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3. Calculate consumption each period based on the assumption that the country
wants to maintain the same level of consumption each period. Step 2 shows us
that PV(Q) = 2079 = PV(C). Therefore, we know that the present value of
4. Calculate the trade balance in each period. Now that we have pinned down output
and consumption, we can calculate the initial trade balance in the year of the
5. Calculate the country’s external wealth and the implied interest payments
paid/received on this debt to calculate net factor income from abroad (NFIA) in
6. Calculate the country’s current account in each period. Recall that the current
Generalizing Using the previous method, we can draw some general conclusions
regarding how consumption changes in response to changes in output in the open
The left-hand side represents the amount paid or received in interest on the amount
borrowed or lent. Solving for the change in consumption, we get
The value of r*/1 + r* must be between 0 and 1. That implies the open economy only
Smoothing Consumption When a Shock Is Permanent If a country faces a permanent
shock to output, then it will be forced to adjust its consumption regardless of whether it is
Summary: Save for a Rainy Day
The previous model shows how a country can save output when it experiences positive
S I D E B A R
Wars and the Current Account
In our example, we assumed no government spending (G). If we incorporate G into the
APPLICATION
Consumption Volatility and Financial Openness
Based on our model, countries with greater financial openness should be in a better
position to smooth consumption. In the data, we can measure this as the ratio of the
Why? In the real world, households are not identical and global capital markets are
not open to every individual or firm. In fact, some people and businesses do not even
participate in the domestic financial market. Thus, financial globalization doesn't reach
consumers in poorer countries. Financial markets in emerging markets and developing
countries may not be fully developed, or may be limited in their access. Financial markets
in emerging market economies often function inefficiently, lacking transparency and
APPLICATION
Precautionary Saving, Reserves, and Sovereign Wealth Funds
If poorer countries are not able to rely on global financial markets, then what is their best
strategy to smooth consumption? One such approach is to rely on precautionary saving,
There are two general forms of precautionary saving: foreign reserves and sovereign
wealth funds. Foreign reserves are foreign assets owned by the central bank, often used
to maintain fixed exchange rates. Sovereign wealth funds are state-owned asset
management companies that invest government savings overseas in safe assets, such as
H E A D L I N E S
Copper-Bottomed Insurance
This article uses the case study of Chile as a copper exporter to discuss how the reliance
on export commodities can lead to output volatility, and how sovereign wealth funds can
help buffer against these shocks.
Background:
■ Chile’s government benefited from profits on its state-owned copper company
Key Statistics:
■ As of December 2014, there was $14.3 billion in the fund. This accounted for
5.4% of Chile’s GDP that year.
■ In 2014, the price of copper fell by 6% compared to 2013.
■ In current international dollars, per capita income in Chile was $23,367 (roughly
38% of Norway’s).
Lessons:
■ Commodity exports such as oil and copper are very volatile in price, and therefore
Discussion Questions:
■ Should Chile set aside these profits? Or should the government spend these profits
3 Gains from Efficient Investment
This section incorporates investment into the previous model, showing how financial
openness benefits the economy through not only consumption smoothing but also
increased investment opportunities.
The Basic Model
From the previous model, we can now assume that output is produced using capital,
which is accumulated through investment, so GNE = C + I. From the LRBC, we can
derive
As before, we will examine two cases:
■ Closed economy: TB = 0 in all periods, so the LRBC is automatically satisfied.
Efficient Investment: A Numerical Example and Generalization
We will consider the previous case, with shocks. Instead of a negative shock to output,
here, we consider a new investment opportunity in year 0. Assume the investment
opportunity requires 16 units of output today and will increase output by 5 units in every
subsequent period.
Before the shock, the present value of output is 2,100 and investment is equal to 0 in
each period. This is identical to the previous case with no shocks.
Now, consider what happens when the investment opportunity arises. To calculate the
implied changes in Q, C, I, TB, NFIA, and external wealth over time, we take steps
similar to the ones outlined previously.
Steps to computing numerical values for Q, C, TB, NFIA, and W over time are as
follows:
1. Identify how much output is needed to finance the investment project. From the
2. Calculate the present value of output, assuming the investment project is
undertaken:
Because Q0 = 100 and output is equal to 105 thereafter,
3. Calculate consumption each period, based on the assumption that the country
wants to maintain the same level of consumption each period. From Step 2, we
know PV(Q) = 2,200 = PV(C) + PV(I ). Therefore, we know that the present value
of consumption is 2,184 (= 2,200 − 16), to be divided equally each period (e.g., to
keep consumption smooth), so C0 = C1 = C2 = C:
4. Calculate the trade balance in each period. Now that we have determined output,
investment, and consumption, we can calculate the initial trade balance in the year
5. Calculate the country’s external wealth and the implied interest payments paid or
received on this debt to calculate NFIA in each period. External wealth is equal to
6. Calculate the country’s current account in each period. Recall that the current
account is the sum of the trade balance, net factor income, and net unilateral
Generalizing The country’s objective is to maximize the present value of consumption.
