Macro Chapter 4 The solow model in a small open economy
Wealth accumulation and capital mobility
:The Solow model for a small open
economy
I n the basic Solow model the only source of domestic investment is the volume of
domestic saving. This is a good approximation to reality as long as international
capital flows are relatively small. However, in recent decades the international
mobility of capital has increased dramatically. In these circumstances a country may
Hnance part of domestic investment via capital imports, or it may invest part of domestic
savings abroad through capital exports.
In this chapter we will develop a Solow model of an open economy to study how the
dynamics of wealth accumulation are affected by international capital mobility. The
rapidly growing mobility of capital is one of the most striking features of the ongoing
process of globali zation. Most economists believe that capital mobility tends to improve the
long-run elliciency of the world economy, but the liberalization of international capital
llows also creates new risks. Indeed, many critics of globalization have argued that
increased capital mobility may destabilize the world economy and expose poor countries
to the shifting moods of international investors. The potential for capitalllows to generate
short-run macroeconomic instability will be discussed in Part 7, whereas the model
developed in the present chapter will highlight the potential long-run beneHts of capital
mobility. Studying this chapter along with those in Part 7 should thus give you a better
understanding of some of the contentious issues in the current debate on globalization.
We will start the chapter by documenting the trend towards growing capital
mobility. We will then set up a Solow model of a small open economy whose domestic
capital market is perfectly integrated with the world capital market. This model will be
used to analyse how an open capital account 1 modifies the dynamics of wealth accumulation
in the individual country, and how capital mobility and the associated opportunity
to incur foreign debt brings beneHts as well as potential costs.
4.1 the increase of capital mobility
Figure 4.1 illustrates trends in the degree of international economic integration from the
late nineteenth century until the end of the twentieth century. The light columns associated
with the left scale measure the volume of international trade (the sum of exports and imports) relative to world GDP . The dark columns associated with the right scale
show the ratio of the total stock of foreign-owned assets to world GDP . Thus the light
columns indicate the degree of trade integration. and the dark columns illustrate the
degree of financial integration (or capital mobility). The tlgure documents an interesting
fact which is often forgotten in the contemporary debate on globalization: before the First
World War international capital mobility was very high, especially considering that the
technological means of communication were less developed than today. Indeed. the
average ratio of foreign assets to GDP was above SO per cent in the early twentieth
century, as a result of large capital exports from the most developed countries (particularly
Great Britain) to the less developed regions in the world. This is why critics of the
economic dominance of the industrialized countries often refer to this period as the
heyday ofWestern imperialism.
The First World War marked the beginning of a long period of economic and political
instability, culminating in the Great Depression ofthe 19 30s and in the catastrophe of the
Second World War. During this dark period in history national governments retrenched
into inward-looking economic policies involving strong trade protection and controls on
capital ilows. In Fig. 4.1 this is rellected in the sharp drop in trade integration and
financial integration after 1914. Indeed. we see that even as late as 1960 the world's
economies were still considerably less open to trade and capital flows than they were
before the First World War. In particular, there was much less fmancial integration in 19 60 than in 1900, because most countries still maintained extensive restrictions on
private capital flows across borders, in an attempt to maintain national autonomy in the
conduct of monetary policy. However, between 19 60 and 1980 the degree of financial
integration roughly doubled. and from 1980 to 199 5 it almost doubled once again, reaching
the highest level ever recorded. To some extent this remarkable increase in capital
mobility was driven by the simultaneous increase in world trade, since a part of international
capital flows takes the form of trade credits granted by exporters to the foreign
importers. But most of the increase in capital flows stemmed from a combination of
llnancialliberalization- \>\lith one government after another abandoning capital controls
- and the rapid improvements in information and communication technologies which
made it easier and cheaper to move capital across borders.
International capital flows are often divided into foreign direct investment (FDI) and
foreign portfolio investment (PI). FDI may take the form of 'greenlleld' investment where
a foreign multinational company sets up a new production plant in a country, but more
often it involves the acquisition by a foreign company of a controlling m.vnership share in
an existing domestic company. If an already established foreign-m.vned company retains
and reinvests its profits in the host country, this is also counted as FDI. The distinguishing
feature of FDI is that the investor is an active controlling owner who often brings along
new production technologies and management know-how with the capital invested.
Because FDI often implies an international transfer of technology and is typically undertaken
by large multinational enterprises. it tends to attract special interest. Table 4.1
shows that FDI has become increasingly important relative to domestic economic activity
in recent years.
While FDI is a more visible form ofinvestment. international portfolio investment (PI)
still accounts for the bulk of international capital flows, as documented in Table 4.1.
International portfolio investment involves international debt flows (e.g., the purchase of
foreign bonds or the extension of bank credit across borders) or the purchase of foreign
shares for purposes of portfolio diversification. International portfolio investors do not
acquire a controlling ownership share in foreign firms and therefore are not actively
engaged in running a business firm abroad.
