## C63 Computational Techniques; Simulation Modeling (Updated!)

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This paper presents and compares Bernoulli iterative approaches for solving linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. I find that Bernoulli methods compare favorably in solving DSGE models to the QZ, providing similar accuracy as measured by the forward error of the solution at a comparable computation burden. The method can guarantee convergence to a particular, e.g., unique stable, solution and can be combined with other iterative methods, such as the Newton method, lending themselves especially to refining solutions.

Crowdfunding platforms offer project initiators the opportunity to acquire funds from the Internet crowd and, therefore, have become a valuable alternative to traditional sources of funding. However, some processes on crowdfunding platforms cause undesirable external effects that influence the funding success of projects. In this context, we focus on the phenomenon of project overfunding. Massively overfunded projects have been discussed to overshadow other crowdfunding projects which in turn receive less funding. We propose a funding redistribution mechanism to internalize these overfunding externalities and to improve overall funding results. To evaluate this concept, we develop and deploy an agent-based model (ABM). This ABM is based on a multi-attribute decision-making approach and is suitable to simulate the dynamic funding processes on a crowdfunding platform. Our evaluation provides evidence that possible modifications of the crowdfunding mechanisms bear the chance to optimize funding results and to alleviate existing flaws.

Many nations incentivize retirement saving by letting workers defer taxes on pension contributions, imposing them when retirees withdraw their funds. Using a dynamic life cycle model, we show how ‘Rothification’ – that is, taxing 401(k) contributions rather than payouts – alters saving, investment, consumption, and Social Security claiming patterns. We find that taxing pension contributions instead of withdrawals leads to delayed retirement, somewhat lower lifetime tax payments, and relatively small reductions in consumption. Indeed, the two tax regimes generate quite similar relative inequality metrics: the relative consumption inequality ratio under TEE is only four percent higher than in the EET case. Moreover, results indicate that the Gini measures are also strikingly similar under the EET and the TEE regimes for lifetime consumption, cash on hand, and 401(k) assets, differing by only 1-4 percent. While tax payments are higher early in life under the TEE regime, they are slightly lower in the long run. Moreover, higher EET tax payments are also accompanied by higher volatility. We therefore find few reasons for policymakers to favor either tax approach on egalitarian or revenue-enhancing grounds.

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.

The authors present and compare Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. They find that Newton-based methods compare favorably in solving DSGE models, providing higher accuracy as measured by the forward error of the solution at a comparable computation burden. The methods, however, suffer from their inability to guarantee convergence to a particular, e.g. unique stable, solution, but their iterative procedures lend themselves to refining solutions either from different methods or parameterizations.