Determinants of employment in rural Montana counties

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1 University of Montana ScholarWorks at University of Montana Graduate Student Theses, Dissertations, & Professional Papers Graduate School 1972 Determinants of employment in rural Montana counties Patrick William Shannon The University of Montana Let us know how access to this document benefits you. Follow this and additional works at: Recommended Citation Shannon, Patrick William, "Determinants of employment in rural Montana counties" (1972). Graduate Student Theses, Dissertations, & Professional Papers This Thesis is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact

2 THE DBrERK HA 3 OF J^LOMWT IK HURAL mwsmk COUNTIES By P u triek..shannon B»S, U n iv e rs ity of Montana, 1970 Presented 5n partial.. fulfilufaent of the reqnii'esaents fo r the degree of M aster o f Science, 15HIYEESIT! OP MOHTAKA Approved JoJL - PT tnarraan ca ' Board Kjf 'l& ad jn ers '^Schooi

3 UMI Number: EP40342 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP40342 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml

4 i-a^ '7^. TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION... 1 XI. SELECTION OF INDEPENDENT VARIABLES... 3 H I. DEPENDENT VARIABLES... 9 IV. EXPECTATIONS REGARDING RELATIONSHIPS OF THE IHDSPEHDHNT VARIABLES TO EKraxftHENT I I V. THE STATISTICAL PROCEDURE...16 VI. THE REGRESSION EQUATIONS v.ij. e ounmahy «< 2y BIBLIOGRAPHY APPENDIXES k x -L *» «- «*» 3Ll J53? I I I.... U3 ^r* IV U7 i i

5 LIST OF TABLES TABLE PAGE 1. Mon-Trade Center Counties , 2. Independent Variables Industries Chosen fo r Analysis il, -Summary of Expected Regression C oefficient S i g n s...lit 3. Business and Repair Services 1960 and 1970 Regression Equations Eating and Drinking Establishm ents 1960 and 1970 Regression Equations Finance, Insurance, and Real. E state 1960 and 1970 R egression E q u a t i o n s Food and Dairy Products 1960 and 1970 Regression Equations. 23 CHART I. Ecanple of Employment Growth Trends iii

6 CHAPTER I INTRODUCTION The p rin cip al objective of the study was to Investigate the factors which have led to changes in eroploynient In certain in d u stries in ru ra l Montana. The investigative procedure was m ultiple lin e a r regression, a s ta tis tic a l technique described in a subsequent section. The most important re s u lt was the derivation of a method by which the trend of employment fo r an industry in a p a rtic u la r county con be predicted. This technique may have p o sitiv e applications for the businessman -who d esire s to know what the fu tu re holds fo r a p articular* county. While the technique w ill not p red ic t the sales fo r an industry, a businessman might lo g ically conclude th a t an increase in employment w ill be q u ite c lo sely co rrelated w ith an. in crease in sa3.es. Variables which are considered to be determinants of employment, or output, were regressed against employment data fo r selected counties. The data were broken down Into a cross section by counties in Montana. Each of the hi counties which do not contain a trade center as defined in Trade Centers and Trade Areas of the Upper Midwes t by J ohn R. Borchert and Russell B. Aclams represent a sample u n it. Although Montana has 56 counties, i t was decided th a t cn3.y the Ip. ru ra l counties 'would be used in the study because investigation uncovered the fa c t th a t there are d is tin c t differences between the more populous counties and the ru ra l counties. These d ifferen ces make segregation by trad e center

7 2 and non-trade center b en eficial. Table 1 l i s t s the Ijl counties from which sample d ata were obtained. TABLE 1. NOE-TRADE C5NTER COUNTIES Beaverhead Big Horn Blaine Broadwater ' Carbon C arter Chouteau Daniels Fallon G arfield G lacier Golden Valley G ranite J efferson Judith Basin Lake L ib erty Lincoln McCone Madison Meagher Mineral 1-fuss el sh ell Petroleum P h illip s Pondera Powder River Powell P ra irie Ravalli Roosevelt Rosebud Sanders Sheridan S tillw a ter Sweet Grass Teton Toole Treasure Wheatland Wibaux. Source: Trade Centers and Trade Areas of the Upner Midwest, by John * 0 ^1 1,.1'n ^ 'i ua.». JH I L.I.II1...uu.a'iuw t i. w i». in mi i w r u i»r -i--i r ir «, l~ui tt ft\ n~r - r -M-Te ^ John R. Borchert and R ussell B. Adamsi Urban Report Number 39 Upper Midwest Economic Study, September, 1963, Table U, p Data fo r I960 and were used to provide two separate studies fo r two separate time periods. between the time periods. This provides a b asis fo r comparison

8 CHAPTER II SELECTION OF D1DEPMDENT VARIABLES Since the p rin cip al objective of the study was to in v estig ate th e determ inants of.employment change, the selected independent v a ria bles were chosen with the b e lie f th a t each i s in flu e n tia l in determining employment change. Although employment in the various industri.es Is not affected by the same variables to the seme degree, employment data fo r each selected in d u stry Trill be regressed against the same independent v ariab les. Table 2 l i s t s the independent variables which hare been selected. These v a ria b le s are defined in the follow ing paragraphs. TABLE 2 INDEPENDENT VARIABLES Population Per Capita Income Percent of Families with incomes under $3000 Percent of Families with incomes over $10,000 Dependency Ratio Distance Square M ies Percent of Labor Force Unemployed P ercent of County Urban Population is the to ta l of a ll persons liv in g in a Montana county in eith er ru ral or urban location. The data are tahen from the 3

