IRA accounts with early withdrawal penalties

[pmgblz]

We would like to simulate IRA accounts with early withdrawal penalties. Our simulation would require the following three extensions to HARK. Do you have already coded up any of the following extensions (but not submitted to HARK) or could share advice on how to create these? Any help would be greatly appreciated!

Here are the extensions:

• Model two savings accounts.

• Each savings account is kinked; i.e. potentially a different borrowing rate than interest rate on saving.

• Ideally, a penalty for withdrawing before a certain date or age. An alternative would be to create time varying interest rates for borrowing and savings.

[mnwhite]

These are not actively being worked on at this time, nor do I think I've made an issue specifically pertaining to this. We do want to add models that have multiple assets, rather than the single asset models that are currently in HARK. These generally come in two flavors:

1. Portfolio allocation problems between a risky and riskless asset. There is an issue for this, and I had a grad student working on it this summer/fall. However, she did not complete the work.

2. Retirement-style accounts, like you propose here.

The HARK team has discussed (2) being a to-do item, with my preference being to implement the example model from Jorgensen and Druedahl's G2EGM paper (JEDC 2017). IIRC, their example model has an inaccessible retirement account, but substantially the same solution method is used if you institute an early withdrawal penalty instead.

I have coded up versions of the G2EGM algorithm (for other models) in OpenCL, interfaced with HARK via the opencl4py package. The "upper envelope" step of G2EGM can be a bit cumbersome, so it's much nicer to have this piece done in a lower level language. That code is hidden in my private fork of HARK (for personal research projects), but I'm planning to write a generic version of it and move it into the main repo sometime in the spring.

However, I don't anticipate that we would merge that branch into the master branch until we get around to "package-ifying" HARK and making it able to be installed by pip. We have tried to make HARK use only packages that come with Anaconda automatically; currently the only exception is joblib for multithreading. Making HARK an install-able package is a priority item for early 2018.

My advice to you is to very carefully read this paper (http://www.sciencedirect.com/science/article/pii/S0165188916301920) and understand the G2EGM solution method. I anticipate that this would be the most efficient way to solve the model you describe, given the multiple kink features. And from a modeling perspective: the IRA account should not have a kink but a bound at zero. You can't borrow on a retirement account with the promise of putting the money back later.

[nomadj1s]

Hello,

I'm on the research team that originally made this request. Thank you for the references. They were very helpful.

Instead of using the G2EGM model, which leverages a functional form assumption to get a closed form solution, I am looking at the Nested Endogenous Grid Method (NEGM) here, also by Jeppe Druedahl. This method relaxes the functional form assumption, uses EGM to pin down the consumption function, but then uses value function iteration (VFI) to pin down the other endogenous variable, in our case deposits or withdrawals from the illiquid account.

My question: are there already tools within the HARK tool kit to implement VFI, or do I need to code that up on my own? If not, do you have a reference for the frontier of VFI?

Thanks

[mnwhite]

Hey there! Patrick Mogensen, a PhD student of Jeppe, is currently working on porting a general-use G2EGM utility tool into HARK. I believe that work is approaching completion.

Once G2EGM is done, he will turn to making a general-purpose NEGM utility, which (if I understand correctly) will incorporate a value-maximization component.* The horizon for that is still 2-3 months away by my estimation.

I don't personally use value maximization (with respect to continuous controls) in my own work, so I don't know what the frontier of methods is. Patrick has been flagged to respond to this thread, and he will probably know more. With the proper incantations, Jeppe could be summoned as well.

*- I don't call this step VFI, as that implies (to me) a backward iteration process across many periods. The explicit value function step in NEGM maximizes control-conditional value within a period.

[nomadj1s]

Great thanks for the response. I will await to see if Patrick chimes in. I also agree that the maximization step in NEGM may be a bit different than standard VFI.

[pkofod]

Instead of using the G2EGM model, which leverages a functional form assumption to get a closed form solution,

It's a bit more than that really, but I understand why the different things might be a bit hard to separate based on reading the paper alone. G2EGM's main point is basically to divide potential problematic cases into "segments" according to different margins being constrained (constrained post decision cash-on hand, constrained retirement savings, everything unconstrained, ...). With a solution for each segment, you then do a simultaneous upper envelope and re-interpolation down to a common grid. It is true that there are closed form expression for each segment, but I guess some of that could still be numerically solved for, and you would still label the solution method as G2EGM, as long as you used the re-interpolate/envelope step (which is what I see as "the G2EGM" method, the authors might have a more nuanced view, I'm actually unsure).

I am looking at the Nested Endogenous Grid Method (NEGM) here, also by Jeppe Druedahl.

Good, I'm sure Jeppe would appreciate knowing that people are reading he manuscript, he's certainly quite enthusiastic about NEGM himself.

My question: are there already tools within the HARK tool kit to implement VFI, or do I need to code that up on my own? If not, do you have a reference for the frontier of VFI?

