1. This exercise applies the sources-of-growth model. We will neglect land and natural resources for simplicity. With this modification, the sources-of-growth equation from the textbook is
g = the growth rate of national product,
a = the residual,
W K , W L = the shares of national income going to capital and to labor, respectively,
g K , g L = the growth rate of the capital stock and the labor force, respectively.
a. Consider an economy in which the labor force grows by 2.7 percent per annum, while the capital stock grows by 4 percent per annum. Suppose 55 percent of national income goes to labor and 45 percent to capital.
(i) If the residual were a = 0, what rate of growth would the economy achieve? (Hint: Plug the numbers into the growth equation and solve for g .)
g =
This is the growth rate that is attributable to the accumulation of capital and labor stocks.
(ii) The country’s actual rate of growth has been 4.5 percent per annum, which is faster than the growth rate generated by the accumulation of capital and labor stocks. Calculate the value of the residual.
a =
(iii) Then explain the economic meaning of the residual: What is causing growth over that which is derived from the accumulation of factors of production?
b. Consider a second economy in which labor’s share of national income is 0.6; the remainder is capital’s share. The capital stock is growing by 5 percent per annum and the labor force is growing by 3 percent per annum, while real GDP is growing by just 1 percent per annum.
(i) Calculate the residual for this economy. a =
(ii) You should find that the value of the residual is disturbingly low this time! What economic conditions might be responsible for such a low residual?
c. From 1970 to 1989 Singapore’s growth rate averaged 8.4 percent per year. A recent growth-accounting study showed that the residual accounted for only 1.2 percent per year of Singapore’s outstanding growth performance. This growth-accounting analysis used weights of 0.33 for labor and 0.67 for capital, including human capital.
(i) Singapore’s labor force grew by 2.6 percent per year during this period. What can you conclude about the annual growth rate of Singapore’s capital stock? (Bear in mind that this includes both physical and human capital.)
(ii) What fraction of the overall 8.4 percent growth rate is attributable to capital investment? (Hint: Calculate W K g K /g .)
(iii) Briefly assess the sources of GDP growth in Singapore. Was the growth performance due primarily to capital accumulation? To population growth? To improvements in total factor productivity, as measured by the residual?
2. Empirical patterns. Figure 3–13 in the textbook shows how the share of
GDP generated in the agricultural sector varies with the level of per capita
PPP GDP in 2004, on average. Let’s examine a variant of this relationship with industrial share using
more recent cross-section data. Table 3–1 shows the share of output
produced by the manufacturing sector (MFG/GDP) in 12 developing
countries in the population range of 15 to 50 million people in 1992. (If
some of these countries aren’t familiar, take a few minutes to look them
up.) The table also shows per capita GNP (based on PPP conversions) for
each country.
a. On Figure 3–4, carefully plot 12 points corresponding to the 12 data observations in Table 3–1. Then use a straight edge to draw the best-fit straight line showing the underlying pattern of changes in MFG/GDP as a function of per capita GNP for this class of countries. (Popular spreadsheet programs provide easy procedures for estimating statistical regression lines of this sort; consult the software manual for details.)
b. The observation for Ethiopia lies above the best-fit line, whereas the observation for Uganda lies well below the line. How can one explain these deviations in MFG/GDP from the underlying pattern? Is it fair to conclude from these observations that Ethiopia has performed well and Uganda has performed poorly relative to the normal structure of economic development? Explain briefly.
