What's a singular model in economics? I've tried google, but I didn't find a definition...
In an article by Ingram et al (1994), they state:
This linear model is singular because it predicts that the current value of consumption is an exact(non-stochastic) function of current output and lagged consumption.
Also, the paper says that any model (RBC and extensions) with a number of shocks smaller than the number of observable endogenous variables, has this particular behaviour. So, the models are not 'singular' as a dictionary definition.
From this I get that any stochastic model, which determines some observable endogenous variable to follown a non-stochastic path, then I can call it singular. Is this correct?
Also, does this definition have any relation to bifurcation? In ODE we have a 'bifurcation' of solutions, when
$\dot x = F(x,\mu)$, and at $\mu=\mu^*$, $DF(x,\mu^*)$ is singular, but non-singular at every other value of $\mu$. The equilibrium will depend continuously on $\mu$ and 'after' stability is lost, new stable equilibria will appear. (this lacks mathematical precision, but I think it suits the purpose of stating the intuition of bifurcation)
Any help would be appreciated.