Online Appendix for "Does Wage Rigidity Make Firms
Riskier? Evidence from Long-horizon Return
Predictability"
Xiaoji Liny
Jack Favilukis
December 15, 2015
Abstract
This appendix reports the solution for the simple model, how we match Fama-French
industries to NIPA, and additional results for Favilukis and Lin (2015, “Does wage
rigidity make …rms riskier? Evidence from long-horizon return predictability”) to
appear at Journal of Monetary Economics.
Corresponding author: Finance Division, University of British Columbia, 2053 Main Mall, Vancouver,
BC, V6T 1Z2, Canada. Tel: 604-822-9414 and E-mail: jack.favilukis@sauder.ubc.ca
y
Department of Finance, Ohio State University, 2100 Neil Ave, 846 Fisher Hall, Columbus, OH 43210.
Tel: 614-292-4318 and E-mail: lin.1376@osu.edu
1
1
Model
The …rm’s value can be recursively written as:
Vt = At
( Wt
Wt = W t
1
1
+ (1
+ (1
) At ) + Et [
At+1
At
Vt+1 ] s:t:
(1)
) At
It is straight forward to guess, and verify that the …rm’s value function is linear in At and
Wt 1 : Vt = VA At + VW Wt 1 . By plugging this into equation 1 and collecting coe¢ cients, we
can show that:
VW =
VA =
where b = E[
1
At+1
At
1
1
1 b
e
1
(1
] and e = E[
) + (1
At+1
At
].
(2)
)VW e
Because At is non-stationary (note that its growth rate
At+1
At
is stationary), it is useful
to transform this into a stationary problem. De…ne vt = Vt =At and wt = Wt =At+1 , then
vt = VA + VW wt
1
and wt+1 =
At
(
At+1
wt
1
+ (1
) ).
To solve the extended model, we similarly rewrite it in terms of stationary variables. The
original model is:
Vt = Xt St + (1
Wt = W t
1
St )At
+ (1
Yt = Xt St + (1
( Wt
) (1
+ (1
1
) (1
St )At ) + Et [
Yt+1
Yt
Vt+1 ] s:t:
(3)
St )At
St )At
Detrending in exactly the same as before, the model is rewritten:
v t = xt S t + 1
wt =
At+1
At
St
( wt
1
+ (1
) (1
St )) + Et [
At+1
At
xt+1 St+1 +1 St+1
xt St +1 St
vt+1 ] s:t:
1
( wt
1
+ (1
) (1
St ))
(4)
We solve this model numerically by value function iteration. There are three state variables:
At
,
At 1
xt , and St . We approximate
At
At 1
and xt by 3-state Markov processes, thus the grid
size for each of these state variables is 3. The only continuous variable is St , which we
approximate with a grid of size 13.
2
Matching Industries
For industry returns we use the 49 Fama and French industries available from Ken French’s
website. We need to collect corporate information such as wage growth and labor share
for these industries. Industry data is available in NIPA Section 6. Wages are in Tables
6.6A (1929-1948), 6.6B (1948-1987), 6.6C (1987-2000), and 6.6D (2000-2011); data on
compensation (Table 6.2), before tax pro…ts (Table 6.18), and capital consumption (Table
6.22) are analogous to wages. Although the aggregate data is available from 1929 to 2011,
some of the industry classi…cations undergo changes in 1948, 1987, and 2000. We do our
best to match NIPA industry names to names in the Fama and French data set. Because
of a change in industry classi…cations, we collect industry data for 1929 to 2000 only.
Although industry data is available post-2000, we were unable to reliably match enough
industries between NIPA post-2000, NIPA pre-2000 and Ken French’s industry returns to
make extending the data set to 2011 worthwhile. In the end we are left with 26 matched
industries1 .
3
Additional Tables
This section presents the results of the additional analysis in the paper.
1
We are also able to match Health Services, however returns data for this industry do not start until
1969. Furthermore, Rubber is missing returns for 1929-1930 and 1943-1944, for this industry we replace
the missing values by BldMat which has the highest correlation (0.83) with Rubber. Similarly, Paper is
missing values in 1929-1930 and 1935-1936, missing values are replaced with Chemical which has the highest
correlation (0.82) with Paper.