9 1 i 960 and 1970 Census of Population. Population i s included as an u independent variable because people demand goods and services and. demand i s sa tisfie d by the output produced by those employed in the industry. Per c a p ita income i s th e quotient of personal income in a Montana county divided by the population of th a t county. Personal income i s a laeasure of income before tax es. I t Includes wage and sa la ry income, other labor income (mainly frin g e b e n e fits of workers including employer co n trib u tio n s to p riv a te pension funds), Income of proprietors of unincorporated business en terp rises, property Income (net re n ta l income, in te re s t, and dividends received by persons), and tra n sfer payments (so cial security, welfare b en efits, unemployment compensation, pensions of r e tir e d public employees, and c e rta in other re la tiv e ly minor payments fo r which no services are rendered cu rren tly ), 2 le s s personal contributions fo r so cial insurance. Because finances are necessary to tra n sla te needs and desires into demands, per capita income, a measure of average welfare w ithin a county, i s considered a determ inant of In d u stry employment. *fhe percentage of fam ilies with incomes under $3000 and the percentage of fam ilies with incomes over $3.0,000 are measures of the lu, S. Bureau of Census, Census of Popu la tions 1970, General Population Ch ar ac t e rl s t l c s - -Pin al Report PC (T) - B28 Montana, Table 3 C p F. so l't h a ih in g to n, D. Gr. TJ. S. Government P rinting O ffice, 1971)5 U. S. Bureau of Census, U. S. Census of Population; I960, General Social and Econom ic'characteristics, Montana Pinal Report P C ~ T i)7 ^ o 7 ^ it " 8 '2 7 p p :T 8 fl3 rt M ^ S B 6 F, l)7 T 7, 1961). 2 U. S. Department of Commerce, Office of Business Economics, Regional Economics Information System, "Unpublished Data, June 8, 1971 j U. S. Department of Commerce, Office of Business Economics. Survey of Currenu Business, 51(8):30-31, August 1971.

10 3 d istrib u tio n of income w ithin a county. These data are taken from $ a 2^> percent sample conducted in conjunction with the census of popu~ la tio n. The need for a d istrib u tio n measure of income as opposed to the average le v el of income, expressed by per capita income, is because of the p o s sib ility th a t two counties could have the same or nearly the same per capitalincomes but y et be very d iffe re n t in the nature of th e ir business a c tiv itie s because of differences in the d istrib u tio n of income among resid en ts. The dependency ra tio i s the percentage of people who are under 18 years of age or over 6U years of age.^ This percentage measures the extent to which a county s re sid e n ts: are very young or very old 3 thus, these two groups may have specialised demands and/or d iffe re n t buying h ab its, and th is may be reflected in industry employment. The distan ce v aria b le i s defined as the distance in highway m iles from the la rg e st c ity, in most cases the county seat, to the nearest trade center. Not only does th is variable measure the re la tiv e iso la tio n of a county, i t represents the co st, in terms of inconvenience and trav el time, of obtaining goods and services from a source other than the home county. Consequently, the distance variable i s a conceivable influence on in d u stry employment w ithin a county. %. S. Bureau of the Census, U. S. Census of Population; I960, General Population C haracteristics, iiont an a--final Report PC'TlT - 2SB", Table 2f, pp~ -ti&w - 2B 6 Jl ash in g to n, D«C*: TJ. S. Government P rin tin g O ffice, l 6l ) ; U. S. Bureau of the Census, Census of 'Population? 1970, General Population Character is t ic s.pitsx ^ p o il/p O XTJ* ~ B2S- liontaha, Table -.2*8-7^ O ^ h ln g io u, It-. C s U. S. Government P rin tin g O ffice, 1971). lju. S. Bureau of the Census, County and City Data Book, 196? (A S ta tis tic a l Abstract Supplement), Table 2, pp. 212 and 222"Trashingbon, D.C.: U. S. Government P rin tin g O ffice, 1967).

11 MONTANA p l c n t y w o o o N C 0 L N U B B Y 9 KAL IS. PELLj ^ r sf v LAC ( ft CUT BANK PONDERA 0 0 L 9 SHELBY 9 CQNRAQ I6ERTY HESTER HAVRE s CHINOOK 9 MALTA \ L L I * 5 GLASGOW, CROTEAU TETON C K U T A U FORTDENTON U C C 0 «t SIDNEY THOMPSON FALLS PO ISO N SUPERIOR 6 GREAT FALLS *nwnwob8w»< CASCADE STANFORD p e t r o l e u m JORDAN GL ENDIVE y/isaux MlNERALjb MIS ms-soula POWELL «l e w is t q w n w h in e t t t e r r y HAMILTON RAVALLI HELENA I M U SS ELSH EL L M E A G H E R WHITE SULPHUR $ HARLOWTOH GOLDE! g r a n i t e DEER LODGE 9 ROUNDUP PHILIPSaURG SPRINGS VALLtY TOWNSEND HYSHAM I FORSYTH Q WHEATLAND BOULDER RYEGATE BROADWATER ANACONDA TREASURE R 0 S E S U 0 YELLOWSTONE 0 E E R SWEET GRASS BUTTE IJEFFERSON LOOGE SILVER. LATIN SOW BIG TIMBER STILLWATER B E A Vg ft H EAD DILLON U A 0 I S 0 N VIRGINIA CITY BOZEMANo ^ 0 I LIVINGSTON JTCQ LW BU S PARK CAR BON RED LODGE BILLINGS HARDIN horn m il e s cnty p o w d e r r i v e r BfiOADUS b a k e r exalaka CIRCLED CITIES INDICATE TRADE CEMTE33 Sources Trade Centers and Trade Areas, of the Upper Midwest,- John R. Bor chert and "SusselT~B'. ^K m sj^rb ^T m p o it IKsaber 3, Upper Midwest Economic Study, September, 1963, Table h, p. 11. ^

