GROWTH AND CONVERGENCE IN THE SPACE ECONOMY : EVIDENCE FROM THE UNITED STATES

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1 GROWTH AND CONVERGENCE IN THE SPACE ECONOMY : EVIDENCE FROM THE UNITED STATES John I. CARRUTHERS *, Michael K. HOLLAR **, Gordon F. MULLIGAN *** Absrac - This paper invesigaes geographic relaionships in a land use based regional adjusmen model conaining equaions for populaion densiy, employmen densiy, and wages in he coninenal Unied Saes during he 1980s and 1990s. The resuls of he analysis sugges ha (1) accouning for spaial inerdependencies appreciably enhances he esimaes; (2) wih his correcion, he viabiliy of he hree-equaion framework used here seems srong; and (3) even as he naion s pos-indusrial economy coninues along is pah of decenralizaion, equilibraing forces work o mainain an uneven paern of developmen characerisic of he well-known, hierarchical sysem of regional economies described by radiional forms of locaion and cenral place heory. Key-words POPULATION DENSITY, EMPLOYMENT DENSITY, WAGES, UNITED STATES, REGIONAL CONVERGENCE, SPATIAL INTERDEPENDENCIES JEL Classificaion : C31, R11, R12, R14, O51 U.S. Deparmen of Housing and Urban Developmen Working Paper # REP 06-05; revised April, This paper was presened a he 2006 meeings of he European Regional Science Associaion in Volos, Greece and a he 2008 meeings of he Wesern Regional Science Associaion, in Kona, Hawaii. The opinions expressed in his paper are hose of he auhors and do no necessarily reflec he opinions of he Deparmen of Housing and Urban Developmen or he U.S. governmen a large. * Corresponding auhor. U.S. Deparmen of Housing and Urban Developmen, Office of Policy Developmen and Research; Universiy of Maryland, Naional Cener for Smar Growh Research and Educaion; john.i.carruhers@hud.gov ** U.S. Deparmen of Housing and Urban Developmen, Office of Policy Developmen and Research ; michael.k.hollar@hud.gov *** Universiy of Arizona, Deparmen of Geography and Regional Developmen ; mulligan@u.arizona.edu Région e Développemen n

2 36 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan 1. INTRODUCTION The objec of his paper is o invesigae geographic relaionships in a dynamic growh model namely, a land use based regional adjusmen model conaining equaions for populaion densiy, employmen densiy, and he average annual wage in he Unied Saes during he 1980s and 1990s. Regional adjusmen models are ideal for sudying growh and selemen paerns because hey accoun for he roles of boh opporuniy and preference in he growh process and exend in a naural way o describe he spaial configuraion of developmen. The heoreical framework underpinning he models originaes from Bors and Sein s (1964) sudy Economic Growh in a Free Marke, which was apparenly he firs o sugges ha populaion growh may drive employmen growh as jobs follow people ino and/or wihin regions in addiion o he oher way around. The core concep was succincly framed in he ile of Muh s (1971) paper, Migraion: Chicken or Egg? and hen fully operaionalized by Seinnes and Fisher (1974) in an analysis of he ineracion beween populaion growh and employmen growh in he Chicago meropolian area. Finally, regional adjusmen models were popularized by Carlino and Mills (1987) and Boarne (1994a, 1994b) and have since emerged as an increasingly common mehod of analyzing he process and oucome of developmen wihin various spaial frames of reference (see, for example, Clark and Murphy, 1996 ; Henry e al., 1997, 1999, 2001 ; Glavac e al., 1999 ; Mulligan e al., 1999 ; Vias and Mulligan, 1999 ; Deller e al., 2001 ; Bao e al., 2004 ; Rey and Boarne, 2004 ; Boarne e al., 2005 ; Carruhers and Vias, 2005; Carruhers and Mulligan, 2006, 2007, 2008 ; Mulligan and Vias, 2006). This paper exends he exising body of research involving regional adjusmen models in several key ways. Firs, building on work done by Carruhers and Mulligan (2008) i expands he radiional wo-equaion specificaion by adding a hird equaion, for wages, so ha populaion densiy, employmen densiy, and he average annual wage are modeled as a funcion of conemporaneous values of one anoher, plus heir own ime-lagged values and a se of oher predeermined facors. Second, each equaion is specified wih a spaially lagged dependen variable and hen esimaed via Kelejian and Prucha s (1998) spaial wo sage leas squares (S2SLS) procedure, which accommodaes he endogenous relaionship among he hree dependen variables and heir own spaial lags. Two alernaive spaial weighing schemes are considered and, for comparison, an aspaial specificaion is also presened. Third, he densiies used in he analysis are measured wih land use daa, so he spaial unis reflec he area acually occupied by socioeconomic aciviy. In addiion, all of he inerdependen variables and mos of he independen variables are expressed as locaion quoiens. This ransformaion ensures ha each observaion is pegged o he sysem as a whole and enable s direc comparison of he relaive imporance of populaion, employmen, and he average annual wage in shaping he growh process a equilibrium. Fourh, he model is applied o he enire coninenal Unied Saes using couny-level daa represening he hree 5-year periods ha comprise he imeframe : , , and And, because he esimaion resuls

