Web Appendix of Han Bleichrodt, Rogier J.D. Potter van Loon, Kirsten I.M. Rohde, & Peter P. Wakker (2013) “A Criticism of Doyle’s Survey of Time Preference: A Correction on the CRDI and CADI Families,” Judgment and Decision Making 8, 630–631 October, 2013 The main text showed how Doyle’s Eq. 33 was based on the incorrect Eq. 4. We show the same here for Doyle’s Eqs. 31 and 32 (Appendix A) and Eqs. 34, 35, and 36 (Appendix B). We reproduce the incorrect Eq. 4 from the main text: D(0) = 1.

(4)

We again assume U(x) = x throughout, following Doyle. As in our paper and in Bleichrodt, Rohde, and Wakker (2009; BRW henceforth), we write ln for the natural logarithm instead of Doyle’s log. As in the main text, (T:F) denotes receiving $F > 0 at time T > 0.

Appendix A. Reproducing Doyle’s results for CRDI+ & CRDI0 We show how Doyle’s analysis in his §3.6.2 essentially uses the incorrect Eq. 4 for Eqs. 1 ( > 0) and 2 ( = 0). The case of Eq. 3 ( < 0) was analyzed in the appendix of the paper. We treat Eqs. 1 and 2 separately.

CASE 1: Eq. 1 ( > 0) We first consider Eq. 1, concerning  > 0. Assume that P is the present value of (T:F), which indeed exists for  > 0: (0:P) ~ (T:F). It implies, assuming the incorrect Eq. 4:

(A.1)

2 P = F..exp(T).

(A.2+)

Doyle’s Eq. 31, i.e. Eq. A.3+ below, now follows: LEMMA A.1+. For Eq. 1 with Eq. 4, Eq. A.1 implies  =

ln (F/P) . T

(A.3+)

PROOF. Consider the following rewritings of Eq. A.2+: F 1 = = exp(T); P exp(T) ln(

F ) = T; P

ln (F/P) = . T



Eq.4, and the above results, are correct if  = 1. See the end of the appendix in the main text.

CASE 2. Eq. 2 ( = 0) We next consider Eq. 2, concerning  = 0. Again assume Eq. A.1, implied by the incorrect Eq. 4.1 Eq. 4 implies: P = F..T .

(A.20)

Doyle’s Eq. 32, i.e. Eq. A.30 below, now follows: LEMMA A.10. For Eq. 2 with Eq. 4, Eq. A.1 implies  =

ln (F/P) . ln(T)

PROOF. Consider the following rewritings of Eq. A.20: 1

In reality, a present value does not exist for  = 0.

(A.30)

3 F 1 =  = T; P T ln(

F ) = ln(T); P

ln (F/P) = . ln(T)



CASE 3. Eq. 3 ( < 0) See the appendix in the paper.

Appendix B. Reproducing Doyle’s results for the CADI family

The CADI family is defined, with parameters  > 0,  > 0, and , by2 If  > 0, then D(T) = .exp(eT) for T;

(B.1)

If  = 0, then D(T) = .exp(T) for T;

(B.2)

If  < 0, then D(T) = .exp(eT) for T.

(B.3)

Unlike CRDI, CADI is defined for all T   regardless of its parameter values. We show how Doyle’s analysis in his §3.6.3 essentially uses the incorrect Eq. 4. We again assume the present value P of Eq. A.1. Unlike with the CRDI family, for the CADI family a present value P always exists, and Eq. A.1 can be satisfied for each of the Eqs. B.1, B.2, and B.3. We consider the three cases of  separately.

CASE 1. Eq. B.1 ( > 0) Eq A.1 implies, assuming the incorrect Eq. 4:

2

BRW, p. 31, use the following notation:  = D, t = T, k = , r =  and c = .

4 P = F..exp(eT).

(B.4+)

Doyle’s Eq. 34, i.e. Eq. B.5+ below, now follows: LEMMA B.1+. For Eq. B.1 with Eq. 4, Eq. A.1 implies  =

ln (F/P) . eT

(B.5+)

PROOF. Consider the following rewritings of Eq. B.4+: F 1 = = exp(eT); P exp(eT) ln(

F ) = eT; P

ln (F/P) = . eT



CASE 2. Eq. B.2 ( = 0) Eq A.1 implies, assuming the incorrect Eq. 4: P = F..exp(T).

(B.40)

Doyle’s Eq. 35, i.e. Eq. B.50 below, now follows: LEMMA B.10. For Eq. B.2 with Eq. 4, Eq. A.1 implies  =

ln (F/P) . T

(B.50)

PROOF. Consider the following rewritings of Eq. B.40: F 1 = = exp(T); P exp(T) ln(

F ) = T; P

ln (F/P) = . T



5

CASE E 3. Eq. B.3 ( < 0) Eq A.1 implies, assuming the incorrect Eq. 4: P = F..exp(eT).

(B.4)

Doyle’s Eq. 36, i.e. Eq. B.5 below, now follows: LEMMA B.1. For Eq. B.3 with Eq. 4, Eq. A.1 implies  =

ln (F/P) . eT

(B.5)

PROOF. Consider the following rewritings of Eq. B.4: F 1 = = exp(eT); P exp(eT) ln(

F ) = eT; P

ln (F/P) = . eT



Web Appendix

We again assume U(x)=x throughout, following Doyle. As in our paper and in. Bleichrodt, Rohde, and Wakker (2009; BRW henceforth), we write ln for the natural.

