What is the interpration of results if adding or subtracting a control variable effects the significance of explanotary variables?

I am conducting some regressions on economic growth determinants and I am disillusioned. Essentially by choosing what groups of variable to regress I can get the desired significance. What does this tell about whether the explanatory variables influence economic growth?

When you run a regression you are making the assumptions of the Gauss Markov Theorem, one of which is that the error is uncorrelated with all of the independent variables (exogeneity).

If you remove from your regression a variable that is correlated with other explanatory variables then the error term and those explanatory variables will be correlated and the Gauss-Markov Theorem will then be violated. The consequence of this is that the estimates produced by the model will be biased. This particular form of bias is known as Omitted Variable Bias.

A consequence of omitted variable bias is that spurious variables can often be made significant be deleting important variables from the model. In these instances, the fact that they become statistically significant doesn't signify that they suddenly became important, it just means that you are estimating a mis-specified model that violates your own assumptions. So we can't just blindly interpret the hypothesis tests associated with a regression model, we must pay attention to whether the model is well-specifiedâ€”including the question of whether all of the relevant variables are included.

Last point: your question is "What does this tell about whether the explanatory variables influence economic growth?" The answer is nothing because a regression in itself will not tell you anything about causality, only whether your variables are correlated. To make a causal connection between variables you have to think about how to build causal identification into your empirical strategy from the beginning.

• Thank you for your comment. Although it is informative, I believe it doesn't address the core of the issue. When you are conducting regression analysis to figure out the determinants of economic growth the issue arises that you try to infer the determinants from the regression. Therefore it is not possible to know whether there is an omitted variable bias. Further the theory itself doesn't know true determinants of economic growth, it argues for certain behaviour, but whether that's the case ought to be confirmed by empirical results. Where we run into the problem mentioned above. Commented Aug 1, 2019 at 19:29
• @PeterSantorin In cases where theory cannot guide the model specification then there are empirical techniquesâ€”such as general-to-specific modelling or fixed effects regressionâ€”to either ensure correct model specification or to mitigate the problem of omitted variable bias. But your question is not about how to solve these issues, it's about how to interpret varying significance in the regression. The answer to that question is that you shouldn't assign much interpretation to it because it is probably caused by model mis-specification. Commented Aug 1, 2019 at 20:13

You seem to say that by choosing what groups of variable to regress ,you can get the desired significance. It means that you can maniipulate the model and get significant result indicating dependence of economic growth on certain explanatory variables. But, such a model is likely to fail if a scrutiny of the Model is carried out by following a scientific procdure. This has been indicated by preceding Answer as well.