Facto poductiity dieences and missing tade poblems in a egional HOV model Andés Atal-Tu, Calos Llano-Veduas, Fancisco Requena-Silente () Dpt. o Economics, Technical Uniesity o Catagena, Pº Alonso XIII, 50, 30203 Catagena, Spain. (e-mail: Andes.atal@upct.es) () Dpt. o Economic Analysis, Autonoma Uniesity o Madid, and CEPREDE, Cento Stone, Lawence R. Klein Institute, 28049 Cantoblanco, Madid, Spain. (e-mail: calos.llano@uam.es) () Dpt. o Applied Economics II, Uniesity o Valencia, Ada. Los Naanjos s/n, 46022 Valencia, Spain. (e-mail: ancisco.equena@u.es) Coesponding autho: Andes.atal@upct.es Shot unning title: Poductiity dieences in a egional HOV model Abstact Recent empiical papes testing the peomance o the Hecksche-Ohlin-Vanek (HOV) model suggest the need o elaxing its estictie assumptions in ode to econcile theoy and data. This pape wondes i intoducing acto poductiity dieences could help to impoe the peomance o the HOV model in a egional setting. Using a new dataset o 17 Spanish egions and thee dieent HOV speciications, we seek o the existence o Hicks-neutal (HN) o acto-augmenting industy-neutal (FAIN) technological dieences. Data suppot the existence o HN technological dieences, which contibutes o a emakable impoement o the egional HOV peomance since the so-called missing tade poblem lagely disappeas. Keywods: Hecksche-Ohlin-Vanek, Facto Regional Tade, Poductiity dieences, Missing tade poblem. JEL classiication: F11, F14. Acknowledgements: The aticle has beneited om the comments o paticipants in Euopean Tade Study Goup (ETSG) 2008 (Wasaw) and INTECO 2008 (Spain). We would like also thank the suggestions made by James Walke. F. Requena is membe o INTECO (GRUPOS03/151). A. Atal and F. Requena acknowledge inancial suppot om the Spanish Ministy o Science and Innoation (poject numbe ECO 2008-04059/ECON). 1
1. Intoduction The Hecksche-Ohlin (HO) model is a ey illustatie example o what a theoy should be: simple, ich, ambitious and ey insightul. No doubt, this explains its ubiquity in the ield o intenational economics, sometimes used as a amewok o studying the location o poduction, othe times o discussing the welae impact o intenational tade lows (Benstein and Weinstein 2002; Dais 1998). Vanek (1968) e-intepeted the model as one o tade in acto seices, stating that, unde some assumptions 1, the model pedicts that net expot o acto seices will be the dieence between a egion s endowment and the endowment typical in the wold o a egion o that size. The impotance o his contibution was establishing a testable elationship between acto endowments, acto input equiements and (net) acto tade, the so-called Hecksche-Ohlin-Vanek (HOV) equation. This contibution obiously stimulated academic cuiosity in ode to see how the model peomed empiically, with ealy tests showing a poo pedictie powe o the HOV model using a lage numbe o counties and actos (Maskus 1985; Bowen et al. 1987). As a esponse, moe ecent contibutions hae ollowed the path o elaxing some o the stict assumptions o the oiginal model, extending it in a way moe consistent with obseed data. In the county appoach, these contibutions hae shown the pominent ole that the assumptions o intenational identical technologies, acto pice equalization, and identical and homothetic peeences play in econciling theoy and eidence (Tele 1995; Dais and Weinstein 2001). 2 Inteegional tade low data athe than intenational tade data can altenatiely be used to test the peomance o the HOV model. A pioi, egional tests o the basic HOV model ae expected to 1 The stict esion assumes: (1) identical constant etuns to scale (CRS) technology; (2) peectly competitie makets in goods and actos; (3) identical and homothetic peeences; (4) acto endowment ae dieent (but not too dieent) acoss counties; and (5) ee tade in goods. 2 Unde the assumption o uniesal acto pice equalization, endowments can be measued in physical units (i.e. numbe o employees) athe than in cuency (i.e. labou compensation) because acto pices ae the same acoss counties. 2
show a supeio peomance, because the thee key assumptions o the model - identical technologies, acto pice equalization and identical and homothetic demands ae moe plausible to hold in a egional setting than in an intenational one. The pionee contibution o Dais et al. (1997), using data on the peectues o Japan, ound that elaxing the wold acto pice equalisation assumption, but maintaining it o Japan, was enough to obtain a emakable impoement o the match between theoy and data. 3 In contast, Atal et al. (2006) and Requena et al. (2008a), using data on 14 Spanish egions, ound a emakable peomance o the stict HOV model when pedicting the diection o acto tade seices, but seious missing tade poblems emain when pedicting the olume o acto tade seices; thei esults show that the theoetical model pedicts much moe acto tade than the one we obsee in data. In this pape we get deepe undestanding o how well the HOV model woks, paying especial attention to whethe technology dieences between tading patnes help impoe the peomance o the HOV model in a egional setting. 4 Ou appoach assumes that egions could pesent dieences in thei unit acto equiements, but aaying solely om the existence o dieences in thei acto poductiities. It allows us still assuming that egions shae identical poduction technologies once we account o poductiity dieences. With this aim, we addess two speciications o technological dieences: Hicks-neutal (HN) and acto-augmenting industy-neutal (FAIN). In the HN speciication, poductiity dies among egions uniomly o all actos, but it is the same ( neutal ) acoss industies; in the FAIN speciication, poductiity is dieent o each egion-acto pai but such dieences emain constant acoss industies. 3 In pactice Dais et al (1997) used the Japanese Input-Output Table athe than the eplaced the US Input-Output Table in the calculation o the measued acto content o tade o the Japanese peectues to show that thee ae impotant dieences in technology acoss counties. 4 Dais et al (1997) did not addess this question because they had only the Japanese Input-Output Table. Requena et al. (2008a) inestigated the impotance o Hicks-neutal technological dieences acoss Spanish egions by simply scaling acto endowments by pe capita GDP dieences as suggested in Tele (1993). The esults showed that such a simple adjustment was not enough to impoe signiicantly the peomance o the HOV model. 3
