Robustness checks

Although the general equilibrium model is built to reflect the Belgian economy, it remains an imperfect representation of reality. For example, the parameter values used in the above‑mentioned model are only estimates of the true behaviour of actors in the model. To avoid excessive reliance on these parameter values, this section compares the economic impact of recent immigration using several sets of exogenous parameters.

More specifically, three alternative sets of parameters will be compared to the baseline (see table 2). The first set strengthens the elasticity of labour supply to the expected income from labour (see table 3). This implies that wage or tax changes have a stronger impact on the labour market participation of individuals. The second set strengthens the elasticity of substitution between age and origin groups, thereby limiting the relative productivity and wage impact of immigration (see table 4). The third set strengthens the elasticity of substitution between goods, essentially removing the market size impact on welfare of individuals (see table 5). Finally, a fourth set of exogenous parameters, standardising the parameters governing the frictional labour market, has been assessed.

However, because recent immigration only showed a negligible impact on unemployment in the baseline model and this is not different using this set of parameters, it will not be discussed separately.

Following recent literature on the estimation of the elasticity of labour supply to labour income, the consensus value of the elasticity is higher than the estimate for Belgium used in the model. More precisely,

the consensus elasticity has been found to be around 0.5  to 1  (e.g. Chetty et  al.,  2011 ; Rogerson and Wallenius,  2013). Using an elasticity of labour supply equal to 0.5, the impact of recent immigration on wages and unemployment appears to be similar to the baseline parametrisation. By  contrast, the stronger elasticity of labour supply to labour income implies that the participation effect of recent immigration will be higher for both natives and immigrants. Consequently, the tax base increases relatively strongly and the tax rate comes down more sharply than in the baseline scenario. When using the consensus elasticities of labour supply to labour income, the income and welfare effects of immigration will thus be more positive than in the baseline scenario.

Alternatively, inserting stronger elasticities of substitution between age and origin groups, the overall welfare effect of recent immigration declines. However, unlike the first set of alternative parameters where both immigrants and natives experience lower welfare standards, the welfare of immigrants appears to increase more strongly than in the baseline model. A different mechanism thus appears behind the lower welfare in this iteration of the model. Looking at the wage change because of immigration, the stronger elasticities of substitution appear to significantly reduce the positive wage impact on natives. In return, the wages of immigrants fall less sharply. Thanks to the reduction of the tax rate, which remains close to the baseline reduction, participation of natives is only slightly lower than in the baseline parametrisation, while it increases more strongly for immigrants.

So, using stronger elasticities between age and origin groups, the welfare gains of natives (and older individuals) Table 2

Impact of recent immigration in baseline parametrisation

Natives Previously established

immigrants Total ¹

Wage (in %) 0.406 −2.022 −0.069

Participation (pp) 0.292 −0.053 0.158

Unemployment (pp) −0.025 −0.073 0.199

Income (in %) 1.003 0.243 0.686

Welfare (in %) 1.498 0.587 1.154

Tax rate (pp) −0.599

Source : NBB calculations.

1 Including recent immigrants

Table 3

Impact of recent immigration with a stronger elasticity of labour supply

Natives Previously established

immigrants Total ¹

Wage (in %) 0.375 −2.004 −0.092

Participation (pp) 1.098 0.227 0.868

Unemployment (pp) −0.073 −0.178 0.141

Income (in %) 0.800 0.158 0.502

Welfare (in %) 2.467 1.079 2.043

Tax rate (pp) −1.113

Source : NBB calculations.

1 Including recent immigrants

at the cost of immigrants (and younger individuals) will be reduced. The positive public finance and market size effects will nevertheless still lead to income and welfare effects similar to the baseline.

The final robustness check involves removing the market size effect from the model. Once again, wage and unemployment effects of immigration remain similar to the baseline parametrisation. However, for both immigrants and natives, the participation effect will be significantly lower because the value of consumption and thus of labour market income will no longer increase with market size. This in turn leads to a slightly lower fall in the tax rate and to a slightly weaker income effect of immigration. Because the market size impact on the welfare of individuals also disappears, the welfare effect of immigration is less than half as large as with the baseline parametrisation. Nonetheless, even without the market size effect, the welfare effect of recent immigration on natives is still positive. But, immigrants are still worse off due to recent immigration in this setting.

