Macroeconomics Growth Accounting

Question

How can I find the growth rate in per capita GDP and then how much of the growth during this period is attributable to increases in L/N?

Answer 1

Hey! I think this is what you were asking for, but to understand growth, we use a production function like: Y=A⋅Kα⋅L1−α Where Y=GDP, A=TFP, K=Capital, L=Labor, and α=capital's share.

1. Finding the Growth Rate in Per Capita GDP (gY/N​)

Goal: Calculate the average annual growth rate of Real GDP per person.

What you need:

1. Real GDP (Y) data for start and end years.
2. Total Population (N) data for start and end years.
3. Number of years (t) in the period.

Steps:

1. Calculate Per Capita GDP for each year: (Y/N)year​=Real GDPyear​/Populationyear​
2. Calculate average annual growth rate (using natural logs for simplicity): gY/N​≈[ln((Y/N)final​)−ln((Y/N)initial​)]/t

2. Attributing Growth to Increases in L/N

Goal: Determine how much of the per capita GDP growth is due to changes in the labor input relative to the population.

The growth accounting equation for per capita GDP is often expressed as: gY/N​≈gA​+α⋅gK/L​+gL/N​

Where:

1. gA​ = TFP growth
2. gK/L​ = growth of capital-labor ratio (capital deepening)
3. gL/N​ = growth of labor per person

What you need:

1. Labor Input (L) data (total employment or hours) for start and end years.
2. Total Population (N) data for start and end years.
3. Number of years (t) in the period.

Steps:

1. Calculate L/N for each year: (L/N)year​=Labor Inputyear​/Populationyear​
2. Calculate the growth rate of L/N (gL/N​): gL/N​≈[ln((L/N)final​)−ln((L/N)initial​)]/t