.~ · .

POPULATION PROJECTIONS: PAST AND PRESENT

1975 - 1978

C. Scott Hromas and Tom G. Crago Office of Research and Evaluation Department of Corrections State of Colorado December, 1978

Document 1178-4 \ INTRODUCTION

A major function of the Office of Research is the projection of inmate commit­

ments and incarcerated populations. These projections have become an integral

part of the Department's budgetary and facilities planning process.

Accuracy in inmate population projections is not a simple task. As this off~.ce

has experienced, it is very difficult to project commitments and incarcerants in

a non-static environment. Changes in parole board policies, legislation, and

the economy have been major factors affecting accuracy of inmate population pro­

j ections.

In ordCl. to better understand the techniques used to project inmate populations,

and the factors contributing to error in them, this report ,.;rill give an over-

view of the Department's population projection techniques from 1975 to the present. Our first attempt at inmate population projections began in July, 1975. As prior research had frequently found that unemployment rates and thc~ number of prison commitments ,vere highly correlated, ,.;re examined that relationship in

Colorado. Using quarterly data, ,ole found a very high correlation bet'tveen Colo- rado's unemployment rate and the number of new court commitments.

Using the Colorado unemployment rate as the driving variable along \vith the state's population and the seasonal variation of commitments, 'tve utilized a multi- pIe linear regression model to predict ne"!;v court commitments. Since commitments affect our total incarcerated population, commitments were combined with parole revocation rates and the percent of determinate sentences received to predict the incarcerated population. Those projections, published in a paper presented to the 1976 ACA convention (Research Document 76-10), were as follO\vs:

February, 1976 Projections and Actual Ex~erience

Projected Actual Proj ected Actual Incarcerated Il1carce17ated Year Commitments Commitments Population Population

1971f 1187 1994 1975 1439 2l1/~ 1976 1401 1311 2117 2260 1977 l330 1276 2105 2lfl!5 1978 1328 2105 1979 l340 2].07 1980 1354 2110

These projections were based on the £ollO\ving assumptions:

L) The unemployment rate would stabilize at an annual average of 1,.2 by

third quarter, 1977.

2.) No diversion would occur.

3.) Average length of stay would be captu~ed by the rate of determinate

sentences received.

4.) No changes in legislation would occur. 5.) The level of parole revocations \>lOuld stabilize at approximately 144

per year.

Actual date compiled for 1976 and 1977 indicated that commitment projections for those two years we're in error by 6.9 pm:cent and 4.2 percent, respectively.

In each year, our stntistical model over-proj ected the numbe.r of commitments.

(See figure 1).

The accuracy in the commitment projections was not achieved by the predictive power of the model itself, but by two factors counter balancing the actual commitments,. First) we had underestimated the unemployment rate (,vhich means that we should have under-projected the number of commitments) and, secondly, we assumed that no diversion would occur (which means '.;Ie should have over­ projected the numher of commitments).

To test the accuracy of the:· model for 1976 and 1977 projections, actual unem­ ployment: rates '.;Iere substituted for the original estimates. The results in­ dicated an error rate of 15 percent in 1976 and 18.9 percent in 1977. This in­ ordinate error rate lead us to further examination of the unemployment rate varial;le used in thl': model.

In the original model, the relationship bet"t·men the unemployment rate (set at a three month lag) and commitments was relatively high ( r = .7410). '~hen actual unemployment rate data were inserted into the model, the. relationship "vas found to be insignificant (1' = .1054). \\lith the loss of this relationship, it became apparent that the error associated \.;Iith this model ,.,ould not allmv uS to quantj.fy the degree to \vhich th(;'. unemployment rate or diversion rate affected the actual number of commitments.

The error r;).te Clssociatcd for the incarcerated population 'was 6.3 percent in 1976

and J.lI percent in 1977. Each year the model under-projected the incal4 ceratcd pop------._------....--,---

ulation. (See figure 2). Firs~, the model had not included any effects of

new legislation. As discussed later, H.B. 1111 did, in fact, have an increas-

ing effect on our incarcerated population. A second factor contributing to the

lo\v proj ections 'vas the inappropriate use of the determinate sentences re-

ceived variable. As the number of determinate sentences received increased

(Hhich ~vould indicate a longer average length of stay), the effect in the model

was to reduce the incarcerated population projection.

