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Table 3 Impatience, present bias, and risk parameters

From: A quasi-hyperbolic discounting approach to smoking behavior

    

Random parameters

 

Log likelihood

Scale parameter

 

δ (constant time preference)

Exp(β) (present bias)

1-γ (relative risk aversion)

Non-smoker

-587.7

0.3299 (0.1197)

Mean

-0.0556 (0.0098)***

0.4578 (0.1909)***

-0.2283 (0.2065)

(N = 241)

S.D.

0.0346 (0.0101)***

0.0617 (0.0790)

0.4064 (0.2101)*

Never-smoker

-440.1

0.2318 (0.1652)

Mean

-0.0542 (0.0131)***

0.4207 (0.1956)**

-0.2172 (0.2438)

(N = 182)

S.D.

0.0261 (0.0120)**

0.0875 (0.0976)

0.0207 (0.7300)

Ex-smoker

-140.1

0.2718 (0.2341)

Mean

-0.0700 (0.0253)***

0.5365 (0.5339)

-0.3697 (0.4689)

(N = 59)

S.D.

0.2077 (0.1219)*

0.0562 (0.0316)*

0.8366 (0.4635)*

Smoker

-57105

0.3575 (0.1073)***

Mean

-0.0683 (0.0133)***

0.3619 (0.1137)***

-0.3658 (0.2186)

(N = 253)

S.D.

0.0421 (0.0127)***

0.0276 (0.1055)

0.6265 (0.2108)***

L-smoker

-226.2

0.3900 (0.2694)

Mean

-0.0587 (0.0211)***

0.2685 (0.1076)**

-0.4843 (0.3617)

(N = 97)

S.D.

0.0341 (0.0192)**

0.0072 (0.1253)

0.6083 (0.3096)**

M-smoker

-255.6

0.3575 (0.1461)**

Mean

-0.0802 (0.0226)***

0.5677 (0.5316)

-0.2035 (0.3468)

(N = 111)

S.D.

0.0465 (0.0188)**

0.1129 (0.3377)

0.7142 (0.3870)*

H-smoker

-93.8

0.3575 (0.1908)*

Mean

-0.0855 (0.0365)**

0.2876 (0.1597)*

-0.5267 (0.5171)

(N = 45)

S.D.

0.0639 (0.0334)*

0.0305 (0.1605)

0.3395 (1.1399)

  1. Note 1: The values in parentheses denote the standard errors of MEAN and S.D. estimates for the random parameters. ***1% significant level (p < 0.01), **5% significant level (p < 0.05), *10% significant level (p < 0.1).
  2. Note 2: δ (constant time preference) and 1-γ (relative risk aversion) are estimated for both time-consistent and time-inconsistent samples, while β (present bias) is estimated only for the time-inconsistent samples.
  3. Note 3: the coefficient is normalized to one for the variable 1n probability, which appear as separate shift parameters (according to the level of probability).