In 2014 USD Relative to the US values (U.S. =1) 1 2 3 4 5 6 Capital per person p
ID: 1137538 • Letter: I
Question
In 2014 USD
Relative to the US values (U.S. =1)
1
2
3
4
5
6
Capital per person
per capita
GDP
Capital per
person
per capita
GDP
Predicted Y*
Implied TFP to match
data
Country
United
States
141,841
51,958
1.000
1.000
1.000
1.000
Canada
128,667
43,376
0.9071
0.8348
0.96.80
0.8624
France
162,207
37,360
1.1436
0.7190
1.046
0.6876
Hong Kong
159,247
45,095
1.1227
0.8679
1.039
0.8351
South
Korea
120,472
34,961
0.8493
0.6729
0.946
0.7105
Indonesia
41,044
9,797
0.2894
0.1886
0.661
0.2851
Argentina
53,821
20,074
0.3794
0.3864
0.723
0.5336
Mexico
45,039
15,521
0.3175
0.2987
0.681
0.4378
Kenya
4,686
2,971
0.0330
0.0572
0.321
0.1782
Ethiopia
3,227
1,505
0.0228
0.0290
0.284
0.1022
7. The importance of capital versus TFP: Create a new table that contains only the last three columns of the table in exercise 5 (previous question in this set). This time, instead of reporting the numbers relative to the U.S. value, report the inverse of these numbers. For example, you should have found that per capita GDP in Kenya relative to that in the United States was 0.057. Now express this number as the ratio of U.S. per capita GDP to Kenya's per capita GDP: 1/0.057 = 17.5. Fill in all three columns for the remaining countries.
(a) Explain in general how to interpret these numbers and in particular how the three columns are related.
(b) In the chapter, we found that about one-third of the differences in per capita GDP across countries were due to differences in capital per person and about two-thirds were due to differences in TFP. Carry out this calculation for Kenya. The United States is 17.5 times richer than Kenya; what fraction of this factor of 27 is due to differences in capital per person and what fraction is due to differences in TFP?
(c) Repeat part (b) for Ethiopia.
In 2014 USD
Relative to the US values (U.S. =1)
1
2
3
4
5
6
Capital per person
per capita
GDP
Capital per
person
per capita
GDP
Predicted Y*
Implied TFP to match
data
Country
United
States
141,841
51,958
1.000
1.000
1.000
1.000
Canada
128,667
43,376
0.9071
0.8348
0.96.80
0.8624
France
162,207
37,360
1.1436
0.7190
1.046
0.6876
Hong Kong
159,247
45,095
1.1227
0.8679
1.039
0.8351
South
Korea
120,472
34,961
0.8493
0.6729
0.946
0.7105
Indonesia
41,044
9,797
0.2894
0.1886
0.661
0.2851
Argentina
53,821
20,074
0.3794
0.3864
0.723
0.5336
Mexico
45,039
15,521
0.3175
0.2987
0.681
0.4378
Kenya
4,686
2,971
0.0330
0.0572
0.321
0.1782
Ethiopia
3,227
1,505
0.0228
0.0290
0.284
0.1022
Explanation / Answer
7. As we calculate the inverse of the numbers obtained in the table (provided in the question). Therefore we enter the values in the table after dividing by 1 as shown below:
Country Per capita GDP Predicted Y* Implied TFP to match data
US 1.000 1.000 1.000
Canada 1.1978 1.0330-04 1.1595
France 1.3908 0.9560 1.4543
Hong Kong 1.1522 0.0009 1.1974
South Korea 1.4861 1.0571 1.4074
Indonesia 5.3022 1.5128 3.5075
Argentina 2.5879 1.3831 1.8740
Mexico 3.3478 1.4684 2.2841
Kenya 17.4825 3.1153 5.6116
Ethopia 34.4827 3.5211 9.7847
a) Per Capita GDP: GDP per capita is a measure of a country's economic output that accounts for its number of people. It divides the country's gross domestic product by its total population. That makes it the best measurement of a country's standard of living. It tells you how prosperous a country feels to each of its citizens.
The formula is GDP/Population. If you’re looking at just one point in time in one country, then you can use regular, “nominal” GDP divided by the current population.
If you want to compare GDP per capita between countries, you must use the purchasing power parity GDP. That creates parity, or equality, between countries by comparing a basket of similar goods. It's a complicated formula that values a country's currency by what it can buy in that country, not just by its value as measured by its exchange rates. You can find every country’s purchasing power parity GDP in the CIA World Factbook.
