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Professor Xiaodong Zhu

Growth Accounting Assignment

Due date and time: January 29, 2019 at 12:00pm

In this assignment you will do an exercise of growth accounting and to study

the impact of investment rate on long-run growth. In the attached excel

file, I provide the data on real GDP, real capital stock, total employment,

average level of human capital and real investment rate in China for the

period 1991-2013.

Some Guidlines:

• In all you calculations, assume that the labor income share is 1/2.

• Always express growth rate as annual average growth rate, and calculate growth rate of a variable x(t) as ln[x(t+1)]-ln[x(t)]

• You need to submit a summary report and the excel spreadsheet that

you used for generating the results.

• The report should be no more than three pages, one-sided, double

space.

I. Do a conventional growth accounting by decomposing China’s real GDP

growth between 1991 and 2013 into the contributions from capital accumulation, employment growth, increase in average human capital level and

TFP growth. According to this decomposition, which is the main source of

China’s GDP growth during this period?

II. As we discussed in the class, the capital accumulation is endogenous and

depends on the growth of the other three variables. Do a theory-based

growth accounting that decompose the GDP growth into the growth in

capital-output ratio, growth in employment, growth in average human capital level and growth in TFP. According to this alternative decomposition,

which is the main source of China’s growth? Explain why the conclusion

from this decomposition is different from the standard decomposition in I.

1

III. As I provided in the excel file, China’s real investment rate has increased

from 15% in 1991 to 32% in 2013. Many people have argued that this increase in the investment rate is a main driving force of China’s growth during

this period. To see if this is true, do the following counterfactual simulation

using the Solow model: Assume that the total employment, average level of

human capital and the TFP remain the same as in the data for the entire

period, and that the initial capital stock and the real GDP in 1991 are also

the same as in the data. However, assume that the investment rate is kept

at 15% for the entire period so that the capital stock and GDP in the years

after 1991 are determined recursively by the following two equations:

Kt+1 = (1 − δ)Kt + 0.15Yt

Yt+1 = At+1K0.5

t+1 (ht+1Lt+1)

0.5

where δ = 0.07 is the depreciation rate and t = 1991, …, 2012. How much

will the capital stock growth rate be reduced as a result of lower investment

rates? What about the GDP growth rate? Based on your calculation,

what do you think is the contribution to growth of the increases in the real

investment rate?

III. Now redo the counterfactual by assuming the investment rates are the

same as in the data, but the TFP level stays at the 1991 lelve, i.e., no TFP

growth. So the capital stock and GDP in the years after 1991 are determined

recursively by the following two equations:

Kt+1 = (1 − δ)Kt + StYt

Yt+1 = A1991K0.5

t+1 (ht+1Lt+1)

0.5

where δ = 0.07 is the depreciation rate, St the investment rate in year t, and

t = 1991, …, 2012. How much will the capital stock growth rate be reduced

as a result of no TFP growth? What about the GDP growth rate? Based

on your calculation, what do you think is the contribution to growth of the

TFP growth?