Macroeconomic estimation methods and results
One of this project’s key outputs is an estimation of the impact of the gender wage gap on economic performance or GDP as a proxy of economic output. In Appendix D, we discussed the range of approaches that have been taken in previous studies to conduct this type of estimation. We have opted to conduct the estimation using a regression technique based on the expansion of the Solow growth model, similar to that used by Klasen (1999; 2002) and Dollar and Gatti (1999). We consider this endogenous econometrics approach to be the most robust modelling technique for our purposes because it reflects the actual nature of the relationships that exist within the broad macroeconomic framework (based on a widely accepted model) without relying on a very strong assumption about the growth processes such as in an exogenous growth model or the strict structure of the calibration model.
As we are studying the impact of the gender wage gap in a particular country - Australia – we need to use time series data for our estimation (as opposed to cross-sectional data which can be used when a number of countries are being studied together). While both cross-sectional and time series data can pose problems for the type of regression analysis we are undertaking here, a single country, time series analysis has a number of advantages. First, the Solow model was originally built to examine the dynamics of one economy (Solow 2001) and although it can be adapted for cross-country analysis, was not explicitly intended for this purpose. Second, some technical problems common to cross-sectional, multi-country studies are less likely to be experienced in a one country, time series studies such as ours6.
We use data from a variety of Australian Bureau of Statistics sources. The variables we include in the model (along with a measure of the gender wage gap) are those common to macroeconomic analysis of the kind being undertaken here. They are GDP, investment, human capital, fertility, labour participation and hours worked. Issues related to data availability (common in single country studies where data points may be limited) have affected both our modelling approach and our results. These issues are discussed in more detail below. In macroeconomic modelling, the longer the time period of data available, the more likely that such a time span smooths out the ups and downs of the business cycle. As one of our key variables – human capital – was only available from 1989 onwards, we were able to include only 20 data points in our analysis. However, we were able to test and adapt our model to address the issue of a relatively short span of data. Nevertheless, these data limitations should be kept in mind when interpreting our results.
The use of time series data raises the issue of the stability of the data over time – referred to as stationarity (Durlauf et al. 2004). In essence, unless we can be reasonably confident that the variables we use have a consistent average over the long run, we cannot be sure that the relationships we see from a regression analysis are accurate, or if in fact they simply (or partly) capture fluctuations over time in the data. We ran a series of tests related to stationarity (described below) and found that we could not be sufficiently confident of the stationarity of our data without making an additional adaptation to our model
In order to adapt the model to overcome possible problems with stationarity, we used first difference equations, rather than equations which use the data in what is known as a level form. This approach resolves problems of data stationarity by subtracting the equation at time t from the equation at time t-1. While this method means that we lose one observation point, the increased confidence that we have in our results due to ‘first differencing’ the model is very important.
Below we describe the database used in our modelling, including details of our rationale for choosing particular variables and data (including issues of data availability), and the characteristics of the data. We then describe our estimation technique, and present detailed results. Finally we discuss how we come up with an estimation of the total impact to the Australian economy of the gender wage gap, and provide details about the limitations of our modelling.
[ top ]
Data and Variables
In this section we describe the ways in which we have operationalised variables for use within our growth model. We then summarise the chosen variables and the data used at the end of each variable description. Finally, the variables we have used and their data sources are provided in Table E1.
Economic Output
As discussed earlier in this report, economic performance is the main variable of interest in this study and it is often measured by economic output, in particular gross domestic product (GDP). GDP is a suitable measure for examining the performance of developed countries, while for developing countries other measures such as the Human Capital Index and the achievement of Millennium Development Goals have been used to measure economic performance. GDP measures the output produced by activities in the economy. However, when using GDP as a measure of economic performance, a set of decisions needs to be made in relation to definitions (and thus in turn about data).
There are three common approaches used to calculate GDP – value added, expenditure and income (Mankiw 1997). The value added approach measures GDP by summing up all goods and services in the economy subtracted by the intermediate products used to produce them. By doing so, the calculation will not “double count” the products that are part of other products. The second approach is based on income. The income approach to GDP is calculated by summing the income of capital, labour, and entrepreneurship having first deducted the cost of tools and materials. Finally, the expenditure approach uses an assumption that for every seller there is a buyer. Therefore, with the expenditure approach, GDP can be calculated by summing up all consumption, investment, government expenditure and net exports.
