Hi all,
the following is bothering me and I cannot help myself with any textbook in exonometrics, each of them leaving me puzzled.
Imagine a simple Simultaneous Equation system of supply and demand, a standard market equilibrium example to motivate 2SLS and IV in many lectures.
I will not write down the full model but refer to the stata help file for 3reg:
http://www.stata.com/manuals13/rreg3.pdf
It is on page 8, example 2.
The model can also be found only marginally different in the following textbooks:
- Hill, Griffiths, Lim (2008): Principles of Econometrics, pp. 304-317.
- Maddala (1992): Introduction to Econometrics, pp. 356-363.
- Greene (2012): Econometric Analysis, pp. 354-377.
- Hayashi (2000): Econometrics, pp. 187-192.
- (similar) Wooldridge (2010): Econometric Analysis of Cross Section and Panel Data, pp. 239-273.
So in words, the general problem is how to estimate the parameters in a set of equations with an endogenous regressor (here: price)?
The procedure recommended in all the textbooks is as follows:
1. Put at least one exogenous (or at leat predetermined) regressor into one of the equations
2. Estimate the effect of all exogenous variables on the endogenous variable using OLS and get a prediction of it (price); the so-called 1st stage
3. Use this predictor in the other equation to get a consistent estimate for the endogenous variable; the 2nd stage
This in fact is the same as an instrumental variable approach, but here comes the clue:
In their example they always look for an exogenous variable which has an impact on either supply or demand, thus the left-hand-side variable (quantity), in order to fit one of the structual equations.
But in fact we want a variable which is correlated with the endogenous variable, thus the right-hand-side variable (price), which is typical IV.
So if I take the wrong variable, the 1st stage (or reduced-form) coefficient of interest might be zero (insignificant), leaving me with a weak instrument.
So in a nutshell my problem is:
- Simultaneous Equation models demand an exogenous variable correlated with the LHS (quantity)
- IV models demand an exogenous variable correlated with the RHS (price)
Both use the exact same estimation method (e.g. 2SLS, or maybe 3SLS), see the stata help file above
I do not know which exogenous variable to use for such a model? The use of the adequate IV is sure of major importance.
There must be something I do not understand because I do not question all the textbooks. They simply do not explain it properly (to me).
I welcome any idea!
Tim
the following is bothering me and I cannot help myself with any textbook in exonometrics, each of them leaving me puzzled.
Imagine a simple Simultaneous Equation system of supply and demand, a standard market equilibrium example to motivate 2SLS and IV in many lectures.
I will not write down the full model but refer to the stata help file for 3reg:
http://www.stata.com/manuals13/rreg3.pdf
It is on page 8, example 2.
The model can also be found only marginally different in the following textbooks:
- Hill, Griffiths, Lim (2008): Principles of Econometrics, pp. 304-317.
- Maddala (1992): Introduction to Econometrics, pp. 356-363.
- Greene (2012): Econometric Analysis, pp. 354-377.
- Hayashi (2000): Econometrics, pp. 187-192.
- (similar) Wooldridge (2010): Econometric Analysis of Cross Section and Panel Data, pp. 239-273.
So in words, the general problem is how to estimate the parameters in a set of equations with an endogenous regressor (here: price)?
The procedure recommended in all the textbooks is as follows:
1. Put at least one exogenous (or at leat predetermined) regressor into one of the equations
2. Estimate the effect of all exogenous variables on the endogenous variable using OLS and get a prediction of it (price); the so-called 1st stage
3. Use this predictor in the other equation to get a consistent estimate for the endogenous variable; the 2nd stage
This in fact is the same as an instrumental variable approach, but here comes the clue:
In their example they always look for an exogenous variable which has an impact on either supply or demand, thus the left-hand-side variable (quantity), in order to fit one of the structual equations.
But in fact we want a variable which is correlated with the endogenous variable, thus the right-hand-side variable (price), which is typical IV.
So if I take the wrong variable, the 1st stage (or reduced-form) coefficient of interest might be zero (insignificant), leaving me with a weak instrument.
So in a nutshell my problem is:
- Simultaneous Equation models demand an exogenous variable correlated with the LHS (quantity)
- IV models demand an exogenous variable correlated with the RHS (price)
Both use the exact same estimation method (e.g. 2SLS, or maybe 3SLS), see the stata help file above
I do not know which exogenous variable to use for such a model? The use of the adequate IV is sure of major importance.
There must be something I do not understand because I do not question all the textbooks. They simply do not explain it properly (to me).
I welcome any idea!
Tim
