C32 Time-Series Models; Dynamic Quantile Regressions (Updated!)
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A common practice in empirical macroeconomics is to examine alternative recursive orderings of the variables in structural vector autogressive (VAR) models. When the implied impulse responses look similar, the estimates are considered trustworthy. When they do not, the estimates are used to bound the true response without directly addressing the identification challenge. A leading example of this practice is the literature on the effects of uncertainty shocks on economic activity. We prove by counterexample that this practice is invalid in general, whether the data generating process is a structural VAR model or a dynamic stochastic general equilibrium model.
Search costs for lenders when evaluating potential borrowers are driven by the quality of the underwriting model and by access to data. Both have undergone radical change over the last years, due to the advent of big data and machine learning. For some, this holds the promise of inclusion and better access to finance. Invisible prime applicants perform better under AI than under traditional metrics. Broader data and more refined models help to detect them without triggering prohibitive costs. However, not all applicants profit to the same extent. Historic training data shape algorithms, biases distort results, and data as well as model quality are not always assured. Against this background, an intense debate over algorithmic discrimination has developed. This paper takes a first step towards developing principles of fair lending in the age of AI. It submits that there are fundamental difficulties in fitting algorithmic discrimination into the traditional regime of anti-discrimination laws. Received doctrine with its focus on causation is in many cases ill-equipped to deal with algorithmic decision-making under both, disparate treatment, and disparate impact doctrine. The paper concludes with a suggestion to reorient the discussion and with the attempt to outline contours of fair lending law in the age of AI.
Search costs for lenders when evaluating potential borrowers are driven by the quality of the underwriting model and by access to data. Both have undergone radical change over the last years, due to the advent of big data and machine learning. For some, this holds the promise of inclusion and better access to finance. Invisible prime applicants perform better under AI than under traditional metrics. Broader data and more refined models help to detect them without triggering prohibitive costs. However, not all applicants profit to the same extent. Historic training data shape algorithms, biases distort results, and data as well as model quality are not always assured. Against this background, an intense debate over algorithmic discrimination has developed. This paper takes a first step towards developing principles of fair lending in the age of AI. It submits that there are fundamental difficulties in fitting algorithmic discrimination into the traditional regime of anti-discrimination laws. Received doctrine with its focus on causation is in many cases ill-equipped to deal with algorithmic decision-making under both, disparate treatment, and disparate impact doctrine. The paper concludes with a suggestion to reorient the discussion and with the attempt to outline contours of fair lending law in the age of AI.
Linear rational-expectations models (LREMs) are conventionally "forwardly" estimated as follows. Structural coefficients are restricted by economic restrictions in terms of deep parameters. For given deep parameters, structural equations are solved for "rational-expectations solution" (RES) equations that determine endogenous variables. For given vector autoregressive (VAR) equations that determine exogenous variables, RES equations reduce to reduced-form VAR equations for endogenous variables with exogenous variables (VARX). The combined endogenous-VARX and exogenous-VAR equations comprise the reduced-form overall VAR (OVAR) equations of all variables in a LREM. The sequence of specified, solved, and combined equations defines a mapping from deep parameters to OVAR coefficients that is used to forwardly estimate a LREM in terms of deep parameters. Forwardly-estimated deep parameters determine forwardly-estimated RES equations that Lucas (1976) advocated for making policy predictions in his critique of policy predictions made with reduced-form equations.
Sims (1980) called economic identifying restrictions on deep parameters of forwardly-estimated LREMs "incredible", because he considered in-sample fits of forwardly-estimated OVAR equations inadequate and out-of-sample policy predictions of forwardly-estimated RES equations inaccurate. Sims (1980, 1986) instead advocated directly estimating OVAR equations restricted by statistical shrinkage restrictions and directly using the directly-estimated OVAR equations to make policy predictions. However, if assumed or predicted out-of-sample policy variables in directly-made policy predictions differ significantly from in-sample values, then, the out-of-sample policy predictions won't satisfy Lucas's critique.
If directly-estimated OVAR equations are reduced-form equations of underlying RES and LREM-structural equations, then, identification 2 derived in the paper can linearly "inversely" estimate the underlying RES equations from the directly-estimated OVAR equations and the inversely-estimated RES equations can be used to make policy predictions that satisfy Lucas's critique. If Sims considered directly-estimated OVAR equations to fit in-sample data adequately (credibly) and their inversely-estimated RES equations to make accurate (credible) out-of-sample policy predictions, then, he should consider the inversely-estimated RES equations to be credible. Thus, inversely-estimated RES equations by identification 2 can reconcile Lucas's advocacy for making policy predictions with RES equations and Sims's advocacy for directly estimating OVAR equations.
The paper also derives identification 1 of structural coefficients from RES coefficients that contributes mainly by showing that directly estimated reduced-form OVAR equations can have underlying LREM-structural equations.