There are investment projects that are not worthwhile because they do not increase output
enough to increase the present value of consumption. To determine which investment
projects are worthy, note that the change in the present value of output is
The change in the present value of investment (equal to the change in capital stock, K) is
The investment project is worthwhile only if the present value of output increases (gains
from the project) more than the present value of investment (cost of the project financed
through borrowing):
The left-hand side shows the annual benefit of the project and the right-hand side is the
cost (interest payments on the debt accumulated). Rearranging the expression gives us
The left-hand side of this expression is the marginal product of capital (MPK), which
Summary: Make Hay While the Sun Shines
In an open economy, a country is able to separate its consumption and investment
decisions. Firms and households can borrow or save through the world capital market. To
choose an efficient level of investment, the country should undertake investment projects
until the MPK is equal to the world real interest rate.
APPLICATION
Delinking Saving from Investment
A massive oil reserve was discovered in the North Sea in the 1960s, but it was very costly
to extract this oil at the time. The world price of oil was low until the oil price shocks in
the 1970s. These shocks turned out to be largely permanent, leading to a permanent
increase in the price of oil that then made the extraction of North Sea oil profitable.
Is this delinking of saving and investment a general result? Feldstein and Horioka
estimated a ratio
β
—the fraction of each additional dollar saved that tended to be invested
in the same country (∆I =
β
∆S). According to our model for financially open economies,
Can Poor Countries Gain from Financial Globalization?
The previous model shows us that countries with MPK > r* should borrow from abroad to
Production Function Approach A production function describes how a country’s output
depends on its inputs. In per worker terms, the production function describes the
relationship between capital per worker (k = K/L) and productivity (q = Q/L). The simple
production function used here is
To determine the efficient level of investment, we need to know the MPK:
where MPK is the slope of the production function. The textbook plots the production
function for the case where A = 1 and = 1/3:
A Benchmark Model: Countries Have Identical Productivity Levels This model
assumes that all countries have the same production function.
■ Suppose a country considers increasing its capital per work by 8 times the current
Now, we consider two different countries.
■ Suppose that a poor country has half the level of output per worker enjoyed in the
rich country.
■ The poor country has an MPK 4 times that of the rich country.
The general result is that the poorer the country, the lower its capital per worker and
therefore the higher its MPK. This relationship is illustrated on Figure 17-7, panel (a).
The Lucas Paradox: Why Doesn’t Capital Flow from Rich to Poor Countries?
The implication from the previous model is clear: capital should flow from rich to poor
countries, and poor countries should implement government policies to attract capital
inflow.
An Augmented Model: Countries Have Different Productivity Levels The augmented
model allows for different countries to have different productivity levels—different
values for A. Let the subscript P denote a poor country and the subscript R denote a rich
country:
The ratio of the MPK in each country is
We can use this expression to understand why the naïve model overlooks a key source of
differences in output per worker—differences in the production function, A. The
benchmark model predicts the MPK in poor countries is much higher than that in rich
APPLICATION
A Versus k
Table 17-5 compares the ratio of output per worker and capital per worker in selected
countries to those in the United States. These ratios can be used to calculate the implied
difference in the productivity levels in poor countries relative to the United States. From
the table, we observe that the implied gains from the benchmark model are much larger
than those implied by the augmented model.
More Bad News? There are other assumptions in the model that we could relax to study
a richer set of explanations for why capital does not flow from rich to poor countries:
■ The model makes no allowance for risk premiums. The existence of a risk
■ Risk premiums may be large enough to cause capital to flow “uphill” from poor
less attractive.
■ The model assumes that investment goods can be acquired at the same relative
■ The model assumes the contribution of capital to production is equal across
■ The model suggests that foreign aid may do no better than foreign investors in
promoting growth. Investments from foreign aid face the same challenges faced
S I D E B A R
What Does the World Bank Do?
The World Bank (http://www.worldbank.org) was established in 1944 as part of the
Bretton Woods Agreement. (Its "twin," the International Monetary Fund, was set up at
H E A D L I N E S
A Brief History of Foreign Aid
This article considers the role of foreign aid in economic growth.
Background:
■ In 1985, Live Aid concerts were performed to raise funds to fight poverty in
Africa.
and received aid.
Lessons:
■ During the Cold War, much foreign aid was offered more for geopolitical
purposes than to promote economic growth, so historical analysis of the effects of
aid may be misleading.
Discussion Questions:
■ What criteria would you establish in offering aid to poor countries?
4 Gains from Diversification of Risk
In the previous section, we observed that in practice, countries may not have access to the
world capital market. Are there other ways to cope with shocks to output? Yes, through
Diversification: A Numerical Example and Generalization
In this section, we assume there are two countries with no borrowing/lending. The two
countries are identical, except that their outputs move in opposite directions. We will
Home Portfolios Assume the countries are closed. In this case, each country owns 100%
World Portfolios Table 17-6, panels (b) and (c), shows outcomes when each country
