Nationalism, cognitive ability, and interpersonal relations

Abstract

Interpersonal relations are shaped by the judgements associated with the social categories that individuals perceive in their social contacts. I develop a model of how those judgments form based on a theory of symbolic values. The model depicts the interaction between two values, one associated with an inherited ethnic trait (“nationality”) and one with an endogenous achievement trait (“income”). Individuals with lower cognitive ability are predicted to invest more value on nationalism and to have hostile relations with immigrants. Multiple equilibria are possible, and better schooling may eliminate equilibria with xenophobia. Econometric findings based on data from three large surveys corroborate the predictions derived from the theoretical model.

Appendix

Proof of Proposition 1

Since parents’ and children’s interests are perfectly aligned and their information sets are identical, an agent’s optimal strategy simply is to maximize (5) with respect to the three control variables e, δ _n and δ _a . To begin with, notice that the optimal strategy entails $\delta_{n}^{\ast} \geq 0$ for a domestic citizen ($\delta_{n}^{\ast} \leq 0$ for an immigrant). Suppose by way of contradiction that the optimal socialization of a domestic citizen entails $\delta_{n}^{\ast}<0.$ Starting from such a situation, a marginal increase in nationalism affects expected utility as follows

$$ \frac{\partial E[U]}{\partial \delta_{n}}=\beta -\frac{\delta_{n}^{\ast}}{\eta}+\frac{|\delta_{a}^{\ast}|-\delta_{n}^{\ast}} {\sigma}>0, $$

which contradicts the assertion that $\delta_{n}^{\ast}<0.$

The four mutually exclusive possible solutions are as follows.

Configuration 1: $\delta_{n}^{\ast }>0, \delta_{a}^{\ast }<0, e^{\ast }=0.$

The FOCs are in this case:

$$ \frac{\partial E[U]}{\partial \delta_{a}}=(2\pi -1)\beta -\frac{\delta _{a}^{\ast}}{\alpha}+\frac{\delta_{n}^{\ast}-\delta_{a}^{\ast}}{\sigma}=0, $$

(7)

$$\frac{\partial E[U]}{\partial \delta_{n}}=\beta -\frac{\delta_{n}^{\ast}}{\eta} -\frac{\delta_{n}^{\ast}-\delta_{a}^{\ast}}{\sigma}=0, $$

(8)

while the corner solution e* = 0 requires

$$ \left(w_{H}-w_{L}\right)+\beta \left(\widehat{v}_{11}-\widehat{v}_{01}+2\delta_{a}^{\ast}\right)+\gamma (\hbox{soc}\,v_{11}-\hbox{soc}\,v_{01})\leq 0. $$

Solving for the FOCs yields:

$$ \begin{aligned} \delta_{a}^{\ast}&=-\frac{\alpha \beta [ (1-2\pi )\sigma -2\pi \eta]} {\alpha +\eta +\sigma},\\ \delta_{n}^{\ast}&=\frac{\beta \eta (\sigma +2\alpha \pi)}{\alpha +\eta +\sigma}. \end{aligned} $$

(9)

Configuration 2: $\delta_{n}^{\ast }>0, \delta_{a}^{\ast }<0, e^{\ast }>0.$

The associated FOCs are

$$ \frac{\partial E[U]}{\partial \delta_{a}}=\left[2\left(\pi +\theta e^{\ast}\right)-1\right]\beta -\frac{\delta_{a}^{\ast}}{\alpha}+\frac{\delta_{n}^{\ast}-\delta_{a}^{\ast}}{\sigma}=0. $$

(10)