3 Région e Développemen 37 represen wha, for all pracical purposes, is he enirey of a more-or-less closed labor marke, hey can reliably be used o evaluae and compare projeced seady sae scenarios for hree poins in ime. Finally, as an exension, he esimaes are used o produce a deailed porrai of how equilibraing endencies influence he geographic disribuion and spaial config uraion of American growh and land use paerns. The remainder of he paper is organized ino hree main secions. The background discussion briefly explains he purpose of regional adjusmen models and oulines he pariculars of he modeling framework used in his sudy. The empirical analysis hen esimaes a series of hree-equaion sysems and evaluaes heir resuls. Las, he paper closes wih a summary of is findings and some general conclusions and recommendaions for fuure research. 2. BACKGROUND The innovaion of regional adjusmen models is ha hey simulaneously capure demand- (employmen) and supply- (populaion) induced growh ha occurs as labor moves from place-o-place and he space economy as a whole searches for an opimal arrangemen of aciviy. I is common for people o relocae for opporuniy, or work, relaed reasons for example, o he Puge Sound region of Washingon Sae o fill jobs creaed by Boeing, Microsof, Sarbucks, or any oher of he region s many high-performing companies bu also for preference, or qualiy of life, relaed reasons. Wheher moves resuling from he laer moivaion are made wih complee disregard for work or no, i is ofen he case ha employmen is generaed in heir wake, especially in he finance, insurance and real esae (FIRE) and service secors. Regional adjusmen models emulae boh of hese mechanisms and he give-and-ake beween hem by describing populaion (employmen) change beween wo poins in ime as a funcion of employmen (populaion) a he end of he ime period, populaion (employmen) a he beginning of he ime period, and a se of oher iniial, or predeermined, condiions. The resul is normally a sysem of wo simulaneous equaions wherein populaion and employmen dynamically adjus via an equilibraing process ha evenually produces a seady sae in which he relaive levels of populaion and employmen remain fixed, even if some zero-sum-movemen sill occurs. The process of geing o his poin is explicily spaial because all acors end up being locaed in such a way ha here is no incenive for furher movemen in oher words, a equilibrium, hey are indifferen among locaions. The logic of he hree-equaion regional adjusmen model used in his paper is analogous o DiPasquale and Wheaon s (1996) hree-secor model of meropolian growh, which connecs he local expor, labor, and real esae markes. As explained, demand-induced growh occurs as a resul of firms needing addiional labor, and supply-induced growh occurs as a resul of households making moves for qualiy of life relaed reasons. Only he firs of hese wo mechanisms is precipiaed by gains in he expor marke bu boh place pressure on he real esae marke, raising rens and, a he same ime, densiies due o more inense compeiion over space. Expressing populaion

4 38 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan and employmen in erms of he densiy of land use ies he regional adjusmen model framework direcly o land ren and gives rise o he wage equaion. Specifically, land use densiy measures he spaial inensiy of aciviy, which is influenced by he average annual wage because of is relaionship o land consumpion: For households, land is a normal good, so, he more hey earn in wages, he more space hey are able o consume, leading o a lower populaion densiy; conversely, for profi-maximizing firms, land is a facor of producion, so, he more hey pay in wages, he less space hey are able consume, leading o a higher employmen densiy. Meanwhile, populaion densiy, which measures how concenraed he supply of labor is, and employmen densiy, which measures how concenraed he demand for labor is, simulaneously drive he average annual wage. Working off of Roback s (1982) mode l of compensaing differenials, Mueser and Graves (1995) show how labor demand, labor supply, and wages combine o form a kind of moving equilibrium ha calls for moreor-less coninuous migraion as he space economy wobbles along a pah of consan, ineracive growh and change, searching for an opimal organizaion of aciviy. See Mulligan e al. (1999) and Carruhers and Mulligan (2006, 2007, 2008) for deailed exposiions of he maerial presened in his and he following several paragraphs. Turning o he model iself, a regional adjusmen model is an applicaion of he parial adjusmen model which was originally used for analyzing business cycles (see, for example, Liner, 1956 ; Lev, 1969) where populaion densiy and employmen densi y are simulaneously deermined. The presen approach expands on he radiional wo-equaion framework by adding a hird endogenous variable, he average annual wage (y), o he sysem : p & = ( p e& = ( e y& = ( y / p / e - / y - ) - ) = δ ) = δ = δ p e y ( ~ p / p ( ~ e / e - ( ~ y / y - ) - ) ) In hese equaions, - and represen wo successive poins in ime ; p&, e&, and y& represen raes of change in populaion densiy, employmen densiy, and he average annual wage; p, e, and y represen he (mobile, in he sense described by Mueser and Graves 1995) equilibrium levels of hose hree variables ; and δ p, δ e, δ y represen fracional adjusmen parameers ha are less han zero and greaer han negaive one, implying a process of convergence oward a sae of spaial equilibrium. The core of he sysem of relaionships in he hree-equaion regional adjusmen model is creaed by expressing each variable s observed rae of change oward spaial equilibrium as a funcion of he observed level of he oher wo a ime, is own level a ime -, and a se of oher predeermined variables : (1)

5 Région e Développemen 39 p & = α e& = β y& = γ α + β + γ p p p - + α + β + γ 2 2 e e e α + β + γ y y y - + α + γ β x 4 x x e- y - p- + ε + ε + ε y p e (2) Here, he αs, βs, and γs represen various esimable parameers (α 1, β 2, and γ 3 replace δ p, δ e, and δ y, respecively) or vecors of esimable parameers; he xs represen vecors of predeermined variables; and ε p, ε e, and ε y represen sochasic error erms. Noe ha, once esimaed, he model s formulaion (see Mulligan e al 1999) allows he equilibrium levels of populaion densiy, employmen densiy, and he average annual wage which are used in he following empirical analysis o examine seady sae scenarios o be derived he following equivalencies : p p ~ = δ e e ~ = δ p e ~ y y = δ y (1 δ δ e p p y ) p (1 δ e) e δ -1 (1 δ y ) y δ -1-1 If raes of change, raher han levels, are used as dependen variables, as hey are in his sudy, he same se of circumsances applies excep ha, in equaion ses (3) and (4), δ p, δ e, and δ y are insead equivalen o 1+α 1, 1+β 2, and 1+γ 3. Wihin he framework jus described, populaion densiy, employmen densiy, and he average annual wage are characerized as pushing one anoher oward equilibrium values in he growh process, meaning ha he sysem is expeced upfron o regiser a paricular paern of feedback among all hree. Specifically : (1) populaion densiy is expeced o be posiively influenced by employmen densiy and negaively influenced by he average annual wage ; (2) employmen densiy is expeced o be posiively influenced by populaion densiy and he average annual wage ; and (3) he average annual wage is expeced o be negaively influenced by populaion densiy and posiively influenced by employmen densiy. The opposie effecs expeced of populaion densiy ( ) and employmen densiy (+) in he wage equaion relae o he difference beween supply- and demand-induced growh : boh mechanisms increase densiies by raising rens, bu only he laer is accompanied by a corresponding increase in wages (DiPasquale and Wheaon, 1996). Finally, esing for dynamic sabiliy in he sysem requires solving for he characerisic roos, or eigenvalues, of a 3 3 marix composed of reduced (3)