227KB Sizes 2 Downloads 415 Views

Recommend Documents

Web Appendix
We again assume U(x)=x throughout, following Doyle. As in our paper and in. Bleichrodt, Rohde, and Wakker (2009; BRW henceforth), we write ln for the natural logarithm instead of Doyle's log. As in the main text, (T:F) denotes receiving $F>0 at time

web appendix
This Web Appendix contains additional information and data analyses that could not be ... report a crime. Since we look at 40 years of crime data, it is impossible to correct reported crimes for the ..... Origin countries: Albania, Algeria, Banglades

WEB APPENDIX FOR
For this level of θ and above, the ruler centralizes the entire territory. .... are log area, major river, agricultural constraints, distance to coast, elevation, malaria, ...

Safe Across the Border: Web Appendix - Michael Colaresi
Dec 3, 2013 - upon only one linear term to control for duration dependence, and then only for contiguous states. Beck, Katz and Tucker .... Partial results from these estimations are included below. Third, Gibler .... Figure 1: Dot plot of Lowest dem

Web-Appendix: On the Demographic Adjustment of ...
Nov 22, 2016 - Geert Mesters: Universitat Pompeu Fabra and Barcelona GSE, email: .... Specifically, drawing on Abowd and Zellner's insight that the bulk of.

Web Appendix for bCommuting, Migration and Local ...
employment locations within the economy. B.2 Computing Counterfactuals Using Changes. We now use the ... #U%'$. QM using the current guesses and data. We start by computing: ?v#U$. Q ...... We find pervasive two&way commuting, with the mean and media

Safe Across the Border: Web Appendix
Dec 3, 2013 - 518,368) generated from the EUGene program, version 3.2 (Bennett and Stam 2000), excluding joiner and ongoing disputes years. ..... them with contiguity to use as interaction terms. We use Bennett and Stam's (2000) ..... Beck, Nathaniel

Online Appendix
Aug 13, 2013 - Online Appendix Figures 3a-4e present further evidence from the survey .... Control variables include age, gender, occupation, education, and ...

Online Appendix
Aug 13, 2013 - Online Appendix Figures 3a-4e present further evidence from the survey responses on the .... Notes: Data from a survey of 70 individuals in 9 villages. ...... You will stay in the assigned room for 20 minutes listening to a.

Online Appendix
Length of business registration in days. 2. Land access sub-score ..... Trends. Province trends. Cluster. Commune. Commune. Commune. Commune. Province.

APPENDIX 12
Certain LFAs, nominated as Dedicated User Areas (DUA), are allocated for special use (such as concentrated helicopter training) and are managed under local ...

Online Appendix
Power Capital Variables adds up all ranking positions by terms (excluding the above top 4 positions). 2 ever held by native officials connected to a commune (in.

Online Appendix
When γ = 1, Equation 3 becomes α(p – c) = 1 + exp(δ – αp). The left-hand ... We averaged daily five-year maturity credit default swap (CDS) spreads on GM debt.

APPENDIX for LABORATORY 3 SHEET APPENDIX A
An Interrupt Service Routine (ISR) or Interrupt Handler is a piece of code that should be executed when an interrupt is triggered. Usually each enabled interrupt has its own ISR. In. AVR assembly language each ISR MUST end with the RETI instruction w

Appendix - Shuchita Prakashan
2012 - Dec [5] (a) Superb Electronics Ltd. is a manufacturer of electronic transformers, semi-conductor devices and other electrical and electronic equipments. During the course of such manufacture, the assessee also manufactured machinery in the nat

Online Appendix
War Draw. 0.006. 0.077. 0. 1. Civil War. 0.109. 0.312. 0. 1. Wealth (unlogged) ..... Sri Lanka. 1968. 2004. 0.405. 0.725. 3. 0.568. 0.835. 3. Sudan. 1968. 2004.

appendix
Mar 28, 2009 - TimE OF ExAmiNATiON. Vocational Subjects. 10.00 am to 12.45 pm [IST] including 15 minutes cool off time ... Physics/Geography/Accountancy.

Appendix
annual grant allocations using the same publicly available data the ... 2001 courtesy of Todd Richardson, and from 1993-2004 from a file on the HUD website ... by Congress (from Richardson (2005) for 1975-2002; HUD online data for .... 1990 Census Su

Online Appendix
(Online Appendix). By Filipe R. Campante and Quoc-Anh Do. This appendix contains two parts: first, the Data Appendix de- scribes the variables and sources used ... (uniformly) “random” deviations do not change the rankings of distributions as ...

Appendix
To measure individuals'transition probabilities pAB from labor force status A ∈ {E,U,N} to labor force status B ..... for different percentiles of the wage distribution.6 Since higher wage leads to higher search intensity of ..... A prominent examp

Online Appendix
to small perturbations of preferences and technologies. Indeed, this equilibrium would break if population 1 earned slightly higher salaries, needed slightly smaller land plots, ..... Figure 6 plots the locus of. (D.7) in the space (E,P) (see solid c

Supplementary Appendix
Substitution of (43) and (44) for m ∈ {s ,0} in (23) gives: dV dp . = −(. Я(8 − 2Я − 3Я2). 8(2 − Я)(4 − Я2)(1 − Я2)2 − (1 − Я). Я(2 − Я2). (4 − Я2)2(1 − Я2)2 \E i {[E{θ |s } − θ ]2}. = −Я. 8(4 − Я2

Appendix G
This processor, which is loosely based on the Cray-. 1, is the foundation for discussion throughout most of this appendix. We will call it VMIPS; its scalar portion ...