No, there isn't. And I think that MNW's following way of characterizing is the correct answer to your question.

*- I don't call this step VFI, as that implies (to me) a backward iteration process across many periods. The explicit value function step in NEGM maximizes control-conditional value within a period.

I think it still remains to be seen when and where which method might shine. It's a bit hard to say much without any details about your models. What functional form assumptions are you uncomfortable with in their paper? I don't recognize neither your names nor your picture, so I can't deduce much from that, but if you want to share something in private, that's fine as well. Fewer people will be able to chime in though.

[nomadj1s]

Thanks for the input. To clarify, here are the two features of G2EGM that I'm alluding to, as discussed in the Nested Endogenous Grid Method (NEGM) paper Jeppe Druedahl:

1. G2EGM requires that the equation system of stacked discrepancies in the first order conditions and post-decision state equations have a unique solution. (pg. 4-5)

2. G2EGM rel[ies] on a complex multi-dimensional upper envelope algorithm, while NEGM rel[ies] on a simple one-dimensional upper envelope. (pg. 5)

The first is achieved in the specific application of the G2EGM paper by assuming the return to assets in the pension account has a strictly concave functional form, i.e. the g(d) function. This delivers a closed form solution for optimal deposits/withdrawals for that account, i.e. equation 3.7 in the G2EGM paper. The specific functional form is not as important as having g'(d) be a function of d.

Both NEGM and G2EGM involve an upper envelope step, but the one in the NEGM approach is not as complicated/doesn't involve constructing triangles or barycentric interpolation. The tradeoff is that NEGM requires a value function maximization step.

The model I'm working on is a standard consumption-savings model, with a liquid account that has interest factor Rboro for borrowing and Rsave for saving, and an illiquid account (IRA) with interest factor Rira. The illiquid account has a minimum balance of zero, and there is a proportional penalty, t, for making withdrawals from the illiquid account before a T_ira. We also impose Rboro > Rira > Rsave.

[pkofod]

doesn't involve constructing triangles or barycentric interpolation. The tradeoff is that NEGM requires a value function maximization step

This part is real... I'm still polishing off the implementation I've been working on, but it's really hard to get some weird behavior here, so I'd be very interested in seeing a horse race between the two (I might be the one doing it, so :) )

[nomadj1s]

Hello,

I have finished a first draft of this model on a branch I created. I have a few follow up questions:

1. Because this model uses the NEGM method, it doesn't exactly nest the standard ConsIndShockModel.py, but in theory, if I shut down the illiquid asset, I should get very similar results to the ConsIndShockModel.py. My question: what is the best way to diagnose my model? Are there particular functions or figures that I should create using my model and the ConsIndShockModel.py to see if I am at least getting the basics right?

2. Once I think the model is up and working, is there a way to share it and have people test it out/suggest improvements?

Thanks

[mnwhite]

1. Being 100% sure that your model is really doing what it's "supposed" to do, and that you didn't make some strange error or overlook some issue, is impossible. It's the major existential crisis that you've signed up for by pursuing this line of research.

As you suggest, the first sanity check is to see if your model reproduces the results (policy function, etc) of some simpler, known model when certain parameters are trivialized to shut down the new features. A basic two asset model with early withdrawal penalties on one (the "retirement fund") turns into ConsIndShock when the withdrawal penalty is set to zero (or the "retirement age" when the withdrawal penalty is removed anyway is set at 0 or 1) and the interest rate on the retirement fund equals Rfree in ConsIndShock (and the interest rate on the other asset is lower). It is never optimal to put any money in the lower return asset, and agents will save in the retirement fund as they would in ConsIndShock.

Beyond that, how to "diagnose" that a model is working correctly is a weird blend of art and science. You can play with parameters and make sure that the model results move in the "right" direction according to your intuition. Or you can try to calculate some object in the model using multiple approaches (a "clever" and "dumb" way) and see if they align. What to do is model-specific.

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2. If your fork is public, then this is easy: Just tell the world about it, and they can simply merge a branch from your fork into a branch on their fork of HARK and test it out. If your fork is private, then you would have to issue a PR into master HARK. Then it's possible to merge your branch in locally and people who follow econ-ark/HARK to play with your branch.

[pkofod]

Beyond that, how to "diagnose" that a model is working correctly is a weird blend of art and science. You can play with parameters and make sure that the model results move in the "right" direction according to your intuition. Or you can try to calculate some object in the model using multiple approaches (a "clever" and "dumb" way) and see if they align. What to do is model-specific.

As you suggest, the first sanity check is to see if your model reproduces the results (policy function, etc) of some simpler, known model when certain parameters are trivialized to shut down the new features.

This is Keane's "make it flat"-advise.

Beyond that, I'd say post it if possible, and we (I? :) ) can have a look.

[nomadj1s]

Thanks for the feedback. I agree with your suggestions. I will make my branch public here, but before doing so, I'd like to run the simplified version and see how well it matches a ConsIndShock model. This will take a day or so.