Figures of GDP which are based on these three approaches are available in the Australian Bureau of Statistics (ABS) publication Australian National Accounts: National Income, Expenditure and Product (Cat. no. 5206.0) in which quarterly data are available from June 1960 and in the publication Australian System of National Accounts (Cat. no. 5204.0) which provides annual data. Conceptually, the income, expenditure and production approaches to measuring GDP should achieve the same results; however this is dependent upon how the data are derived. In Australia, prior to 1994-95, these estimates were produced independently, and consequently there are statistical discrepancies between each estimate. However, over the period in which these estimates were calculated separately, the ABS also provided a compilation number, representing the average of these three approaches. Since 1994-95, there are no discrepancies between any of the estimates, with the exception of the quarterly estimates for the June 1994 quarter (ABS 2009).
Another issue in relation to the use of GDP as a proxy of economic output is whether to use GDP in constant or current prices. Current price GDP means that the currency amount of products in one economy is calculated based on the price of the product at that year or quarter. However, if our interest in GDP is to conduct economic growth analysis, and as this is based on the production (supply) side of the economy, we need the representation of quantity produced in the economy where the change in the value of output is not merely caused by the current prices of those outputs. The constant price GDP provides this representation since although it is reported in currency units it nevertheless is based on estimated fixed prices in the base year. Therefore, the changes in GDP value will represent the changes in the quantity of goods and services produced, avoiding the effects of price changes on the output calculation. The ABS now uses a chain volume measure of GDP in the Australian System of National Accounts as their measure of constant price GDP. The ABS uses the chain volume measure because it takes into account different growth rates of unit prices of goods and services as well as the growth rate of their quantities, which results in changes in price relativities. The chain index used in chain volume GDP is calculated based on annual changes so that price relativities remain the same (5216.0 - Australian National Accounts: Concepts, Sources and Methods, 2000).
Variable:Gross domestic product (GDP)
Data used: Chain volume measure of GDP, annual series, ABS Australian System of National Accounts (Cat. no. 5204.0)
Capital and Investment
Capital stock is one of the two major inputs that produce economic output (the other is labour). The addition to capital stock is known as ‘investment’. Data measuring capital stock are available annually in the publication Australian System of National Accounts (ABS Cat. no. 5204.0). Investment can be calculated by an increase or decrease in capital stock. However, a more direct measure of investment is gross fixed capital formation, available in the publication Australian National Accounts: National Income, Expenditure and Product (ABS Cat. no. 5206.0) or total capital accumulation and net lending, available in the publication Australian System of National Accounts (ABS Cat. no. 5204.0). We opted to use total capital accumulation and net lending in the Australian System of National Accounts since this takes into account changes in financial capital as well in physical capital. We use this variable measured as a ratio of GDP (i.e. the rate of investment).
In most of the growth models discussed earlier, investment predicts economic performance. This theory is supported by empirical results that estimate the robustness of this variable compared with other growth determinants (Barro 1991, Levine and Renelt 1992, Mankiw et al. 1992, Caselli et al. 1996). Nevertheless, studies that compare the effects of investment and income on economic growth have shown that the superiority of investment as a predictor of economic growth is not as strong as earlier predictions would suggest (Mankiw et al. 1992; Easterly and Levine 2001). Moreover, the direction of causality could be from growth to investment rather than vice versa (Blomstrom et al. 1996). Barro (1996) shares this view by claiming that high growth prospects are one of the main drivers of high investment7.
Variables: Gross fixed capital accumulation (Total investment)
Data used: Chain volume measure of gross fixed capital accumulation, Australian National Accounts: National Income, Expenditure and Product (Cat. No. 5206.0)
Labour and Fertility
In addition to capital, labour is the other major input to economic growth. There are several ways to measure labour input, including the number of people participating in the labour force, hours of work and their cost (i.e. wages). In the publication - Labour Force, Australia, Detailed, Quarterly (Cat. no. 6291.0.55.003), the ABS provides two of the three measures of labour input, which are the number of employed persons by full-time and part-time status and their hours of work. We use these measures rather than a wages measure, as the former are more commonly used in Australian macroeconomic modelling, and in order to better separate our labour variable from our gender wage gap variable (which is, of course, based on wages).
It is also important to include fertility in growth models such as the one we are using in this study. The Solow growth model (on which our estimation technique is based) has a strong assumption of diminishing marginal returns of labour. This means that although an increase in labour is likely to increase economic output, theoretically it will decrease labour productivity if there is no change in other inputs or aspects of the economy. In addition, the model also assumes that the labour force is growing in the rate of population growth. As a result, an increase in labour can also decrease the output or income per capita of an economy given that it is solely boosted by population growth. Most cross-country studies have supported this hypothesis. The strongest result to confirm this negative impact of population growth on economic growth is from Mankiw et al. (1992) while Levine and Renelt (1992) produce a less significant relationship. However, if the fertility rate is controlled for in economic growth models, the impact of population growth on income per capita may also have a positive sign. Barro and Lee (1994) argue that this positive result is due to either positive net migration (reflecting an increase in skilled workers which has a positive impact on growth) or a low mortality rate that indicates a better health system.
