1.1e-12 9.7e+09 2.7e-12 4.95e-04
32 68 3.052e+01 1.46e-13 1.46e-13 2.2e-12 1.2e+09 5.4e-12 4.95e-04
33 70 3.052e+01 2.90e-14 2.93e-14 4.4e-13 2.4e+10 1.1e-12 4.95e-04
34 72 3.052e+01 5.89e-14 5.85e-14 8.8e-13 3.0e+09 2.1e-12 4.95e-04
35 74 3.052e+01 1.15e-14 1.17e-14 1.8e-13 6.1e+10 4.3e-13 4.95e-04
36 76 3.052e+01 2.21e-15 2.34e-15 3.5e-14 3.0e+11 8.6e-14 4.95e-04
37 78 3.052e+01 4.77e-15 4.68e-15 7.0e-14 3.8e+10 1.7e-13 4.95e-04
38 80 3.052e+01 9.31e-16 9.37e-16 1.4e-14 7.6e+11 3.4e-14 4.95e-04
39 82 3.052e+01 1.63e-15 1.87e-15 2.8e-14 9.9e+10 6.9e-14 4.95e-04
40 84 3.052e+01 6.99e-16 3.75e-16 5.6e-15 1.9e+12 1.4e-14 4.95e-04
41 86 3.052e+01 6.99e-16 7.49e-16 1.1e-14 2.4e+11 2.8e-14 4.95e-04
42 88 3.052e+01 1.51e-15 1.50e-15 2.3e-14 1.2e+11 5.5e-14 4.95e-04
43 90 3.052e+01 -3.28e+08 3.00e-16 4.5e-15 2.4e+12 1.1e-14 4.95e-04
***** FALSE CONVERGENCE *****
FUNCTION 3.051616e+01 RELDX 4.531e-15
FUNC. EVALS 90 GRAD. EVALS 43
PRELDF 2.997e-16 NPRELDF 4.950e-04
I FINAL X(I) D(I) G(I)
1 3.979787e-01 1.000e+00 1.603e-01
2 9.066644e-01 1.000e+00 6.165e-01
3 1.927955e-15 1.000e+00 5.339e-01| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| a0 | 0.3979787 | 21.237439 | 0.0187395 | 0.9850489 |
| a1 | 0.9066644 | 7.961838 | 0.1138763 | 0.9093359 |
| b1 | 0.0000000 | 9.934228 | 0.0000000 | 1.0000000 |
ANH ARMA Results
Call:
arma(x = CRR$`ANH SJ Equity`)
Coefficient(s):
ar1 ma1 intercept
0.985697 -1.429753 -0.001061
Call:
arma(x = BASR$`ANH SJ Equity`)
Coefficient(s):
ar1 ma1 intercept
1.086 -1.345 -16.324
Call:
arma(x = TQR$`ANH SJ Equity`)
Coefficient(s):
ar1 ma1 intercept
0.61586 -0.01218 0.61909 Pearson Correlation Matrix
The Pearson correlation matrix measures the linear correlation between two variables, in order to test for multicollinearity (Carrion-i-Silvestre, & Sansó, 2006). It is important to ensure that the data in this study does not illustrate any autocorrelation or multicollinearity between the variables; the correlation between variables will diminish the quality of the relationship between liquidity and firm value that this study aims to investigate.
