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A number of times ive seen the Neoclassical Growth Model and Overlapping Generation Model setups referred to as a "workhorse of modern macroeconomics". What does this mean exactly?

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It is meant in a way that these models are highly influential and many papers are based on them.

From my own experience it is impossible to attend macroeconomic conference without having couple of papers that are based on models of overlapping generations or on neoclassical growth model.

The reason for that is that the models are quite useful and easily to adapt in lot of different settings. You can use overlapping generations model to examine anything from simple household savings decision to topics that are even outside the realm of macroeconomics such as optimal wealth taxation or environmental policy.

When it comes to the Neoclasical growth theory, for better or worse most of the research in the literature on economic growth in past few decades heavily focused on Solow-Swan model. In mainstream the only competition to Solow-Swan is the endogenous growth model (for which Romer got his Nobel Prize), but due to difficulties in verifying it empirically Solow-Swan is still dominant growth model.

Both of the above mentioned models can be adapted to so many settings that it would not be completely incorrect to think of them more of as a mathematical tools like for example Lagrangian optimization and hence many call them workhorse models since they do most of the work in the mainstream macroeconomics. Essentially, with a little bit of demagoguery you could say that for a decent academic career in macro it is enough to learn how to solve and play with one of the above mentioned models.

For an illustration consider this: In quite popular macro handbook - Advanced Macroeconomics from David Romer, first two chapters are about Solow-Swan and overlapping generations model. By word count almost 1/6 of the handbook is devoted to them, and beside these two models, only other models that have separate chapters devoted to them are the endogenous growth, real business cycle and dynamic stochastic general equilibrium model, other chapters usually squeeze multiple different models in themselves showcasing how important the above mentioned are.

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    $\begingroup$ In addition the undergraduate textbook from Weil on economic growth covers just a single model 20 chapters long: Solow-Swan (in different versions of course) $\endgroup$ – Maarten Punt Apr 22 at 9:23

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