Frequency domain analysis of DSGE and stochastic volatility models
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In this dissertation, we use frequency domain methods to address issues related to identification and estimation in linearized dynamic stochastic general equilibrium (DSGE) and stochastic volatility models. The first chapter provides a necessary and sufficient condition for the local identification of the structural parameters based on the (first and) second order properties of the linearized DSGE model. The condition is flexible and simple to verify. It is extended to study identification through a subset of frequencies, partial identification, conditional identification, and constrained identification. When lack of identification is detected, the method can be used to trace out nonidentification curves. For estimation in nonsingular systems, we consider a frequency domain quasi-maximum likelihood (FDQML) estimator and present its asymptotic properties, which can be different from existing results due to the structure of the DSGE model. Finally, we discuss a quasi-Bayesian procedure for estimation and inference that can incorporate relevant prior distributions and is computationally attractive. The second chapter analyzes a popular medium scale DSGE model of Smets and Wouters (2007) using the framework developed in the previous chapter. For identification, in addition to checking parameter identifiability, we derive the corresponding nonidentification curve. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to find notably different parameter values and impulse response functions. A further comparison between the non-parametrically estimated and model implied spectra suggests that the business cycle based method delivers better estimates of the features that the model is intended to capture. The final chapter proposes an FDQML estimator of the integrated volatility of financial assets in the noisy high frequency data setting. The approach allows for the microstructure noise to be a stationary linear process, and is analytically tractable. In practice, we approximate the noise process by a finite order autoregression, where the order is chosen using the Akaike information criterion (AIC). The simulation study shows that the finite sample performance of the estimator is very similar to its time domain analogue in the case of i.i.d. noise, and is substantially better when more sophisticated noise specifications are considered .
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