Ou analysis will ocus on the Spanish inteegional tade lows, which accounts o 80% o total Spanish tade. Requena et al. (2008b) show that the uneen distibution o poduction actos that induces intanational specialisation and dieent egional acto pices is not an issue o Spain. Since acto endowments dieences ae not too lage acoss Spanish egions (i.e. national FPE holds), intanational space becomes a good setting to inestigate the impact o technology dieences on the acto tade model. A ist noelty o the pape is to apply thee dieent speciications in testing the peomance o the HOV model: the standad model, the pai-wise model, and the elatie model. The ist one is the most commonly used in the liteatue to ealuate the HOV model and it is based on a egion by egion compaison o each acto. The second one ollows Hakua (2001) and it is based on compaisons between all pais o egions o each acto. The thid one ollows Debaee (2003) and it is based on compaisons o acto contents and acto abundances between pais o egions o each pai o actos. The pai-wise model and the elatie model hae two adantages egading the standad model. Fist, bilateal compaisons incease the numbe o obseations employed in the tests, impoing the obustness o the esults. Second, although less impotant in a egional amewok, is the act that compaisons between egions do not equie a ecto o wold o national endowments. 5 A second noelty o the pape is the use o a new database o Spanish Input-Output egional tables (Llano, 2004a, 2004b; Péez et al, 2008). This newly constucted data set poides homogeneous inomation on tade lows, goss poduction, absoption pattens and technical coeicients o 17 Spanish egions, notably impoing the data set chaacteistics, and allowing us to eliminate common measuement eos (Dais and Weinstein 2001). The new database expands the scope o peious execises incopoating inomation not beoe aailable o thee Spanish egions (Mucia, Cantabia 4
and La Rioja). Moeoe, all data used in the estimation o egional technology paametes in the empiical execise is now poided by a unique souce, the Lawence-Klein Institute at the Autonoma Uniesity o Madid, who deeloped an intense statistical eot o data homogenisation when building the whole egional Input-Output amewok. 6 Gains in quality o data ae o salient eleance, gien that peious data sets wee sueyed sepaately by 14 dieent egional statistical agencies (see, Atal et al. 2006). 7 Ou esults poide eidence on the impotance o accounting o technological dieences in a egional HOV amewok. Fist, the capacity to pedict the diection o acto tade seices impoes compaed to the benchmak HOV model that assumes no poductiity dieences acoss egions. Second, and moe inteestingly, the missing tade poblem lagely disappeas. This noel esult indicates that egional poductiity dieences ae the main eason why the HOV model was not accuately pedicting the obseed olume o acto seices acoss Spanish egions. The HN speciication seems to wok slightly bette in the egional HOV case, although the FAIN speciication ollows ey closely. Ate this intoduction, the emainde o the pape is oganised as ollows. Section 2 deines thee dieent methods employed in testing the extended esion o the model. Section 3 descibes the econometic speciication in ode to estimate poductiity dieences among the Spanish egions. Section 4 includes the data set and discusses the esults o the eseach, while section 5 states the conclusions o the pape. 2. Thee HOV speciications copying with poductiity dieences In this section we pesent the HOV model and intoduce eiciency adjustments in the use o the poduction actos acoss egions in a manne compatible with the act that all egions use the same input 5 This popety o the bilateal compaisons is moe impotant when using intenational data due to the diiculty o computing a ecto o wold endowments and the subsequent poblems o statistical homogeneity (see Debaee 2003). 6 Fo uthe details on the database, see Llano-Veduas (2004) and CEPREDE (www.c-inteeg.es/index.asp). 5
equiements measued in eiciency units in each industy. Ou model builds on thee dieent appoaches to the HOV equation: the standad, the pai-wise and the elatie esions. Fist we pesent the basic speciication o each HOV equation and then extend it to its poductiity-adjusted speciication, which will be uthe employed in testing the modiied model s peomance. 2.1 The standad HOV model Let, i, and index egions, industies, and actos, espectiely, with county S (o Spain) haing R egions, I industies, and F pimay actos. Let T = E M be the inteegional net tade ecto o egion, constucted as the dieence between the expot and impot ectos o egion, and D 1 S (I B ) S be county s S technology matix that tansoms good lows into thei total (diect and indiect) embodied acto seices. The elements o matix D ae deined as atios between domestic acto endowment by industy by the coesponding output. The elements o matix B ae deined as atios between domestic usage o each input and industy output. 8 The obseed acto content in egion expesses the quantity o acto embodied in the net expots o egion and is obtained om multiplying the Spanish technology matix times the ecto o net expots o egion, D (I B S S ) 1 T. I a S is a ecto o the technological matix, the measued content o tade in acto in egion is F S = a T. S Let V and V S be the endowment o acto in egion and county S, espectiely; Y be the goss national poduct (GNP) o egion, Y S be county s S GNP, and N be the tade balance o egion 7 In addition, we use a new measue o the stock o physical capital poided by Fundación BBVA (2006). 8 1 i i j ji Each element (i) o matix DS (I B S ) is a S = d S a j S bs, that is, the diect acto input plus the sum o each industy j o the indiect acto input, whee the latte takes into account all intemediated inputs to industy i. Notice that the diect input matix and the input-output matices o each egion also include only the usage o domestically poduced intemediates. 6
