llorracc
commented
4 years ago Good catch.
The inconsistency reflects the fact that one of the things that was not possible in dolo, and which turned out to take a very substantial amount of work in creation of dolARK, was mixing of different kinds of statistical distributions. Dolo could handle lognormal, or it could handle Poisson, but it could not handle a mixture of Poisson and lognormal. At the time I created the BufferStockTheory notebook you are looking at, the comparator to my code was just dolo, so had to adapt the model from its original description to something that could be solved by the existing (dolo) tools -- which I did by abandoning the small risk of unemployment shocks. (This is an illustration of the tradeoff between general-purpose solution methods, like those in dolo, and the flexibility you have when you hand-craft a solution).
The downside of restricting the distribution of the shocks, mathematically, is that it means that there is some amount of income that people are perfectly certain to receive (whatever is the minimum discrete draw in each period), and the logic of the model says that you should be able to borrow against whatever is your guaranteed minimum income. But that's kind of an uncomfortable place to be, because nobody really has an absolute guarantee of a minimum income (unless they are retired and receiving Social Security benefits). So, the standard thing to do is to couple the existence of a minimum possible level of income with the assumption of a borrowing constraint, so that even if formally the model says that you're guaranteed an income of, say, $20,000 a year, you can't actually borrow, say, $200,000 against that when the interest rate is 10 percent). Implicitly the argument is that the model does not allow for the possibility of default, but default is obviously possible in reality. (And turns out to be amazingly messy to handle mathematically).
One of the things that @albop and his team have done since I made the notebook you are looking at is to figure out how to allow mixtures of distributions. I hadn't really remembered that this means that the notebook can now implement an exact correspondence with the original problem in my BufferStockTheory paper. (BTW, a subtext of the intro to that paper is a complaint about the extent to which the existing theoretical literature had imposed conditions, like explicit liquidity constraints, that were mathematically convenient in order to use off-the-shelf theorems. It's not that I doubt the existence of liquidity constraints; but my experience is that people stop thinking carefully about the problem as soon as constraints are introduced, because they mistakenly think that constraints explain everything. My point is that the logic by which low levels of wealth are associated with a high marginal propensity to consume is a general proposition, not just one that results from the imposition of liquidity constraints.
sbenthall
@llorracc I'm confused about the parameterization of the buffer stock model here.
The original paper, and the REMARK, both explicitly model unemployment shocks.
This
chimeranotebook says "The unemployment (zero-income event) shocks are turned off". This is consistent with the equations given but not consistent with the parameters given in the first table or in the HARK model code, which still have theππππππΏππandπΈπππππππvariables.There is also a note that "An explicit liqudity constraint is added (ctβ€mtctβ€mt); that is, the consumer is prohibited from borrowing". But I don't believe this constraint is written into the equations above this line.
My reading is that the "For the purposes of this notebook..." section is meant to override what comes prior to it and was perhaps added without editing other code brought in from other sources. But I wanted to double check that I understood the intended model before making edits accordingly and bringing in simulation code.