6 40 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan form parameers; wihin hese soluions, he dominan roo mus be less han one in order for he sysem o converge on an equilibrium oucome. Furher, because here is feedback among populaion densiy, employmen densiy, and he average annual wage, he resuling uni vecor, or eigenvecor, describing he equilibrium oucome is composed of all hree influences. Evidence of he expeced forms of feedback and an equilibrium soluion ha is empirically reasonable may be inerpreed as an affirmaion of he hree-equaion regional adjusmen model. The following secions invesigae he viabiliy of he framework and he imporance of geographic relaionships wihin i by esimaing a series of hree-equaion sysems involving all counies in he coninenal Unied Saes and evaluaing he resuls Model Specificaion 3. EMPIRICAL ANALYSIS The operaional model shown in equaion se (2) is specified wih daa from all 3,073 counies and couny equivalens ha make up he coninenal Unied Saes for he ime periods , , and In order o accoun for spaial dependence among counies, each equaion is expanded o conain a spaial lag of he dependen variable, resuling in he following operaional specificaion (see Anselin 1988) : p & = α e& = β y& = γ ρ pwp + α p α e α y β 4 x + ρ ewe + β p β e β y β4 x + ρ Wy + γ p + γ e + γ y + β x y p-5 e-5 y -5 + ε + ε + ε e y p (4) Here, all noaion is he same as above expec ha he s indicae ha he core variables are expressed in naural logarihmic form; he W is a 3,073 3,073 (n n) row-sandardized weighs marix ha describes he spaial arrangemen of he daa se; and he ρs are esimable parameers measuring he influence of he spaially lagged variables. Several weighing schemes were consruced and esed for he purposes of his analysis. In he firs sep, he populaion weighed cener ha is, a mean poin idenifying where people are concenraed, raher han he geographic cener was calculaed for each couny in he counry using rac-level daa from he 1990 Census of Populaion. The ceners, mapped in Figure 1, were hen used o consruc weighs marices based on 25-, 50-, and 100-mile spaial lags, plus a weighs marix based on a single neares neighbor; in he disance-based marices, he single neares neighbor was used in he even ha here was no populaion cener wihin he specified range. As illusraed in Figure 2, all counies have a neares neighbor, bu no all counies also are a neares neighbor. For example, he mos remoe couny in he counry is Aroosook Couny, in Maine; Aroosook s neares neighbor, locaed 111 miles away, is Piscaaquis Couny, which is, in urn, jus 31 miles from is neares neighbor, Penobsco Couny. In his way, he weighing schemes accoun for he acual paern of selemen, no jus arbirary space.

7 Région e Développemen 41 Noe ha because each dependen variable depends on is value in neighboring counies, Wp, We, and Wy, are endogenous o p &, e&, and y &, respecively. Tha is, raes of change in populaion densiy, employmen densiy, and he average wage in couny i depend on he conemporaneous levels of hese variables in surrounding counies, creaing ye anoher chickenor-egg problem ha mus be resolved by choosing an appropriae procedure for esimaing he sysem. The approach used here is a spaial wo-sage leas squares (S2SLS) sraegy developed by Kelejian and Prucha (1998). The firs sage involves regressing Wp, We, and Wy, on insrumens developed using he hree-group mehod where he insrumenal variable is assigned a 1, 0, or 1 depending on wheher he value of he original variables is in he boom, op, or middle hird of is ordinal ranking (Kennedy 2003) plus x and Wx, o produce prediced values of he spaial lags (see, for example, Fingleon e al 2005). The second sage hen uses he prediced values in place of he observed values o arrive a he parameer esimaes. In pracice, he sysem shown in equaion se (4) already requires an esimaion sraegy ha handles endogeneiy, so all of he inerdependen variables end up being regressed on x, Wx, and a se of addiional insrumens specific o each in a single S2SLS esimaion process. See Rey and Boarne (2004) for an exended discussion of various spaial economeric specificaions of regional adjusmen models. The daa used o esimae he models comes from a number of Unied Saes governmen sources. Firs, densiies were calculaed using populaion and employmen measures from he Bureau of Economic Analysis (BEA) Regional Economic Informaion Sysem (REIS), plus land use measures from he Deparmen of Agriculure s (USDA) Naional Resources Invenory. Second, average annual wages, based on employmen locaion, were also obained from he BEA. Third, he vecor x in each equaion conains: (1) he percenage of oal earnings in he FIRE, manufacuring, and service secors in he base year, obained from he REIS daabase; (2) iniial size, measured as oal populaion, oal employmen, or oal annual wages, depending on he equaion, in he base year, obained from he REIS; (3) a composie naural ameniy index (excluded from he employmen equaion) measuring he araciveness of he local climae and landscape, obained from he USDA s Economic Research Service (see McGranahan, 1999); 1 (4) a composie expor price index (excluded from he populaion equaion) measuring local economic performance in he base year developed using daa from he Bureau of Labor Saisics (see Penningon- Cross, 1997); 2 and (5) each couny s longiude and laiude. All of he variables involved in he analysis excep for longiude and laiude are expressed as locaion quoiens, or he raio of he local value o he mean value naionally for he relevan year in he daa se. 1 The naural ameniy index measures January sunshine, January emperaure, July humidiy, July sunshine, opography, and waer area. 2 The expor price index measures oupu price changes in he expor marke.

