I want to keep my comments here tightly focussed, as this could easily degenerate into a much wider debate about Dynamic Stochastic General Equilibrium (DGSE) models.
I seek to avoid the debate about "debt burdens"; the problem is that a "debt burden" is not a very well defined concept. Instead, I will just look at a more limited, yet interested problem: could an OLG model tell us anything useful about how the economy will evolve as the "baby boom" generation moves into retirement (under current policy settings, or under alternative settings)? If a model offer a description of this evolution, which is of crucial importance for fiscal dynamics, I am hard pressed to see how the model can offer insights to even more abstract problems.
Professor Farmer helpfully lists some articles to read, as well as some books. Since I currently have a backlog of things to read, I only looked at the articles. I have read other DSGE textbooks, and each one only covers OLG models where households live for 2 or 3 periods. I explain elsewhere why I reject the usefulness of such models, with their very long time increments.
Olivier Blanchard's Debt, Deficits and Infinite Horizons (1984) is described in that article as:
Olivier Blanchard, the research director of the IMF, developed an elegant version of the OLG model in which people have long lives, but they die each period with some probability.I have already sketched out a longer discussion of this paper. I would not describe this article as being an OLG model, as all households are akin to J.R.R. Tolkien's elves: they do not die of old age, but they can die for other reasons (accidents, orcs). Mathematically, all living households have the same finite expected life span. Even with the addition of declining incomes, this does not fit the longevity profile of a real world population; in particular the issues associated with the "baby boom" generation.
Since I am not interested in the fate of individual model households, rather the aggregate economy, this model looks to me just like the Ramsey models used by central banks, but with a modified consumption function. Once we close the model with a central bank reaction function, it looks to me like the effect of fiscal policy will be the same as in the Ramsey model away from the zero bound: nothing. This raises a lot of issues that are a distraction relative to the topic of this article.
This is an interesting paper, but I would be hard pressed to see why this model would be any easier to fit to the demographic profile of the baby boom generation than the Ramsey model. But since I would not consider this a true OLG model, it does not contradict my earlier statements about them.
Kehoe and Levine 
I only glanced at the paper Comparative Statics and Perfect Foresight in Infinite Horizon Economies, by Timothy J. Kehoe and David K. Levine (Econometrica, 1985). The OLG portion of the paper had households that were only within the model for two periods. Whatever merits this paper has, it does not address my concerns about long time increments.
Auerbach, Gokhale and Kotlikoff
The paper Generational Accounts: A Meaningful Alternative to Deficit Accounting, by Auerbach, Gokhale and Kotlikoff, develops a detailed breakdown of net spending over time, including different scenarios. Their objective is to demonstrate whether different generations are being treated fairly relative to each other.
I will not address their logic, other than to say that I find it highly questionable. I will instead whether their work constitutes an "economic model". I would characterise their work as "an accounting framework", and not a model. There is no attempt to model variables such as inflation and unemployment. These are critical for the determination of the fiscal balance, and are dependent upon fiscal policy choices.
In other word, the trajectory of the economy is exogenous to the accounting framework. I imagine that this exercise could be extended by "dynamic scoring", but without an actual model, how do we do the "scoring"?
The CBO does this sort of accounting framework, and they were famously worried about U.S. Treasury debt disappearing a few years back. This might not have happened if they used an actual economy model which includes feedback effects between different sectors.
More generally, I have seen other OLG models with a fine-grained time increment (for example, annual) applied to things like retirement savings. These were closer to true economic models, with optimising households trading assets with each other. However, these models were only able to simulate some portion of the economy (for example, financial markets), and all of the interesting economic variables were largely exogenous.
Lacking a means of calculating those exogenous variables means that these accounting exercises are only of limited usefulness to policymakers. All they can do is reproduce the effects of the exogenously determined variables, and we have no way of determining whether those exogenous variables are internally consistent with policy settings.
Leaving aside the question of whether the Blanchard model is an OLG model, I still have not seen an OLG model framework that could be applied to the following problem.
- Time increments no longer than a year.
- Simulation of the age profile and longevity of the baby boom generation.
- Private and public pensions.
- Tax rates are set by policy makers and hence the fiscal balance is endogenous.
- Unemployment and inflation rates determined within the model (although one might assume inflation is always at the inflation target).
- Capital stock determined within the model.
Additionally, it would be nice to handle:
- private sector financial assets;
- different savings profiles based on wealth cohort;
- external sector, including the effect of the large holdings of U.S. financial assets by foreigners.
And this is not an impossible task, as long as we drop the strange insistence upon model-consistent rational expectations. A stock-flow consistent modelling framework could be adapted to this problem; all that needs to be done is to dis-aggregate the household sector into annual cohorts. (As an aside, it's a project which I am slowly working on.)
(c) Brian Romanchuk 2015