Category Archives: Government Agency Budgeting

The Fallacy of New Money Needed for Budgeting for Progressive Pay for Teachers (Increment Costs)

White Paper Executive Summary

Young teacher pointing at notes in his pupil copybook

In the American workplace, it is common to find a formalized structure of pay by position with a substructure or lanes of compensation that within a position or lane pays for experience and longevity with the employer. Progression in pay also occurs across lanes for individuals with increasing skills, certification, or job responsibilities. Within the teaching profession, this is known as the “single salary” schedule that came into general use following World War I. In describing the origin of the single salary system, Cuban and Tyack observed:

“teachers themselves fought to install in schools, from World War I forward, a single salary schedule for all public school teachers. While supporting salaries calibrated to training and years of experience teachers opposed “class distinctions” in pay based on position or sex and endorsed the fundamental intrinsic equality of all good teaching. To ensure that all teachers were, in fact, professionals–they worked to require special training and certification as prerequisites for employment in teaching.”

Universal Single Salary System

Today, the system is almost universal in school districts across the country. The single salary system is also frequently referred to as the increment or step system. Herein, it will also be referred to as “progressive pay” (or by the acronym ILL to refer to the Increment, Longevity, and Lane change). This system is also common in government at the local, state, and federal levels but also exists in some form in some corporate structures. In recent years, due to the economic downturn, jurisdictions facing budget shortfalls, have chosen to curtail the pay adjustments of positions associated with progressive pay along with withholding Cost of Living Adjustments (COLAs). In the process of rationalizing this course of action financial officers and government
officials frequently use what the author calls a “rule of thumb” where the claim is made that progressive pay costs, at whatever percentage, (e.g. 3% for the increment component), will lead directly to a 3% increase in payroll costs (in terms of additional new money needed ) if granted.

The Logical Mind Trap

I have heard this claim made for years, observed that it arises from an intuitive
“logical mind trap” (LMT) arising from the concept of focusing on individuals and their salaries as opposed to tracking positions, the numbers of individuals at each position, and the aggregate salaries for each position while at the same time accounting for the normal cyclical process of retirees, dropouts and new hires. As a result of seeing how teachers in my local area were denied both COLAs and progressive pay for four of the last five years, I set out to formally study the concept through a computer-based mathematical model. The model, employing Harford County, Maryland Public School (HCPS) data as input, to represent a typical educational workforce, explicitly confirms the following:

  1. The rule of thumb is totally invalid as a predictor of follow-on new money costs added to preceding base year costs when increments, longevity, and lane change (ILL) pay adjustments are provided to the workforce. Even in a wholly unlikely case of no retirees, no dropouts, and no new hires, providing a 3% ILL pay adjustment leads to a nominal 1.7 % to 1.9% increase due to the fact that top of the pay scale staff receives no increments and infrequent or no longevity and lane change pay adjustments. A parametric study for a range of parameters likely to span the possible scenarios indicates that providing the ILL adjustment during a period with the current level of retirees, dropouts, and new hires, leads to a nominal change in payroll costs of -.27 %, with variations rarely expected outside the range of (-.5% to .5%).
  2. Withholding the ILL pay is not cost-neutral. In a given year when ILL is withheld (along with a normal situation of retirees and new hires) the payroll cost (all other factors being equal) is actually reduced by – 2.0% from the previous year with variations between -1.5% and -2.2 %. This results in salary component budget surpluses (from salary costs) which are usually attributable to good fiscal management without explicitly acknowledging or understanding that the result was from an actual pay cut when based on positions rather than individuals or alternatively the funds are used to cover budget shortages elsewhere.
  3. The cost differential associated with progressive pay is strongly affected (drops strongly) with an increased number of retirees. The cost drops strongly with an increasing average level of the dropouts but at a significantly lower level than retirees due to the difference in salary levels.
  4. The extension of the rule of thumb, which leads to the suggestion that a COLA increase and progressive pay are additive, (e.g. a 5% COLA added to a so-called average 3% ILL increase leads to a needed 8% budget increase) is also totally invalid. Typical parametric calculations using the model show that the true cost of a 3% ILL, as described in 1. above, adds the range of “true ILL cost” increase in the absence of a COLA plus the COLA plus a negligible amount (product of the “true ILL cost”, times the COLA fraction).
  5. Failure to include Turnover in budgeting for ILL costs leads to a gross overestimation of budgeted “fixed charges” associated with employer-paid social security, medicare, and pension system withholdings. See Appendix B of the full white paper for a description of how the HCPS system adds these erroneous fixed charges to the erroneous estimation of the ILL cost.