8 42 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan Table 1. Descripive Saisics Min. Max. Mean Med. Sd. Dev. Populaion Densiy ,03 41,05 2,12 1,78 1, ,03 41,96 1,97 1,67 1, ,04 42,07 1,88 1,61 1, , ,76 1,51 1,64 Employmen Densiy ,02 25,96 0,74 0,52 1, ,01 26,26 0,75 0,51 1, ,01 24,89 0,74 0,52 1, ,01 24,27 0,73 0,51 1,02 Average Annual Wage , , , , , , , , , , , , , , , , , , , ,56 % Earnings in FIRE ,00 0,24 0,04 0,03 0, ,00 0,25 0,03 0,03 0, ,00 0,26 0,04 0,03 0,02 % Earnings in Manufacuring ,00 0,84 0,21 0,19 0, ,00 0,82 0,21 0,19 0, ,00 0,82 0,21 0,18 0,15 % Earnings in Services ,00 0,74 0,15 0,15 0, ,00 0,70 0,16 0,16 0, ,00 0,86 0,18 0,17 0,08 Toal Populaion , , , , , , , , , , , , , , ,37 Toal Employmen , , , , , , , , , , , , , , ,88 Toal Annual Wages , , , , , , , , , , , , , , ,20 Naural Ameniy Index 3,60 21,17 10,06 9,86 2,29 Expor Price Index , ,62 68,52 65,26 31, ,35 603,95 73,72 72,00 15, ,79 394,66 86,06 84,98 9,29 Longiude 124,20 67,48 91,79 90,36 11,46 Laiude 24,74 48,85 38,28 38,35 4,86

9 Région e Développemen 43 This ransformaion ensures ha each observaion is pegged o he sysem as a whole and, because he resul is uni free, enables direc comparison of populaion densiy, employmen densiy, and he average annual wage a equilibrium. Descripive saisics for all of he underlying daa ha is, for he variables hemselves, no heir ransformed values involved in he analysis are provided in Table Esimaion Resuls As already noed, equaion se (4) was esimaed for each of he hree ime periods wih a spaial la g represening a single neares neighbor, wih 25-, 50-, and 100-mile spaial lags, and wih no spaial lag; in all, a oal of 15 sysems were esimaed. The differences beween models esimaed wih he hree disance-based spaial lags were minor perhaps due o he large size of he unis of observaion so only he resuls for he 50-mile spaial lag are repored here. This disance is he mos reasonable given commuing endencies in he Unied Saes, and, maybe for ha reason, equaion-for-equaion he 50- mile lag produced higher adjused R 2 values han eiher he 25- or 100-mile lag. I is worh noing, oo, ha applying he 100-mile lag o he 3,073 counies in he daa se yields a grand oal of over 135,000 spaial relaionships! This compares o he 25- and 50-mile lag operaions, which produce abou 6,500 and 34,000 spaial relaionships, respecively. In oher words, wihin a 50-mile radius, he average couny in he daase has abou 11 neighbors, based on he locaion of he populaion ceners shown in Figures 1 and 2. The following paragraphs discuss some diagnosics for each of he hree ses of resuls hen describe he findings from he group as a whole. Firs, esimaion resuls for he models specified wih a neares neighbor spaial lag are presened in Tables 2a-2c. Only he panel regisers he expeced paern of feedback in all hree-equaions: Populaion densiy (a measure of labor supply) is no significan and carries he wrong sign (+) in he panel s wage equaion and is no quie significan in he panel s wage equaion. In all hree panels, he dominan characerisic roo, λ, which is derived from reduced form esimaes (see Carlino and Mills, 1987), is less han one. The uni vecors which measure he raio, or relaive imporance, of populaion, employmen, and wages, respecively, a he projeced equilibrium scenarios (see Carruhers and Mulligan, 2008) are (p = : e = : y = 02245) for he panel; (p = : e = : y = ) for he panel; and (p = : e = : y = ) for he panel. The spaial lag iself is always significan excep for in he panel s employmen densiy equaion; noe ha he negaive sign on he spaial lag in his equaion and ha of he subsequen panels is logical because i mos likely regisers he presence of employmen densiy gradiens. The adjused-r 2 s, hough small, are all in he viciniy of he expeced size (say, ~0.20) for rae of change oriened regional adjusmen models.

10 44 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan Table 2a. S2SLS Esimaes of Neares Neighbor Regional Adjusmen Model, ln ( p& ) ln ( e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 6.40E-02 *** E-02 ** E-02 * 1.74 Spaial Lag 4.53E-02 *** E-03 n/s E-02 *** 9.80 Adjusmen Variables ln Populaion Densiy 1.83E-01 *** E-01 *** E-04 n/s 0.09 ln Employmen Densiy 1.42E-01 *** E-01 *** E-02 *** 8.47 ln Average Wage 1.27E-01 *** E-01 *** E-01 *** Indusrial Composiion % Earnings in FIRE 1.31E-03 n/s E-02 *** E-03 n/s 0.99 % Earnings in Manufacuring 6.31E-03 *** E-02 *** E-02 *** % Earnings in Services 5.43E-03 n/s E-02 *** E-04 n/s 0.17 Size and Comparaive Advanage Populaion/Employmen/Wages 1.54E-03 *** E-03 n/s E-04 *** 3.33 Naural Ameniy Index 1.95E-02 *** E-02 *** 3.53 Expor Price Index E-04 n/s E-03 ** 2.16 Locaion Longiude 3.45E-04 *** E-04 n/s E-04 n/s 0.97 Laiude 7.98E-04 n/s E-03 *** E-03 *** 5.82 Adjused R Dominan λ 0.96 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae; all hypohesis ess are wo-ailed; *** denoes significan a p < 0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p < 0.10 ; n/s denoes no significan. Table 2b. S2SLS Esimaes of Neares Neighbor Regional Adjusmen Model, ln ( p& ) ln ( e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 1.38E-02 n/s E-01 *** E-03 n/s 0.37 Spaial Lag 4.16E-02 *** E-02 *** E-02 *** 7.54 Adjusmen Variables ln Populaion Densiy 1.63E-01 *** E-01 *** E-03 n/s 1.57 ln Employmen Densiy 1.37E-01 *** E-01 *** E-02 *** 7.14 ln Average Wage 9.97E-02 *** E-02 ** E-01 *** Indusrial Composiion % Earnings in FIRE 9.50E-03 *** E-03 n/s E-03 n/s 1.27 % Earnings in Manufacuring 7.71E-03 *** E-03 * E-04 n/s 0.39 % Earnings in Services 7.42E-03 n/s E-02 *** E-03 n/s 1.37 Size and Comparaive Advanage Populaion/Employmen/Wages 4.35E-04 n/s E-03 *** E-04 *** 3.04 Naural Ameniy Index 2.31E-02 *** E-03 n/s 0.73 Expor Price Index E-02 *** E-02 *** 4.70 Locaion Longiude 7.20E-05 n/s E-04 *** E-05 n/s 0.81 Laiude 3.73E-04 n/s E-04 n/s E-04 *** 2.76 Adjused R Dominan λ 0.98 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae ; all hypohesis ess are wo-ailed ; *** denoes significan a p<0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan.