STEP 7: Correlation tests were run. In addition to the Pearson test, the Spearman and Kendall tests were conducted in order to ensure a robust set of results were found. ##### Correlation Test Results
| estimate | statistic | p.value | parameter | conf.low | conf.high | method | alternative |
|---|---|---|---|---|---|---|---|
| -0.0802309 | -1.759779 | 0.0790849 | 478 | -0.1685213 | 0.0093366 | Pearson’s product-moment correlation | two.sided |
| estimate | statistic | p.value | method | alternative |
|---|---|---|---|---|
| -0.1102179 | 20463447 | 0.0156998 | Spearman’s rank correlation rho | two.sided |
| estimate | statistic | p.value | method | alternative |
|---|---|---|---|---|
| -0.0698372 | -2.286609 | 0.0222187 | Kendall’s rank correlation tau | two.sided |
| estimate | statistic | p.value | parameter | conf.low | conf.high | method | alternative |
|---|---|---|---|---|---|---|---|
| -0.0316522 | -0.6923666 | 0.4890433 | 478 | -0.1208105 | 0.0580126 | Pearson’s product-moment correlation | two.sided |
| estimate | statistic | p.value | method | alternative |
|---|---|---|---|---|
| 0.1921445 | 14890328 | 2.25e-05 | Spearman’s rank correlation rho | two.sided |
| estimate | statistic | p.value | method | alternative |
|---|---|---|---|---|
| 0.1272635 | 4.166769 | 3.09e-05 | Kendall’s rank correlation tau | two.sided |
STEP 8: The unit roots of the data were plotted. ##### ACF, PACF and Unit Root Plots
| lag | acf |
|---|---|
| 0 | 1.0000000 |
| 1 | 0.0726341 |
| 2 | 0.0474427 |
| 3 | 0.0878762 |
| 4 | 0.0491821 |
| 5 | 0.0363731 |
| 6 | 0.0061307 |
| 7 | 0.2716310 |
| 8 | -0.0574859 |
| 9 | -0.0209035 |
| 10 | -0.0228550 |
| 11 | -0.0216141 |
| 12 | -0.0246261 |
| 13 | -0.0514566 |
| 14 | 0.0411613 |
| 15 | -0.1165288 |
| lag | acf |
|---|---|
| 1 | 0.0726341 |
| 2 | 0.0423906 |
| 3 | 0.0820770 |
| 4 | 0.0361712 |
| 5 | 0.0241174 |
| 6 | -0.0082290 |
| 7 | 0.2666546 |
| 8 | -0.1071792 |
| 9 | -0.0305288 |
| 10 | -0.0612913 |
| 11 | -0.0183737 |
| 12 | -0.0274555 |
| 13 | -0.0317830 |
| 14 | -0.0205516 |
| 15 | -0.0722298 |
| lag | acf |
|---|---|
| 0 | 1.0000000 |
| 1 | 0.2223909 |
| 2 | 0.1525661 |
| 3 | 0.1023416 |
| 4 | 0.2048958 |
| 5 | 0.1975029 |
| 6 | 0.2780695 |
| 7 | 0.0742906 |
| 8 | 0.0234894 |
| 9 | -0.0530754 |
| 10 | -0.0503504 |
| 11 | -0.0601418 |
| 12 | -0.0408967 |
| 13 | -0.0243932 |
| 14 | -0.0791361 |
| 15 | -0.0930621 |
| lag | acf |
|---|---|
| 1 | 0.2223909 |
| 2 | 0.1084733 |
| 3 | 0.0510660 |
| 4 | 0.1695047 |
| 5 | 0.1218971 |
| 6 | 0.1997947 |
| 7 | -0.0547493 |
| 8 | -0.0716960 |
| 9 | -0.1326891 |
| 10 | -0.1379943 |
| 11 | -0.1085995 |
| 12 | -0.0631955 |
| 13 | 0.0472229 |
| 14 | 0.0087513 |
| 15 | 0.0362437 |
| lag | acf |
|---|---|
| 0 | 1.0000000 |
| 1 | 0.5757199 |
| 2 | 0.3308634 |
| 3 | 0.1925086 |
| 4 | 0.0026801 |
| 5 | -0.0647363 |
| 6 | -0.2499209 |
| 7 | -0.2531007 |
| 8 | -0.1803171 |
| 9 | -0.2064241 |
| 10 | -0.1381732 |
| 11 | -0.0949936 |
| 12 | -0.1153724 |
| 13 | -0.1197062 |
| 14 | -0.0498270 |
