Immigration and Job Creation

Abstract

Chassamboulli discusses recent research on the effect of immigration policies on job creation. New findings show that various types of immigrants can have a positive impact on employers’ incentives to post vacancies and create new jobs, which benefits also competing natives. Policies that restrict the presence of foreign labour in the labour market are less beneficial to natives compared to policies that do not decrease immigration, but shift instead its composition towards the types of immigrants that benefit the natives the most. We explore one such policy combination that eliminates illegal immigration but allows for foreigners to enter on temporary work permits. Chassamboulli shows that this policy can help attenuate the negative job creation effect of fewer illegal immigrants in the market.

Appendix

1.1 Model Details

1.1.1 Bellman Equations

The Bellman equations describing the values of job vacancies for unskilled and skilled workers in country 1 are as follows:

$$ r{V}_u=-{c}_u+q\left({\theta}_u\right)\left[\frac{u_I}{u_u}{J}_I+\frac{u_{uL}}{u_u}{J}_{uL}+\frac{u_{uN}}{u_u}{J}_{uN}\right] $$

(5.22)

$$ r{V}_s=-{c}_s+q\left({\theta}_s\right)\left[\frac{u_{sL}}{u_s}{J}_{sL}+\frac{u_{sN}}{u_s}{J}_{sN}\right] $$

(5.23)

Next, the value of a job depends on the type of worker filling the job:

$$ r{J}_{sN}={p}_s-{w}_{sN}+\left({s}_s+\tau \right)\left[{V}_s-{J}_{sN}\right] $$

(5.24)

$$ r{J}_{uN}={p}_u-{w}_{uN}+{x}_T{J}_T+\left({s}_u+\tau \right)\left[{V}_u-{J}_{uN}\right] $$

(5.25)

$$ r{J}_{sL}=\lambda {p}_s-{w}_{sL}+\left({s}_s+{d}_L+\tau \right)\left[{V}_s-{J}_{sL}\right] $$

(5.26)

$$ r{J}_{uL}={p}_u-{w}_{uL}+{x}_T{J}_T+\left({s}_u+{d}_L+\tau \right)\left[{V}_u-{J}_{uL}\right] $$

(5.27)

$$ r{J}_T={p}_u-{w}_T+\left({d}_T+\tau \right)\left[{V}_u-{J}_T\right] $$

(5.28)

$$ r{J}_I={p}_u-{w}_I+{x}_T{J}_T+\left({s}_u+{d}_I+\tau \right)\left[{V}_u-{J}_I\right] $$

(5.29)

The value of unemployment for each worker type satisfies:

$$ \left(r+\tau \right){U}_{iN}={b}_i-m\left({\theta}_i\right)+\left[{E}_{iN}-{U}_{iN}\right],\kern0.5em i=\left[s,u\right] $$

(5.30)

$$ \left(r+\tau \right){U}_{iL}={b}_i-{\pi}_L+m\left({\theta}_s\right)\left[{E}_{iL}-{U}_{iL}\right]+{d}_L\left[{U}_i^2-{U}_{iL}\right] $$

(5.31)

$$ \left(r+\tau \right){U}_I={b}_u-{\pi}_I+m\left({\theta}_u\right)\left[{E}_I-{U}_I\right]+{d}_I\left[{U}_u^2-{U}_I\right] $$

(5.32)

There is no value of being unemployed in country 1 for an immigrant on temporary work permit, since, as already mentioned, stay in country 1, in this case, is conditional on having a job. All immigrants on temporary work permits are employed, otherwise they must return home.

Finally, the value of being employed in steady state is given by the following five conditions relative to each country and worker type:

$$ \left(r+\tau \right){E}_{iN}={w}_{iN}+{s}_i\left[{U}_{iN}-{E}_{iN}\right],\kern0.5em i=\left[s,u\right] $$

(5.33)

$$ \left(r+\tau \right){E}_{iL}={w}_{iL}+{s}_i\left[{U}_{iL}-{E}_{iL}\right]+{d}_L\left[{U}_i^2-{E}_{iL}\right] $$

(5.34)

$$ \left(r+\tau \right){E}_I={w}_I+{s}_u\left[{U}_I-{E}_I\right]+{d}_I\left[{U}_u^2-{E}_I\right] $$