11 Région e Développemen 45 Table 2c. S2SLS Esimaes of Neares Neighbor Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 1.35E-02 n/s E-01 *** E-02 *** 2.48 Spaial Lag 4.39E-02 *** E-03 * E-02 *** 6.64 Adjusmen Variables ln Populaion Densiy 2.25E-01 *** E-02 *** E-02 ** 2.12 ln Employmen Densiy 1.69E-01 *** E-02 *** E-02 ** 2.14 ln Average Wage 1.68E-01 *** E-02 ** E-01 *** Indusrial Composiion % Earnings in FIRE 5.76E-03 * E-02 *** E-03 *** 2.55 % Earnings in Manufacuring 1.01E-02 *** E-03 n/s E-02 *** 6.65 % Earnings in Services 1.37E-02 * E-02 *** E-03 n/s 1.70 Size and Comparaive Advanage Populaion/Employmen/Wages 1.49E-03 *** E-04 n/s E-03 *** 2.57 Naural Ameniy Index 5.07E-02 *** E-02 *** 2.93 Expor Price Index E-01 *** E-02 *** 5.07 Locaion Longiude 1.05E-04 n/s E-04 ** E-05 n/s 0.24 Laiude 4.71E-04 n/s E-04 n/s E-04 *** 2.82 Adjused R Dominan λ 0.98 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae ; all hypohesis ess are wo-ailed; *** denoes significan a p <0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan. When levels, raher han raes of change, are used, he resuls remain essenially he same, excep ha he own-lagged coefficiens are invered and he adjused-r 2 s, soar o nearly one, reflecing he auological fac ha he single bigges predicor of each of he hree dependen variables oday is wha heir value was yeserday. Nex, esimaion resuls for he models specified wih a 50-mile spaial lag or he neares neighbor if no populaion cener is wihin range are presened in Tables 3a-3c. This specificaion exhibis a disinc improvemen: All of he panels regiser he expeced paern of feedback among he inerdependen variables and, in each case, he dominan characerisic roo remains less han one, indicaing ha he models predic a sable equilibrium oucome (see Rogers, 1971). Here, he uni vecors are (p = : e = : y = ) for he panel; (p = : e = : y = ) for he panel; and (p = : e = : y = ) for he panel. Like before, he spaial lag is always significan excep for in he panel s employmen densiy equaion and i carries is expeced sign paern. Again, his sign paern is posiive in he populaion and wage equaions, bu negaive in he employmen equaion wih he laer effec likely being due o he very seep employmen densiy gradiens found in mos American regions.

12 46 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan Table 3a. S2SLS Esimaes of 50-mile Spaial Lag Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 7.47E-02 *** E-02 * E-02 ** 2.34 Spaial Lag 6.88E-02 *** E-03 n/s E-01 *** Adjusmen Variables ln Populaion Densiy 1.98E-01 *** E-01 *** E-02 ** 2.23 ln Employmen Densiy 1.50E-01 *** E-01 *** E-02 *** ln Average Wage 1.30E-01 *** E-01 *** E-01 *** Indusrial Composiion % Earnings in FIRE 4.19E-03 n/s E-02 *** E-04 n/s 0.31 % Earnings in Manufacuring 1.09E-02 *** E-02 *** E-02 *** 9.86 % Earnings in Services 2.81E-03 n/s E-02 *** E-03 n/s 0.28 Size and Comparaive Advanage Populaion/Employmen/Wages 1.64E-03 *** E-03 n/s E-04 *** 3.10 Naural Ameniy Index 1.14E-02 n/s E-03 * 1.87 Expor Price Index E-05 n/s E-03 ** 2.23 Locaion Longiude 3.44E-04 *** E-04 * E-04 n/s 1.23 Laiude 8.27E-04 ** E-03 *** E-03 *** 6.33 Adjused R Dominan λ 0.96 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae; all hypohesis ess are wo-ailed ; *** denoes significan a p<0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan. Table 3b. S2SLS Esimaes of 50-mile Spaial Lag Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 4.25E-02 ** E-01 *** E-02 n/s 0.80 Spaial Lag 8.06E-02 *** E-02 *** E-01 *** Adjusmen Variables ln Populaion Densiy 1.97E-01 *** E-01 *** E-02 *** 3.91 ln Employmen Densiy 1.57E-01 *** E-01 *** E-02 *** 8.46 ln Average Wage 1.24E-01 *** E-02 *** E-01 *** Indusrial Composiion % Earnings in FIRE 8.35E-03 *** E-03 n/s E-03 n/s 0.73 % Earnings in Manufacuring 1.48E-02 *** E-02 ** E-03 n/s 0.51 % Earnings in Services 3.28E-03 n/s E-02 *** E-03 n/s 0.99 Size and Comparaive Advanage Populaion/Employmen/Wages 5.99E-04 n/s E-03 *** E-04 *** 2.94 Naural Ameniy Index 1.21E-02 n/s E-03 ** 1.93 Expor Price Index E-02 *** E-02 *** 5.45 Locaion Longiude 3.61E-05 n/s E-04 *** E-05 n/s 0.86 Laiude 4.92E-04 n/s E-05 n/s E-04 *** 3.06 Adjused R Dominan λ 0.98 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae ; all hypohesis ess are wo-ailed ; *** denoes significan a p<0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan.