Finally, the leve1 of revocations did not stabilize at 144 but incl~eased to

nearly the level experienced prior to the Norissey vs. Brewer decision. (A su-

preme court decision that stimulated legislation mandating due process be fol-

lmved for all parole revocations).

A Second Attempt.

In late 1976, the Office of Research published 5-year population projections in

the 1977 Corrections Haster Plan.

These projections were based on the following assumptions:

1.) Unemployment will peak at 6% by calendar year 1977.

2.) Average length of stay had stabilized at 20 months.

3.) H.B. 1111 impact will not occur all at once but 'viII be phased over

time, up to a maximum of 492 ADA per year by 1981.

4.) Diversion will occur over time up to 10% by 1982.

These new projections were as follows:

December, 1976 PopulatiOI~ Pro,icctions and A.Etua1 EX!2.erience

Proj ected Actual Calendar Proj ected Actual Incareerated Incarcerated Year Commitments Commitments Populn t io.I}. poptll~.tio_ll

1977 1376 1276 2351 2l. l15 1978 1379 2/169 1979 1387 2586 1980 1395 2650 198J. 1401 26118 Actual 1977 data indicated that the Department received 1,276 nm.; court commit­

ments and had an average incarcerated population of 2,L,L,5. Therefore, our new

court commitment projection was in error by 7.8 percent (ovci-projected), and

the incarcerated population proj ection ~.;as in error by 3.8 percent (under-pro­

jected). (See figure 3 and 4).

In retrospect, this error can be at~ributed to several factors associated \.;ith

the commitment and incarcerated population projection methodology.

A.) New court commitments - The key vm:'iable in the commitment model was the

future trend of the state's unemployment rate. In order to proj ect ne\.; court

commitments, we had to estimate the future trend of Colorado's unemployment rate.

From information gathered from state and private organizations, ~.;e estimated the

state's unemployment rate to peak at 6.0 percent during 1977. Actual unemploy­ ment rate data revealed an average rate of 5.6 percent in 1977 - Etn error in our

estimation by . L, percent.

'1'0 test the error associated by the unemployment rate estimates used in our model,

we substituted actual unemployment rate data for the original estimates. The model then proj ected 1,353 conmlitments. With actual data, the overall (I.rror'rate

\.;as reduced to 6.0 percent. Therefore, our unemployment rate estimates contri­

buted ~.8 percent of the overall error in the projections.

Reasons for the overall error rate of 6.0 percent in this projection methodology

(an over-estimation of commitments by 77 offenders), are difficult to pinpoint.

In a pure statisUcal sense, \.;e could attribute all error to the model itself.

Howcve:r, we feel that the presence of a state diversion program accounted for

part of this total error. Unfortunately, \.;e are not certain to \.;hat degree di­

version has affcctc.:d the rate of commitments and therefore nre unable to quantify ------~-~~------

the truE effect of diversion.

E.) Incarcerated Population - As stated before, the incarcerated population pro­

jections for 1977 ,,,ere in error by 3.8 percent. Again, 've feel this error rate

was not due entirely to the model itself but due to sev~ral unforseen factors

affecting the system.

First, the 1976 projections ,,,ere based on an estimated t1ggregate length of stay

of 20 months. In fact, it was closer to 24 months. The. additional II month

length of stay, coupled '''ith the actual Imver rate of commitments, ,acted as

counter effects on the actual population.

Second, the commitment pro;-:ection error associated ,dth the rate of diversion

,,\las apparently counter-balanced by an increased number of shock probation re­

leases. Overall, probation releases increased from 74 in 1976 to 114 in 1977.

Finally, it is felt that the effects of H.B. 1111 occurred faster than originally

estimated in the 1977 corrections plan.

First Update

In February, 1978) a population projection update ,vas published in Correct:i.ons

Five Year Plan. The projections were based on the following assumptions:

1.) H.B. 1589 was vetoed.

