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

Economic Growth, Productivity and Immigration

1. Introduction.

a) Overview

· Objective

In this lecture, we are going to explore why income disparities between large metropolitan areas (CMA) and small city/rural areas (for short referred to as other jurisdictions).

To this end, we will proceed by:

· establishing key facts with respect to income disparities and its potential drivers,

· suggesting why firms/governments might have an incentive to create head offices in specific geographic locations,

· discussing the role of skilled immigration and the economic rationales for its concentration in large metropolitan areas.

· Analytical tools

We will augment the Solow model with the following two characteristics:

· human capital in addition to physical capital.

· introduce a linear per worker production function.

2. Key facts.

1. Overview

In this section, we will attempt to make the link between the increases in within-provincial income inequality and the concentration of head offices in the large metropolitan areas that disproportionately employ high-skilled workers.

We will also explore the role of immigration policy reforms that favour skilled immigration in raising productivity and increasing income inequality between large CMAs and other jurisdictions. Studying the location choice of new immigrants is particularly beneficial as they are more likely to choose the location they arrive in for economic reasons.

1. Within-provincial inequality and metropolitan areas

In this section, we would like to explore the relationship between recent increases in within-province income inequality and corresponding increase in the market share of income among the top 1 % in the large CMAs.

Figure 1 indicates that the largest increases in within-regional income inequality are concentrated in Alberta, British Columbia, and Ontario. These three provinces are among the most urbanized and have large CMAs with large concentration of head offices.

Figure 1

Source: IRPP (2016)

Figure 2 reveals that the largest increases among the top 1 % of the CMAs across the jurisdictions were those with the largest concentration of head offices, i.e., Toronto, Montreal, Vancouver, and Calgary.

The location of provincial capitals and private sector head offices across in different cities within the same province allows us to elicit that most of the largest increases among the top 1 % earners of each CMA are concentrated in the private sector.

Figure 2

Source: IRPP (2016)

Who are top 1 %? According to IPRR (2016), it is a mix of business executives and high-paid professionals (e.g., physicians, lawyers).

The primary focus of this lecture will be to explain why the uneven geographic distribution of human capital is a contributing factor to rising within-provincial income inequality.

3. Kremer O Ring Model

a) Overview

In this section, we would:

· demonstrate that firms have an incentive to set up plants that employ workers of similar productivity,

· explain the phenomenon of geographic concentration of high-skilled workers in large metropolitan areas and of low-skilled workers in small cities and rural areas.

b) Mechanics

· Main assumptions:

A1: There are many firms, each with two plants. Each plant employs two workers.

A2: The production function of a plant: .

A3: There are many workers: half with low productivity and half with high productivity , where .

· Labour market

There is a labour market, in which firm plants and workers are matched to produce output.

Each firm hires two workers with productivity and two with productivity .

c) Results

· Matching workers across plants

The main decision faced by each firm is how to assign the hired four workers across its two plants.

Each firm face two options:

Option 1: pair workers with the same productivity in each plant.

Option 2: pair workers of different productivity in each plant.

The objective of a firm is to compare which of the two options generates higher total output from the two plants.

Let’s assume that option 1 generates more output.

What we must show is that assumption is sound algebraically. If not, the sign of the inequality must be reversed.

Algebraically, we know that squared terms are non-negative, i.e.,.

To rule out equality, we note that .

· Main result:

A firm maximizes output if it hires two high productivity workers in one plant and two low productivity workers in other plant.

· Implications for income disparities

Firms set up:

· plants that employ high-skilled workers in geographic locations such as large metropolitan areas,

· plants that employ low-skilled workers in geographic locations such as small cities and rural areas,

4. Solow growth model with a linear per worker production function and human capital.

a) Overview

In this lecture, we are going to augment the Solow growth model in two respects:

· modifying the shape of the per worker production function, ,

· introducing human capital in addition to physical capital in the aggregate production function, .

Modifying the shape of the per worker production function could help us explain the presence of divergence, i.e., the perpetual increase of income inequality across jurisdictions as jurisdictions do not converge to a steady state.

Assuming a linear per capita production function captures the idea that as the capital stock per worker increases, output per worker increases at a constant rate (constant slope). In the preceding two versions of the model, output per worker was assumed to grow at a decreasing rate (positive slope increasing at a decreasing rate) as capital per worker increases.

The introduction of these new model characteristic would enable us to explain the following phenomenon:

· income disparities across jurisdictions perpetually increase,

· income per capita across all jurisdictions are perpetually increasing.

Introducing human capital as an input in the production function of the Solow model provides a positive view of population growth as more skilled population could be contributing to raising living standards.

