Posts by Collection

Two Endogenous State Variables in Continuous-Time: Wealth and Human Capital

2020

This note describes a deterministic human capital accumulation problem in continuous time with one financial asset, and offers a solution algorithm using the finite-difference method. Agents can accumulate financial assets and human capital by dividing their time between labor and education. Human capital is accumulated via a DRS production function and depreciates over time. Labor income receives a wage per unit of time worked and per unit of human capital.

Aiyagari Model with Non-homothetic CES Preferences and Multiple Sectors: Steady State and Transition

2022

How to robustly solve for the steady state and transition paths of an Aiyagari model in continuous-time with non-homothetic CES preferences (as in Lashkari-et-al (2021)) and three sectors? The Matlab code below proposes an algorithm based on a predefined approximation of inverse of marginal utility of expenditure using the so-called ‘Chebyshev technology’. Transition path in response to one or several series of MIT shocks can be efficiently solved for, using a first-order perturbation of the approximant of the inverse of marginal utility and perturbed relative prices along the transition path. The code is written for three sectors, but the code remain as efficient for large number of sectors (as long as the production functions are static and relative prices can be solved for as it is with the current model). The implementation below uses the excellent ‘Chebfun’ package of Matlab, but a similar implementation is available in Julia (upon request).

Model with Two Assets and Kinked Adjustment Costs (HANK)

2024

We introduce a new algorithm for solving continuous time problems with multiple endogenous state variables in a finite–difference scheme. The algorithm extends the logic of up–winding to its logical extreme in a way that meets the necessary conditions for local convergence (Barles and Souganidis, 1991). It is consistent because the directions of state–drift are never in conflict, and constraints are applied non–linearly. It is efficient because it nests the search for these state–drifts in a way that ensures costly root–finding is only performed after other alternatives are exhausted. The algorithm improves on the existing ‘split–drift’ approach from (Kaplan et al., 2018; Achdou et al., 2022), which can fail under some parameter settings because it is not guaranteed to be consistent.

Impulse, Response, and Anticipation in Trajectory-Space Jacobians

2025

This paper presents a simple method of calculating the continuous-time transition path of a heterogeneous-agent economy in steady state in response to a perturbation path (aka MIT shock path) affecting a price or another variable. In other words, it is a continuous-time counterpart of (Auclert et al. 2021). The goal is to introduce a method that satisfies the following criteria to the extent possible: efficiency, simplicity (e.g., no analytical derivative is needed) and general applicability. The method has three main building block: Dirac’s Delta function for impulses, fast matrix exponentiation methods for forward response path, and a simple linearisation theorem to capture the anticipation effects backwards. [Code and Draft Coming Soon]

The Solow Model

Published: October 15, 2023

Solow model in discrete time. BGP and the steady state. The Uzawa theorem. Transition paths. Convergence and Speed of convergence. Kaldor facts and the Solow model. Non-unitary elasticity of substitution between labour and capital (CES production function). CES production function and comparative statics. The Golden rule consumption.

Neoclassical Growth

Published: October 22, 2023

Neoclassical Growth model. (Representative) Firm and Household problems. Characterization of the equilibrium. The Consumption Euler equation. Equilibrium, and welfare. Recursive formulation. Bellman equations for the original, and detrended problem. Solving the Bellman equation with Guess and Verify. The Value function iteration (VFI): intro to numerical methods. Transitional dynamics, saving rates, and elasticity of inter-temporal substitution.

Stagnation -> Modern Growth

Published: October 30, 2023

England (1260-2016): population, living standards and industrialisation. Facts of economic stagnation. The Malthusian model of stagnation. Land in production and the fertility-income relation. Transition after negative population shock (the Plague), and positive land shock (the American Frontier).

Industrialisation (and Food!)

Published: November 08, 2023

Does the essentiality of food matter for take-off to the modern growth? A model with non-homothetic preferences. Subsistence level and possibility of Malthusian trap. The Malthusian disaster. Successful industrialisation in England.

The Romer’s Model

Published: November 22, 2023

Growth, technology and production of ``Ideas’’. The Economics of ideas. How are ideas produced? How to model the R&D. The Romer’s model with expanding (input) variety. The equilibrium and the endogenous growth. Pareto optimality and welfare theorems. Optimal growth path.

The Creative Destruction

Published: November 30, 2023

Growth and creative destruction. A quality ladder model of growth. The innovation technology. Innovation on the balanced growth path. Solving for the balanced growth rate in closed form.

Portfolio item number 1

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Hofstadter, D. R. (1999). Gödel, Escher, Bach: an Eternal Golden Braid

Translated into Persian, with Morteza Khazanehdari, and Abdolreza Khazanehdari

Reproducibility and Data Policy for Small (Open) Journals

Report on the state of reproducibility in the economic journals, best practices, costs and limits of current practices, and feasible solutions for Data and Code policy for smaller journals, commissioned by Economica.

Évaluation du plan France Relance à l’aide d’un modèle de HANK [Evaluation of the France Relance programme using a HANK model]

with Adrien Couturier , Ben Moll and Ricardo Reis

We use a HANK-type model to evaluate the impact of France Relance fiscal stimulus, run in the aftermath of the pandemic, on the French economy, both in terms of the aggregate variables and the gain distribution across households.

Impulse, Response, and Anticipation in Trajectory-Space Jacobians (Or How to Stop Worrying and Love Dirac’s Delta!)

with Stephan Hobler

An efficient method of calculating the continuous-time transition path of a heterogeneous-agent economy in response to a perturbation path (aka MIT shock path) affecting a price or another variable, a continuous-time counterpart of (Auclert et al. 2021).

The Nested-Drift Algorithm

with Patrick Schneider

Robust and efficient method of implementing finite difference algorithms for solving heterogeneous agent models in continuous time with multiple endogenous state variables, using the two-asset HANK model of Kaplan-Moll-Violante (2018) as the lead example.

Business Cycles Along the Development Path

[Draft coming soon]

The Unproductive Wealth of Nations: The Case of Gold in India

[Draft coming soon]

Talk 1 on Relevant Topic in Your Field

Published: March 01, 2012

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Tutorial 1 on Relevant Topic in Your Field

Published: March 01, 2013

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Talk 2 on Relevant Topic in Your Field

Published: February 01, 2014

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Conference Proceeding talk 3 on Relevant Topic in Your Field

Published: March 01, 2014

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Macroeconomics (EC102)

Undergraduate, LSE

Teaching Evaluation: 2020-2021 (4.2/5)

Micro- and Macro-economics for the 1st year undergraduate students.

Macroeconomics (EC1B5)

Undergraduate, LSE

Teaching Evaluation: 2023, Spring (5/5)

Course Manager. Macroeconomics for the 1st year undergraduate students.

Advanced Economic Analysis (EC301)

Undergraduate, LSE

Teaching Evaluation: 2022, Spring (no teacher evaluation report) ; 2023, Spring (4.6/5)

Economic Growth

Math Boot Camp (EC400)

Graduate, LSE

Teaching Evaluation: 2023 (4.8/5)

Static optimisation and fixed point theory. Dynamic optimisation (mathematics for macroeconomics)

Macroeconomics (EC413)

Graduate, LSE

Teaching Evaluation: 2023, Fall, Growth (4.9/5) ; 2024, Spring, Monetary (4.8/5) ; 2024, Fall, Growth (4.9/5)

Class Teacher Award: 2023 (highly commended)