| 15 | 0.1260122 |
| lag | acf |
|---|---|
| 1 | 0.5757199 |
| 2 | -0.0008827 |
| 3 | 0.0035360 |
| 4 | -0.1635195 |
| 5 | -0.0058898 |
| 6 | -0.2690919 |
| 7 | 0.0392478 |
| 8 | 0.0141052 |
| 9 | -0.0903555 |
| 10 | -0.0048107 |
| 11 | -0.0147481 |
| 12 | -0.1386196 |
| 13 | -0.0971943 |
| 14 | 0.0997774 |
| 15 | 0.1931402 |
Series: CRR$`ANH SJ Equity`
ARIMA(0,1,1)
Coefficients:
ma1
-0.8604
s.e. 0.0985
sigma^2 estimated as 0.08699: log likelihood=-6.3
AIC=16.61 AICc=17.03 BIC=19.47
Training set error measures:
ME RMSE MAE MPE MAPE MASE
Training set 0.04716468 0.2855799 0.1292126 -3.395246 32.40907 0.7714182
ACF1
Training set -0.08216305
Series: BASR$`ANH SJ Equity`
ARIMA(0,1,1)
Coefficients:
ma1
-0.8007
s.e. 0.0970
sigma^2 estimated as 80133: log likelihood=-219.01
AIC=442.02 AICc=442.45 BIC=444.89
Training set error measures:
ME RMSE MAE MPE MAPE MASE
Training set -48.67193 274.0892 155.5461 -32.88887 42.10253 1.12912
ACF1
Training set -0.06832392
Series: TQR$`ANH SJ Equity`
ARIMA(1,0,0) with non-zero mean
Coefficients:
ar1 mean
0.6036 1.5876
s.e. 0.1421 0.0879
sigma^2 estimated as 0.04438: log likelihood=5.24
AIC=-4.48 AICc=-3.62 BIC=-0.08
Training set error measures:
ME RMSE MAE MPE MAPE MASE
Training set 0.004678813 0.2039689 0.1433988 -1.432472 9.347842 0.9511649
ACF1
Training set -0.005562654
VECM And Cointegration
A vector error correction model (VECM) is designed for use with nonstationary series that are known to be cointegrated. The cointegration term is known as the error correction term since the deviation from long-run equilibrium is corrected gradually through a series of partial short-run adjustments (Carrion-i-Silvestre, & Sansó, 2006). Cointegration is a possible characteristic of time series data. It is defined through concepts of stationarity and the order of integration of the series (Carrion-i-Silvestre, & Sansó, 2006). A stationary series is one with a mean value which will not vary with the sampling period. The study conducted by Andrei & Andrei (2015) which investigates the use of VECM in explaining the association of some macroeconomic variables in Romania provides the grounds for the use of a similar methodology in this research proposal based on the nature of the time series data.
The regression equation form for VECM is as follows:
STEP 9: In this step, a Vector Error Correlation model was run using the tsDyn package. I was able to create a multivariate model by adding an exogen to the existing function.I have supressed the unncessary results in order to avoid clutter.
library(tsDyn)
bounds = list(a=c(CRR> 0))
bounds = list(a=c(BASR> 0))
bounds = list(a=c(TQR> 0))
VECM1 <- VECM(CRR, lag = 1, r = 1, include = c("none"),
beta = NULL, estim = c("2OLS"), LRinclude = c("none"), exogen = TQR)
VECM2 <- VECM(BASR, lag = 1, r = 1, include = c("none"),
beta = NULL, estim = c("2OLS"), LRinclude = c("none"), exogen = TQR)library(kableExtra)
kable(tidy(VECM1$coefficients))%>%
kable_styling(bootstrap_options = "striped", full_width = T, position = "left")%>%
