R/ffd_opt_caschool_prep_i.R
df_opt_caschool_prep_i.Rd\(\text{ID}_i\): individual id \(D^{\text{max}}_{i}\): maximimum discrete allocation each person, in addition to existing levels \(D^{\text{o}}_{i}\): what I call observed allocation, just any comparison allocation, in addition to existing levels, this is the additional allocation (ignoring existing levels), this is the not the total allocation. If fully redistributing, this could be the observed level of allocation. \(\Omega_{i}\): This is the expected outcome when the input of interest is completely zero, \(\Omega_{i}\neq A_{i,l=0}\), because \(l=0\) does not mean input is zero, using \(\Omega_i\) rather than \(A_i\) to avoid confusion because \(A_i\) sounds like \(A_i = A_{i, l=0}\), but again, the problem does not start with allocation at zero, but each district already has some existing number of teachers. \(\theta_{i}\): coefficient in front of student teacher ratio \(\beta_{i}\): i specific preference \(\text{enrltot}_{i}\): enrollment per district/school, assume no within district variations \(\text{teachers}_{i}\): teacher per distrct/school \(\text{stravg}_{i}\): average of student teacher ratio district/school
data(df_opt_caschool_prep_i)csv
https://fmwww.bc.edu/ec-p/data/stockwatson/caschool.des https://fanwangecon.github.io/PrjOptiAlloc/articles/ffv_opt_sodis_rkone_casch_allrw.html
Stock, James H. and Mark W. Watson (2003) Introduction to Econometrics, Addison-Wesley Educational Publishers, chapter 4–7.
data(df_opt_caschool_prep_i)
head(df_opt_caschool_prep_i, 30)
#> id_i D_max_i D_o_i Omega_i theta_i beta_i enrltot teachers stravg
#> 1 1 11 2 706.2218 -0.8699505 0.002380952 195 11 17.72727
#> 2 2 11 2 673.2570 -0.8699505 0.002380952 240 11 21.81818
#> 3 3 83 17 657.0958 -0.8699505 0.002380952 1550 83 18.67470
#> 4 4 14 3 656.3883 -0.8699505 0.002380952 243 14 17.35714
#> 5 5 72 14 655.5153 -0.8699505 0.002380952 1335 72 18.54167
#> 6 6 6 1 645.3442 -0.8699505 0.002380952 137 6 22.83333
#> 7 7 10 2 629.8211 -0.8699505 0.002380952 195 10 19.50000
#> 8 8 42 8 635.6090 -0.8699505 0.002380952 888 42 21.14286
#> 9 9 19 4 642.0002 -0.8699505 0.002380952 379 19 19.94737
#> 10 10 108 22 640.0966 -0.8699505 0.002380952 2247 108 20.80556
#> 11 11 21 4 644.5079 -0.8699505 0.002380952 446 21 21.23810
#> 12 12 47 9 639.3819 -0.8699505 0.002380952 987 47 21.00000
#> 13 13 5 1 639.7038 -0.8699505 0.002380952 103 5 20.60000
#> 14 14 24 5 652.1242 -0.8699505 0.002380952 487 24 20.29167
#> 15 15 36 7 652.4853 -0.8699505 0.002380952 649 36 18.02778
#> 16 16 42 8 641.9899 -0.8699505 0.002380952 852 42 20.28571
#> 17 17 29 6 636.8108 -0.8699505 0.002380952 491 29 16.93103
#> 18 18 26 5 648.4906 -0.8699505 0.002380952 421 26 16.19231
#> 19 19 303 61 640.4754 -0.8699505 0.002380952 6880 303 22.70627
#> 20 20 135 27 639.6701 -0.8699505 0.002380952 2688 135 19.91111
#> 21 21 24 5 638.0266 -0.8699505 0.002380952 440 24 18.33333
#> 22 22 21 4 643.5756 -0.8699505 0.002380952 475 21 22.61905
#> 23 23 130 26 652.8261 -0.8699505 0.002380952 2538 130 19.52308
#> 24 24 19 4 638.9334 -0.8699505 0.002380952 476 19 25.05263
#> 25 25 114 23 641.6650 -0.8699505 0.002380952 2357 114 20.67544
#> 26 26 85 17 647.3510 -0.8699505 0.002380952 1588 85 18.68235
#> 27 27 320 64 637.3398 -0.8699505 0.002380952 7306 320 22.83125
#> 28 28 135 27 640.1394 -0.8699505 0.002380952 2601 135 19.26667
#> 29 29 44 9 644.2859 -0.8699505 0.002380952 847 44 19.25000
#> 30 30 22 4 649.6760 -0.8699505 0.002380952 452 22 20.54545
#> distcod county district grspan avginc testscr
#> 1 75119 Alameda Sunol Glen Unified KK-08 22.690001 690.80
#> 2 61499 Butte Manzanita Elementary KK-08 9.824000 661.20
#> 3 61549 Butte Thermalito Union Elementary KK-08 8.978000 643.60
#> 4 61457 Butte Golden Feather Union Elementary KK-08 8.978000 647.70
#> 5 61523 Butte Palermo Union Elementary KK-08 9.080333 640.85
#> 6 62042 Fresno Burrel Union Elementary KK-08 10.415000 605.55
#> 7 68536 San Joaquin Holt Union Elementary KK-08 6.577000 606.75
#> 8 63834 Kern Vineland Elementary KK-08 8.174000 609.00
#> 9 62331 Fresno Orange Center Elementary KK-08 7.385000 612.50
#> 10 67306 Sacramento Del Paso Heights Elementary KK-06 11.613333 612.65
#> 11 65722 Merced Le Grand Union Elementary KK-08 8.931000 615.75
#> 12 62174 Fresno West Fresno Elementary KK-08 7.385000 616.30
#> 13 71795 Tulare Allensworth Elementary KK-08 5.335000 616.30
#> 14 72181 Tulare Sunnyside Union Elementary KK-08 8.279000 616.30
#> 15 72298 Tulare Woodville Elementary KK-08 9.630000 616.45
#> 16 72041 Tulare Pixley Union Elementary KK-08 7.454000 617.35
#> 17 63594 Kern Lost Hills Union Elementary KK-08 6.216000 618.05
#> 18 63370 Kern Buttonwillow Union Elementary KK-08 7.764000 618.30
#> 19 64709 Los Angeles Lennox Elementary KK-08 7.022000 619.80
#> 20 63560 Kern Lamont Elementary KK-08 5.699000 620.30
#> 21 63230 Imperial Westmorland Union Elementary KK-08 7.941000 620.50
#> 22 72058 Tulare Pleasant View Elementary KK-08 9.630000 621.40
#> 23 63842 Kern Wasco Union Elementary KK-08 7.405000 621.75
#> 24 71811 Tulare Alta Vista Elementary KK-08 9.630000 622.05
#> 25 65748 Merced Livingston Union Elementary KK-08 8.019000 622.60
#> 26 72272 Tulare Woodlake Union Elementary KK-08 8.523000 623.10
#> 27 65961 Monterey Alisal Union Elementary KK-06 7.983181 623.20
#> 28 63313 Kern Arvin Union Elementary KK-08 7.305000 623.45
#> 29 72199 Tulare Terra Bella Union Elementary KK-08 8.934000 623.60
#> 30 72215 Tulare Tipton Elementary KK-08 8.554000 624.15