Estimating natural rate of unemployment (NAIRU) is important for understanding the joint dynamics of unemployment, inflation, and inflation expectation. However, existing literature falls short in endogenizing inflation expectation together with NAIRU in a model consistent way. We develop and estimate a structural model with forward and backward looking Phillips curve. Inflation expectation is treated as a function of state variables and we use survey data as its observations. We find out that the estimated NAIRU using our methodology tracks the unemployment process closely except for the high inflation period around 1970. Moreover, the estimated Bayesian credible sets are narrower and our model leads to better inflation and unemployment forecasts. These results suggest that monetary policy was very effective during the sample periods and there was not much room for policy improvement.