scroll_box(width = "750px", height = "600px")| .rownames | ECT | ANH.SJ.Equity..1 | BTI.SJ.Equity..1 | BIL.SJ.Equity..1 | AGL.SJ.Equity..1 | SOL.SJ.Equity..1 | MTN.SJ.Equity..1 | AMS.SJ.Equity..1 | SHP.SJ.Equity..1 | REM.SJ.Equity..1 | APN.SJ.Equity..1 | HMN.SJ.Equity..1 | BVT.SJ.Equity..1 | EXX.SJ.Equity..1 | MRP.SJ.Equity..1 | TBS.SJ.Equity..1 | ANH.SJ.Equity | BTI.SJ.Equity | BIL.SJ.Equity | AGL.SJ.Equity | SOL.SJ.Equity | MTN.SJ.Equity | AMS.SJ.Equity | SHP.SJ.Equity | REM.SJ.Equity | APN.SJ.Equity | HMN.SJ.Equity | BVT.SJ.Equity | EXX.SJ.Equity | MRP.SJ.Equity | TBS.SJ.Equity |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Equation ANH SJ Equity | -0.4052249 | 0.1229058 | -4.1801791 | -1.0326822 | -1.4398304 | 0.0815695 | 0.7566044 | -0.1304156 | 1.5336859 | 0.4447693 | -0.7985915 | -0.1643748 | -1.4071576 | 0.5825052 | 0.4164346 | -0.3108212 | 0.9937676 | 0.1760452 | 1.1905617 | 0.0602651 | -0.2720087 | -0.4505315 | -0.1130371 | -0.4719674 | -0.7184080 | -0.1048291 | -0.3966720 | -0.6169612 | -0.1295535 | 0.2342045 | NA |
| Equation BTI SJ Equity | -0.3983218 | 0.2486507 | -0.3348103 | -0.0766260 | 0.1772351 | 0.3955999 | 0.4845295 | -0.2325224 | -0.2463932 | 0.0454104 | 0.4437431 | 0.0035350 | -1.0157467 | -0.0729026 | -0.1770201 | 0.7624818 | -0.3908449 | -0.1126649 | -0.3491817 | -0.0849927 | -0.0757887 | 0.0185435 | 0.1493602 | 0.2072877 | 0.1564022 | 0.0769002 | 0.8142849 | -0.0110941 | -0.0049395 | -0.0372125 | NA |
| Equation BIL SJ Equity | 1.4874451 | -0.7193952 | -3.6563369 | 0.0793882 | -0.3677164 | -0.0790798 | 1.9200706 | 1.4259607 | 0.2542709 | 0.1644179 | -0.6856143 | -0.2689126 | 1.7926290 | 0.1551274 | 0.4225425 | -4.8147092 | 1.2678693 | -0.0513354 | -0.2669480 | 3.6906374 | 0.2025448 | -0.2996937 | -1.0836180 | -0.0814204 | -0.5871900 | 0.4320762 | -1.2114447 | -1.1860701 | -0.1602979 | 0.0358390 | NA |
| Equation AGL SJ Equity | 2.0256538 | -1.0930418 | -1.2550391 | -0.2345288 | -0.2361108 | -0.7882497 | 0.1848288 | -0.1955028 | -1.4071324 | 0.0691648 | -0.5398583 | -0.2189960 | 0.4718024 | 0.3255354 | 0.8037323 | -3.0506729 | 1.8277107 | 0.1071886 | 0.2266992 | 2.4749255 | 0.1954684 | 0.0079032 | -0.8340208 | -0.3663705 | -1.0022395 | 0.0927071 | -2.8175725 | -0.6001668 | 0.0258008 | 0.0992404 | NA |
| Equation SOL SJ Equity | 0.6765990 | -0.2457572 | -1.8677060 | 0.1421278 | -0.1436696 | -0.4510320 | -0.4450746 | 0.5903587 | 0.6397572 | -0.0472818 | -0.4063075 | 0.2041698 | 1.3349853 | 0.0768505 | 0.5192745 | -2.0579839 | 0.7881348 | 0.0298352 | 0.4722966 | 1.0675951 | 0.2577873 | 0.0534467 | -0.5361462 | -0.2560360 | -0.1576891 | 0.0832451 | -0.7485608 | -0.9892982 | -0.1360658 | 0.0675299 | NA |
| Equation MTN SJ Equity | -0.5636063 | 0.2905883 | 1.1461887 | 0.0283225 | -0.5259213 | -0.5335222 | -1.2395731 | -0.3099667 | 0.5905656 | -0.1611738 | 0.1962580 | 0.2832931 | -0.6176549 | 0.0547217 | -0.2547463 | 1.0828640 | -0.9772048 | 0.1962426 | 0.5722639 | -2.3792676 | -0.2059706 | 0.0589620 | 0.5742339 | -0.2053874 | 0.1407970 | -0.3346257 | 2.2176697 | 0.0520508 | 0.2497157 | 0.0841483 | NA |
