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Table 1Means of U.S. asset returns
A. Returns for the period 1948:1-1987:4
Asset Mean*
Short-term bond return: T-bills
0.80
Long-term bond return: long-term U.S. gov't debt
0.78
Stock return: S&P 500 8.90
*Annualized quarterly returns, percent per year. Source: SBBI
B. Returns for the period 1800 - 1990
Asset Mean*
Short-term bond return: 3.13
Long-term bond return: 3.71
Stock return: 7.77
*Returns measured as percent per year. Source: Siegel (1992)
Table 2Model predictions for mean returns
A. Stationary process for productivity
riskaversion
adjustmentcosts
Rf-1 (Rb/Rf)-1 (Re/Rf)-1
fixedlabor
variablelabor
habitformat'
fixedlabor
variablelabor
habitformat'
fixedlabor
variablelabor
habitformat'
τ=2 low 6.48 6.49 6.48 0.008 0.005 0.011 0.006 0.006 0.008
mod 6.46 6.48 6.41 0.048 0.025 0.140 0.055 0.034 0.148
high 6.43 6.47 6.15 0.103 0.038 0.750 0.130 0.055 0.806
τ=10 low 6.29 6.47 6.27 0.092 0.015 0.109 0.028 0.010 0.043
mod 6.11 6.42 5.98 0.331 0.088 0.498 0.275 0.094 0.425
high 5.61 6.35 4.67 1.091 0.201 2.749 1.096 0.234 2.744
B. Random-walk process for productivity
riskaversion
adjustmentcosts
Rf-1 (Rb/Rf )-1 (Re/Rf)-1
fixedlabor
variablelabor
habitformat'
fixedlabor
variablelabor
habitformat'
fixedlabor
variablelabor
habitformat'
τ=2 low 6.46 6.49 6.45 -0.044 -0.020 -0.040 0.007 0.006 0.014
mod 6.44 6.48 6.36 -0.035 -0.014 0.041 0.043 0.025 0.158
high 6.42 6.47 6.12 -0.021 -0.008 0.456 0.105 0.059 0.750
τ=10 low 4.50 6.37 4.31 -0.751 -0.091 -0.669 -0.272 0.010 -0.187
mod 4.43 6.35 3.77 -0.679 -0.072 -0.158 -0.158 0.057 0.421
high 4.28 6.32 2.00 -0.530 -0.045 1.950 0.104 0.136 2.850
Notes: All entries are quarterly returns, expressed as annualized percentage points.Mnemonics for the returns are: Rf = Risk-free rate of return; Rb = Bond return;Re= Equity return.
Table 3: Business cycle statisticsCCmodel and US data
Preferencespecification
Business-cyclestatistic
US data:1960-1991
low adj. costs;ττ=2
mod. adj. costs;ττ=10
high adj. costs;ττ=2
high adj. costs;ττ=10
Std(y) 0.0098 0.0086 0.0085 0.0086 0.0085
Fixed labor Std(c)/Std(y) 0.74 0.46 0.51 1.12 1.23
Std(i)/Std(y) 2.65 2.54 2.37 0.65 0.34
STATIONARY Std(y) 0.0098 0.0116 0.0097 0.079 0.0084
SHOCKS Variable labor Std(c)/Std(y) 0.74 0.48 0.78 1.18 1.05
Std(i)/Std(y) 2.65 2.47 1.63 0.50 0.86
Std(y) 0.0098 0.0086 0.0085 0.0086 0.0086
Habit formation Std(c)/Std(y) 0.74 0.26 0.27 0.79 0.44
Std(i)/Std(y) 2.65 3.28 3.23 1.85 2.82
Std(y) 0.0098 0.0085 0.0085 0.0085 0.0085
Fixed labor Std(c)/Std(y) 0.74 0.87 1.19 1.17 1.23
Std(i)/Std(y) 2.65 1.36 0.46 0.51 0.34
RANDOM Std(y) 0.0098 .0099 .0082 .0079 .0078
WALK Variable labor Std(c)/Std(y) 0.74 0.72 1.07 1.16 1.18
SHOCKS Std(i)/Std(y) 2.65 1.80 0.82 0.54 0.48
Std(y) 0.0098 0.0085 0.0085 0.0085 0.0085
Habit formation Std(c)/Std(y) 0.74 0.49 0.64 0.85 0.73
Std(i)/Std(y) 2.65 2.80 2.51 1.71 2.26
Notes: U.S. data is from the OECD. Data and model were filtered with the first-difference filter.
Table 4Habit formation model
Autocorrelation coefficients of consumption growth rates
adjustmentcosts
shockprocess
riskaversion
Autocorrelation coefficients at lag
1 2 3 4 5
stationary τ=2 .63 .40 .27 .19 .14
low τ=10 .61 .38 .24 .15 .11
randomwalk
τ=2 .61 .38 .25 .17 .13
τ=10 .59 .36 .21 .13 .08
stationary τ=2 .29 .06 .00 -.03 -.04
high τ=10 .47 .20 .07 .01 -.02
randomwalk
τ=2 .33 .11 .04 .01 .01
τ=10 .50 .25 .13 .06 .03
Table 5Financial leverage and dividend volatility
Habit formation model with high capital adjustment costs
A. The equity premium
shockprocess
riskaversion
noleverage
leverage parameter ν= 0.6 ν = 0.8 ν = 1.2
maturity (in quarters)
20 40 40 40
stat. τ=2 0.81 1.02 0.91 0.98 1.36
[-] [.50(.02)] [.41(.01)] [.54(.02)] [.82(.03)]
τ=10 2.74 3.67 3.13 3.39 4.53
[-] [.48(.04)] [.40(.03)] [.53(.04)] [.80(.06)]
random τ=2 0.75 1.01 0.94 1.06 1.79
walk [-] [.50(.05)] [.42(.05)] [.56(.06)] [.84(.10)]
τ=10 2.85 3.05 3.01 3.02 3.20
[-] [.29(.01)] [.25(.01)] [.33(.02)] [.50(.03)]
Figures in brackets denote mean leverage ratios defined as debt divided by total firm value with standarddeviations in parentheses.
B. Standard deviation of quarterly dividend growth rates
shockprocess
riskaversion
noleverage
leverage parameter, ν = 0.6 ν = 0.8 ν = 1.2
maturity (in quarters)
1 20 40 40 40
stat. τ=2 1.53 249.01 13.10 3.75 6.86 26.08
τ=10 2.96 147.97 16.18 3.92 8.37 31.17
random τ=2 1.52 238.32 9.35 2.34 4.15 15.49
walk τ=10 2.33 129.44 10.49 2.54 4.48 10.09