Table 2 |
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Microsimulation steps for estimating the cost of productivity losses due to CFS. |
|
| Step |
Equation |
|
|
|
| 1. Divide the study sample data into two groups: Fatigued (F), N = 3,528, and Non-Fatigued
(NF), N = 3,634. Estimate logistic regressions to obtain the probability that an individual
is employed for F, P[W = Y/F], and NF, P[W = Y/NF], subsamples, as a function of human
capital characteristics, as displayed in equations 1a and 1b. |
|
| a. P[W = Y/F] = f(age, sex, ethnicity, education, suspected CFS, CFS, history of diseases
that exclude respondent from CFS diagnosis) |
|
| b. P[W = Y/NF] = f(age, sex, ethnicity, education, history of diseases that exclude
respondent from CFS diagnosis) |
|
| 2. Estimate ordinary least squares regressions to predict the natural log of income
(I) given employment for the F, E[I/W = Y,F], and NF, E[I/W = Y,NF], subsamples, as
a function of human capital characteristics, as displayed in equations 2a and 2b. |
|
| a. E[I/W = Y,F] = f(age, sex, ethnicity, education, suspected CFS, CFS, history of
diseases that exclude respondent from CFS diagnosis, occupation) |
|
| b. E[I/W = Y,NF] = f(age, sex, ethnicity, education, history of diseases that exclude
respondent from CFS diagnosis, occupation) |
|
| Note: Once these regressions are estimated, only the sample of 43 individuals with CFS are used for the remainder of the microsimulation
to estimate mean labor force and household productivity by age and sex in the presence
and absence of CFS. |
|
| 3. Calculate predicted mean F and NF employment rates by age and sex categories, weighting
by sampling weights. Multiply the coefficient estimates from the F (Blf) and NF (Blnf)
Logit regressions by the human capital characteristics of the 43 individuals with
CFS (X) to obtain their F (P[W = Y/F]) and NF (P[W = Y/NF) employment rates, respectively,
as shown in equations 3a and 3b. Then, calculate the mean employment rate across the
43 individuals with CFS for each age and sex category weighting these means to reflect
the survey sampling rates. |
|
| a. P[W = Y/F] = {exp(X*Blf)/1+exp(X*Blf) |
|
| b. P[W = Y/NF] = {exp(X*Blnf)/1+exp(X*Blnf) |
|
| 4. Calculate predicted mean F and NF income given employment by age and sex categories
weighting by sampling weight. Multiply the coefficient estimates from the F (Bolsf)
and NF (Bolsnf) OLS income regressions by the human capital characteristics of the
43 individuals with CFS (X) to obtain their F (E[I/W = Y,F]) and NF (E[I/W = Y,NF)
income given employment, respectively. Then, apply the smearing adjustment to the
exponent of these F and NF products, as shown in equations 4a and 4b, to correct for
the "retransformation" bias that arises from estimating impacts using loglinear models
and to protect against data issues such as heteroskedasticity1. The smearing factors for the regressions among individuals with F (Sf) and in the
absence of F (Snf) are equal to the means of the anti-logs of the residuals of the
respective income regressions. Calculate predicted F and NF income given employment
for each age and sex category weighting by the survey sampling weights, and adjust
these means from 1997 to 2002 dollars to account for inflation using the Department
of Labor, Bureau of Labor Statistics Consumer Price Index from 1997 to 20022. Apply an adjustment factor for the difference between mean income in Wichita and
the nation based on analysis by the U.S. Department of Commerce3 increasing the estimated losses by 1.3 percent. In addition, to account for fringe
benefits, multiply predicted income by a factor of 1.338, which is obtained from the
Bureau of Labor Statistics Report on Employer Costs for Employee Compensation – June
20024. |
|
| a. E[I/W = Y,F] = {exp(X*Bolsf)*Sf}*1.114*1.013*1.338 |
|
| b. E[I/W = Y,NF] = {exp(X*Bolsnf)*Snf}*1.114*1.013*1.338 |
|
| 5. Calculate predicted household productivity given employment and no employment in
absence of F. The value of household productivity by sex, age, and employment status
