We develop a structural framework illustrating how penalized regression algorithms affect Goodhart bias when training data is clean but covariates are manipulated at cost by future agents facing prediction models. With quadratic manipulation costs, bias is proportional to sum-of-squared slopes, micro-founding Ridge. Lasso is micro-founded in the limit under increasingly steep cost functions. However, standard penalization is inappropriate if costs depend upon percentage rather than absolute manipulation. Nevertheless, with known costs of either form, the following algorithm is proven manipulation-proof: Within training data, evaluate candidate coefficient vectors at their respective incentive-compatible manipulation configuration. Moreover, we obtain analytical expressions for the resulting coefficient adjustments: slopes (intercept) shift downward if costs depend upon percentage (absolute) manipulation. Statisticians ignoring agent borne manipulation costs select socially suboptimal penalization, resulting in socially excessive, and futile, manipulation. Model averaging, especially over Lasso or ensemble estimators, reduces manipulation costs significantly. Standard cross-validation fails to detect Goodhart bias.

We contrast ex ante information (signal) production and interim effort in open RCTs versus environments where agents choose treatment/control, evaluating/improving RCT transportability. Information production is high under discretion, since signals improve treatment/control choice, raising consumer surplus. Moreover, agents with-signal have added motivation to follow-through with effort to test signal quality. Nevertheless, if signals have sufficiently small effect on consumer surplus, a unique RCT treatment probability recovers population average discretionary treatment effects (ADTE). Here, self-reported treatment preference rates equal observational data rates, a diagnostic. We sign bias and propose RCTs testing/achieving transportability. Preference shocks recover local ADTE.

We establish limitations to the usage of direct revelation mechanisms (DRMs) by corporations seeking decision-relevant information in economies with securities markets. In this environment, posting a DRM increases the informed agent's outside option: if the agent rejects the DRM, he convinces the market he is uninformed, and he can aggressively trade with low price impact, thereby generating large (off-equilibrium) trading gains. This endogenous outside option may make using a DRM to screen uninformed agents impossible. When screening is possible, solely relying on the market for information is optimal if the increase in outside option is sufficiently large.

We incorporate structural modellers into the economy they model. Using the traditional moment-matching method, they ignore policy feedback and estimate parameters using a structural model that treats policy changes as zero probability (or exogenous) "counterfactuals." Estimation bias occurs since the economy's actual agents, in contrast to model agents, understand policy changes are positive probability endogenous events guided by the modellers. We characterize equilibrium bias. Depending on technologies, downward, upward, or sign bias occurs. Potential bias magnitudes are illustrated by calibrating the Leland (1994) model to the Tax Cuts and Jobs Act of 2017. Regarding parameter identification, we show the traditional structural identifying assumption, constant moment partial derivative sign, is incorrect for economies with endogenous policy optimization: The correct identifying assumption is constant moment total derivative sign accounting for estimation-policy feedback. Under this assumption, model agent expectations can be updated iteratively until the modellers' policy advice converges to agent expectations, with bias vanishing.

Causal evidence from random assignment has been labeled "the most credible." We argue it is generally incomplete in finance/economics, omitting central parts of the true empirical causal chain. Random assignment, in eliminating self-selection, simultaneously precludes signaling via treatment choice. However, outside experiments, agents enjoy discretion to signal, thereby causing changes in beliefs and outcomes. Therefore, if the goal is informing discretionary decisions, rather than predicting outcomes after forced/mistaken actions, randomization is problematic. As shown, signaling can amplify, attenuate, or reverse signs of causal effects. Thus, traditional methods of empirical finance, e.g. event studies, are often more credible/useful.

This paper analyses extrapolation and inference using tax experiments in dynamic economies when shock processes are latent regime-shifting Markov chains. Belief revisions result in severe parameter drift: Response signs and magnitudes vary widely over time despite ideal exogeneity. Even with linear causal effects, shock responses are non-linear, preventing direct extrapolation. Analytical formulae are derived for extrapolating responses or inferring causal parameters. Extrapolation and inference hinges upon shock histories and correct assumptions regarding potential data generating processes. A martingale condition is necessary and sufficient for shock responses to directly recover comparative statics, but stochastic monotonicity is insufficient for correct sign inference. (C) 2020 Published by Elsevier B.V.

ABSTRACTWe 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.

According to conventional wisdom, RCTs and natural experiments represent especially credible bases for econometric inference, facilitating evidence-based policymaking. We assess credibility in dynamic settings, examining robustness of evidence derived from an exogenous first-stage randomization applied to measure zero subjects. If government is able (unable) to alter policy in response, experimental evidence is contaminated (uncontaminated) by ex post policy endogeneity: Measured responses depend upon the government objective function into which the evidence will be fed. Similarly, if government perceives experimental evidence as credible (non-credible), the very act of observation changes (does not change) agent behavior. Thus, paradoxically, the experimental evidence is contaminated if and only if government is willing and able to use it. Ex post endogeneity causes measured responses to hinge upon (unknown) parameters of the governmental objective function, as well as a priori beliefs regarding the causal parameters to be estimated. Moreover, heterogeneous causal effect parameters induce endogenous belief heterogeneity. This link between beliefs and causal effect parameters makes it difficult, and potentially impossible, to isolate the latter using experimental evidence. Finally, we show treatment-control differences in RCTs are contaminated unless stock variable accumulation cost functions satisfy strong functional form assumptions: zero fixed costs, equality of buy and sell prices, and quadratic adjustment costs.

