C61 Optimization Techniques; Programming Models; Dynamic Analysis
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This chapter aims to provide a hands-on approach to New Keynesian models and their uses for macroeconomic policy analysis. It starts by reviewing the origins of the New Keynesian approach, the key model ingredients and representative models. Building blocks of current-generation dynamic stochastic general equilibrium (DSGE) models are discussed in detail. These models address the famous Lucas critique by deriving behavioral equations systematically from the optimizing and forward-looking decision-making of households and firms subject to well-defined constraints. State-of-the-art methods for solving and estimating such models are reviewed and presented in examples. The chapter goes beyond the mere presentation of the most popular benchmark model by providing a framework for model comparison along with a database that includes a wide variety of macroeconomic models. Thus, it offers a convenient approach for comparing new models to available benchmarks and for investigating whether particular policy recommendations are robust to model uncertainty. Such robustness analysis is illustrated by evaluating the performance of simple monetary policy rules across a range of recently-estimated models including some with financial market imperfections and by reviewing recent comparative findings regarding the magnitude of government spending multipliers. The chapter concludes with a discussion of important objectives for on-going and future research using the New Keynesian framework.
We introduce a new measure of systemic risk, the change in the conditional joint probability of default, which assesses the effects of the interdependence in the financial system on the general default risk of sovereign debtors. We apply our measure to examine the fragility of the European financial system during the ongoing sovereign debt crisis. Our analysis documents an increase in systemic risk contributions in the euro area during the post-Lehman global recession and especially after the beginning of the euro area sovereign debt crisis. We also find a considerable potential for cascade effects from small to large euro area sovereigns. When we investigate the effect of sovereign default on the European Union banking system, we find that bigger banks, banks with riskier activities, with poor asset quality, and funding and liquidity constraints tend to be more vulnerable to a sovereign default. Surprisingly, an increase in leverage does not seem to influence systemic vulnerability.
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.
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.
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.
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.
Inflation-targeting central banks have only imperfect knowledge about the effect of policy decisions on inflation. An important source of uncertainty is the relationship between inflation and unemployment. This paper studies the optimal monetary policy in the presence of uncertainty about the natural unemployment rate, the short-run inflation-unemployment tradeoff and the degree of inflation persistence in a simple macroeconomic model, which incorporates rational learning by the central bank as well as private sector agents. Two conflicting motives drive the optimal policy. In the static version of the model, uncertainty provides a motive for the policymaker to move more cautiously than she would if she knew the true parameters. In the dynamic version, uncertainty also motivates an element of experimentation in policy. I find that the optimal policy that balances the cautionary and activist motives typically exhibits gradualism, that is, it still remains less aggressive than a policy that disregards parameter uncertainty. Exceptions occur when uncertainty is very high and in inflation close to target.
The authors propose a new method to forecast macroeconomic variables that combines two existing approaches to mixed-frequency data in DSGE models. The first existing approach estimates the DSGE model in a quarterly frequency and uses higher frequency auxiliary data only for forecasting. The second method transforms a quarterly state space into a monthly frequency. Their algorithm combines the advantages of these two existing approaches.They compare the new method with the existing methods using simulated data and real-world data. With simulated data, the new method outperforms all other methods, including forecasts from the standard quarterly model. With real world data, incorporating auxiliary variables as in their method substantially decreases forecasting errors for recessions, but casting the model in a monthly frequency delivers better forecasts in normal times.
Academic contributions on the demutualization of stock exchanges so far have been predominantly devoted to social welfare issues, whereas there is scarce empirical literature referring to the impact of a governance change on the exchange itself. While there is consensus that the case for demutualization is predominantly driven by the need to improve the exchange's competitiveness in a changing business environment, it remains unclear how different governance regimes actually affect stock exchange performance. Some authors propose that a public listing is the best suited governance arrangement to improve an exchange's competitiveness. By employing a panel data set of 28 stock exchanges for the years 1999-2003 we seek to shed light on this topic by comparing the efficiency and productivity of exchanges with differing governance arrangements. For this purpose we calculate in a first step individual efficiency and productivity values via DEA. In a second step we regress the derived values against variables that - amongst others - map the institutional arrangement of the exchanges in order to determine efficiency and productivity differences between (1) mutuals (2) demutualized but customer-owned exchanges and (3) publicly listed and thus at least partly outsider-owned exchanges. We find evidence that demutualized exchanges exhibit higher technical efficiency than mutuals. However, they perform relatively poor as far as productivity growth is concerned. Furthermore, we find no evidence that publicly listed exchanges possess higher efficiency and productivity values than demutualized exchanges with a customer-dominated structure. We conclude that the merits of outside ownership lie possibly in other areas such as solving conflicts of interest between too heterogeneous members.
In recent years stock exchanges have been increasingly diversifying their operations into related business areas such as derivatives trading, post-trading services and software sales. This trend can be observed most notably among profit-oriented trading venues. While the pursuit for diversification is likely to be driven by the attractiveness of these investment opportunities, it is yet an open question whether certain integration activities are also efficient, both from a social welfare and from the exchanges' perspective. Academic contributions so far analyzed different business models primarily from the social welfare perspective, whereas there is only little literature considering their impact on the exchange itself. By employing a panel data set of 28 stock exchanges for the years 1999-2003 we seek to shed light on this topic by comparing the factor productivity of exchanges with different business models. Our findings suggest three conclusions: (1) Integration activity comes at the cost of increased operational complexity which in some cases outweigh the potential synergies between related activities and therefore leads to technical inefficiencies and lower productivity growth. (2) We find no evidence that vertical integration is more efficient and productive than other business models. This finding could contribute to the ongoing discussion about the merits of vertical integration from a social welfare perspective. (3) The existence of a strong in-house IT-competence seems to be beneficial to overcome.