Read the full treatise

A Simple Analogy for Understanding the Added Cost of Steps

I sent this simple analysis to Harford County, Maryland budget authority officials in February 1979 seeking to have them correct their erroneous claim regarding the “new/additional money” needed to provide steps or increments for teachers and other personnel.

Because Harford County officials have continued to make similar false assertions ( circa 2014-2016) regarding the added cost, this retired mathematician has examined the issue anew (this time more formally), created a web site, and placed the analysis therein. Hopefully, the widespread and readily available analysis will work toward officials ceasing to make false claims and accordingly chose to treat its employees fairly by routinely providing steps or increments since the added cost is negligible-as proven by the author’s analysis.

An experience increment of $500 dollars paid to an employee earning $11,000 per year amounts to approximately a 4% increase in salary. Discussion of the Harford County budget for the coming year in the local press indicates that the county treasurer and chief of administration plus certain writers analyzing the budget believe that an additional 4% over the previous year must be budgeted for each employee receiving the increment. This I claimed in my letter and enclosure of January 30, 1979, is not
correct. The enclosure contained a mathematical analysis which showed that a payroll system was cyclic in that people in the high experience levels, whose salary contained many increments, retired and thus compensated for many employees moving up the increment scale. I observed that the experience “shift” from year to year could cause an increase (or equally a decrease) depending on the experience statistics of the workforce. I claimed that the budgeting of 4% (as in my example above) was an
absolute upper bound that applied only in the unlikely circumstance of no retirees in a given year. The analogy below helps to put the problem in perspective and aids in understanding the point of contention.


Consider a classroom of 30 students and a teacher. Assume the 30 children are sitting in a row of chairs facing the teacher as depicted below.

C1          C2          C3 . . . C30

The student sitting in C1 has one piece of candy, the student sitting in C2 has two pieces of candy, etc. and the student sitting in C30 has thirty pieces of candy. The candy is analogous to the experience increments. The teacher instructs the child sitting in C30 to leave the room (analogous to retiring) and to leave his/her 30 pieces of candy on the vacated chair. The teacher then instructs each of the remaining 29 students to stand, leave their candy on their vacated chair, and to be seated in the adjacent chair to their left. The teacher then goes into the hallway and returns with a child whom
she seats in C1.

Happy laughing pupils of primary school having fun during break with their teacher, playing musical chairs

Now each child has one piece of candy more than when this exercise of chair moving began. Yet the teacher has not had to produce a single piece of additional candy. The moving from one chair to another is equivalent to personnel moving up in salary due to an additional year of experience. The child brought in from the hall is analogous to a new employee entering at a base salary. The analogy illustrates the point that when a workforce is stable or in steady-state, as far as average experience, then the year to year cost increase due to the increment is expected to be zero. Alternatively, in the absence of this steady-state, an average taken over a suitable number of years will find the increases are balanced by decreases.

Fallacy of Increment Costs-Experience in Jefferson County Kentucky

One of the hoped-for benefits of posting my paper on Increment costs on the Internet (on this web site) was that it would lead to a consensus of validation and support for the concept that progressive pay/increment systems lead to the need for little or no “new money” for projected year funding compared to a prior reference year payroll.

The availability of the paper led to my exchange of correspondence with Mr. Brent Mckim, a physics teacher in Jefferson County (Louisville), Kentucky, who was on leave of absence serving as his school district’s Teacher Association President. In that role, he engaged in a discussion with his Jefferson County Board of Education (JCBE) chief financial officer (CFO) who claimed that an annual 1.8% increase in funding was needed to pay for that County’s increment system.

This claim is essentially identical to the claim made by the Harford County, Maryland School system as documented in this post, which includes my full white paper. In a series of e-mails with me, Mr. Mckim first described a thought process (gedankenexperiment) that lead him to the conclusion that the year-to-year budget should be largely unaffected by the increment. In a follow-up e-mail, he thereafter cited how the state of Kentucky mandated that each school district must provide annual data to a master state database listing average teacher salaries for the year. In the correspondence, Mr. Mckim then showed how analysis of that data confirmed the thesis that providing the increment leads to the need for little or no new money to fund the increment. Below is the email sequence between Brent Mckim and me, the full details of which can be downloaded here.

