Labour Economics Problem Set 3: Migration and Inequality & Minimum Wage
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Labour Economics
Problem Set 3: Migration and Inequality & Minimum Wage
Migration
1. Roy Model & Chiquiar/Hansen Consider the study Chiquiar/Hansen (2005), which also presents an empirical version of the Roy model, and the corresponding lecture slides.
(a) The presented model stresses the importance of migration costs and schooling. First,
consider the case of constant moving costs. Using the equations and graph presented in the study and on the slides, describe formally a situation in which none would move from Mexico to the US.
(b) Now, consider the case of decreasing moving costs. Formally describe two hypothetical
situations in which none would move to the US. [Hint: Also think about the schooling distribution in Mexico.]
(c) The figures 3 a and 4 a & b in Chiaquar/Hanson (2005) present actual and counterfac- tual wage distributions of Mexican residents and immigrants in the US, respectively. Describe (consulting as well the paper) what the first and the second pair of figures exactly display.
(d) What does ”counterfactual”refer to in the context of Chiaquar/Hanson (2005)?
(e) On which main assumption does the counterfactual wage distribution for immigrants
rely?
(f) What do we learn from the graphs about the self-selection of Mexican immigrants into the US (Figures 4a and 4b)?
(g) Finally, consider the OLS wage regressions, lecture slide 34. What do the results tell us
about the evolution of the returns to schooling of Mexican Immigrants once they are in the U.S. (i.e., assimilation over time)?
Inequality & Minimum Wages
2. Earnings Inequalities & Skill-Biased Technological Change We saw in the lecture evidence for di↵erent phenomena of earnings inequality across the distribution. How much of these evidence patterns can be theoretically replicated by a simple ”canonical model” addressing the skill- biased technological change? Such a model introduces di↵erent skill groups: high- and low-skilled workers. Moreover, the model assumes as well the following:
– Competitive labour market
– The two skill groups, high and low skilled, work in di↵erent occupations and are thus imperfect substitutes in production. L and H are the total supply of low skilled and high
skilled labour, respectively (each containing a certain amount of workers, respectively).
– Assume a CES production function for the economy: Y = h(AL L) +(AH H)] σ−1 whereby σ 2 [0, 1) is the elasticity of substitution between high skill and low skill labour.
– AH and AL are factor- augmenting technologies. I.e., technological change (a change in A) increases productivity of either high or low skill workers or both (but the used technologies do not replace or abolish certain skills).
Now, let us derive predictions from this model and assess them in the above-mentioned context.
(a) Derive the two FOC for wL and wH , keeping in mind that the labour market is com-
petitive (i .e . , wage equals marginal product of labour) .
(b) What happens in case of technological change? Thus, consider the comparative statics of how high- and low-skilled wages are a↵ected by improvements in AH and in AL , respectively. What are the signs of these four derivatives? Interpret them in the context of the above-mentioned evidence . Which phenomena can they predict, which not?
(c) Next, compute the skill premium (relative price of skills), i .e . ! = . Rewrite the result also in logs .
(d) Now, let us consider Tinbergen’s race of technology vs . education . Within this model, the first can be best represented as relative skill bias of technology, , the second as relative supply of (high) skills, i .e . . Using the result in logs from (c), show how the (ln) skill premium is a↵ected by changes in (i) the amount of the (ln) skill bias of technology and (ii) the (ln) relative supply of skills? Interpret the results in the context of Tinbergen’s race .
(e) Considering all the results and insights above: Which key phenomena of earnings in-
equality across the distribution can be explained by such a simple ”canonical model”? Which cannot?
3. Minimum Wages Some theoretical considerations and an empirical study, Dickens et al .
(1999), on the e↵ect of minimum wages on earnings in the UK . You do not need to read the whole study to find the replies to the questions; it should be sufficient to have a look at the empirical part where necessary.
(a) Based on the lecture, briefly explain under which assumptions and circumstances min-
imum wages can lead to positive employment e↵ects .
(b) Draw a graph that illustrates this prediction .
(c) Name at least one example of an application where these assumptions could be reason- able .
(d) Now, consider the study by Dickens et al . (1999) who investigated the e↵ects of min- imum wages set by industry-specific Wage Councils on employment and earnings out- comes .
Consider Table 3 in the study. Explain the empirical measure they use to capture the minimum wage e↵ect, i .e . , ”toughness” .
(e) What can you conclude from Table 3 with respect to the estimated e↵ect of the imposed minimum wages on employment and hours? Does this support the classical theoretical view (without monopsony power) or rather not?
(f) The authors also assess how the minimum wages a↵ect the whole wage distribution.
This is done in Table 2 of the study. Based on these results, explain how the minimum wages a↵ect the di↵erent parts of the wage distribution . What do the results in total mean for the shape of the wage distribution (as compared to a counterfactual where no minimum wage is present)?
2023-04-17