TheFRB and CBO have recently projected the evolution of key macroeconomic variables including real GDP and the rate of unemployment. In our blog, we have developed a very accurate model linking the rate of unemployment in the US to the rate of real GDP (per capita) growth: (A series of posts has resulted in a working paper.) The following relationship (Okun’s law) has been estimated:

du = -0.465dlnG + 1.113, (1)

When integrated between t0 and t, equation (1) can be rewritten in the following form:

u(t) = u(t0) -0.465bln[G/G0] +1.113(t-t0) + c (2)

Without loss of generality, we assume t0=0. The intercept c≡0, as is clear for t=t0. Instead of integrating (2), we calculate cumulative sums of the annual estimates of du and lnG with appropriate initial conditions. The cumulative sum of du’s is the time series of the unemployment rate. Figure 1 depicts the measured and observed curves for the period between 1958 and 2011. The agreement is excellent and has been obtained by a formal statistical method (LSQR).

The FRB and CBO explicitly projected the growth rate of real GDP, rGDP, and the rate of unemployment, UE, through 2014. Table 1 lists the most probable rates for 2012 to 2014, with the FRB providing broader ranges of expected values with specially highlighted central tendencies. We have calculated the average values for the most probable ranges. CBO gives much higher rates of unemployment for 2012 and 2013 but lower long term rate, i.e. the rate projected to 2018-2022. At the same time, the growth rate of real GDP projected by CBO is lower for 2012 and 2013.

Table 1

Year | 2011 | 2012 | 2013 | 2014 | Long term trend |

FRB rGDP | - | 2.4 | 3.0 | 3.7 | 2.45 |

CBO rGDP | 1.6 | 2.2 | 1.0 | 4.0 | 2.5 |

FRB UE | - | 8.35 | 7.75 | 7.15 | 5.6 |

CBO UE | 9.0 | 8.8 | 9.1 | 7.0 | 5.4 |

From (1) it follows that higher rates of GDP growth decrease the rate of unemployment. Since our model is based on real GDP per capita we have to reduce the growth rates in Table 1 by 0.8% per year, which is the growth in the overall population. This gives the estimates of the growth rate of GDP per capita. Using (2) we calculate the rate of unemployment which will correspond to the projected real GDP.

Figure 2 compares the unemployment rate in the US between 2012 and 2014 as projected by the FRB and CBO and predicted from their relevant projections of real GDP per capita. The FRB and CBO have wrongly projected the pair unemployment/GDP which is driven by Okun’s law. The best match is observed between the unemployment projection made by CBO and the GDP projection by the FRB.

In this post, we do not state that any of these projections is right or wrong. We just show that, when interpreted jointly, the projections of UE and GDP are not consistent with each other. In other words, the growth rate of real GDP projected by the FRB and CBO cannot provide the projected rates of unemployment. One may check these projections in 2015.

Figure 2. Comparison of the unemployment rate in the US between 2012 and 2014 as projected by the FRB and CBO and predicted from the projections of real GDP per capita.

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