I want to test how granted patent, R&D & their ratio predicts real & excess market return. I am doing 2 robust linear regressions:

\begin{align} \text{Real Return} \left( t + 1 \right) = \text{constant} + \beta_1 \text{patent granted} + \beta_2 \frac{\text{patent}}{\text{R&D}} + \beta_3 \text{R&D} + \beta_4 \text{wealth-consumption ratio (cay)} + \mu_{t + 1} \end{align}

\begin{align} \text{Excess Return}\left(t + 1\right) = \text{constant} + \beta_1 \text{patent granted} + \beta_2 \frac{\text{patent}}{\text{R&D}} + \beta_3 \text{R&D} + \beta_4 \text{wealth-consumption ratio (cay)} + \mu_{t + 1} \end{align}

All are time series annual data, the explanatory variables are in time period $t$ observation number $n = 55$, $\text{real return, patent growth, R&D, cay}$ are in $\log$, $\text{excess return} = \log\left(\text{real return}\right) - \text{3 month t-bill rate}$, $\frac{\text{patent}}{\text{R&D}} = \text{innovative efficiency (IE)}$. I have first differenced patent, R&D and IE data, standardized all 4 explanatory var, then performed PCA on patent granted & IE as VIF was over 10. Robust linear & Newey-West gives same coefficient and very close SE, the coefficient on IE is significant at 10% level for the 1st regression but insignificant in the 2nd regression. I understand I have small sample but what could be the explanation for the insignificance in the excess return regression? One other study using similar regression but having quarterly data had significance in both real & excess return.


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