CheepflowingIf this were true, how would firms and entrepreneurs respond? They would haincentives to move capital out of rich countries, where the return to capital is low.into poor countries, where the return to capital is supposed to be high. And yet theare not the directions of capital flows that we see in the data. Instead, recall from Cter 2, for example that the United States has nun very large trade deficits for mostthe past three decades. And in fact, China has an enormous trade surplus. The cnese are saving more than they are investing, and much of that difference isto the United States. Capital is flowing "backward" relative to what theFigure 4.4 would suggest. Hence, the Lucas question: Why doesn't capital flow from86 Chapter 4 A Model of Productionsimple sductivitystory irich to poor countries?y across couny useful...The short answer is that the simple production model with no differences in tcountries is misguided. We will pursue this explanation in detail belomot insight into the explanation, however, is provided in a recent paper bFrancesco Casell of the London School of Economics and James Feyrer of Dartmoufunction to measure the marginal product of capital directly for many countries aroundCollege Caselli and Fevrer use data on GDP. capital, and the shape of the productionthe world. What they find is striking: the marginal product of capital is quite similaacross a range of countries In fact, the marginal product in rich countries is slichtmore than the marginal product in poor countries, at 8.4 and 6.9 percent, respectivelyThe puzzle, then, is not why capital fails to flow to poor countries. The puzzle is, rathewhy the marginal product of capital in poor countries is not much higher, given that thehave so little capital. A key part of the explanation turns out to be that poor countries12have low levels of the productivity parameter, as we discuss next.5Productivity Differences: Improving the Fit of the ModelRecent research in macroeconomics has employed the production model in adifferent way to explain differences in incomes across countries. This approach isbased on the up-to-now mysterious parameter A. Recall our original production function:Y = F(K,L) = AK 1/312/3.0s TheodIf a country has a high value of A, it will have a higher level of output for anygiven values of K and L. What is A? We can interpret it as an efficiency aproductivity parameter: it measures how productive countries are at using thefactor inputs (in this case K and L) to produce output. For this reason, A is oftenreferred to as total factor productivity, or TFP.75 For more details related to this case study, see Robert E. Lucas Ir.. "Why Doesn't Capital Flow from RichPoor Countries?" American Economic Review Papers and Proceedings, vol. 80 (May 1990), pp. 92-96; and FranceCaselli and James Feyrer, "The Marginal Product of Capital," Quarterly Journal of Economics, vol. 122 (May 20Pp. 535-68*It is also sometimes called multifactor productivity.Gone Too Far?" in NBER Macroeconomics Annual, Ben Bernanke and Julio Rotemberg, eds. (Cambridge, MaSec, for example, Peter Klenow and Andrés Rodríguez, "The Neoclassical Revival in Growth Economics HeMore Output per Worker Than Others?" Quarterly Journal of Economics (February 1999), pp. 83-116.Press, 1997), pp. 73-102; and Robert E. Hall and Charles I. Jones, "Why Do Some Countries Produce So Ma4.3 Analyzing the Production Model 87Now recall how this parameter shows up in the equilibrium of our productionmodel:y-AusWhat we have seen so far is that if 7-1 for all countries, the model predicts(4.10)that most countries should be substantially richer than they are. One way ofexplaining why they are not so rich, then, is by assigning them values of A thatare less than 1. Countries can be rich either because they have a high level ofcapital per person or because they use their capital and labor very efficiently andtherefore exhibit a high level of TFP (Ā).An important limitation on our ability to implement the production modelwith TFP is that we have no independent measure of this efficiency parameter.For capital, we could count the number of machines, factories, computers, and soon in the economy, but for TFP there is nothing comparable we can do.Instead, we exploit the fact that we do possess data on per capita GDP andcapital per person. That is, we have data on every term in equation (4.10) otherthan TFP. As a way of moving forward, then, we can assume our model is correctand calculate the level of TFP for each country that would be needed to makeequation (4.10) hold exactly.This is best understood in the context of an example. Recall from Table 4.3that Italy's capital per person is equal to 0.80 times the U.S. level but its GDP isonly about 0.68 times the U.S. level. Now we take this information and apply itto equation (4.10). That is, we computeA=(4.11)Thus for Italy is equal to 0.73 times the U.S. level, since 0.68/(0.80)1/3=0.73.It must be the case that Italy is significantly less efficient in using its machinesthan the United States is, at