Toward Empirical Tests of Alternative Theories of Stagflation
by
James Devine
Econ. Dept./Loyola Marymount University
Los Angeles, CA 900468410
http://bellarmine.lmu.edu/~JDevine
click here for the main paper.
1. Two theories contrasted:
[1N] 
p = b (U  N) + shock + l p^{e} 
The "triangle model" NRH Phillips Curve. 
Under the canonical NRH assumptions (l = 1 and shock = 0), equilibrium with p = p^{e} is a vertical longrun PC at U = N (the equilibrium U rate, the NAIRU). Further, in the hardcore NRH literature, N is unique, independent of U, and equal to the structuralfrictional unemployment rate, U_{SF}.
[1C] 
p = a  b (U  U_{SF}) + shock + l p^{H} 
the "conflict theory" Phillips Curve. 
[2C] 
a = a _{R }+ a _{W} 
excessive claims on the product 
where p^{H} is "hangover inflation" (including p^{e}), and a _{R} is capital's – and a _{W} labor's – excessive claim on the total product. Following Brenner's research, assume that workers' aspirations were either constant or falling during the period after 1950 or so (a _{W} is constant). So, under the profitdriven theory:
[3C] 
a = g (r^{T}  r*); g (0) = 0; g ' > 0 
r* is the fullcapacity profit rate. 
Making the canonical NRH assumptions:
[4C] 
p = a  b (U  U_{SF}) + p^{H} 
conflict PC w/ canonical NRH assumptions. 
If we now allow for partialadjustment determination of p^{H}, this in turn implies inflationary acceleration even at U = U_{SF}. Thus the equilibrium unemployment rate – the NAIRU – equals:
[5C] 
N = U_{SF} + U_{B} 
two types of U at the NAIRU. 
where U_{B} is bargainingpower unemployment, equal to
[6C] 
U_{B} = a /b = g (r^{T}  r*)/b 
the reserve army 
Dropping the canonical NRH assumptions,
[7C] 
p = g (r^{T}  r*)  b (U  U_{SF}) + shock + l p^{H} 
the full model, where the PC shifts outward if the rate of profit falls. 

=  b (U  U_{SF}  U_{B}) + shock + l p^{H} 
2. Measuring stagflation:
We can define the "stagflation potential factor" (SPF) as:
[8C] 
p + b ·U = b (U_{SF} + U_{B}) + shock + l p^{H} 
the RHS is possible causes of stagflation. 
where I usually assume that b = 1, so that the SPF equals the "misery index." In the regressions, r^{T} is also assumed constant. So they involve comparing p + U and r*, typically measured as r/cu.
Table 1: Different SPFs versus NFCB r*, 196098 

Stagflation Potential Factor based on: 

CPIU 
core CPIU 
CPIUX1 
GDP price 
C deflator 

Constant 
6.2578 
6.2594 
6.1359 
5.6734 
6.0735 

Std Err of Y Est 
0.1922 
0.1787 
0.1788 
0.2053 
0.1903 

adj. RSquared 
0.6419 
0.6743 
0.6625 
0.5370 
0.6291 

ln(r*) coefficient 
1.6789 
1.6756 
1.6338 
1.4480 
1.6180 

tstat 
8.3135 
8.9252 
8.6950 
6.7135 
8.0897 

(a) 
(b) 
(c) 
(d) 
(e) 

Note: Regressions use annual data and are loglinear. Each had 37 d.f. 