| Equation AMS SJ Equity | 0.2274757 | -0.3958430 | 1.6025912 | -0.3098226 | -0.1415458 | -0.7392660 | -1.5161634 | -0.4136796 | -0.0287127 | -0.2130149 | 0.3918843 | -0.0458854 | -0.5758425 | -0.0813013 | 0.5552273 | 0.1879445 | -0.4293671 | 0.0801643 | 0.2950362 | -1.7663143 | -0.2642968 | -0.0984432 | 0.4381800 | -0.0755666 | 0.7274741 | -0.1721960 | 1.9462421 | -0.3705784 | 0.1482447 | -0.0150780 | NA |
| Equation SHP SJ Equity | 0.0314963 | -0.0019206 | 1.0460572 | -0.0186836 | 0.2160850 | -0.2386482 | -0.5797201 | -0.2146995 | -0.2957457 | -0.0926439 | 0.1515897 | 0.0315730 | 0.3270204 | 0.0283563 | -0.3252641 | -0.1922357 | -0.1736254 | -0.0280712 | -0.1165820 | -0.3639312 | 0.1391172 | 0.0747349 | 0.0902985 | 0.0237961 | 0.0492551 | -0.0090863 | 0.1560114 | 0.0907528 | 0.0822318 | -0.0134073 | NA |
| Equation REM SJ Equity | 4.3388363 | -1.6947495 | -5.9980432 | 0.2937686 | 3.1246819 | 3.9484078 | 9.6137733 | 1.4083670 | -6.8299883 | 0.8225464 | -0.7638989 | -2.1240272 | 5.2073279 | -0.2067918 | -1.5581712 | -3.7082721 | 5.2297905 | -1.1519210 | -3.9949263 | 15.6764992 | -0.7277470 | -0.3299400 | -3.4758297 | 1.9690685 | -1.1835149 | 2.5617655 | -12.0961691 | -0.2430921 | -1.1358685 | -0.7137157 | NA |
| Equation APN SJ Equity | 1.0108531 | -0.8021747 | -1.1228313 | -0.0598106 | -0.0687053 | -0.0804569 | -0.0415420 | 0.2104401 | -0.9304158 | -0.0295320 | -0.4678796 | -0.1694266 | 2.6510309 | -0.0550074 | 0.4266262 | -1.7575106 | 0.8481297 | -0.0581615 | 0.0299425 | 1.3524669 | -0.1429029 | 0.2891769 | -0.3705963 | -0.1651890 | -0.3965815 | 0.1195218 | -1.5192783 | -0.3686884 | -0.0488914 | 0.0621003 | NA |
| Equation HMN SJ Equity | 0.0168782 | 0.2403457 | 1.9556083 | 0.2190245 | -0.4522659 | -1.0550149 | -2.2390136 | -0.8430211 | 0.7303309 | -0.2386160 | 0.7627374 | -0.6130764 | -3.4679510 | -0.1760158 | 0.8669952 | 2.2209441 | -0.7324933 | 0.3046148 | 0.5093607 | -3.7707727 | 0.1994667 | 0.4622786 | 1.1602618 | -0.2785891 | 0.3294438 | -0.4746963 | -0.8757857 | 1.0667190 | -0.0225972 | 0.1062419 | NA |
| Equation BVT SJ Equity | 0.0659428 | -0.0300407 | 0.1292939 | 0.0832035 | 0.0267789 | 0.0284542 | -0.0173571 | 0.0036477 | -0.1108080 | 0.0028014 | -0.0981654 | -0.0338014 | 0.1970985 | -0.0050701 | -0.1541749 | 0.0149744 | 0.0192827 | -0.0271167 | -0.0515263 | 0.0765975 | 0.0275791 | -0.0162725 | -0.0052597 | 0.0552600 | -0.0492486 | 0.0620008 | -0.2109945 | 0.0042548 | 0.0058517 | 0.0000236 | NA |
| Equation EXX SJ Equity | -2.0411040 | 0.5712018 | -0.6026311 | 0.1308808 | 0.6647914 | 0.2367492 | 3.2441437 | -0.2983767 | -1.5532361 | 0.1518935 | 0.9157265 | 0.7236558 | -4.1718520 | -0.6908567 | 0.2173068 | -1.5515928 | 0.3193881 | -0.5690627 | -1.7389834 | 2.0064253 | -0.7465877 | -0.0255698 | -0.0376370 | 0.8197337 | 0.7458135 | 0.3737626 | 5.9582611 | -2.6974674 | -0.0859404 | -0.3017540 | NA |
