Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

Income and Occupational Inequality in Labour Markets

Part II

1. Income and occupational inequality.

a) Overview

In the first part of this lecture, we have explained the declining share of labour income. We have also demonstrated that the immigration policy reforms by the federal government was a contributing factor.

In the second part of this lecture, we are going to explore why there is:

· growing income inequality across workers,

· involuntary unemployment.

Our first task we will be to document these two facts. Then, we will build two economic models to explain these phenomena. Finally, we will analyze the economic impact of skill acquisition and educational attainment on economic inequality.

The first model is the efficiency wage model, which is a labour market model that explains involuntary unemployment as an equilibrium outcome.

The second model is the Harris-Todaro model, which explains why the acquisition of skills/education could result in:

· more unequal distribution of labour income,

· higher unemployment rate.

An underlying assumption is that:

· the labour market for unskilled jobs is represented by the competitive model from the first part of the lecture,

· the labour market for skilled jobs is represented by the efficiency wage model from the second part of the lecture.

b) Evidence

Figure 1 reveals that the relative share of the middle-class earnings has declined, while the correspond shares of both higher and lower earnings has increased.

This general pattern holds for both males’ and females’ earnings.

Lower earnings are defined as those below 50 % of the median earnings.

Middle class earnings are defined as those between 50 % and 200 % of the median earnings.

Higher earnings are defined as those above 200 % of the median earnings.

Figure 1

Source: IRPP (2016)

Table 1 reveals that a further decomposition by gender and type of employment (full-time, full-year) reveals a similar pattern.

The reason that we would like to focus on the full-time, full-year category is to isolate the impact of hours worked and have per hour wages being comparable.

Part-time work could be due to schooling, parenting or involuntary underemployment.

Table 1

Source: IRPP (2016)

2. Efficiency Wage Model

a) Overview

In the competitive model, we have found that there always exists an equilibrium wage, for which labour demand equals labour supply. Consequently, all workers who are willing to take a job at the market-clearing wage are employed. That is, there is no involuntary unemployment.

Note: At the market-clearing wage, labour supply equals labour demand. In the competitive model, the equilibrium (or prevailing) wage is also the market-clearing wage.

In this section, we will develop the efficiency wage model, in which we demonstrate that in equilibrium:

· the prevailing wage is set above the market-clearing wage,

· There is involuntary employment.

b) Mechanism

Firms have an incentive to pay a higher wage in order to induce workers to exert a higher effort level.

Firms maximize profit by choosing the highest effort per wage ratio. That I, firms offer a contract to each worker that specifies two elements: a wage, and effort, .

We will show that the contract that maximizes firm profits results in:

· higher equilibrium wage than the market clearing wage, i.e., ,

· lower employment than the market clearing employment, .

Why is this outcome self-sustaining?

This hiring scheme is profit-maximizing profit because it induces the hired workers to exert a higher effort level by paying them a higher wage than in competitive markets.

What if there are no competitive markets, in which workers can find alternative employment? The presence of involuntary unemployment provides an even greater incentive for those hired to exert the specified in the contract effort level.

c) Mechanics

Each firm maximizes profit:

· by offering a wage that maximizes workers' effort per dollar cost ().

· by choosing employment according to the labour demand curve such that the revenue from each hired worker is at least large as the cost – the wage .

Figure 2

Effort curve – shows the relationship between worker effort, E, and the real wage workers (w) receive.

Assumption: effort curve is upward sloping, S-shaped.

Effort is maximized, where the line from the origin is tangent to the effort curve.

Efficiency wage – the wage, for which worker effort per wage is maximized.

Numerical example:

Suppose that there are 200 workers willing to accept employment at any wage.

Suppose a firm that faces the labour demand curve is given by can offer one of the following four contracts.

Table 2

Contract	Wage	Effort	Effort per wage ratio	Profit maximized
1	8	7	0.88	No
2	10	10	1.00	No
3	12	15	1.25	Yes
4	14	17	1.21	No

The equilibrium is determined in two steps:

1) Each firm maximizes the profit from each worker whenever the maximum effort per wage is exerted.

For the numerical example, the maximum effort per wage is maximized for , which is the efficiency wage.

2) Each firm maximizes total profit by choosing to hire such that , i.e., the firm just makes positive profit from hiring the last worker it hires.

The left-hand side of the labour demand curve is the cost of hiring a worker, while the right-hand side represents the revenue generated from hiring a worker.

This requires solving for employment only from the labour demand curve.

For the numerical example, this requires solving the equation

for upon inserting the contract values .

Note that the equilibrium employment is , which is less than the number of workers, , willing to work at this wage .

The equilibrium unemployment is

Figure 3

3. Harris-Todaro Model

a) Overview

The Harris-Todaro model is used to describe two types of phenomena:

· geographic migration, e.g., rural-urban,

· skill acquisition (migration from one skill level to another).

