Labor market effects of COVID-19 shocks

To analyze supply-side effects associated with the Covid-19 pandemic crisis, we apply the standard labor market model as represented by Blanchard [2021]. According to this model, the equilibrium in the labor market is determined by the wage and the price setting relationships. The wage setting relationship is given by

1 W=Pe⋅F(u,z) $$W = {P^e} \cdot F(u,z)$$

where wage (W) setting depends on

The aggregate nominal wage depends positively on the expected price level, as an anticipated rise in the price level leads to higher wage claims of workers and their labor unions. Likewise, there is a negative relationship between the aggregate nominal wage (W) and the unemployment rate (u), which is in line with the traditional Phillips curve [Phillips, 1958]: A lower unemployment rate leads to better outside-options for workers and makes it more expensive for employers to find workers. This leads to a stronger bargaining position of workers and thus higher wages. The variable (z) captures all other factors (e.g., unemployment benefits and preferences for leisure) that affect the aggregate nominal wage, given the expected price level and the unemployment rate.

For simplicity and consistency with the traditional model, we assume static expectations, i.e., the expected price is equal to the current price (P^e = P). We also assume that the real wage (W/P) can be expressed by the following linear function: F(u,z) = z – u. Using this relationship in equation (1) together with static expectation leads to:

2 WP=z−u $${W \over P} = z - u$$

While wage setting depends on the bargaining position of workers, prices are set by firms and depend on their cost structure. The cost structure of a firm is in turn determined by the underlying production function. Assuming that labor is the only factor of production, we apply the following production function:

3 Y=A⋅N $$Y = A \cdot N$$

where Y is output, N is employment, and A is labor productivity.¹

The quantity of output produced depends on the number of workers employed and labor productivity. Total cost of producing Y is the product of the amount of labor required to produce Y, which - according to (3) - is Y/A, and the wage rate. Hence, total cost of producing Y is (Y/A) ⋅ W. Marginal cost - i.e., the first derivative of the cost function with respect to output - is W/A.

We assume the following price setting relation:

4 P=(1+μ)⋅WA⇒WP=A1+μ $$P = (1 + \mu ) \cdot {W \over A} \Rightarrow {W \over P} = {A \over {1 + \mu }}$$

Prices are determined by marginal costs (W/A) and the mark-up (μ). Given the market power of firms, firms can raise prices over marginal costs. Therefore, the mark-up can be interpreted either as a profit margin or as compensation for price changes of other input factors such as material or energy.

Equating the wage setting relationship (2) and the price setting relationship (4) yields the equilibrium real wage and the corresponding natural rate of unemployment for the economy under consideration:

5 z−u=A1+μ⇒u=z−A1+μ $$z - u = {A \over {1 + \mu }} \Rightarrow u = z - {A \over {1 + \mu }}$$

The natural rate of unemployment characterizes the equilibrium in the labor market in which the real wage chosen by wage setters is equal to the real wage implied by price setters. The equilibrium level of unemployment is not a natural constant, but rather reflects the structure of the economy designed by policy makers and the institutional framework. For instance, changes of the unemployment insurance schemes or the minimum wage would change the natural rate of unemployment. We later give more specific examples of how the market outcome and hence the natural rate of unemployment changes due to government intervention. For example, we discuss the effects of changes of the size of unemployment benefits or the time period for which unemployment benefits are granted. Additionally, the government also influences the mark-up by a tighter or softer competition policy, which affects μ and thereby the equilibrium rate of unemployment.

Figure 1 illustrates the wage setting relationship (WS) and the price setting relationships (PS). The price setting curve is a horizontal line. Since there exists a negative relationship between the unemployment rate and the real wage, the WS curve is downward sloping. In point A, the labor market is in equilibrium.

Figure 1.

We apply a numerical example to the WS–PS model in order to derive the effects of various supply shocks on the labor market. The values for the different exogenous variables and parameters as well as the size of the exogenous shocks were chosen arbitrarily to illustrate the main results in a simple way.

The baseline scenario is characterized by the following parameters:

Using these assumptions, we can derive the equilibrium in the labor market, which is represented by the natural rate of unemployment.

6 u=z−A1+μ=1.8−21+0.25=0.2 $$u = z - {A \over {1 + \mu }} = 1.8 - {2 \over {1 + 0.25}} = 0.2$$

Thus, the natural rate of unemployment is given by u = 0.2 and the natural rate of employment is given by 1 – 0.2 = 0.8. Substituting the values for labor force (L) and the natural rate of unemployment (u) into the following equation yields:

7 N=L⋅(1−u)=1,250⋅(1−0.2)=1,000 $$N = L \cdot (1 - u) = 1,250 \cdot (1 - 0.2) = 1,000$$

Hence, the number of employees is given by N = 1,000. Given the production function, this information allows us to determine the natural level of output.