| Equation MRP SJ Equity | 0.1842184 | -0.0407605 | -2.8859605 | 0.3112275 | -0.1673364 | -0.3889045 | 0.7679044 | 0.2301186 | -0.2620571 | 0.1588129 | -0.2415573 | -0.1233284 | -0.5741355 | 0.1428169 | -0.0091471 | -0.8584024 | 0.4622870 | -0.1137717 | 0.1981825 | 0.9569518 | 0.0064048 | 0.0443110 | -0.2459301 | -0.0058251 | -0.6137048 | 0.2918279 | -0.6475989 | -0.5984463 | -0.2004693 | 0.1078852 | NA |
| Equation TBS SJ Equity | 0.0083015 | -0.0687735 | -0.1325696 | 0.4244121 | 0.0784701 | -0.2187727 | -0.1943810 | -0.0875062 | -0.2851813 | -0.0465362 | -0.2416106 | -0.0501124 | 0.7968921 | 0.0014539 | 0.1268197 | -0.5331418 | 0.0968575 | 0.0424854 | 0.1257097 | 0.4952858 | -0.0729363 | 0.0770738 | -0.2262501 | -0.0848231 | -0.0381074 | 0.0427321 | -0.6187643 | -0.0734940 | 0.0493105 | 0.0255314 | NA |
A table illustrating the coefficient results from the VECM for the Cash Ratio v Tobin’s Q
kable(tidy(VECM2$coefficients)) %>%
kable_styling(bootstrap_options = "striped", full_width = T, position = "left")%>%
scroll_box(width = "750px", height = "600px")| .rownames | ECT | ANH.SJ.Equity..1 | BTI.SJ.Equity..1 | BIL.SJ.Equity..1 | AGL.SJ.Equity..1 | SOL.SJ.Equity..1 | MTN.SJ.Equity..1 | AMS.SJ.Equity..1 | SHP.SJ.Equity..1 | REM.SJ.Equity..1 | APN.SJ.Equity..1 | HMN.SJ.Equity..1 | BVT.SJ.Equity..1 | EXX.SJ.Equity..1 | MRP.SJ.Equity..1 | TBS.SJ.Equity..1 | ANH.SJ.Equity | BTI.SJ.Equity | BIL.SJ.Equity | AGL.SJ.Equity | SOL.SJ.Equity | MTN.SJ.Equity | AMS.SJ.Equity | SHP.SJ.Equity | REM.SJ.Equity | APN.SJ.Equity | HMN.SJ.Equity | BVT.SJ.Equity | EXX.SJ.Equity | MRP.SJ.Equity | TBS.SJ.Equity |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Equation ANH SJ Equity | -1.2410702 | -1.0130552 | -26.3351610 | -36.3144286 | 57.9397310 | -94.1910400 | 253.6215460 | 32.9716073 | -3.6555753 | -61.7231418 | 66.5394144 | -42.9180812 | -65.3346553 | 70.7455467 | 31.6272990 | -62.8151056 | 4323.341900 | -245.6696572 | -1075.703896 | -2102.439585 | -3557.026641 | -2491.65070 | 960.880506 | 282.7240099 | 913.3773867 | -826.521566 | 6465.78802 | -37.639488 | 2262.816168 | -587.905383 | NA |
| Equation BTI SJ Equity | 0.0053604 | 0.0056474 | -0.6645171 | -1.6579861 | 1.4944329 | 2.8248776 | -3.3942490 | -0.6589235 | -0.9740275 | 1.2018210 | 1.0423021 | 0.9157130 | 1.5566120 | -1.9815415 | -1.1288160 | 1.3000963 | -79.870730 | 14.9213325 | 52.593243 | 23.900979 | 27.992905 | 59.56779 | -18.478038 | -7.8486242 | 0.7704192 | 17.208225 | -128.65748 | -18.748676 | -54.773926 | 10.897830 | NA |
| Equation BIL SJ Equity | -0.0078200 | 0.0156527 | 0.0879107 | 0.7405203 | -1.0538685 | 3.5689437 | -6.3498228 | -0.9617235 | 0.0496973 | 2.3968815 | -0.3106742 | 1.3313581 | 1.9754730 | -2.2860241 | -2.3844867 | 2.4702463 | -126.278241 | 13.7921708 | 62.705782 | 15.402309 | 98.280467 | 96.38761 | -17.074519 | -22.0920203 | -43.7807048 | 17.107481 | -244.21314 | 21.098544 | -81.775314 | 23.142111 | NA |