Variables: Labour: Number of employed persons and hours of work; Fertility: Total Fertility Rate
Data used: Labour: Labour Force, Australia, Detailed, Quarterly (Cat. no. 6291.0.55.003)
Fertility: Fertility data in Australia is available annually in Births, Australia publication (ABS cat. no. 3301.0) or in Australian Historical Population Statistics (ABS cat. no. 3105.0.65.001).
Human Capital
Human capital is the most common additional variable used in growth estimations (Durlauf et al. 2004). Lucas (1988) defined human capital as a general skill level, indicating that human capital contributes to production by increasing worker productivity as well as directly increasing output through its contribution to technological improvement. Research has shown that the impact of human capital accumulation contributes to greater technical progress or Total Factor Productivity (TFP) growth by affecting knowledge accumulation (Romer 1990). The indirect impact of human capital accumulation mostly occurs through lower fertility or population growth (Becker et al. 1990; Galor and Weil 2000).
There are various types of human capital measurement, which are based on (i) health – mostly using life expectancy as a proxy; and (ii) education, mostly using school attainment as a proxy. Previous studies that have discussed gender inequality in human capital have mostly focused on education (Galor and Weil 2000; Klasen 1999; Seguino 2000), and that is the measure we use in this study. Annual data for this educational proxy of human capital, is available in ABS data on educational attainment in the publication Education and Work, Australia (ABS cat. no. 6227.0). Data begins in 1989, with details for the number of persons and workers by their highest educational attainment (in terms of non-school qualifications).
Variables: Proportion of persons with non school qualification
Data used: Education and Work, Australia (ABS cat. no. 6227.0)
Gender Wage Gap
The gender wage gap is the main input variable of interest in this study as our primary aim is to estimate the impact of the gender wage gap on economic growth. The connectivity between the gender wage gap and economic growth has been discussed in other parts of this report. The ABS conducts several surveys which have data and information about the gender wage gap. In this estimation we will use Average Weekly Earnings, Australia (Cat. no. 6302.0), which provides quarterly estimates of average gross weekly earnings of workers in Australia. Average Weekly Earnings data was chosen because it provides the longest time span of consistent data on wages.
Variable: Ratio of wage difference between male and female to male wage
Data used: Average Weekly Earnings, Australia (Cat. no. 6302.0) (Full time adults, ordinary time earnings)
Table E1 Summary of Variables and Data Used
| Variable |
Proxy |
Sources |
Availability |
| Economic Output |
GDP |
Australian System of National Accounts (Cat. No. 5204.0) |
Annually |
| Economic Input |
|
|
|
| Investment |
Gross Fixed Capital Formation |
Australian National Accounts: National Income, Expenditure and Product (Cat. No. 5206.0) |
Annually and quarterly |
| Labour |
Labour participation (Number of employed persons full time and part time) |
Labour Force, Australia, Detailed, Quarterly (Cat. No. 6291.0.55.003) |
Quarterly |
|
Hours of work |
Labour Force, Australia, Detailed, Quarterly (Cat. No. 6291.0.55.003) |
Quarterly |
| Fertility |
Total fertility rate |
Births, Australian Publication (Cat. No. 3301.0) |
Annually |
|
|
Australian Historical Population Statistics (Cat. No. 3105.065.001) |
Annually |
| Human capital (Education) |
Proportion of persons with non school qualifications |
Education and Work, Australia (Cat. No. 6227.0) |
Annually |
| Gender wage gap |
Ratio of wage difference between male and female to male wage |
Average Weekly Earnings, Australia (Cat. No. 6302.0) |
Annually and quarterly |
|
|
|
|
[ top ]
Statistical Summary
During the past two decades Australia’s GDP based on the chain volume measure grew by 3.4 per cent annually from $585 billion in 1989 to $1,084 billion in 2008. Meanwhile GDP per capita grew by 2.1 per cent annually from $35,000 in 1989 to $51,000 in 2008. Although both GDP and GDP per capita showed an increasing trend during this period, there was slight negative economic growth (especially in terms of GDP per capita) in the period 1991-1992. The overall increasing growth trend was also experienced by capital stocks, which increased from $1,750 billion in 1989 to $3,178 billion in 2008. This included an exponential trend in capital stocks between 2000 and 2008. However, there was a considerable drop in the flow of investment during 1989-1992, before experiencing a steady increase since then.