(5.35)

$$ \left(r+\tau \right){E}_T={w}_T+{d}_T\left[{U}_s^2-{E}_T\right] $$

(5.36)

1.1.2 Steady-State Conditions

By equating the outflow of immigrants of each type, which includes returns to the home country and labour force exits, to the inflow of new immigrants into each group we obtain the steady-state conditions for the number of legal immigrants, skilled and unskilled, L_s and L_u, respectively, the number of temporary workers, T, and the number of illegal immigrants, I:

$$ \left({d}_L+\tau \right){L}_i={x}_L{u}_i^2F\left({\tilde{z}}_{iL}\right) $$

(5.37)

$$ \left({d}_T+\tau \right)T={x}_T\left({e}_{uN}+{e}_{uL}+{e}_I\right) $$

(5.38)

$$ \left({d}_I+\tau \right)I={x}_I{u}_u^2F\left({\tilde{z}}_I\right) $$

(5.39)

where e_uL = L_u − u_uL is the number of unskilled legal immigrants that are employed, e_I = I − u_I is the number of unskilled illegal immigrants that are employed and e_uN = 1 − S − u_uN is the number of unskilled natives that are employed.

The conditions for the steady-state unemployment of natives (u_sN and u_uN), legal immigrants (u_sL and u_uL) and illegal immigrants (u_I) are as follows

$$ \tau \kern0.28em S+{s}_s\left(S-{u}_{sN}\right)=\left(m\left({\theta}_s\right)+\tau \right){u}_{sN} $$

(5.40)

$$ \tau \kern0.28em \left(1-S\right)+{s}_u\left(1-S-{u}_{uN}\right)=\left(m\left({\theta}_u\right)+\tau \right){u}_{uN} $$

(5.41)

$$ {s}_i\left({L}_{iL}-{u}_{iL}\right)+{x}_L{u}_i^2F\left({\tilde{z}}_{iL}\right)=\left(m\left({\theta}_i\right)+{d}_L+\tau \right){u}_{iL} $$

(5.42)

$$ {s}_u\left(I-{u}_I\right)+{x}_I{u}_u^2F\left({\tilde{z}}_I\right)=\left(m\left({\theta}_u\right)+{d}_I+\tau \right){u}_I $$

(5.43)

1.1.3 Wages

Using the Bellman Eqs. (5.22)–(5.36), the free-entry conditions (5.6), the Nash bargaining conditions (5.7)–(5.9) and the immigration conditions in (5.10) and (5.11), we can solve for the equilibrium wage rates:

$$ {w}_{sN}=\beta {p}_s+\left(1-\beta \right)\left[{b}_s+\beta m\left({\theta}_s\right){S}_{sN}\right] $$

(5.44)

$$ {w}_{uN}=\beta \left[{p}_u+{x}_T{J}_T\right]+\left(1-\beta \right)\left[{b}_u+\beta m\left({\theta}_u\right){S}_{uN}\right] $$

(5.45)

$$ {w}_{sL}=\beta \lambda {p}_s+\left(1-\beta \right)\left[{b}_s-{\pi}_L+\beta m\left({\theta}_s\right){S}_{sN}\right] $$

(5.46)

$$ {w}_{uL}=\beta \left[{p}_u+{x}_T{J}_T\right]+\left(1-\beta \right)\left[{b}_u-{\pi}_L+\beta m\left({\theta}_u\right){S}_{uN}\right] $$

(5.47)

$$ {w}_I=\beta \left[{p}_u+{x}_T{J}_T\right]+\left(1-\beta \right)\left[{b}_u-{\pi}_I+\beta m\left({\theta}_u\right){S}_I\right] $$

(5.48)

$$ {w}_T=\beta {p}_u+\left(1-\beta \right)\left(r+\tau \right){U}_u^2 $$

(5.49)