13 Région e Développemen 47 Table 3c. S2SLS Esimaes of 50-mile Spaial Lag Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 1.04E-02 n/s E-01 *** E-02 *** 2.54 Spaial Lag 7.47E-02 *** E-02 ** E-02 *** 9.64 Adjusmen Variables ln Populaion Densiy 2.50E-01 *** E-02 *** E-02 *** 3.82 ln Employmen Densiy 1.85E-01 *** E-01 *** E-02 *** 3.51 ln Average Wage 1.87E-01 *** E-02 ** E-01 *** Indusrial Composiion % Earnings in FIRE 5.88E-03 * E-02 *** E-03 *** 2.80 % Earnings in Manufacuring 1.52E-02 *** E-03 n/s E-02 *** 6.58 % Earnings in Services 1.78E-02 *** E-02 *** E-03 * 1.51 Size and Comparaive Advanage Populaion/Employmen/Wages 1.75E-03 *** E-05 n/s E-03 *** 2.52 Naural Ameniy Index 4.04E-02 *** E-02 *** 3.28 Expor Price Index E-01 *** E-02 *** 5.66 Locaion Longiude 1.27E-04 n/s E-04 ** E-05 n/s 0.26 Laiude 3.65E-04 n/s E-04 n/s E-04 *** 2.76 Adjused R Dominan λ 0.98 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae; all hypohesis ess are wo-ailed ; *** denoes significan a p<0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan. Overall, he adjused-r 2 s are somewha improved from he neares neighbor spaial lag, reflecing he more accurae represenaion of he spaial relaionships expressed by his model. As noed, shifing o he 25-mile or 100- mile spaial lag does no improve he models performance and, in fac, i akes away from i, a leas in erms of explanaory power as measured by he adjused R 2 s. Sill, he differences among he spaial specificaions suggess ha, even a his relaively high (couny) level of aggregaion, regional adjusmen models are sensiive o he spaial dependencies ha mediae he growh processes hey emulae. Fuure work in his vein should focus on developing weighing schemes perhaps based on ravel coss, raher han disances ha more precisely reflec he naure of regional conneciviy. For comparison, esimaion resuls for aspaial models are presened in Tables 4a-4c. No surprisingly, his version of he model is ineffecive compared o he oher wo: Many of he inerrelaed variables are no saisically significan; hey do no always carry heir expeced signs; and he dominan characerisic roo is less han one only in he panel. Furher, he adjused-r 2 s reflec he fac ha his version of he model explains less of he variaion in he sysem s dependen variables han eiher of he wo spaial lag models. Even based on he simples of regression diagnosics, he aspaial models fall shor of heir spaial counerpars a finding ha reinforces he need o accoun for he inerconnecedness of growh and change across geographic space.

14 48 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan Table 4a. 2SLS Esimaes of Aspaial Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 2.97E-02 n/s E-02 * E-02 n/s 1.52 Spaial Lag Adjusmen Variables ln Populaion Densiy 1.50E-01 *** E-01 *** E-02 *** 2.53 ln Employmen Densiy 1.34E-01 *** E-01 *** E-02 *** 6.56 ln Average Wage 1.14E-01 *** E-01 *** E-01 *** Indusrial Composiion % Earnings in FIRE 4.59E-04 n/s E-02 *** E-03 n/s 0.99 % Earnings in Manufacuring 1.07E-03 n/s E-02 *** E-02 *** % Earnings in Services 8.46E-03 n/s E-02 *** E-03 n/s 1.02 Size and Comparaive Advanage Populaion/Employmen/Wages 2.25E-03 *** E-03 n/s E-04 *** 3.28 Naural Ameniy Index 2.59E-02 *** E-02 *** 4.33 Expor Price Index E-04 n/s E-03 * 1.92 Locaion Longiude 3.20E-04 ** E-04 * E-05 n/s 0.50 Laiude 5.11E-04 n/s E-03 *** E-03 *** 5.86 Adjused R Dominan λ 1.01 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae; all hypohesis ess are wo-ailed; *** denoes significan a p < 0.01 ; ** denoes significan a p < 0.05 ; * denoes significan a p < 0.10 ; n/s denoes no significan. Table 4b. 2SLS Esimaes of Aspaial Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 2.35E-02 n/s E-01 *** E-03 n/s 0.28 Spaial Lag Adjusmen Variables ln Populaion Densiy 1.19E-01 *** E-01 *** E-03 n/s 0.44 ln Employmen Densiy 1.15E-01 *** E-01 *** E-02 *** 5.72 ln Average Wage 6.65E-02 *** E-02 n/s E-01 *** Indusrial Composiion % Earnings in FIRE 1.03E-02 *** E-03 n/s E-03 n/s 1.04 % Earnings in Manufacuring 2.53E-03 n/s E-03 n/s E-03 n/s 0.55 % Earnings in Services 1.26E-02 ** E-02 *** E-03 ** 2.10 Size and Comparaive Advanage Populaion/Employmen/Wages 9.08E-04 ** E-03 *** E-04 *** 2.94 Naural Ameniy Index 2.82E-02 *** E-03 n/s 0.42 Expor Price Index E-02 *** E-02 *** 4.91 Locaion Longiude 1.34E-04 n/s E-04 *** E-05 n/s 0.38 Laiude 1.68E-04 n/s E-04 n/s E-04 *** 2.74 Adjused R Dominan λ 1.00 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae ; all hypohesis ess are wo-ailed; *** denoes significan a p<0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan.