In the same period of 1989-2008, labour grew by 2.0 per cent annually, from 7.7 million people participating in the labour force in 1989, to 10.8 million people by 2008. In line with the fall in investment flow between 1990 and 1992, there was also a drop in labour force numbers over that period, but this was less marked than the drop in investment. The amount of hours of worked grew at a somewhat lower pace than overall labour force participation, at 1.8 per cent annually: from 267,000 hours a week in 1989 to 355,000 hours a week in 2008. Putting together the data on persons in the labour force with the information about hours worked, we find that the average hours of work of those in the labour force dropped by 0.2 per cent annually over the period, falling from 34.6 hours per week in 1989 to 32.9 hours per week in 2008. In terms of total hours of work, there was also negative growth in 2001 and 2006, as well as negative growth during the 1991-1992 downturns.
Overall population numbers grew slower than the number of labour force participants during the 1989-2008 period. At 1.3 per cent annually, the population grew from 16.7 million people in 1989 to 21.2 million people in 2008. The growth rate actually slumped from 1.8 per cent in 1989 to below 1.0 per cent in 1999. However, the growth rate then increased steadily to 1.2 per cent in 2005 and more gradually to 1.7 per cent in 2008. The latest increase in population growth is driven in part by the a jump in the Total Fertility Rate from 1.7 live births per 1000 women in the 2001 calendar year to 1.9 live births per 1000 women in 2007. This happened after fertility gradually decreased from 1.9 live births per 1000 women in 1990.
The percentage of persons aged 15-64 who attained a non-school qualification or tertiary education also increased substantially between 1989 and 2008. In 1989, 39.2 per cent of persons aged 15-64 held a non school qualification. This had increased to 53.9 per cent in 2008. The trend shows that the percentage of persons with non-school qualifications or tertiary education generally grew from year to year except for 1993, 1994 and 1997. In terms of gender inequality, the school attainment gap has closed considerably. In 1989, 45.4 per cent of men aged 15-64 had a non school qualification, compared to 39.2 per cent of women. These figures had increased to 55.3 per cent for men and by 52.6 per cent for women by 2008.
[ top ]
Stationarity
To be able to produce a reliable and consistent estimate when conducting econometric estimation, it is necessary that all variables have a stationary data stream – that is, that they are not being unduly influenced by other factors such as the normal peaks and troughs of the business cycle. Stationarity means that the variable is likely to converge to a single value or a trend path in the long run, and thus ensures that the mean, variance and relationships we are going to estimate will be achieved in the long run (Enders 1995). Without stationarity, we risk estimating a ‘false’ relationship that is based on insufficient serial autocorrelation within each variable. In addition, it is always important that the value that represents a variable at one moment, in a certain set of conditions, shows a consistent long run value, given everything else being the same, and not a value that will be likely to change in the short term.
Thus before undertaking the sort of estimation procedure we are using in this project, it was important to find out if the variables we are using have stationarity or not. Well-established tests exist to identify this, and we used these to explore the extent of non-stationarity in our data8. These tests, and the results from our preliminary modelling, when considered overall, led us to the conclusion that there was some degree of non-stationarity in our data. We addressed this through incorporating a first differencing approach into our modelling, as described in the following section.
[ top ]
The estimation model and procedure
The Growth Model
Having completed our preliminary testing, and drawing lessons from our initial results, we then went on to develop our final estimation approach.
First, one of the most important findings from the stationarity tests of the potential variables was that our capital stock variable was not stationary in either the level (original) form or the first difference form. As a result, we could not use that variable to build the model. This in turns means that we cannot develop the model based on the growth accounting structure (i.e., equation D6 in Appendix D). Therefore, the model was built based on the Solow growth model, in particular, the structure that is offered by Mankiw et al. (1992) which is known as the augmented Solow growth model in the form of:
(E1)
where A is Total Factor Productivity (TFP), Y is output (GDP), I is physical capital accumulation or investment, L is labour9, h is human capital level (proxied by the proportion of population with non school qualifications) and n is population growth (proxied by the fertility rate). Following Seguino (2000), the technological or TFP change is formulated in the form of:
(E2)
where Ci is a country-specific variable which in our case should be constant because we only use one country, Ø is the time effect and Wgap is the gender wage gap, calculated as 
where wm is average gross weekly earnings of male workers and wf is average gross weekly earnings of female workers.
