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

Economic Growth, Regional Inequality and Fiscal Federalism

1. Economic growth and regional inequality.

a) Objectives

In the previous lecture, we found evidence that regional inequality has followed an inverted U-shape by first increasing until the 1930s and then decreasing since then.

In this lecture, we would like to build economic theory that helps us:

· Identify the economic forces that contribute to a high standard of living.

· Identify the economic forces that give rise to regional differences in living standards in the short-run and long-run.

· Describe the role of government policy in contributing to high standard of living and alleviating regional income inequality.

b) Relationship between economic growth and income

To address the objectives of this lecture, we first need to explore the dynamic relationship between income (GDP per capita) and economic growth.

Income grows exponentially over time as the level of income in each year depends on the income level of the preceding year, i.e., , where is aggregate income in year and is the economic growth rate.

To calculate the average growth rate, , over an extended period of time, we must use the following relationship.

We will use this equation to solve for .

Note: In the absence of population growth, the ratio of aggregate income, , equals the ratio of per capita income, .

Table 1 demonstrates that a small difference in the average economic growth rate could contribute to closing in a large gap between two income capita of two countries.

Table 1

Country	Real GDP per capita 1870	Real GDP per capita 2006	Annual growth rate 1870-2006
Australia	3,273	24,343	1.5 %
Canada	1,695	24,951	2.0 %

For cross-country inequality between Australia and Canada to decrease, we require that for the initial conditions , . This framework could be expanded to study the impact of regional inequality among Canadian provinces.

c) Causes

· Economic forces

In this lecture, we are going to build an economic model using mathematical tools to address the objectives set in this lecture.

An economic model is a simplified version of reality that allows us to observe, understand, and make predictions about economic behaviour. The purpose of a model is to take a complex, real-world situation and pare it down to the essentials by abstracting away from non-relevant characteristics.

A useful model is:

· is simple enough to be understood while complex enough to capture key information,

· able to provide predictions that explain phenomena observed in the data.

Economic models rely on:

· algebra to provide precise relationships,

· graphs to illustrate the key ideas.

2. Economic Growth Model.

a) Model overview

In this section, we will go over the Solow growth model, which is used to:

· Identify the economic forces that contribute to economic growth,

· Explain why regional income disparities across provinces (or countries) may narrow/widen/persist over time.

b) Setup of the model:

· Per-worker variables (small letters) and aggregate variables (capital letters).

Output:

Capital:

Consumption:

The aggregate production function is given by

In the aggregate production function: capital, and labour, are the inputs used to produce output, . Typically, we assume that more input of each input increase output. In addition, is a productivity parameter that measures the ability of a province (or country) to produce more output by using the same number of inputs.

Per worker production function:

We will primarily work with the per worker production function as will be interested in comparing per worker/per capita living standards, i.e., abstracting away from population size.

c) Steady state equilibrium:

Two opposing forces:

· savings: , where s is the savings rate.

We will assume that all savings are invested into new capital.

· capital requirement: , where is the population growth rate and is the depreciation rate.

The capital requirement indicates how much capital needs to be replenished to replace the obsolete capital stock (e.g. retired equipment) and to keep up with an increasing population.

Equilibrium condition:

In equilibrium, the investment in per worker capital stock just replenishes the obsolete capital stock per worker and accounting for population growth.

Figure 1

Source: Williamson (2013)

· Endogenous and exogenous variables:

· endogenous variables – variables determined in the model ()

· exogenous variables – variables whose value is taken as given (); also known as parameters.

· Steady state equilibrium:

In a steady state, a variable maintains the same value over time.

· What makes a steady state an equilibrium?

- initial value of k.

show k remains equal to

If because amount of created capital equals amount of destroyed capital.

Then, i.e., stays constant.

· What makes a steady state equilibrium stable?

Step 1:

, show converges to

If ,

keeps on increasing until it reaches .

Step 2:

, show converges to

If ,

keeps on decreasing until it reaches .

No matter what the initial value converges to . If this statement is not true, the equilibrium is unstable.

If an economy is not in a steady state equilibrium, it does not converge instantaneously to a steady state. This process occurs over a number of periods as gets closer and closer to the equilibrium.

d) Model predictions:

· Convergence

· provinces converge to the same (differences in living standards across provinces should disappear over time if provinces have the same values for the parameters .