Overall, the section shows that the findings of this Part III are robust to changes in the parametrisation of the exogenous variables employed.

Table 4

Impact of recent immigration with stronger elasticities of substitution between age and origin groups

Natives Previously established

immigrants Total ¹

Wage (in %) 0.118 −0.729 −0.113

Participation (pp) 0.254 0.121 0.158

Unemployment (pp) −0.034 −0.086 0.189

Income (in %) 0.795 1.104 0.649

Welfare (in %) 1.300 1.375 1.114

Tax rate (pp) −0.577

Source : NBB calculations.

1 Including recent immigrants.

Table 5

Impact of recent immigration without market size effects

Natives Previously established

immigrants Total ¹

Wage (in %) 0.401 −2.048 −0.052

Participation (pp) 0.192 −0.142 0.057

Unemployment (pp) −0.026 −0.077 0.238

Income (in %) 0.857 0.076 0.528

Welfare (in %) 0.789 −0.139 0.436

Tax rate (pp) −0.531

Source : NBB calculations.

1 Including recent immigrants

4.2 Assumptions

In the presented model of the Belgian economy, we disregard other countries. The way immigration alters trade and investment flows between countries and its impact on the economy could therefore not be modelled.

Trade and investment links between countries is more thoroughly discussed in section 4.3 as an element of the productivity impact of immigration.

A second assumption of the model is perfectly mobile capital. This implies that capital will immediately flow to places where the highest return can be achieved, immediately depressing it. This essentially leads to constant returns to capital, because the capital stock immediately adapts to any changes in the stock of other production factors such as labour. This is found to the be most likely assumption according to e.g. Ottaviano and Peri (2012) in the US. In  Belgium, being a small open economy, this assumption is even more likely to hold. If  capital is imperfectly mobile, the distinction between a short‑ and long‑run effect could be made. Because of a shortage of capital in the short run, labour will not be optimally productive, leading to a negative effect in the short run.

As capital stocks adapt to the labour supply in the long run, this negative effect disappears.

Third, the labour market is assumed to be perfectly competitive, which implies that wage differences in the model are perfectly attributable to productivity differences. However, there is ample evidence of labour market discrimination against immigrants (see section 2.5 of Part II). This is the case in the selection process for potential employees (Baert et al., 2015) as well as in the wage earned of employed workers with the same productivity level (Solé and Parella, 2003 ; Harris et al., 2006). Since our model is calibrated on the observed wage differences between immigrants and natives, the actual productivity gap is over‑estimated, as is immigrants’ disutility of entering the labour market and their separation rate. Nonetheless, assuming discrimination remains stable over time, the outcomes should remain representative for the Belgian economy. However, it is important to bear in mind that the model under‑estimates the productivity of immigrants, and that reducing discrimination in the selection process is also a factor with potential to improve the economic performance of immigrants.

Fourth, our model imposes a flat income tax rate. Should taxation be progressive instead, government revenues would depend relatively more on high‑skilled incomes. As  the recent wave of immigrants is more often high‑skilled than the native average, recent immigration would even further increase government incomes under progressive taxation. Through redistribution, higher government revenue would also imply higher native incomes.

Another assumption that could have a big impact on the findings of the model is its static nature. As  the complementarity between groups of individuals is fixed by exogenous parameters, individuals are assumed to never change their skill set. However, empirical evidence shows that an immigrant inflow in European economies leads to native occupational shifts from manual jobs to more complex jobs (D’Amuri and Peri, 2010 ; Cattaneo et  al.,  2015). Consequently, immigration has positive effects on native low skilled wages, employment and occupational mobility (Foged and Peri, 2016). Low‑skilled natives are thus clearly found to adapt their skill set to become more complementary to the inflow of immigrants. In the same vein, it is quite likely that immigrants will adapt their skill set to better resemble the skills of natives over time (e.g. language classes). Note that the report makes use of a five‑year immigration shock, which is deemed sufficiently short to accept the assumption.