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

Property Rights and Income Disparities across First Nations Reserves

1. Introduction.

a) Key analytical tools and regional inequality

In the previous two topics, we have developed a key set of analytical tools:

· measuring economic inequality,

· analyzing time trends,

· building an economic model of economic growth.

We have built these analytical tools to explain key facts about regional inequality across Canadian provinces with respect to:

· short-run dynamics (convergence to a steady state),

· long-run dynamics (elimination of regional inequality for unconditional convergence vs. persistent regional inequality for conditional convergence).

b) Focus of this topic

Figure 1

Source: Aragon (2015)

In this lecture, we will attempt to explain why there is a growing income disparity between two groups First Nations reserves that differ with respect to treaties status:

· First Nations reserves with treaties;

· First Nations reserves without treaties.

Figure 2

Source: Aragon (2015)

Figure 2 shows that the two groups of reserves had:

· comparable initial conditions (higher income per capita for treaty FNRs),

· similar income growth rates until the early 1990s.

Two structural breaks, one in the early 1990s and one in the early/mid 2000s, led to growing income disparities between the two groups.

These two structural breaks closely follow two waves of modern treaties (Comprehensive Land Claim Settlements) between federal/provincial governments and First Nations bands. Until then, the only type of treaties in place were historical treaties signed prior to 1923.

The mechanism through which modern treaties could be influencing an increase in average income on FNRs is through improved property rights and more specifically reduced transaction costs.

According to Aragon (2015), modern treaties clarify property rights by:

· delimiting the boundaries,

· specifying the property rights to the land and natural resources.

The improved property rights lower transaction costs (e.g., expenses incurred for legal disputes) that have the following implications:

· $ 1 of savings translate into $ 1 of investment in the absence of transaction costs,

· $ 1 of savings translate into less than $ 1 of investment in the presence of transaction costs.

We are going to use this framework of transaction costs and integrate it into the Solow growth model.

c) Economic significance of raising living standards on FNRs

Why should be concerned about the economic implications?

The average income in approximately 80 % of FNRs is below the national poverty line (Statistics Canada, 2016).

The poverty rates among the Aboriginal population are disproportionately higher relative to those of the entire Canadian population.

To this end, Figure 3 provides a time trend of the poverty rate for the Aboriginal population living off-reserve. However, the poverty rate among FNRs on-reserve is substantially larger relative to those living off-reserve (Statistics Canada, 2019).

Figure 3

Source: FRPP (2016)

The encouraging data from Figure 4 is that more Aboriginal people get out of poverty than fall into it in the period 2005 – 2010 relative to the period 1993 – 1998.

An interesting question is to what extent is this reduction in poverty rates among FNP contributable to treaty rights.

Figure 4

Source: IRPP (2016)

2. Solow model with transaction costs.

a) Overview

In this lecture, we will augment the Solow model from the previous lecture with transaction costs. To capture this idea, we will modify the assumption, , i.e., $ 1 of savings is translated into $ 1 of investment into new capital.

The modified assumption is, , where measures the aggregate transaction costs that could take the form of legal fees to establish property rights.

The corresponding per worker equation is, where measures the per worker transaction costs. Graphically, the savings function shifts downwards, and it no longer passes through origin.

Figure 5

There are two main implications of introducing transactions costs that affect:

· the equilibrium equation, which now becomes ,

· the two steady states, both of which take on positive values. The lower steady state is now economically meaningful.

As a result, both the short-run and long-run dynamics of regional inequality could differ remarkably from the baseline model introduced in the previous lecture.

b) Steady state equilibria and transitional dynamics

The steady state equilibria occur at the intersection of the savings curve and the capital requirement curve as shown in the previous lecture.

Numerical example:

In addition, suppose that and . Solve for the equilibrium state.

Start with the equilibrium condition:

Substitute the production function into it:

Insert the numerical values into it:

Use a variable substitution, , to derive a quadratic equation.

Re-arranging yields:

It is more convenient to work this equation if both sides are multiplied by 5:

To find the roots of the quadratic equation, you may use the formula:

They are and .

Substituting back each steady state into yields the steady states of capital per worker: and .

Figure 6

Quiz: Identify the typo in Figure 6.

The corresponding steady state levels of output per worker and consumption per worker are determined as follows.

The production function implies that:

Figure 7

The consumption quantities are:

c) Key insights

· Income disparities

The unstable steady state equilibrium occurs for and is now economically meaningful. The Solow growth model can now explain why:

· long-run differences between FNRs could persist even if they share the same parameter values.

This occurs if some FNRs are at the high steady state, , while the other FNRs are at the low steady state, . Unlike the model without transaction costs, this income disparity occurs for the same parameter values.

· long-run income disparities between FNRs could be perpetually increasing even if they share the same parameter values.

This occurs for a specific set of initial conditions:

For FNRs with initial conditions, , income per worker grows until they reach the steady state, .

For FNRs with initial conditions, , income per worker perpetually declines.

The transitional dynamics associated with these transitional dynamics could be easily verified for the numerical example at hand.

For

Let’s verify if indeed

For

Let’s verify if indeed

Due to the positive relationship between and , this implies that whenever , it is also the case that .

· Poverty trap and big push policy

The transitional dynamics in the preceding section imply that for any , a FNR finds itself in a poverty trap. In each subsequent period, both capital per worker and output per worker decline.

To escape a poverty trap, a FNR requires sufficiently largely investment such that the capital stock per worker exceeds . This is necessary to change the nature of the transitional dynamics for a FNR to escape from the poverty trap.

Changes in the transitional dynamics to the extent that an economy starts to converge to a different equilibrium is an example of a big push policy.

In our context, a sufficiently large investment acts as a big push policy. Due to the small population size of most FNR, even a single large project is capable of letting a FNR escape the poverty trap.

3. Empirical evidence.

a) Key facts and model predictions

Figure 1 indicates that there is:

· a growing income disparity between the treaty FNRs and the non-treaty FNRs,

· Income per capita of both treaty FNRs and non-treaty FNRs grew over time.

Figure 1

Source: Aragon (2015)

The Solow model with transaction costs could explain each one of the facts in isolation but not both simultaneously.

b) Challenging the closed economy assumption

The closed economy assumption is not reasonable for most FNRs for the following two reasons:

· FNRs rely on various forms of government assistance generated outside of the FNR economy,

· Large-scale investment in the capital stock is generated outside of the FNR economy and not through savings within the FNRs.

The implication of modifying could reconcile the model’s predictions with the key facts.

· Government programs

Government assistance programs primarily increase consumption and, therefore, do not increase the capital stock. This implies that income per capita rises but output per capita does not.

In fact, it is possible FNRs to experience a declining capital per worker and output per worker, while income per capita is rising due to government assistance programs.

· Investment projects

A large-scale investment project could contribute to a large increase in capital per worker in a single period such that a FNR escapes the poverty trap.

The corresponding large increase in output that occurs in a single period allows domestic savings to also increase dramatically. Even if outsiders stop investing into the FNR, the domestic savings generated in the FNR are sufficient to sustain and change the nature of the transitional dynamics.

c) Final remarks

By augmenting the Solow model with transaction costs and modifying the closed economy assumption, we were able to explain:

· the poverty trap many FNRs face,

· the income disparities between treaty FNRs and non-treaty FNRs.

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