the cost of the teacher’s experience increment in harford county

The Cost of the Teacher’s Experience Increment in Harford County

An Historic Misperception on the Added Yearly Cost When the

Increment is Provided

What is the Perception

The Perception (and Official Claim) is that to Grant the Increment the budget to fund salaries must be

increased (from prior year) by a 3% increase.[Some Historic Claims Put the Figure at 3.5% and 4%.]

How Did This MisperceptionBecome Ingrained

Misperception Goes Back Several Decades in Harford County but Persists to This Day

Presentation is Based on an Extensive Paper That Has Analyzed The Issue In Depth

Examples of What Has Caused This Cost Perception

2012: Harford County Executive quoted in the Sun “ proposed 1% pay raise, plus step and longevity pay, will cost the Board of Education approximately $10 million … “also comes with a cost –the loss of both administrative and teaching positions.” Computes to a 3% increment & 1% COLA for a $250 M budget

1979: Harford County Director of Administration: “If the average increment increase in the teachers’s pay plan is 4.5% and the entire pay plan is increased by 6.5% the total increase would be 11% in teacher’s salaries.”

1984: Aegis Editorial titled “ The Percentage Game” :The Aegis referred to taxpayers being “deceived by percentage figures” and suggested the “abolition of the increment system.”

1984: The Harford County Superintendent of Schools Budgeted 3.5% for the Increment.

Paper Addresses the Issue from First Principles with Extensive HCPS Data

• Presentation is Based on Extracts from Paper titled:

“The Mathematics of Budgeting for Experience Increments in a Teaching System or Other Workforce”

• The paper will be placed on the Internet • I Invite Critique of the Math and Data Used

Inherent Cost Components/Features of a System With Pay Progression (Increments)

• Increment Pay Schedule Tied to Certification and Experience

• Continual Refreshment/Renewal of Staff (Turnover from Retirements and Dropouts)

Continual Refreshment of StaffNumber of Teachers by Years Experience-

Comparison of HCPS to Recent National Data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Teacher Experience- National and

HCPS

Years of Experience

Num

ber

of T

each

ers

Rel

ative

to

Year

One National 1987-1988

National 2007-2008

HCPS Current

The Gist of the Computations

• Want to Compute the % Change in Payroll (PCP) if the Increment is Provided

PCP = % Due to Pay Progression (PCIA) - % Due to Inherent Staff Renewal (PCTO)

PCP = PCIA -PCTO

Computing PCIA

• P1 = Reference Year Payroll cost• P2i = Projected Year Payroll Cost

• PCIA = 100 x (P2i – P1) / P1

• Note: Data used and computations apply to 2979 HCPS certificated staff

The Actual Numbers versus the Perception [An Advance Look]

• The Perception PCP=3%, 3.5% or 4.%

• Actuality• For current nominal HCPS Conditions• PCIA= 1.78 %• PCTO= 2.09 %• PCP = - .31 %• Variability in PCP [At the End]

What Data Do We Need To Make Calculations

• Pay Schedule by Certification and Experience

• Experience Distribution of Staff

• Data on Turnover

Extract of Data Set for HCPS Increment Pay Schedule [Complete Data Set Extends to 48 Years]

Sched/Year 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

BAP 0 0 0 0 46799 46799 48205 48205 49652

BSP 41583 42829 42829 44114 44114 45437 45437 46799 46799 48205

DR 45937 47299 47299 48705 48705 50151 50151 51639 51639 53450

M30 45437 46799 46799 48205 48205 49651 49651 51139 51139 52950

MPC 44114 45437 45437 46799 46799 48205 48205 49651 49651 51139

PRO 41583 42829 42829 44114 44114 35007 35007 35225 35225 35445

ES(y) 42435 0 43792 0 45031 0 46629 0 48316 0

Sched/Year 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

BAP 49652 51139 51139 52675 52675 54254 54254 55883 55883 57558

BSP 48205 49651 49651 51139 51139 52675 52675 54254 54254 54254

DR 53450 55985 55985 58096 58096 60214 60214 62326 62326 64444

M30 52950 55485 55485 57596 57596 59714 59714 61826 61826 63944

MPC 51139 52675 52675 54254 54254 55883 55883 57558 57558 59286

PRO 35445 35662 35662 35882 35882 36099 36099 36388 36388 36764

ES(y) 50030 0 52140 0 53889 0 55787 0 57526 0

Table A-3 HCPS Annual Salaries by Professional Certificate Expanded to 48 Years Experience