, so that s = ( Y N ) / YS captues the inal consumption shaes o egion in the national space. 9 In this amewok, the standad egional HOV model shows that, unde standad assumptions, the pedicted acto content o tade o acto in egion is equal to the dieence between the egion s acto R V = 1 endowments ( V ) and the national endowments ( ) adjusted by the inal consumption shae o egion in the county ( s ). I the theoy is coect, the HOV equation can be witten as: F S = V s R = 1 V, = 1 F, = 1 R (1) whee the let hand side expession is the measued acto content o tade and the ight hand side is the pedicted acto content o tade. Depating om the standad model by intoducing egional acto-poductiity dieences equies the use o a technology paamete,, such that i V is the acto endowment o in egion, then V = V would be the coesponding acto endowment measued in poductiity-equialent units. 10 We assume identical technologies at the poductiity-equialent leel and nomalize acto -1-1 poductiity o county S to be equal to one: A (I-B ) = A (I-B ), =1 R, with S S being the poductiity o egion elatie to county S o acto. 11 Then equation (2) poides a speciication o the poductiity-adjusted standad HOV model, with the ight hand side o the expession captuing the excess o egion s endowments supply in eiciency tems: F S R = V s V, = 1 F, = 1 R (2) = 1 Notice that the expession in let hand side (the measued acto content o tade) has not changed. 9 Since egions ae open-economies, thei tade balances epesent a highe pecentage o thei GDP compaed to Spanish s tade balance. 10 We assume that all dieences in technology acoss egions aise in the om o acto-augmenting poductiity dieences (HN o FAIN), ollowing Tele (1993) s insight. 7
2.2 The pai-wise HOV model In ode to obtain the pai-wise HOV model (Staige et al. 1987; Hakua 2001), we adopt a twoegion esion o the stict Vanek equation (1) o two gien egions 1 and 2, and acto : 12 F1 αf2 = V1 αv2 (3) whee α = s / s, 1 2 F1 αf2 is the measued pai-wise acto content o tade 1 F = and F 2 = D2(I B 2 ) T2 ), and 1 ( 1 D1(I B1) T1 V1 αv2 is the pedicted pai-wise acto content o tade. 13 This esion equies all assumptions o the basic HOV model to hold. Futhe, we can elax the -1-1 -1 assumption o identical egional technology, with A (I-B ) A (I-B ) A (I-B ),, S S obtaining in this way the esion populaised by Staige et al. (1987) and moe ecently used by Hakua (2001). In ode to speciy the model in its poductiity-equialent esion, we stat deining a ecto o technology paametes o the om that captues the poductiity atio by pais o egions in county S. Gien that poductiity dieences ae the unique technology dieences allowed o in the model, egions will shae the same technology matix at the poductiity-equialent leel o eey acto, that -1-1 is, A(I-B) = (I-B ) A, with FPE holding at a national leel (Tele 1993, 1995). 11 We nomalize espect to the county technology by conenience, but one could hae nomalized espect to a egion o eeence as it is usual in the county appoaches (see, o example, Tele 1993, 1995). R R 12 Deining F1 = V1 s1 V, F2 = V2 s2 V, α = s / s 1 2, cancelling V and eodeing tems, we = 1 = 1 = 1 obtain equation (3). 13 Note that in the stict pai-wise egional esion we assume identical technologies at the national leel, with -1-1 A(I-B) =A(I-B) S S,. 8 R
Intoducing poductiity dieences o two gien egions 1 and 2, leads to the ollowing speciication o the model 14 : F1 αf2 = 21V1 αv2 (4) with equation (4) expessing the pai-wise HOV equation in poductiity-equialent units, in tems o egion 2 s technology. 2.3 The elatie HOV model The elatie esion o the Vanek equation was poposed by Debaee (2003) as an extension o the basic HOV model, and it is based on compaisons o endowments and obseed acto tade seices by pais o actos and egions. In ode to obtain the simple esion o the elatie HOV model, we stat with the stict Vanek equation o a egion and a acto, unde standad assumptions, as displayed in (1). Diiding both sides o equation (1) by the egional consumption shae (s ), and deining = F s and V s = yields, = V R = 1. Extending this expession o two gien egions and, taking the dieence between them, and diiding both sides o the esulting equation by the sum o both egion s nomalised endowments, ( ) ( ) = ( ) ( )., we obtain 14-1 -1 Deiation o the pai-wise HOV model with acto-poductiity adjustments assumes that A 1(I-B 1) 12A 2(I-B 2). -1-1 Applying it o egion 1 and acto, we hae two equations: (1) 12 A(I-B) 2 2 T 1 = V 1 12 A(I-B) 2 2 C 1 and (2) -1 = V2-1 1 A(I-B) 2 2 T2 A(I-B) 2 2 C. 2 Pe-multiplying (1) with -1-1 12 = 21 = A 2(I-B 2) A 1(I-B 1) and (2) with α, taking the dieence between the two equations, and noting that in the pai-wise esion C1 = αc2 (Staige et al. 1987; Beche and Choudi 1988), we obtain equation (4). = 9
10 Now, i we compute this expession o a supplementay acto and again take dieences, we obtain the basic esion o the elatie HOV equation. Debaee s poposal poides a testable modiied esion o the standad HOV model that compaes standadized elatie acto contents o tade and endowments by pais o actos between egions: = (5) Intoducing egional poductiity dieences in the elatie HOV model equies pemultiplying eey egion s acto endowment by its poductiity measue in equation (5). In ode to make it simple, we again nomalize acto poductiity o county S to unity ( = -1-1 S S A (I-B ) A (I-B ), =1 R), with being the poductiity o egion elatie to county S, o acto. Then, we deine acto endowments at the poductiity-equialent leel as s V s V = = =, with the poductiity-adjusted elatie model yielding: = (6) and / / s s = = -1-1 S S A(I-A) T A(I-B) T o acto. 3. Estimating egional acto poductiity dieences We hae just deined the theoetical amewok o the inestigation, both in the basic speciication and in the poductiity-adjusted extension. In this section, we estimate the actoaugmenting paametes o the thee esions o the HOV model, uthe incopoating them in the extended models in ode to see how these new speciications aect the peomance o the model, with a pimay ocus on missing tade questions.