4.2 the solow model of a small open economy
In this section we develop a growth model of a so-called small open economy with perlect
mobility of commodities and capital. but \o\lith no labour mobility at all. This rellects the
empirical fact that commodities and capital move much more across country borders than
persons do. As examples of small open economies with free capital movements you may
think of practically any of the countries in Western Europe, since even the larger
economies like those of Britain, France or Germany are small compared to the size of the
world economy.
The small open economy
The open economy considered is so small that its own economic activity does not signillcantly
afiect economic conditions in the rest of the world. In particular, the economy is
so small that the volume of domestic saving and investment does not have any noticeable
impact on world interest rates. Capital is assumed to be perfectly mobile between the domestic economy and the rest of the world. Under perfect capital mobility domestic and
foreign assets are perfect substitutes, and investors can instantaneously and costlessly
s\>Vitch between domestic and foreign assets. For concreteness, let us assume that foreign
as well as domestic Hrms Hnance their investment in real capital by issuing bonds in the
international capital market (alternatively we might assume that part of business investment
is nuanced by issuing shares which are perfect substitutes for bonds in the eyes of
Hnancial investors). Under perfect capital mobility all of these bonds must then pay the
same rate of interest. For example, if domestic bonds h ad a lower return than foreign
bonds, international Hnancial investors would immediately sell domestic bonds in order to
buy foreign bonds, thereby driving dm>VIl domestic bond prices until the rates of return
would be equalized. Given that this arbitrage can occur instantaneously and costlessly,
bond returns (and hence ellective foreign and domestic interest yields) must be equalized
at any point in time.
For the small open economy this means that the domestic interest rate is ellectively
given by the world interest rate which the domestic economy cannot allect. Denmark is a
good example of a small open economy in which the interest rate L~ more or less given from
abroad. A~ shown in Fig. 4.3, the real rate of interest on Danish long-term bonds has
followed the Gennan interest rate quite closely in recent years. 3
Just as foreign and domestic assets are taken to be perfect substitutes, we assume that
the goods produced in the small domestic economy are perfect substitutes for (some of the)
goods produced in other countries. With free trade in commodities this means that the
prices of domestic goods must equal the prices determined in the world market (with the possible addition of some exogenous transport cost). From the viewpoint of the small
domestic economy the prices of exported as well as imported goods and services are thus
exogenously given from abroad, that is. the ratio of the domestic to the foreign price level
is exogenously fJXed. For simplicity we will therefore set this exogenous relative price
equal to unity. This is equivalent to assuming that all economies in the world produce the
same single good. With th is assumption our model cannot explain the international
pattern of commodity trade (i.e., which countries end up producing which types of goods)
and the welfare gains from such trade. Our intention here is to understand the implications
of international capital mobility lor wealth accumulation and the potential gains
from capital mobility.
:The Solow model for a small open
economy
I n the basic Solow model the only source of domestic investment is the volume of
domestic saving. This is a good approximation to reality as long as international
capital flows are relatively small. However, in recent decades the international
mobility of capital has increased dramatically. In these circumstances a country may
Hnance part of domestic investment via capital imports, or it may invest part of domestic
savings abroad through capital exports.
In this chapter we will develop a Solow model of an open economy to study how the
dynamics of wealth accumulation are affected by international capital mobility. The
rapidly growing mobility of capital is one of the most striking features of the ongoing
process of globali zation. Most economists believe that capital mobility tends to improve the
long-run elliciency of the world economy, but the liberalization of international capital
llows also creates new risks. Indeed, many critics of globalization have argued that
increased capital mobility may destabilize the world economy and expose poor countries
to the shifting moods of international investors. The potential for capitalllows to generate
short-run macroeconomic instability will be discussed in Part 7, whereas the model
developed in the present chapter will highlight the potential long-run beneHts of capital
mobility. Studying this chapter along with those in Part 7 should thus give you a better
understanding of some of the contentious issues in the current debate on globalization.
We will start the chapter by documenting the trend towards growing capital
mobility. We will then set up a Solow model of a small open economy whose domestic
capital market is perfectly integrated with the world capital market. This model will be
used to analyse how an open capital account 1 modifies the dynamics of wealth accumulation
in the individual country, and how capital mobility and the associated opportunity
to incur foreign debt brings beneHts as well as potential costs.
4.1 the increase of capital mobility
Figure 4.1 illustrates trends in the degree of international economic integration from the
late nineteenth century until the end of the twentieth century. The light columns associated
with the left scale measure the volume of international trade (the sum of exports and imports) relative to world GDP . The dark columns associated with the right scale
show the ratio of the total stock of foreign-owned assets to world GDP . Thus the light
columns indicate the degree of trade integration. and the dark columns illustrate the
degree of financial integration (or capital mobility). The tlgure documents an interesting
fact which is often forgotten in the contemporary debate on globalization: before the First
World War international capital mobility was very high, especially considering that the
technological means of communication were less developed than today. Indeed. the
average ratio of foreign assets to GDP was above SO per cent in the early twentieth
century, as a result of large capital exports from the most developed countries (particularly
Great Britain) to the less developed regions in the world. This is why critics of the
economic dominance of the industrialized countries often refer to this period as the
heyday ofWestern imperialism.
