For historical, social and institutional reasons, there is a gap between male and female wages. While the gap has been declining over the last decades, it remains particularly high especially in advanced economies. Using OECD data (OECD 2022), figure 1.1 shows the gender wage gap in year 2019 for OECD countries (for employees only).1 The gender wage gap is calculated as the difference between the median wage of male workers and the median wage of female workers in relation to the median wage of male workers. In the European Union (EU27) the gender wage gap is 11.12%, below the OECD value of 12.6%. Empirical studies have demonstrated how closing the gender wage gap would have an expansionary effect on the economy.2
Figure 1.1: Gender wage gap for employees in OECD countries, 2019. Source OECD (2022).
In the next section, we will include the gender wage gap in a simple short-run macroeconomic model for the closed economy developed in the post-Keynesian / Kaleckian tradition. Through a simple comparative statics exercise, we will then investigate the macroeconomic impact of greater wage equality on some key variables of interest like distribution and aggregate demand.
We now try to integrate in a stylized form some gender aspects into a simple macroeconomic model. To do this, we will use a macroeconomic model developed in the post-Keynesian / Kaleckian tradition where a gender wage gap is introduced into a basic (one good) closed economy model for the short run.3 The objective of the following exercise is to demonstrate from a theoretical point of view the effect of closing the gender wage gap on some variables of macroeconomic interest such as income distribution and aggregate demand. Let us now turn to describing the model equations.
The basic structure of the model
We begin to describe the basic features of the model. The model consists of two classes, workers and capitalists. The capitalist class is not divided by gender while workers (\(N\)) are split between male workers (\(N_M\)) and female workers (\(N_F\)).
\[\begin{equation} N = N_M + N_F \tag{2.1} \end{equation}\]
The parameter \(\rho\) indicates the fraction of male workers in total employment (\(\rho = N_M/N\)).4
\[\begin{equation} N = \rho N + (1 - \rho) N \tag{2.2} \end{equation}\]
As we saw in the previous section, in modern economies the (nominal) wage of female workers represents often a fraction of the (nominal) wage of male workers. In our model, this is captured by the parameter \(\epsilon\) that we can call gender wage equality parameter. It follows that the term \((1 - \epsilon)\) captures the gender wage gap. The \(\epsilon\) parameter captures all those historical, social and institutional characteristics that determine the gender wage gap. In our model, we will assume that the \(\epsilon\) parameter is exogenous and will be the focus of our simple simulation below.
In equation (2.3), the term \(w_M\) denotes the male nominal salary and the term \(w_F\) stands for the female nominal salary, where the parameter \(\epsilon\) is by definition bounded between \(0\) and \(1\). A value of the parameter \(\epsilon\) equal to \(1\) implies perfect equality in the distribution of wages between male workers and female workers.
\[\begin{equation} w_F = \epsilon w_M, \space 0 < \epsilon \leq 1 \tag{2.3} \end{equation}\]
Nominal income (\(pY\)) is distributed between wage income for male workers (\(W_M = w_M N_M\)), wage income for female workers (\(W_F = w_F N_F\)) and profits (\(\Pi\)) or capital income (\(rpK\)).