(8) and (6). Solving the equation system yields

$$ \begin{aligned} e^{\ast}&=\frac{\theta \omega \left\{ \left(\Updelta w+\beta \left(\widehat{v}_{11}- \widehat{v}_{01}\right)+\gamma \Updelta \widehat{\hbox{soc}\,v}\right)(\alpha +\eta +\sigma)+2\alpha \beta^{2}[\eta -(1-2\pi )(\eta +\sigma )]\right\}}{\alpha +\eta +\sigma -4\alpha \beta^{2}\theta^{2}\omega (\eta +\sigma )} \\ \delta_{a}^{\ast }&=-\frac{\alpha \beta \left\{ (1-2\pi )\sigma -2\pi \eta -2\omega \theta^{2}\left[\Updelta w+\beta \left(\widehat{v}_{11}-\widehat{v} _{01}\right)+\gamma \Updelta \widehat{\hbox{soc}\,v}\right](\eta +\sigma )\right\}}{\alpha +\eta +\sigma -4\alpha \beta^{2}\theta^{2}\omega (\eta +\sigma )}\\ \delta_{n}^{\ast }&=\frac{\beta \eta \left\{ \sigma +2\alpha \pi +2\alpha \theta^{2}\omega \left[ \Updelta w+\beta \left(\widehat{v}_{11}-\widehat{v} _{01}\right)+\gamma \Updelta \widehat{\hbox{soc}\,v}-2\beta^{2}\sigma \right]\right\}}{\alpha +\eta +\sigma -4\alpha \beta^{2}\theta^{2}\omega (\eta +\sigma )}. \end{aligned} $$

(11)

Configuration 3: $\delta_{n}^{\ast }>0, \delta_{a}^{\ast }=0, e^{\ast }>0.$

The FOCs are (8) and (6). The corner solution $\delta_{a}^{\ast }=0$ requires

$$ \left[2\left(\pi +\theta e^{\ast }\right)-1\right]\beta -\frac{\delta_{n}^{\ast}}{\sigma} \leq 0 $$

(12)

and

$$ \left[2\left(\pi +\theta e^{\ast}\right)-1\right]\beta +\frac{\delta_{n}^{\ast }}{\sigma } \geq 0. $$

(13)

The optimal strategy has (6) andConfiguration 4:

$$ \delta_{n}^{\ast}=\frac{\beta \eta \sigma }{\eta +\sigma }. $$

(14)

$\delta_{n}^{\ast }>0, \delta_{a}^{\ast }>0, e^{\ast }>0.$

The FOCs are

$$ \frac{\partial E[U]}{\partial \delta_{a}}=\left[2\left(\pi +\theta e^{\ast}\right)-1\right] \beta -\frac{\delta_{a}^{\ast}}{\alpha}-\frac{\delta_{n}^{\ast}+\delta_{a}^{\ast}} {\sigma}=0, $$

(15)

$$ \frac{\partial E[U]}{\partial \delta_{n}}=\beta -\frac{\delta_{n}^{\ast}}{\eta}-\frac{\delta_{n}^{\ast}+\delta_{a}^{\ast}}{\sigma}=0, $$

(16)

and (6). Solving the equation system yields

$$ \begin{aligned} e^{\ast}&=\frac{\theta \omega \left\{ \left(\Updelta w+\beta \left(\widehat{v}_{11}- \widehat{v}_{01}\right)+\gamma \Updelta \widehat{\hbox{soc}\,v}\right)(\alpha +\eta +\sigma )+2\alpha \beta^{2}[(2\pi -1)(\eta +\sigma )-\eta ]\right\}}{\alpha +\eta +\sigma -4\alpha \beta^{2}\theta^{2}\omega (\eta +\sigma )}\\ \delta_{a}^{\ast}&=\frac{\alpha \beta \left\{ (2\pi -1)(\eta +\sigma )-\eta +2\omega \theta^{2}\left[\Updelta w+\beta \left(\widehat{v}_{11}-\widehat{v} _{01}\right)+\gamma \Updelta \widehat{\hbox{soc}\,v}\right](\eta +\sigma )\right\}}{\alpha +\eta +\sigma -4\alpha \beta^{2}\theta^{2}\omega (\eta +\sigma )}\\ \delta_{n}^{\ast }&=\frac{\beta \eta \left\{ \sigma +2\alpha (1-\pi )-2\alpha \theta^{2}\omega \left[\Updelta w+\beta \left(\widehat{v}_{11}- \widehat{v}_{01}\right)+\gamma \Updelta \widehat{\hbox{soc}\,v}+2\beta^{2}\sigma \right]\right\} }{\alpha +\eta +\sigma -4\alpha \beta^{2}\theta^{2}\omega (\eta +\sigma )}. \end{aligned} $$

(17)

