Analysis Of Vice Chancellors’ Remuneration Packages In Australia

Descriptive statistics

Descriptive Statistics

The mean remuneration of the states is obtained as 801. This implies that the average remuneration of Vice Chancellors’ in different states of Australia is 801.  The mean of university ranks is 337.  This indicates that average rank of universities obtained from Time Higher education is 337. The mean of studnum is 38410. That means there are 38410 number of students enrolled in the University on an average.

The primary measures of dispersion include standard deviation, variance and range. The range of remuneration is 650. The remuneration to Vice Chancellors lies between 1095 and 445. The standard deviation of remuneration of 168.064.  SD shows the divergence of data points from the mean value. SD is less than average implying the coefficient of variation is less than 1. This means the distribution of remuneration is not much volatile. The range of rand and student number are 416 and 230347 respectively.  The standard deviations of rank and student numbers are 141.6549 and 36641.54944 respectively. This indicates the distribution of rank and student number are dispersed widely from mean.

The estimated regression model of remuneration is

The regression result is obtained as

The coefficient of rank is -0.6867. This implies with 1 percent increase in rank remuneration decline by 0.69 percent. The estimated t value of the coefficient is (-0.6867/0.1635) = -4.2.The critical t value is 2.8. As the absolute value of computed t is greater than the critical t value, the null hypothesis no significant relation between rank and remuneration is rejected. The result is further supported by p value. P value of the estimate is 0.0002. The p value is less than the significance value of 0.05. Therefore, the variable rank is significant at 5% level of significance.

A model of remuneration is to be estimated using log-log specification which is given as follows

The obtained regression result is given below

The coefficient of log (rank) is -0.1650. The implication is that with every 1% increase in log(rank), log(remuneration) falls by 0.17%. The computed t value is (-0.1650/0.0042) =-3.7330. The absolute value of computed t is greater than critical value implying rejection of null hypothesis of no significant relation between log(rank) and log (remuneration). P value for the coefficient is 0.0007. The p value less than significant value of 0.05 which supports the result obtained from critical t value approach. The variable log(rank) therefore is a negative significant determinant of log (remuneration). Higher university rank is an indicator of poor performance. This therefore likely to have an adverse effect on remuneration. The sign of the estimated co-efficient thus matches with the expectation.

Regression model of remuneration on rank

The next mode is t estimate to relate remuneration with rank and number of students

Goodness of the fit of a regression model is determined from the value of R square. The R square value indicates how close the data set are fitted to the estimated regression model. For the fitted model in ii), the R square value is obtained as 0.34. This means rank can explain only 34% variation in remuneration. This is not a good fitted model.  For regression model including more than one independent variable the adjusted R square is used for this purpose. After including student number as an independent variable along with rank R square value increases to 0.50. Now, the independent variables can explain 50% variation in remuneration. The second model is thus fitted well as compared to that in ii.

The log-log model that is to be estimated is

The regression result is obtained as

The estimated regression equation is

The elasticity of remuneration with respect to student number is 0.1475. The computed t value of for studnum is (0.1475/0.0532) = 2.77. The critical t value at 1% level of significance is 2.7195. The computed t value thus falls in the rejection region. The rejection of null hypothesis of no significant relation a statistically significant relation exists between remuneration and student number. The p value of the concerned variable is 0.0089. The p value is less than significance value of 0.01. This again indicates the variable is statistically significant.

The coefficient of rank is -0.1381. Negative sign of the coefficient implies a negative relation between the two variables. The computed t value is (-0.1381/0.0417)= -3.31. The computed t value in absolute term is greater than the critical t value of 2.72 at 1% level of significance. The variable therefore is statistically significant. The corresponding p value is 0.0022. The p value is less than the significance level implying studnum is statistically significant at 1% level of significance.

The new proposed model is

Estimated regression equation

Computed t value for each of the independent variable is

The computed t values for all the four independent variables are less than the critical t value. This indicates all the variables are statistically insignificant. The result obtained from critical t value approach is supported from the p value where all the p values are less than significance value of 0.01.

Simple regression model with a log-log specification

In order to test overall significance F test needs to be conducted

The hypotheses of the F test are

Null hypothesis (H0):

Alternative hypothesis (H1); at least one of βs is not zero.

From the regression result the computed value of F is obtained as

The tabulated value of  at 5% level of significance is 2.668. The computed F value is greater than the tabulated F value. Therefore, the null hypothesis stating the model is overall insignificant is rejected. The model therefore has an overall significance. The p value corresponding to the F statistics is 0.000. As the p value is less than the significance value of 0.05, again suggesting rejection of the null hypothesis. Hence, is can be concluded that the model is overall significant at 5% level of significance.

The critical F value at 1% level of significance is 3.9694. This is again less than computed F value implying an overall significance of the model at 1% level of significance.

In order to test whether Vice Chancellors of universities located in Victoria are paid a higher remuneration as compared to other state, a dummy variable called state dummy generated. The variable assumes a value 1 if the state is Victoria and a value of 0 otherwise. The regression equation to be estimated is

The framed hypothesis is

Null hypothesis (H0): The variable state dummy has no significant relation with remuneration

Alternative Hypothesis (H1): The variable state dummy has a statistically significant relation with remuneration.

The regression results are given below

Computed t value for the state dummy is (0.0401/0.0674) = 0.5952. The computed t value is less than the critical t value of 2.0281 at 1% level of significance. As the t computed t values fall in the acceptance region, it therefore indicates acceptance of the null hypothesis. The state dummy therefore does not have any significant influence on remuneration. The result can be further supported by observing the p value of 0.5558, which is greater than the significance level of 0.05. Therefore, it can be concluded that the Vice Chancellors of Victoria are not likely to receive a higher remuneration as compared to those in other states.

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