Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. www.econstor.eu Terms of use: Documents in Working Paper SeriesThe risk premium channel and long-term growth No 2114 / December 2017 AbstractWe study a quantitative DSGE model linking a state of the art asset pricing framework à la Kung and Schmid (2015) with a constraint on leverage as in Gertler and Kiyotaki (2010). We show that a mere increase in the probability of firms being financially constrained leads to an increase in risk premia. Even for a small adverse shock to productivity a drop in asset valuation restrains firms from outside financing and by that induces a persistent low growth environment. In our framework a constraint on leverage induces countercyclical risk premia in equity markets even when it does not bind.Keywords: risk premia, financial accelerator, asset pricing, endogenous growthECB Working Paper Series No 2114 / December 2017 1 Non-technical summaryThe Financial Crisis of 2007-08 was characterised by a steep drop in consumption and output followed by protracted low real growth. At the same time global financial markets underwent a period of great uncertainty and volatility followed by excess returns in equities. In this paper we attempt to link these two phenomena and try to answer the question how excess leverage could increase risk premia and how to align the deleveraging of the firm with overall low growth rates in the aftermath of a joint downturn of the real economy and financial markets.To this end, we then built a DSGE model that combines a state-of-the-art asset pricing framework with a standard financial accelerator mechanism and show that these, on the face of it, two distinct phenomenona can be explained jointly.More specifically, in our framework output growth is endogenously generated by innovators, which are solely financed by equity and develop new products used in the production of final goods. The production sector is owned by a financial intermediary acquiring outside financing from households and features financial accelerator characteristics. The ability to acquire funds from households is limited as the household will only lend to viable (likely to pay back equity) intermediaries. The agents in our economy care about long-run fluctuations in consumption growth.Our model is able to generate a low and stable risk free rate and a sizable and countercyclical equity risk premium. We explain in the paper how risk premia affect growth dynamics: an initial adverse productivity shock lowers interest rates as safe as...

The analysis of dynamic economic models routinely leads to the mathematical problem of determining an unknown function for which no closed-form solution exists. Economists must then resort to methods of numerical approximation when analyzing such models. Among the computational methods that have been successfully applied in economics and finance, one set of techniques stands out due to its flexibility and robustness: projection methods. In this article, we describe the basic steps of these methods for several different applications, surveying many successful applications of projection methods to dynamic economic models. Importantly, we emphasize that the ever-increasing complexity and dimensionality of dynamic models have made the previously used simpler methods obsolete and the applications of projection methods all but mandatory. We closely examine the most recent endeavors in the literature on solving economic models with projection methods. Expected final online publication date for the Annual Review of Economics, Volume 12 is August 3, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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