12 The numbex" of square m iles 3.n a county often re fle c ts certain ch a ra cte ristic s of a county, one of them being th a t Montana counties with larg er areas tend to be ag ricultu rally oriented and le s s populated than the sm aller counties. I t i s probable th a t the size of a county has an economic e ffe c t and thus deserves in v e stig a tio n regarding employment change w ithin Montana cou n ties. The unemployment percentage fo r a county i s considered a determinant of employment change. Since employment i s a measure of labor u n its, i t may be influenced by labor market conditions. Since the unemployment percentage i s such a measure i t has been included. The percent urban variable measures the s p a tia l concentration of population within a county. The size of th is variable may be in flu e n tia l in determining employment in certain industri.es, especia lly those dependent upon the b e n e fits of economies of sc a le. The percent urban variable i s the percentage of a county's population? which resides in the la rg e st census tr a c t in th a t county. Conceptually, each of the shove variables can be expected to influ en ce, in some way, in d u stry enroloyment. However, some v ariab les ^ Ib ld., pp. 212 and 222. ^U. S. Bureau of the Census, U. S. Census of Population; I960, General Social, and Economic C h aracteristics, Montana--Final Report PC.( IT - 256, Tabie~53, p p."2 S ri3 ^II^li?S feh g to n,' D. C.s TJ. S. Government P rinting O ffice, 1961}j U. S. Bureau of the Census, Census of Population; 1970, General Social, and Economic Characteristics -! '" HnaL Report ~PCT~(T) - C28""Montana,'Table' 12l7 pp 210 (Washington, D. C.: U. S. Government P rin tin g O ffice, 1971).?U. S. Bureau of the Census, S_. Census of Populatio n; 1970, Humber of InhaM.lan ls-.~pin a l Report PCT (l}, 'IteS Ilbntana (Washington, B. C.; U. S. Government P rin tin g O ffice, 1970).

13 8 have more inpact on employment of one industry than fo r another industry. I t w ill be l e f t to the regression technique to select those variables which are most highly correlated with employment in each industry.

14 CHAPTER III DEPENDENT VARIABLES The regression procedure requires th a t data on. one or more dependent varisb3.es be regressed against various independent variables Industry employment figures are the dependent variables which are re gressed against the independent v aria b les of th e previous sectio n. Some in d u stries serve a national market and th e ir demand i s p a rtia lly exogenous to the - region where the production takes place. Other andustries produce fo r lo c al consumption. For these in d u stries production and consumption occur w ithin the sane area. Such indus**. tr ie s are considered to be endogenous to the lo c a lity in which they are physically situated; th a t i s, the demand fo r endogenous output is determined by lo c al co n d itio n s.. Table 3 l i s t s the four in d u stries chosen fo r use in th is study. TABLE 3 INDUSTRIES CHOSEN FOR ANALYSIS Food and Dairy Product Stores Eating and Drinking Pieces Business and Repair Services Finance, Insurance, 'and Real E state These four in d u stries were selected because they a ll are considered endogenous in the sense th a t the output i s influenced by lo c a l facto rs

15 10 county data are available fo r these in d u strie s. The next few paragraphs describe the in d u stries. The food and dairy products industry provides the essen tial foods, to the consumers w ithin a county. In Montana th is industry is composed of many of the small "ma end pa1' type businesses which stock only a small assortment of item s. In addition, th ere are various a ffilia te s of national chain organisations which provide a seemingly unlim ited sxpply and assortment of food item s. The eating and drinking industry i s composed of a ll types of restau ran ts, cafes and d riv e-in s. These places all!, serve prepared food to the customers. Also included in th is industry are b ars, saloons, and liquor sto res. Drinking places are considered to be p rim arily those p laces th a t serve alcoholic beverages. The business and rep air service industry i s d ire c tly involved in the support of businesses and re sid e n ts w ithin an area. Such s e r vices as accounting o ffices, data processing, office machine rep air services, ja n ito ria l sexurices, etc. are included in business services. Repair services consist of auto mechanics, f i x - i t shops and other places which e x is t to re p a ir used equipment. The finance, insurance and real estate industry includes comm ercial banks and c re d it agencies of a ll types. Brokerage firms and insurance agencies also are p a rt of th is industry.

16 CHAPTER IV.. EXPECTATIONS REGARDING RELATIONSHIPS OF THE INDEPENDENT VARIABLES TO EMPLOYMENT The regression co efficien t fo r an Independent variable in d i cates th a t v ariab le s impact on the predicted value of the dependent v ariable. This in ta c t or relationship to the dependent v ariab le, of course, can. be e ith e r p o sitiv e or negative as indicated by the sign of the regression co efficien t. The size of the regression co efficien t of an Independent v a ria b le, -holding a ll other variables constant, corresponds to the change in the predicted value of the dependent variable fo r every one u n it change In the value of th a t independent variable. The population variable represents both the demand and supply side of the economic situ a tio n. An increase in population means more people to demand, but also a greater supply of labor to meet the demand. Thus, the erpected sign of the population variable fo r a ll in d u stries is p o sitiv e. An increase in to ta l population, holding other fa c to rs co n stan t, vd.ll increase employment,. Per capita income i s a measure, o f the average le v el of welfare w ithin a prescribed area. In general, an increase in income leads to an increase in consumption demand, suggesting th a t income w ill be p o sitiv ely related to deployment. Although i t might be possible 'for per c a p ita income to be negatively c o rre la te d to in d u stry employment 11