If you want to compare GDP per capita over time, then you must use real GDP per capita. That removes the effects of price changes.
GDP per capita allows you to compare the prosperity of countries with different population sizes. U.S. GDP was $19.36 trillion in 2017 according to the CIA World Factbook. But one reason America is so prosperous is it has so many people. It's the third most populous country after China and India. The United States must spread its wealth among 327 million people. As a result, the U.S. GDP per capita is $59,500. That makes it the 18th most prosperous country per person.
China has the largest GDP in the world, producing $23.12 trillion in 2017. But its GDP per capita was only $16,600 because it has four times the number of people as the United States. It's the most populous country in the world, with 1.38 billion people.
The European Union is the world's second most prosperous economy, at $19.97 trillion. It's an economy made up of 28 separate countries. Its GDP per capita was only $39,200 because it must spread the wealth among 516 million people. India's GDP was $9.45 trillion, but spread among its 1.3 billion people, its GDP per capita was $7,200. Japan's GDP is $5.41 trillion, the fifth largest in the world. Its GDP per capita was $42,700 since it has 126 million people.
GDP per capita is an important indicator of economic performance and a useful unit to make cross-country comparisons of average living standards and economic wellbeing. However, GDP per capita is not a measure of personal income and using it for cross-country comparisons also has some known weaknesses. In particular, GDP per capita does not take into account income distribution in a country. In addition, cross-country comparisons based on the U.S. dollar can be distorted by exchange rate fluctuations and often don’t reflect the purchasing power in the countries being compared.
Predicted Output:
Calculating GDP (gross domestic product) is the most popular measure of national output. The main challenge in using this method is how to avoid counting the same product more than once. Logically, the total output should be equal to the value of all goods and services produced in a country, but in counting every good and service, one actually ends up counting the same output again and again, at multiple stages of production. One way of tackling the problem of over counting is to, consider only value addition, i.e., the new output created at each stage of production.
To illustrate, we can take a dressmaker who purchased a dress material for 500 rupees, then stitched and put final touches on the dress. She then sold the dress for 800 rupees (her costs of finishing the dress were 150 rupees). We can then say that she added 150 rupees worth of output to the dress, as opposed to saying that she produced 800 rupees worth of output. So value addition is equal to the sales price of a good or service, minus all the non-labour costs used to produce it.
To avoid the issue of over-counting, one can also focus entirely on final sales, where, though not directly but implicitly, all prior stage of output creation are accounted for.
Even though both methods are widely acknowledged to be accurate, the second method is known as the expenditure method and is used more widely, and is the standard method of calculation of GDP in most countries. The logic behind using the expenditure method is that if all the expenditures on final goods are added up, the sum should total the total production because the every produced good is eventually produced in some form or the other.
In both these methods, one has to be wary of the fact that consumption includes all spending by households, but business investment does not include all spending by firms, because if it did this would result in massive double counting because many of the things firms buy are processed and resold to consumers. As a result, investment only includes expenditures on output that is not expected to be used up in the short run.
Another possible way in which one may over count is if imports are involved. If a foreign individual or firm bought a product from some other country, e.g., if an American firm bought a Cambodian manufactured good, then this expenditure cannot be counted in the consumer expenditures in American GDP since the output being purchased is foreign. To correct this issue, imports are eliminated from GDP.
Taking all this into account, we see that
A third way to calculate national output is to focus on income. In this method, we look at income which is paid to factors of production and labour for their services in producing the output. This is usually paid in the form of wages and salaries; it can also be paid in the form of royalties, rent, dividends, etc. Because income is a payment for output, it is assumed that total income should eventually be equal to total output.
TFP: Total Factor Productivity (TFP) has become the choice measure of productivity. TFP is often referred to as the Solow residual, and it is just that, namely a residual. Of course, TFP need not be derived from a Cobb-Douglas production function as it was in Solow's original work. There are today many more sophisticated indices available, such as the Fisher and Törnqvist superlative measures that are exact for flexible functional forms of the production function. Nonetheless, as suggested by the above quote, the fact remains that TFP is rather opaque as to the nature of the phenomena that it pertains to measure. TFP captures the effects of changes in technology, institutions, and other productivity shocks, but it gives little insights as to what takes place inside the black box of technology.
Conceptually, total factor productivity refers to how efficiently and intensely inputs are used in the production process. Total factor productivity (TFP) is sometimes referred to as "multi-factor productivity," and, under certain assumptions, can be thought of as a measure of level of technology or knowledge.
