Slide 10. The Basic Model

$$\mathrm{Equation\ 1}: x_{t}=E_{t}x_{t+1}-\sigma\left(\hat{\imath}_{t}-E_{t}\pi_{t+1}-\hat{r}_{t}^{n}\right)$$ $$\mathrm{Equation\ 2}: \pi_{t}=\kappa x_{t} + \beta E_{t}\pi_{t+1}$$ $$\mathrm{Equation\ 3}: \hat{\imath}_{t}=\overline{i_{t}}+\phi_{\pi}\left(\pi_{t}-\bar{\pi}\right)+\phi_{x}\left(x_{t}-\bar{x}\right)/4$$

where
$x_{t}$ is the output gap, $\hat{y}_{t}-\hat{y}_{t}^{n}$;
$\hat{y}_{t}^{n}$ is an exogenous variable, representing variations in the natural rate of output;
$\pi_{t}$ is the rate of inflation;
$\hat{\imath}_{t}$ is the interest rate;
$\overline{i_{t}}$ is an exogenous, possibly time-varying, intercept of the Taylor Rule.

Slide 11. Figure: Estimates of the Real Natural Rate of Interest from Different Macroeconomic Models

Quarterly
Percent
Period Minimum estimate Average estimate Maximum estimate
1985:Q3 1.75 4.26 8.20
1985:Q4 1.43 4.48 7.02
1986:Q1 2.59 4.38 6.21
1986:Q2 -1.51 2.35 4.89
1986:Q3 -4.60 1.44 3.93
1986:Q4 3.34 4.61 7.01
1987:Q1 3.63 6.31 11.62
1987:Q2 3.76 4.51 4.92
1987:Q3 1.80 3.37 4.14
1987:Q4 3.14 3.97 4.91
1988:Q1 3.16 5.77 8.03
1988:Q2 2.88 4.81 5.85
1988:Q3 4.32 7.21 10.87
1988:Q4 4.18 5.85 6.66
1989:Q1 5.19 6.41 8.55
1989:Q2 4.86 6.08 7.06
1989:Q3 3.81 6.01 6.99
1989:Q4 4.97 8.05 12.40
1990:Q1 2.13 4.95 6.30
1990:Q2 5.14 8.13 12.27
1990:Q3 3.68 6.83 10.34
1990:Q4 3.26 5.00 6.38
1991:Q1 2.14 4.02 6.09
1991:Q2 1.89 3.81 6.14
1991:Q3 0.55 1.80 2.50
1991:Q4 -1.34 0.73 2.24
1992:Q1 0.75 2.92 7.26
1992:Q2 -4.96 -0.64 1.43
1992:Q3 -1.35 1.05 3.14
1992:Q4 0.00 1.20 1.94
1993:Q1 -0.44 0.38 2.17
1993:Q2 -0.11 1.47 2.44
1993:Q3 0.79 3.31 4.89
1993:Q4 -0.46 0.43 1.31
1994:Q1 1.04 2.01 2.71
1994:Q2 1.57 2.96 5.26
1994:Q3 2.32 4.67 7.23
1994:Q4 2.59 3.19 3.78
1995:Q1 3.23 5.12 9.11
1995:Q2 2.71 5.69 8.99
1995:Q3 2.80 4.26 5.67
1995:Q4 2.66 3.67 4.84
1996:Q1 1.97 3.97 5.79
1996:Q2 1.12 2.79 3.78
1996:Q3 2.75 3.54 4.45
1996:Q4 2.86 4.52 6.30
1997:Q1 3.05 4.39 5.80
1997:Q2 2.66 4.07 5.20
1997:Q3 3.98 4.95 5.97
1997:Q4 3.40 4.87 5.43
1998:Q1 3.18 4.61 6.74
1998:Q2 3.50 5.32 7.32
1998:Q3 3.55 4.44 5.07
1998:Q4 2.07 3.02 3.87
1999:Q1 3.00 4.68 7.73
1999:Q2 2.80 3.78 4.63
1999:Q3 3.02 3.80 4.65
1999:Q4 4.19 6.35 9.47
2000:Q1 3.53 5.18 7.48
2000:Q2 4.91 6.36 9.43
2000:Q3 3.92 6.35 10.40
2000:Q4 3.77 6.32 9.29
2001:Q1 1.34 5.23 6.89
2001:Q2 -0.21 3.26 4.98