Simple algebraic manipulations show that the eight remaining possible configurations can never be optimal. $\square$

Proof of Proposition 2

Equilibrium existence follows from standard theorems of existence of Nash equilibrium for nonatomic games, see e.g., Rath (1992). Equilibrium multiplicity can be ruled out for γ = 0, while standard social-multiplier arguments show that for γ sufficiently large multiple equilibria arise. $\square$

Proof of Proposition 3

For later use, define

$$ \Upgamma \equiv w_{H}-w_{L}+\beta \left(\widehat{v}_{11}-\widehat{v}_{01}\right)+\gamma (\hbox{soc}\,v_{11}-\hbox{soc}\,v_{01}) $$

and denote by

$$ \Uptheta \equiv \frac{\alpha +\eta +\sigma }{4\alpha \beta^{2}\omega (\eta +\sigma )} $$

the largest possible value of θ².

Configuration 1: Parameter restrictions are necessary to guarantee $\delta_{a}^{\ast }<0$ and e* = 0. If $\Upgamma >0,$ the condition for e* = 0 is necessary and sufficient for the existence of configuration 1; it can be written as

$$ \pi \leq \frac{2\alpha \beta^{2}\sigma -(\alpha +\eta +\sigma )\Upgamma }{4\alpha \beta^{2}(\eta +\sigma )}\equiv \pi_{1}. $$

This configuration only exists if π₁ > 0, which is assumed to be the case. By differentiating (9), one obtains $\partial \delta_{n}^{\ast }/\partial \pi >0.$

Configuration 2: It is easy to check that the parameter restriction that implies e* > 0 also guarantees $\delta_{n}^{\ast}>0.$ That restriction is

$$ \pi >\pi_{1}. $$

In order for configuration 2 to exist, parameters must also guarantee $\delta_{a}^{\ast}<0.$ This condition can be written as

$$ \pi <\frac{\sigma -2\theta^{2}\omega (\eta +\sigma )\Upgamma } {2(\eta +\sigma )}\equiv \pi_{2}\left(\theta^{2}\right). $$

As it is easily checked, π₂(θ²) > π₁ if $\theta^{2}\in (0,\Uptheta )$ and $\pi_{2}(\Uptheta )=\pi_{1},$ which shows that configuration 2 occurs if π₁ < π < π₂(θ²). By differentiating (11) one obtains $\partial \delta_{n}^{\ast }/\partial \pi >0.$

Configuration 3: Parameter restrictions are only required to ensure that $\delta_{a}^{\ast}=0.$ Condition (13) is equivalent to

$$ \pi \geq \pi_{2}\left(\theta^{2}\right). $$

Condition (12) is equivalent to

$$ \pi \leq \frac{\sigma +2\eta -2\theta^{2}\omega (\eta +\sigma )\Upgamma }{2(\eta +\sigma )}\equiv \pi_{3}\left(\theta^{2}\right). $$

As it is easily checked, π₃(θ²) > π₂(θ²), which shows that configuration 3 occurs if π₂(θ²) ≤ π ≤ π₃(θ²). By differentiating (14) one obtains $\partial \delta_{n}^{\ast}/\partial \pi =0.$

Configuration 4: The parameter restriction for $\delta_{a}^{\ast}>0$ also ensures e* > 0. Condition $\delta_{a}^{\ast }>0$ is equivalent to

$$ \pi >\pi_{3}\left(\theta^{2}\right). $$

The equilibrium condition $\delta_{n}^{\ast }>0$ requires

$$ \pi <\frac{\sigma +2\alpha -2\alpha \theta^{2}\omega \Upgamma -4\alpha \beta ^{2}\sigma \theta^{2}\omega }{2} \equiv \pi_{4}\left(\theta^{2}\right). $$

As it is easily checked, π₄(θ²) > π₃(θ²) if $\theta^{2}\in (0,\Uptheta)$ and $\pi_{4}(\Uptheta)=\pi_{3}(\Uptheta),$ which shows that configuration 4 occurs if $\pi_{3}(\Uptheta )<\pi <\pi_{4}\left(\theta^{2}\right).$ By differentiating (17) one obtains $\partial \delta_{n}^{\ast }/\partial \pi <0.$ $\square$