Katonah-Lewisboro Parent Report in Response to Proposed School Closure

8/13/2019 Katonah-Lewisboro Parent Report in Response to Proposed School Closure

1/32

Whither KLSD?A Discussion of Enrollment Forecasts, Their Uses,

Requirements and Limitations

Claire Aldrich and Satya NittaAcknowledgments: Chris Sommers

1Disclaimer: The analysis performed in the following pages is to be considered as opinions expressed by the authors only


2/32

Executive Summary

Demographers application of CSR method is invalid

CSR approach is inappropriate for cyclical situations

Historical data reveals enrollment could be

recovering soon

Multivariable linear regression may be a more useful

tool

Data requirements persist to complete analysis

Data thus far suggest the risk and cost of being

wrong are still too high

2


3/32


4/32

Outline

Critical review of the Grip report and conclusions

Review of cyclicality in enrollment

Multivariable linear regression

Observations and discussion

4


5/32


6/32

...which reflects the major limitations of the CS method for this situation, further exacerbated

by its flawed application.

Summary of C-SR method

2 parts to a standard Cohort Survival Ratio method.

Cohort survival method

KG enrollment prediction

C-SR Method: Start with current enrollments, by grade, then advance students one

grade for each year of the forecast. Thus, the current years kindergarteners

become next years first graders. The current years first graders become nextyears second graders, and so on.

KG Enrollment Prediction: The cohort survival method needs some way to obtain

future kindergarten enrollments. The study done for KLSD assumes that the recent

trend in kindergarten enrollments will continue.

Ex: If kindergarten enrollment declined by 5% annually during the last five years,kindergarten enrollment is assumed to continue to decline by 5%.

Mr. Grip used a variation. Average 3 years of birth data, used a fixed (1.25x) multiplier

based on 6 yr BK ratio taken during the recent downturn of the Great Recession.

6


7/32

Major Issues With Demographers Report

Does not consider growth in home sales which is the single

biggest source of increased enrollment in KLSD (statistical

proof later in this document)

Fixed births

Fixed birth to survival ratio of 1.25: - B-K survival ratios

could not be computed for the entire 20 year period b/c

KLSD geocoded data was not available. As a result, Dr. Grip

notes he could only use 5 and 6 year averages (p 12, Nov

2013 report). This dramatically skews the forecast

downward.

Misleading error projections. Claims enrollment can be

predicted within 1% for 5 years.

Implied suggestion that housing growth, macroeconomic

conditions etc are all being predicted to BETTER than 1% for 5

years

Very few first principles models in the physical sciences comeanywhere near this number, leave alone social sciences

Cannot model human behavior accurately (yet)

C-S method not appropriate for cyclical variations

irrespective of size of districts

Misunderstood our SAC/HU ratio historyhas been as high

as 1.25 (a fact overlooked by Dr G, but on the BOE website)

Chip Timing Models

5% accuracy outstanding

7


8/32

Two major disadvantages:

The first problem is that the method for calculating future kindergarten enrollments is likely

to be problematic when the trend in kindergarten enrollments is changing.

The second major problem with the K Linear Cohort Survival method is that it will poorly

forecast enrollments if migration patterns are changing. The most likely situation for this to

occur is when there is a substantial change in housing

Disadvantages of the Cohort-Survival Method

Berk & Associates, 2008

its accuracy as a long-term predictive

tool is poor to questionable CSR is only able to accurately forecast

for a very short interval into the future

Beyond one to two years, the

projections tend to be highly suspect since

CSRs major assumption is a linear trend

which may not hold true after a few years

Ref: Grip and Young, Planning and

Changing, 1999

Berk & Associates, 2008

8


9/32

Could this Be Us?Case Study: Washington State Mis-projection using Cohort-Survival method

Above graph shows the kindergarten trend in the State during the two time periods. Note that

kindergarten enrollments were declining during the 1997-2002 period, but rose (swiftly and

strongly) during the 2003-2007 period. Continuing the trendunderstated future kindergartenenrollments.

9


10/32

Outline





10


11/32

Two Major Questions

Is cyclicality a relevant issue for us to factor in?

If the C-SR method is not reliable, what is?

Lets consider our cyclicality

11


12/32

Based on Superintendent Kreutzers graph, it looks

like enrollment is going down..

