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Dynamic Stochastic General Equilibrium (DSGE) models are often solved and estimated under specific assumptions as to whether the exogenous variables are difference or trend stationary. However, even mild departures of the data generating process from these assumptions can severely bias the estimates of the model parameters. This paper proposes new estimators that do not require researchers to take a stand on whether shocks have permanent or transitory effects. These procedures have two key features. First, the same filter is applied to both the data and the model variables. Second, the filtered variables are stationary when evaluated at the true parameter vector. The estimators are approximately normally distributed not only when the shocks are mildly persistent, but also when they have near or exact unit roots. Simulations show that these robust estimators perform well especially when the shocks are highly persistent yet stationary. In such cases, linear detrending and first differencing are shown to yield biased or imprecise estimates.

Estimation of DSGE Models When the Data are Persistent