Ricardian vs Non-Ricardian policy identification

Question

I am reading Sala (2004) and I think I have found a mistake in the paper. On page 7 the author argues that one can differentiate between Ricardian and Non-Ricardian policy regimes by considering correlations between primary surpluses and their effect on real debt. See this picture.

Where $s_t$ is current primary surplus, $\alpha_t$ is the discount factor and $b_t$ is the real debt.

He says:

if the response of $b_t$ to $s_t$ is negative, the regime is Ricardian; if the response of $b_t$ to $s_t$ is nonnegative, the regime is Non Ricardian

While I agree with this, I don't agree with what he wrote in the picture I linked to. I.e that case 1 represents the Ricardian regime and case 2 the non-RIcardian regime.

In case 1 there is no correlation between current primary surplus ($s_t$) and future surpluses ($s_{t+k})$, thus the real value of debt is constant. How is this consistent with the quote above? To me, case 3, i.e the one where $\text{corr}(s_{t},s_{t+k}) < 0$ should be the Ricardian regime because high surpluses today imply low surpluses tomorrow.

Have I misunderstood the author or did he mean to write 'Case 2 and 3 allow for regime identification'?

Answer 1

I think you're misreading what Sala wrote. The first sentence in the image you linked is just saying that in the worlds where either Case 1 or Case 2 occurs, the response of $b_t$ to a shock in $s_t$ allows us to differentiate between Ricardian and non-Ricardian regimes since there are no identification issues. In other words, if either the Case 1 inequalities or the Case 2 inequalities hold, then we can be confident that we have identified a non-Ricardian regime from a Ricardian regime.

According to Sala, it seems that we cannot as easily identify Ricardian regimes from non-Ricardian regimes in Case 3 due to identification issues related to co-movements in real debt.