C63 Computational Techniques; Simulation Modeling (Updated!)
Refine
Document Type
- Working Paper (5)
Language
- English (5) (remove)
Has Fulltext
- yes (5)
Is part of the Bibliography
- no (5)
Keywords
- DSGE (4)
- Numerical accuracy (4)
- Solution methods (4)
- 401(k) plan (1)
- Backward error (1)
- Condition number (1)
- Forward error (1)
- Social Security claiming (1)
- inequality (1)
- pensions (1)
Institute
- Sustainable Architecture for Finance in Europe (SAFE) (5) (remove)
This paper applies structure preserving doubling methods to solve the matrix quadratic underlying the recursive solution of linear DSGE models. We present and compare two Structure-Preserving Doubling Algorithms ( SDAs) to other competing methods – the QZ method, a Newton algorithm, and an iterative Bernoulli approach – as well as the related cyclic and logarithmic reduction algorithms. Our comparison is completed 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. We find that both SDAs perform very favorably relative to QZ, with generally more accurate solutions computed in less time. While we collect theoretical convergence results that promise quadratic convergence rates to a unique stable solution, the algorithms may fail to converge when there is a breakdown due to singularity of the coefficient matrices in the recursion. One of the proposed algorithms can overcome this problem by an appropriate (re)initialization. This SDA also performs particular well in refining solutions of different methods or from nearby parameterizations.
This paper develops and implements a backward and forward error analysis of and condition numbers for the numerical stability of the solutions of linear dynamic stochastic general equilibrium (DSGE) models. Comparing seven different solution methods from the literature, I demonstrate an economically significant loss of accuracy specifically in standard, generalized Schur (or QZ) decomposition based solutions methods resulting from large backward errors in solving the associated matrix quadratic problem. This is illustrated in the monetary macro model of Smets and Wouters (2007) and two production-based asset pricing models, a simple model of external habits with a readily available symbolic solution and the model of Jermann (1998) that lacks such a symbolic solution - QZ-based numerical solutions miss the equity premium by up to several annualized percentage points for parameterizations that either match the chosen calibration targets or are nearby to the parameterization in the literature. While the numerical solution methods from the literature failed to give any indication of these potential errors, easily implementable backward-error metrics and condition numbers are shown to successfully warn of such potential inaccuracies. The analysis is then performed for a database of roughly 100 DSGE models from the literature and a large set of draws from the model of Smets and Wouters (2007). While economically relevant errors do not appear pervasive from these latter applications, accuracies that differ by several orders of magnitude persist.
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.
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.
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.