absent F is calculated on the basis of data on the number of hours spent on household
chores for the NF sample, given employment (HH hours/W = Y,NF) and no employment (hours/W
= N, NF). Value these hours at the average hourly wage for a service industry worker
as estimated on the basis of the March Supplement of the Current Population Survey
2002 or $9.20. Similar to employment income, increase the value of the service industry
worker wage by a factor of 1.338 to account for the value fringe benefits. This equation
is displayed in 5a and 5b. |
|
| a. E[HH/W = Y,NF] = E[HH Hours/W = Y, NF]*$9.20*1.338 |
|
| b. E[HH/W = N,NF] = E[HH Hours/W = N, NF]*$9.20*1.338 |
|
| 6. Calculate predicted household productivity given F. Assume that the percentage
reduction in employment related income, given work, is equal to the percentage reduction
in household productivity. Apply a reduction factor representing the estimated reduction
in employment-related income, given work, resulting from CFS to the predicted values
of household productivity, given employment and no employment, as displayed in 6a
and 6b. Calculate reduction factors separately for males and females. |
|
| a. E[HH/W = Y,F] = E[HH/W = Y,NF] * E[I/W = Y,F]/E[I/W = Y,NF] |
|
| b. E[HH/W = N,F] = E[HH/W = N,NF] * E[I/W = Y,F]/E[I/W = Y,NF] |
|
| 7. Calculate predicted mean F and NF total productivity for each CFS individual. Overall,
each CFS individual's expected total productivity in the presence or absence of F,
E[Y/F] or E[Y/NF] respectively, is equal to the probability that they participate
in the labor force, P[W = Y/F] or P[W = Y/NF], times the expected value of their total
labor force and household productivity if they participate in the labor force plus
the probability they choose not to participate in the labor force, P[W = N/F] or P[W
= N/NF], times the expected value of their household productivity when they do not
participate in the labor force. Equations 7a and 7b display expected productivity. |
|
| a. E[Y/F] = P[W = Y/F]{E[I/W = Y,F] + E[HH/W = Y,F]} + P(W = N/F) {E[I/W = N,F] +
E[HH/W = N,F]} |
|
| b. E[Y/NF] = P[W = Y/NF]{E[I/W = Y,NF] + E[HH/W = Y,NF]} + P(W = N/NF) {E[I/W = N,NF]
+ E[HH/W = N,NF]} |
|
| 8. Calculate estimated number of individuals with CFS nationally by age and sex. Using
the Wichita Prevalence Study data, calculate the prevalence of CFS per 100,000 by
age and sex cells and then use national population data from the Current Population
Survey to calculate the number of individuals in each age and sex category with CFS. |
|
| 9. Calculate individual and societal productivity losses due to CFS. Compute the difference
between predicted mean total productivity without and with F, (E[Y/NF]-E[Y/F]), by
age and sex category to estimate the individual loss for each age and sex cell and
then multiply these differences for each sex and age cell by the estimated by number
of individuals with CFS nationally in each cell and sum across the cells to estimate
the total societal cost of lost productivity due to CFS. |
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1Duan N. Smearing Estimates: A non-parametric retransformation technique. J Am Stat Assoc 1983,383:605–10. 2Consumer Price Index from 1997 to 2002. Department of Labor, Bureau of Labor Statistics. (http://data.bls.gov/cgi-bin/surveymost?cu webcite, then select U.S. All items, 1982-84=100 CUUR0000SA0) 3Per capita net earnings ($) Metro Comparisons. Department of Economics, Iowa State University, Midwest Profiles, Public Resources Online. (http://www.bea.doc.gov/bea/regional/reis/ webcite, then select Personal income and population summary estimates (CA1-3) plus per capita personal income plus Metropolitan Statistical Areas*)4Employer Costs for Employee Compensation – June 2002. Bureau of Labor Statistics, September 2002. (http://http//data.bls.gov/cgi-bin/surveymost?cc webcite, then click on Civilian, All workers, Total compensation - CCU110000100000D) |
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Reynolds et al. Cost Effectiveness and Resource Allocation 2004 2:4 doi:10.1186/1478-7547-2-4 |
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