A SIMPLE MODEL OF GROWTH AND DEVELOPMENT
6.4 GLOBALIZATION AND TRADE
Adopting foreign technologies is a particular kind of openness that can contribute to economic growth. As we saw in Figure 1.5, openness in terms of greater imports and exports of goods and services is also asso- ciated with faster growth over the last fi fty years. From the perspective of our model, we can incorporate explicit trade in intermediate goods to accommodate the stylized fact captured by Figure 1.5.
149 G LO BALIZATI O N AN D TRAD E
The primary change is to the production function, which is altered from equation (6.1) to be
Y = L1-a L
h+m 0
xjadj. (6.9)
Here, the number of varieties of intermediate goods is equal to h, those produced domestically, plus m varieties imported from other countries.
A country grows as it learns to adopt new technologies, increasing h, and can also grow by expanding the number of goods that it imports, increasing m.
We’ll again treat all the intermediate goods, both domestic and imported, as symmetric, so that the fi nal-goods sector uses xj = x for all j. In a closed economy, with m = 0, the amount used of each type is exactly equal to the amount produced. With trade, though, it is no longer necessary that this is true. Domestically, let z be the amount produced of each of the h types of intermediate goods that a country has learned how to make.
As before, each unit of intermediate good is produced using one unit of raw capital. For the h domestically produced goods, this means that
h(t)z(t) = K(t).
Of this production, the country keeps h(t)x(t) units of intermediate goods for its own use, leaving K(t) - h(t)x(t) to pay for intermediate goods produced by foreign countries. These foreign intermediate goods consist of m different types, each in the amount x, leading to
K(t) - h(t)x(t) = m(t)x(t). (6.10) There are two ways we can interpret this relationship. First, as strict trade in goods and services, the h(z - x) net intermediate goods pro- duced domestically are shipped as exports to foreign countries in exchange for imports of mx in foreign intermediate goods. In this case openness is refl ected in the size of exports and imports.
Alternatively, we can think of this as foreign direct investment (FDI) done in each direction. That is, the home country owns K units of capital, but only hx of those are located inside the country itself. The other mx units of capital are located in a foreign country, for example, Intel’s chip manufacturing plant in Costa Rica. An equivalent amount
of foreign capital is invested in the home country, for example, Toyo- ta’s assembly plant in Tennessee. In this case, intermediate goods are not traded directly. Rather, ownership of capital is traded. In this case, equation (6.10) says that the amount of outward FDI done by a country equals the inward FDI fl owing into the country.
In either interpretation, we’ve presumed that trade is balanced;
imports equal exports or outward FDI equals inward FDI. Capturing persistent surpluses or defi cits in trade of either kind would require us to specify something that differentiates countries of the world. It could be differences in their preference for consumption today versus the future, differences in their institutional structure, or differences in the productivity of intermediate goods. Our presumption of balanced trade allows us to look at the effect of trade on economic growth in the long run, but we won’t be able to predict anything regarding the exact pattern of trade between particular countries.6
In reality, both trade in goods and FDI occur. For our purposes the exact nature of trade is not going to infl uence the outcome. In either case, equation (6.10) can be rearranged to
K(t) = x(t)[h(t) + m(t)],
and combined with the production function in equation (6.9) gives a familiar result:
Y = Ka[(h + m)L]1-a.
Here, the term h + m enters as a labor-augmenting technology. Already, we can see that more foreign intermediate goods, m, raise output. To work with this further, rearrange this production function slightly to be
Y = Ka(hL)1-aa1 + m hb1-a.
We have a production function nearly identical to equation (6.3), with the extra term scaling the production function depending on the number of foreign intermediate goods relative to the number of domestic ones.
6We have also implicitly assumed that the law of one price holds, so that there is no need to deal with exchange rates explicitly.
151 G LO BALIZATI O N AN D TRAD E
From here, we can adopt all the remaining assumptions of Section 6.1 regarding physical capital and human capital accumulation as well as the growth rate of the world technology frontier. The analysis of the balanced growth path follows Section 6.2 directly, with the only difference being that we will carry along the extra scaling term for trade. In the end, we get an expression for output per worker along the balanced growth path:
y*(t) = a sK
n + g + dba>1-aam
gecub1>ga1 + m
hbA*(t). (6.11) This is nearly identical to equation (6.8). If a country is completely closed to trade in goods and capital, so that m = 0, then it is exactly the same.
We can also capture a crude measure of openness by looking at the ratio of imports to total GDP,
Imports
GDP = mx
Y = m
m + h K
Y. (6.12)
where the second equality follows from the trade balance in equation (6.10). This equation, combined with (6.11), shows the positive rela- tionship between output per worker along the balanced growth path and openness. As the ratio m>h rises, this acts similarly to raising the savings rate (sK) or amount of education (u). There is a level effect on income per capita, and immediately after opening up, a country will grow relatively quickly along its transition path to the new balanced growth path. Additionally, when m>h rises, the import to GDP ratio also rises as more of the intermediate goods are sourced from abroad.7
This is just what we see in the data from Figure 1.5. It is important to note that this relationship is not driven solely by increasing exports from some countries. In China, imports accounted for less than 3 per- cent of GDP in 1960, but were 27 percent in 2008. For South Korea, imports were 13 percent of GDP in 1960, rising to 54 percent by 2008.
In terms of our model, both countries have expanded the fraction of intermediate goods provided by foreign countries.
7As we have modeled intermediate goods as being produced by capital, the capital/out- put ratio shows up in the import to GDP ratio as well. Countries that save more will more capital available to produce intermediate goods that they can trade for imports.
The effect of trade actually depends on the ratio m>h, and not simply m itself. Along the balanced growth path, we know that h is growing at the rate g, so the ratio m>h will actually fall over time unless the coun- try continues to add new foreign intermediate goods into its production process. Research by Christian Broda, Joshua Greenfi eld, and David Wein- stein (2010) document just such an increase in the number of intermediate goods imported by countries across the world. In 1994, the median coun- try in their sample imported about thirty thousand different intermediate goods, and this rose to over forty-one thousand by 2003. That translates to a growth rate of roughly 3.5 percent per year. Of the overall expansion in the value of imports in this period, 92 percent was due to increases in the varieties of goods imported, as opposed to the amount of any specifi c good. Globalization has been associated with an expansion in the number of types of intermediate goods used by countries around the world. The increase in the number of imported varieties over the last few decades is consistent with an increase in the absolute size of m in our model. More- over, in 1994 about 10.5 percent of all the varieties of intermediate goods in the world were traded, but this had risen to 13 percent by 2003. From this it would appear that the ratio m>h has increased over the last decade as well.
Broda, Greenfi eld, and Weinstein (2010) use a model similar to ours to calculate the effect on the growth rate of output per worker due to this increase in imported varieties. They fi nd that, starting from a bal- anced growth rate of 2 percent, growth rises to 2.6 percent per year for the median country in their sample due to the increase in varieties imported. This is transitional, but they fi nd that growth remains above 2 percent for nearly seventy-fi ve years before returning to the steady- state growth rate. This implies a substantial level effect from increased openness, and a potentially substantial gain in welfare.