Workers in Questionville speak one of two languages: A and B. Employers in Questionville are native speakers of language A, and they have a rudimentary understanding of language B. Each worker has a constant marginal product of labour, which is different for different workers. The marginal product of labour for the average worker is MP¯¯¯¯¯¯¯¯¯=150; this is the same for speakers of language A and speakers of language B. Employers do not observe workers' productivity; however, they do interview each worker, which gives employers an imperfect signal, S, of that worker's productivity. The labour market in Questionville is competitive, so employers pay workers what they believe to be their marginal product of labour. Thus, the wage an employer will pay a worker who gives a signal of S is equal to:

W=ρMP¯¯¯¯¯¯¯¯¯+(1−ρ)S

The weight ρ is contingent on group: ρA=0.2 and ρB=0.4.

(a) Offer an intuitive explanation for why ρB>ρA

(b) Builds on Question a] A worker who speaks language A gives a signal S=160, and earns the same wage as a worker who speaks language B and gives a signal S=S′. What is S′?

(c) [Builds on Questions a & b] You conduct a survey of Question Ville employees. You collect data on wages (W ), interview performance (S), and language spoken, and you estimate following regressions of W on S separately for speakers of languages A and B. These regression estimates allow you to compute average wages for speakers of languages A and B in the following way:

W¯¯¯¯¯A=α^A+β^AS¯¯¯A

and

W¯¯¯¯¯B=α^B+β^BS¯¯¯B

You obtain the following regression estimates: α^A=30,β^A=0.8,α^B=40,β^B=0.6. Are these results consistent with the wage setting rule described in part (a)? Explain.

(d) [Builds on Questions a, b & c] You learn that S¯¯¯A=155 and S¯¯¯B=148. Decompose the language-based wage gap into a portion due to differences in the average signal, and a portion due to discrimination.