12

0

500

1000

1500

2000

1990 1995 2000 2005 2010 2015

Elementary

Elementary


13/32

Based on preliminary data, however, a full history suggests we

are in a trough that could be on the verge of recovery

0

500

1000

1500

2000

2500

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020

KLSD Elementary Enrollment

Elementary Enrollment

ElementaryEnrollment

Year 13


14/32

Interestingly, Chappaqua follows very much the same

pattern

0

500

1000

1500

2000

2500

1975 1980 1985 1990 1995 2000 2005 2010 2015

Chappaqua

Katonah

1. Chappaqua, 2013: surprise Elementary enrollment increase of 39 students this year (58 total

across all grades). Attributed to existing home sales

2. KLSD 1998: Surprise increase of 91 students in grades 1-6 from the prior year's K-5, due to

home sales.

3. KLSD 1999: Additional 80 students

Chappaqua vs Katonah, Elementary Enrollment

14


15/32

So, if CSR is not reliable for cyclical

situations, What is?

The goal of this study was to construct a regression model tomore accurately predict enrollments than calculated by either theCohort-Survival Ratio method or by moving averages for a timeframe of one to seven years into the future

Although this *CSR+ is very accurate in short-term planning, its accuracy

as a long-term predictive tool is poor to questionable CSR is only able to accurately forecast for a very short interval into the

future

Beyond one to two years, the projections tend to be highly suspectsince CSRs major assumption is a linear trend which may not hold trueafter a few years

In a separate study to test whether regression analysis was abetter method of prediction than the Cohort-Survival Ratio,Webster (1970) found a regression model to be significantly moreaccurate than the CSR.

Source: R.S. Grip & J. W. Young, Planning and Changing (1999).15


16/32

Outline





16


17/32

How common are Regression algorithms?

One of the most popular projection algorithms

Used everywhere:

Epidemiology: Ex: Relation of smoking to mortality

Finance: Ex: Capital pricing asset models

Economics: Ex: Predict consumption spending

Real Estate: Ex: Predict housing prices

Physical Sciences: Ex: Complexity

Behavioral Sciences: Ex: Athletics world records

17


18/32

Multivariable Linear Regression: Inputs to the model

Housing

Birth rates

18


19/32

Housing strongly correlates with Enrollment

R = 0.6816

0

500

1000

1500

2000

2500

0 100 200 300 400 500

Total Elementary Enrollment

Total Elementary Enrollment

Linear (Total Elementary

Enrollment)

19

0

50

100

150

200

250

300

350

400

450

500

0

500

1000

1500

2000

2500

1975 1985 1995 2005 2015

Enrollment vs Housing

Elementary

EnrollmentHouses Sold

C-SR method applied during a growth cycle


20/32

Multivariable Linear Regression:

How good is this model?

0

500

1000

1500

2000

2500

2000 2002 2004 2006 2008 2010 2012 2014

Actual

Predicted

Limitations:Fits training data very well if data is linear (R2~ 0.9), but

Need independent variable trends

Accuracy improves with dataif cyclicality is considered, need more mathematical rigor (and

perhaps use polynomial regression or normalization)

Independent variables should not be strongly correlated (sufficient to establish housing and

birth rates are not highly correlated)

Enrollment = f(Housing, Birth Rates)

20

0

500

1000

1500

2000

2500

1990 1995 2000 2005 2010 2015

Elementary

Projections


21/32

So - What factors might drive a recovery home

sales forecast?

Economic indicatorsstock market up, unemployment claims down, GDP up..

Affluent Echo boomers nearing peak move to suburbs with children age

(KLSD) Empty nester pent up supply (needs more research- can we geocodelocations? Work w. R/E brokers to do surveys?)

Early signs of life in KLSD: In our townfirst grade class up 7%; Preschool classes also seeing growth

Home sales up 12%, now at 200 annual run rate

Last cyclehome sales went from 200 to 300 in one year and remained onaverage over 300 for the next 13 years...

Other notes:

FYI - Our SAC/HU ratio historyhas been as high as 1.25 (a fact overlooked by DrG, but on the BOE website.). Stock ratio, likely higher for new home sales.

