Essays on trend inflation: Optimal policy, estimation bias, and unemployment volatility

In this dissertation, I cover the theoretical effects of positive trend inflation on welfare, monetary policy, estimation biases, and unemployment volatility.;In the first chapter, I derive the welfare-based loss function under positive trend inflation and find the optimal policy to be followed by a welfare-concerned central bank when assigned an inflation target that is not necessarily welfare-optimal. In this regard, I treat the inflation target as the trend inflation. The main findings are that the relative weight on the volatility of the output gap decreases with trend inflation in the welfare-based loss function. As for the optimal policy, positive trend inflation makes it even more inertial than the standard time-consistent optimal policy suggests.;In the second chapter, I build large artificial data sets (2,000,000 quarters) from a nonlinear DSGE model to test whether the common use of loglinearized models to approximate the likelihood function on inference exercises can account for the puzzle between micro versus macro evidence on Calvo parameter of price rigidity. The puzzle is then explained by estimation inconsistency by using the wrong model: loglinearized version instead of the nonlinear model. I find that the estimation bias is significant, can explain the puzzle, and is present even when the trend inflation is zero.;In the third chapter, I show that positive trend inflation may account for the large relative volatilities found in US data in the labor market. My model has no wage rigidity, has standard preference and production functions, and is only affected by the aggregate homogeneous productivity shock. The main mechanism is due to the distortionary effects of the inflation trend in reducing both the workers' and firms' surpluses on average. As a consequence, small movements in productivity have great impact in the total surplus. Therefore larger inflation trends have magnifying effects in unemployment fluctuation.