C61 Optimization Techniques; Programming Models; Dynamic Analysis
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We present a tractable model of the effects of nonfinancial risk on intertemporal choice. Our purpose is to provide a simple framework that can be adopted in fields like representative-agent macroeconomics, corporate finance, or political economy, where most modelers have chosen not to incorporate serious nonfinancial risk because available methods were too complex to yield transparent insights. Our model produces an intuitive analytical formula for target assets, and we show how to analyze transition dynamics using a familiar Ramsey-style phase diagram. Despite its starkness, our model captures most of the key implications of nonfinancial risk for intertemporal choice.
We model the motives for residents of a country to hold foreign assets, including the precautionary motive that has been omitted from much previous literature as intractable. Our model captures many of the principal insights from the existing specialized literature on the precautionary motive, deriving a convenient formula for the economy’s target value of assets. The target is the level of assets that balances impatience, prudence, risk, intertemporal substitution, and the rate of return. We use the model to shed light on two topical questions: The “upstream” flows of capital from developing countries to advanced countries, and the long-run impact of resorbing global financial imbalances
This paper proposes a new approach for modeling investor fear after rare disasters. The key element is to take into account that investors’ information about fundamentals driving rare downward jumps in the dividend process is not perfect. Bayesian learning implies that beliefs about the likelihood of rare disasters drop to a much more pessimistic level once a disaster has occurred. Such a shift in beliefs can trigger massive declines in price-dividend ratios. Pessimistic beliefs persist for some time. Thus, belief dynamics are a source of apparent excess volatility relative to a rational expectations benchmark. Due to the low frequency of disasters, even an infinitely-lived investor will remain uncertain about the exact probability. Our analysis is conducted in continuous time and offers closed-form solutions for asset prices. We distinguish between rational and adaptive Bayesian learning. Rational learners account for the possibility of future changes in beliefs in determining their demand for risky assets, while adaptive learners take beliefs as given. Thus, risky assets tend to be lower-valued and price-dividend ratios vary less under adaptive versus rational learning for identical priors. Keywords: beliefs, Bayesian learning, controlled diffusions and jump processes, learning about jumps, adaptive learning, rational learning. JEL classification: D83, G11, C11, D91, E21, D81, C61
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.
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.
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.
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.
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.
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.