## Friday, June 29, 2012

### New Paper

In my "real" academic life, I just finished a new paper, "Continuous-Time Linear Models," find it here if you're curious.  It's a pedagogical piece really, showing how to do all the familiar discrete-time time-series tricks in continuous time.  Comments welcome. I thought of advertising it as evidence that blogging hasn't turned my mind to mush, but I'm afraid real continuous-time econometricians will see it as proof of the opposite proposition.

1. I think Paul Krugman would say that your mind is mush whether you blog or not...

2. John,
here is a serious question - a more philosophical one.
If one can do everything in discrete time, why would you WANT to do it in continuous time? What do you gain in doing things in continuous time, and especially, is there any additional *economic* insight that one cannot gain from the discrete counterpart?

1. Continuous time is often a lot cleaner. Two examples:

1) Get from the standard asset pricing equation 0 = E(beta u'(c_t+1)/u'(c_t) Re_t+1) to the expected return-consumption beta relationship E(Re_t+1) = gamma cov(R_t+1,delta c_t+1) where gamma is risk aversion. This is fast in continuous time, needs ugly approximations in discrete time.

2) Discrete time models have lots of timing conventions that are easy to trip up. Is it k_t+1 = (1+r)(k_t + i_t) or k_t+1 = (1+r)k_t + i_t? A deeper example, new Keynesian model dynamics depends tremendously on timing in the Taylor rule. (See "determinacy and identification with Taylor rules")
Discrete time models often mix up observation intervals with economically important lags.

Mostly, I think it's best to know both tools and use the one that works best for a given application. Don't discount the value of prettier, simpler and clearer!

2. Hey JHC, longtime reader, first time commenter:

Per 1) In what sense is 0 = E(beta u'(c_t+1)/u'(c_t) Re_t+1) harder to estimate than E(Re_t+1) = gamma cov(R_t+1,delta c_t+1)? Aren't all relevant proxies for c from monthly data at their 'most continuous.'

3. I know you have to justify your position at a prestigious university, but I am convinced that the only true economists as defined in the traditional sense "Moral scientists" are down south. I think this is why David Friedman Suggests George Mason University. Chicago is fast loosing it's purpose. Economics is supposed to study relationships between people. If you want to use price discovery in a casino where the game is rigged you are not studying people. Please change your title to something other than economist if the structure you are describing has nothing to do with humans. We true economists are getting a bad rap by PROFESSORS changing the definition of economics. There are still plenty of great things to discover and better ways to describe the HUMAN CONDITION left within the traditional Moral Science. This kind of stuff is destroying our good image as MORAL scientists. Please change your ways.

4. Doctors identify and cure biological Diseases.
Economists identify and cure social Diseases.
The terms doctor and economist are bothe misplaced in Chicago. Please try to incorporate philosophy into your Teaching. A classical education is a treasure. But just like a monkey can find no INTEREST, or VALUE. In gold, Chicago can find no interest or value in MORALITY. Or MORTALITY as a less personal more ACCADEMIC relationship to those who fund their occupations. An economist is supposed to be the person society looks to to understand the consequences of human actions. An economist is our last attempt to save HUMANITY. Please don't spend your time trying to sterilize mankind. We need people to defend freedom. This kind of stuff makes the rest of us look as if we don't care about the human condition. I should be grateful that this work will never be seen by the Layman. The only image they are presented with is P.C. Paul Krugman. Serious problem.

5. Although I wish that more economics was accessible to the layman, the bottom line is you can't have science without data and there isn't much economic data that doesn't involve numbers. Sadly, once we get to numbers, there must also be math. That seems to be the great disconnect between some of the old and the new schools, and the layman and the professional economist.

If it were just an essay contest, there would be no need to use up so much of society's resources for studying economics at all, since in reality we would already be admitting that there was nothing that could be known about it anyway.

6. That is a valid issue, but it is not the most important issue of our day, where the public is moving toward socialism. Just look at the SOSH department. Lack of education, extreme. You may agree with Roberts. "it is not our job to protect people from their political choices". True. But it is our job to help them understand their political choices. Paid Liars like P.C. Krugman are leading the population. He does not represent our peer reviewed science. But they think he does. If you have children and you put them in danger, I.e. placing them in a communist country. You clearly love your country more than your own children.

7. Countinuous time model isn't popular in Macro,is it? My expierience of SDE is usually they need some regulatory conditions which are hard to satisfy.

PS what about chaos models? A promising tool?

8. I am reading this paper now and find it is useful. I also read asset pricing and the time series note. I am a second year finance phd student and in order to understand continuous time finance, I took the probability class from math dept but I find as an economist, the modeling skill is more important than the rigor of math.
You ll see what I mean if you compare texts like duffie's, Antonio mele's etc with cochrane's way of writing: reference V.S. text. I really enjoy reading prof Cochrane 's asset pricing in that it connects different models in a systematical way and summarize them. I have engineering background before coming to business school and it is just the way I like especially it feels like a physics book.

Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.