least if the model is correct.Because we don't have independent measures of A but rather compute it assum-ing the model holds, we can also think of A as a measure of how big the gap isbetween our model and the data. In addition to being called TFP, therefore, Ais sometimes also referred to as "the residual" or "a measure of our ignorance."Table 4.4 shows the TFP measures for the same countries as in Table 4.3. Perapita GDP in the first column is equal to the product of capital per person (raisedto the 1/3 power) in the second column and "implied TFP" in the third. As we sawearlier, if countries differed only in terms of capital per person, we would expectthe t countries to be much richer. The fact that they are not suggests thatpoorestthey must have TFP levels that are substantially below that in the United States.For example, given its capital per person, we would expect China to have a percapita income of about 65 percent of the U.S. level if its TFP were the same as thatof the United States. Instead, its income is only 28 percent of the U.S. level. Ourmodel suggests that the way to understand China's lower income is that its TFPis only about 0.43 times the U.S. level. So if we gave China the same amount ofcapital per person as the United States, we would still expect its per capita GDPto be only 43 percent of that in the United States.The comparison between China and the United States is shown graphically inFigure 4.6. With a TFP level equal to about 43 percent of the U.S. level, China'sproduction function is shifted down substantially relative to the U.S. production 3.(a) We saw in Chapter 4 that the TFP for Brazil is about 0.43 (=43%). Brieflyand clearly explain what this number 0.43 tells us.OTFP refers to Total Factor Productivity of a nation, and it measures howeffective is an economy by applying all factors of production. At thegiven question, Ithe 0.43 TFP for Brazil refers to the quantity producedusing 100% of inputs.(b) Relative to the USA, Argentina's y = 0.30 and k = 0.18. Calculate its TFP (Ā)using the production model we studied (round to the 2nd decimal place).y=Ak¹/30.30= A*(0.18)¹3A= 3.33333A=3.334. (a) Explain clearly the job separation rates and the job finding rate f in thebathtub model of unemployment. Write out the formula for each rate.OIn the bathtub model, the separation rate captures the number ofemployed people who lose their job. While Job finding rate captures the

Question

CheepflowingIf this were true, how would firms and entrepreneurs respond? They would haincentives to move capital out of rich countries, where the return to capital is low.into poor countries, where the return to capital is supposed to be high. And yet theare not the directions of capital flows that we see in the data. Instead, recall from Cter 2, for example that the United States has nun very large trade deficits for mostthe past three decades. And in fact, China has an enormous trade surplus. The cnese are saving more than they are investing, and much of that difference isto the United States. Capital is flowing &#34;backward&#34; relative to what theFigure 4.4 would suggest. Hence, the Lucas question: Why doesn't capital flow from86 Chapter 4 A Model of Productionsimple sductivitystory irich to poor countries?y across couny useful...The short answer is that the simple production model with no differences in tcountries is misguided. We will pursue this explanation in detail belomot insight into the explanation, however, is provided in a recent paper bFrancesco Casell of the London School of Economics and James Feyrer of Dartmoufunction to measure the marginal product of capital directly for many countries aroundCollege Caselli and Fevrer use data on GDP. capital, and the shape of the productionthe world. What they find is striking: the marginal product of capital is quite similaacross a range of countries In fact, the marginal product in rich countries is slichtmore than the marginal product in poor countries, at 8.4 and 6.9 percent, respectivelyThe puzzle, then, is not why capital fails to flow to poor countries. The puzzle is, rathewhy the marginal product of capital in poor countries is not much higher, given that thehave so little capital. A key part of the explanation turns out to be that poor countries12have low levels of the productivity parameter, as we discuss next.5Productivity Differences: Improving the Fit of the ModelRecent research in macroeconomics has employed the production model in adifferent way to explain differences in incomes across countries. This approach isbased on the up-to-now mysterious parameter A. Recall our original production function:Y = F(K,L) = AK 1/312/3.0s TheodIf a country has a high value of A, it will have a higher level of output for anygiven values of K and L. What is A? We can interpret it as an efficiency aproductivity parameter: it measures how productive countries are at using thefactor inputs (in this case K and L) to produce output. For this reason, A is oftenreferred to as total factor productivity, or TFP.75 For more details related to this case study, see Robert E. Lucas Ir.. &#34;Why Doesn't Capital Flow from RichPoor Countries?