Do Higher Order Approximations Help Identify Structural Parameters?

In my first chapter I analyze whether second order and higher approximations to DSGE models help identify structural parameters in theory and empirical calibration. I discuss a method to obtain the numerical derivative of higher order approximation terms with respect to a model's structural parameters. I discuss a necessary condition that if this Jacobian is not full rank then all parameters are not identified. I show that in a simple growth model using a second order approximation will satisfy this necessary condition for local identification. Finally, I show that in a large new Keynesian model several structural parameters are not locally identified with a first order approximation estimation routine. I observe problems in jointly identifying the discount factor and inflation target for this class of models. Using a second order approximation I show that the necessary condition for local identification is met for a large set of structural parameters. In my second chapter I use a New Keynesian model with Ricardian and non-Ricardian agents to analyze the effectiveness of fiscal policy. To estimate the structural parameters of this model I use a second order approximation to the policy functions with a Bayesian likelihood approach. From the estimated model I calculate present value multipliers. I show that these multipliers vary with the size of the shock being used to generate the impulse and the state variables of the economy. I discuss the implications of this finding for policymakers by showing the evolution of fiscal multipliers over the last decade. My estimated model implies that the government consumption multiplier is countercyclical and the government transfer multiplier increases with the size of the initial shock.

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