Hate at first sight? Dynamic aspects of the electoral impact of migration: the case of Ukip

Abstract

In this paper, we test the hypothesis that the causal effect of immigrant presence on anti-immigrant votes is a short-run effect. For this purpose, we consider a distributed lag model and adapt the standard instrumental variable approach proposed by Altonji and Card (1991) to a dynamic framework. The evidence from our case study, votes for the UK Independent Party (Ukip) in recent European elections, supports our hypothesis. Furthermore, we find that this effect is robust to differences across areas in terms of population density and socioeconomic characteristics, and it is only partly explained by integration issues.

Appendices

Appendix 1. Biases of mis-specified lag structures

$$ {y}_{i,t}=\alpha +\beta {x}_{i,t}+{\gamma w}_{it}+{\varepsilon}_{it} $$

(5)

If instead the true relationship has a dynamic dimension, such a model is mis-specified since a more general case of Eq. 1 should be considered. The consistent estimator $\hat{\beta}$ for the parameter β of Eq. 5 would be a consistent estimator of the parameter β⁰ of the true model in Eq. 1 only if there is no serial correlation of x; thus, we can consider each lag as a different omitted variable which does not affect the correlation with the error term. A lack of serial correlation is clearly not so for the case of the immigration level variable. Conversely, if the x_{i, t} serial correlation is 1, the estimated coefficient $\hat{\beta}$ estimated would be a consistent estimator of the sum of all the coefficients β⁰, β¹, . . , β^L since the lags of x converge in plim to x. The unit root test that we performed confirms that this scenario is also not the case for immigration in the UK. In all other cases, the estimated $\hat{\beta}$ would be a consistent estimator of a linear combination of the true parameters β⁰, β¹, . . , β^L with weight given by the serial correlation of x with each specific lag l. In cases in which the coefficients may have different signs, as the one of this paper, the estimated $\hat{\beta}$ could also have the opposite sign of both the “true” coefficient β⁰ and the sum of all coefficients.

In our specific case, since the effect of new flows is different from the effect of overall immigration, the bias of the estimations of the overall effect of immigration will be higher when flows and stock are less correlated, that is, when there is a process of change in the location of migrants. The sensitivity of the results to the large city/country found in the literature that we have considered in Sect. 2 could be the result of the different effect of immigration in new, rather than the oldest, destinations of migration.

Appendix 2. Identification of OLS and IV estimations in the case of Eqs. 2 and 3

The finite lag model can be interpreted as a nonlinear case based on the lag operator. Using Wooldridge’s (2010, pg. 342) notation, we can write the following:

$$ y=m\left(x,{\boldsymbol{\theta}}_{\mathbf{0}}\right)+u=\alpha +{\beta}^0x+\theta g(x)+u $$

(6)

where using the lag operator L (which maps x_t onto x_t − l), the function g(x) is equal to Lx for Eq. 2 and to (1 − L)x for Eq. 3. Since the specifications are linear in the parameters (the lag operator is an algebraic function), if we have an instrument z_t for x_t at any t ∈ (1 − l; 1; …; T − l; T), we can rely on standard 2SLS estimations by adding g(z) as instrument for g(x) (ibid pg. 235). It is analogous to the linear case of two distinct endogenous variables instrumented with two distinct instruments.

Regarding the identification conditions, the order condition is satisfied since we have in each equation the number of excluded endogenous variables, and the number of included exogenous ones corresponds; however, for the rank condition, the dynamic relation between the instruments impose a further condition. Indeed, the covariance matrix of the estimator is given in the two cases of Eqs. 2 and 3, respectively, by the following:

$$ \left[\begin{array}{cc}{x}_t^{\prime }{z}_t& {x}_t^{\prime }{z}_{t-l}\\ {}{x}_{t-l}^{\prime }{z}_t& {x}_{t-l}^{\prime }{z}_{t-l}\end{array}\right] $$

(7)

$$ \left[\begin{array}{cc}{x}_t^{\prime }{z}_t& {x}_t^{\prime}\left({z}_t-{z}_{t-l}\right)\\ {}\left({x}_t-{x}_{t-l}\right)^{\prime }{z}_t& \left({x}_t-{x}_{t-l}\right)^{\prime}\left({z}_t-{z}_{t-l}\right)\end{array}\right] $$

(8)

If one of the two variables x and z has unit roots, in both cases, the expectation and the plim of this matrix would not have full ranks. In the case in Eq. 7, the rows or the column would correspond; in the second case, one column or one raw number would be null.

Appendix 3. Results using the specification in Eq. 2

We report in Table 12 an alternative version of Table 6 with regressions on the original FDL specification in Eq. 2. By construction, the coefficient of the lagged immigrant share is equal to the opposite of the coefficient of the flows in Table 6, while the coefficient of the first raw number is equal to the sum of the coefficients of the two first raw numbers in Table 6. While standard errors change, the results are all confirmed.

Table 12 Main results using the original FDL specification in Eq. 2

Appendix 4. Regressions by population density

In this appendix, we report the underlying regressions to the Figs. 7 and 8 on the average marginal effects of the immigrant share and of the immigration flows. In column (1), in order to reproduce previous findings, we change our model by removing the immigration flows and by adding the interaction term of the immigrant share with the population density (as a continuous variable); in column (2), we add an interaction term of the immigration flows too.

Table 13 Regressions with the interaction terms with the population density