1.1.4 Value of a Job

Setting V_i = 0 in (5.24)–(5.29), we get:

$$ {J}_{sN}=\frac{p_s-{w}_{sN}}{r+{s}_s+\tau } $$

(5.50)

$$ {J}_{uN}=\frac{p_u+{x}_T{J}_T-{w}_{uN}}{r+{s}_u+\tau } $$

(5.51)

$$ {J}_{sL}=\frac{\lambda {p}_s-{w}_{sL}}{r+{s}_s+{d}_L+\tau } $$

(5.52)

$$ {J}_{uL}=\frac{p_u+{x}_T{J}_T-{w}_{uL}}{r+{s}_u+{d}_L+\tau } $$

(5.53)

$$ {J}_I=\frac{p_u+{x}_T{J}_T-{w}_I}{r+{s}_u+{d}_I+\tau } $$

(5.54)

$$ {J}_T=\frac{p_u-{w}_T}{r+{d}_T+\tau } $$

(5.55)

Apparently, the values of jobs to the firms increase with the worker’s productivity and decrease with the worker’s break up probability and wage, while the possibility of hiring a temporary worker increases the value of unskilled jobs.

Substituting the equilibrium wages (given in Eqs. (5.44)–(5.49)) into the equations above and using the Nash bargaining conditions in (5.7)–(5.9) we can write:

$$ {J}_{sN}=\left(1-\beta \right){S}_{sN}=\frac{\left(1-\beta \right)\left({p}_s-{b}_s\right)}{r+{s}_s+\tau +\beta m\left({\theta}_s\right)} $$

(5.56)

$$ {J}_{uN}=\left(1-\beta \right){S}_{uN}=\frac{\left(1-\beta \right)\left({p}_u-{b}_u\right)+{x}_T{J}_T}{r+{s}_u+\tau +\beta m\left({\theta}_u\right)} $$

(5.57)

$$ {J}_{sL}=\left(1-\beta \right){S}_{sL}=\frac{\left(1-\beta \right)\left(\lambda {p}_s-{b}_s+{\pi}_L\right)}{r+{s}_s+{d}_L+\tau +\beta m\left({\theta}_s\right)} $$

(5.58)

$$ {J}_{uL}=\left(1-\beta \right){S}_{uL}=\frac{\left(1-\beta \right)\left({p}_u-{b}_u+{\pi}_L\right)+{x}_T{J}_T}{r+{s}_u+{d}_L+\tau +\beta m\left({\theta}_u\right)} $$

(5.59)

$$ {J}_I=\left(1-\beta \right){S}_I=\frac{\left(1-\beta \right)\left({p}_u-{b}_u+{\pi}_I\right)+{x}_T{J}_T}{r+{s}_u+{d}_I+\tau +\beta m\left({\theta}_u\right)} $$

(5.60)

$$ {J}_T=\left(1-\beta \right){S}_I=\frac{\left(1-\beta \right)\left({p}_u-\left(r+\tau \right){U}_s^2\right)}{r+{d}_T+\tau } $$

(5.61)

1.1.5 Net Income

The net income of natives is given by the following expression:

$$ \tilde{Y}=Y+{b}_s{u}_{sN}+{b}_u{u}_{uN}-{c}_s{v}_s-{c}_u{v}_u-{w}_{sL}{e}_{sL}-{w}_{uL}{e}_{uL}-{w}_I{e}_I-{w}_TT $$

The expression above assumes that employers are natives and it shows that net income to natives includes total wage income to natives plus unemployment income to natives minus the cost of vacancy posting and the wages paid to immigrants. An alternative definition can be obtained by omitting the natives’ unemployment income.

$$ {\tilde{Y}}_1=\tilde{Y}-{b}_s{u}_{sN}+{b}_u{u}_{uN} $$

1.2 Parameterization of the Model

Table 5.2 Parameterization and matched moments

1.3 Sensitivity Checks

In the benchmark parameterization we set the duration of work permits to 12 months. In Table 5.3 below we examine how the results of the policy combination of replacing illegal immigrants with temporary workers change when the duration of work permits changes. The effects are robust to changes in the duration of work permits, since in all cases considered, both types of natives benefit in terms of job creation. We see that the positive job creation effect on unskilled workers decreases as the duration increases, mainly because with longer duration of work permits the inflow of temporary workers necessary to replace illegal immigrants is smaller. This means that opportunities to hire temporary workers are less frequent (i.e. x_T is smaller), which implies, in turn, that firms’ benefit less from the introduction of the temporary-worker programme.

Table 5.3 Sensitivity analysis with respect to the duration of work permits