Counter-intuitive results with Bold-Brunell panel data estimator (DV-INDEX)

[SylviaS]

Hi All,

I am doing Brunell-Bond panel data analysis and the results seem completely counter-intuitive. The DV is a food prices index - and so if its values increase it implies more difficulty with accessing food.

Is the problem with the index? Is there any way to transform it or should I use another DV (where if its values increase it would be positive)

Thanks.

[Dason]

I don't believe you've actually told us what the problem is other than you think your results are counter-intuitive. What even were your results?

[SylviaS]

I don't believe you've actually told us what the problem is other than you think your results are counter-intuitive. What even were your results?

Thanks, for example I have a large negative coefficient for urbanization (proportion urban) and positive coefficients for technology (different internet, mobile use indicators) and level of development.

So for example: if the level of development increases, the food price index also increases, which is not true - we observe the opposite. So, all significant coefficient show counter-intuitive results...

[Dason]

Ok so that's what happens you run the analysis with multiple predictors. If you run it with just the single predictor (level of development) do you see the result you expected?

[SylviaS]

I will need to check tomorrow at school as don't have STATA on my laptop. Do you suggest running several models with one predictor at a time (so I can't control for other variables?)? Also, which post estimation tests should I do? I tried Sargan, but it did not look very good. Thank you.

[Dason]

No I don't suggest that. It's just that the interpretation you're trying to apply to determine if the results are counter intuitive or not don't really work well when you have multiple predictors. If, on the other hand, when you only used a single predictor and things were flipped it might indicate something was coded wrong (or maybe you just don't understand the process as much as you thought).

[Dason]

For example let's say I had two predictors (x1 and x2) and one response (y). x1 and y might have a nice positive relationship:



And x2 and y might also have a nice positive relationship:



But when I do a regression using both x1 and x2 this is what I end up with:

(Intercept)           x1           x2  
      3.178        1.451       -0.634

Which tells me my estimated regression line is

But clearly x2 and y have a positive relationship! The problem is that when you're interpreting the slope on it's own you completely ignore the effect of x1. In this case x1 and x2 are highly related. If x1 is large then x2 is large as well (as a matter of fact I created x2 by adding a uniform random variable to x1). So the interpretation of the parameter associated with x2 is the change in the prediction if we increase x2 by 1 unit and hold everything else constant. But I just told you how I created x2 so "holding everything else constant" isn't necessarily something that can be done.

Just for the record I generated that data by setting

x1 <- 1:20
x2 <- x1 + runif(20)
y <- 3 + x1 -.2*x2 + rnorm(20, 0, .3)

So x1 = 1, ..., 20
x2 = x1 + random uniform on (0,1)

The true relationship between y and x1, x2 being
where

[SylviaS]

Thanks for taking the time to explain! What I was thinking is that the way index is constructed might also cause a problem. At first the direction of the association seems ok - e.g. level of development increases or technology, the value of FPI (food price index) increases, but the problem is that if FDI increases it is actually negative, because the higher the index, the worse access to food.

Does it make sense? Can that be a problem and if so is there a way to transform this index (the values are between 100 and around 300, mostly between 100 and 150).

I will do more work on that tomorrow, maybe try a different variable...