17 in a few cases, i t i s e je c te d th a t the relationship w ill be p o sitiv e 1 2 fo r the in d u stries selected fo r study in th is paper. Thus an increase in income, holding other facto rs constant, w ill re s u lt in an increase in employment. ' I t i s expected th a t the income d istrib u tio n variable (percent of fam ilies with incomes below $3000 or over $10,000) w ill have some e ffe c t on industry output. But, the nature of the e ffect i s d if fic u lt to p re d ic t. I t is d iffic u lt to discern the spending p a tte rn of people without knowing more about the social climate,.of the area in which they resid e. For example, some fam ilies with incomes over $10,000 may have g reater use fo r the serv ices offered by the fin an ce, in s u r ance aid re a l estate industry than others in the same category. Also, the higher income fam ilies may p refer to shop in trade centers away from th o ir horae county, indicating th a t lo cal demand might be reduced with an increase in th is v ariable. I t i s d iffic u lt to say with certa in ty which countervailing force w ill dominate. For these reasons, no a pxj.or i sign i s given to th is variab le. The dependency ra tio, which provides an indication of the re la tiv e age d is trib u tio n w ithin a county, i s another determ inant of consumer" demand. However, here again the direction of the relatio n sh ip between th is independent variable and employment i s not e n tire ly clear. For example, i t may be th a t young people spend a greater p a rt of th e ir incomes in eating and drinking establishments than do older people. Since a change in the dependency ra tio may be a re s u lt of e ith e r a change In number of people under 18 or the number over 6!;, I t is d if fic u lt to p red ict the impact of an increase in the dependency ra tio

18 13 on th e demand fo r goods and services produced by the- various industr ie s. Since, once again, there are countervailing forces at work, the a p rio ri sign of the co efficien t i s not predicted. The distance variable, the distance from the c ity of la rg e st population in each county to the trade center city* located clo sest in highway m iles, i s a measure of the re la tiv e iso la tio n of a county. I t seems reasonable to assume th a t the fa rth e r a county i s from a trade center, holding other facto rs constant, the greater w ill be the output demanded of lo cal in d u stries. For example, i f the residents of a county were faced with trav elin g 100 miles fo r sn after-work drink at a fav o rite bar, they would very lik e ly "quit drinking" or open a sim ilar sendee center closer to home. The la tte r i s the more probable. The greater the distance to the trade center the more th e ir w illingness to buy close to home. Consequently, i t i s f e l t th a t the sign of the distance variable w ill generally be p o sitiv e with respect to employment in the selected in d u s trie s. The relationship between the area of a. county and employment in various in d u stries w ithin th a t county i s d if fic u lt to p red ic t. A p rio ri knowledge of the sta te of Montana provides some in sig h t. As previously mentioned, i t i s the general, case th a t the larg er counties in terms of area, such as Beaverhead, are prim arily ag ricu ltu ral and for the most p a rt are low in population. The sm aller counties, such as S ilver Bow, are prim arily non ag ricu ltu ral and in most cases have f a ir ly large populations. Because population i s expected to have a p o s itiv e in f lu ence on employment, the larg er and more sparsely populated, the -lass should be industry employment. Consequently, the a p rio ri sign fo r square m iles, holding other fa c to rs co nstant, i s negative.

19 1U The impact of unemployment i s also d if fic u lt to p re d ic t. On one hand, high unemployment could in d ic a te the presence of over-supply of labor. There may be a w illingness to work a t lower wages, thus inducing some employers to h ir e, increasing employment in some in d u strie s. On the other hand, excessive unemployment may reduce demand fo r industry output, resu ltin g in le ss output produced said, loner employment. Which of these forces w ill be dominating i s impossible to p re d ic t. Consequently, no a p rio ri sign i s given to the unemployment v aria b le, The percent urban variable provides an indication of the density of population w ithin one or more specified areas in a county. I t is reasoned th a t the larg er the percent urban, the greater the p ro b ab ility of goods and services being.supplied lo c ally. The thought i s th a t the grouping of the population around a specific area would re s u lt in a higher proportion of lo cal purchases. Economies of scale might well accrue to the urban, areas, giving ris e to greater supply to meet the demand. Thus, the expected sign on the co efficien t fo r the percent urban variable i s p o sitiv e. TABLE U SmiLAICf OF EXPECTED REGRESSION COEFFICIENT SIGNS V ariable Population Per Capita Income Distance Square holes Percent Under $3000 Percent Over $10,000 Dependency Ratio Unemployment Sign Positive Positive Positive Negative Undetermined Undetermined Undetermined Undetermine d

20 The preceding section has outlined the independent variables which m i l be used to fonn the regression equations. In addition* a p rio ri predictions of co efficien t signs h^cire been explained. The l i s t of independent variables i s by no means e ll inclusivej however** data avail a b ility presents a lim it to the extent th at variables can be included.

21 CHAPTER V THE STATISTICAL PROCEDURE M ultiple-linear regression i s the s ta tis tic a l to o l used to formulate the equations fo r employment prediction. This procedure i s based upon the le a s t squares method fo r f ittin g a stra ig h t lin e. That i s, in theory a ll possible stra ig h t lin e s on every possible plane are f itte d to the data, and th e sum of the distances squat'ed from the data points to each lin e i s determined. The regression procedure selects the lin e which gives lowest value fo r th is sum of the squares. The study uses a p a rtic u la r extension of m ultiple lin e a r regression called stepwise m ultiple'regression.. This procedure has been programmed fo r computer use by J. N-, Boles, and the equations which appear in a subsequent section are the re s u lt of the use of h is program.^ The stepwise regression process, also known as the forward s e le c tio n procedure, used in the study reg resses each dependent v a r i able (employment) f o r s. p a r tic u la r in d u stry against successive independent v ariab les. The basic procedure i s as follows; F irs t, dependent variable (T) is regressed against the independent variable (X) m th which i t i s most highly correlated, and a f i r s t order, lin e a r Boles, ho Series-~StepTri.se Regression System; (Berkeley; C alifornia A gricultural Experiment S tation, Bep'artaient (^ A g ric u ltu ra l Economics, U niversity of C alifo rn ia, 196)i). 16