2
3
W
p-val
R2
p-val
p-val
W
p-val
R2
p-val
p-val
W
p-val
R2
p-val
p-val
s
W
+
W
+
W
+
W E[
W E[
W E[
]
]
]
-2.98
0.04
-10.53
0.63
10.82
0.64
0.08
-2.69
0.03
0.04
0.16
-0.04
0.16
0.08
-2.83
0.03
-0.09
0.56
0.15
0.56
0.07
1
-8.75
0.01
1.01
0.46
-0.58
0.46
0.19
-7.68
0.00
0.05
0.20
-0.05
0.19
0.22
-8.58
0.00
-0.73
0.60
0.66
0.60
0.19
2
-8.43
0.04
11.35
0.39
-11.03
0.39
0.12
-6.80
0.05
0.06
0.25
-0.06
0.25
0.18
-8.89
0.02
3.23
0.29
-3.29
0.29
0.14
3
5
6
=
AC
(
W
)
t
t
-12.90 -17.57 -21.03
0.01
0.01
0.01
2.39
-1.11
2.32
0.35
0.59
0.40
-2.56
0.85
-2.52
0.35
0.58
0.40
0.20
0.23
0.24
t = 1=V OLt ( W )
-10.27 -15.01 -17.64
0.04
0.02
0.03
0.12
0.15
0.18
0.16
0.19
0.20
-0.12
-0.15
-0.18
0.16
0.19
0.20
0.21
0.25
0.28
t = DEMt
-12.52 -17.46 -18.77
0.04
0.02
0.04
33.41 45.36 17.76
0.34
0.31
0.41
-33.26 -45.66 -19.21
0.34
0.31
0.41
0.16
0.21
0.24
4
-17.51
0.09
44.13
0.36
-46.35
0.36
0.22
-16.57
0.07
0.27
0.17
-0.26
0.17
0.23
-19.69
0.04
4.68
0.35
-4.71
0.35
0.16
7
-25.61
0.04
71.98
0.32
-74.59
0.31
0.29
-24.57
0.04
0.33
0.16
-0.33
0.15
0.28
-27.94
0.02
16.81
0.19
-16.51
0.19
0.23
8
-34.00
0.02
140.67
0.18
-143.06
0.17
0.33
-31.03
0.04
0.43
0.14
-0.43
0.14
0.31
-34.99
0.01
22.85
0.16
-22.46
0.16
0.26
9
-50.42
0.01
275.00
0.04
-275.99
0.03
0.43
-44.76
0.02
0.68
0.08
-0.66
0.08
0.44
-47.03
0.01
19.45
0.23
-19.26
0.23
0.33
10
-19.64
0.01
63.01
0.23
-63.89
0.22
0.23
-17.70
0.02
0.23
0.13
-0.23
0.13
0.25
-20.15
0.01
6.98
0.27
-6.96
0.26
0.20
Avg
This table presents results from forecasting regressions of aggregate future stock returns at various horizons (denoted by s) on wage growth conditional on a rolling proxy for rigidity t .
Speci…cally, the regression takes the form Rt;t+s = 0 +
W +
W t ) Wt + t;t+s .
t +(
t is either the 5-year backward looking autocorrelation of wage growth, the inverse of
the 5-year backward looking volatility of wage growth, or the Democrat share of votes in the previous presidential election. We report the average dependence of returns on wage growth
, and the cross-dependence
W +
W E[ ], the dependence on rigidity alone
W . All p-values are obtained by a boot strapping procedure described in the text.
Table A1: Aggregate Predictability with Rolling Measures of Rigidity
4
W
p-val
p-val
p-val
W
p-val
p-val
p-val
W
p-val
p-val
p-val
W
p-val
s
W
+
W
+
W
+
W E[
W E[
W E[
]
]
]
-0.53
0.15
0.02
0.08
-0.02
0.08
0.24
0.70
1.39
0.10
-1.37
0.10
-2.06
0.01
0.04
0.03
-0.04
0.03
-0.41
0.20
2.09
0.16
-2.04
0.16
-0.68
0.16
15.70
0.16
-15.77
0.15
-1.16
0.09
0.36
0.70
0.49
0.88
-5.94
0.77
5.64
0.76
2
1
-3.36
0.01
0.05
0.07
-0.05
0.07
-1.34
0.04
1.82
0.29
-1.78
0.29
-1.70
0.03
42.51
0.02
-42.25
0.02
-2.60
0.03
3
5
6
Univariate
-3.14
-4.33
-4.88
0.04
0.03
0.04
t = LSt
-2.16
-2.94
-3.09
0.03
0.03
0.07
61.97 68.67 54.14
0.01
0.02
0.11
-61.34 -68.10 -54.11
0.01
0.02
0.11
t = ACt ( W )
-1.93
-2.39
-2.40
0.03
0.03
0.07
2.31
1.24
2.56
0.31
0.47
0.41
-2.32
-1.36
-2.70
0.31
0.46
0.40
t = 1=V OLt ( W )
-3.77
-4.77
-6.87
0.03
0.03
0.01
0.05
0.05
0.09
0.10
0.20
0.11
-0.05
-0.05
-0.09
0.10
0.19
0.11
4
-8.10
0.02
0.12
0.08
-0.12
0.07
-1.82
0.16
4.17
0.38
-4.39
0.36
-3.04
0.13
0.02
0.56
-1.54
0.56
-5.92
0.04
7
-11.71
0.01
0.17
0.05
-0.17
0.05
-4.70
0.03
4.37
0.43
-4.65
0.41
-6.31
0.02
36.45
0.33
-37.34
0.33
-10.24
0.01
8
-12.50
0.03
0.20
0.07
-0.20
0.07
-5.97
0.03
4.78
0.46
-5.07
0.45
-7.34
0.03
98.61
0.14
-99.11
0.14
-10.69
0.02
9
-13.34
0.04
0.17
0.18
-0.17
0.17
-7.49
0.02
4.04
0.55
-4.41
0.53
-9.07
0.03
66.54
0.28
-69.14
0.28