Extract of Data Set for HCPS Teacher Experience [Complete Data Set Extends to 46 Years]

Schd/Exp 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

BAP 1 1 5 4 6 9.8

BSP 144.8 83.8 2 74 1 70 32.5 57 29 25

DR 3

M30 13 5.5 4 8 3 5 10 11

MPC 45 39 31 37.5 31 82 83.6 2 109.1

PRO 2

Sub Tot 207.8 128.3 2 110 1 116.5 71.5 148 128.6 2 154.9

Schd/Exp 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5BAP 8 2 10 8 2 11 1 11 2 11 20 3BSP 2 14 2 4 1 10 1 2 1 0.5DR 1 2 1M30 11 1 9 22 23.5 18 3 28.3 3 25 2MPC 6.6 85.5 9.5 74 11 54.1 9 70.4 7 61.6 12 50.7 17 55 11PRO 1 1

Table A-4 Number of HCPS Teachers by Experience and Professional Schedule 11/4/13

Let’s Look at PCIA

• PCIA = Percentage Change in Increment Alone• Assumes same staff size (and incumbents) • Increment is provided by standard schedule• Assumes no retirees and no separations

(dropouts). All staff move up one year in experience (and pay if eligible)

Need to Compute two Quantities P1 and P2i

Computing P1, P2i and PCIA

• P1 is the payroll in the “Reference year”• P2i is a fictitious * payroll in “Projected Year”

• PCIA= 100x (P2i – P1)/P1

• *Though fictitious it’s a stepping stone, convenient for computation, and very illustrative in outcome

Spread Sheet Calculation of Reference Year Cost (P1)

Sched/Year 0 0.5 1 1.5 2 . . . 46.0 46.5 47.0 Total

BAP 0 0 0 0 1 . . . 296.8BSP 144.8 0 83.8 2 74 . . . 563.6DR 3 0 0 0 0 . . . 1.0 14M30 13 0 5.5 0 4 . . . 571.8MPC 45 0 39 0 31 . . . 1528.8PRO 2 0 0 0 0 1.0 4Total 207.8 0 128.3 2 110 2979

BAP 0 0 0 0 46799 72,781 72,781 72,781 BSP 41,583 42,829 42,829 44,114 44,114 62,254 62,254 62,254 DR 45,937 47,299 47,299 48,705 48,705 80,905 80,905 80,905 M30 45,437 46,799 46,799 48,205 48,205 80,405 80,405 80,405 MPC 44,114 45,437 45,437 46,799 46,799 74,726 74,726 74,726 PRO 41,583 42,829 42,829 44,114 44,114 46,242 46,242 46,242 ES(y) 42,435 - 43,792 - 45,044 77,566 - 77,566

Reference Year Payroll Cost Sub TotalsBAP - - - - 46,799 0 0 0 19045694BSP 6,021,218 - 3,589,070 88,228 3,264,436 0 0 0 25573025.1DR 137,811 - - - - 0 0 0 927456M30 590,681 - 257,395 - 192,820 0 0 0 40361705.6MPC 1,985,130 - 1,772,043 - 1,450,769 74726 0 0 92504234.1PRO 83,166 - - - - 0 0 0 156318

178,568,433 Reference Year Payroll Cost P1

Number of Teachers by Certification z and Experience y

HCPS Pay Schedule by Certification z and Experience y

Spread Sheet Calculation of Projected Year Cost With the Increment (P2i)

Sched/Year 0 0.5 1 1.5 2. . . 46.0 46.5 47.0TotalNumber of Teachers by Certification z and Experience yBAP 0 0 0 0 1. . . 296.8BSP 144.8 0 83.8 2 74. . . 563.6DR 3 0 0 0 0. . . 1.0 14M30 13 0 5.5 0 4. . . 571.8MPC 45 0 39 0 31. . . 1528.8PRO 2 0 0 0 0 1.0 4

Total 207.8 0 128.3 2 110 2979

HCPS Pay Schedule by Certification z and Experience yBAP 0 0 0 0 46799 72,781 72,781 72,781 BSP 41,583 42,829 42,829 44,114 44,114 62,254 62,254 62,254 DR 45,937 47,299 47,299 48,705 48,705 80,905 80,905 80,905 M30 45,437 46,799 46,799 48,205 48,205 80,405 80,405 80,405 MPC 44,114 45,437 45,437 46,799 46,799 74,726 74,726 74,726 PRO 41,583 42,829 42,829 44,114 44,114 46,242 46,242 46,242 ES(y) 42,435 - 43,792 - 45,044 77,566 - 77,566