2001:Q3 -1.32 1.65 3.14
2001:Q4 -5.71 -0.47 4.28
2002:Q1 -3.08 -0.96 1.32
2002:Q2 -2.58 0.06 2.88
2002:Q3 -3.96 -0.83 2.80
2002:Q4 -2.20 0.94 2.80
2003:Q1 -3.23 -0.86 2.18
2003:Q2 -6.69 -2.12 0.59
2003:Q3 -4.68 -1.99 -0.11
2003:Q4 -2.69 -1.48 0.81
2004:Q1 -1.88 -0.29 1.44
2004:Q2 -3.70 -1.82 0.11
2004:Q3 -1.75 -0.26 1.52
2004:Q4 -1.27 0.01 1.36
2005:Q1 -2.32 -0.37 1.30
2005:Q2 -0.94 0.78 2.76
2005:Q3 -1.88 0.64 2.86
2005:Q4 0.09 2.32 3.66
2006:Q1 0.04 1.57 3.48
2006:Q2 0.70 3.48 5.34
2006:Q3 0.83 3.13 5.36
2006:Q4 1.83 5.13 6.66
2007:Q1 1.76 4.29 5.89
2007:Q2 1.92 2.85 4.48
2007:Q3 2.39 3.55 4.75
2007:Q4 1.31 3.19 4.67
2008:Q1 0.81 3.41 4.56
2008:Q2 -0.49 1.61 4.13
2008:Q3 -2.37 0.11 2.42
2008:Q4 -2.82 0.64 3.17
2009:Q1 -9.00 -2.32 2.19
2009:Q2 -10.69 -3.92 0.99
2009:Q3 -13.26 -6.03 -2.59
2009:Q4 -8.73 -5.43 -3.18
2010:Q1 -8.73 -4.76 -1.70
2010:Q2 -10.79 -5.22 -2.34
2010:Q3 -6.68 -3.56 -1.25
2010:Q4 -5.74 -2.82 -0.38
2011:Q1 -3.74 -2.27 -0.93
2011:Q2 -4.95 -3.07 -1.41
2011:Q3 -3.89 -2.77 -0.49
2011:Q4 -10.65 -5.28 -2.59
2012:Q1 -5.37 -2.93 -1.21
2012:Q2 -6.86 -3.62 -1.78
2012:Q3 -5.80 -3.20 -1.67
2012:Q4 -5.50 -3.06 -1.05
2013:Q1 -5.99 -3.19 -1.06
2013:Q2 -4.49 -2.86 -1.16
2013:Q3 -5.22 -3.19 -1.48
2013:Q4 -3.47 -1.35 0.31
2014:Q1 -3.18 -2.34 -1.55
2014:Q2 -4.37 -2.41 -0.96
2014:Q3 -3.05 -1.88 -0.45
2014:Q4 -0.73 0.32 2.44
2015:Q1 -2.23 -0.96 0.49
2015:Q2 -0.99 -0.46 -0.08
2015:Q3 -0.87 -0.35 -0.07

*This exhibit was drawn from figure 1 in Janet Yellen, "The Economic Outlook and Monetary Policy," remarks at the Economic Club of Washington, December 2.

Note: The shaded bars indicate periods of business recession as defined by the National Bureau of Economic Research: July 1990-March 1991, March 2001-November 2001, and December 2007-June 2009.

Source: The estimates are drawn from four models: (1) a dynamic stochastic general equilibrium (DSGE) model developed by the staff of the Federal Reserve Board and described in Kiley (2013); (2) a DSGE model developed by the staff of the Federal Reserve Bank of New York and described in Del Negro and others (2013); (3) a DSGE model developed by the staff of the Federal Reserve Board based on Christiano, Motto, and Rostagno (2014); and (4) a DSGE model developed by the staff of the Federal Reserve Board based on Guerrieri and Iacoviello (2013 [rev. 2014]).

Last Update: May 19, 2016