Beyond Random Assignment: Credible Inference and Extrapolation in Dynamic Economies

Abstract

We derive analytical relationships between shock responses and theory‐implied causal effects (comparative statics) in dynamic settings with linear profits and linear‐quadratic stock accumulation costs. For permanent profitability shocks, responses can have incorrect signs, undershoot, or overshoot depending on the size and sign of realized changes. For profitability shocks that are i.i.d., uniformly distributed, binary, or unanticipated and temporary, there is attenuation bias, which exceeds 50% under plausible parameterizations. We derive a novel sufficient condition for profitability shock responses to equal causal effects: martingale profitability. We establish a battery of sufficient conditions for correct sign estimation, including stochastic monotonicity. Simple extrapolation/error correction formulas are presented.

Learning, parameter drift, and the credibility revolution

“…In this paper, we show an analogous result obtains even if agents do not know the data generating process. However, in contrast to Hennessy and Strebulaev (2019), we show that stochastic monotonicity of all potential data generating processes is insufficient to ensure shock responses correctly recover the sign of theory-implied causal effects.…”

“…Undermining such assertions of credibility, Pischke (2009, 2010) never formally demonstrate the connection between quasi-natural experiments and causal parameters. To the contrary, Hennessy and Strebulaev (2019) show that in dynamic economies, responses to exogenous shocks generally fail to recover two important causal parameters: theory-implied causal effects (comparative statics) and policy-invariant adjustment cost parameters determining causal effect magnitudes. However, responses to specific policy variable transitions do forecast responses to identical policy variable transitions in the setting they consider.…”

“…Conveniently, progress has been made in developing quasistructural methods for recovering causal parameters in quasi-experimental settings featuring dynamic uncertainty and/or changes in underlying stochastic processes, e.g. Heckman and Navarro (2007) and Hennessy and Strebulaev (2019). However, reduced-form econometricians often object to using these methods since they demand making "strong" distributional assumptions.…”

“…As a second constructive result, we derive an auxiliary identifying assumption, beyond random assignment, that is necessary and sufficient for shock responses to directly recover theory-implied causal effects (comparative statics) in economies where agents and econometricians learn over time: For all potential data generating processes the tax rate is a martingale. Intuitively, Hennessy and Strebulaev (2019) show that in economies where profitability is driven by a known Markov chain, martingale profitability is sufficient for shadow values to behave as if shocks are completely unanticipated and permanent, so that shock responses directly recover comparative statics. In this paper, we show an analogous result obtains even if agents do not know the data generating process.…”

“…Of course, none of the learning papers discussed analyzes implications for empirical work exploiting natural experiments. In contrast, Hennessy and Strebulaev (2019) do analyze natural experiments, but they do not allow for the possibility of model uncertainty.…”