Projected Year Payroll Cost Sub Totals BAP - - - - 46,799 0 0 0 19,264,892 BSP 6,201,639 - 3,696,753 90,874 3,362,338 0 0 0 26,293,312 DR 141,897 - - - - 0 0 0 944,008 M30 608,387 - 265,128 - 198,604 0 0 0 40,875,461 MPC 2,044,665 - 1,825,161 - 1,494,355 74726 0 0 94,215,613 PRO 85,658 - - - - 0 0 0 159,548

Projected Year Payroll Cost P2i 181,752,833 Percentage Change Increment Alone Reference Year Payroll Cost P1 178,568,433 PCIA = 100* (181,752,833 - 178,568,433)/ 178,568,433 = 1.78%

Outcome should Not Have Been a Surprise

Sched/Year 1 2 3 4 5 6 7 8 9 10 11 12 13BAP 0 0 0 46799 48205 49652 51139 52675 54254 55883 57558 59286 61064BSP 41583 42829 44114 45437 46799 48205 49651 51139 52675 54254 54254 54254 54254DR 45937 47299 48705 50151 51639 53450 55985 58096 60214 62326 64444 66562 68676M30 45437 46799 48205 49651 51139 52950 55485 57596 59714 61826 63944 66062 68176MPC 44114 45437 46799 48205 49651 51139 52675 54254 55883 57558 59286 61064 62898PRO 41583 42829 44114 35007 35225 35445 35662 35882 36099 36388 36764 37126 37509



Sched/Year 40 41 42 43 44 45 46BAP 72781 72781 72781 72781 72781 72781 72781BSP 62254 62254 62254 62254 62254 62254 62254DR 80905 80905 80905 80905 80905 80905 80905M30 80405 80405 80405 80405 80405 80405 80405MPC 74726 74726 74726 74726 74726 74726 74726PRO 46242 46242 46242 46242 46242 46242 46242

Table A-3 HCPS Annual Salaries by Professional Certification Expanded to 46 Years Experience [ Matrix S(z, y ]

Retirements and Dropouts (Turnover)

• A Natural and Integral Component of a Progressive Pay System

• Patterns are Largely Predictable for Large Relatively Stable Systems

• The Model Addresses Variability from Driving Components such as Nret and Ndo, Dolev and Replev and Experience Distribution

Modeling Turnover Pto and PCTO

• Cost Reduction from Retirees = A2r• Cost Reduction from dropouts = A2d• Cost Increase Replacing Retirees = A1r• Cost Increase Replacing Dropouts = A1d• Pto = A2r +A2d – A1r-A1d• PCTO = 100 x Pto/ P1

Important Note for Calculations

• Retirees and Dropouts Salaries were computed in P2i at their Experience year y + 1

• To compute turnover changes in salaries their salaries (A2r and A2d) must be computed at years y + 1

Extract of 3 Year HCPS Data on Retirees and Their Years of Service

Retirees Retirees Retirees Years Get Count of 2010-2011 2011-2012 2012-2013 of Service 3 Year Avg No.Years of Service

Years of Service

Years of Service

at Retirement

of Retirees per Year

15 37 29 50 0.00028 24 22 49 0.00038 35 41 48 0.33319 25 27 47 0.00021 39 19 46 0.33310 35 33 45 0.33328 32 29 44 0.00019 24 24 43 1.00014 34 26 42 1.66727 22 32 41 3.00040 33 31 40 3.66736 18 32 39 3.33316 21 15 38 4.66714 4 11 37 3.00026 37 20 36 5.00025 18 19 35 3.66731 39 27 34 2.33333 22 39 33 6.00035 27 20 32 3.33329 14 24 31 2.66733 32 15 30 1.66735 33 27 29 3.333

…. …. …. ….. …….3 Year Average Total 93

Effective Weighted 3 Year Average Total 85

HCPS Retirement Distribution by Experience [Array RT(y) is a Key Component of the Model]

HCPS 3 Year Data on Numbers of Appointments, Separations and Retirements (2010-11 and 2011-12)

2010-2011Date of Report Appointments Separations

Weighted Separations Retirements

Weighted Retirements

9-Aug-10 0 17 17 1 113-Sep-10 172 27 27 4 411-Oct-10 11 2 1.8 1 0.98-Nov-10 1 1 0.8 3 2.4

