I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) of one model is small-growth portfolio returns and the DV of another model is small-value portfolio returns.

So, my question is what should be the degrees of freedom if I want to calculate the p-value associated with the t-statistics? Is it just N-k?

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    $\begingroup$ There will be many common causes to these returns, since both are controlled by economic and other external factors. Thus, expect strong correlation among the dependent variables and plan to account for it. You cannot do so in terms of statistics from the two models separately: at some stage you must model the bivariate response (small-growth, small-value) simultaneously. $\endgroup$ – whuber Jun 19 '18 at 13:29
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    $\begingroup$ @whuber Many thanks for your reply. Does it mean that it's not right to perform two models separately even if I account for the autocorrelation and heteroskedasticity in error terms? Could you please recommend the test or model that can be used to model the bivariate response simultaneously? $\endgroup$ – SNU Jun 19 '18 at 15:01
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    $\begingroup$ Look into multivariate (not "multiple"!) regression models. These allow for vector-valued responses and account for correlations between the components (as well as autocorrelation and heteroscedasticity within each component). $\endgroup$ – whuber Jun 19 '18 at 15:04
  • $\begingroup$ @whuber Really thanks for your help and information! $\endgroup$ – SNU Jun 19 '18 at 15:06

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