| Equation AGL SJ Equity | 0.0077989 | 0.0053500 | 0.1527813 | 1.8499344 | -1.3635861 | 4.0996556 | -9.0191809 | -1.1802737 | 0.2587916 | 2.6684119 | 0.0265694 | 1.5765532 | 2.3027895 | -2.6186540 | -2.8493787 | 2.8957294 | -137.687960 | 14.8445262 | 69.713138 | 6.876573 | 113.884943 | 103.80123 | -16.101498 | -13.0194377 | -34.7136223 | 26.099868 | -284.57651 | 16.706424 | -101.847374 | 20.998918 | NA |
| Equation SOL SJ Equity | 0.0509539 | -0.0527168 | 0.5173119 | -4.6941426 | 6.5710532 | 5.5622943 | -16.5052349 | -1.4263187 | 0.5935473 | 4.7485949 | 1.3035691 | 1.6631089 | 0.6666199 | -4.5383852 | -2.8865636 | 5.4098416 | -135.681993 | 20.7032796 | 205.965978 | -356.756466 | 183.971769 | 136.80124 | 44.908914 | -37.2815737 | 52.9053171 | -42.262372 | -617.49918 | 173.293008 | -129.533648 | 25.091679 | NA |
| Equation MTN SJ Equity | 0.0161623 | -0.0098875 | 0.0705109 | -1.2470683 | 1.1797895 | 1.1129517 | -1.6901645 | -0.3590143 | 0.2075649 | 0.7084654 | -0.1602889 | 0.3484274 | -0.0036626 | -0.8181294 | -0.6311084 | 0.3844268 | -27.278443 | 1.7407870 | 14.622573 | -16.367183 | 33.493839 | 23.51526 | 2.527015 | -1.7380782 | -18.6676030 | 6.106541 | -76.68476 | 18.839148 | -26.167685 | 4.335295 | NA |
| Equation AMS SJ Equity | -0.1044494 | -0.0069450 | 0.0968780 | -0.2463887 | -2.3016780 | -8.0725369 | 12.2823596 | 2.0109582 | 0.0787183 | -3.1506996 | 1.6742993 | -2.9515592 | -2.3323223 | 5.4833422 | 4.6916995 | -2.3036424 | 236.156721 | -17.3491609 | 3.915339 | -206.548869 | -207.026647 | -148.99257 | 33.277311 | -12.6070201 | 210.4170132 | -86.775349 | 149.80123 | 41.678853 | 190.964243 | -23.399259 | NA |
| Equation SHP SJ Equity | 0.0855220 | -0.0496926 | 0.4298545 | 0.3217464 | 1.4611487 | 3.4289882 | -10.2698213 | -0.9125026 | 0.7925174 | 2.4210151 | 0.8170858 | 1.0535317 | -1.8805858 | -2.4469135 | -3.6395827 | 3.1913292 | -74.420232 | 6.5038172 | 94.218774 | -212.239439 | 144.566508 | 60.55478 | 32.932900 | -11.8341412 | -2.0807932 | -10.136781 | -290.46403 | 82.731288 | -79.481848 | 11.902245 | NA |
| Equation REM SJ Equity | 0.0250998 | -0.0106059 | 0.3945689 | 0.6815910 | 0.0274151 | 1.4584217 | -4.8699742 | -0.6237844 | 0.8197341 | 0.9487098 | -0.6035871 | 0.5949950 | 0.2636251 | -1.0606038 | -1.3906942 | 1.8434159 | -77.003958 | 12.4630772 | 39.932949 | -103.097991 | 89.984537 | 33.59797 | 16.618565 | -9.6865622 | -7.8669795 | -5.152983 | -137.64285 | 57.836853 | -43.739226 | 8.048343 | NA |
| Equation APN SJ Equity | 0.0635414 | -0.0107111 | 0.7235047 | 1.9843208 | 0.3988019 | 11.2030569 | -23.9027010 | -3.2690054 | 1.0173928 | 6.8204202 | -1.2127856 | 4.1252991 | 5.5202476 | -7.4862508 | -6.9948165 | 7.3161916 | -349.269880 | 30.6109405 | 174.643777 | -59.724050 | 304.456422 | 258.17421 | -14.074495 | -26.2952221 | -87.5792256 | 58.130124 | -664.94002 | 51.420033 | -264.543520 | 50.342035 | NA |
| Equation HMN SJ Equity | 0.6177372 | -0.2057768 | 3.4401954 | 12.8124872 | 2.0175386 | 28.8834399 | -77.3566097 | -9.8696110 | 7.6830285 | 18.8246328 | -0.2287179 | 10.2223770 | -4.3879774 | -20.8806810 | -25.2395480 | 18.5805248 | -610.134047 | 32.3323598 | 304.481578 | -261.655837 | 1247.391892 | 503.00466 | -33.417297 | 2.8524751 | -403.5097118 | 136.680404 | -1878.74494 | 300.324124 | -747.142160 | 70.329602 | NA |
