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The Economic Costs of Alcohol and Drug Abuse in the United States - 1992

Appendix B, Table B.4

Outline for Estimation of Lost Earnings Using the RAND Microsimulation Technique for the Alcohol Dependent Population

(Note that making estimates for the drug dependent population is directly parallel to the following steps). For the Non-Alcohol Dependent (non-AD) population (but including anyone drug dependent) with earnings in the past month, estimate the following regression:

(1) Ln (Y) = f(Age, Ethnicity, Rural/Urban, Children, Depression, Drug Dependence)

Where Y = earnings in the past month.

Estimate with Ordinary Least Squares

For the Alcohol Dependent (AD) population (only if alcohol dependent, whether or not start drinking by 15th birthday)

(2) Ln (Y) = f(Age, Ethnicity, Rural/Urban, Children, Depression, Drug Dependence, Drink by 15)

Estimate with Ordinary Least Squares

Calculate the smearing coefficient for the non-AD (Sn) and AD (Sa) populations respectively. This is done by saving residuals from the respective regressions and calculating the mean of the anti-logs of the residuals.

Calculate the impact of AD:

Predicted earnings of AD population if NOT AD, given coefficients (Bn) of characteristics X in Regression (1) estimated on the non-AD population: Age, Ethnicity, Rural/Urban, Children, Depression, DRUG DEPENDENCE

(3) E(Yn) = {exp(X*Bn) * Sn}

Predicted earnings of AD population if AD, given coefficients (Ba) of characteristics X in Regression (2) estimated on the AD population: Age, Ethnicity, Rural/Urban, Children, Depression, Drug Dependence, Drinnk by 15.

(4) E(Ya) = {exp(X*Ba) * Sa}

Estimated dollar impact of AD on the individual:

E(Ya) - E(Yn) = {exp(X*Ba)*Sa} - {exp(X*Bn)*Sn}

Sum these values (using appropriate sampling weights) to develop total population estimates. Adjust estimates for observations with missing data by adjusting the estimates up in proportion to the difference between the total population in the group and the weighted population from the survey.

Approach to Estimation of Losses From Excess Unemployment

A second level of analysis is necessary in order to estimate the costs of excessive unemployment among the AD population. This analysis couples selected regression results from the above analysis with the results from logistical regression analysis of unemployment and AD.

Estimate for the non-AD and AD populations, respectively:

Probability of Employment/Earnings (for males and females, respectively)

Pr(EMn) = f(Age, Ethnicity, Rural/Urban, Children, Depression, Drug Dependence)

Estimate with Logistical Regression in SAS

Calculate the expected earnings if not affected (averaging in the expectancy of being employed and the expected wage if employed) for the AD population. This value for a given individual would be equal to their probability of being employed times their expected earnings if employed, based on the product of the logistical regression prediction of probability of being employed, and the smearing adjusted OLS regression results.

Defining Earned Income (EI) as the average across all individuals, including both those with and without employment (EM) and earnings (Y) in the period being analyzed, then expected Earned Income based on the experience of the non-AD population for a given individual with characteristics X is:

E(EIn) = Pr(EMn) * E(Yn) * Sn

evaluated at their values for X, with the smearing adjustment Sn. expected Earned Income for this AD individual with characteristics X is:

E(EIa) = Pr(EMa) * E(Ya) * Sa

Next, calculate the average and total earnings for the AD population using both of these measures. The loss in Earned Income for the AD population, factoring in both the employed and unemployed is equal to the difference in these two values:

Loss = E(EIa) - E(EIn)

This dollar estimate of total loss in Earned Income can be compared to their predicted earned income E(EIa).

Part of the total loss of Earned Income was estimated above in the analysis of loss of Earnings (Y) for the employed population, and this estimate of total loss can be disaggregated into the loss associated with the impact on Earnings (Y) if employed, and the loss from reduced levels of Employment (EM).


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