In the basic esions o eey HOV model, standad, pai-wise o elatie, we assume the existence o identical technologies in a national-fpe amewok, with all egions o county S haing the same technology matix ( A(I-B) =A(I-B) ), and consequently eey egional industy i -1-1 S S i i pesenting the same unit total (diect and indiect) acto equiement o eey acto ( a = a, ). Within the new amewok, once we allow o egional technological dieences in the om o acto eiciency gaps, egions will continue to shae identical poduction technologies but now at the poductiity-equialent leel, obseing the equality o adjusted total unit acto equiements: S i i S a a =, with i i a a = and epesenting poductiity o acto in egion elatie to county S. Following this appoach, we estimate two types o acto-augmenting technological dieences by egessing unit total acto equiements o county S (Spain) against those o egion. In the ist speciication we allow o acto-augmenting poductiities common to eey acto in egion and industy i, that is, in a HN ashion ( =, ): i i i as = a ε (7) In the second speciication o the technological paametes, we allow o the existence o egional poductiity dieences speciic to eey acto, in a acto-augmenting industy-neutal speciication (, ), and estimate the ollowing equation: i i i as = a ε (8) Equations (7) and (8) allows o egional technological dieences aising in the om o poductiity dieences. Both equations ae estimated using data that ay acoss 20 industies o each o the 17 egions though seemingly unelated equations egessions (SURE), what ensues that the 11
estimation o poductiity paametes is not only consistent but also eicient. This pocedue is used o the standad and elatie esions o the HOV model. In estimating poductiity paametes in the paiwise esion o the model, we apply the next speciication o eey egional pai: a = ε (9) i i 2 21a 1 i i 2 21a 1 i 1 a = ε (10) i 1 whee 21 is the poductiity o egion 2 in tems o egion 1, uniom o all actos in equation (9) o acto-speciic in equation (10). Both equations allows us estimating inteegional poductiity dieences, now o all binay combination o egions athe than simply o each egion elatie to Spain, the county o eeence. In all cases, we assume that acto equiements ae geneated by a pocess obeying to the HN o FAIN assumptions, with measuement eos andomly distibuted aound zeo and embodied in the esidual tems. 15 Ate equations (7)-(10) hae been estimated, we incopoate the poductiity estimates in the extended esions o the HOV model [eithe equation (2), (4) o (6)], and then exploe how it aects the peomance o the model though the standad tests o sign, aiance atios and slope o the egessions o actual esus pedicted acto contents o tade o the Spanish egions. 16 4. Data and esults 4.1 Data The eseach is based pimaily on inomation coming om a set o homogeneous input-output (IO) tables o 17 Spanish egions, deeloped by the Lawence-Klein Institute at the Autonoma Uniesity o Madid with the aim o estimating the ist Spanish inte-egional Input-Output model. The 15 This pocedue pemits the model staying at the poductiity-equialent amewok, aoiding at the same time the citicism by Gabaix (1997) to the oiginal Tele s (1993) appoach, which was peiously implemented in Requena et al (2008a). 12
impotance o this newly constucted data set is that it poides compaable data on tade lows, goss poduction, absoption pattens and technical coeicients o all o the Spanish egions in the yea 1995, signiicantly impoing aailable inomation to date, which only could be obtained by the compilation o inomation poided -o dieent yeas and dissimila methodologies- by 14 dieent egional statistical oices, with all the heteogeneity it intoduces in the model. This new data set also allows us to incopoate thee new Spanish egions to the study, La Rioja, Mucia and Cantabia, egions o whom thee wee not aailable inomation to date. The egional data set is equally compatible with the county o national statistical amewok, with aggegated egional inomation coheently epoducing the national accounting system, what makedly impoes peious data set chaacteistics, and it is impotant in tems o eiciently captuing the poduction and absoption (consumption plus inestment) pattens pesent in the HOV amewok. In this way, the homogeneity o egional IO data allows us to compute compaable technical coeicients o eey Spanish egion, what then will be used to estimate ou poductiity paametes. Additionally, we will use the input-output table o Spain in 1995 when computing the acto content o tade o the stict and extended esions o the egional HOV model, and, though the use o its technical coeicients, it will poide the technology o eeence when estimating ou egional speciic poductiity estimates. Diect input equiements ae constucted as acto endowments diided by goss output, while total input equiements imply multiplying diect equiement ectos by coesponding Leontie inese tables. Tade lows come om the Input-Output tables, which allow us to beakdown the tade ectos o eey Spanish egion in thei inteegional and intenational lows. We use thee poduction actos: physical capital (K), high educated labou (H), low educated labou (L). Endowment data is taken om Encuesta de Población Actia and om National Accounts 16 The tests employed in the pape ae standads in the HOV liteatue. We descibe them in moe detail in the ollowing 13