We develop a formal model of placebo effects. If subjects in seemingly-ideal single-stage RCTs update beliefs about breakthroughs based upon personal physiological responses, mental effects differ across medications received, treatment versus control. Consequently, the average cross-arm health difference becomes a biased estimator. Constructively, we show: bias can be altered through choice of control; higher-efficacy controls mitigate upward bias; and efficacy states can be revealed through controls of intermediate efficacy or controls that mimic a subset of efficacy states. Consistent with experimental evidence, our theory implies outcomes within-arm and cross-arm differences can be non-monotone in treatment probability. Finally, we develop novel differences-in-differences and triangle equality tests to detect RCT bias.

This article develops and empirically tests a tractable general equilibrium model of corporate financing and investment dynamics in a trade-off economy where heterogeneous firms face unobservable disaster risk and engage in rational Bayesian learning. The model sheds light on leverage cycles. During periods absent disasters: equity premia decrease; credit spreads decrease; expected loss-given-default increases; and leverage ratios increase. Time-since-prior-disaster is the key model conditioning variable. In response to a disaster, risk premia increase while firms sharply reduce labor, capital and leverage, with response size increasing in time-since-prior-disasters. Firms with high bankruptcy costs are most responsive to the time-since-disaster variable. Disaster responses are more pronounced than in an otherwise equivalent economy featuring observed disaster risk. Empirical tests of novel corporate finance predictions are conducted. Consistent with the model, we find empirically that leverage and investment are increasing in time-since-prior-recessions, with the effect more pronounced for firms with low recovery ratios.

Absent theoretical guidance, empiricists have been forced to rely upon numerical comparative statics from constant tax rate models in formulating testable implications of tradeoff theory in the context of natural experiments. We fill the theoretical void by solving in closed-form a dynamic tradeoff theoretic model in which corporate taxes follow a Markov process with exogenous rate changes. We simulate ideal difference-in-differences estimations, finding that constant tax rate models offer poor guidance regarding testable implications. While constant rate models predict large symmetric responses to rate changes, our model with stochastic tax rates predicts small, asymmetric, and often statistically insignificant responses. Even with very long regimes (one decade), under plausible parameterizations, the true underlying theory—that taxes matter—is incorrectly rejected in about half the simulated natural experiments. Moreover, tax response coefficients are actually smaller in simulated economies with larger tax-induced welfare losses.

The objective of applied structural microeconometrics is to identify policy-invariant parameters so alternative policies can be assessed. As we show, the practice of treating policy changes as zero probability counterfactuals violates rational expectations: Agents inside the model understand policy changes are positive probability events which the structural estimation isintended to inform. We analytically characterize the implications for moment-based parameter inference. As shown, if a policy change is optimal, inference is biased. Further, the standard identifying assumption, constant partial derivative sign, is neither necessary nor sufficient with policy control. We offer an alternative identifying assumption: constant total differential sign with inference-policy feedback. It is shown that under this assumption, rational expectations can be imposed computationally (algorithmically) to generate unbiased inference and optimal policy.The quantitative importance of these effects in applied settings is illustrated by calibrating theLeland (1994) model to the Tax Cuts and Jobs Act of 2017.

We We demonstrate limitations on the use of direct revelation mechanisms (DRMs) by corporations inhabiting economies with securities markets. Posting a standard DRM in an environment with a securities market endogenously increases the reservation value of the informed agent. If the informed agent rejects said DRM, then she convinces the market that she is uninformed, and she can trade aggressively sans price impact, generating large (off-equilibrium) trading gains. Due to this endogenous reservation value effect, using a DRM to screen out uninformed agents may be impossible. Even when screening is possible, refraining from posting a mechanism and instead relying on markets for information is optimal if the endogenous reservation value effect is sufficiently large. Finally, even if posting a DRM dominates relying on markets, outcomes are improved by introducing a search friction, which randomly limits the agent's ability to observe the DRM. Friday, September 29, 2017, 10:30-12:00 Room 126, Extranef building at the University of Lausanne Markets vs. Mechanisms∗ Raphael Boleslavsky Christopher Hennessy David L. Kelly

We demonstrate constraints on usage of direct revelation mechanisms (DRMs) by corporations inhabiting economies with securities markets. We consider a corporation seeking to acquire decision relevant information. Posting a standard DRM in an environment with a securities market endogenously increases the outside option of the informed agent. If the informed agent rejects said DRM, then she convinces the market that she is uninformed, and she can trade aggressively sans price impact, generating large (off-equilibrium) trading gains. Due to this endogenous outside option effect, using a DRM to screen out uninformed agents may be impossible. Even when screening is possible, refraining from posting a mechanism and instead relying on markets for information is optimal if the endogenous change in outside option value is sufficiently large. Finally, even if posting a DRM dominates relying on markets, outcomes are improved by introducing a search friction, which randomly limits the agent’s ability to observe the DRM, forcing the firm to sometimes rely on markets for information.

