Significant F, insignificant t-stats: what is going on?

Question

You regress monthly returns on two macro variables. The overall F-test is highly significant ( $p < 0.001$ ) and $R^2 = 0.40$ , yet neither variable's individual t-statistic clears the 5 percent bar.

What is the most likely explanation for a jointly significant model with no individually significant coefficient?

Accepted Answer

The tell-tale pattern. A significant F with insignificant individual t-statistics is the textbook fingerprint of multicollinearity: the two regressors are highly correlated with each other. Why the two tests disagree. The F-test asks whether the regressors together explain the response. The two macro variables jointly carry a strong signal, so the F is large and R^2 is healthy. Each t-test asks whether that variable adds something beyond the other. Because the two move together, neither adds much once the other is included; the unique contribution of each is small and swamped by an inflated s…

Significant F, insignificant t-stats: what is going on?

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