22 regression equation, Y = f (ip) i s obtained* The independent variable producing the highest p a rtia l correlation co efficien t Tilth the dependent variable i s the next variable selected. The p a rtia l correlation co efficien t i s mathematically the equivalent to finding the correlation of resid u als, that, i s, the difference between the predicted value and the actu al value, of the equation Y f(x^) and the re sid u a ls of th e equation i f each other independent v aria b le were regressed ag ain st the included independent variable 9 This procedure continues lin til a l l v aria b les are entered in to the equation Appendix XV provides a. ste p- by-step example of th e form ulation of the i 960 equation f o r eating and drinking establishm ents. For each ste p, th e selected independent variable is id e n tified and the R squared value, standard erro r, and T ra tio are calculated There are sev eral means of se lec tin g the most d e sira b le equation from the step equations The method used in th is study i s to s e le c t 10 the equation which provides the la rg e st R E ssentially, R' is the percentage of the v ariatio n in the dependent variable accounted fo r by the independent variables in the equation adjusted fo r degrees of freedom. The downward adjustment is an inverse function of the sample size and a d irect function of the number of coefficients to be estimated. The reasoning behind se le c tin g the equation with th e h ig h est _J2 o 0 R over th e equation with the h ig h est R i s th a t R~ w ill continue to 17 9 N. R. Draper and FI, Smith, Applied Regression Analysis (Hew Yorks John waley and Sons, Ince, iy o b), p» 169. l^ronald J Uonnacott and Thomas H Vlonnacobi, Econometrics (Hew York: John Wiley and Sons, I n c., 1970), p. 311 * ' "

23 18 increase with each added independent variable while the w ill reach a maximum a t some le v e l of v ariab less indicating th a t the remainder of independent variables are not sig n ific a n tly adding to the explained v aria tio n.

24 .CHAPTER VI THE REGRESSION EQUATIONS This sectio n p resen ts th e equations which have been selected. The subsequent paragraphs examine these equations, which appear in Table f>. The signs of the co efficien ts w ill be compared to the a p rio ri predictions summarised in Table h. In ad d itio n..th e I960 'equations wild, be compared to the 1970 equations. The equations fo r the business and rep air industry d iffe r between I960 and 1970., Table 5> shows th a t the unemployment ra te, population, per capita, income, and percent of fam ilies under $3000 income are present in both the I960 and 1970 equations. Distance and dependency ra tio are sig n ifican t variables in the I960 equation while square miles ore sig n ific an t in the 1970 equation. There are cases in which the signs fo r the co efficien ts d iffe r from the a p rio ri expectations. For example, the I960 equation shows a negative sign fo r income. A possible explanation i s th a t an increase in income re su lts in people being able to afford to trav e l to other counties fo r goods and services. In addition, the case ex ists where the sign fo r unemployment percentage i s p o sitiv e for one year and negative in the other. This is not illo g ic a l because e a rlie r i t was shown th a t the co efficien t could be eith er p o sitiv e or negative. The I960 and 1970 equations fo r the eating and drinking estab lishment industry are rad ic ally d iffe re n t. Table 6 shows th a t the only 19

25 TABLE 5 BUSINESS AMD REPAIR SERVICES I960 AMD 1970 REGRESSION EQUATIONS I960; Employment =* < Unemployed) (Pop.) (in c.) +.7U282( Under $3000) (.71311) (.00069) (.0050U) (.28579) -2. 9hOOJ; R ;3 I 2 = (Dependency Ratio) (Distance) (.92203) (.07998) ; Employment = *01l65($ Unemployed) (?op.) o(lnc.) U9h(^ Under $3000) ( ) (.00101) (.00598) (.79713) R2 =.7ltU33 R2 = l3(Square Miles) (.00613) Note; Beneath each coefficien t are lis te d the standard error and the,rt" sta tistic.

26 TABLE 6 EATING AND DRINKING ESTABLISHMENTS I960 AND 1970 REGRESSION EQUATIONS i960: Snployment = l69(Pop.) -.0lU59(Inc.) l23( Dependency) +.21?55(Dlstance) (.0012)4.5 (.01013) (1.7911*1) (.15069) U9 l.u il UU369 R2 = H2 =.7U l592(^ Urban) (.32731) : Employment s (5 Unemployed) +.0l62l(Pop.) +,$26l\2(% Urban) +,00268(Square Miles) ( ) (.00125) (.31119) (.00307) I. 3321I4-12.9^ R2 = S2» Note: Beneath each coefficien t are lis te d the standard error and the nt" sta tistic.

