# What's a singular model in economics?

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.

• I'd think singular means non-simultaneous in this context. Meaning that the equation is identifiable. I can be wrong though – EconJohn Apr 25 '18 at 3:19
• Are you referring to Ingram, B., Kocherlakota, N., Savin, N.E., 1994. Explaining business cycles: A multiple shock approach. Journal of Monetary Economics 34, pp 415-428? It would be helpful to include a link in your question. – Adam Bailey Apr 25 '18 at 10:02

## 3 Answers

The authors are referring to "stochastically singular models". What you state above is basically the definition: a number of shocks smaller than the number of observable endogenous variables. The intro to Zhongjun Qu's working paper "A Composite Likelihood Framework for Analyzing Singular DSGE Models" surveys the literature on the topic.

I assume the term comes from measure theory. If you have $n$ observable variables but they lie in a lower-dimensional subspace, then the probability measure is singular with respect to Lesbesgue measure. (Understanding this is not important for understanding the concept.)

I have tried to grab the article to read it, but my library apparently doesn't subscribe to JME as full text. However, when I have seen the word singular used in economics it is usually in the framework of a singular matrix. As this article appears to be a criticism of another model, it would appear they are arguing the other model would not give rise to an invertible matrix. In the above set of comments, it is implying that the stochastic component is vanishing and that the model is deterministic, despite the fact, there are no actual deterministic models in economics if you have to measure things.

My guess is that they are criticizing the other model by showing it can't work.

• Dave, thanks for the answer. Search for sci-hub. it's a nice thing. ;) – An old man in the sea. Apr 25 '18 at 15:28

# singular

adjective: unusual and easily noticed:

His campaign was singular because he talked about issues and did not attack his opponents' personal lives.

Cambridge Dictionary Link

Without further context to consider, it is most probable that the use of the word is not with regard to the field of Economics or Mathematics, but rather it is used as an adjective to denote how remarkable the linear model is, similar to the example above.

Therefore, it is illogical to conclude that one may refer to "any stochastic model, which determines some observable endogenous variable to follown [sic] a non-stochastic path" as "singular" based on this use of the word alone.

Likewise, it is doubtful that the statement bears any effect on your understanding or use of bifurcation.

• Kharma, welcome to the this site. I would advise you to reconsider your answer as it is, and read the reference I give in the question. 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 as 'singular' as the dictionary definition you give. – An old man in the sea. Apr 24 '18 at 20:30
• Then, I would advise you to add the particular context you are referring to within your question. If you know the answer, then answer it yourself. ;) – Kharmageddon Apr 24 '18 at 21:39