-13.18
0.02
10
-6.70
0.01
0.10
0.08
-0.10
0.08
-2.82
0.03
2.88
0.41
-3.01
0.41
-3.59
0.03
43.87
0.15
-44.31
0.16
-5.58
0.01
Avg
This table presents Fama-MacBeth regressions to test return predictability for industries. In particular, in every period t we regress future realized returns Rt+1;t+s (realized at t + 1 and
i
i
i
i
after) on industry characteristics known at time t: Rt;t+s
= 0;t + ;t it + ( W;t +
W;t t ) Wt + t;t+s . This produces coe¢ cients for every year of the data set and we report the
average of these. it indicates the speci…c industry characteristic, it is either labor share or one of two proxies of wage rigidity. The proxies are the 5-year backward looking autocorrelation of
wage growth, or the inverse of the 5-year backward looking volatility of wage growth. All p-values are obtained by a boot strapping procedure described in the text.
Table A2: Fama-MacBeth with Rolling Measures of Rigidity: Industry
5
W
p-val
p-val
p-val
W
p-val
p-val
p-val
W
p-val
p-val
p-val
W
p-val
p-val
p-val
W
p-val
s
W
+
W
+
W
+
W
+
W E[
W E[
W E[
W E[
]
]
]
]
-0.22
0.18
-5.26
0.92
5.12
0.92
-0.13
0.26
0.03
0.09
-0.03
0.10
-0.12
0.28
-0.55
0.73
0.55
0..73
-0.55
0.11
-7.46
0.84
7.35
0.84
-0.66
0.07
-0.03
0.66
0.03
0.66
-0.58
0.09
3.41
0.10
-3.32
0.10
-0.64
0.10
-5.65
0.73
5.78
0.74
-0.80
0.05
-0.23
0.16
-0.21
0.20
-5.57
0.85
5.51
0.86
2
1
-1.05
0.04
-4.63
0.59
4.79
0.60
-1.24
0.02
-0.06
0.69
0.06
0.70
-0.99
0.06
5.22
0.07
-5.09
0.06
-1.35
0.04
3.41
0.41
-3.10
0.41
-1.35
0.02
3
5
6
Univariate
-2.81 -3.41
-3.11
0.00
0.00
0.00
t = LSt
-2.84 -3.66
-3.35
0.00
0.00
0.00
-3.47
3.92
4.42
0.64
0.49
0.49
3.61
-3.65
-3.99
0.64
0.48
0.49
t = ACt ( W )
-2.55 -3.45
-3.19
0.00
0.00
0.00
4.40
2.99
2.76
0.20
0.41
0.47
-4.27 -2.81
-2.49
0.20
0.41
0.48
t = 1=V OLt ( W )
-2.73 -3.54
-3.08
0.00
0.00
0.00
-0.01
0.03
-0.03
0.37
0.18
0.34
0.01
-0.03
0.02
0.37
0.17
0.34
t = DEMt
-2.50 -3.20
-2.98
0.00
0.00
0.00
2.81 14.01 24.27
0.29
0.10
0.04
-2.41 -13.18 -23.12
0.29
0.10
0.04
4
-1.93
0.03
37.23
0.01
-35.35
0.01
-1.65
0.05
-0.14
0.69
0.14
0.70
-1.97
0.04
5.24
0.34
-4.84
0.35
-2.35
0.03
9.27
0.41
-8.43
0.42
-2.15
0.03
7
-1.28
0.11
36.83
0.03
-34.63
0.03
-0.69
0.14
-0.18
0.70
0.17
0.69
-1.54
0.07
5.49
0.40
-4.99
0.41
-1.50
0.12
9.14
0.44
-8.14
0.44
-1.50
0.09
8
-0.47
0.20
30.50
0.07
-28.06
0.08
0.27
0.28
-0.26
0.81
0.25
0.81
-0.78
0.14
8.25
0.30
-7.66
0.31
-0.48
0.27
8.41
0.45
-7.28
0.46
-0.83
0.16
9
-0.85
0.14
24.63
0.13
-22.28
0.14
0.33
0.28
-0.22
0.66
0.21
0.66
-1.01
0.14
17.45
0.08
-16.73
0.09
-0.71
0.26
11.77
0.41
-10.70
0.41
-1.03
0.15
10
-1.50
0.01
15.29
0.08
-14.18
0.08
-1.31
0.03
-0.09
0.60
0.08
0.60
-1.62
0.02
5.47
0.23
-5.17
0.24
-1.71
0.02
3.56
0.49
-3.04
0.48
-1.72
0.02
Avg
This table presents Fama-MacBeth regressions to test return predictability for states. In particular, in every period t we regress future realized returns Rt+1;t+s (realized at t + 1 and after)
i
i
i
i
on state characteristics known at time t: Rt;t+s
= 0;t + ;t it + ( W;t +
W;t t ) Wt + t;t+s . This produces coe¢ cients for every year of the data set and we report the average of
these. it indicates the speci…c state characteristic, it is either labor share or one of three proxies of wage rigidity. The proxies are the 5-year backward looking autocorrelation of wage growth,
the inverse of the 5-year backward looking volatility of wage growth, or the Democrat share of total votes. All p-values are obtained by a boot strapping procedure described in the text.
