macroeconomics, rational expectations, unemployment

Thomas J. Sargent

English

Research Papers in Economics

THOMAS J.  SARGENT 
University  of Minnesota 
"Rational  Expectations": 
A Correction 
I HAVE  DISCOVERED  an error  in the computations  of regression  (3) and 
the regressions  in Table 1 in my paper  in Brookings  Papers  on Economic 
Activity  (2:1973), on pages 452-53 and 460. With the exception  of the 
lagged  unemployment  rates  in those  regressions,  the instrumental  variables 
in Ot were  all inadvertently  lagged  four more quarters  than is reported  in 
the paper.  For example,  mti_  in equation  (3) is actually  mt_5.  The correct 
calculations  are reported  here  in regression  (3) and Table 1. 
The F-statistic  for regression  (3) is now 4.5, which  exceeds  the value of 
2.503 reported  in my paper,  and so is even more significant  statistically. 
Thus,  the test continues  to point toward  rejection  of the natural  rate hy- 
pothesis.  The corrected  results  for Table 1 now detect  neither  a short-run 
nor a long-run  Phillips  curve  using  the log of the GNP deflator,  p, the co- 
efficient  on the systematic  part  of Ap having  t-statistics  close to zero. The 
t-statistic  on the systematic  part  of wage  inflation  in regression  (5.2)  is now 
-  1.28,  and fails  to support  rejection  of the natural  rate  hypothesis.  How- 
ever,  the coefficient  on the "random"  part  of w in (5.2) is now larger  than 
before  both in absolute  value and in statistical  significance,  so that the 
amended  results  for w are more  favorable  to the hypothesis  of a tradeoff 
between  unemployment  and the surprise  component  of wage  inflation. 
(3)  Unt =  54.556 +  0.773 Unt-1 -  0.357 Unt-2  -  0.027 Unt-3 
(15.819) (0.175)  (0.212)  (0.136) 
-2.809  mt-i  -  10.046 mt-2  +  4.868 mt3  -  0.003 De 
(7.109)  (12.522)  (7.434)  (0.013) 
-0.240  Deft2  -  0.023 Deft-3 -  17.151 Pt-  -7.967  Pt-2 
(0.018)  (0.016)  (17.468)  (21.767) 
-14.502  Pt-3  +  28.156  pct-1  +  13.122  pCt-2  +  10.917 pCt-3 
(18.157)  (20.014)  (22.101)  (19.059) 
+13.274  wrt,  -  11.730 wrt-2 +  11.546 wrt.3 +  2.536 gt-i 
(6.969)  (9.164)  (7.079)  (2.620) 
Note: I would like to thank Thomas  Turner  for performing  the calculations. 
799 800  Brookings Papers on Economic Activity, 3:1973 
-7.224  gt-2  +  0.345 gt-3  -  11.132  ngt-l  +  2.311  ngt-2 
(3.652)  (2.745)  (7.237)  (11.061) 
-  0.938  ngt-3  -  16.814  yt-_ +  15.477  Yt-2 +  3.840  Yt-3. 
(8.519)  (5.240)  (6.562)  (5.544) 
K2  = 0.9652; standard  error  of estimate = 0.216; Durbin-Watson  statistic =  1.941; 
F (24,48)  =  4.500. 
Table 1.  Regression Results for Alternative  Tests of the Natural 
Unemployment  Rate Hypothesisa 
Variable  and  Regression 
regression  statistic  4.1  4.2  5.1  5.2 
Variable 
Constant  0.420  0.420  0.696  0.696 
(0.218)  (0.220) 
Unemployment  rate lagged  1.715  1.715  1.666  1.666 
one quarter,  Un-,  (0.115)  (0.116) 
Unemployment  rate lagged  -1.046  -1.046  -0.999  -0.999 
two quarters,  Un-2  (0.198)  (0.196) 
Unemployment  rate lagged  0.245  0.245  0.216  0.216 
three quarters,  Un-3  (0.115)  (0.114) 
Random  (unexpected)  part of 
inflation, based on the GNP 
deflator, p,  or the wage 
index,  w 
p-pl  30.322  ...  ...  ... 
(19.976) 
p-  p  ...  61.848  ...  ... 
(37.420) 
w -w)7V  ...  ...  -11.924  ... 
(9.447) 
w-w  ...  ...  ...  -100.852 
(56.064) 
Systematic  (expected)  part 
of inflation 
pl-P-1  -0.170  -0.170  ...  ... 
(11.380)  (11.627) 
w7V  -  w_  ...  ...  -13.282  -13.282 
(7.154)  (10.361) 
Regression  statistic 
R2  0.925  ...  0.928  ... 
Durbin-Watson  statistic  1.935  ...  1.958 
a  1.01  1.00  -0.11  0.87 
t-statistic  -0.01  -0.01  -1.86  -1.28 
Source: Derived from equations (24) and (24') of original article, using relevant official U.S. series from 
the data bank of the Wharton Econometric Model. 
a.  The period of fit is 1952:1-1970:4. The dependent variable is the unemployment rate. Standard  errors 
are in parentheses. The standard errors for coefficients for regression (4.2) and (5.2) are asymptotic. For 
detailed definitions of symbols, see text of original article. 

"Rational Expectations": A Correction

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"Rational Expectations": A Correction

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