2.) Colorado's unemployment rate would drop to 5.4 percent

by 1978-79.

3.) The average length of stay had stabilized at 211 months.

4.) No ne,v legislation ,."ould be passed which 'vould significantly

effect sentencing or length of stay.

5.) No change in the diversion rate would occur over the next

five years.

------~- Calendar Year ->->Conmli ----- t men t s Incarcerated Population 1978 1320 2536 1979 1323 2585 1980 1331 2648 1981 13lf5 2667 1982 1359 2694

Inspection of the actual data compiled during the first nine months of 1978 would indicate the commitment and population projections for 1978 ~vill be relatively accurate. (See figure 5 and 6). However, the accuracy of the long range pop- ulation projection is suspect due to some recent research findings.

A study funded by NrC (National Institute of Corrections) and coordinated through the Office of Reserrch this summer documented aggregate lengths of stay for of- fenders received over a five year period, 1973-1977. This study revealed a pro- jected 26.2 month aggregate length of stay for offenders received in the th:lrd quarter of 1977. This figure is 2.2 months higher than the 24 month estimate used to project incarcerated population in the five year plan.

In addition, a recent publicat:ton by the Department of Labor and Employment

(Colorado Har?ower Review, April-·1978) estimated that between Octover, 1978, and September, 1979, Colorado's unemployment rate 'viII average 6.0 percent.

I.n light of these new findings, an update to our population projections seems necessary. These ne~v population proj ections are based on the following as- sumptions:

1.) H.B. 1589 has been vetoed.

2.) Colol:ado' s unemployment rate \vi11 rise to 6.0% by 1979-80.

3.) The average length of stay has stabilized at 26.2 months.

If.) No l1e\v legislatiOll \-1ill be passed \-1hich would s:tgnificantly effect

sentencing or length of stay. 5.) No change in the diversion rate will occur over the next five years.

Yam.. Commitments Population

1978 1265 2491 1979 1318 2679 1980 1350 2867 1981 1350 2936 1982 135/f 2950

These. projections are used in the FY 1979-80 budget request nnd are the most rec0nt projections available, based on the above mentioned assumptions. (See figure

7 and 8).

CONCLUSION

The Office of Research continually monitors the assumptions u.nder1ying its most recent proj ections. As tve have shown, a significant change in any assumption can produce errors that make both short-term and long-term projection accuracy difficu.1t to achieve.

In future months, we \vi11 attempt to quantify the rate of diversion that is ef- fecting the new commitment proj ections. "ath this variable quantified, along

'with a reliable unemployment rate estimate, we feel that COlmnitment projections can achieve greater accuracy than in the past.

Incarcerated population projections are more difficult to monitor. This part of thiO! projection model is most affected by unforseen factors, such as pat:ole policy, legislation, and offender length of sentence.

The main factor that will certainly affect future incarcerated population pro- jections is the outcome of Colorado's netoi' sentencing legislation. As that bill becomes 18\01, tole tvi1l analyze its effects upon the incarcera ted popuJ at;i,on and update projections appropriately. Corunitment Projections and Actual Experience

