Markov Chain regression in political study

[fan]

Dear Tom, I am trying to estimate how economic conditions, expansions and recessions, in the election years (yr34) would affect the political power transition between the two parties, democratic party and republican party, in the U.S. by applying Markov Chain regressions. Unfortunately, I could not find a relevant Rats example I could study. Therefore, I am seeking for your help to conduct the estimation. The attachments are my transition equations and sample set. Thank you in advance

[TomDoan]

How is that different from any other MS model with time-varying TP? Also, why don't you have a constant in the logistic indexes?

[fan]

How is that different from any other MS model with time-varying TP? Also, why don't you have a constant in the logistic indexes?

Thank you for the quick reply.There should be constants in the indexes. I accidentally missed them in the equations. In most MS examples, states/regimes are latent; and the switching between the states is continuous; while, the political power transition is observable and it happens every 4 year. The MS examples I studied are mean, variance or/and coefficients switching models. Here, I am only interested in the betas and alfas in the transition equations. I am wondering how to write the likelihood function, whether it will be the same as the likelihood function for logit.

[TomDoan]

Isn't that just separate logit models depending upon the lagged value of S?

[fan]

Isn't that just separate logit models depending upon the lagged value of S?

Dear Tom, thank you for the prompt reply. Please, allow me to rephrase my question. What I am really interested is to estimate the probabilities for the incumbent parties (Democratic Party and Republican Party ) will stay in the White House after the election, and the impact on the probabilities from the economic expansions and expansions in the election years. The election outcome is not observed here. Therefore, I think it requires more than just separate logit models depending upon the lagged value of S. My conjecture is that I need to use MSPmat instruction but I could not be sure that is the right instruction to use. In addition, different from the examples where the regime-switching is continuous, the political power switching is only happening in the last year of the incumbent president. How can I take care of this difference. Thank you for your great patience and help.

[TomDoan]

How is the election outcome "not observed"?

Wouldn't you have separate logit models for 3 years to election, 2 years to election, etc.?

[fan]

How is the election outcome "not observed"?

Wouldn't you have separate logit models for 3 years to election, 2 years to election, etc.?

Hi Tom, Thank you for your reply. What I mean is that the election outcome is not observed before the election; therefore the probability of the incumbent party to stay in power is interested. Of course, the election outcome will be observed once the election is over. Please, allow me to simplify my question a little here. Now, I have the presidents after the world war 2 and the numbers of recessions and expansions occurred during each individual presidents. How can I estimate the transition probabilities (P[D|D] and P[R|R]); and the influence on the probabilities from the economic expansions and recessions?

[TomDoan]

You're confusing yourself. MS models are complicated because the regime is unobservable, so you have to do inference indirectly from things you can observe. Your regimes are observable, so you just have a standard logit formulation (or probit if you find that more convenient). The fact that elections come every four years most likely means that the four separate years in a cycle are governed by independent models (I believe it's fairly well-known that a recession early in a term has little if any effect on re-election chances). I can't really say much more than that.

[fan]

You're confusing yourself. MS models are complicated because the regime is unobservable, so you have to do inference indirectly from things you can observe. Your regimes are observable, so you just have a standard logit formulation (or probit if you find that more convenient). The fact that elections come every four years most likely means that the four separate years in a cycle are governed by independent models (I believe it's fairly well-known that a recession early in a term has little if any effect on re-election chances). I can't really say much more than that.

Dear Tom, thank you for the explanation. Now, I have some new understanding about the MS model. Even though the states are not observed in the MS, we still can inference the state for each time period indirectly from the observed variables. In other words, for instance, based on the observed growth rate, we are still able to classify each period into state of expansion or recession somehow, like comparing with the initial guessed values for expansion and recession. Then based on the inference states, we use logit or probit model to obtain the transition probabilities (P00 and P11) by conditional on past state, and the effects of the other variables on the probabilities. Please, kindly let me know if my understanding is not correct. Many thanks in advance

[TomDoan]

Aren't you treating recession and expansion as observables? In Hamilton's work, the only observable is GDP growth and the regime is inferred from that---it so happens that (over the correct sample), that that comes fairly close to reproducing the NBER cycles. You would do a completely different estimation if you took the NBER cycles as given.

[fan]

Aren't you treating recession and expansion as observables? In Hamilton's work, the only observable is GDP growth and the regime is inferred from that---it so happens that (over the correct sample), that that comes fairly close to reproducing the NBER cycles. You would do a completely different estimation if you took the NBER cycles as given.

Thanks for the quick reply. Recessions and Expansions are not observed but inferred from the GDP growth, not from NBER. What I would like to know is that whether the each period needs to classify into one of the two states before doing the logit model; and if so, how to assign each period into one of the states based on growth rats.

[TomDoan]

I think you're getting the wrong takeaway from Hamilton's work. The fact that a relatively simple model, using only GNP growth as data was able to almost exactly reproduce the NBER cycles was quite impressive. However, as you discovered, that result only holds for a very specific range of data---over a broader range, the "Markov" part breaks down and you just have some scattered periods of negative growth. The regimes inferred from the Hamilton model are just a non-linear function of output growth. If this is to be used as input to another model, why wouldn't you just use output growth itself as the exogenous variable? After all, 1% growth would be just as much as "expansion" as 5% growth, through the former would probably be seen as a negative for re-election and the latter would be a strong positive.

[fan]

I think you're getting the wrong takeaway from Hamilton's work. The fact that a relatively simple model, using only GNP growth as data was able to almost exactly reproduce the NBER cycles was quite impressive. However, as you discovered, that result only holds for a very specific range of data---over a broader range, the "Markov" part breaks down and you just have some scattered periods of negative growth. The regimes inferred from the Hamilton model are just a non-linear function of output growth. If this is to be used as input to another model, why wouldn't you just use output growth itself as the exogenous variable? After all, 1% growth would be just as much as "expansion" as 5% growth, through the former would probably be seen as a negative for re-election and the latter would be a strong positive.

Thank you so much for the explanation. I understand better now.