Teaching

ECO2101 — Macroeconomic Theory II. The fourth quarter of the PhD first-year macroeconomics sequence at the University of Toronto, Winter 2026. The course builds up heterogeneous-agent macroeconomics from dynamic programming through firm dynamics and aggregate risk to sequence-space Jacobian methods, following recent papers and two open-access textbooks.

These slides lean heavily on teaching material that others have generously made freely available — among them Chris Edmond, Fatih Guvenen, Ben Moll, Ludwig Straub and Gianluca Violante — and on the papers and textbooks listed below. Some slides follow those sources very closely. I claim no originality or intellectual property in this material: it is posted for my students and for anyone else who finds it useful, and the original sources are the ones to cite. Any errors introduced along the way are mine.

Lectures

Introduction to Modern Macroeconomics What a modern macro model specifies — the stochastic dynamic environment, equilibrium and recursion — and why balanced growth restricts admissible preferences. Slides
Dynamic Programming I: Fixed Points, Contractions, and Optimal Stopping Fixed-point theory, contraction mappings and Markov dynamics, developed throughout on a firm with stochastic productivity. Threshold policies, monotonicity and continuation values. Slides
Dynamic Programming II: Efficient Algorithms for the Household Problem Markov decision processes and the VFI / HPI / OPI family, endogenous gridpoints and envelope conditions, and discrete–continuous choice with extreme-value shocks. Slides
Firm Dynamics: Entry, Exit, and Misallocation Hopenhayn (1992) on entry, exit and long-run equilibrium, with the computational procedure worked through; then Hopenhayn and Rogerson (1993) on nonconvex adjustment costs, inaction regions and their aggregate consequences. Slides
Entrepreneurship and Financial Frictions The canonical occupational-choice model — Aiyagari with entrepreneurs and collateral constraints — followed by Quadrini (2000), Buera and Shin (2013), and Moll (2014) on whether self-financing undoes misallocation. Slides
Aggregate Risk in Heterogeneous Agent Economies Krusell and Smith (1998): the distribution as a state variable, bounded-rationality forecasting rules, approximate aggregation, and the computational algorithm. Slides
Aggregate Risk in Heterogeneous Agent Economies: Applications Three tests of when and why heterogeneity matters for aggregates: lumpy investment (Khan and Thomas, 2008), credit shocks (Khan and Thomas, 2013), and uncertainty shocks (Bloom et al., 2018). Slides
Sequence-Space Jacobians Auclert, Bardóczy, Rognlie and Straub (2021): writing equilibrium as H(K, Z) = 0 in the sequence space, impulse responses from a single matrix, and certainty equivalence as a consequence of linearization rather than an assumption. Slides
Sequence-Space Jacobians II: The Fake News Algorithm, DAGs, and HANK Computing the Jacobians efficiently via the fake news algorithm, composing blocks along a directed acyclic graph, and an application to one-asset HANK. Slides

References

Textbooks

Azzimonti, M., P. Krusell, A. McKay and T. Mukoyama. Macroeconomics. Open access: phdmacrobook.org
Sargent, T. J. and J. Stachurski. Dynamic Programming. Open access: dp.quantecon.org
Heer, B. and A. Maussner (2009). Dynamic General Equilibrium Modeling, 2nd ed. Springer, chapters 8–9. doi

Papers

Algan, Y., O. Allais, W. J. Den Haan and P. Rendahl (2014). “Solving and Simulating Models with Heterogeneous Agents and Aggregate Uncertainty.” Handbook of Computational Economics, Vol. 3, ch. 6, 277–324. doi
Arellano, C., Y. Bai and P. Kehoe (2019). “Financial Frictions and Fluctuations in Volatility.” Journal of Political Economy, 127(5), 2049–2103. doi
Auclert, A., B. Bardóczy, M. Rognlie and L. Straub (2021). “Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models.” Econometrica, 89(5), 2375–2408. doi
Bloom, N., M. Floetotto, N. Jaimovich, I. Saporta-Eksten and S. Terry (2018). “Really Uncertain Business Cycles.” Econometrica, 86(3), 1031–1065. doi
Boppart, T., P. Krusell and K. Mitman (2018). “Exploiting MIT Shocks in Heterogeneous-Agent Economies: The Impulse Response as a Numerical Derivative.” Journal of Economic Dynamics and Control, 89, 68–92. doi
Buera, F. and Y. Shin (2013). “Financial Frictions and the Persistence of History.” Journal of Political Economy, 121(2), 221–272. doi
Cagetti, M. and M. De Nardi (2006). “Entrepreneurship, Frictions, and Wealth.” Journal of Political Economy, 114(5), 835–870. doi
Carroll, C. D. (2006). The method of endogenous gridpoints.
Den Haan, W. J. (2010). “Comparison of Solutions to the Incomplete Markets Model with Aggregate Uncertainty.” JEDC, 34(1), 4–27. doi
Den Haan, W. J. (2010). “Assessing the Accuracy of the Aggregate Law of Motion in Models with Heterogeneous Agents.” JEDC, 34(1), 79–99. doi
Den Haan, W. J. and P. Rendahl (2010). “Solving the Incomplete Markets Model with Aggregate Uncertainty Using Explicit Aggregation.” JEDC, 34(1), 69–78. doi
Hopenhayn, H. (1992). “Entry, Exit, and Firm Dynamics in Long Run Equilibrium.” Econometrica, 60(5), 1127–1150. doi
Hopenhayn, H. and R. Rogerson (1993). “Job Turnover and Policy Evaluation: A General Equilibrium Analysis.” Journal of Political Economy, 101(5), 915–938. doi
Hsieh, C.-T. and P. Klenow (2009). “Misallocation and Manufacturing TFP in China and India.” Quarterly Journal of Economics, 124(4), 1403–1448. doi
Iskhakov, F., T. Jørgensen, J. Rust and B. Schjerning (2017). DCEGM. Quantitative Economics.
Kaplan, G., B. Moll and G. Violante (2018). “Monetary Policy According to HANK.” American Economic Review, 108(3), 697–743. doi
Khan, A. and J. Thomas (2008). “Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics.” Econometrica, 76(2), 395–436. doi
Khan, A. and J. Thomas (2013). “Credit Shocks and Aggregate Fluctuations in an Economy with Production Heterogeneity.” Journal of Political Economy, 121(6), 1055–1107. doi
Krusell, P. and A. A. Smith, Jr. (1998). “Income and Wealth Heterogeneity in the Macroeconomy.” Journal of Political Economy, 106(5), 867–896. doi
Maliar, L. and S. Maliar (2013). Envelope condition methods.
McKay, A., E. Nakamura and J. Steinsson (2016). “The Power of Forward Guidance Revisited.” American Economic Review, 106(10), 3133–3158. doi
Moll, B. (2014). “Productivity Losses from Financial Frictions: Can Self-Financing Undo Capital Misallocation?” American Economic Review, 104(10), 3186–3221. doi
Quadrini, V. (2000). “Entrepreneurship, Saving, and Social Mobility.” Review of Economic Dynamics, 3(1), 1–40. doi
Quadrini, V. (2009). “Entrepreneurship in Macroeconomics.” Annals of Finance, 5, 295–311.
Reiter, M. (2009). “Solving Heterogeneous-Agent Models by Projection and Perturbation.” JEDC, 33(3), 649–665. doi

Code

Sequence-space Jacobian toolkit: github.com/shade-econ/sequence-jacobian