Sectoral Impacts of International Labour Migration and Population Ageing in the Czech Republic

Abstract

This study assesses macroeconomic and sectoral impacts of demographic changes in the Czech Republic as a result of population ageing and international migration. To do so, it develops a unique dynamic Overlapping Generations Computable General Equilibrium (OLG–CGE) model with detailed representation of individuals of different ages, educational attainment and occupations, as well as interrelations among industrial sectors in producing intermediate and final outputs. The numerical simulations show that the Czech economy will face a substantial reduction in its effective labour supply and changes in aggregate as well as sectoral demand patterns, leading to lower economic growth (4.4% lower GDP by 2050 in absence of technological progress), increase in unit labour costs (5.2% higher wages in absence of inflation) and lower competitiveness of the economy as a whole. Replacement migration may alleviate the pressure, yet the current gross immigration would need to increase by at least 8-17 thousand individuals per year compared to the UN projections (a 15–34% increase) without changing emigration patterns in order to offset the adverse long-term effects.

Appendices

Appendix

The following text expands on the model description from Section 3 and provides additional details on the computation methodology.

Model equilibrium

The economy is assumed to be in an equilibrium in each period. The concept of equilibrium uses a recursive representation of the consumer’s problem following Heer & Maussner (2009) and is characterised by the following properties:

• 1. Individual and aggregate behaviour are consistent:

  $$\begin{aligned} N_t&= \sum \limits _{s=1}^{T} \sum \limits _{z \in Z} e_{s,z} w_{z,t} \end{aligned}$$

  (16)
  $$\begin{aligned} K_t&= \sum \limits _{s=1}^{T+T^R} \sum \limits _{z \in Z} A_{s,z,t} \end{aligned}$$

  (17)
  $$\begin{aligned} C_t&= \sum \limits _{s=1}^{T+T^R} \sum \limits _{z \in Z} C_{s,z,t} \end{aligned}$$

  (18)

• 2. Agents’ dynamic programs and firms’ optimisation problems are solved by satisfying Eqs. (2)–(13) using the relative prices ${w_t,r_t}$, pensions, and the individual policy rules $C_s(.)$ and $A_{s+1}(.)$.

• 3. The goods market clears:

  $$\begin{aligned} X_{t} = C_t + K_{t+1} - (1-\delta )K_t, \end{aligned}$$

  (19)

• 4. Intermediate goods $V_{i,p,t}$ and value added $Y_{p,t}$ are sufficient to generate production in each sector:

  $$\begin{aligned} X_{t}&\le \alpha _p^y \cdot Y_{p,t} \end{aligned}$$

  (20)
  $$\begin{aligned} X_{t}&\le \alpha _p^v \cdot V_{i,p,t} \end{aligned}$$

  (21)

• 5. Prices of goods and services $P_{p,t}^c$ are set so that the sectoral goods market clears given Eqs. 7, 8:

  $$\begin{aligned} X_{p,t} = Q_{p,t}^d \end{aligned}$$

  (22)

1.1 Solution Method

The simulation algorithm used in this study is based on Stepanek (2019), which follows earlier works of Heer & Maussner (2009) and Nishiyama & Smetters (2007), and further developed to work in a multi-sectoral environment following principally the works of Garau et al. (2013) and Fehr (2009). It utilises value function iteration to compute agents’ policy functions governing their optimal consumption and savings patterns conditional on the economic situation in each period. With a set of police functions for each group of agents z, firms set prices $P_{p,t}^c$ to put the sectoral demand and supply in equilibrium.

Specifically, the agent’s decision functions are calculated using backward induction, i.e. by analysing the optimal behaviour in the last period of agent’s live and, conditional on that, in all preceding periods. Let $V_s(A_{s,z},z_{s})$ be the value of the objective function of an s-year old agent from group z with wealth $A_{s,z}$. $V_s(A_{s,z},z)$ is defined as the solution to the dynamic program:

$$\begin{aligned} V_s(A_{s,z},z) = \max \limits _{A_{s+1},c_t} \{ \, U(s,z) + \pi _{s} \, \mathbb {E}[V_{s+1}(A_{s+1},z) (1+\rho )^{-1} \; | \; A_{s,z}, z] \} \end{aligned}$$

(23)

That is, subject to the budget constraints, optimal decision rules for consumption and next-period capital stock are functions of wealth and the idiosyncratic productivity shock, and associated with every optimal next period capital stock $A_{s+1}(A_{s,z},z)$ is an optimal consumption policy C(s, z) . Consequently, in each period, all agents can calculate the optimal aggregate consumption and saving behaviour in that period given their age, income group, probability of death, and other variables in the model.

Given the total consumption policy C(s, z) , agents then determine their sectoral consumption given the set of prices $P_{p,t}^q$ according to Eq. 8. At the same time, firms use the available capital and effective labour to produce goods and services for consumption. If there is a mismatch between demand and supply at the sectoral and/or aggregate level, prices $P_{p,t}^q$, $w_t$ and $r_t$ adjust accordingly.

The main simulation process can thus be characterised as follows:

• 1. Parametrise the model using behavioural parameters, calculate the optimal consumption and savings profile and set the scaling constants so that the outputs correspond to the empirical data in period $t = 1$.

• 2. In each subsequent period, use the outputs from the previous period $t - 1$ as a starting point and demographic changes as a source of variation to compute changes in $w_t$ and $r_t$ and, consequently, the set of endogenous parameters, such as pensions.

• 3. Compute the household’s decision functions by backward induction as for $t = 1$, resulting in the optimal aggregate consumption and saving behaviour for each cohort alive in period t.

• 4. Calculate the optimal sectoral demand and supply of goods and services.

• 5. Update prices $P_{p,t}^q$, $w_t$ and $r_t$ to increase/decrease the amount of consumption, savings and production to minimise the demand/supply differences.

• 6. Repeat steps 2-5 until the sectoral and aggregate demand and supply are in balance and proceed to the next period.

Fig. 5

Source CSO (2018)

Total number of employees and median wage by sector, occupation group and educational attainment.

Table 4 Industry, education and occupation classifications

Table 5 Value-added elasticity of substitution parameters used in the model

Fig. 6

Source CSO (2018)

Selected income profiles used in the model.

Table 6 Changes in the equilibrium wage by sector (% change compared to 2019), baseline scenario

Fig. 7

Effective labour supply as a result of migration