Hello, I am trying to define and estimate the parameters from a log likelihood function using minimum wage data and unemployment and wage data from the National Agricultural Workers Survey. The individual likelihood contributions are defined as follows (from Flinn (2006): Minimum Wage Effects on Labor Market Outcomes under Search, Matching, and Endogenous Contact Rates):

For unemployed individuals Array



For employed individuals earning the minimum wage: Array



For employed individuals earning above the minimum wage: Array



where m denotes the minimum wage, w denotes the wage of individuals who are paid at least $0.50 above the minimum wage, rho*V_n(m) is denoted by the parameter "theta" in the code below, G() denotes the CDF of the lognormal distribution, and g() denotes the PDF of the lognormal distribution. So far I have specified my program as follows: I want to estimate mu and sigma (which are embedded in the G() and g() functions), as well as the parameters alpha, theta, lambda, and eta. Here is the code I have been using so far:

use "C:\Users\Zach\Dropbox\Confidential NAWS Data\Confidential NAWS Data 2018\Raw Files\NAWS Datasets (Stata)\nawscrtdvars1db18_STATA.dta", clear
rename *, lower
gen year = year(cs2)
merge m:1 state year using "C:\Users\Zach\Dropbox\AEWR Project\Data Files\Generated Data Files\State Minimum Wages No FY 1990-2018.dta"
drop _m
merge m:1 year using "C:\Users\Zach\Dropbox\AEWR Project\Data Files\Generated Data Files\Federal Minimum Wages No FY 1990-2018.dta"
drop _m
replace fed_min_wage = 3.35 if year==1988 | year==1989 //impute fed min wage data that is missing
replace min_wage = fed_min_wage if real_min_wage==. //impute fed min wage for states with no min wage
replace min_wage = fed_min_wage if state=="GA" | state=="WY" //impute fed min wage for states with lower min wage
replace fwweeks = 52 if fwweeks>52 //round down weeks for leap year
replace fwweeks = fwweeks/52 //normalize work weeks to 52 weeks = 1
gen unemployed = fwweeks < 52 //identify workers who were unemployed during year
gen ti = 52 - fwweeks if fwweeks<52 //identify length of unemployment spell
gen paid_min_wage = waget1<=(min_wage + .50) //identify individuals paid about the min wage
replace waget1 = min_wage if waget1<=(min_wage+.50) //replace wages for individuals who make min wage + .50
gen paid_above_min_wage = waget1>(min_wage+.50) //identify individuals paid above min wage
gen ln_mw=ln(min_wage) //generate the log of min wage
gen waget1_hi = waget1 if waget1>(min_wage +.50) //generate wages for individuals who make above min
gen ln_waget1_hi = ln(waget1) if waget1>(min_wage +.50) //take log of wages for those above min wage
replace paid_min_wage=0 if unemployed==1 //classify individuals as not paid min wage if classified as unemployed
replace paid_above_min_wage=0 if unemployed==1 //classifiy individual as not paid hi wage if classified as unemployed
program drop AEWR_1
program define AEWR_1
version 1.0
args llf mu sigma alpha theta lambda eta
tempvar G1 G2 G3 T1 T2 T3 T4 T5 T6
generate double `G1' = normal(sqrt((ln_mw - `mu')/`sigma')^2)
generate double `G2' = normal([(ln_mw - (1 - `alpha')*`theta')/`alpha' - `mu']/`sigma')
generate double `G3' = normalden([(ln_waget1_hi - (1 - `alpha')*`theta')/`alpha' - `mu']/`sigma')/(`sigma'*waget1_hi)
generate double `T1' = ln(sqrt(`lambda')^2) - ln(sqrt(`eta' + `lambda'*`G1')^2)
generate double `T2' = ln(sqrt(`eta')^2) + ln(sqrt(`G1')^2) if unemployed==1
generate double `T3' = -sqrt(`lambda'*`G1'*ti)^2 if unemployed==1
generate double `T4' = ln(sqrt(`G1' - `G2')^2) if paid_min_wage==1
generate double `T5' = -ln(sqrt(`alpha')^2) if paid_above_min_wage==1
generate double `T6' = ln(sqrt(`G3')^2) if paid_above_min_wage==1
quietly replace `llf' = `T1' + `T2' + `T3' if unemployed==1
quietly replace `llf' = `T1' + `T4' if paid_min_wage==1
quietly replace `llf' = `T1' + `T5' + `T6' if paid_above_min_wage==1
end

ml model lf AEWR_1 () () () () () ()
ml check
ml search, repeat()
ml maximize, iterate(50) difficult
ml graph
exit

I get this message indicating that feasible values cannot be found. Array



First of all, I am not sure if I should be using the lf model or if I should switch to using the d0 estimator. Also, I am not sure if I am specifying the equations correctly in terms of the () () ... () after the ml model lf AEWR_1 command. At this point, I do not want my dependent variables (i.e., ln_mw, ln_waget1_hi, and ti) to depend on other variables, which is why I left the () without an equation in them. Is this how I should be doing it? Any help you could provide would be greatly appreciated, as I have spent the past two days trying to figure this out.