(INE-National Statistics Institute; www.ine.es) o the labou oce, which classiies the labou oce egional ectos in tems o education leels, with high educated indiiduals deined as those with seconday and aboe leels o enolment and low educated ones as those that hae not inished the seconday studies o hae a lowe leel o education. Data on physical capital stock comes om the new database launched by Fundación BBVA, which applies a methodological eision to its pecedent wok in El stock y los seicios del capital en España y su distibución teitoial (1964-2005). Nuea metodología, ollowing new methodological ecommendations o the OECD (see, www.bba.es, o uthe details). 17 Ou database then compiles a new data set o 20-industies, including pimay, seconday and tetiay actiities, o 17 Spanish egions plus the county as a whole, and o 3 poduction actos (K, H and L). Moe details on the data composition can be ound in the Appendix. 4.2 Results Table 1 pesents the esults o estimating poductiity paametes o the egions o Spain. We include two types o esults: in the ist data column o the table we epot the poductiity estimates o Spanish egions elatie to those o Spain as a whole o eey acto in the HN speciication ( ) (equation 7). The ollowing thee columns o the table include the same inomation o the FAIN speciication ( ) (equation 8). We do not epot a table containing the estimated pai-wise poductiity subsection. 17 Out o the thee new measues o capital stock poposed by Fundación BBVA (goss, net and poductie), we choose goss capital stock as it is the one moe closely elated to the concept o endowment. 14
paametes because o the geat numbe o esults it supposes: o each acto unde the HN speciication we estimate 272 paametes (=1716). 18 Poductiity estimates o the egions o Spain in the HN assumption show that Madid is the most poductie egion; the alue o 1.29 means that Madid uses 29 pecent less o each acto to poduce one inal unit o output in all industies than Spain as a whole does. It is ollowed by Canay Islands (1.10), Catalonia (1.03) and Basque county (1.00). The least poductie egions in Spain appea to be Extemadua (0.60), Castille-La Mancha (0.69) and Andalusia (0.78). The degee o dispesion in the alue o coeicients anging om 0.60 to 1.29 eeals the existence o substantial egional poductiity dieences, and theeoe, o eiciency-based acto endowments dieences acoss egions. In addition the degee o adjustment shows a emakable achieement o the estimation by SURE pocedue. All egions exhibit a 2 R statistic equal to o geate than 0.9 except o Extemadua (0.68) and Astuias (0.89). In tems o indiidual actos, now unde the FAIN assumption, we obsee clea dieences with espect to the HN estimates in all thee actos o poduction. Fo example, in the case o Madid, eiciency gains in tems o capital unit equiements in the FAIN speciication coincide in alue (1.29) with those obtained o the thee actos jointly in the HN speciication. Howee, the FAIN speciication eeals that Madid is less eicient than othe egions in the use o high-educated labou (up to 19 pecent ineio) while it is highly eicient in the use o low-educated labou acoss industies (up to 43 pecent moe than the entie county). In geneal, the coeicients obtained o the physical capital in the FAIN speciication appea to be close to those obtained in the HN speciication, while bigge dieences seem to emege o the two types o labou. Fo example, in the case o low-educated labou acto (L), some egions (Mucia, Valencian Region, Castille-La Mancha, Catalonia and Baleaic 18 As usual, inomation is aailable upon equest to the authos. 15
Islands) expeience impotant poductiity gains in compaison with thei HN estimates and othes egions (Naaa, Madid, La Rioja and Aagon) lose positions in the national anking. When we tested whethe the FAIN coeicients o the thee acto wee the same as the one obtained om the HN speciication, in all cases the null hypothesis o equality was ejected at conentional signiicance leels. Theeoe, and a pioi, the FAIN speciication is peeed to the HN speciication om an econometic point o iew. Ate computing egional technological paametes, we apply ou poductiity estimates to the thee esions o the HOV model in ode to check how technological assumption aects its peomance in a egional setting. We un thee commonly used tests in testing the peomance o the HOV model: the sign test, the aiance atio and the slope test. The thee tests compae both sides o the models equation: the actual s the pedicted acto contents o tade. The sign test counts the numbe o signs that match in both sides o the equation. Theeoe the test examines whethe the diection o the actual acto content o tade coincides with the diection that the model pedicts. The aiance atio compaes the aiance o both the actual and the pedicted acto content o tade. The lage the aiance atio, the moe olume o the acto content o net expots is explained by the model. A aiance atio a below one means that the amount o acto tade pedicted by the model is much lage than the amount o actual (obseed) acto tade: the so-called missing tade poblem. The coeicient o the slope test is the esult o the egession o the nomalised alue o the actual acto content o tade against the pedicted acto content o tade. As in the othe two tests, the slope coeicient should be equal to one in ode to achiee a peect peomance o the HOV model (Tele 1995). 19 Table 2 pesents the esults o the thee esions o the HOV model (standad, pai-wise and elatie), with eey column containing the esults o the basic and extended models (HN and FAIN). 16