\[\begin{equation} pY = W_M + W_F + \Pi = w_M N_M + w_F N_F + rpK \tag{2.4} \end{equation}\]
After few manipulations, (2.4) becomes:
\[\begin{equation} pY = w_M[\rho + \epsilon(i - \rho)]N + rpK\nonumber \\ \tag{2.5} \end{equation}\]
Pricing decision and income distribution
We now turn to describing the equations that determine the distribution of income between capital and labor, and also between male labour and female labour. We begin by looking at the firms’ pricing behaviour in incompletely competitive markets. The firms’ mark-up pricing function, where \(m\) stands for the mark-up (\(m > 0\)), is given by (2.6):5
\[\begin{equation} p = (1 + m) \frac{w_M N_M + w_F N_F}{Y} = (1 + m) \frac{w_M N_M + w_F N_F}{Y} = (1 + m)\frac{w_M [\rho + \epsilon (1 - \rho)]}{Y} \tag{2.6} \end{equation}\]
From (2.6), we can derive total profits (\(\Pi\)):
\[\begin{equation} \Pi = m(w_M N_M + w_F N_F) = m w_M [\rho + \epsilon (1 - \rho)] \tag{2.7} \end{equation}\]
The profit share of national income (\(h\)) is thus given by:
\[\begin{equation} h = \frac{\Pi}{pY} = \frac{\Pi}{W_M + W_F + \Pi} = \frac{m w_M [\rho + \epsilon (1 - \rho)]}{(1 + m) w_M [\rho + \epsilon (1 - \rho)]} = \frac{m}{1 + m} \tag{2.8} \end{equation}\]
In turn, the wage share of national income (\(\Omega\)) is given by:
\[\begin{equation} \Omega = 1 - h = \frac{W_M + W_F}{pY} = \frac{W_M + W_F}{W_M + W_F + \Pi} = \frac{w_M [\rho + \epsilon (1 - \rho)]}{(1 + m) w_M [\rho + \epsilon (1 - \rho)]} = \frac{1}{1 + m} \tag{2.9} \end{equation}\]
By definition, we have that:
\[\begin{equation} h + \Omega = \frac{m}{1 + m} + \frac{1}{1 + m} = 1 \tag{2.10} \end{equation}\]
Equations (2.8) and (2.9) are essential components in every basic Kaleckian model. We must now extend the model by determining the wage share of male workers (\(\Omega_W\)) and female workers (\(\Omega_F\)) in national income.
\[\begin{equation} \Omega_M = \frac{W_M}{pY} = \frac{W_M}{W_M + W_F + \Pi} = \frac{w_M \rho}{(1 + m) w_M[\rho + \epsilon (1 + \rho)]} = \Omega \frac{\rho}{\rho + \epsilon (1 - \rho)} \tag{2.11} \end{equation}\]
\[\begin{equation} \Omega_F = \frac{W_M}{pY} = \frac{W_M}{W_M + W_F + \Pi} = \frac{w_M \rho}{(1 + m) w_M[\rho + \epsilon (1 + \rho)]} = \Omega \frac{\epsilon (1 - \rho)}{\rho + \epsilon (1 - \rho)} \tag{2.12} \end{equation}\]
Let’s make a numerical example to clarify the idea. Let’s assume that the profit share (\(h\)) is equal to 40% of national income. It follows that the wage share (\(\Omega\)) will be equal to 60%. We also assume that the male employment share (\(\rho\)) is 50%. What is the wage share of male and female workers assuming a value for the equality parameter (\(\epsilon\)) equal to \(0.2\), meaning an high gender wage gap?
\[\begin{equation} \Omega_M = 0.6 \frac{0.5}{0.5 + 0.2(1 - 0.5)} = 0.5 \tag{2.13} \end{equation}\]
\[\begin{equation} \Omega_F = 0.6 \frac{0.2(1 - 0.5)}{0.5 + 0.2(1 - 0.5)} = 0.1 \tag{2.14} \end{equation}\]
Figure 2.1: Factor shares in national income (left) and gender wage shares (right).
From figure 2.1 we can observe that the male wage share of national income is equal to 50% while the female wage share is equal to 10%.
What is the effect of closing the gender wage gap (an increase in the \(\epsilon\) parameter) on the male wage share and the female wage share?6
\[\begin{equation} \frac{\partial \Omega_M}{\partial \epsilon} = \frac{- \Omega \rho (1 - \rho)}{[\rho + \epsilon (1 - \rho)]^2} = \frac{-\rho (1 - \rho)}{(1 + m)[\rho + \epsilon (1 - \rho)]^2} < 0 \tag{2.15} \end{equation}\]
\[\begin{equation} \frac{\partial \Omega_F}{\partial \epsilon} = \frac{\Omega \rho (1 - \rho)}{[\rho + \epsilon (1 - \rho)]^2} = \frac{\rho (1 - \rho)}{(1 + m)[\rho + \epsilon (1 - \rho)]^2} > 0 \tag{2.16} \end{equation}\]
The derivative of the male share with respect to the parameter \(\epsilon\) is negative (the sign of the derivative is negative). This implies that (not surprisingly) an increase in gender wage equality will decrease the male wage share. In contrast, the derivative of the female wage share with respect to the parameter \(\epsilon\) is positive (the sign of the derivative is positive). This implies that (also no surprise), an increase in gender wage equality will increase the female wage share at the expense of the male wage share.7
Continuing to assume the values of the previous example, with an increase of the \(\epsilon\) parameter to 1 (no gender wage gap), the wage share will be equally divided between male and female workers (30%, respectively).8 This situation is visualized with figure 2.2.