February, 1976 __ Actual ____ Projected

, 550 ': i'; I ~ ~'II j BTl' r"!'I':!~71'TmT=I1ITt nfl"TIJT ,m:I' fl r-r 'iT, ii' ;'-l"!,r -1 i·f·T..I~lTI·1 ill'~1 I 'PI: 'r~I!'·~·I-'TI··'I,~vl'T I ~III 'I III I .,' '1:1 ; I i,l' 500 ;,'~: I n·! ~ ;'1 ~: I i'rTl J,,11: .Ull i·t" ·I .. JJ. ill I~ JilL.ul i ,'.L_, .! ri;~ '~lL lL0."1.Lr-~ .~,l~ .. ,-,- "··I.J, LL .LL -L. ! I'! .I, I ' !~Ll.i ;.t~1'r;:·!~ 1·!,·l-ti]illll'j'.ll.ll11·ilf,lj'jl.t 1'11~1 j,~·.li ·,lY':I::r l :··I'il !. 'I' J'li 1'1'1 ':[11'11 fil! 11·I.i.!.,'.', r,!TII,·il'l! ! : • ''"7 r" I • ~ : \ 1 ! t" , ! I I" : I ..:. I.' r~ !, ,,' I H I I I I' I :, II' I '( I I 'I' I' II II r: t..:=J- ': I"," ,1.:_1_:: ,: " .!.lL JJ I· '! L w':':":~:r .,~ .. ~. ,.!lL L/,,'.'. ,.:.ill. J.:;+~. ti.' ': ..L, J '1. ,_'. • "J __ , _. ~rJ. 'L:"~ ..J ... ~.' . r' I 1 Ul 4JOI:l·~1··~"-·'''i':''''..1'''ill~ ';·I!'I IIW·,r. :111 [.'1 11 I:'J'II"~' :Ii rl·l, i":' III1 'l'l'l rn·!' llll'll' 1"lll • Til' j'I'!·,"·I,[ ~ i·:':'~'~'LT~I·i.t1:~·I.I,':~·;·rl·L !,'.l.I . .',lr:i, ,~" 'i',l ILl;,! !I:"', 11·II'l,·!·Jfll,,'I·l j"1 , 1'1' I'!., 1I'III'~'111~'I''i'li. i!'l~"

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Figure 1 Projected Incarcerated Population and Actual Experience

February, 1976 Actual --____ Projected

3000 ~, r iii lffiI'HJrH!+JlillT UJl1m1 Inlllirl !!rUln m:Tljrmr ,]ll[ 1m. UT j'l1J ur!" ITll,[[[ rr~ l i I 2900 ;"'-I~~"~T~ '\-- i /"j' ,11'11 ,,: l'l~l""I' .;j"iT ,1':1 'li I ., Ill I'!'l[" ' f:/1 III" 1111 I!JII"I ' h~'i~ ,Hjj I ij \L nLl il.: i :11:1! iJl )lE:l !L, !:: [_ .! ,j !~ JJt-r 11 i'!. lIlt J .. j JI,! 1,i Il" 11,. --,W ",:r+ If: Llj+!]. U 2800 1 r.!.:·~-:·li,~r~'I.r~·:~·!,·.lI:!l'i'I'j:llTI illl' !1 ,.) f'I'll \I:,':)'l ii'il' i)l'l ,1:,',! 11{jl,l!'j'j 1iQl' ,,~n 1~I'·IlI"!!I'1'l'III:',"j'l TIIII I1II r!d'" !"'" !" - ,',"', l£if .," i" ';'1"'1 'j -" " l'l "I',,,', · f ~ 11 'f 1·,', " I I I 'I II I r 1'\ , 2700 i 'j i" (J) 2600 ii~ ;,~'Il~:; if- '~;H 11".\';: :~j~i: tn:h" I,l: i-1j'j:l '111'1"1 i! i fi'fi- -r l:jl TI~i r In tJ'I'/ T IT! 11rl- Hlllrrr qlT mi IT! I' r:: .. t II .. t'\'.!.'·--I 1 .. ·,i-:- '\'·I+·I'I·j,r.JI·-'",:I·-I' .. !'!Tr III'I T CiS I;",~ ~~i~1J.~"'-'!':';'f"".· .. td..~lllLI·..!..II·JI,·~.!,~. I'i';' ,; '1:' I ~+~1"II-.-.;I·-!,'1 I :1 ,I ~P'':I::'" ~"1'7-J""'~'l'',r l " 'J 'J ll·tl':I·'~"1 'I. l" 'rr·l+rii~'I lll'\'l' H 2500 :'·~··I':"';:-: ~,-,: '~':+7 1"f:"-1I',I"" :, .. , "1', "j:1 1-1.1' !'! r' ;,":"",1 ~!'i' II I" 'I, . I '1" J' I ., II ,'Ii'-"1 CIJ _...... '.. '.. ·1 ...... ' " .... ,I.!,! ,I"~ 11,Y I" X 'II', J I I, I, I' (j H Cil 2400 -;1::1 r,; 'I' ,..-\1:,' t'r:' : :.. '!'Ij+\ ,- T ·rl'll. "1:1' "lITt 1"1"'1-' I\.!.',\" '/'\' (j ' ~ :~7.~1·~ :l ~ ~ ~:,;. ~+i- ~f; 7,'1"il~'I" :N1~r~~' ~~~ ~~1:7]1'-1 ;I+~·[:· 'h~!"TI Yl+',' ll"r II' r~1 tt~ll: r:: :1 -, ;::,:.~ ;i:;~ ,~j~j" tiT! t':,"! :ji' "~-,,:,, ,I, u:u ", II II, i.LL ~I' ;ii'l ,: I 'ill" ,I II; 'I,:: 2300 ~ I' rTr t ,J Hi ~~;.;' ~j'~:;'1 ;.:',~ ;'I"fu~ 'i'~;' :I'in ,,-' ',r' . :r'tt ·l..,'t :' +1'-1' _1]:1...0. '-II r:ri' lj1 ·',1,11"·~ fl"T,' '-l'·~tl' 'r'l' rt :.: "I' rt ",'ll' -:rrr ,: ""r'l'~I"1iTf 11;;, :.!.;.: 'j',',','i ill!"'!' I ').1:'" 'tl'l I" ,'I ! I ·1' I, I, I,'· eil'l, ,',',1. I:..r!~, ,. • .'. I I' ,', 1::,' • I • I I 2200 ' I r· "r. .,:'ll'[!"1 . J "t i "1 I j , L. p, ; - I I"- ~' ,-·'t·,! -----,'I : I • _.-""''-n'l" -1- !-" ••.'-- ' •. " - , 'r ,!' ., .• ~,'. -••!..- I .... ,' ••• ,' 't'" ,I .... r 'r' .. '" '1 '" '-'11'" I 'j"-" 11'"'" ·~I"1-r.I 'ITfI ! ' • .~ .... i' ,i'! :!' L . (I-f I iii I . ,~' , I ,I I ,\. I I I l I' , I ' , ,~ : 2100