27 TABLE 7 FINANCE, INSURANCE, AND REAL ESTATE I960 AND'1970 REGRESSION EQUATIONS, I960: Hrroloyment- = l;26-3*0li568(5 Urban) (?op.) (5 over $10,000) jXDistance) ( ) (.00195) (I.0ii7l6) (.179iiW l67hU R2 =.55U7 k R2 =.U9111 -,00368(Scmare Miles) (.00323) U 1970: Sriployment R2 * R ljl0 +.00ii65(Pop.) (5 Under $3000) (Square Miles) (.00060) (-56320) (.00190) U Note: Beneath each coefficien t are lis te d the standard error and the "t,t sta tistic. ro ro

28 TABLE 8 FOOD AM) DA1KT PRODUCTS I960 AMS REGRESSION EQUATIONS I960: Bnployment = (5 Unemployed) +.00>83(Pop.) -,69hll(5 Under $3000) (.95518) (.00095) (-3U730) 1.1* U )2 R2 '» I 2 = : Erployment = (Pop.) (5 Under $3000) +.775U0(Distance) +, {% Urban) (.00055) (.515UD (.07661). (.161*79) (Square Miles) (.00168) -2.09U96 R2 = R2» Note: Beneath each coefficien t are lis te d the standard error and the "t" sta tistic. ro

29 Independent v aria b les which th e two equations have in common are popula tio n and percent urban. The income variable in the I960 equation has a negative sign fo r p o ssib ly the same reason as discussed in connection with the equations fo r the business and re p a ir in d u stry. The two equations fo r the finance, insurance end re a l e sta te industry are very d iffe re n t. Table 7 indicates th a t the population and square m iles v aria b les are the only common independent v a ria b le s. The signs fo r the co efficien ts of a ll the independent variables s a tis fy expectations. Table 8 shows th a t the I960 and 1970 food and dairy product industry equations have in common population and percent of fam ilies with incomes under $3000. Without exception, the signs of the co efficien ts satisfy - previous expectations. I t i s readily observed th a t, regardless of the industry examined, the equations fo r I960 and 1970 are quite d iffe re n t. This seems to indicate th a t time has a way of changing things. Since the independent variables attempt to explain v ariatio n in the dependent v ariable, i t i s possible th a t time has altered the relationship among the v ariables. I f the stru ctu re of the economic indicators i s unstable,, the use of these.regression equations fo r predictive purposes i s questionable. This need not, however, destroy th e ir p ra c tic a l value. The primary objective of the study was to investigate the factors which lead to changes in employment. The purpose of the regression equations i s to p red ict the trend of employment change. The basis fo r predicting employment change i s found in Appendix I I. Appendix II"provides values for the difference between predictions and actual employment fo r -each county fo r each of the four d ifferen t in d u strie s. These values, derived

30 25 from I960 equations and data, show which comities had eith er le sse r or greater employment'than estimated hy the equations. I f the equations are to "be u sefu l in p red ic tin g employment, there should he a comparativ e ly slow growth in actual employment between i 960 and 1970 whenever the residual indicates excess employment in I960. The opposite should be true fo r residuals which show employment levels to be too low. An examination of Appendix I I, which shows the I960 residuals fo r each county and Appendix I I I, which shows th e 1970 actual employment, v e r i fie s th a t when the residual in d icates excess employment in a comity in a p a rtic u la r industry, fo r i 960, th a t industry showed only a slow growth in employment through This i s compared to counties and in d u stries which had an employment le v el in i 960 indicating d eficien t employment and which had by 1970 s u b s ta n tia lly increased employment. (See Chart I ). A p o sitiv e residual (actual employment greater than employment estim ated by the equation) suggests an excess supply conditio n, which w ill tend to slow the. growth of future employment. In fa c t, in lh of 18 counties for the food and dairy industry where a positiv e sign appears on the resid u al, employment actually declined. In 1? of ' the 23 counties with negative resid u als, employment increased- Sim ilar re s u lts can be seen fo r the other In d u stries. Consequently, while the equations are not 100 percent e ffectiv e, the i 960 equation would have improved the a b ility to forecast the trend of employment between I960 and I t i s conceivable, but improvable, th a t the 1970 equations w ill also provide a b e tte r than guessing in d i cation of the growth tren d in employment.

31 26 CHART I EXAMPLE OF EMPLOYMENT GROWTH TRENDS $ A 25>0 2h3 200 i o i l So - i 960 Line A A, - Lake Comity - Eating and drink establishm ent in d u stry. Tills county and industry had a residual indicating th a t the I960 actual employment was le ss than the equation predicted. Thus, as expected, employment grew su b stan tially by 1970 as reflected by the slope of M. Line KB - Big Horn County - Eating and drinking establishm ent in d u stry. This county has a residual indicating th a t the i 960 actual ernploynent was 'more than the equation predicted. Thus, as expected, employment grew only a t a slow r a te between I960 and Line CC - Carbon County ~ Eating and drinking establishm ent in d u stry. This county has a p o sitiv e residual indicating excess employment in I960. Hot only did employment not grow as ra p id ly as in Lake County (Line-AA), i t ac tu a lly declined by Sources App endix XI.

32 27 While the study has developed equations capsble of forecasting the trend of employment change, i t has not helped in the problem of accurately predicting the le v e l of employment. I t i s noted th a t the I960 and 1970 equations contain certain marked differences in the variables included in the equations. This indication of in s ta b ility threatens the predictive value of the equations. An examination of the residuals derived from plugging 1970 data into the i 960 equations w ill give an indication of whether or not the I960 equations will, be useful fo r predicting the 1970 level of employment. I f the resid u als are "small" i t might be the case th a t the reasons behind the change in independent variables from i 960 to 1970 do not impair the pred ictiv e usefulness of the equations. The method of comparison id.ll be to examine the absolute residuals using the i 960 equations and the 1970 data. The absolute residual indicates the degree to which the equation f a ils to p red ict co rrectly I960 employment. The to ta l of absolute residuals i s taken as a percentage of the to ta l actual employment in I960 fo r the I4I counties. This percentage re fle c ts the average percentage erro r in prediction resu ltin g from the use of 1970 data in the i 960 equations, Appendix I presents the residuals fo r the i 960 equations using 1970 data. The values fo r the food and dairy products industry indicate th a t the average absolute residual in 31. 8Lj. percent of the actual value. This means th a t fo r th is industry, the I960 equations, using 1970 d ata, w ill m ispredict the employment by an average of 31.81* p e r cent.