Figure 2.2: Factor shares in national income (left) and gender wage shares (right) after that the equality parameter rises to 1 (no gender wage gap).
Short-run goods market equilibrium with gender wage gap
Let us begin by describing the investment function (\(pI\)). As in the neo-Kaleckian inspired models, the investment function will depend positively on autonomous investment (\(pI_a\)), representing animal spirits, and on (expected) demand through the accelerator effect (\(\beta\)). We assume that both autonomous investment and the accelerator effect are positive (\(pI_a, \beta > 0\)).
\[\begin{equation} pI = pI_a + \beta pY \tag{2.17} \end{equation}\]
Aggregate saving (\(S\)) are determined by the sum of saving from profits (\(S_\pi\)) and wages, both male (\(S_M\)) and female (\(S_F\)). In turn, the saving function is determined by the propensity to save out profit (\(s_\Pi\)), out of male wages (\(s_M\)) and out of female wages (\(s_F\)). Following Kalecki, we assume that the propensity to save of profits is higher than the male and female propensity to save. Whether the male propensity to save is higher than the female propensity to save is an open question and it will be central in identifying the effect of increased gender equality on aggregate demand, as we shall see in a moment.9
\[\begin{equation} S = S_\Pi + S_M + S_F = (s_\pi \Pi + s_M \Omega_M + s_F \Omega_F), \space 0 \leq s_M, s_F < s_\Pi \leq 1 \tag{2.18} \end{equation}\]
By plugging in (2.11) and (2.12) in (2.18), we obtain:
\[\begin{equation} S = \Biggl\{ h \biggr[ s_\Pi - \frac{s_M \rho + s_F \epsilon (1 - \rho)}{\rho + \epsilon(1 - \rho)} \biggr] + \biggr[ \frac{s_M \rho + s_F \epsilon (1 - \rho)}{\rho + \epsilon(1 - \rho)} \biggr] \Biggl\} pY \tag{2.19} \end{equation}\]
In (2.19), the term \(\frac{s_M \rho + s_F \epsilon (1 - \rho)}{\rho + \epsilon(1 - \rho)}\) is nothing more than the weighted average between the male and the female propensity to save weighted by the respective employment shares.10 Defining the overall propensity to save out of wages as \(s_W\), we can rewrite (2.19) as follows:
\[\begin{equation} S = \{ h[s_{\Pi} - s_W] + s_W \} pY \tag{2.20} \end{equation}\]
What will be the effect of increasing gender wage equality on the overall propensity to save? Let us take the derivative of \(s_W\) with respect to \(\epsilon\).
\[\begin{equation} \frac{\partial s_W}{\partial \epsilon} = \frac{-(1 - \rho)\rho(s_M - s_F)}{[\rho + \epsilon(1 - \rho)]^2} \tag{2.21} \end{equation}\]
The derivative is negative (the sign of the derivative is negative). An improvement in the gender wage gap will reduce the overall propensity to save but only if male workers’ propensity to save (\(s_M\)) is greater than female workers’ propensity to save (\(s_F\)). If this is not the case, the term \((s_M - s_F)\) would be negative and the sign of the derivative would turn positive.