Substituting this TFP formulation into the equation (1), we will have
(E3)10
The next step is to relax the assumption that the growth of labour will be equal to population growth, which allows us to better measure labour participation. This is done because we want to explore the impact of the wage gap on workers’ productivity based on the total hours of work that they offer, rather than just whether or not they work at all. With the need to include the gender wage gap in the equation, we then adjust equation (E3) to be:
(E4)
where Hw is hours of work and P is the total population so the average hours of work is calculated as 
. With this equation, we can examine the direct effect of the gender wage gap on economic growth.
[ top ]
1.2 Estimation Methodology
As discussed elsewhere, there are several possible modelling options within the overall framework described above, and we need to know more about the possible presence of indirect channels within the model in order to decide on a suitable estimation approach. Therefore, we first carried out a sensitivity analysis to examine the existence of indirect channels from the gender wage gap to economic growth, by taking in and out of the model variables that the literature suggests may be indirect channels of the gender wage gap’s impact on economic growth (for example, fertility and investment). We found that when we added in and removed variables there were changes in the magnitude of the coefficients of the gender wage gap and that the coefficients of the gender wage gap in various combinations of specifications were not robust. These findings confirm the existence of indirect channels (if the only effect of the wage gap on economic growth was direct, then we would expect to see little change in the coefficients when variables are added into or removed from the model). These findings show that our best estimation option was to conduct simultaneous equations using three-stage least squares in which the independent variables are mostly endogenous, allowing us to examine the direct and indirect channels together.
The essential component of the three-stage least squares estimation is the existence of enough instrumental variables11 to allow us to have combinations that have sufficient explanatory power in relation to the variable that is instrumented12. This should include adequate exogenous instrumental variable(s), otherwise the equations will end up in perfectly multicollinearity. In other words, we need to have variables in our model which explain much of the variation in the instrumented variable (here, rate of investment, average hours of work, fertility, human capital and labour participation), but are not determined by the outcome variable (which here is GDP per capita) which would retain the endogeneity problem. To achieve this, we use the lag of instrumented variables as the exogenous instrumental variables, given that the lag variables are likely to determine current conditions (that is, current GDP per capita) but theoretically cannot be determined by current GDP per capita. Using these lag variables means that we use the instrumented variable at time t-1, t-2 and so on until we get a reasonable estimate of the instrumented variable at time t. Unfortunately, in doing so, we are losing the ability to estimate the impact of the gender wage gap through human capital accumulation, as data for this variable is not available before 1989. Introducing a human capital lag would cut many of the available observations in the model, and as the other instrumented variables are available from 1985 or earlier, we decided to take advantage of this longer period of data for the other variables, despite losing our ability to use human capital accumulation as an indirect channel. The human capital variable is still included in the model, but the extent to which the gender wage gap may operate through it to impact on GDP per capita cannot be estimated.
As our stationarity tests had given us slightly inconclusive results in regard to the stationarity of our variables (the tests suggested a possible problem with stationarity, but when analysed carefully did not provide sufficiently strong evidence to absolutely reject the possibility that our data was stationary), we needed to conduct some initial modelling in order to further inform our understanding of possible problems with stationarity. If overall we considered stationarity to be a problem, then we would need to address this by using first difference terms of our variables (subtracting the equation at time t from the equation at time t-1), rather than the original (or level) variables.
We conducted several estimations using both the level term and the first difference term of the variables, in order to see if our results could provide any further information about which of these approaches we should use. We found that, using the level terms, we came up with a very high R2 value (99 per cent)13. Very high R2 values like this are a cause for concern. In this case, such a high value may be an indication of model misspecification and also may point to the existence of spurious regression caused by variables that are not sufficiently stationary. In contrast, the estimation based on first difference variables produced an R2 value of 77 per cent. Based on these findings, and in the light of the stationarity testing, we opted to estimate the impact of gender wage gap on economic growth using a first difference equation14.
To estimate the equation using a first difference equation, we subtract equation (E4) with
(E5)
and produce
(E6)
The next step is to build the system to recognise the endogeneity of the growth determinants and hence the indirect effect of the wage gap through other growth determinants. As with the main growth equation, we also estimate all equations in this system using the first difference form, especially given the variables we use in these subsequent equations are simply the first difference terms of those used in the main growth equation. This system can be written as:
(E7)
(E8)
(E9)
(E10)
(E11)
Estimation Results
Tables E2 to E7 show the estimation result of equations (E6)-(E11). The system is estimated using the data described above with t from 1990 to 2008. We utilise the coefficients from these tables to generate the impact coefficient that we use to estimate the impact of the gender wage gap on economic growth as shown in Table E8.
