Conclusion: In order to prevent the unemployment rate from rising, the real GDP must grow as fast as the potential GDP.
Okun's original paper, Okun, A.M. (1962) "Potential GNP: Its Measurement and Significance."
It is the foundation of macroeconomics and an important basic tool for analyzing macroeconomic fluctuations. However, the direct Okun's law is not valid in China, and most people attribute it to the inaccurate statistics of unemployment data in China, so it is necessary to use Okun's law and Phillips curve for deformation and indirect research. Because of the inaccurate understanding of Okun's law, serious mistakes occurred in the deformation process and wrong conclusions were drawn. This misunderstanding is not only easy for beginners to make, but also very serious among China economists, including some famous economists, and it can be said that it has not attracted enough attention. Let me explain why Wu's two explanations are correct and equivalent, while Jiang Cai's and He Jianchun's are wrong.
Okun's law is essentially an empirical rule, which is called one of the most useful empirical rules in macroeconomics, but it also has theoretical basis. This can start with a simple production function: Y=aN, where y stands for output, a stands for labor productivity and n stands for the number of employed people. The actual value is expressed by a subscript with time t, the potential value is expressed by a subscript with n, l represents the total labor force, u represents the number of unemployed people, and N=L-U, which is substituted into the production function: Y=a(L-U), and the actual output is divided by the potential output to obtain yt/yn = at (lt-ut)/[at (lt-un)] = (. De: (yt-yn)/yn =-[1(1-un)] (ut-un), where ut = ut/lt and un = un/lt represent the actual unemployment rate and the natural unemployment rate respectively. It is usually assumed that un is constant in the short term and 1/( 1-un) is close to 1, then we can get: (Yt-Yn)/Yn=-(ut-un), but in fact, the change of unemployment does not completely correspond to the change of output (see blanchard's detailed explanation on this). So the exact form of Okun's law should be: ut-un=-β[(Yt-Yn)/Yn], where β >; 0。 So: "Okun's Law: If the unemployment rate is higher than the natural unemployment rate 1%, the actual output is about 3% lower than the potential output" is correct. That is, β= 1/3, which is aimed at the situation in the United States. In fact, there are great differences among countries, and it is worth further study in China, because China is a developing country with obvious dual economy.
Another explanation:
Assuming that un is a constant and Yn is a variable, take the time differential of ut-un=-β[(Yt-Yn)/Yn] and get: △ut=-β(Yt/Yn)(△Yt/Yt-△Yn/Yn), where △ represents the difference sign, such as △ UT = UT-U.