The standad HOV model (ist column o ist panel), shows a limited pedictie capacity in its stict esion o pooled actos, with a sign alue o 0.57 (0.35 o K, 0.71 o H and 0.65 o L, indiidually), a aiance test alue o 0.55 (0.54 o K, 0.81 o H and 0.37 o L) and the slope test epots a coeicient o 0.08 which is not statistically signiicant. In addition the slope coeicients o K and L exhibit negatie alues. Extending the standad HOV equation to accommodate HN technology dieences (ist column o second panel), clealy impoes the peomance o the model, eaching alues o pooled actos o 0.75 in the sign test (0.65 o K, 0.88 o H and 0.71 o L) and showing a positie alue o the thee indiidual coeicients in the slope tests (0.29 o pooled actos), although they emain not statistically signiicant. Moeoe, intoducing the HN assumption o the standad HOV equation clealy makes the missing tade poblem nealy disappeaing, pushing the aiance atio to a alue o 0.90 o pooled actos (0.87 o K, 0.93 o H and 0.90 o L). Intoducing the FAIN technology assumption in the standad model (ist column o thid panel) also poides a emakable impoement o the Vanek equation peomance, with pooled actos showing slightly below alues in all tests in compaison with the HN extension: 0.71 in the sign test, 0.86 in the aiance atio and 0.20 in the slope test. In this way, it seems that o the Vanek equation esion, extending the HOV model though the intoduction o measuement o actos in eiciency tems clealy impoes its peomance, not just pushing up its pedictie capacity in tems o diection and olume o tade, but also making the missing tade poblem almost disappeaing. Moing to the esults o the pai-wise esion o the HOV model (second column o ist panel), we obsee that the stict pai-wise speciication epots simila esults than those o the standad HOV 19 Note than in the slope test we ae not just measuing how the model pedicts the olume o acto tade seices, but the way in which the ankings o pedicted and actual acto tade ae also matching o all egions. 17
model. It peoms badly in tems o sign, aiance atio and slope test, with alues o 0.55, 0.55 and 0.07 o pooled actos, espectiely. Extending the pai-wise HOV model by intoducing HN technology adjustments (second column o second panel) impoes the peomance o the model paticulaly in tems o the aiance atio, nealy soling the missing tade poblem o physical capital (with a aiance atio o 0.91) and emakably educing missing tade o the othe two actos, with test alues o 0.85 o H and 0.79 o L. Slope test alues impoe again o K and L, with the pooled acto alue shiting om 0.07 in the basic pai-wise esion to 0.27 in the pai-wise HN extension, with all estimated coeicients now being statistically signiicants. The FAIN extension o the pai-wise HOV model elects an impoement in the model s peomance o appoximately the same magnitude than that o the HN case, although all alues systematically ae slightly lowe than those o the HN case. Finally, in the elatie HOV model case, we obsee that the stict esion (column 3 o ist panel) peoms a little bit bette than the Standad and the Pai-wise stict esions, with test alues eaching 0.62, 0.66 and 0.16, o the sign, the aiance atio and the slope tests, espectiely. Although being conscious that these test alues still elect a poo peomance o the elatie HOV model in its stict esion, it is inteesting to note that the slope test alues o acto pais (K/L, K/H and L/H) depat om moe ationale alues (0.28 o K/L and 0.17 o K/H) than in the othe two basic esions o the model, while the missing tade poblem is o much less impotance in this basic elatie HOV speciication (0.72 o K/L and 0.71 o L/H), what seems to elect some o the adantages that the elatie model pesents in compaison with the othe two speciications. Once we intoduce the HN extension in the elatie HOV model (column 3 o second panel), we obsee an impoement in the model s peomance in tems o missing tade and slope test alues, but not a emakable impoement in the capacity o the model to pedict the acto tade diection, with sign test alues emaining 18
elatiely stable. The FAIN extension (column 3 o thid panel) yields simila esults, with the aiance atio and the slope test showing alues that ae just a bit smalle than those ound in the HN case. Ou esults point out that, in geneal, a bette measuement o endowments in eiciency tems allows o an impoement o the model s peomance in a egional HOV amewok, makedly educing the missing tade poblem. In tems o pedicting the diection o tade, intoducing technological dieences in the HOV model also impoes the pedictie capacity o the HOV model, but thee ae dieences in the size o the impoement: it is lage o the standad esion but not so much o the pai-wise and elatie HOV esions. We also obsee that coecting o poductiity dieences aises the alue o the coeicient o the slope test and made the coeicients statistically signiicant in all thee esions. Finally, the peomance o the standad HOV speciication is moe sensitie to the intoduction o endowment measues in eiciency tems compaed to the pai-wise