Any secular concerns need to be addressed with hard data, not hunches oranecdotes

21


22/32

Linear Regression Projections

Capacity footnotes: BottomLine (A) 1380 = capacity with all 61 standard classrooms

Top line (B) 1440 = capacity in event of unlucky surprise: +60 students, across 3 grades and 2 schools need +6

extra classrooms in 2 schools. Note also violates ideal school size of 400 as shown in literature.

22

0

50

100

150

200

250

300

350

400

450

500

0

500

1000

1500

2000

2500

1970 1980 1990 2000 2010 2020

Chart Title

Elementary Enrollment

Enrollment

Enrollment

Enrollment

Grip Projections

Houses Sold

A*

B*


23/32

Our forecast thus far

Our forecast thus far:

Housing assumptions

Conservative: Housing stays flat, 210 sales a year

Moderate: 210300 growth over 5 years

Strong Recovery: 210330 growth over 5 years

Historical data show that home sales rose from 200 to 300 in one year

and remained on average above 300 for the next 13 years

23


24/32

Simple math and The Perfect Storm

(You tell me housing, Ill tell you enrollment)

Additional housing comes on line (Falcon

Ridge, Oakridge), housing market recovers, we

get a surprise increase K, 1stand 2ndgraders,

we need 3 extra classrooms at 1, 2, or 3schools.

Class sizes rise from 200 to 300 annually

enrollment reaches 1450 in 3 yrs (300 275 250200 200 200)

School size rises above 450+

24


25/32

Outline





25


26/32

What if were wrong?

What if were wrong? (How do we pass the What were you thinking

test?)

Is it appropriate to make decisions in the trough?

Especially where young children and their education is involved?

Would closing a school now be the equivalent of shorting the market?

If Jamie Dimon could not time it, and Alan Greenspan couldnt either

why should we be able to?

As we all know, its virtually impossible to time the market.

The only way to win long term is to stay invested and not to be going in

and out of the market. Capacity issues - caution re squeezing. MBA 101: NEVER run your plant

over 85% capacity

26


27/32

Other issues

Slippery slope risk: Need to keep our school system attractive to attract future

buyers and keep our community vibrant. MBA 101: Successful businessesmaintain and invest in their brands. They are sacred.

Impact of school sizeA survey of the literature shows that 400 students is the

ideal school size- could it be that all of our elementary schools were designed with

this principle deliberately in mind?

Tax cap issuesto reopenor grow when necessary

Execution riskthoughtful redistricting, physical simulation of bus routes still to be

done, as well as many other transition plans

27

Recap


28/32

Recap Demographers enrollment projections invalid.

Not appropriate for cyclical situations - ignored housing growth as a key predictor

Our district, like our peers, has cyclic enrollments. We are in a trough, and may berecovering soon.

We showed housing is a strong predictor

We built a multi-variable regression model. Predicted the past accurately. Needs work.

Initial regression model suggests strong correlation with housing

Over-predicting test data

A recovery could be underwaybut no one can accurately predict housing growth.

Chappaqua shows strong and sudden growth in enrollment and housing. We are very similar (recall

comparison)

In the absence of a credible enrollment forecast, there is no case to close a school.

At a minimum, we need more time to study and collect data

In a broader sense, even after further analysis, it may not be appropriate to

recommend closing a school in a period of cyclical recovery: (Not if, but when)

Respectfully submit that in faithfully upholding its stewardship of young children

and their education, it is not the province of a school administration (or any of us)

to be speculating on the future of housing. We are a school system, not a hedge

fund. 28


29/32

Appendix

Claire Aldrich Holds a BA in Economics and Political Science from Yale

University and a CFA. Claire has worked as a credit

analyst on Wall Street for 30 years.

Satya Nitta

- Holds a Ph. D in Chemical Engineering from Rensselaer

Polytechnic Institute. Master Inventor at IBM T J Watson

Research center. 15 years of experience in Nanoelectronicsinventing and developing future chip technologies. Recent

focus is on applications of Cognitive Computing.

29

i i l i d


30/32

Hypothesis:

Parameters:

Cost Function:

Goal:

Linear Regression Explained

30


31/32

0

1

J(0,1)

31


32/32

Gradient descent algorithm

Correct: Simultaneous update Incorrect:

32

Documents

Katonah-Lewisboro Parent Report in Response to Proposed School Closure