Economic Growth 7 - Measuring Productivity

Question 1

What is Productivity?

Answer 1

The effectiveness with which factors of production are converted into output.

Question 2

Other than accumulated factors of production, what explains differences between countries in their output?

Answer 2

The effectiveness with which they combine these factors of production to produce output—that is, in their productivity.

Question 3

Which two methods will we use in this cha[ter to explain differences in productivity?

Answer 3

Development Accounting

Growth Accounting.

Question 4

Comparing productivity among countries is problematic if the only information at our disposal is the countries’ levels of output and factor accumulation.
What is the difference between looking at Figures and looking at real-world data when analyzing productivity?

Answer 4

In the real world, we do not necessarily see what the production function looks like. Instead, we see only data on output and factor accumulation. Our task is to infer something about productivity from these data.

Question 5

In which 2 ways will we be able to make two other improvements over the graphical approach in analyzing productivity?

Answer 5

-We will go beyond the general case in which we measure factors of production on the horizontal axis and instead use real data on physical capital and human capital.
We will go beyond the question of which country has higher productivity and examine by how much productivity differs.

Question 6

How will our new approach help us understand productivity?

Answer 6

We will be able to look quantitatively at productivity gaps among countries. With quantitative measures of productivity differences, we will also be able to determine how much of the variation among countries’ income per capita is explained by the variations in productivity and how much is explained by the accumulation of factors of production.

Question 7

The per-worker production function is
y = Ak^(α)h^(1-α).
What is a useful way of looking at this expression to help isolate productivity?

Answer 7

output = productivity × factors of production.

The two factors of production (physical capital and human capital) are combined into a single aggregate called “factors of production,” which is then used in producing output where we can write: factors of production = kαh1-α

Question 8

Which equation compares productivity between 2 countries?

Answer 8

y1/y2 = (A1/A2) ( k1^(α)h1^(1-α) / k2^(α)h2^(1-α) )

Question 9

If the two countries were identical in their factor accumulation—that is, if they had equal levels of human and physical capital—then What would the ratio of output in the two countries would be the same as?

Answer 9

The ratio of productivity (A1/A2)

Question 10

The second term on the right side of the equation is the ratio of inputs from factors of production. i.e. ( k1^(α)h1^(1-α) / k2^(α)h2^(1-α) )
What can we think of this term as representing?

Answer 10

What the ratio of output in Country 1 to output in Country 2 would be if the two countries had the same level of productivity—that is, if the only difference in their output were the result of differences in factor accumulation.

Question 11

What is the actual ratio of income in two countries according to this updated model?

Answer 11

The product of the ratio of productivity in the two countries and the ratio of factor accumulation in the two countries:
ratio of output = ratio of productivity × ratio of factors of production.

Question 12

How does the equation
ratio of output = ratio of productivity × ratio of factors of production
also gives us a method for measuring productivity differences?

Answer 12

Two of the three pieces of this equation are directly observable: output and factor accumulation in the various countries. We cannot measure productivity directly, but we can use the equation to measure it indirectly.

Question 13

Which basic equation allows us to indirectly measure productivity?

Answer 13

ratio of productivity = ratio of output/ratio of factors of production

Question 14

How should one interpret the equation:

ratio of productivity = ratio of output/ratio of factors of production

Answer 14

The larger the ratio of output in the two countries, the larger a productivity gap we would infer. Conversely, the larger the gap in the accumulation of factors, the smaller the productivity gap we would infer. In other words, the larger the difference in output between two countries that is explained by differences in factor accumulation, the less reason there is to conclude that a difference in productivity is the source of differences in income between the two countries.

Question 15

Which sophisticated equation allows us to indirectly measure productivity?

Answer 15

(A1/A2) = y1/y2 / ( k1^(α)h1^(1-α) / k2^(α)h2^(1-α) )

Question 16

What is development accounting?

Answer 16

The technique for breaking down differences in income into the part that is accounted for by differences in productivity and the part accounted for by differences in factor accumulation.

Question 17

If there is a deficiency with productivity measures, what does it probably results from and why?

Answer 17

Problems in measuring factors of production.
-Productivity is the part of differences in output that is “left over” when differences in factors of production are accounted for. If we do not properly measure factors of production, then we will not properly account for their effect on differences in income among countries. As a result, the differences in output that are attributed to productivity also will be incorrect.

Question 18

What can explain deficiencies in measuring physical capital, particularly in developing countries?

Answer 18

Much of the money that is allegedly spent on investment in new capital is diverted along the way into other uses. i.e. Corruption and Waste.

Question 19

In many developing countries, the diversion of investment funds away from the actual building of new capital is particularly severe. Which 2 reasons explain why this is?

Answer 19

• A large fraction of investment in these countries is done by governments, which tend to be less efficient than the private sector in converting investment spending into capital.
• Both governments and private-sector corporations in many developing countries are corrupt.

Question 20

With respect to the current chapter, the relevance of Pritchett’s argument (about waste and corruption) is that it implies that our measures of productivity may be wrong. Why is this?

Answer 20

Measuring productivity requires a measure of the stock of physical capital. In many countries, the quantity of investment that economists think is taking place is larger than what is actually taking place. Therefore, the quantity of capital that economists think is present is much larger than what is actually there.

Question 21

Because the overstatement of the capital stock is likely to be a bigger problem in poor countries than in rich countries, the actual gap between capital stocks in rich and poor countries is larger than the gap in capital stocks estimated by economists. What does this discrepancy imply?

Answer 21

That actual gaps in productivity between rich and poor countries are smaller than economists have estimated because the productivity gap is what is required to explain differences in output that are not explained by the accumulation of factors such as capital.

Question 22

What is Growth Accounting?

Answer 22

The technique for examining of how much of a country’s income growth is accounted for by growth in productivity and how much by growth in the quantity of factors of production.
Specifically, given data on a country’s growth rates of output, physical capital, and human capital, we can measure its growth rate of productivity.

Question 23

Which 2 question does growth accounting seek to answer?

Answer 23

• How much income growth on average is accounted for by productivity growth, and how much by increases in factors of production?
• When we look at variation in growth rates among countries (i.e., at fast-growing versus slow-growing countries), how much of this variation is explained by variation in productivity growth, and how much by variation in growth in the quantity of factors of production?

Question 24

Which equation relates the growth rates of output, productivity, and factors of production?

Answer 24

growth rate of output = growth rate of productivity

+ growth rate of factors of production.

Question 25

What is the simplified equation for growth rate in productivity?

Answer 25

growth rate of productivity = growth rate of output

− growth rate of factors of production.

Question 26

What is the sophisticated equation for growth rate in productivity derived using calculus?

Answer 26

A^ = y^ - αk^ - (1-α) h^

When ^ here signifies growth rate

Question 27

Why are the results of this exercise often called “a measure of our ignorance.”

Answer 27

Although we can measure the coefficient A, we do not know what it really is because we cannot observe A directly. Rather, we have observed the inputs and outputs of production and inferred the value of A from these.