Given the macro model: Yt = ZtF(Kt,Lt), Total Factor Productivity (TFP) is defined to be Yt/F(Kt,Lt)
Likewise, given Yt = ZtF(Kt,Lt,Et,Mt), TFP is Yt/F(Kt,Lt,Et,Mt)
The Solow residual is a measure of TFP. TFP presumably changes over time. There is disagreement in the literature over the question of whether the Solow residual measures technology shocks. Efforts to change the inputs, like Kt, to adjust for utilization rate and so forth, have the effect of changing the Solow residual and thus the measure of TFP. But the idea of TFP is well defined for each model of this kind.
TFP is not necessarily a measure of technology since the TFP could be a function of other things like military spending, or monetary shocks, or the political party in power.
"Growth in total-factor productivity (TFP) represents output growth not accounted for by the growth in inputs." — Hornstein and Krusell (1996).
Y = AF (L, K, N)
Where Y = Gross domestic product (GDP)
A = Total factor productivity
L = The quantity of labour input
K = The size of capital stock
N = The quantity of natural resources.
In the studies of sources of growth, the natural resources are given as constant and human capital is added as a separate factor for determining growth in Gross Domestic Product. With these changes then the production function becomes
Y = AF (L, K, H)
Where H represents the quantity of human capital. An important way to assess the contribution of a resource to the production of goods and services is its productivity. By productivity we mean the ratio of output produced to the quantity of input used to produce it. We can measure productivity of a single factor such as labour or capital.
To measure the productivity of all inputs together the concept of total factor productivity (TFP) is employed. The total factor productivity means the ratio of output produced to the amount all inputs used. Total factor productivity is index of overall productivity of the economy. In fact, technical progress in the economy is measured by the annual increase in total factor productivity.
Now, the economic growth depends on the increase in factor inputs and technological progress that is taking place in the economy. Improvement in technology makes factor inputs or resources more productive. If the quantity of resources is increasing and total factor productivity is rising, then output would grow faster than the increase in the quantity of resources. Therefore, rate of economic growth achieved will depend on the growth in resources (i.e factor inputs such as labour, capital and the rate of increase in total factor productivity. Thus:
Economic growth – growth rate of supply of resources + rate of increase in total factor productivity:
Now, the amount by which output increases due to the increase in labour input depends on the contribution of labour to it. Similarly, the amount by which output increases due to accumulation of capital depends on the contribution of capital to it. Assuming no change in natural resources and taking two factor production function, then the growth in real output resulting from the increases in labour and capital inputs can be obtained from multiplying the increases in labour and capital by their respective contributions to the production of output.
Following the neoclassical economists such as Solow, and Meade” the economists generally use the shares in national income (GDP) of labour and capital to measure their contributions to output. From the recent production function studies conducted for the US economy it has been found that labour’s share is about 70 per cent and capital’s share is about 30 per cent of national income. We can obtain the growth in output, (i.e. GDP) by using the following growth equation.
% GDP = % TFP + 0.70 (% L) + 0.30 (%K)
Where
GDP = Gross Domestic Product
TFP = Change in total factor productivity
L = Increase in the quantity of labour
K = Increase in the capital stock
The above growth equation shows how growth in GDP depends on changes in total factor productivity (TFP) and changes in factors such as labour and capital. Recall that change in total factor productivity measures technological progress that is taking place in the economy.
The technical progress that is, changes in total factor productivity is a crucial factor in determining gross of output. For example, if total factor productivity is increasing at the rate of 2 per cent per annum, then even with capital stock and labour force being held constant, gross domestic product (GDP) will increase at the rate of 2 per cent per annum.
If labour input increases by 2 per cent and capital stock increases by 3 per cent per annum each, then applying the above growth equation:
%GDP = 2 + 0.70 (2) + 0.30 (3)
= 2 + 1.40 + 0.90
= 4.3
Thus, GDP will grow at the rate of 4.3 per cent per annum.
It is worth noting here that higher growth rate achieved by Japan in the past was not only due to rapid growth rate of capital stock but also because of relatively higher growth rate in total factor productivity (TFP), that is, technological progress.
Further, from 1973 to mid nineties, lower growth rate in the United States has been due to slowdown in growth in total factor productivity. It may be further noted that differences in growth rates across countries can be explained in terms of differences in growth rates of capital stock and of total factor productivity.
b) 1/3rd of capital per person + 2/3rd of TFP
Calculation of above for Kenya:
1/3(0.0330) + 2/3(0.1782)
=10.1010+3.7411
=13.8421
c) Calculation for Ethopia:
1/3(0.0228) + 2/3(0.1022)
=14.6198+6.5231
=21.1429
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