The equilibrium condition of the goods market implies that planned saving are equal to investment.
\[\begin{equation} pI = S \tag{2.22} \end{equation}\]
The following condition must be met for the stability of the goods market equilibrium.
\[\begin{equation} \frac{\partial S}{\partial (pY)} - \frac{\partial (pI)}{\partial (pY)} > 0 \tag{2.23} \end{equation}\]
This means that saving has to react more elastically than investments to a change in income for the equilibrium in the goods market to be stable. In formulas, we have that:
\[\begin{equation} h(s_\Pi - s_W) + s_W - \beta > 0 \tag{2.24} \end{equation}\]
We can find the equilibrium income by plugging (2.17) and (2.20) into the equilibrium condition (2.22).
Equilibrium income is given by:
\[\begin{equation} pY^* = \frac{pI_a}{h (s_\Pi - s_W) + s_W - \beta} \tag{2.25} \end{equation}\]
Equilibrium investment / saving is given by:
\[\begin{equation} pI^* = S^* = \frac{pI_a [h (s_{\Pi} - s_W) + s_W]}{h (s_\Pi - s_W) + s_W - \beta} \tag{2.26} \end{equation}\]
We can also obtain equilibrium profits by multiplying equilibrium income (\(pY^*\)) by the profit share (\(h\)).
\[\begin{equation} \Pi^* = \frac{h pI_a}{h (s_\Pi - s_W) + s_W - \beta} \tag{2.26} \end{equation}\]
In the model, the paradox of saving is valid. An increase in the propensity to save (for all classes and genders) has a negative effect on the equilibrium values of the endogenous variables (income, investment / saving and the level of profits). In addition we have that in the model the economy is wage-led. This means that an increase in the wage share (a decrease in the profit share) leads to an increase in equilibrium income and equilibrium investment / saving.
What will be the effect of greater gender wage equality on the equilibrium values of income and equilibrium investment / saving and profits? Let us make the derivative of the endogenous variable with respect to the parameter \(\epsilon\). The result is shown with the following equations:
\[\begin{equation} \frac{\partial (pY)^*}{\partial \epsilon} = \frac{pI_a (1 - h)(1 - \rho)\rho(s_M - s_F)}{\{[h(s_\Pi - s_W) + s_W - \beta][\rho + \epsilon (1 - \rho)]\}^2} \tag{2.27} \end{equation}\]
\[\begin{equation} \frac{\partial (pI_a)^*}{\partial \epsilon} = \frac{\beta pI_a (1 - h)(1 - \rho)\rho(s_M - s_F)}{\{[h(s_\Pi - s_W) + s_W - \beta][\rho + \epsilon (1 - \rho)]\}^2} \tag{2.28} \end{equation}\]
\[\begin{equation} \frac{\partial \Pi^*}{\partial \epsilon} = \frac{h pI_a (1 - h)(1 - \rho)\rho(s_M - s_F)}{\{[h(s_\Pi - s_W) + s_W - \beta][\rho + \epsilon (1 - \rho)]\}^2} \tag{2.29} \end{equation}\]
What do theses three equations tell us? In all three equations we can see that an improvement towards gender equality will have an expansionary effect only in the case that the propensity to save out of male wages (\(s_M\)) is higher than the propensity to save out of female wages (\(s_F\)). This means that the term \((s_M - s_F)\) in the numerator of (2.27), (2.28), and (2.29) is positive (and therefore the derivative is positive) only in the case that \(s_M > s_F\).
We can therefore conclude that in our simple model, an increase in the female wage share at the expense of the male wage share can have an expansionary effect on the economy provided that \(s_M > s_F\). The economy can thus be called gender equality-led.
Graphical analysis
Figure 2.3 shows the equilibrium in the goods market. The intersection of the saving function (\(S\)) and the investment function(\(pI\)) gives the value of equilibrium income (\(pY^*\)) and equilibrium investment / saving (\(S^* = pI^*\)).11
Figure 2.3: Goods market equilibrium with gender wage gap in the saving fucntion in the closed economy model.
In figure 2.4 we can observe the effect of a reduction in gender wage gap on the equilibrium values of income, saving and investment. The reduction in the gender wage gap is modeled as an increase in the \(\epsilon\) parameter to \(1\), i.e. perfect equality in the gender wage distribution (\(w_M = w_F\)). With an increase in gender wage equality the saving function will rotate to the right. Equilibrium income as well as equilibrium investment / saving will move towards a new and now higher equilibrium value (\(pY^*_1\)).
