Using two-stage least squares

[Georgie]

Hey guys,

I have a regression equation in which the unemployment rate is the dependent variable and the independent variables are the oil price, exchange rate, export and two time dummy's. I'm required to check out if the unemployment rate does not have a causal effect on the dependent variables because reverse causality is not allowed. Unfortunately I have no knowledge with Two-Stage Least Squares. What's a proper instrument variable? I was thinking on employed and unemployed people.

[startz]

Hey guys,

I have a regression equation in which the unemployment rate is the dependent variable and the independent variables are the oil price, exchange rate, export and two time dummy's. I'm required to check out if the unemployment rate does not have a causal effect on the dependent variables because reverse causality is not allowed. Unfortunately I have no knowledge with Two-Stage Least Squares. What's a proper instrument variable? I was thinking on employed and unemployed people.

This is a little confusing as you say that the unemployment rate is the dependent variable. Assuming you meant no effect on the independent variables, the answer is no. You need to find instruments that are correlated with the RHS variables and not correlated with the error term. Employed and Unemployed people are certainly correlated with the error term.

[Georgie]

Hey guys,

I have a regression equation in which the unemployment rate is the dependent variable and the independent variables are the oil price, exchange rate, export and two time dummy's. I'm required to check out if the unemployment rate does not have a causal effect on the dependent variables because reverse causality is not allowed. Unfortunately I have no knowledge with Two-Stage Least Squares. What's a proper instrument variable? I was thinking on employed and unemployed people.

This is a little confusing as you say that the unemployment rate is the dependent variable. Assuming you meant no effect on the independent variables, the answer is no. You need to find instruments that are correlated with the RHS variables and not correlated with the error term. Employed and Unemployed people are certainly correlated with the error term.

I'm sorry, let me rephrase it. I did a LS-regression to check what effect the independent variables had on the dependent variable (unemployment rate). I also did a Granger-causality test to see if oil price (the focus of my regression) had a causal effect on unemployment rate and it did. The Granger-test also showed that unemployment rate has no causal effect on oil price, so it's one-directional. But I was still required to do a two-stage least squares regression to check for reverse causality. My supervisor told me to use lagged variables of all the independent variables, but I don't know what to do.

[startz]

Something like

tsls y c x1 x2 @ c x1(-1) x2(-1)

[Georgie]

Something like

tsls y c x1 x2 @ c x1(-1) x2(-1)

So using the lagged variables in the 'Instrument Variables section' ?

[startz]

If your supervisor thinks these should be instruments, then that's where to put them.

[Georgie]

If your supervisor thinks these should be instruments, then that's where to put them.

So how does two-stage least squares prove that there is no reverse causality from Y to the X-variables? I did what you said, using lagged variables as instrument variables and I got a negative R-squared value.

[startz]

There's nothing wrong with a negative R-squared.

Two-stage least squares--with valid instruments--does not prove anything about reverse causality. It "adjusts" for the effects of reverse causality. To see if reverse causality changes anything, consider using a Hausman test.

[Georgie]

There's nothing wrong with a negative R-squared.

Two-stage least squares--with valid instruments--does not prove anything about reverse causality. It "adjusts" for the effects of reverse causality. To see if reverse causality changes anything, consider using a Hausman test.

Alright. Is it true that if the assumption of no serial correlation is met in OLS there's no need to do a 2SLS? Because at first I did an OLS-regression and it met all the assumptions like normal distribution, homoscedasticity, no serial correlation etc.

[startz]

No. Serial correlation has nothing to do with 2SLS.

[Georgie]

No. Serial correlation has nothing to do with 2SLS.

I want to thank you for the quick responses, really appreciate it.

I have a last question, so one image is with OLS and the other with 2SLS (using lagged variables of the independent variables as the instruments).
How do I interpret the difference between the results of OLS and 2SLS? A lower absolute R-squared with 2SLS indicates that 'adjustments' have been made for reverse causality?

[startz]

An idea of 2SLS is indeed that it adjusts for reverse causality, but the R^2 has nothing to do with it.

Look for "Hausman test" in the help files.

[Georgie]

An idea of 2SLS is indeed that it adjusts for reverse causality, but the R^2 has nothing to do with it.

Look for "Hausman test" in the help files.

My supervisor specifically wants me to do a 2SLS-test but how do I interpret the difference between the OLS-results and 2SLS-results?

[startz]

You're asking good questions. It might be time to go do a little background reading on 2SLS and instrumental variables to get a better idea of what's going on.

[Georgie]

You're asking good questions. It might be time to go do a little background reading on 2SLS and instrumental variables to get a better idea of what's going on.

I'll go do that. Thanks for the quick responses.