33 28 For the "business and rep air service industry, the i 960 equation using 1970 data has sn average absolute, error of 81j,.66 percent of actu al employment. The finance, insurance and real, estate industry equation fo r I960 m ispredicts the actu al employment by an average of 172.2i. p ercen t. The eating and drirfcing places industry has an average absolute re sid u a l o f percent o f actu al employment. These values are much too high to estab lish hope of s ta b ility between the I960 and 1970 equations. Consequently, the primary use of the equations w ill be to forecast employment growth trends in Montana counties.

34 CHAPTER VII } STM'MT The study has examined employment in ru ra l Bant ana, I n te r county v ariatio n s in employment fo r selected in d u stries have "been related to differences In the um ber of resid en ts, th e ir economic well being, and the geographical and economic structure of th e region. In general, these fa c to rs were successful in explaining employment v a r i ations. M ultiple lin e a r regression was applied to cross section data, to estim ate equations which w ill forecast employment trends fo r the 111 ru ra l Montana counties used in the study. These equations w ill be used to determine employment predictions. I f the predicted, eiployment d iffe rs from the actual le v el in a p a rtic u la r county, the d irectio n of th is difference indicates the trend of employment growth fo r the v a rious in d u strie s. For example, i f the expected employment i s le ss than the actual employment fo r a given year, the growth trend fo r employment in future years i s expected to be le ss rapid than i f the predicted employment had been g reater than actual employment. Although the outgrowth of th is study does not provide a means of accurately estim ating employment, i t does present a method by which the trend of employment can b e accurately predicted. I f employment i s a v a lid proxy fo r output, a businessman can use the fo recasted employment trends to a s s is t planning fo r expansion and business growth in a 29

35 p a rtic u la r county. Consequently, th is study presents an additional consideration fo r the businessmen and i s intended to be applied in conjunction u ith other fa c e ts o f business decision making.

36 BIBLIOGRAPHY

37 BIBLIOGRAPHY Boles, J. H. lio Seri es--5tepwise Regression System, Berkeley: C alifornia A gricultural Experiment S tatio n, Department of Agri c ul tu rc l Economics, U niversity of C alifornia, 196U. Borchert, John R., and Russell B. Adams. Trade Centers and Trade?" Areas of the Upper Midwest. Urban Report limber 3, T-foper*ltldw eit ^onoiric Study, September Draper, H. R., and H, Smith. Applied Regression A nalysis. Hew York: John Wiley and Sons, I n c., 1^66. ~ Due, John F., and Robert. W. Clower. Interm ediate Economic Analysis. Homewood, I llin o is : Richard D. Irwin, In c., i 960. "Survey of Buying Power," Sales Management, the Marketing Magazine U. S. Bureau of the Census. Census of Popu la tion^ i 960. General P opul at ion Ch ar ac t e ri s t l c s, ^Montana. jpin sl^eporttpc TIT - 26B. Washington, D. C.: U. S. Government P rin tin g O ffice, U. S. Bureau of the Census. Census of Population: General Pop u la tion C haracteris ti c s. Final Report Fc ( l) - B28 Montana. itasllngbon, D. C.: tlt S. Government P rin tin g O ffice, U«S. Bureau of th e Census. Census of PoprIatlon: I960. General Social and Economic Ch ar ac t e r i s t t c s Montana. F inal Report PC (3.) 2Sc7 itasfingtdn, $71). U.. 'Government 'P rin tin g O ffice, 1961.' U. S. Bureau of th e Census. Census of Population: General U. S. Bureau of the Census. Census of -Popu la tions Humber of In h ab itants. F inal Report PC (,lt ~ A2F"liontaiia7~^e^Iiington, D. C.: 17. S. Government P rin tin g O ffice, 1971* U. S Bureau of the Census. County and City Data Book, A S ta tis tic a l A bstract Supplement. vtashington, D. C : tj* S. Government P ointing.o ffice, U. S. Department of Commerce, Office of Business Economics. Regional Economics Inform ation System, June 8, (Unpublished d ata.) 32

38 U. S. Department of Commerce, Office of Business Bconord.cs. Survey of Current Business, Vol. 3 1, No. 8, August Wormacott, Ronald J., and Thomas H. Wonnacott. Econometrics. Net* Xork: John Wiley and Sons, I n c.,

39 APPENDIXES

40 APPENDIX I FOOD At DAIRY PRODUCT STORES F {% UNEaiPLOXMElJT, POPULATION, PERCENT UNDER $3000) I960 EQUATION, 1970 DATA County Actual P redicted Residuu Beaverhead Big Horn Blaine Broadwater li.ls.22 ~1*.1*22 Carbon U C arter Chouteau * *3 Daniels F allon 1*1* * G arfield G lacier Golden Valley G ranite U.53U U Jefferson * Ju d ith Basin Lake ,811 L iberty Lincoln *. 699 McCone Nadison *1* Meagher 20, *1*3-10.1*1*3 Mineral *8.01* *3 M usselshell ill *1.271* Petroleum P h illip s *6, Pondera Powder River Powell P ra irie R avalli 10U *89 Roo sev elt Rosebud 51*.000 1* Sanders ' Sheridan * S tillw a te r Sweet Grass Teton 5U.ooo 52.1* Toole 1* * ,226 Treasure Wheatland * *6 Wibaux 11,000 I8.l-.3l* -7.1*31*

