Density-Conditional Forecasts in Dynamic Multivariate Models

Abstract

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. Abstract When generating conditional forecasts in dynamic models it is common to impose the conditions as restrictions on future structural shocks. However, these conditional forecasts often ignore that there may be uncertainty about the future development of the restricted variables. Our paper therefore proposes a generalization such that the conditions can be given as the full distribution of the restricted variables. We demonstrate, in two empirical applications, that ignoring the uncertainty about the conditions implies that the distributions of the unrestricted variables are too narrow. Terms of use: Documents in

Conditional Forecasts in Large Bayesian VARs with Multiple Soft and Hard Constraints

“…Examples along this line of work include Andersson, Palmqvist, and Waggoner (2010), Giannone, Lenza, Pill, and Reichlin (2012); Giannone, Lenza, Momferatou, and Onorante (2014), Altavilla, Giannone, andLenzaa (2016), Aastveit, Carriero, Clark, andMarcellino (2017), Giannone, Lenza, and Reichlin (2019), and Tallman and Zaman (2020). In practice, assuming that the conditions are generated by all structural shocks of the model may be undesirable and economically irrelevant, and there are, therefore, reasons to prefer a more structural approach, where the conditional forecasts are obtained from a sequence of specific shocks derived from a (point or set) identified structural VAR.…”

“…3,4 A second and equally important consideration when producing conditional forecasts is whether one wants to fix the future paths of the conditioned variables at specific values (i.e., hard or equality conditions) or instead prefers to allow the future values of the conditioned variables to lie within a certain range (i.e., inequality conditions). The equality constraint case is the most commonly employed approach in the literature (see again Giannone, Lenza, Pill, and Reichlin (2012); Giannone, Lenza, Momferatou, and Onorante (2014) as well as Jarocinski and Smets (2008) and Lenza, Pill, and Reichlin (2010)), while to date there has been only limited work with inequality constrained conditional forecasts (in addition to Waggoner and Zha (1999), see also Andersson, Palmqvist, and Waggoner (2010)). This is largely due to the computational challenges that the inequality constraints entail.…”

“…In addition, inequality constraints allow the forecaster to acknowledge the uncertainty surrounding the future realization path of the constrained endogenous variables. For example, Andersson, Palmqvist, and Waggoner (2010) show that ignoring the uncertainty about the conditions can lead to density forecasts of the unrestricted variables that are too narrow.…”

“…Third, our approach can be used to produce conditional forecasts and structural scenario analysis under both equality and inequality conditions without compromising the computational efficiency and scalability of the algorithm. This is in contrast to the traditional methods available in the literature, such as Waggoner and Zha (1999) and Andersson, Palmqvist, and Waggoner (2010). 5 To accomplish this, we pair the use of the precision sampler of Chan and Jeliazkov (2009) to the exponential minimax tilting method of Botev (2017), which allows us 5 Andersson, Palmqvist, and Waggoner (2010) show how to implement the inequality restrictions using a Gibbs sampler instead of the original accept-reject method introduced in Waggoner and Zha (1999).…”

“…We show that our approach generates exactly the same conditional forecasts and credible sets as the three existing methods but is substantially less demanding computationally. Next, we investigate the accuracy and computational efficiency of our inequality constraint precision-based approach algorithm by comparing it against the Zha (1999), andAndersson, Palmqvist, andWaggoner (2010) accept-reject methods (both Ba ńbura, Giannone, and Lenza (2015) and Antolín-Díaz, Petrella, and Rubio-Ramírez (2021) are not designed to generate conditional forecasts in the presence of inequality constraints) and once again find that our inequality constraint algorithm is significantly faster than the existing alternatives. For example, using the Waggoner and Zha (1999) algorithm, it takes about 80 and 459 minutes to generate the inand out-of-sample conditional forecasts from a small dimension VAR with only one inequality constraint.…”