8 Yn=A⋅Nn=2⋅1,000=2,000 $${Y_n} = A \cdot {N_n} = 2 \cdot 1,000 = 2,000$$

The natural level of output is reached when the labor market is in equilibrium. Table 1 summarizes the numerical values for the baseline scenario.

During the Covid-19 crisis, firms around the world faced new regulatory standards related to health measures. Studies show that government regulations during the pandemic led to adverse effects in the labor market [Dreger and Gros, 2021; Raimo et al., 2021]. In particular, firms that provide services, e.g., hair salons, movie theaters, and restaurants had to introduce measures to protect customers and employees and were required by law to operate at reduced capacity. Rio-Chanona et al. [2020] show that especially low-wage occupations are more vulnerable to shocks during the pandemic. For example, in the case of a hair salon, the following measures were introduced:

These measures were particularly cost-intensive. Prices, therefore, had to be adjusted virtually across the board. The price increase only covered additional costs and did not lead to higher profits.

To analyze the impact of higher costs faced by firms during the Covid-19 crisis on the labor market and the natural rate of output, we modify the baseline scenario such that higher production costs take the form of a higher mark-up on the costs until then. For this reason, we allow for a certain percentage increase in prices that is shown by a higher mark-up, which then affects the price setting relationship. We do not interpret the mark-up adjustment as an increase in profit margin. Rather, the higher mark-up is necessary to cover the additional costs such as masks, disinfection, etc. Applying this to equation (4) leads to

9 P=(1+μ↑)⋅WA⇒WP=A1+μ↑ $$P = (1 + \mu \uparrow ) \cdot {W \over A} \Rightarrow {W \over P} = {A \over {1 + \mu \uparrow }}$$

In the labor market model, the increase in the mark-up is associated with higher costs and affects the PS relationship. For instance, at a given wage level firms will increase prices owing to the new health care regulations. This leads to a lower real wage. In Figure 1, the PS curve shifts downwards. Workers accept the lower real wage owing to an increasing unemployment rate (movement along the WS curve from point A to point B). Therefore, the natural rate of unemployment increases until the new labor market equilibrium is reached. Figure 1 shows the changes in the labor market when mark-up increases.

These results are confirmed by the numerical example. Table 1 displays the results of an increase in the mark-up. With additional production costs, we assume an increase of the mark-up from μ = 0.25 to μ = 1/3. Keeping labor productivity and the catch-all variable constant at A = 2 and z = 1.8, respectively, we can derive the labor market equilibrium for the mark-up shock scenario.

10 WP=A1+μ↑=21+0.333=1.5 $${W \over P} = {A \over {1 + \mu \uparrow }} = {2 \over {1 + 0.333}} = 1.5$$

Applying the PS relation, the increase in the mark-up leads to a lower real wage of 1.5. Equating the PS relationship and the wage-setting relationship yields the effect on the natural rate of unemployment.

11 u=z−A1+μ↑=1.8−21+0.333=0.3 $$u = z - {A \over {1 + \mu \uparrow }} = 1.8 - {2 \over {1 + 0.333}} = 0.3$$

Consequently, unemployment rises to u = 0.3 and the natural level of employment declines to N = 875. This in turn results in a lower natural level of output equal to 1,750.

The Covid-19 pandemic crisis had a negative impact on the supply side because of higher costs and because of lower labor productivity [Bloom et al., 2020]. For example, because restaurants were less busy during the pandemic and hairdressers were only able to serve one customer at a time, labor productivity declined significantly.

To analyze the impact of lower labor productivity during the Covid-19 crisis on the labor market and the natural rate of output, we modify the baseline scenario to account for a decline in the labor productivity variable A. According to the labor market model used in this analysis, lower labor productivity affects the PS relation as follows:

12 P=(1+μ)⋅WA↓⇒WP=A↓1+μ $$P = (1 + \mu ) \cdot {W \over {A \downarrow }} \Rightarrow {W \over P} = {{A \downarrow } \over {1 + \mu }}$$

The decline in labor productivity is associated with higher prices, because firms can only produce less if all other factors remain constant. Hence, the price increase results in a lower real wage. In Figure 2 the PS curve shifts downwards. This leads to a lower real wage and a higher unemployment rate (movement along the WS curve from point A to point B).

Figure 2.