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Figure 2 Commitment Projections and Actual Experience

December, 1976 -- Actual ____ Projected

Figure 3 Projected Incarcerated Population and Actual Experience

December, 1976 __ Actual ____ Projected

3000

2900

U) ~ 2800 ~ (:j l-< ~ u 2700 l-< co u 2600 ~ H

4-l 0 2500 l-< aJ 2400 ...0s :l z 2300

2200

2100

2000

1900

1800

0 Qtr. Yaar

Figure 4 Commitment Projections and Actual Experience

February, 1978 Actual --____ Projected

.

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I:;·~·~ ~~'i.~' 1;·!1 ~I,rl ·l,\·j !.II~·l·ll.llj "~I' III \'1'1 L \'11 III! I I I' II I 'Il~l !llrt:; 1 ... - .. - -~ ... ~ 'J 1'\' 11 L • 'I ., ,1\ 1..1 I I I I \ I! III lil ~ I 1 I'I I II I· I, '\ J 150::~:.~'11·:~·~:~ '~';:;~I'~:I'~i \I'I:'~ n~I~I'I·;II"ll IT'l '~'+H+tl-I'~!tT' 'H-!-I:t ·Iil,r"· 'J' I r· , l\·_,····!,·,I-l\J..I+ \ .1.IIIT·I!IU ::r~~ 1j'-ri. I 1:II .1' ,. i, ' , .l I' I 1'1 I W" I! J·,· ' ... - ~.I ,_...r~ ~ !I /.,'r t I" J , ·r 1ill· .. \ . 'i II I III I'I• J ',i,,' I ! I 'll I .... . , I . ,I. I I I'1 ~ 100 , -..:.....:...:. ~r.~ -- ...... -~- ... ..". .\ ..... _.. ,. ,--,.:. 'r -..~ ....L. 'f···· ...... '- _. . ~, ...... , .. w. "1'. -" ., .~ '·I·',rl"""" 'I-,I r ,1.,,1 .. \.\._., I'''' .' '1' I . II, I I 11-\1 1.\ I n I' ~ I II' 5 0 ~+~i )i~ ~ ;: 4.lf +1!~1'~ r'm;"Jl LI i+,' ~ +1\: 'rI, ..' .' 'j'" ]111-\' ++.L1ll'l'fi ~jl' ~UJ:"IrHo 'f,'1' II ~ +r ":J--l~' ,.. I "i . ~I- I .[[' T-I; I': ;·H·'.·!:! li"l ,1. 1 I lJJl:.1. ,I.. ·1· 1'1 I· . 11' 1'1" ' . I' . I I ~ • • 'I. r ,,, I.... I, \ ,. ~ I' • II ,.\ I I. I' I I I Ill''I '1 1 ' 1 ! I I ! It·I .• o i,:J.. L:_ .c~~.t.U.:!l ±tLL J.lLL' I' ~. .I! " . ,_ ..ill .. : ,:,L_L I .... ~.I .1 ....L •. .;.J.. __ , • .l:J. 1 • _ 11 !