13-Dec-10 2 1 0.7 0 010-Jan-11 13 5 3 6 3.614-Feb-11 3 2 1 3 1.514-Mar-11 1 3 1.2 1 0.426-Apr-11 0 4 1.2 2 0.6

23-May-11 0 2 0.4 3 0.613-Jun-11 0 2 0.2 1 0.111-Jul-11 0 61 61 60 60

2010-2011 Totals 203 127 115.3 85 75.12011-2012 Date Report Appointments Separations

Weighted Separations Retirements

Weighted Retirements

8-Aug-11 0 17 17 15 1526-Sep-11 147 19 19 8 824-Oct-11 7 9 8.1 3 2.7

21-Nov-11 2 3 2.4 2 1.619-Dec-11 2 4 2.8 3 2.123-Jan-12 2 2 1.2 5 327-Feb-12 7 0 0 0 026-Mar-12 1 1 0.4 2 0.830-Apr-12 0 2 0.6 1 0.3

21-May-12 0 2 0.4 1 0.225-Jun-12 0 0 0 0 0

9-Jul-12 0 69 69 71 71

2011-2012 Totals 168 128 120.9 111 104.7

HCPS 3 Year Data on Numbers of Appointments, Separations and Retirements (2012-13)

2012-2013Date of Report

Appointments Separations Weighted Separations

Retirements Weighted Retirements

13-Aug-12 0 43 43 6 6

182 10 10 5 5

22-Oct-12 5 6 5.4 2 1.8

19-Nov-12 5 5 4 2 1.6

17-Dec-12 11 4 2.8 0 0

28-Jan-13 1 4 2.4 7 4.2

25-Feb-13 13 6 3 4 2

25-Mar-13 7 7 2.8 3 1.2

22-Apr-13 3 3 0.9 1 0.3

28-May-13 0 1 0.2 0 0

24-Jun-13 0 0 0 0 0

29-Jul-13 0 88 88 52 52

2012-2013 Totals

227 177 162.5 82 74.1

Analysis of 3 Year Data to Determine Effective Number of Retirees and Dropouts

Analysis of the Three Year Data

Appointments Separations (Dropouts)

Weighted* Separations

Retirements Weighted* Retirements

3 Year Totals 598 432 398.7 278 253.9 3 Year Average

199 144 133 93 85

Effective Number of Dropouts and Retirees that are Removed and Replaced from

the Budget in a Single Projected Year 3 Year Staff Changes = Appointments - Separations - Retirees [598-432-278]

-112 3 year drop in staff

Of the 432 Separations , the fraction (432-112)/432 were replaced

0.741 fraction replaced

Yearly Average Number of Weighted Retiree Salaries Replaced

85

Average No. of Weighted Dropout Salaries Replaced 133* .741 98 Note: Number of Dropouts should probably be increased by 15 t0 25 for Leaves of Absence (LOA) for the fraction of the LOA who apparently (according to the Monthly Reports ) don't return. Accordingly to match the 208 staffers in the first year of employment, Ndo should have a value of 123 (123+85 =208). *Separations and Retirements are weighted by the actual number of months during the school year for those separations and retirements that occurred during the school year.

Accounting for Retirees

• A2r Cost Eliminated by Nret Retirees• A1r Cost Incurred by Replacement for Nret Retirees

• A2r = Sum [RT(y) x ES(y+1)/Nretref] x Nret =[Avg. Retirement Salary] x Nret

• A1r = Nret x ES(Replev)

• RT(y) No. of retirements with experience y• ES(y) Weighted Average Salary for retirees in year y• Replev Replacement Level

Accounting for Dropouts

• A2d = Cost Eliminated by Ndo Dropouts• A1d = Cost Incurred by Replacement for Ndo

Dropouts

• A2d = Ndo x ES(Dolev +1)• A1d = Ndo x ES(Replev)

Turnover Computations*

• A2r = $72,383 x 85 = $6,152,524• A2d = $52,140 x 123= $6,861,801

• A1r = $42,435 x 80 = $3,606,980• A1d = $42,435 x 123 = $5,219,513

• Pto = A2r +A2d –A1r –A1d = $3,739,240

• See Table MS-2 in the paper• MY Note: 5/30/2014 The final numbers above (as in the presentation) are correct per Table MS-2. Paper as presented to Board of Ed had two

errors. The number for Ndo was incorrectly listed as 128 rather than the corrected 123. The number for G4 in A2d was listed as $46,629 and it should have been the corrected $52,140. The final $ numbers on the right however were correct as they were lifted from the computed final numbers in Table MS-2.

