Jesse Perla

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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The first chapter proposes a flexible non-parametric method using Recurrent Neural Networks (RNN) to estimate a generalized model of expectation formation. This approach does not rely on restrictive assumptions of functional forms and parametric methods yet nests the standard approaches of empirical studies on expectation formation. Applying this approach to data on macroeconomic expectations from the Michigan Survey of Consumers (MSC) and a rich set of signals available to U.S. households, I document three novel findings: (1) agents' expectations about the future economic condition have asymmetric and non-linear responses to signals; (2) agents' attentions shift from signals about the current state to signals about the future: they behave as adaptive learners in ordinary periods and become forward-looking as the state of economy gets worse; (3) the content of signals on economic conditions, rather than the amount of news coverage on these signals, plays the most important role in creating the attention-shift. Double Machine Learning approach is then used to obtain statistical inferences of these empirical findings. The second chapter shows these stylized facts can be generated by a model with rational inattention. In this model, the value of information increases as the state of the economy deteriorates due to the non-linearity in the agent's consumption-saving problem. For this reason, the optimal choices of information depend on realized economic status. In particular, the households put more effort to acquire information about the future when economic status worsens. This leads to both the attention-shift and non-linearity in their expectation formation process. The third chapter performs a structural test in framework of the noisy information model and shows that individual forms their expectations on multiple macroeconomic variables jointly rather than independently, thus causing these expectations to be correlated with each other. In particular, they have a subjective model about the economy. They believe economic conditions will be worse during episodes with extensive inflation news, even if there is only mild inflation, causing their average expectation on inflation to co-move with that of unemployment and business condition.

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