Accounting for the Sources of economic growth

It is a very important equation in Macro, which is also named as “增长核算公式”, it aims to find out the growth in total output $\Delta Y/Y$

For the Intermediate Macro, there are only 3 different sources, which are

1. Contribution of capital stock (K)
2. Contribution of labor
3. Contribution of technology

In conclusion, the Growth Accounting Equation could be expressed as:

$$\frac{\Delta Y}{Y}=\alpha \frac{\Delta K}{K}+(1-\alpha )\frac{\Delta L}{L}+(1-\alpha )\frac{\Delta E}{E}$$

但是在网上也有这种写法：

$$\frac{\Delta Y}{Y}={\alpha }_K\frac{\Delta K}{K}+{\alpha }_L\frac{\Delta L}{L}+\frac{\Delta A}{A}$$

也许是说明 ${\alpha }_K$ 和 ${\alpha }_L$ 不一定是互补的关系，只有当是 Cobb-Douglas Production Function 才会有这样的性质

The value of $\alpha$ is usually around 0.25-3

Then we can come to Solow Residual, which is described as

$$(1-\alpha )\frac{\Delta E}{E}=\frac{\Delta A}{A}$$

Also, we can calculate the Relative Contribution to test which component has a great influence. (maybe like Principal Component Analysis?)