Qtr. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 Lf 1 2 3 4 1 2 3 4· 1 2 3 4 1 2 3 4 1 2 3 4 Year 1974 1975 1976 1977 1978 1979 1980 1981 1982

Figure 5 Projected Incarcerated Population and Actual Experience

February, 1978

__ Actual ____ Projected

I ,• '..'" ,.,"

Figure 6 ------,---,------

Commitment Projections and Actual Experience

September, 1978 __ Actual ____ Projected

, ,~ .

550 '7:~,"'!''''::' Ir'\: nT ..I·fT.'i~I'I'·it'

Figure 7 Projected Incarcerated Population and Actual Experience

September, 1978

--- Actual Projected

3000

2900

(I) LJ 2800 c::: C'j !-I aJ u 2700 !-I Cil u c::: 2600 H 'Ha 2500 ~ aJ A 2400 ~ :z; 2300

2200

2100

2000

1900

1800

0 Qtr. Year

Figure 8

'------~ Population Projections Data

2/76 12/76 2/78 9/78 Year ~ Pro.i ections Projection~ Projections Proj ections Actual

1974 1 1961 2 2000 3 2017 4 1999 1975 1 2033 2 2109 3 2153 LI 2160 1976 1 2140 2184 2 2134 2267 3 2097 2280 -, LI 2098 2308 1977 1 2126 2346 21.04 2 2119 2382 2l.95 3 2087 2338 2/.64 If 2089 2336 2419 1978 1 2122 21185 2453 2l.38 2 2118 2483 2525 247 l, 3 2087 2lf5/{ 2580 2511 2512 4 2091 2l.53 2584 2541 1979 1 2125 2601 2560 2549 2 2120 2600 2553 2649 3 2089 2572 258£1 2738 4 2093 2571 26/11 2778 1980 1 2127 2665 2M3 285l. 2 2122 2664 261/6 2873 3 2092 2636 2650 2858 4 2096 2635 2651, 288l 1981 1 2130 2662 2659 2939 2 2661 2664 2953 3 2634 2670 2923 4 2633 2676 2927 1982 1 2683 2968 2 2690 2969 3 2697 2931 II 27011 2932 1983 1 2711 2973 2 2718 2975 3 4 Commitment Projection Data - (,

2/76 12/76 2/78 9/78 Year Pro jec. t ions ~ .~~C?J cction~ Proj ection\o- Proj ection~_ Actual

197 LI 1 311 2 309 3 281 4 286 1975 1 346 2 404 3 355 LI 334 1976 1 353 2 374 343 3 322 270 L, 322 345 1977 1 362 368 379 2 353 367 361 3 306 321 269 I, 309 320 267 1978 1 357 368 35il 347 2 351 367 352 3/fl 3 307 322 296 286 i, 313 322 315 291 1979 1 360 370 .355 31.,9 2 354 369 353 354 3 310 324 298 305 4 316 32/1 317 310 1980 1 36L. 372 357 364 2 357 372 355 364 3 313 326 300 311 4 320 326 319 311 1981 1 368 375 360 364 2 374 358 364 3 329 30l. 311 i. 329 323 311 1982 1 3M 365 2 362 365 3 307 312 4 326 312 · :;: i,.. ~" .,. 11 .... fIo ,