E-Mail Correspondence Discussing the Fallacious Claim of Required New Money to Fund Increment Pay Systems

Sept. 7, 2014, e-mail

FW: Actual cost of a 1% raise

Thank you for sharing your rigorous analysis of step increase costs relative to turnover savings for the Harford County, MD school system. Below is an approach I recently used with our school board in Jefferson County (Louisville), Kentucky. I used a gedankenexperiment in which we assume a 10-year period with only step increases and no raises. I ask if we really expect the same salary schedule with the same pay in every cell to cost far more ten years from now than it does today if the salaries in each cell
have not changed.

Thanks again,

Internal Jefferson County E-mail attached to above Sept. 7, 2014, e-mail

From: Brent McKim
Sent: Friday, June 13, 2014 8:04 AM
To: Names Witheld by Request (NWBR)

Subject: Actual cost of a 1% raise

Q: Since step increases amount to an average of about a 1.8% increase in salary, wouldn’t a 1% teacher raise actually cost the school district 2.8% more in salary, benefits, and related expenses?
A: No, a 1% raise will only cost the district 1% more in salary benefits, and related expenses because the savings that occur when higher-paid teachers leave the district and are replaced by lower-paid teachers balances the additional costs associated with step increases.

There are micro and macro perspectives on teacher compensation costs.
From a micro perspective, we could say this ten-year teacher, who receives a 1% raise and a step represents a 2.8% cost increase for the district. This 30-year teacher with a Master’s degree who retires and is replaced by a beginning teacher with a Bachelor’s degree represents a 45% cost decrease for the district. And this veteran teacher who receives a 1% raise but does not receive a step represents a 1% cost increase for the district.

All of these micro perspectives are individually accurate and are occurring simultaneously. Notice that one 45% decrease offsets several 1% and 2.8% increases, and it would be inaccurate and unfair to the employees to only consider the 2.8% increases and make decisions based on the premise that the summation of these multiple micro perspectives yields a macro perspective in which the cost increase
for the group is 2.8%.

So what would the group cost increase amount to?

Given that we are dealing with a large sample of around 6,000 employees, the group is almost certainly in very nearly a steady state from year to year in which the savings that occur due to the replacement of more expensive teachers with less expensive teachers balances the cost increases associated with steps.

One can see this from a thought experiment in which we think of a scattergram of JCPS teachers for the next 10 years during which the district provides step increases but no raises at all. If no raises are offered, would the fact that the average teacher step amounts to a 1.8% cost increase for the individual teacher mean that 10 years from now employee costs for the exact same salary schedule that we have now (because we are assuming no raises in this thought experiment) would be 18%, more even though
there have been no raises? No, it would not. The actual year-by-year scattergrams of how many teachers are making specific salaries will be slightly different each year, with some years costing a little less and other years costing a little more; however, the total cost from year to year for the exact same salary schedule will not change in any significant measure. This shows that the cost of steps is statistically balanced by the savings that occur when more expensive teachers exit the district.

So, apart from some random noise from year-to-year variations in exactly how many teachers are in specific cells on the salary grid, a 1% increase to the salary schedule will cost the district 1% more.

This is absolutely the most accurate way to look at this. If the school board commits the district to a 1% increase on the salary schedule, the cost increase to the district for salaries, benefits, and related expenses will be almost exactly 1% more.

The CFO only chooses to focus on the cost of step increases. In the micro examples above, this is like only considering the teacher who costs the district 2.8% more without acknowledging the teacher who costs the district 45% less. In my opinion, this intellectually misleads the school board and creates an inaccurate perspective of what is occurring on the macro level that intentionally overstates the cost of employee raises and thereby discourages the school board from considering teacher raises in a way that
is more fair and accurate toward teachers.


Sept.13, 2014, e-mail

Hi Brent:

I really appreciated your letter and analysis because I feel so lonely in my advocacy for creating an understanding and acceptance of the true increment cost or as I put it “needed new money”, Your email reinforced my thinking that it is important to so many teachers and other workers to fix what I have described as this “logical mind trap”. I am attaching three old items from my first entry into this argument over thirty years ago. The first attachment is an editorial from our leading newspaper–a paper that has led a “jihad” for over 30 years against teacher’s pay and increments. The second is an analogy I forwarded to local officials who might not have followed the details of my first paper. The third item is a 1984 letter to the editor five years after I first joined the argument with my first paper.