and the elatie esions. We conclude ou analysis by poiding a compaison o ou esults with those ound peiously in the empiical liteatue. So a, thee ae othe thee papes that hae analysed the HOV model using inta-national tade lows. Dais et al (1997) o Japan peectues did not hae egional IO tables so tade was estimated as the dieence between poduction and consumption. Since they hae only the IO table o Japan, they could not inestigate the ole o technological dieences. Atal et al (2006) and Requena et al (2008a) used 14 Spanish egional IO tables, which wee not peectly compaable, so they did not attempt to estimate technological dieences acoss egions. By contast, ou pape employs a new and homogeneous data set o 17 Spanish egions, making it appopiate to estimate poductiity gaps between egions. Alike us, Dais et al (1997) used thee poduction actos (K,L,H), Atal et al. (2006) used an additional land acto and Requena et al. (2008a) did it o aable land and pastue, woodland and R&D capital. Anothe dieence between those papes is the ecto o tade employed. 19
Dais et al (1997) and Requena et al (2008a) use total (inta and intenational) tade lows, while Atal et al (2006) and ou pape use only inta-national tade lows. Table 3 compaes the esults o the ou papes mentioned aboe. The diection-o-tade test (sign test) display simila esults acoss the dieent papes. The coeicient o the slope test emains a om 1 acoss all the papes. The most notable impoement occus in the aiance atio ate intoducing HN technological dieences in the HOV model, moing om a test alue o 0.55 to anothe o 0.90. 5. Conclusions The stict esion o HOV model has been epeatedly ejected empiically using intenational data. Relaxing identical technology and FPE assumptions at a uniesal leel has been mandatoy in ode to achiee a good peomance o the HOV model using county-leel data. In this pape we exploe whethe the intoduction o technological dieences at a egional leel (in a setting whee FPE holds) may help to impoe the peomance o the HOV model, paticulaly inestigating its eects on the impotant missing tade poblem ound in peious execises. With this aim, we estimate acto-poductiity paametes om each egion s actual technologies, and addess two speciications o technological dieences: Hicks-neutal (HN) and acto-augmenting industy-neutal (FAIN). Then, we extend the model allowing o acto poductiity-adjusted esions and test how these changes aect the model s peomance o thee dieent HOV speciications: the standad model, the pai-wise model, and the elatie model. Using a new data set o 17 Spanish egions, we ind eidence suppoting the assumption o HN technological dieences, with all test alues impoing makedly in the standad HOV equation case. The pai-wise and the elatie esions o the model equally show how the missing tade poblem almost disappeas once we account o this kind o model extension. In this context, ou esults indicate that accounting o poductiity dieences is also an appopiate modiication o HOV models at a egional 20
scale, as it has been shown in the county execises, although HN is eealed as slightly moe adequate in captuing egional technological dieences than the FAIN assumption. The contibution hee is to show that a simple technical modiication can establish consideable gains in the pedictie peomance o the HOV model, nealy soling the missing tade poblem, with FPE still holding at a national scale. Theeoe, impoing the measuement o endowments is showed as a pimay way o educing the missing tade poblems in a egional HOV amewok, a esult that contibutes to impoe peious indings o the egional HOV liteatue. 21
Reeences Atal A, Castillo J, Requena F (2006) Contastación empíica del modelo de dotaciones actoiales paa el comecio inteegional de España. Inestigaciones Económicas 30: 283-316 Benstein J R, Weinstein D E (2002) Do Endowments Pedict the Location o Poduction? Eidence om National and Intenational Data. Jounal o Intenational Economics 56: 55-76 Bowen H P, Leame E, Seikauskas L (1987) Multicounty, Multiacto Tests o the Facto Abundance Theoy. Ameican Economic Reiew 77 (5): 791-809 Beche R A, Choudi E U (1988) The acto content o consumption in Canada and the United States: A two county test o the Hecksche-Ohlin-Vanek model. In: Feensta R.C. (ed) Empiical Methods o Intenational Tade. MIT Pess, Cambidge Dais D R (1998) Does Euopean Unemployment Pop up Ameican Wages? National Labo Makets and Global Tade. Ameican Economic Reiew 88 (3): 478-494 Dais D R, Weinstein DE, Badod SC, Shimpo K (1997) Using Intenational and Japanese Regional Data to Detemine When the Facto Abundance Theoy o Tade Woks. Ameican Economic Reiew 87: 421-46 Dais D R, Weinstein D E (2001) An Account o Global Facto Tade. Ameican Economic Reiew 91 (5): 1423-1453 Debaee P (2003) Relatie Facto Abundance and Tade. Jounal o Political Economy 111 (3): 589-610 Gabaix X (1997) The Facto Content o Tade: A Rejection o the Hecksche-Ohlin-Leontie Hypothesis. Haad Uniesity, mimeo Hakua D (2001) Why does HOV ail? The ole o technological dieences within the EC. Jounal o Intenational Economics 54: 361-382 Llano C (2004a) Economía sectoial y espacial: el comecio inteegional en el maco input-output. Instituto de Estudios Fiscales. Colección Inestigaciones 1 Llano C (2004b) The Inteegional Tade in the Context o a Multiegional Input-Output Model o Spain. Estudios de Economía Aplicada 22: 1-34 Maskus K E (1985) A test o the Hecksche-Ohlin-Vanek Theoem: The Leontie commonplace. Jounal o Intenational Economics 19 (3-4): 201-212 Maskus K E, Nishioka S (2009) Deelopment-Related Biases in Facto Poductiities and the HOV Model o Tade, Canadian Jounal o Economics, othcoming Péez J, Dones M, Llano C (2008) An Inteegional impact analysis o the EU Spanish Stuctual Funds in Spain (1995-1999). Papes in Regional Science, othcoming 22