Table E2 Growth Equation
|
|
Coefficient |
|
Standard Error |
 |
R2= 0.7693 |
|
|
|
| (GDP per capita) |
|
|
|
|
|
 |
0.081 |
** |
0.032 |
|
 |
0.060 |
|
0.065 |
|
 |
0.222 |
*** |
0.077 |
|
 |
0.695 |
*** |
0.117 |
|
 |
-0.182 |
|
0.082 |
|
 |
-0.250 |
|
0.313 |
|
constant |
0.017 |
|
0.002 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The result of estimating equation (E6)
Table E3 Investment Equation
|
|
Coefficient |
|
Standard Error |
 |
R2= 0.7139 |
|
|
|
| (Investment/GDP) |
|
|
|
|
|
 |
-0.097 |
|
0.205 |
|
 |
-0.263 |
|
0.18 |
|
 |
-0.024 |
|
0.149 |
|
 |
4.722 |
*** |
1.288 |
|
 |
-0.485 |
|
0.434 |
|
 |
-0.913 |
|
0.593 |
|
 |
-1.124 |
|
1.373 |
|
 |
0.751 |
|
0.542 |
|
 |
-0.261 |
|
2.377 |
|
constant |
-0.088 |
*** |
0.029 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The result of estimating equation (E7)
Table E4 Hours of Work Equation
|
|
Coefficient |
|
Standard Error |
 |
R2= 0.7102 |
|
|
|
| (Average hours of work) |
|
|
|
|
|
 |
0.101 |
|
0.168 |
|
 |
-0.27 |
** |
0.115 |
|
 |
-0.33 |
*** |
0.122 |
|
 |
1.449 |
*** |
0.429 |
|
 |
-0.156 |
|
0.134 |
|
 |
-0.064 |
|
0.073 |
|
 |
-0.886 |
** |
0.441 |
|
 |
0.457 |
** |
0.21 |
|
 |
-1.432 |
** |
0.563 |
|
constant |
-0.027 |
*** |
0.008 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The result of estimating equation (E8)
Table E5 Labour Participation Equation
|
|
Coefficient |
|
Standard Error |
 |
R2= 0.7593 |
|
|
|
| (Labour Participation) |
|
|
|
|
|
 |
0.013 |
|
0.115 |
|
 |
-0.132 |
|
0.102 |
|
 |
-0.033 |
|
0.087 |
|
 |
1.029 |
*** |
0.175 |
|
 |
0.013 |
|
0.076 |
|
 |
-0.241 |
** |
0.103 |
|
 |
-0.033 |
|
0.041 |
|
 |
0.294 |
*** |
0.093 |
|
 |
0.378 |
|
0.355 |
|
constant |
-0.016 |
*** |
0.004 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The result of estimating equation (E9)
Table E6 Fertility Equation
|
|
Coefficient |
|
Standard Error |
|
R2= 0.5038 |
|
|
|
| (Fertility) |
|
|
|
|
|
 |
0.259 |
|
0.188 |
|
 |
0.921 |
** |
0.372 |
|
 |
-0.2 |
|
0.339 |
|
 |
-1.038 |
*** |
0.365 |
|
 |
-0.567 |
|
0.709 |
|
 |
0.019 |
|
0.17 |
|
 |
0.187 |
|
0.226 |
|
 |
0.42 |
|
0.492 |
|
 |
0.231 |
* |
0.123 |
|
 |
0.993 |
|
0.747 |
|
constant |
0.008 |
|
0.013 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The result of estimating equation (E10)
Table E7 Wage Gap Equation
|
|
Coefficient |
|
Standard Error |
|
R2= 0.5516 |
|
|
|
| (Gender wage gap) |
|
|
|
|
|
 |
-0.463 |
** |
0.182 |
|
 |
-0.087 |
|
0.179 |
|
 |
0.352 |
* |
0.188 |
|
 |
0.032 |
|
0.14 |
|
 |
-0.006 |
|
0.042 |
|
 |
-0.118 |
** |
0.05 |
|
 |
-0.034 |
|
0.121 |
|
 |
0.037 |
|
0.027 |
|
 |
0.141 |
** |
0.056 |
|
constant |
-0.001 |
|
0.003 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The result of estimating equation (E11)
[ top ]
Estimating the Impact
Estimation Coefficients
The coefficients that have been produced from the regression system above allow us to calculate the impact of the wage gap on economic growth. For example the coefficient 
°in the main growth equation (i.e., equation (E4)) represents the impact of the wage gap on economic growth while holding other variables constant (referred to as partial impact). This impact can be estimated as follows:
where 
(E12)
In the same way, the partial impact of other growth determinants on economic growth can be estimated.
