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I would like to determine the relationship between r&d expenses and capital structure using the data of 12 industrial companies for 10 years. Running the pooled ols,it showed that 4 of my 5 independent variables are significant, random effects model says only 2 independent variable are significant, while fixed effects says 1 independent variable is significant. The pooled ols model is homoscedastic, shows no autocorrelation, and has no multicollinearity according to tests I have conducted. While the fixed effects and random effects have problems of autocorrrelation and homoscedasticity. The results of Hausman test, Breusch Pagan LM, and F-Test tells me to use the fixed effects. But I think the pooled ols model is better. How can I justify the use of the pooled ols model.Is there any way for me to use the pooled ols because the results are in line with my related literature and explains the relationship between r&d expenses and capital structure.

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  • $\begingroup$ Note that pooled ols has serial/auto correlated errors by definition - No matter what any test says, this will always be so $\endgroup$ – Repmat Feb 7 at 8:27
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I do not think you can justify not using fixed and or random effects model in this instance. Your best option is probably to report all three models. Even if you can manage to come up with an argument for excluding fixed/random effect models, virtually every competent econometrician/statistician will doubt your findings as a result.

Standard errors will always be larger when using fixed/random effects as apposed to classical OLS and as a result less coefficients will be significantly different from zero. This is rightfully so, you have 120 observations but only 12 distinct industries (of who's variables are bound to be somewhat correlated over time) so the effective sample size is a lot lower than classical OLS gives credit.

Fixed/random effect models account for the above by estimating correlation for with-in group residual terms. I suppose if you could find extremly convincing evidence that the residuals are iid, you could go with OLS. But this is hard to do, a simple test for auto correlation or heteroskedacity is really not convincing enough, at least for most professionals.

Also, the existence of auto-correlation and heteroscedasticity in the residuals of fixed/random effect models is not in and of itself concerning, since these methods account for the existence of such features in their standard errors.

You can always report both OLS and fixed/random effect model results. In fact, this is very standard practice. And if you can cite previous literature, you can make the evidence for your argument more convincing.

If you where extremely ambitious, you could also do a Bayesian regression whereupon you developed an informative prior based on previous literature and use it in a fixed/random effects regression. This will bring your results closer to that of the previous literature and coincides well with the logic you articulated in your post. But this is probably way more than what you want to deal with.

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