Figure 2.4: The effect of closing the gender wage gap on equilibrium investment /saving and income in the closed economy model.
The app accessible at the following link allows to experience interactively the effects of closing the gender wage gap on demand and distribution in our simple post-Keynesian / Kaleckian model for the closed economy. In the app, the user can control of the gender wage equality parameter (\(\epsilon\)) as well as of all the other parameters (and exogenous variables) of the saving function and of the investment function. The user may try one of the following exercises or may decide to use the app freely.
In this short minicourse we have included a gender wage gap in a closed economy post-Keynesian / Kaleckian macroeconomic model for the short run. We assumed that the workers class is divided into male and female workers. We then assumed that female wages are a fraction of male wages, as confirmed also by the OECD data in the introduction to this minicourse. We have derived the equilibrium condition in the goods market and we have seen that closing the gender wage gap could have an expansionary effect on the economy provided that the propensity to save from wages of male workers is greater than the propensity to save from wages of female workers. In this case, we have defined our model economy gender equality-led.
| Abbreviation | Name | Color* |
|---|---|---|
| \(\rho\) | Male employment share | # |
| \(\epsilon\) | Gender wage equality parameter | # |
| \(\Omega\) | Wage share | # |
| \(\Omega_F\) | Female wage share | # |
| \(\Omega_M\) | Male wage share | # |
| \(\Pi\) | Profits | # |
| \(h\) | Profit share | # |
| \(m\) | Mark-up on unit labour cost | # |
| \(N\) | Numbers of workers | # |
| \(N_F\) | Numbers of female workers | # |
| \(N_M\) | Numbers of male workers | # |
| \(p\) | Price level | # |
| \(pI\) | Investment function | # |
| \(pI_a\) | Nominal autonomous investment | # |
| \(pY\) | Total nominal income | # |
| \(pY^*\) | Equilibrium nominal income | # |
| \(s_\Pi\) | Propensity to save out of profits | # |
| \(s_F\) | Propensity to save out of female wages | # |
| \(s_M\) | Propensity to save out of male wages | # |
| \(s_W\) | Propensity to save out of wages | # |
| \(S\) | Saving function | # |
| \(w_F\) | Nominal wage for female work | # |
| \(w_M\) | Nominal wage for male work | # |
| \(W_F\) | Total female wages | # |
| \(W_M\) | Total male wages | # |
| * Color in pictures (if applicable) |
For complete time series, see the OECD website. Figure 1.1 show data for full-time employees only. Data for self-employed workers are available on the OECD website.↩︎
See for example Onaran, Oyvat, and Fotopoulou (2022).↩︎
The following minicourse is based on Hein (2023) and partially on Hein (2020). In Hein (2020), the effect of closing the gender wage gap is also analyzed in the long run on capital accumulation and productivity growth.↩︎
For the full set of assumptions, see Hein (2020).↩︎
We are going to assume that the mark-up will stay constant.↩︎
A change in the equality parameter \(\epsilon\) has no effect on the profit share (\(\frac{\partial h}{\partial \epsilon} = 0\)) and wage share (\(\frac{\partial \Omega}{\partial \epsilon} = 0\)).↩︎
We are assuming that the nominal wage of male workers (\(w_M\)) remains constant and that functions as an anchor for the female nominal wage (\(w_F\)). We are also assuming a constant mark-up and labour productivity.↩︎
We have seen that closing the wage gap has no effect on the profit share and the wage share. The female wage share grows at the expense of the male wage share. This is not the case if we extend the model to the open economy case. An increase in the \(\epsilon\) parameter would lead to an increase in the total wage share lowering the profit share. On this see Hein (2020) and Hein (2023).↩︎
For a more detailed description of this issue, see Hein (2020) and Hein (2023).↩︎
For the derivation, see Hein (2020) and Hein (2023).↩︎
The values of the variables are purely indicative and should be interpreted as a simple example.↩︎