Sign flip after using Instrument variable

[xu wang]

Hi Statalist,

I met a problem when I was using the IV approach to estimate an equation, I am using Stata 14 and ivreg2.

The equation takes the following form:

y=c+a*X1+b*X2+eps

and I instrument X1 with Z.

After doing the IVreg2, the coefficient a has the same sign as OLS but coefficient b flips to the opposite sign.

What could this suggest? or why would this happen?

Best
Xu

[Phil Bromiley]

You will increase your chances of useful answer by following the FAQ on asking questions – provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

Strictly speaking, I think that the endogeneity of X1 means that the parameter estimates on both X1 and X2 are biased when you estimate it with OLS. Consequently, switching to the consistent instrumental variable estimator can change the parameters both on the endogenous variable and the other variables.

It is little odd to get a sign switch, but it can happen. You don't tell us if these parameters are statistically significant. If there estimated with a large standard error or very close to zero, small changes can switch signs easily.

[xu wang]

Thanks for your reply, Phil. Please allow me to make it more detail.

The variable of my interest is X2. However it is very hard to find a good instrument for my X2. I came across a paper which looked at the similar question but their approach was to instrument for X1 instead. I just followed their approach and want to know how that looks with my data set. And also I want to compare how different the results are when compared to my method, which is instrumenting X2 with Z2 directly. I attached my result.

The code I used are as follows:

since the outcome variable is binary, I used probit for the OLS:

Probit Y X1 X2 ...X12 (see column 1)

For the IV model, since my X are not all continuous, so I didn't use ivprobit. I used ivreg2:

ivreg2 Y (X1 = Z1) X2 X3....X11, first robust (see column 2)

Since I am not sure whether Z1 is a good instrument for X1, I used a different IV for X2:

ivreg2 Y X1 (X2=Z2) X3....X11, first robust (see column 3)

And I also check how the model will perform if I instrument both X1 and X2:

ivreg2 Y ( X1 X2 = Z1 Z2) X3....X11, first robust (see column 4)

Column 5-8 just shows the results where I control for X12.

My concern is that in column 2, when I instrument X1 with Z1, the coefficient of X2 flip the sign and is significant. I need to give a valid explanation, otherwise it's hard to argue I have a good IV. In my case, once I instrument X1 with Z1, the coefficient of X2 fliped, This sounds like my Z1 also affect my outcome Y through the channel of X2, which I think may suggest that this is not a good IV.

Column 3 is the result of instrumenting X2 directly with a different IV Z2. It also flip the sign but didn't flip the sign of other covariates, which I feel like is a better IV. But if the coefficient of X2 in column 3 has the same sign as in column 2, it can mean that both IV are good or both are bad, which I can't tell.

Column 4 is the result of instrumenting both.

If you have any comments, please let me know. I really appreciate your patience and help.

Thanks.

Xu