Double-blind RCTs are viewed as the gold standard in eliminating placebo effects and identifying non-placebo physiological effects. Expectancy theory posits that subjects have better present health in response to better expected future health. We show that if subjects Bayesian update about efficacy based upon physiological responses during a single-stage RCT, expected placebo effects are generally unequal across treatment and control groups. Thus, the difference between mean health across treatment and control groups is a biased estimator of the mean non-placebo physiological effect. RCTs featuring low treatment probabilities are robust: Bias approaches zero as the treated group measure approaches zero.

We develop and empirically test a theory of optimal security design under adverse selection accounting for strategic trading by uninformed investors who will liquidate a security in secondary markets only if their idiosyncratic carrying costs exceed the security's expected trading loss. Such investors demand primary market discounts equaling expected carrying costs borne plus trading losses incurred. Issuers minimize the total illiquidity discount by splitting cash-flow into tranched debt claims with liquidity predicted to increase with seniority, while the optimal number of tranches increases with underlying cash-flow risk. Empirical tests confirm our model predictions.

Double-blind RCTs are viewed as the gold standard in eliminating placebo effects and identifying non-placebo physiological effects. Expectancy theory posits that subjects have better present health in response to better expected future health. We show that if subjects Bayesian update about efficacy based upon physiological responses during a single-stage RCT, expected placebo effects are generally unequal across treatment and control groups. Thus, the difference between mean health across treatment and control groups is a biased estimator of the mean non-placebo physiological effect. RCTs featuring low treatment probabilities are robust: Bias approaches zero as the treated group measure approaches zero.

We develop and test an agency-based contingent claims model that features debt renegotiation for cross-sectional stock returns. Our model performs well for cross-sectional returns of portfolios formed on financial leverage, book-to-market equity, and asset growth portfolios, because the time-varying stock-cash flow sensitivity we estimate in a closed-form solution captures default risk over the business cycle. Moreover, our structural estimation overcomes the difficulty of finding empirical proxies for unobservable bargaining power at debt renegotiation and provides the first direct evidence that the bargaining power helps alleviate equity risk, particularly during recessions when default probabilities are high.

We show random assignment is insu¢ cient for valid inference regarding signs and magnitudes of causal eects in dynamic environments. In such settings, measured treatment responses are contingent upon the typically unmodeled policy generating process. With binary assignment, this results in signi…cant attenuation bias. With more than two policy states, treatment re- sponses can be biased downward, upward, or have the wrong sign. Further, it is not only generally invalid to extrapolate elasticities across processes, as argued by Lucas (1976), but also to extrapolate within the same policy process. We derive auxiliary assumptions beyond random assignment for valid inference in dynamic settings. If all possible policy transitions are rare events, treatment responses approximate causal eects. However, reliance on rare events is overly-restrictive as the necessary and su¢ cient condition for equality of treatment responses and causal eects is that all possible policy variable changes have mean zero. If these conditions are not met, we show how treatment responses can nevertheless be corrected and mapped back to causal eects or extrapolated to forecast responses to future policy changes within or across policy processes. A correction is also provided for structural parameter inference in dynamic treatment settings.

We argue exogenous random treatment is insufficient for valid inference regarding the sign and magnitude of causal effects in dynamic environments. In such settings, treatment responses must be understood as contingent upon the typically unmodeled policy generating process. With binary assignment, this results in quantitatively significant attenuation bias. With more than two policy states, treatment responses can be biased downward, upward, or have the wrong sign. Further, it is not only generally invalid to extrapolate elasticities across policy processes, as argued by Lucas (1976), but also to extrapolate within the same policy process. We derive auxiliary assumptions beyond exogeneity for valid inference in dynamic settings. If all possible policy transitions are rare events, treatment responses approximate causal effects. However, reliance on rare events is overly-restrictive as the necessary and sufficient conditions for equality of treatment responses and causal effects is that policy variable changes have mean zero. If these conditions are not met, we show how treatment responses can nevertheless be corrected and mapped back to causal effects or extrapolated to forecast responses to future policy changes. Christopher A. Hennessy London Business School Regents Park London NW14SA UK chennessy@london.edu Ilya A. Strebulaev Graduate School of Business Stanford University 655 Knight Way Stanford, CA 94305 and NBER istrebulaev@stanford.edu