15 Région e Développemen 49 Table 4c. 2SLS Esimaes of Aspaial Regional Adjusmen Model, ln ( p& ) ln (e& ) ln ( y& ) Es. Parameer -value Es. Parameer -value Es. Parameer -value Consan 5.61E-02 *** E-01 *** E-02 *** 3.00 Spaial Lag Adjusmen Variables ln Populaion Densiy 1.84E-01 *** E-02 *** E-03 n/s 0.72 ln Employmen Densiy 1.49E-01 *** E-02 *** E-03 n/s 0.68 ln Average Wage 1.31E-01 *** E-02 * E-01 *** Indusrial Composiion % Earnings in FIRE 7.72E-03 *** E-02 *** E-03 *** 2.96 % Earnings in Manufacuring 5.73E-03 ** E-03 n/s E-02 *** 7.24 % Earnings in Services 9.81E-03 n/s E-02 *** E-02 *** 2.81 Size and Comparaive Advanage Populaion/Employmen/Wages 1.87E-03 *** E-05 n/s E-03 *** 2.54 Naural Ameniy Index 5.78E-02 *** E-02 *** 3.08 Expor Price Index E-01 *** E-02 *** 5.66 Locaion Longiude 5.06E-05 n/s E-04 * E-05 n/s 0.54 Laiude 7.77E-04 ** E-04 n/s E-04 *** 2.72 Adjused R Dominan λ 0.97 Noes : The number of observaions in all cases is 3,073 ; all equaions were esimaed using Whieadjused sandard errors clusered by sae ; all hypohesis ess are wo-ailed ; *** denoes significan a p<0.01 ; ** denoes significan a p<0.05 ; * denoes significan a p<0.10 ; n/s denoes no significan. Moving on, he esimaion resuls repored for he 50-mile spaial lag model in Table 3a-3c ell a sraighforward sory. In he populaion densiy equaion, over he imeframe, he negaive effec of iniial populaion densiy becomes progressively sronger reflecing he kind of broad shifs especially o he Wes and Souh of he Unied Saes ha have occurred over he pas hree decades. As a resul, by he end of he sudy period, regions wih high concenraions of populaion relaive o he naion as a whole experienced subsanially lower raes of change in densiy han hey did jus 15 years before. Meanwhile, he role of naural ameniies in driving his process (as documened by McGranahan, 1999, among ohers) also grew more powerful. The naural ameniy index is no significan in he panel, is a bi closer o being significan in he panel, and is highly significan in he panel. The rise of his variable is brough ino relief by he decline of he longiude and laiude variables: Boh are highly significan in he panel and indicae ha counies locaed in he Eas and Souh of he Unied Saes experienced gains in populaion densiy, bu hese fall ou of significance as he ameniy index ransiions ino significance during he and panels. In he employmen equaion, he effec of iniial employmen densiy ges progressively weaker and smaller over he 15-year imeframe. A he same ime, he role of manufacuring declines bu, in an experience known, for beer or for worse, in many pars of he counry, manufacuring is ulimaely replaced by he FIRE and service secors. Likewise, in he average wage equaion he effec iniial wage concenraion grows boh weaker and smaller and so oo does he influence of iniial employmen densiy.

16 50 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan Addiionally, over he course of he hree panels, he influence of he naural ameniy index reverses iself from a srong posiive effec in he panel o a srong negaive effec in he panel; he negaive effec is he expeced effec wihin he kind of compensaing differenials framework ha regional adjusmen models emulae. The fac ha each of hese findings follows a logical progression over he sudy period is encouraging because i suggess ha he models are, in fac, regisering he kind of broad srucural shifs in he space economy ha hey were designed o characerize. If so, hey also reinforce he noion ha an equilibraing process is responsible for mediaing growh and land use paerns hroughou he naion. Coming back, for a momen, o he uni vecors from he models specified wih a 50-mile spaial lag, noe how he weigh of he populaion and employmen componens shifs from he firs wo panels o he hird panel. Pas evidence suggess ha he raio beween he wo normally is in he range beween 1.5 : 1 and 2.2 : 1 when employmen includes full-ime, par-ime, and seasonal workers (Carruhers and Mulligan, 2007). By his benchmark, he and panels seem o almos perfecly capure he balance beween people and jobs in he equilibraing process bu his is a odds wih previous findings (Carruhers and Mulligan, 2008) ha suggesing ha he panel, which is cenered squarely on a recession, 3 is he oulier. Tha analysis, however, deal wih meropolian areas only, so i did no capure he complee sysem, plus mos of is models had dominan characerisic roos greaer han one, meaning ha hey failed o sele on sable equilibrium growh pahs. The presen finding is ineresing because i raises he possibiliy ha he employmen effec grows, maybe jus emporarily, in he wake of a recession. Whaever he case may be, furher work on his diagnosic is clearly required before he characerisic vecors can be used o eiher accep or rejec a paricular regional adjusmen model. Bu given he models srong and consisen performance overall, hey in general, and he hree-equaion varian especially, coninue o sand up as an excellen lens hrough wih o view he processes of regional growh and land use change. Las, i is worh acknowledging here ha he models jus discussed are sparse in he sense ha each equaion conains only a small number of predeermined explanaory variables. In order o be used he kind of policy analysis hey are inended for, he specificaion of he hree-equaion sysem needs o be exended and, along he way, experimened wih o speak direcly o he kinds of issues ha praciioners are faced wih. For example, Carruhers and Vias (2005) developed a (wo-equaion) land use based regional adjusmen model o examine paerns and processes of sprawl in he Mounain Wes region of he Unied Saes and were able o come o he very angible conclusion ha he long-erm prosperiy of he region depends, crucially, on he preservaion of he high qualiy of life i offers. Toward ha end, hey sugges ha policymakers in he region should pursue several specific acions aimed a 3 According o he Naional Bureau of Economic Research s daing procedure, his recession ran from July 1990 o March 1991.

