The equilibrium real interest rate (r*) is the short-term real interest rate that, in the long run, is consistent with aggregate production at potential and stable inflation. Estimation of r* faces considerable econometric and empirical challenges. On the econometric front, classical inference confronts the "pile-up" problem. Empirically, the co-movement of output, inflation, unemployment, and real interest rates is too weak to yield precise estimates of r*. These challenges are addressed by applying Bayesian methods and examining the role of several "demand shifters", including asset prices, fiscal policy, and credit conditions. We find that the data provide relatively little information on the r* data-generating process, as the posterior distribution of this process lies very close to its prior. This result contrasts sharply with those for the trend growth or natural rate of unemployment processes. Second, credit spreads are very important for the estimated links between output and interest rates and hence for estimates of r*. Estimates of r* that account for this range of considerations are more stable than other estimates, with r* at the end of 2014 equal to approximately 1-1/4 percent.