The First World War marked the beginning of a long period of economic and political
instability, culminating in the Great Depression ofthe 19 30s and in the catastrophe of the
Second World War. During this dark period in history national governments retrenched
into inward-looking economic policies involving strong trade protection and controls on
capital ilows. In Fig. 4.1 this is rellected in the sharp drop in trade integration and
financial integration after 1914. Indeed. we see that even as late as 1960 the world's
economies were still considerably less open to trade and capital flows than they were
before the First World War. In particular, there was much less fmancial integration in 19 60 than in 1900, because most countries still maintained extensive restrictions on
private capital flows across borders, in an attempt to maintain national autonomy in the
conduct of monetary policy. However, between 19 60 and 1980 the degree of financial
integration roughly doubled. and from 1980 to 199 5 it almost doubled once again, reaching
the highest level ever recorded. To some extent this remarkable increase in capital
mobility was driven by the simultaneous increase in world trade, since a part of international
capital flows takes the form of trade credits granted by exporters to the foreign
importers. But most of the increase in capital flows stemmed from a combination of
llnancialliberalization- \>\lith one government after another abandoning capital controls
- and the rapid improvements in information and communication technologies which
made it easier and cheaper to move capital across borders.
International capital flows are often divided into foreign direct investment (FDI) and
foreign portfolio investment (PI). FDI may take the form of 'greenlleld' investment where
a foreign multinational company sets up a new production plant in a country, but more
often it involves the acquisition by a foreign company of a controlling m.vnership share in
an existing domestic company. If an already established foreign-m.vned company retains
and reinvests its profits in the host country, this is also counted as FDI. The distinguishing
feature of FDI is that the investor is an active controlling owner who often brings along
new production technologies and management know-how with the capital invested.
Because FDI often implies an international transfer of technology and is typically undertaken
by large multinational enterprises. it tends to attract special interest. Table 4.1
shows that FDI has become increasingly important relative to domestic economic activity
in recent years.
While FDI is a more visible form ofinvestment. international portfolio investment (PI)
still accounts for the bulk of international capital flows, as documented in Table 4.1.
International portfolio investment involves international debt flows (e.g., the purchase of
foreign bonds or the extension of bank credit across borders) or the purchase of foreign
shares for purposes of portfolio diversification. International portfolio investors do not
acquire a controlling ownership share in foreign firms and therefore are not actively
engaged in running a business firm abroad.
4.2 the solow model of a small open economy
In this section we develop a growth model of a so-called small open economy with perlect
mobility of commodities and capital. but \o\lith no labour mobility at all. This rellects the
empirical fact that commodities and capital move much more across country borders than
persons do. As examples of small open economies with free capital movements you may
think of practically any of the countries in Western Europe, since even the larger
economies like those of Britain, France or Germany are small compared to the size of the
world economy.
The small open economy
The open economy considered is so small that its own economic activity does not signillcantly
afiect economic conditions in the rest of the world. In particular, the economy is
so small that the volume of domestic saving and investment does not have any noticeable
impact on world interest rates. Capital is assumed to be perfectly mobile between the domestic economy and the rest of the world. Under perfect capital mobility domestic and
foreign assets are perfect substitutes, and investors can instantaneously and costlessly
s\>Vitch between domestic and foreign assets. For concreteness, let us assume that foreign
as well as domestic Hrms Hnance their investment in real capital by issuing bonds in the
international capital market (alternatively we might assume that part of business investment
is nuanced by issuing shares which are perfect substitutes for bonds in the eyes of
Hnancial investors). Under perfect capital mobility all of these bonds must then pay the
same rate of interest. For example, if domestic bonds h ad a lower return than foreign
bonds, international Hnancial investors would immediately sell domestic bonds in order to
buy foreign bonds, thereby driving dm>VIl domestic bond prices until the rates of return
would be equalized. Given that this arbitrage can occur instantaneously and costlessly,
bond returns (and hence ellective foreign and domestic interest yields) must be equalized
at any point in time.
For the small open economy this means that the domestic interest rate is ellectively
given by the world interest rate which the domestic economy cannot allect. Denmark is a
good example of a small open economy in which the interest rate L~ more or less given from
abroad. A~ shown in Fig. 4.3, the real rate of interest on Danish long-term bonds has
followed the Gennan interest rate quite closely in recent years. 3
Just as foreign and domestic assets are taken to be perfect substitutes, we assume that
the goods produced in the small domestic economy are perfect substitutes for (some of the)
goods produced in other countries. With free trade in commodities this means that the
prices of domestic goods must equal the prices determined in the world market (with the possible addition of some exogenous transport cost). From the viewpoint of the small
domestic economy the prices of exported as well as imported goods and services are thus
exogenously given from abroad, that is. the ratio of the domestic to the foreign price level
is exogenously fJXed. For simplicity we will therefore set this exogenous relative price
equal to unity. This is equivalent to assuming that all economies in the world produce the
same single good. With th is assumption our model cannot explain the international
pattern of commodity trade (i.e., which countries end up producing which types of goods)
and the welfare gains from such trade. Our intention here is to understand the implications
of international capital mobility lor wealth accumulation and the potential gains
from capital mobility.
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