41 36 F (% Unemployment, APPENDIX I (Continued) BUSINESS AND REPAIR SERVICES Population, Income, Square M iles, I960 EQUATION, 1970 DATA % Under $3000) County, Actual P redicted Residual Beaverhead L Big Horn B laine ?h Broadwater Carbon C arter Chouteau Daniels F a llo n U h5.325 G arfield h2 5i.5h2 G lacier hJ.i9 Golden V alley G ranite hh Jefferso n 3U.OOO i h. 595 l9.ho5 Ju d ith Basin Lake U L iberty h58 8.5U2 Lincoln HcCone h2 h8.2h2 Madi son Meagher Mineral M usselshell 55.ooo Petroleum ; 25.06U P h illip s U Pondera Powder River Powell P ra irie U h26 R avalli Roosevelt IOO.367 Rosebud J 467. Sanders ; -39.h30 Sheridan U :66,916 S tillw ater Sweet Grass h97. 2hJ.i?7 Teton v26h Toole h o U9 >28.*051 Treasure Wheatland Wibaux

42 APPENDIX I (Continued) EATING AND. DRINKING PLACES f (% unemployment, p o p u latio n, income, square m ile s, dependency) i9 6 0 EQUATION, 1970 DATA County A ctual P re d ic te d Residui Beaverhead l l B ig Horn ll* *1* B laine 12l* Bro adw ater *. 1*90 Carbon *6 1*1.3 U C a rte r U 10.8 Chouteau * l6 8 D a n iels 1* F a llo n l* G a rfie ld *3 G la cier lli* U Golden V a lle y I* G ra n ite l*.l* *31 Je ffe rso n 1*1* * *8 Ju d ith Basin Lake 21* L ib e rty 1* L in co ln McCone 1* *3.812 Madison Meagher 3.ooo '38.1*68 ~3. 1j.68 M ineral IP-U M usselshell ill*.-00 l a Petroleum * * P h illip s *00 Pondera Powder R iver * Pow ell P r a ir ie * R a v a lli R oosevelt Rosebud *1*. 36 Sanders i o.o o o S heridan *80 S tillw a te r * Sweet Grans l 8-7.l 8 Teton Toole *3-3' T rea su re *18 "Wheatland 1* io l. [*.896 Wibaux

43 33 APPENDIX I (Continued) FINANCE, INSURANCE, AMD REAL ESTATE F {% TOTEMPLOXMEMT, POPULATION, SQUARE MILES, % OVER $10,000,.DISTANCE) I960 EQUATION, 1970 DATA County Actual P redicted Residu Beaverhead *2.072 Big Horn Blaine o -?.6 0 Bro adwater Carbon o o C arter Chouteau o o Daniels *7.182 Fallon l.?8 0 G arfield U.000 2?.0 l l G lacier U ,693 Golden Valley G ranite Jefferson *31-1*0. 1*31 Ju d ith Basin *8.607 Lake Liberty.000 8I4.OU *8 Lincoln McCone ,327 Madison l.000 o. o8-3. Q 8 Meagher ,318 Mineral * *. 882 Musselshell i.o o o Petroleum.000 l!*.l l* -ll*.l k P h illip s Pondera 1* Powder River *1*. 100 Powell i.o o o li6. 92 P ra irie Ravalli lo li.o o o *98 Roosevelt 3.ooo * - 1*. 731* Rosebud *2. 3li *6 Sanders *. 1* U92 Sheridan *1* -l*.l*l* S tillw ater *21* Sweet Grass *222 Teton Toole * - 1*37991* Treasure ? -37'. 93b Wheatland * Ij.52 Wibaux

44 39 APPENDIX II FOOD AIID DAIHT PRODUCT STORES F (% UNEMPLOYMENT, POPULATION, % UNDER $3000) I960 County Actual P redicted Residual Beaverhead ' Big Horn ( (10 Blaine Bro adwater ? Carbon Carter ( (3 Chouteau I> Daniels o o F allon G arfield ( G lacier l1.l4.Oli Golden Valley 2l( G ranite 1( Jefferso n h6.ooo t lli.286 Judith Basin '2l( I. ak lib e rty Lincoln 11( l ie Cone Madison I Meagher Mineral ( M usselshell U J(.d3 Petroleum IU.667 P h illip s ( U.122 Pondera Powder River U.911( Powell 6i ll. l( 0 l( P ra irie 2l( ( 6 J4l( R avalli *1*6-10.1(1(6 Roosevelt Rosebud k3. 6b,l (1 Sanders Sheridan ( S tillw ater U U Sweet Grass Teton U U.933. Toole ( -~ 23., 8-U ' Treasure N3U3-1.31(3'. Wheatland Wibaux

45 iio APPENDIX II '(Continued) FBIAI'ICEj INSURANCE, AND' HEAL ESTATE t (% UMH'JPLOXMEMT, POPULATION, SQUARE MILES, % OVER $10,000, DISTANCE) I960 County Actual P redicted Residual. Beaverhead x Big Horn x Blaine 1x x Broadwater Carbon C arter Chouteau h i.366 Daniels U.037 -lx.037 F allon G arfield U -3»5oIx G lacier x Golden V alley U (2x7-6.2x2x7 G ranite Jefferso n I& -21.?2ilx Ju d ith Basin x Lake x Jx L ib erty Lincoln h McCone l l T-.U03-5.2x03 Madison L l.o o o h Meagher ?.713 Mineral ix.000 U M usselshell Petroleum P h illip s 2t6.ooo 2x Pondera x73 Powder River ? Powell P ra irie R avalli k Roosevelt 2x Rosebud lx.0?9 Sanders rUi5a Sherid an U x9 S tillw a te r Sweet Grans x3 Teton x.09l Toole hix Treasure ,965 Wheatland 2U.000 2x Wibaux '