I guess I have to come out to reply to those who concern with the nature rate of unemployment First, What is the natural rate of unemployment? It is assumed to be the unemployment rate at the steady state or equilibrium. Note that equilibrium here is not referred to the common demand-supply equilibrium, but to a state at which things are not changed, or remain the same. More specifically, suppose we can have an economy that could be expressed by the following f(y1-1,6,E1) where y, is a vector of economic variables which could include price, quantity, employment etc e is a vector of parameters and E, is a vector of random shock. At the steady state, first a could assume to be a zero vector( no shock) while y,=y-l=y*. Apparently the steady state y* could be resolved by assuming y, =y,- and 8,=0. The solution of y* should be a function of the parameter 0 Note that in reality the economy may ne at the steady state due to the shock, but we could expect it will fluctuate around the steady Now back to our problem, at the steady state, we should have Ee LL where u* is the nature rate of unemployment. The question is then what determine u* if such steady state exist Next, I will focus only on how to define the employment in period t, that is, E. There could have two ways depending on how do you think on the addition of labor force gL,-. If it is added at the beginning of period t(or the end of [-1)then E,=E-1+f(U1-1+gL1)- that is, the employment in t should be equal to the employment in the last period plus those who are unemployed at the beginning of I but find job in t minus those who are employed at the beginning of t but lose the job within t. Note that here at the beginning of t, new labor for L-I can be regarded as unemployed
I guess I have to come out to reply to those who concern with the nature rate of unemployment. First, What is the natural rate of unemployment? It is assumed to be the unemployment rate at the steady state or equilibrium. Note that equilibrium here is not referred to the common demand-supply equilibrium, but to a state at which things are not changed, or remain the same. More specifically, suppose we can have an economy that could be expressed by the following dynamic system ( , , ) t t 1 t y f y = − where t y is a vector of economic variables which could include price, quantity, employment etc., is a vector of parameters and t is a vector of random shock. At the steady state, first t could assume to be a zero vector ( no shock) while yt = yt−1 = y * . Apparently the steady state y* could be resolved by assuming t = t−1 y y and t =0. The solution of y* should be a function of the parameter . Note that in reality the economy may not stay at the steady state due to the shock, but we could expect it will fluctuate around the steady state. Now back to our problem, at the steady state, we should have: 1 * 1 1 u L E L E t t t t = = − − − where u* is the nature rate of unemployment. The question is then what determine u* if such steady state exist. Next, I will focus only on how to define the employment in period t, that is, Et . There could have two ways depending on how do you think on the addition of labor force gLt−1 . If it is added at the beginning of period t (or the end of t-1) then 1 1 1 1 ( ) t = t− + t− + t− − t− E E f U gL sE that is, the employment in t should be equal to the employment in the last period plus those who are unemployed at the beginning of t but find job in t minus those who are employed at the beginning of t but lose the job within t. Note that here at the beginning of t, new labor force gLt−1 can be regarded as unemployed
One the hand, if gl,- is assumed to be added at the end of period t, then the above formula come E1=E-1+fU1-1-sE-1 i hope my answer will satisfy you
One the hand, if gLt−1 is assumed to be added at the end of period t, then the above formula should become t = t−1 + t−1 − t−1 E E fU sE I hope my answer will satisfy you. Best wishes Gang