&#34; American Economic Review Papers and Proceedings, vol. 80 (May 1990), pp. 92-96; and FranceCaselli and James Feyrer, &#34;The Marginal Product of Capital,&#34; Quarterly Journal of Economics, vol. 122 (May 20Pp. 535-68*It is also sometimes called multifactor productivity.Gone Too Far?&#34; in NBER Macroeconomics Annual, Ben Bernanke and Julio Rotemberg, eds. (Cambridge, MaSec, for example, Peter Klenow and Andrés Rodríguez, &#34;The Neoclassical Revival in Growth Economics HeMore Output per Worker Than Others?&#34; Quarterly Journal of Economics (February 1999), pp. 83-116.Press, 1997), pp. 73-102; and Robert E. Hall and Charles I. Jones, &#34;Why Do Some Countries Produce So Ma4.3 Analyzing the Production Model 87Now recall how this parameter shows up in the equilibrium of our productionmodel:y-AusWhat we have seen so far is that if 7-1 for all countries, the model predicts(4.10)that most countries should be substantially richer than they are. One way ofexplaining why they are not so rich, then, is by assigning them values of A thatare less than 1. Countries can be rich either because they have a high level ofcapital per person or because they use their capital and labor very efficiently andtherefore exhibit a high level of TFP (Ā).An important limitation on our ability to implement the production modelwith TFP is that we have no independent measure of this efficiency parameter.For capital, we could count the number of machines, factories, computers, and soon in the economy, but for TFP there is nothing comparable we can do.Instead, we exploit the fact that we do possess data on per capita GDP andcapital per person. That is, we have data on every term in equation (4.10) otherthan TFP. As a way of moving forward, then, we can assume our model is correctand calculate the level of TFP for each country that would be needed to makeequation (4.10) hold exactly.This is best understood in the context of an example. Recall from Table 4.3that Italy's capital per person is equal to 0.80 times the U.S. level but its GDP isonly about 0.68 times the U.S. level. Now we take this information and apply itto equation (4.10). That is, we computeA=(4.11)Thus for Italy is equal to 0.73 times the U.S. level, since 0.68/(0.80)1/3=0.73.It must be the case that Italy is significantly less efficient in using its machinesthan the United States is, at least if the model is correct.Because we don't have independent measures of A but rather compute it assum-ing the model holds, we can also think of A as a measure of how big the gap isbetween our model and the data. In addition to being called TFP, therefore, Ais sometimes also referred to as &#34;the residual&#34; or &#34;a measure of our ignorance.&#34;Table 4.4 shows the TFP measures for the same countries as in Table 4.3. Perapita GDP in the first column is equal to the product of capital per person (raisedto the 1/3 power) in the second column and &#34;implied TFP&#34; in the third. As we sawearlier, if countries differed only in terms of capital per person, we would expectthe t countries to be much richer. The fact that they are not suggests thatpoorestthey must have TFP levels that are substantially below that in the United States.For example, given its capital per person, we would expect China to have a percapita income of about 65 percent of the U.S. level if its TFP were the same as thatof the United States. Instead, its income is only 28 percent of the U.S. level. Ourmodel suggests that the way to understand China's lower income is that its TFPis only about 0.43 times the U.S. level. So if we gave China the same amount ofcapital per person as the United States, we would still expect its per capita GDPto be only 43 percent of that in the United States.The comparison between China and the United States is shown graphically inFigure 4.6. With a TFP level equal to about 43 percent of the U.S. level, China'sproduction function is shifted down substantially relative to the U.S. production 3.(a) We saw in Chapter 4 that the TFP for Brazil is about 0.43 (=43%). Brieflyand clearly explain what this number 0.43 tells us.OTFP refers to Total Factor Productivity of a nation, and it measures howeffective is an economy by applying all factors of production. At thegiven question, Ithe 0.43 TFP for Brazil refers to the quantity producedusing 100% of inputs.(b) Relative to the USA, Argentina's y = 0.30 and k = 0.18. Calculate its TFP (Ā)using the production model we studied (round to the 2nd decimal place).y=Ak¹/30.30= A*(0.18)¹3A= 3.33333A=3.334. (a) Explain clearly the job separation rates and the job finding rate f in thebathtub model of unemployment. Write out the formula for each rate.OIn the bathtub model, the separation rate captures the number ofemployed people who lose their job. While Job finding rate captures the

Accepted Answer

TFP is the total factor productivity. 
This shows how efficient or productive an economy is. 
This…