These results are confirmed by our numerical example. Column 4 of Table 1 shows the results for this scenario. Given lower productivity, we assume a decline in the parameter A from A = 2 to A = 1.875.

Keeping the values for the mark-up and the variable z - which reflects all other labor market settings - constant at μ = 0.25 and z = 1.8, respectively, we can derive the labor market equilibrium for the labor productivity shock scenario.

13 WP=A↓1+μ=1.8751+0.25=1.5 $${W \over P} = {{A \downarrow } \over {1 + \mu }} = {{1.875} \over {1 + 0.25}} = 1.5$$

Using the PS relation, the decline in labor productivity leads to a lower real wage of 1.5 in the labor market. Equating the price setting and wage setting relation yields the effect on the natural rate of unemployment.

14 u=z−A↓1+μ=1.8−1.8751+0.25=0.3 $$u = z - {{A \downarrow } \over {1 + \mu }} = 1.8 - {{1.875} \over {1 + 0.25}} = 0.3$$

Hence, unemployment increases to u = 0.3 and the natural level of employment declines to N = 875. It can be shown that, depending on the magnitude of the decline in labor productivity, the same effects on the labor market can be derived as in case of the mark-up shock scenario.

However, the impact on the natural level of output is twofold. First, the negative impact on employment through the PS channel, as derived above, lowers output. Second, given the lower level of labor productivity, the natural rate of output per se will be lower.

15 Yn=A⋅Nn=1.875⋅875≈1,641 $${Y_n} = A \cdot {N_n} = 1.875 \cdot 875 \approx 1,641$$

Hence, fewer workers are employed and their productivity is lower.

The final shock we analyze is a change in the variable z. This variable reflects all factors that affect wages given the expected price level and the unemployment rate. According to our model, an increase in z implies an increase in the reservation wage. The reservation wage is defined as the lowest wage rate at which the workers would accept a job. Previous studies show that the reservation wage depends on factors such as personal characteristics, duration of unemployment, and unemployment benefits [Christensen, 2001; Brown and Taylor, 2013].

In the wake of the Covid-19 pandemic crisis, the reservation wage has trended upwards. This is due, in particular, to the increase in unemployment benefits during the pandemic in several countries, e.g., the United States. In addition, the risk perception of going to work increased, especially in those areas in which it is almost impossible to avoid personal contact. Previous studies show the macroeconomic impact of cutting back on work in order to reduce the risk of getting infected [Eichenbaum et al., 2020]. In this case, workers might prefer to stay at home and collect benefits rather than continue to work. Therefore, the risk premium to go to work increases, leading to a higher reservation wage. The same applies to mandatory vaccination in some sectors such as the health sector or schools. Beland et al. [2020] examine the short-term effects of the Covid-19 crisis on employment and wages and conclude a reduction in labor force participation and an increase in unemployment.

To analyze the impact of a higher reservation wage on the labor market and the natural rate of output, we modify the baseline scenario allowing for an increase of the parameter z. Figure 3 shows the changes in the labor market when the reservation wage rises.

Figure 3.

A higher risk perception associated with a certain occupation or an increase of unemployment benefits results in higher wage demand by workers for a given rate of unemployment. This is reflected in Figure 3 in an upward shift of the WS curve. As firms are unwilling to pay a higher real wage, given the tight situation in the labor market, unemployment will rise, as reflected in Figure 3 in the movement along the PS curve from point A to point B. Therefore, the natural rate of unemployment will increase until a new labor market equilibrium is reached.

These results are supported by our numerical example. Column 5 of Table 1 shows the effects of an increase in the value taken by the variable z from z = 1.8 to z = 1.9. As Figure 3 shows, this shock leads to a higher level of unemployment.

16 u=z↑−A1+μ=1.9−21+0.25=0.3 $$u = z \uparrow - {A \over {1 + \mu }} = 1.9 - {2 \over {1 + 0.25}} = 0.3$$

However, the real wage is unaffected:

17 WP=z↑−u=1.9−0.3=1.6 $${W \over P} = z \uparrow - u = 1.9 - 0.3 = 1.6$$

In equilibrium, the natural rate of unemployment rises to 0.3 and the real wage remains unaffected at its level of 1.6. However, the increase in the unemployment rate is associated with a decline in employment, and thus, a lower level of output.

18 Yn=A⋅Nn=2⋅875=1,750 $${Y_n} = A \cdot {N_n} = 2 \cdot 875 = 1,750$$

The effects of the reservation wage shock on the natural rate of unemployment and the natural rate of output are comparable to the effects of the mark-up shock.