Final Computation* for PCPPercentage Change Due to Increment

• PCP = PCIA (Increment Alone) – PCTO (Turnover)

• PCIA Was 1.78 % [Previous Computation]

• PCTO = 100 x Pto/P1 [Pto and P1 Previous computation]

• PCTO = 100 x 3,739,240 /178,568,433 = 2.09%

• PCP = 1.78% - 2.09% = -.31 %

• Contrast -.31% versus the Perception of 3%, 3.5% or 4% * See Table MS-2 in paper

Variation of PCP With Key Parameters

Parameter Symbol Parameter Range

PCP Range

Dropout Level Dolev 8 to 2 -.56% to .18%Replacement Level Replev 1-2 -.31% to -.15%No. of Retirees Nret 40 to 100 .44% to -.56%No. of Dropouts Ndo 60 to 130 .03% to -.35%No. of Teachers Nemp 2800 to 3200 -.44% to -.11% Nominal CurrentParameters

-.31%

No Increment Current Turnover -1.95% Increment Alone No Turnover

No retirees or dropouts

1.78%

See Tables SS-1 to SS-7 in paper for Effect of Variability due to Experience Distribution

Added Observation: Withholding the Increment is Not Cost “Neutral” (PCIWH)

• Withholding the Increment Leads to a “drop” in Payroll Costs by a Nominal 1.95%

*For Certificated Teachersand a $179M payroll that is a drop of $3.5M *For 5000 plus HCPS staff with a $250 M payroll that is a drop of $4.9M

Value of Single Stream Model

• Provides a very robust mechanism to study the effect of experience distribution

• Conclusion Based on Single Stream Model Calculations:

• As the staff moves toward “forward year” experience humps PCP gets smaller and generally negative

Next Steps

• Place Paper on the Internet• Engender Peer Review

My Hope: *Teachers, all HCPS and County Employees be Treated Fairly*If and When the Increment is Withheld, They be Told the Truth about the Cost Basis

High Level Overview of Computational Scheme

Table 1: Components of the Model to Predict Percentage Change in Payroll (PCP) Due to the Increment or Step System

% Change in Payroll (PCP) =% Change Due to Increment Alone (PCIA) -% Change Due to Turnover(PCTO): PCP = PCIA – PCTO

Components of the Model

Symbol Description of Component High Level Formulas for the Components*

P1 The total payroll for all teachers (or other type employees) in the model in the “reference year”

P2 Total payroll in the “projected year” allowing for the increment and a COLA and adjusting for retirees and dropouts and their replacements

P2i Total payroll (without adjustment for retirees and dropouts) projected for all teachers or employees in the projected year, with everyone gaining one year experience and salary change prescribed by the normal increment schedule, adjusted by COLA multiplier (1+CL) where CL = 0 implies no COLA.

This computation is done with the assumption that there are no retirees and no dropouts and the number of employees remains the same as for the computation of P1.

A2 Reduction in salaries (to be excluded in P2) (previously included in in P2i above)for projected Nret retirees and Ndo dropouts.[A2r is the retiree component of A2 , A2d is the dropout component of A2]

A2=A2r + A2d

A1 Increase in salaries (to be included in P2) due to replacing retirees and dropouts. [A1r is the retiree component of A1 , A1d is the dropout component of A1]

A1 = A1r + A1d

Pto Adjustment for Turnover Pto = (A2r + A2d)- (A1 + A1d)P1, P2and PCP

By Definition PCP = 100x (P2 – P1)/P1This is the % Change in Payroll in the projected year compared to the reference year

P2 = P2i –PtoP2-P1= (P2i-P1) –Pto(P2-P1)/P1 = (P2i-P1)/P1 – Pto/P1

PCP % Change in Payroll = % Change Due to Increment Alone - % Change Due to TurnoverPCP = PCIA – PCTO

PCP = 100x (P2 – P1)/P1PCIA= 100x (P2i-P1)/P1PCTO= 100*Pto/P1PCP = PCIA – PCTO

*Expanded definition for each component, to facilitate the modeling is developed in the paper.

the cost of the teacher’s experience increment in harford county

Documents