The macroeconomic impact of COVID-19 on occupations

Abstract

We adopt a pandemic-macroeconomic model to simulate the macroeconomic impact of COVID-19 on various occupations under both laissez-faire and government lockdown scenarios. We integrate a SIR model of virus transmission into a simplified neoclassical model and categorize occupations into two groups based on their ability to work remotely. Subsequently, we assess the shock impact of the pandemic on GDP, consumption, and working hours of flexible and rigid occupations. We find that these three variables declined during the pandemic, yet the consumption varied among individuals with different health status. The labour market experienced a recession, with workers in flexible occupations experiencing a relatively milder impact compared to those in rigid occupations. A larger proportion of remote work mitigated the recessionary effects, although it accentuated the disparities between occupations' income and working hours. The implementation of lockdown policies detrimentally affects welfare, similar to the pandemic itself, but the impact on flexible and rigid occupations differs from that in a laissez-faire scenario.

Appendices

Appendix 1: Computing the first-order conditions

This appendix summarizes the equations used to compute the competitive equilibrium of the benchmark SIR-macro model. We take the first-order conditions for the key variables.

We take the first-order conditions for $n_{f,t}^{s} ,n_{q,t}^{s} ,n_{f,t}^{i} ,n_{q,t}^{i} ,n_{f,t}^{r} ,n_{q,t}^{r}$:

$$\theta n_{f,t}^{s} = \lambda_{t}^{b} w_{f,t} + (\frac{1 - \kappa }{{(\phi^{f} - 1)\kappa + 1}})^{2} \lambda_{t}^{\tau } \pi_{2} (I_{t} N_{f,t}^{i} )$$

$$\theta n_{q,t}^{s} = \lambda_{t}^{b} w_{q,t} + (\frac{1 - \kappa }{{(\phi^{q} - 1)\kappa + 1}})^{2} \lambda_{t}^{\tau } \pi_{3} (I_{t} N_{q,t}^{i} )$$

$$\theta n_{f,t}^{i} = \lambda_{t}^{b} w_{f,t}$$

$$\theta n_{q,t}^{i} = \lambda_{t}^{b} w_{q,t}$$

$$\theta n_{f,t}^{r} = \lambda_{t}^{b} w_{f,t}$$

$$\theta n_{q,t}^{r} = \lambda_{t}^{b} w_{q,t}$$

Combined with the SIR model in households, the first-order conditions for $s_{t + 1} ,i_{t + 1} ,r_{t + 1}$ are:

$$\begin{gathered} \ln c_{t + 1}^{s} - \frac{\theta }{2}(n_{f,t + 1}^{s} )^{2} - \frac{\theta }{2}(n_{q,t + 1}^{s} )^{2} + \lambda_{{t{ + }1}}^{\tau } [\pi_{1} c_{{t{ + }1}}^{s} (I_{{t{ + }1}} C_{{t{ + }1}}^{i} ) + (\frac{1 - \kappa }{{(\phi^{f} - 1)\kappa + 1}})^{2} \pi_{2} n_{{f,t{ + }1}}^{s} (I_{{t{ + }1}} N_{{t{ + }1}}^{i} ) \hfill \\ +\; (\frac{1 - \kappa }{{(\phi^{q} - 1)\kappa + 1}})^{2} \pi_{3} n_{{q,t{ + }1}}^{s} (I_{{t{ + }1}} N_{{t{ + }1}}^{i} ) + \pi_{4} I_{{t{ + }1}} ]{ + }\lambda_{{t{ + }1}}^{b} \left[ {w_{f,t + 1} n_{f,t + 1}^{s} + w_{q,t + 1} n_{q,t + 1}^{s} - c_{t + 1}^{s} } \right] - \lambda_{t}^{s} /\beta + \lambda_{t + 1}^{s} = 0 \hfill \\ \end{gathered}$$

$$\begin{gathered} \ln c_{t + 1}^{i} - \frac{\theta }{2}(n_{f,t + 1}^{i} )^{2} - \frac{\theta }{2}(n_{q,t + 1}^{i} )^{2} + \lambda_{{t{ + }1}}^{b} \left[ {w_{f,t + 1} n_{f,t + 1}^{i} + w_{q,t + 1} n_{f,t + 1}^{i} - c_{t + 1}^{i} } \right] - \lambda_{t}^{i} /\beta \hfill \\ +\; \lambda_{t + 1}^{i} (1 - \pi_{r} - \pi_{d} ) + \lambda_{{t{ + }1}}^{r} \pi_{r} = 0 \hfill \\ \end{gathered}$$

$$\ln c_{t + 1}^{r} - \frac{\theta }{2}(n_{f,t + 1}^{r} )^{2} - \frac{\theta }{2}(n_{q,t + 1}^{r} )^{2} + \lambda_{t + 1}^{b} (w_{f,t + 1} n_{f,t + 1}^{r} + w_{q,t + 1} n_{q,t + 1}^{r} - c_{t + 1}^{r} ) - \lambda_{t}^{r} /\beta + \lambda_{t + 1}^{r} = 0$$

The first order condition for $\tau_{t}$ is:

$$\lambda_{t}^{i} = \lambda_{t}^{\tau } + \lambda_{t}^{s}$$

Appendix 2: Robustness with respect to $\kappa$

Figure 6 shows that when $\kappa = 0.3$, working hours decrease by 14.33 percent in flexible occupations and by 15.43 percent in rigid occupations. Hourly wages increase by 9.58 percent in flexible occupations and 10.72 percent in rigid occupations. Labour income experiences a decline of 6.12 percent in flexible occupations and 6.35 percent in rigid occupations.

Fig. 6

Response of working hours, wages, labour income in different occupations (k = 0.3)

Figure 7 shows that under $\kappa = 0.5$, working hours decline by 11.9 percent in flexible occupations and 15.21 percent in rigid occupations. Hourly wages increase by 7.49 percent in flexible occupations and 10.83 percent in rigid occupations. Moreover, labour income decreases by 5.3 percent in flexible occupations and 6.02 percent in rigid occupations.

Fig. 7

Response of working hours, wages, labour income in different occupations (k = 0.5)