I like your explanation of the gedanskanexperiment. I had to google it to get the origin of the term. Comments I have received on my paper include the observation that it is too difficult for many to follow in particular the local officials who make budget decisions. Accordingly, I would like to use your e-mail as a supportive analysis of my work and conclusion. In particular, I would like to post it on my website but I would do so only with your permission.

Please advise.

BTW: What has your experience been in your County’s reaction to your analysis? Is there any official acceptance that there is little or no ‘new money” cost from the increment? Related to that: My analysis suggests that there is a small (negligible) compounding effect when both the COLA and the increment are given. See Section 6 (g), page 27.

Best wishes,

Sept. 14, 2014,reply e-mail


Your point regarding the complexity of explaining how turnover savings essentially balance the cost of step increases is well-taken. We have certainly encountered that here. Consequently, I have opted to engage the same issue from a different direction. Specifically, I am in process of asking very specific questions of the district CFO, based on the previously claimed cost of the step increase versus the documented actual cost, viewed through the lens of average teacher salaries in the district.

Basically, if the step increases actually cost what they were claimed to cost, this should have shown up as increases in the average teacher salary. One could simply divide the extra cost asserted for step increases by the number of teachers to see how much this additional amount (which is supposed to be going into teacher paychecks) should elevate the average teacher salary BEYOND what one would expect from the pay raise alone. (See below.) Of course, no such additional increase in average salaries occurred. So the obvious question then becomes “Why?”

What I am working towards is having the CFO actually provide turnover savings as the reason why average salaries did not increase as one would expect based on the asserted cost of step increases. In short, I am hoping a patient and persistent focus on average salaries will be an easier framework with which to build a shared understanding (especially among a lay audience) of this complex issue than just
working on step increase costs/turnover savings alone.


Internal e-mail attached to above Sept. 14, 2014, e-mail

Subject: Avg JCPS Teacher Salaries

Here is a link to the page on the KY Department of Education website where the KDE provides a spreadsheet with year-by-year data showing the average classroom teacher salary for every district in Kentucky (it is important to select the classroom teacher spreadsheet, rather than the certified staff spreadsheet which includes administrators).

As you know, the KDE calculates this information based on the information officially reported to the department by each school district.

Below is the portion of the KDE spreadsheet showing the average JCPS teacher salary for each of the past three years, as well as the percentage change between these years.

Click here to see the table on page 5 of 6 in the white paper.

As you can see, in 2012-13, when JCPS teachers received a 1% raise on the salary schedule, the average teacher salary in Jefferson County increased by only 0.9%. This is presumably the case because the turnover savings from more experienced teachers leaving the district and being replaced by less experienced (and therefore less expensive) teachers was greater than the additional cost of step increases for those teachers who did not leave the district. Similarly, in 2013-14, when JCPS teachers
received a 0% raise, the average teacher salary in Jefferson County actually decreased by 0.2%. Again, this is presumably the case because the turnover savings from more experienced teachers leaving the district and being replaced by less experienced teachers was greater than the additional cost of step increase for those teachers who did not leave the district.

Question #1:
Can you explain why you have indicated to both the JCTA and the JCBE that the average teacher salary increased by more than the percent raise in each of the last two years while the information provided by JCPS to the Kentucky Department of Education indicates that the average teacher salary in JCPS increased by less than the percent raises?

When the Association and the District were negotiating last summer, you indicated to both the JCTA and JCBE that although the district was providing no raise for teachers, step increases would increase salary costs in JCPS by $10.2 million dollars in 2013-14, compared to 2012-13. Since teachers account for approximately half of the total salary expense in JCPS, step increases for teachers would have been approximately $5 million, based on the total cost you provided. However, the information provided by JCPS to the KY Department of Education indicates the average teacher salary actually decreased by $115 from 12-13 to 13-14, which would mean the 13-14 teacher salary schedule with no raise actually cost JCPS less than the year before.

Question #2:
If step increases had caused teacher compensation to cost $5 million dollars more in 13-14, we could determine the average salary increase this would lead to (by dividing the $5 million by the number of teachers in JCPS) (6,830). This calculation indicates that if step increases had caused teacher salary costs in JCPS to increase by $5 million dollars in 13-14, the average teacher salary should have increased by approximately $732. Could you explain why the information JCPS reported to the Kentucky department
of Education indicates the average teacher salary went down by $115 in 2013-14 rather than increasing by $732, as would have been expected?