| Equation BVT SJ Equity | 0.0028854 | -0.0047146 | 0.0298779 | -0.1726473 | 0.1264721 | 0.3973835 | -0.3944312 | -0.0455105 | 0.2352354 | 0.2146615 | -0.0284287 | 0.0812563 | 0.3719518 | -0.2182014 | -0.1919699 | 0.3774745 | -17.102197 | -0.6005839 | 10.138113 | -31.029320 | 5.581135 | 11.12675 | 6.631848 | -0.9241802 | 9.6637850 | -3.571127 | -15.31457 | 5.756468 | -4.500436 | 1.961240 | NA |
| Equation EXX SJ Equity | 0.0116127 | -0.0327181 | -0.2344702 | -1.3618512 | 2.4858607 | 1.2505071 | -1.7523956 | -0.0788883 | -0.2082720 | 0.2989272 | 0.7994839 | 0.1605242 | 0.7977216 | -1.1193253 | -0.7780495 | 0.7825198 | 8.797957 | 4.9391178 | 62.347667 | -109.673728 | 11.398932 | 22.75965 | 19.860442 | -14.1026501 | 9.3524002 | -20.964679 | -119.68527 | 33.960679 | -19.804979 | 5.648005 | NA |
| Equation MRP SJ Equity | 0.0459531 | -0.0288486 | 0.4280670 | -3.8205093 | 4.5576968 | 5.2255847 | -10.2875695 | -1.4432104 | 0.2324267 | 3.3645361 | -0.3989785 | 1.6980533 | 2.0827838 | -3.6844447 | -2.9092672 | 3.1184972 | -146.463636 | 16.4278298 | 105.791568 | -143.343554 | 146.702771 | 114.64977 | 16.567526 | -22.8287626 | -26.0637350 | 3.139600 | -356.32397 | 78.113737 | -108.356494 | 23.568255 | NA |
| Equation TBS SJ Equity | 0.0580951 | -0.0660414 | -0.1995845 | -7.2266640 | 8.8988401 | 0.7237750 | -4.3272486 | -0.2505620 | -0.4522267 | 0.8675406 | 1.7336549 | -0.2473028 | -2.5720523 | -0.8733291 | 1.5585554 | -0.5451133 | 48.272696 | 3.0302939 | 42.792523 | -215.301147 | 15.454860 | -15.67361 | 49.444731 | 8.9435056 | 36.6036438 | -16.793489 | -169.37759 | 107.425101 | -14.093556 | -11.573369 | NA |
A table illustrating the coefficient results from the VECM for the Bid-Ask Spread v Tobin’s Q
Granger Causality Test
Granger causality is a way to investigate causality between two variables in a time series (Engel & Granger, 1987). The method is a probabilistic account of causality; it uses empirical data sets to find patterns of correlation. With regards to this research, the causal relationship between the variables of liquidity and firm market value will be tested for causality.
STEP 10: The final step involves a test of causality between the liquidity and firm market value of each firm. The Granger Causality test was run using the zoo and lmtest packages. This is the ultimate step of this research project, and so we end here.
# install.packages("urca")
# install.packages("zoo")
# install.packages("lmtest")
library(zoo)
library(lmtest)
library(urca)
kable(tidy(grangertest.default(CRR$`ANH SJ Equity`, TQR$`ANH SJ Equity`, order = 1)))| res.df | df | statistic | p.value |
|---|---|---|---|
| 28 | NA | NA | NA |
| 29 | -1 | 0.9417632 | 0.3401338 |
| res.df | df | statistic | p.value |
|---|---|---|---|
| 28 | NA | NA | NA |
| 29 | -1 | 1.602337 | 0.2160038 |