17 Région e Développemen 51 achieving broader environmenal and economic developmen goals. Bu, arriving a hese kinds of conclusions requires posiing specific policy quesions ha can be addressed via hypohesis esing and, ulimaely, measuremen. Alhough his paper sops far shor of doing ha, i offers up he hree-equaion regional adjusmen model wih he belief ha i will be an effecive ool for conducing consequenial policy analysis Spaial Oucomes A deeper look ino he spaial oucomes of he adjusmen process is provided in Figures 2 and 3, which are based on he 50-mile spaial lag repored in Tables 3a-3c. Using he equivale ncies given in equaion se (3), Figure 2 shows projeced equilibrium scenarios for 1987 (Figures 2a-2c), 1992 (Figures 2d-2f), and 1997 (Figures 2g-2i). In hese maps, he whie areas denoe a projeced locaion quoien of less han one, or below he average densiies or annual wage; grey areas denoe a locaion quoien of one o one-and-a-half, or from 100% up o 150% of he naional averages; and black areas denoe a locaion quoien of greaer han one and a half, or more han 150% of he naional averages. Inspecion of he densiy maps reveals a ransiion away from he buil-up areas of he Norheas and a gradual densificaion of he Wes and Souh. A similar paern is observed in he wage maps, which seem o show a sligh evening ou of wages, excep in he Grea Plains, where he gulf remains as wide as ever. Figure 3 documens wheher hese scenarios call for an increase or a decrease in he relaive concenraion of people and wages compared o iniial (1982, 1987, and 1992) condiions in oher words, he direcion in which he equilibraing process was pushing he space economy. In paricular, he whie areas on he maps denoe projeced decreases ( p < p -5, e < e -5, y < y -5 ) and he black areas denoe projeced increases ( p > p -5, e > e -5, y > y -5 ) as he sysem moves oward a sae of spaial equilibrium. Ineresingly, he maps peraining o populaion densiy and employmen densiy indicae a endency oward gains in many comparaively disadvanaged, rural areas of he Unied Saes, especially a he inerior. The wage maps show a similar paern ha ges sronger over he 15-year imeframe : by 1997, he equilibraing scenario calls for higher wages hroughou much of he inerior, and lower wages in he rapidly growing Wes and Souhwes likely due o he large par played by supply-induced growh in hese pars of he counry. Going back o he discussion above, hese paerns may well be he produc of he rise in he imporance of naural ameniies during he sudy period, which, of course, are key drivers of supply-induced growh. Even wih an overall paern of spaial convergence, however, he wo ses of maps also documen he clear persisence of a hierarchical sysem of regional economies described by radiional forms of locaion heory (see, for example, Lösch, 1954 ; Isard, 1956 ; Beckmann, 1968 ; Mulligan, 1984 ; Fujia e al., 1998), suggesing ha he longsanding paern of cenral places is no easily broken.

18 52 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan 4. CONCLUSION The sudy documened in his paper highlighs he imporance of geographic relaionships in a land use based regional adjusmen model conaining equaions for populaion densiy, employmen densiy, and he average annual wage. There are key findings are hree : (1) accouning for spaial inerdependencies subsanially enhances he performance of land use based regional adjusmen models ; (2) wih his correcion, he viabiliy of he hree-equaion framework used here (an exension of he radiional wo equaion framework) seems very srong; and (3) even as he naion s posindusrial economy coninues along is pah of decenralizaion, i reains an uneven paern of developmen characerisic of he well-known, hierarchical sysem of regional economies described by radiional forms of locaion heory. The laer of hese findings is especially ineresing because i indicaes ha he longsanding paerns of cenral places are no easily broken. Having furher esablished he hree-equaion approach, he work presened here could be profiably exended in a number of ways. To begin wih, more formal diagnosic work, paricularly involving he uni vecors, is needed in order o discriminae among various spaial models and, as imporan, processes wih any real confidence. Geography clearly maers and i should be aken seriously, which means going beyond simple economeric correcions like he spaial lags experimened wih here and delving more deeply ino he naure of he relaionships hemselves. Once his is accomplished, he hree-equaion regional adjusmen model will be an excellen ool for urban and regional policy analysis aimed a, among oher hings, qualiaive quesions concerning he role of naural ameniies and he expor price index. Exploring hese relaionships in deail may involve developing he kind of spaial mulipliers described by Anselin (2003) in order o observe how place-specific effecs play ou hrough he naional sysem. Furher, here is meri o evaluaing how regional adjusmen models compare o he kind of convergence models developed by Barro and Sala -i-marin (2004). Broad avenues of research have recenly opened up in his area of spaial analysis (see, for example, Rey and Monouri, 1999; Fingleon, 2003; Rey and Boarne, 2004; Rey and Janikas, 2005; Arbia, 2006) and he models presened here sand o make subsanive conribuions. Las, addiional work also needs o be done o fully connec he resuls of he hree-equaion regional adjusmen model o paerns described by locaion and cenral place heory. Each of hese seps holds considerable promise for expanding he exising body of heory and evidence on he naure of growh and land use change in he conemporary space economy.

19 Figure 1. Couny Populaion Ceners - Shading is by Disance Région e Développemen 53

20 54 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan Figure 2. Connecions o Neares Neighbors

21 Région e Développemen 55 Figures 3a-3i and 4a-4i (Noe: whie areas denoe LQ>1 ; grey areas denoe LQ ; dark grey areas denoe LQ > 1.5) 3a. Equilibrium Populaion Densiy, b. Equilibrium Employmen Densiy, c. Equilibrium Average Wage, d. Equilibrium Populaion Densiy, e. Equilibrium Employmen Densiy, f. Equilibrium Average Wage, 1992

22 56 John I. Carruhers, Michael K. Hollar and Gordon F. Mulligan 3g. Equilibrium Populaion Densiy, h. Equilibrium Employmen Densiy, i. Equilibrium Average Wage, a. Equilibrium Trend for Populaion Densiy b. Equilibrium Trend for Employmen Densiy c. Equilibrium Trend for Average Wage, 1987

23 Région e Développemen 57 4d. Equilibrium Trend for Populaion Densiy, g. Equilibrium Trend for Populaion Densiy, e. Equilibrium Trend for Employmen Densiy, h. Equilibrium Trend for Employmen Densiy, f. Equilibrium Trend for Average Wage, i. Equilibrium Trend for Average Wage, 1997