Question

The data below, adapted from research by Xiaolei Qian and Russel Smyth, document growth in several regions of China as well as the country as a whole from 1990 to 2000. You should assume that capital's share is 0.5. Y/L %AY %A(Y/L) %AA 2.29% Region Beijing Shanghai Sichuan All of China %AK 12.82% 16.78% iii 12.68% %AL 3.04% 2.79% 0.47% 11.41% 9.86% 10.64% %A(K/L) 9.78% vii 11.26% 11.72% vi 9.39% 9.68% in 1990 6225 8420 1612 2694 3.76% 3.82% iv For parts (1)-(vii) fill in the associated missing entries based on the growth accounting framework. You n the growth accounting can use the approximation A%(A/B) = %AA-%AB to help fill in the columns involving growth rates of ratios. %AY ~ %AA+a%AK + (1 - a)%AL %A(Y/L) ~ %AA + a %Ak

Answer 1

The growth accounting table is calculated using the formulas below

1. 
   ΔΥ & ΔΑ + 0.5 x ΔK + 0.5 x %ΔL
   
2. 
   ΔΥ/L) x %ΔΥ – ΔL
   
3. 
   ΔΑ ΔΥ – 0.5 x ΔΚ – 0.5 x ΔL
   
4. 
   %AK/L %AK – %AL
   
5. 
   ΔLa ΔΥ - Δ(Y/L)
   

Given these formulas, the table is calculated as

Region	%ΔY	%ΔK	%ΔL	%ΔA	%Δ(Y/L)	%Δ(K/L)	Y/L in 1990
Beijing	10.22%	12.82%	3.04%	2.29%	7.18%	9.78%	6225
Shanghai	11.41%	16.78%	2.79%	1.63%	8.62%	13.99%	8420
Sichuan	9.86%	11.73%	0.47%	3.76%	9.39%	11.26%	1612
All of China	10.64%	12.68%	0.96%	3.82%	9.68%	11.72%	2694