The impact of investment: 
(E13),
The impact of fertility:
(E14),
The impact of labour participation: 
(E15),
The impact of average hours of work:
(E16),
The equations (E7)-(E10) in the system provide further information about how much these growth determinants will change if there is change in the wage gap. This can estimated as,
The impact on investment: 
(E17),
The impact on fertility: 
(E18),
The impact on labour participation: 
(E19),
The impact on average hours of work: 
(E20).
By substituting the equations in (E17)-(E20) into the equations in (E13)-(E16), we will have the impact estimate of the wage gap through other growth determinants as follows:
The impact through investment: 
(E21)
The impact through fertility:
(E22)
The impact through labour participation: (E23)
The impact through average hours of work: (E24)
Therefore, the total differential of growth on the wage gap provides the total impact of the wage gap on growth as
(E25)
Table E8 shows the impact estimate of the gender wage gap on economic growth
Table E8 The impact coefficients of the gender wage gap on economic growth
|
|
 |
Impact Coefficient |
|
|
|
|
|
|
| Wage gap à economic growth |
-0.25 |
|
|
|
-0.250 |
|
|
|
|
|
|
| Wage gapàinvestmentàeconomic growth |
-0.261 |
|
0.081 |
** |
-0.021 |
| Wage gapàfertilityàeconomic growth |
0.993 |
|
-0.182 |
|
-0.181 |
| Wage gapàaverage hours of workàeconomic growth |
-1.432 |
** |
0.222 |
*** |
-0.318 |
| Wage gapàlabour participationàeconomic growth |
0.378 |
|
0.695 |
*** |
0.263 |
|
|
|
|
|
|
| Total effects |
|
|
|
|
-0.507 |
Note: *, **, *** is the10%, 5% and 1% significance level, respectively
Source: The coefficient from tables E2 to E7
Estimating the Total Impact on GDP
The previous section has shown how to get the total impact coefficient of the wage gap on GDP. The final step is to calculate the total volume of GDP change (in dollars) which would result from a decrease or increase of the wage gap. To do so, we should rearrange equation (25) as
(E26)
and multiply both the right hand side and the left hand side of equation (26) by Pt to get
(E27).
Knowing that the wage gap is currently 0.17 and the chain volume GDP is at $1,084,146.00 million we can calculate the impact of a change of one percentage point in the gender wage gap, as well as the cost of the whole 17 per cent of the gender wage gap as seen in Table E9.
Table E9. Estimates of gender wage gap impact on economic output
|
Current GDP ($ millions) |
Change in GDP economic growth (%) |
Change in GDP ($ millions) |
| Gender wage gap increases by one percentage point |
1,084,146.00 |
-0.50 |
-5,496.65 |
| Total cost of wage gap ( wage gap is eliminated by 17 percentage points) |
1,084,146.00 |
8.50 |
93,443.06 |
The confidence level
While the coefficient estimates of our main growth equation have relatively low standard errors (which meant that coefficients were statistically significant and thus supported the direction expected by the theoretical growth model), we did however find high standard errors when estimating the impact of the gender wage gap directly on growth and most of its components. This was a drawback of our model. The lack of observations available to us is the likely cause of this. The high standard errors mean that our impact estimate has wide confidence intervals. Nevertheless, the coefficient estimate of the main growth equation (equation (E6)) is significant and shows a relationship between the gender wage gap and GDP per capita that is supported by growth theory. Therefore, despite data availability issues and high standard errors, our result is one which makes sense theoretically.
The question is, to what extent we expect that our estimation reflects true relationships in the economy. As can be seen in table E8, the impact of the gender wage gap on economic growth through an increase in average hours of work is the only impact that we found to be statistically significant at the 5% significance level. That means that we can be confident that there is 95% probability that this will actually be the outcome of a change in the gender wage gap.
In this interpretation, we have taken into account in calculating the total gap the impact of all channels – both significant and non-significant. However, what would the gap look like if we only took into account the impact of the one significant channel (hours of work)? As shown in Table E10, the impact is still in the same direction, and still very substantial – if we take only the significant channel into account, we still see that for an increase in the gender wage gap of one percentage point, GDP falls by 0.318 per cent. Thus we find that just this single channel accounts for 62.7 per cent of the total expected impact.
Another way of considering these issues is to think about what would happen to the apparent impact of the gender wage gap on GDP if we lowered our confidence level to 80%. Would we still see only one significant channel, and would the apparent impact change? We did this (see Table E10), and found that this added another significant channel to the model. With a confidence level of 80% we found that the gender wage gap affected both fertility and hours of work significantly. If we then use the impact of these two channels only to estimate the effects of the gender wage gap on GDP, we find that this effect (at -0.499) is very similar in magnitude to the total effect when all channels are used.
