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Alfred Anate Bodurin Mayaki

On the OBR's Overlapping Generations (OLG) model

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Edited by Alfred Anate Bodurin Mayaki, Sunday 4 May 2025 at 10:57

Great spending some much valued time asking clarification questions about an open role at the Office of Budget Responsibility (OBR) - reporting directly to its Senior Economist. The role is a perfect fit at first glance. I like it because its responsibilities include ownership of a mixture of economic modelling and publishing work. The OBR was formed in May 2010 by the (then) Chancellor of the Exchequer, Rt Hon. George Osborne, who at the time felt that more scrutiny was required to justify UK Government's fiscal positioning in relation to its borrowing path. Enter the OBR, an independent forecaster, which puts out its own research to hold the government to account. The significance of this Great British arms-length body is as one of three government pillars – the other two being the Treasury and the Bank of England.

Speaking with Senior Economist James Watson (OBR), via Teams, who the Economist/Data Scientist role reports to, the very first thing I asked him, ten seconds in, was for clarification on this April 2025 working paper which he co-authored alongside Adam Brzezinski (London School of Economics and Political Science) and Arno Hantzsche (Bank of England). What was I thinking? Well, my idea was simply around a so-called No-Ponzi constraint that Dr. Stefan Niemann (University of Konstanz) mentioned to his students in an advanced macro lecture in the old LTB. No-Ponzi is transversal and can exist as a boundary condition on the terminal value of the household budget in the infinitely-lived agent model of the UK economy. However, as James clarified, since its inception in 2010, the OBR has moved gradually towards an overlapping generations (OLG) framework where finite time is considered more pragmatic. As such, the household’s budget has a crucial distinction from the infinitely-lived model. Since the No-Ponzi constraint is an endogenous factor in most neo-classical growth models, which I have encountered, I wanted to know what James thought about its omission from the OBR’s modelling framework – a framework, which the successful applicant will be responsible for upholding and progressing.

The OLG paper is a great read. Just over halfway in you'll find it to be highly nostalgic to some of my previous work on economic growth, and a thrill to review partly because from a 'Labor Econ' perspective, it has two central provisions which fascinate me. First and foremost and importantly, the omission of inheritances, which imply “asset holdings may not be negative,” and secondly, in line with standard Ramsey model intuition – a life-cycle problem which is in-fact an i.i.d stylized fact that accounts for “annual variation in pay” across time in the OLG model. Yes, this is something I mentioned to James. He speaks very eloquently on the model’s structure, which I notice also includes a perfectly-competitive market-clearing wage and a fabled interest rate, which depend on the OLG’s standard transversality condition.

James (unsure if his name is pronounced in Spanish dialect or not) revealed he works alongside three important senior execs within the OBR – one being Richard Hughes, the other being David Miles and last but not least, Tom Josephs, who each form the budget responsibility committee of the OBR and have a good relationship with the organisation. Shortly after, I revealed my approval of the civil service recruiting process to James at that particular juncture. What I found interesting is the time it takes for the OBR to publish its proprietary research. Some 3-6 months it can take and indeed it took James, Adam and Arno that long to publish the OLG paper this month. Hopefully, we can keep the great work going if I am selected to join the OBR team. For now, I look forward to a positive reply from the civil service recruitment team.

Great call.

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A picture of Russell Larke

The Time Horizon as a Boundary Decision: OLG and the No-Ponzi Constraint

Reading back through older posts for inspiration, this one is doing systems thinking at a level of technical precision that most systems writing never reaches. The choice between the infinitely-lived agent model and the overlapping generations framework is not a technical preference. It is a boundary decision about the time horizon of the system. The infinitely-lived agent model draws the boundary at infinity. The household optimises over an unbounded time horizon. The No-Ponzi constraint then functions as a terminal condition — a boundary condition on the value of the system at the limit. It prevents the household from running a debt path that never resolves. That is a structural constraint, not a behavioural assumption. The shift to OLG moves the boundary. Finite time becomes the constraint. Households are no longer immortal. They are born, they live, they die, and they are replaced. The system now has a generational turnover that the infinitely-lived model cannot represent. The transversality condition still applies, but its role changes. It is no longer a condition at infinity. It is a condition across generations. James's clarification that the OBR moved gradually toward OLG "where finite time is considered more pragmatic" is the key line. Pragmatic is a boundary decision. The OBR is not claiming that OLG is more true. It is claiming that finite time is more useful for the modelling problem at hand. That is a systems argument. The boundary is chosen for the purpose, not for the ontology. The omission of inheritances is the same kind of decision. It removes a flow between generations. That changes the dynamics. It changes what the model can show about asset accumulation, inequality, and intergenerational transfers. The model is not wrong to omit it. It is drawing a boundary. The question is whether the boundary is the right one for the question being asked. This is what makes the OBR's work interesting from a systems perspective. It is not just forecasting. It is making explicit choices about what counts as the system and what is environment. Those choices determine what the forecast can see. The role is not just economic modelling. It is boundary work. Regards,
Russell Larke
BA (Hons) Business Management | MSc Candidate (Systems Thinking)
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