That is, by acquiring skills unskilled workers ‘migrate’ to the labour market of the skilled workers.

For the rest of the analysis, we will consider two markets: one for skilled labour and one for unskilled labour.

We will assume that the two markets are segmented for the following reasons:

· Unskilled labour is not qualified to do the tasks of skilled labour,

· Skilled labour is ‘overqualified’ to do the tasks of unskilled labour.

b) Key facts

I will lay out several key facts about the earnings of the two groups of workers.

· Composition of labour force

The share of skilled labour force has risen due to skill acquisition, e.g., enrollment into postsecondary institutions.

For instance, the share of university graduates more than doubled from 1981 to 2010 (Kelly and Green, 2016).

· Earnings

The emergence of high variation in earnings among skilled workers.

· Avg. earnings of skilled workers > Avg. earnings of unskilled workers

University graduate earned between 21 - 30 % more than high school graduates between 1981 and 2010 (Kelly and Green, 2016).

· Avg. earnings of skilled worked not employed in the efficiency wage model < Avg. income of unskilled workers

Kelly and Green (2016) report that there is a larger within-group variation than between-group variation.

Within-group variation refers to income inequality between workers of the same skill, while between-group variation refers to income inequality across groups of different skill level.

The reasons for low earnings among skilled workers include:

· unemployment and underemployment,

· employment in low-paying jobs for skilled workers.

Low-paying jobs may employ the residual skilled labour but in jobs with a range of undesirable characteristics, e.g., low pay, less safe, few/no benefits, little/no job security, etc.

We will explore why it is in people’s self-interest to acquire skills by attending postsecondary institutions even if they end up in employment with worse pay relative to an unskilled job.

c) Model’s assumptions

Consider two sectors of the economy: one for skilled labour and one for unskilled labour.

We will assume that the two markets are segmented for the following reasons:

· Unskilled labour is not qualified to do the tasks of skilled labour,

· Skilled labour is ‘overqualified’ to do the tasks of unskilled labour.

The corresponding labour markets for:

· Unskilled – competitive labour market

· Skilled – efficiency wage labour market

Table 3

Variable	Skilled labour	Unskilled labour
Wage
Labour force
Employed
Unemployed

d) Predictions

· The expected income differential between skilled and unskilled labour is

· If , people will choose to acquire skills,

· If , there are no incentives to acquire skills.

· Equilibrium condition: (no incentives to acquire skills)

(Avg. income of skilled labour = Avg. income of unskilled labour)

· Transition to equilibrium:

=> and

(Avg. income of skilled labour > Avg. income of unskilled labour)

Next, we will explore how many unskilled workers pursue pose-secondary education (skill acquisition) in response to a new job posting?

Since , one new posting requiring post-secondary education entices more than one unskilled worker to pursue post-secondary education.

The implication of that is involuntary unemployment in the skilled sector and higher variation in earnings than in the unskilled sector.

Numerical example: Suppose that

One new skilled job entices 2 unskilled workers to acquire skills.

Implications: Twice as large wage differential between skilled and unskilled labour results in 50 % unemployment rate among skilled workers.

e) Main insights

· Labour market implications

· full employment () in the labour market for unskilled labour;

· involuntary unemployment () in the labour market for skilled labour.

The probability, , of finding an skilled labour job is: .

· Macroeconomic implications:

· income per capita rises;

· income inequality increases;

· variation in earnings among skilled workers emerges.

· The within-variation among skilled workers’ earnings is larger than the between-variation of workers of different skill level.

· Micro-level decision-making:

People can rationally choose to pursue post-secondary education even in the presence of substantial unemployment among skilled workers.

· Policy implications:

Skilled job creation leads to an increase in unemployment among skilled workers.

What is more commonly observed among skilled workers is the formation of a secondary market of low-paid jobs for the residual supply of workers who do not find jobs in the primary (efficiency wage) market.

f) Model’s performance

To assess the model’s performance, we must assess whether the model explains the key facts.

The model is able to explain that a higher average wage among university graduates (skilled workers) increases post-secondary enrollment and graduation rates.

A more controversial aspect of the model’s results is about the evidence on within-variation and between-variation as it goes against the conventional wisdom used by policy makers.

Figure 4 indicates that for the period from 1980-2000:

· (initial condition) the between-group variance was substantially smaller than the within-group variance,

· (general relationship) the total variance substantially increased – an effect that was driven primary by the substantial increase in within-group variance

In conclusion, the policy achieves the exact opposite of the intended objectives. The rise in within-group variation was dominant and led to a large increase in labour income inequality.

As Kelly and Green (2016) say it best “Why More Education Will Not Solve Rising Inequality (and May Make It Worse).

Figure 4

Source: IRPP (2016)

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