Question; Growth Accounting Assume the Cobb-Douglas production function (1) determines aggregate real GDP. a) Derive a “growth rate” version of (1) which shows how the growth rate of real GDP is determined by the growth rates of technology, employment, and capital. b) Now collect at least ten years of annual data on: Real GDP (https://fred.stlouisfed.org/series/GDPCA allows download into excel file)

QUESTION

Question; Growth Accounting
Assume the Cobb-Douglas production function (1) determines aggregate real GDP.
a) Derive a “growth rate” version of (1) which shows how the growth rate of real GDP
is determined by the growth rates of technology, employment, and capital.
b) Now collect at least ten years of annual data on:
Real GDP (https://fred.stlouisfed.org/series/GDPCA allows download into excel
file)
Employment (https://fred.stlouisfed.org/series/B4701C0A222NBEA
allows download into excel file)
Capital (https://fred.stlouisfed.org/series/RKNANPUSA666NRUG allows download
into excel file).
c) Compute the annual growth rate of each of the data series you downloaded or
otherwise collected in b). Compute the implied annual growth rate of technology at
each date. Now compute the sample average annual growth rates of all four
variables.
d) Using the equation you derived in a), and your results in c), what fraction of real
GDP annual average growth over your sample period is accounted for by i) capital
growth, ii) employment growth, and iii) technological change.

ANSWER

Growth Accounting: Analyzing the Factors Driving Economic Growth

Introduction

Growth accounting is an essential economic framework used to analyze the sources of economic growth in an economy. By decomposing the growth rate of real GDP into the contributions of various factors such as technology, employment, and capital, we can gain valuable insights into the drivers of economic expansion. In this essay, we will follow a step-by-step approach to perform growth accounting using the Cobb-Douglas production function and annual data collected over a ten-year period.

Deriving the Growth Rate Version of the Cobb-Douglas Production Function

The Cobb-Douglas production function provides a foundation for understanding the relationship between real GDP, technology, employment, and capital. By taking the natural logarithm of the production function and differentiating, we obtain a growth rate version of the equation (Cobb-Douglas Production Function | INOMICS, 2020). This growth rate equation demonstrates how the growth rate of real GDP is influenced by the growth rates of technology, capital, and employment.

Collecting and Analyzing Data

To perform growth accounting, we gather ten years of annual data on key variables: real GDP, employment, and capital. Reliable sources like the Federal Reserve Economic Data (FRED) platform provide access to downloadable datasets for these variables. Once we have obtained the data, we proceed to compute the annual growth rates for each series (Senbet, 2022). This involves taking the difference in the natural logarithm of each variable between consecutive years and converting it into a percentage growth rate.

Computing Technological Growth and Averages

To determine the implied annual growth rate of technology, we utilize the growth rate version of the Cobb-Douglas production function derived earlier (Greer, 2022). By rearranging the equation, we can solve for the annual growth rate of technology. Substituting the calculated values of real GDP, capital, and employment growth rates, we obtain the growth rate of technology for each year.

Additionally, we compute the average annual growth rates for all four variables by calculating the arithmetic mean of their respective growth rates over the ten-year period. These averages provide a useful basis for understanding the overall performance and contributions of each factor.

Analyzing Contributions to Real GDP Growth

Using the growth rate equation derived from the Cobb-Douglas production function and the computed growth rates, we can determine the contribution of each factor to the average annual growth of real GDP over the sample period.

Firstly, we calculate the contribution of capital growth by multiplying the average annual growth rate of capital by the coefficient α in the Cobb-Douglas production function, representing the share of capital in the production process.

Secondly, we determine the contribution of employment growth by multiplying the average annual growth rate of employment by the coefficient (1-α), representing the share of labor.

Lastly, the contribution of technological change is equal to the average annual growth rate of technology.

By summing up these three contributions, we can ascertain the fraction of real GDP’s annual average growth accounted for by capital growth, employment growth, and technological change, respectively.

Conclusion

Growth accounting provides a comprehensive framework for analyzing the sources of economic growth. By utilizing the Cobb-Douglas production function and annual data, we can unravel the contributions of technology, employment, and capital to real GDP growth. This analysis aids policymakers and economists in making informed decisions and formulating strategies to promote sustainable economic expansion. By understanding the underlying factors driving economic growth, societies can foster innovation, enhance productivity, and achieve long-term prosperity.

References

Cobb-Douglas Production Function | INOMICS. (2020, April 15). INOMICS. https://inomics.com/terms/cobb-douglas-production-function-1456726 

Greer, M. L. (2022). The Economics (and Econometrics) of Cost Modeling. In Elsevier eBooks (pp. 175–209). https://doi.org/10.1016/b978-0-12-821365-0.00001-3 

Senbet, D. &. W. T. (2022). Growth Accounting: Sources of Economic Growth in Ethiopia. ideas.repec.org. https://ideas.repec.org/a/ags/afjecr/330305.html