Table 2: SPFs versus NFCB r* and time, 196098 

Stagflation Potential Factor based on: 

CPIU 
core CPIU 
CPIUX1 
GDP price 
C deflator 

Constant 
7.4545 
7.1808 
7.1753 
7.0744 
7.4051 

Std Err of Y Est 
0.1670 
0.1638 
0.1590 
0.1718 
0.1574 

adj. RSquared 
0.7295 
0.7261 
0.7333 
0.6757 
0.7463 

Time coefficient 
0.0103 
0.0079 
0.0090 
0.0121 
0.0115 

tstat 
3.6037 
2.8285 
3.2881 
4.1017 
4.2546 

ln(r*) coefficient 
2.1030 
2.0022 
2.0022 
1.9445 
2.0900 

tstat 
9.9518 
9.6589 
9.9540 
8.9467 
10.4940 

(a) 
(b) 
(c) 
(d) 
(e) 

Note: Regressions use annual data and are loglinear. Each had 36 d.f. 

Table 3: SPFs vs. NFCB r*, time, and 198698 dummy 

Stagflation Potential Factor based on: 

CPIU 
core CPIU 
CPIUX1 
GDP price 
C deflator 

Constant 
6.3788 
6.1770 
6.1479 
5.9439 
6.4245 

Std Err of Y Est 
0.1220 
0.1248 
0.1157 
0.1229 
0.1183 

adj. Rsquared 
0.8557 
0.8410 
0.8586 
0.8341 
0.8566 

Time coefficient 
0.0077 
0.0089 
0.0083 
0.0069 
0.0050 

tstat 
2.0368 
2.2911 
2.2981 
1.8020 
1.3496 

Dummy coefficient 
0.4448 
0.4150 
0.4248 
0.4674 
0.4054 

tstat 
5.7010 
5.1986 
5.7379 
5.9485 
5.3558 

ln(r*) coefficient 
1.7295 
1.6536 
1.6455 
1.5520 
1.7495 

tstat 
10.3156 
9.6384 
10.3431 
9.1903 
10.7545 

(a) 
(b) 
(c) 
(d) 
(e) 

Note: Regressions use annual data and are loglinear. Each had 35 d.f. 

Table 4: Duménil and Lévy data. 194897 

The tstatistics on Misery Index using various sectors and definitions. 

dependent variable: log of the misery index; independent: log of r* 

measure of the profit rate 

sector 
grossest measure of the profit rate 
BeforeTax profit rate, not including interest 
BeforeTax profit rate, including interest 
gross BeforeTax profit rate 
gross BeforeTax profit rate, including interest 
AfterTax profit rate, not including interest 
average tstat, excluding [6] 

NFCB 
6.476 
4.358 
3.676 
5.224 
4.392 
2.927 
4.825 

Total Business 
6.554 
4.575 
4.621 
5.145 
5.265 
n.a. 
5.232 

average tstat 
6.515 
4.467 
4.148 
5.185 
4.829 
2.927 
5.029 

[1] 
[2] 
[3] 
[4] 
[5] 
[6] 
[7] 

49 degrees of freedom. 

Table 5: Liebling data, 194877 

The tstatistics on Misery Index using various methods of cyclical correction. 

dependent variable: log of the misery index; independent: log of rate of return. 

Method of Cyclical Correction of Rate of Return. 

Type of NFCB Rate of Return. 
actual (uncorrected) 
CEA gap 
STL gap 
PW gap 
"trend" gap 
Devine correction (r/cu) 
Devine2 correction 
average tstat 

Beforetax without Interest 
6.769 
4.719 
5.359 
6.813 
5.977 
6.537 
5.300 
5.925 

Beforetax including Interest 
5.265 
3.322 
4.125 
5.900 
4.703 
5.076 
4.102 
4.642 

Aftertax without Interest 
5.382 
3.868 
4.375 
5.220 
5.009 
5.031 
4.235 
4.732 

Aftertax including Interest 
2.365 
1.089 
1.302 
2.854 
2.154 
1.888 
1.516 
1.881 

average tstat 
4.337 
2.760 
3.267 
4.658 
3.955 
3.998 
3.284 
3.751 

[1] 
[2] 
[3] 
[4] 
[5] 
[6] 
[7] 
[8] 

29 degrees of freedom, except for those using the PW gap, which had 23 d.f. 