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I've seen them summed somewhere but I cannot exactly remember where. Ultimately I don't think that it makes much difference. The quarterly sum is just the average multiplied by three. Since local projections are just a bunch of OLS - one for each horizon, this is how you can think about the issue: If $y_{t+h} = \alpha^h + \beta_h news\_shock_t + \sum_{j=1}^{... 5 Given $$Y = Af(K,L,Z)$$ it follows that $$\dot Y = \dot A f + A\frac{\partial f}{\partial K}\dot K + A \frac{\partial f}{\partial L} \dot L + A \frac{\partial f}{\partial Z} \dot Z,$$ where dotted expression are time derivatives and dividing with$Y$it follows$\$\frac{\dot Y}{Y} = \frac{\dot A}{A} + \left[A\frac{\partial f}{\partial K}\right]\frac{\dot K}{...