· provinces converge to the same because

· provinces converge to the same because .

Numerical example:

Suppose that the per capita production is given by . In addition, and .

Solve for the steady state values of , , and .

There are two steady states:

implies that

is equivalent to and to

This implies that .

The production function implies that:

The consumption quantities are:

· Unconditional vs. Conditional convergence.

· Unconditional convergence:

If provinces have identical characteristics, i.e., the same values for all the parameters used in the model Provinces converge to the same steady state, and .

· Conditional convergence:

If provinces could have different characteristics, i.e., they differ in the values for at least one of the parameters in the model .

· Main implications of convergence:

Each country converges to a different steady state and .

Conditional convergence can potentially explain why provinces differ in their standard of living (GDP per capita).

Why potentially? Parameter values of must be such that they predict for each country that is consistent with the data.

For instance, the model may predict that (Alberta) (Ontario), while in the data we observe (Alberta) (Ontario).

If model makes predictions that are inconsistent with the data, either the model's assumptions should be modified or the model should be entirely abandoned.

e) Empirical evidence

· Convergence measurement

A crude way to check for unconditional convergence is to explore whether we require that for , the relationship between average growth rates, , is maintained. This relationship must hold for each pair of provinces.

Figure 2 provides no evidence of unconditional convergence since indicates that , which is contrary to the model predicts.

Figure 2

Source: Statistics Canada (2019)

We will explore an alternative, more sophisticated method, for checking for convergence called Sigma ()-convergence.

Sigma ()-convergence occurs when the dispersion of the income levels across provinces tends to decrease over time. That is, , i.e., sigma convergence declines in each subsequent year. Provinces are in proximity to the steady state as .

Figure 3

Source: Statistics Canada (2019)

· Evidence

Figure 3 reveals that there is evidence of:

· unconditional convergence for all provinces until the 1970s and,

· unconditional convergence for the non-resourced based provinces since the 1970s.

For detect unconditional convergence, there must be a steady downward-sloping time trend over time without sizable fluctuations.

Figure 4 reveals that the provinces whose economies are resource-based (Alberta, Saskatchewan, Newfoundland and Labrador) appear to have different characteristics than the rest of the provinces with respect to the composition of the economies.

In addition, the fluctuations Figure 3 since the 1970s correspond to fluctuations in oil prices and other natural resources.

Figure 4

Source: Olfert (2016)

f) Economic Policies:

· Increasing living standards:

Government policy could target any of the following parameters:

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

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

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

· any additional parameters introduced into the model.

· Comment about sources of long-term growth:

· Role of productivity

Raising productivity is the only source to achieving sustained long-term growth. Why? There are bounds on and, and respectively.

· Decreasing regional income disparities:

Two policies approaches:

· Equalize parameters of ‘have-not’ provinces to those of ‘have’ provinces.

· Redistribute income from the have provinces to the have-not provinces.

3. Fiscal federalism and equalization payments.

a) Program details

The equalization payments (EP) program is a redistributive program run by the Canadian federal government that redistributes income to ‘have-not’ provinces.

The main rationale for running the EP program is that it could speed up the convergence to the same steady state in the presence of unconditional convergence.

In the case of conditional convergence, the main impact of the policy would be towards bridging the gap in current incomes but not addressing the underlying problem of regional disparities due to convergence to different steady states.

A controversial component of this policy has been that there are no strings attached as to how the redistributed funds are spent by provincial governments.

b) Economic effects of the EP program

· Increases in investment vs. consumption influences short-term economic growth.

Whether the equalization payments program has an impact on economic growth, it is critical whether it is spent on government consumption or on government investment projects.

· If on government investment, it increases total investment, and in turn, it increases future output.

· If on government consumption, it increases only current output at the program has no impact on future output.

In the program as it stands, there are no strings attached to spend any of the equalizations on investment projects or human capital initiatives.

The debate whether to allocate more resources to investment (equivalent to future consumption) or to consumption (equivalent to current consumption) is not resolved. It is more of a question how much of it achieves the right balance.

· Empirical evidence

Figure 5

Source: Olfert (2016)

The equalization payments program has contributed to bridging the regional income disparities at two levels:

· Current income levels,

· Future income levels (in transition to a steady state).

The controversial aspect of the EP program has been the second aspect.

Figure 4 provides evidence that over time provinces have become less reliant on EP to finance public services.

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