The Phillips curve and the information transfer index

Brad DeLong wrote about the Phillips curve yesterday, which inspired me to take on the Phillips curve again. I've long tried to understand it with the information transfer model. In my most recent attempt I noted that with constant information transfer index $\kappa$, there is no direct relationship between employment and inflation [1].
However, that leaves out changing $\kappa$ (I sometimes use the inverse and label it $k$). The model (see the draft paper) uses the form
$$
\frac{1}{k} = \kappa = \frac{\log M/(\gamma M_{0})}{\log N/(\gamma M_{0})}
$$

which means that a shock to $N =$ NGDP (a recession) is a shock to $\kappa$. That is how NGDP changes can impact the price level. The question is: what is the magnitude of the impact on inflation?
I solved for the coefficient of the leading order term in $\delta N$ taking $N \rightarrow N + \delta N$, deriving the coefficient $\alpha$ such that $\delta \pi \simeq \alpha \delta N/N$. Here is $\alpha$ vs time:

We can see that $\alpha$ is positive (and approximately 0.05) through the 60s and 70s, falling to approximately zero by the year 2000. That is to say a negative shock to NGDP reduces inflation during the 60s and 70s -- an NGDP shock of 5% should reduce inflation by 0.25 percentage points.
Now according to the link [1] above, NGDP shocks are roughly equal to labor shocks, so
$$
\delta \pi \simeq \alpha \frac{\delta N}{N} \simeq \alpha \frac{\delta L}{L}
$$

That means a negative shock to labor (a rise in unemployment) should result in a lower inflation rate. That is the traditional Phillips curve. It basically goes away after the 1970s -- interestingly coinciding with the adoption of the expectation-augmented version.