Table A3: Fama-MacBeth with Rolling Measures of Rigidity: State
6
Transportation
Communication
Electric, gas, and
sanitary services
Wholesale trade
Retail trade and automobile services
Security and commodity
brokers, and services
Insurance carriers
Real estate
Hotels and other lodging places
Personal services
60
62
63
58
52
53
56
61
62
58
56
50
51
55
38
46
49
31
32
33
35
38
46
49
31
32
33
35
Hotels and other lodging places
Personal services
Real estate
Motor vehicles and equipment
Food and kindred products
Tobacco manufactures
Textile mill products
Apparel and other
textile products
Paper and allied products
Printing and publishing
Chemicals and allied products
Rubber and miscellaneous
plastics products
Transportation
Communication
Electric, gas, and
sanitary services
Wholesale trade
Retail trade
Security and commodity
brokers
Insurance carriers
61
62
58
56
50
51
55
38
46
49
31
32
33
35
22
27
28
29
30
22
27
28
29
30
Motor vehicles and equipment
Food and kindred products
Tobacco manufactures
Textile mill products
Apparel and other
textile products
Paper and allied products
Printing and publishing
Chemicals and allied products
Rubber products
23
27
28
29
30
Hotels and other lodging places
Personal services
Real estate
Industrial machinery
and equipment
Motor vehicles and equipment
Food and kindred products
Tobacco products
Textile mill products
Apparel and other
textile products
Paper and allied products
Printing and publishing
Chemicals and allied products
Rubber and miscellaneous
plastics products
Transportation
Communications
Electric, gas, and
sanitary services
Wholesale trade
Retail trade
Security and commodity
brokers
Insurance carriers
20
20
Machinery, except electrical
6C number and name
4
Agriculture, forestry,
and …sheries
8
Metal mining
9
Coal mining
10
Oil and gas extraction
12
Construction
18
Primary metal industries
6B number and name
4
Agriculture, forestry,
and …sheries
8
Metal mining
9
Coal mining
10
Oil and gas extraction
12
Construction
18
Primary metal industries
6A number and name
4
Agriculture, forestry,
and …sheries
8
Metal mining
9
Anthracite mining
11
Crude petroleum and natural gas
13
Contract construction
19
Iron and steel and
their products, including ordnance
21
Machinery, except electrical
Goods
Goods
Goods
Goods
Transportation
Communications
Electric, gas, and
sanitary services
Wholesale trade
Retail trade
Finance, Insurance,
and Real Estate
Finance, Insurance,
and Real Estate
Finance, Insurance,
and Real Estate
Services
Services
Nondurable
Nondurable
Nondurable
Nondurable
Durable Goods
Nondurable Goods
Nondurable Goods
Nondurable Goods
Nondurable Goods
Durable Goods
6 coarse name
Agriculture, forestry,
and …sheries
Mining
Mining
Mining
Construction
Durable Goods
44
33
47
46
42
43
48
41
32
31
39
8
14
15
23
2
5
16
10
21
28
29
30
18
19
Meals
PerSv
RlEst
Insur
Whlsl
Rtail
Fin
Trans
Telcm
Util
Paper
Books
Chems
Rubbr
Autos
Food
Smoke
Txtls
Clths
Mach
Mines
Coal
Oil
Cnstr
Steel
FF number and name
1
Agric
In this table we present the industry name and number from NIPA tables 6.XA, 6.XB, 6.XC and the matched industry in the Fama and French 49 industry data set. Here X is 6 for wages, 2
for compensation, 18 for before tax pro…ts, and 22 for capital consumption.
Table A4: Matching industries