These results provide further support for our overall findings – they suggest that even when we adjust various aspects of the assumptions built into our modelling, the overall story about the impact of the gender wage gap on GDP per capita remains much the same.
Table E10. The impact of wage gap in different confidence level
Gender wage gap increases by one percentage point |
Change in GDP economic growth (%) |
Compared to total impact (%) |
Change in GDP ($ millions) |
| Total Impact with all channels |
-0.507 |
|
-5,496.65 |
| Total Impact with only channels significant at95% confidence level |
-0.318 |
62.7 |
-3,447.58 |
| Total Impact with only those channels significant at 80% confidence level |
-0.499 |
98.4 |
-5,409.89 |
Source: Authors’ calculations
[ top ]
Model Limitations
The discussion in this appendix has shown that our model is placed strongly within current approaches to growth modelling, has been rigorously tested, and is capable of providing an estimate of the impact of the gender wage gap on economic growth, and the indirect channels through which such an impact may be occurring. However, this model is subject to some weaknesses and limitations, and these are to some extent reflected in our results. We discuss these limitations here.
The main source of weakness in our model is the fact that it relies on a limited (20 year) data span. These data limitations affected the choices we made about model specification and also the strength of our estimation.
Because not all variables which we needed to include in the model were available on a quarterly basis, we had to use annual data, with 1990 as the starting year. Because we needed to use a first difference equation in addition to using lagged versions of our variables in order to achieve a robust estimate of the coefficient of growth determinant, we set 1990 as our base year (i.e., at time t), which means that we needed to use data from 1985 to construct the lag variables. Our preliminary data testing showed that the combination of instrumental variables can only give a good estimation of the channels if we include three lags to explain the behaviour of each channel, except for fertility which needed four lags.
Therefore, we only have 19 years of observations for the estimation given that we use 2008 data as the end of the observation period. As noted earlier, the short data span meant that our variables were less likely to be significantly stationary in the level form, and this contributed to our decisions about model specification.
One of the key decisions we had to make was to use the first difference form rather than the level form of our equations. The very high coefficient of determination (R2) of 99 per cent in the level form is likely a result of the short data span. While our tests of stationarity did not conclusively reject the level form data, this high R2, as noted earlier, raises substantial concerns about the possibility of a spurious regression. On the other hand, the coefficient of determination (R2) of 77 per cent in the first difference form is the better choice since this means that the model can still explain the variation of the dependent variable with a reasonable range of error. However, the use of first differences also means that the result may not give a picture of long term equilibrium. With only 19 years of data this is an expected result, since the average rate of convergence in growth models is around 35 years.
Another decision we had to make was not to estimate the impact of the wage gap through the indirect channel of human capital. While the short data span available to us is mostly due to the length of human capital data available from the Education and Work Survey, we nevertheless considered the inclusion of human capital in our model as being of significant theoretical importance. Our estimation result bears this out, showing that the inclusion of human capital is almost as important as the inclusion of physical capital investment (see Table E2). This can be seen from the magnitude of the human capital coefficient in the main growth equation at 0.06 compared to 0.08 for physical capital investment. The fact that human capital is so important in predicting growth, and our inability to model this indirect channel in this study, means that our model in fact may underestimate the overall effects of the gender wage gap on GDP – that is, had we been able to examine the human capital channel, this might have further contributed to the impact of the gender wage gap on economic growth. This is particularly so as some of our preliminary modelling showed that the wage gap may have a negative impact on human capital accumulation. However, given the high standard error of the human capital coefficient in our final model, we do not expect that such underestimation would be of a large magnitude.
As noted above, the impacts of the wage gap on growth components within our model have relatively high standard errors. These relatively high standard errors are another weakness of our model, making it difficult to detect statistically significant relationships between channels of impact and economic growth. The only channel for which we have statistically significant results is for the average hours of work variable, which shows that a decrease in the wage gap will increase the average hours of work and thus eventually increase economic output. However, as discussed above, our findings related to the total impact of the gender wage gap on GDP per capita appear fairly robust.
The final limitation of the model is that we cannot separate the impact of the gender wage gap on growth components based on gender. The short data span is partly the reason, but most importantly the high collinearity of the time series data between the two genders of labour force participation made this decision necessary – that is, male labour force participation and female labour force participation were too highly correlated with each other to be able to effectively separate out their explanatory power in the model. If variables which are highly collinear are used in a model such as the one developed here, the model will be both inefficient and liable to give misleading results.