In contrast, in the baseline model, a positive population growth rate curbs economic growth. This view is controversial and since it is supportive of any policies that reduce population size (e.g., increasing mortality rates).

Introducing human capital in the production function provides some insights with respect to policies that encourage higher educational attainment, skill acquisition and the selection of skilled immigrants.

1. Model

· Linear per worker production function

The concavity assumption is modified and now the per worker production function is assumed to be linear instead of concave (the slope is increasing at a decreasing rate).

· Human capital

If the aggregate production function of the Solow model is augmented with human capital, i.e. , educated population is a contributor to economic growth.

Numerical example:

For the aggregate production function , the human capital per worker is accumulated according to . is a parameter that measures the substitutability of the two forms of capital in the production process. Derive the per capita production function.

In this context, could have the interpretation of skilled labour and the interpretation of unskilled labour.

Divide both sides of by : and simplify further to and further to and finally convert into per capita: .

Substitute into to obtain: .

Figure 3

1. Model's predictions:

· Growth rates of capital and output

To derive long-term growth rate of capital, we proceed in the following steps:

The long-term growth rate of capital is solved for in a similar manner:

Numerical example: Suppose that . Calculate and

· Key predictions

The model predicts divergence, i.e., no convergence to a steady state, if .

· If , per capita income grows perpetually and any initial income inequality between the relatively rich and relatively poor jurisdictions grows over time perpetually.

· If , per capita income declines to the steady state , . Income inequality across jurisdictions is eliminated in the long run (when everyone is dead).

· Key distinction between conditional convergence and divergence

· Conditional convergence – convergence to different steady states by different jurisdictions (some differences in per capita income across jurisdictions are generated but these differences stop growing once jurisdictions reach their respective steady states)

· Divergence – no convergence to a steady state (differences in income per capita across jurisdictions increase perpetually).

d) Policy implications

· Increasing living standards:

Government policy could target any of the following parameters:

· savings rate (e.g., mandatory pensions plans CPP/QPP);

· population growth rate (e.g., lowering birth rates);

· productivity (e.g., worker productivity, technological improvements as well as improvements in both public and corporate governance);

· any additional parameters introduced into the model (e.g., the substitutability of the two forms of capital).

A change in parameter increases the magnitude of .

· Decreasing disparities across jurisdictions

To eliminate income inequality across jurisdictions, a two-step policy must be pursued.

Two-step policy:

Suppose that there are two jurisdictions with initial conditions

Step 1: allow for parameters to differ such that

Step 2: once , equalize parameters of the relatively less well-off jurisdictions to those of relatively well-off jurisdictions.

e) Role of immigration policy

· Immigration policy reform

The immigration reform introduced in the 1960s that favoured skilled immigration resulted in a dramatic change in the destination of new immigrants.

· Prior to reform (general pattern): settlement of low-skilled immigrants into small towns (mostly in the Prairies),

· After the reform (general pattern): predominant settlement of high-skilled immigrants into large metropolitan areas.

Figure 4

Source: IRPP (2016)

Figure 4 examines the relative composition of immigrant cohorts with respect to their skill type.

· Initial conditions: the composition of skill type of the 1970 -1974 immigration cohorts.

· General trend:

· Upward for non-routine cognitive and analytical skills,

· Downward for manual routine and non-routine skills,

· Variability: a major structural break in the 1990s when the trends of non-routine cognitive, analytical and interactive skills sharply increased at the expense of the manual routine and non-routine skills.

Note: there is no publicly available data for the initial phase of the reform; the 1970 – 1974 immigration were already impacted by the shift towards skilled immigration.

· Economic impact

The economic impact of increasing the share of skilled immigration is suggested to have been beneficial to increasing productivity in the recipient jurisdictions (predominantly large metropolitan areas).

However, this uneven distribution of skilled immigrants across jurisdictions has contributed to an increased income inequality across jurisdictions (between recipients and non-recipients of skilled immigration). Why?

Initial conditions: Large CMAs had a higher standard of living than other jurisdictions.

Growth rate of output: An increase in productivity in large CMAs led to an increase in in large CMAs but not in other jurisdictions.

Income disparities across jurisdictions: Income disparities across the two groups of jurisdictions have been increasing.

f) Key insights

We were able to explain in part why within-provincial income inequality has increased in recent decades, while regional (across-province) income inequality has been decreasing. They key source is the increase in productivity observed in large CMAs but not in other jurisdictions.

Immigration policy appears to have produced unintended consequences. In the absence of restriction on initial destination, skilled immigrants have chosen to settle into large CMAs for economic reasons.

These unintended consequences have resulted in recent immigration reforms that aim to attract and retain workers in jurisdictions outside of large CMAs.

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