StudySpace: Economics in Development, 6th Edition

Worked Example:Examining Cross-Country Development Patterns

Cross-country data are frequently used for the inductive analysis of development patterns and also for testing theoretical hypotheses about development. Let’s see what the data reveal about patterns of change in infant mortality rates.

In Figure 1–1 the horizontal axis measures GNP per capita (call this Y) in 1992 U.S. dollars, based on the PPP method of comparison. The vertical axis measures the infant mortality rate (call this IM) per 1,000 live births in 1992. The data for each country can be considered as one snapshot observation of an underlying dynamic relationship between Y and IM. For present purposes we use only the data reported in textbook Table 1–3 for low- and lower-middleincome countries. The result is the scatter plot of points shown in Figure 1–1.

There is a visible pattern to the scatter plot of points. To quantify this pattern, economists use statistical techniques such as regression analysis; you can think of it as a calculation of the best-fit line through the data points. The line PP in Figure 1–1 is the best-fit regression line for the plotted data. The exact equation for the line, calculated using a standard spreadsheet program, is IM = 113.7 – 0.022Y.

The various points obviously don’t stick very closely to line PP. Deviations from the line could be explained by considering other explanatory variables. In addition to GNP per capita, one might expect the level of education to be an important determinant of IM. Indeed, in countries such as China, Sri Lanka, and the Philippines, which all have IM values well below the “pattern” line, adult illiteracy is also low. In contrast, Mali, Pakistan, and Egypt have IM values well above the line PP; in each case adult illiteracy rates are quite high. As always, there are exceptions: have a careful look at the data for Bolivia and Indonesia.

Two Notes to Students

When you encounter references to countries that you don’t know much about, it is a good idea to look them up. Any handy encyclopedia will do. You can also form a mental picture of economic conditions in each country by scanning the data tables in the back of the latest World Development Report, which should be available in your library.

Examine the horizontal axis in the textbook graphs. Equal distances along the axis do not represent equal increments in GNP per capita. The X axis is drawn using a natural logarithmic scale, so equal distances along the axis represent equal proportional changes. The points 10,000 and 20,000 are separated by the same horizontal distance as the points 500 and 1,000. Given wide differences in GNP per capita, with lots of countries clustered at low values, the logarithmic scale tends to spread out the data plot and provide a clearer picture of patterns. Scanning these graphs, you should interpret each jump to the right as a proportional increase in per capita income.

Exercises
1. Now it is your turn to examine a development pattern. Consider differences in the child mortality rate (call this CMR) across the continuum of development, as measured by GNP per capita (call this Y). The database for this exercise is given in Table 1–1. (The topic of health is covered in detail in Chapter 10.)

a. To simplify your work, the graph will be drawn using only three group-wise average values of CMR and Y. From the data in Table 1–1, calculate the average values of CMR and Y for

Low-income countries: CMR = ; Y = . Lower-middle-income countries: CMR = ; Y = . Upper-middle-income countries: CMR = ; Y = .

b.

(i) In Figure 1–2 plot the three points corresponding to the averages you calculated in part a. Then draw line segments connecting the three data points.

(ii) What do you observe about the general relationship between Y and CMR?

c. Now examine several individual countries in relation to the pattern that you derived from the group averages.

(i) From Table 1–1, what are the values of CMR and Y for each of the following eight countries?

CMR		Y
Ethiopia		$
China		$
Honduras		$
Pakistan		$
Cameroon		$
Sri Lanka		$
Brazil		$
Malaysia		$

(ii) Plot these eight data points on Figure 1–2.

(iii) What factors other than Y might account for the deviations between CMR values and the average pattern established in part b? Give two plausible answers.

d. Do the country-specific statistics invalidate the presumption that there is a pattern to the changes in child mortality rates that occur in the course of economic development?

2. This exercise uses stylized graphs to capture some basic patterns of development.

a.  Figure 1–3 shows a cross-country development pattern, but the labels are missing. Think about the relationship expressed by the two lines in this figure. Then pair each item in the left-hand column of the following table to the appropriate letter label from the graph.

Item	Letter Label
Percentage of age group enrolled in a primary school
GNP per capita
1965
1995

 

b. In Figure 1– 4, line A shows a negative correlation between per capita income and variable X, while line B shows a positive correlation.

FIGURE 1– 4

Consider the variables in the following list as alternative definitions of X, one by one. For each variable, indicate whether line A or line B best captures its relationship with per capita income, as countries move through the development continuum. The first blank is filled in as an example.                                

Development characteristic	Line
Infant morality rates	A
Energy consumption per capita
Adult literacy
Life expectancy
Share of population living in rural areas
Share of industry in GNP
Percentage of population with access to clean water

3. The story of Rachmina Abdullah portrays a set of working conditions, living standards, and aspirations that differ greatly from the lifestyle of most citizens of the world’s industrial countries.

a. Write a brief word portrait conveying your impressions of how the life of a 17-year-old girl from a Malaysian village differs from that of a 17-year-old girl in a small town in Massachusetts.

b. Write a brief word portrait conveying your impressions of how the life of a lathe operator in Maputo, Mozambique, differs from that of a lathe operator in Tokyo.

c. Write a brief word portrait conveying your impressions of how life on a small family farm in Malawi differs from life on a small family farm in Wisconsin.

4.   The text mentions that when income per capita grows by 4 percent per year, average incomes “double in less than a generation.” A convenient way to grasp the significance of different growth rates is to calculate “doubling times.” How long does it take for a variable to double in value if it grows continuously at the rate R percent per year? One way to answer this question is to use the equation for compound growth:

(Value at year T )/(initial value) = erT
where T is the time, in years, and r = R/100 is the growth rate expressed in decimal form. For this particular problem, we want the ratio on the left-hand side to equal exactly 2, representing a doubling of the value. Taking the logarithm of both sides, the equation can be expressed as 1n 2 = rT, or 100 ×1n 2 = RT when the growth rate is expressed in percentage units rather than decimal units. Since 1n 2 = 0.7, approximately, the formula reduces to 70 = RT, or T = 70/R. If income per capita grows at R = 4 percent per year, then doubling takes approximately T = 70/4 = 17.5 years.

a. Using the growth rates of GDP per capita from textbook Table 1–2 for 1980-2003, calculate the number of years required for GDP per capita to double in each of the following countries:

Growth rate		Doubling time
India	%	years
Sri Lanka	%	years
Honduras	%	years
Ghana	%	years
Korea, Republic of	%	years

b. Even moderate differences in growth rates can cause astonishing differ­ences in the doubling time. This is most apparent when we look at longer periods of time. Notice that when income doubles once, twice, and then three times, the overall value is multiplied eightfold (2 ×2 ×2). Thus, three doubling periods generate an eightfold increase. Suppose that the growth rate experienced by each country listed can be sustained indefi­nitely. How many years are needed for each country’s GDI per capita to grow eightfold? Also, what level of GDI per capita (in 2003 dollars) would each country attain after an eightfold increase? (Table 1–1 in the textbook gives initial values needed to answer the second part of the question.) For this exercise, use GNI and GDP interchangeably.

 

	Time required to  grow eightfold	GNP per capita after growing eightfold
India	Years	$
Sri Lanka	Years	$
Honduras	Years	$
Ghana	Years	$
Korea, Republic of	Years	$

 

 

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