Through the Looking Glass: Indirect Inference via Simple Equilibria

A two-step indirect inference approach to estimate the long-run risk asset pricing model

“…However, the simplification comes at the cost of an inconsistency: When simulating the LRR model usingz * andz * m , the means of the simulated z t and z m,t series will be different from the fixed values. For example, using the LRR model parameter values calibrated by BY, andz * = 6.96 andz * m = 5.95, as chosen by Calvet and Czellar (2015), to simulate LRR model-implied data series with T =100k, we obtain a sample mean of the log price-consumption ratio equal to 5.87 and a sample mean of the log price-dividend ratio equal to 5.19. These differences are large in economic terms.…”

“…The formulas for the time aggregation of the LRR model variables over h periods, provided by Calvet and Czellar (2015), are as follows: The first-step auxiliary parameter vector θ M = (θ HAR , µ g , σ g ) is defined by the moment conditions:…”

“…Some subsequent empirical studies report estimates of all LRR model parameters though, sometimes with remarkable precision (Constantinides and Ghosh, 2011;Hasseltoft, 2012;Bansal, Kiku, and Yaron, 2012b). Calvet and Czellar (2015) estimate a simplified version of the LRR model using an exactly identifying auxiliary model with an indirect inference estimation approach. They also report estimates of all model parameters, but their simplification, which greatly facilitates the model simulation, is not without implications (see Section 2.2).…”

“…The appropriate formulas are provided byCalvet and Czellar (2015) and given in Appendix A.3. 7 A similar philosophy is pursued byCecchetti, Lam, and Nelson (1993), who estimate by GMM the parameters of the endowment process in a macro asset pricing model in a first step, while computing confidence bounds for the investor's preference parameters in a second stage.…”

A Two-Step Indirect Inference Approach to Estimate the Long-Run Risk Asset Pricing Model

“…Some subsequent empirical studies report estimates of all LRR model parameters though, sometimes with remarkable precision (Constantinides and Ghosh, 2011;Hasseltoft, 2012;Bansal, Kiku, and Yaron, 2012b). Calvet and Czellar (2015) estimate a simplified version of the LRR model using an exactly identifying auxiliary model with an indirect inference estimation approach. They also report estimates of all model parameters, but their simplification, which greatly facilitates the model simulation, is not without implications (see Section 2.2).…”