UBC Theses and Dissertations

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UBC Theses and Dissertations

Essays on theory and computation in economics Ebrahimi Kahou, Mahdi


The first chapter: I propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The curse of dimensionality is alleviated thanks to three techniques: (1) exploiting symmetry in the approximate law of motion and the policy function; (2) constructing a concentration of measure to calculate high-dimensional expectations using a single Monte Carlo draw from the distribution of idiosyncratic shocks; and (3) designing and training deep learning architectures that exploit symmetry and concentration of measure. As an application, I find a global solution of a multi-firm version of the classic Lucan and Prescott (1971) model of investment under uncertainty. First, I compare the solution against a linear-quadratic Gaussian version for benchmarking. Next, I solve the nonlinear version where no accurate or closed-form solution exists. Finally, I describe how this approach applies to a large class of models in economics. The second chapter: in the long run, we are all dead. Nonetheless, even when investigating short-run dynamics, models require boundary conditions on long-run, forward-looking behavior (e.g., transversality condition). In this chapter, in sequential setups, I show how deep learning approximations can automatically fulfill these conditions despite not directly calculating the steady state and balanced growth path. The main implication is that one can solve for transition dynamics with forward-looking agents, confident that long-run boundary conditions will implicitly discipline the short-run decisions, even converging towards the correct equilibria in cases with steady-state multiplicity. While this chapter analyzes benchmark models such as the neoclassical growth model, the results suggest deep learning may allow us to calculate accurate transition dynamics with high-dimensional state spaces, and without directly solving for long-run behavior. The third chapter: the sequential models studied in the previous chapter can be very useful to study deterministic setups and one-time shocks to economic variables. In this chapter I focus on the recursive setups. I consider the recursive version of the neoclassical growth model, which can be extended to study investment decisions under uncertainty. I show how deep learning approximations automatically fulfill these boundary conditions.

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