Requena F, Atal A, Castillo J (2008a) Testing Hecksche-Ohlin-Vanek model using Spanish egional data. Intenational Regional Science Reiew 31 (2): 159-184 Requena F, Castillo J, Atal A (2008b) Is Spain a lumpy county? A dynamic analysis o the lens condition. Applied Economic Lettes 15 (3): 175-180 Staige R M, Deado A V, Sten R M (1987) An Ealuation o Facto Endowments and Potection as Deteminants o Japanese and Ameican Foeign Tade. Canadian Jounal o Economics 20: 449-463 Tele D (1993) Intenational Facto Pice Dieences: Leontie was Right!. Jounal o Political Economy 101: 961-987 Tele D (1995) The Case o Missing Tade and Othe Mysteies. Ameican Economic Reiew 85 (5): 1029-1046 Vanek J (1968) The acto popotions theoy: the n-acto case. Kyklos 4: 749-756 Van de Linden J A, and Oostehaen J (1995) Intecounty EC input-output elations: constuction method and main esults o 1965-1985. Economic System Reseach, 7 (3): 249 269 23
24 APPENDIX A) Technical Appendix As Debaee (2003) demonstated, equation (5) is diectly elated to elatie acto abundance as showed in equation (A1): = 2 (A1) Fo any two actos and, a egion is said to be elatiely abundant in acto compaed to egion always that >. Debaee (2003) showed that this statement holds i and only i ( ) ( ) >, which detemines the sign o the ight-hand side o equation (A1). It establishes a diect elationship between elatie acto abundance and the ight-hand side o equation (5), what leads this equation to be named as the elatie abundance equation. Rewiting elatie acto abundance as: / / / / > > > = > (A2) we obtain that in the acto-augmenting case, the elatie acto abundance atio without poductiity adjustments ( / o / ) is the poduct o the poductiity-equialent elatie acto abundance atio ( / o / ) and the acto-poductiity atio ( / o / ). In the Hicks-neutal (HN) case, acto-poductiity atios emain the same o eey acto o and eey pai o egions and ( / / = ), and consequently both deinitions o elatie acto abundance ae identical
25 with o without poductiity adjustments (Debaee, 2003, p. 609). Neetheless, in the acto-augmenting industy-neutal (FAIN) case, whee poductiities o actos could die inside a egion ( / / ), the elatie acto abundance deinition dies om the basic speciication (Maskus and Nishioka, 2009): > > > > (A3) now holding when: > > > 1 ) ( ) ( > > (A4)
B) Data Appendix In this pape we use a set o 17 homogeneous input-output (IO) tables deeloped o the Spanish egions, and eeed to 1995. This database was built in the context o a lage poject with the aim o estimating the ist Spanish Inte-egional Input-Output model. The pocedue o the estimation o this model has been epoted in Llano (2004a, 2004b). Moe ecently, a ecent application to the EU Funds based in this model has also been published (Péez et al, 2008). Following Van de Linden and Oostehaen (1995) in the case o the EU IRIO, the estimation o the 1995 Spanish Inte-Regional Input-Output table (SIRIO table) was conceied as the disaggegation o the 1995 National IO table, o as the inteconnection o a ull-set o 18 1995-Single-Region IO tables (SRIO), one pe each o the R= 18, Spanish egions at the NUTS II leel. 20 Since not all the Spanish egions had a suey input-output table, non-suey techniques (bi-popotional RAS pocedue) wee used o updating and estimating the old o non-existing ones. Due to the heteogeneous situation o the egions in tems o the aailability o SRIO tables, the estimation had to deal with thee dieent situations: a) By that time, 6 egions had oicial SRIO tables o 1995 o 1996 21. b) In the case o 6 egions with no 1995 SRIO table 22 but with old SRIO tables, we wee able to obtain an up-dated 1995 SRIO using the RAS pocedue, the stuctue o the peious tables and the magins om the National and the Regional Accounts. c) Finally, o the emaining 6 egions 23, whee a suey SRIO table had nee been estimated, a non-suey 1995 SRIO table was obtained using the RAS pocedue, the 20 We wok with 17 egions instead o 18. The omitted egion is Ceuta and Melilla, the two Spanish autonomous cities located in Aica. 21 Naaa, 1995; Madid, 1996; Basque County, 1995; Astuias, 1995; Andalusia, 1995; Castille and Leon, 1995. 22 Comunidad Valenciana, 1990; Galicia, 1990; Extemadua, 1990; Canay Islands, 1992; Aagón, 1992; Catalonia, 1987. 23 The SRIO o Mucia was based on the 1995 Comunidad Valenciana s SRIOT; the one o La Rioja was based on the 1992 Aagon s SRIOT; the one o Cantabia was based on the 1995 Basque County s SRIOT; the one o Castille-La Mancha was based on 1990 Extemadua s SRIOT, the one o the Baleaic Islands was based on the 1992 Canay Island SRIOT and the one o Ceuta and Melilla was based on the 1995 Andalusia s SRIOT. In the case o Catalonia, although thee was an old SRIO table o 1987, we used the 1995 Comunidad Valenciana s SRIOT. 26
stuctue om the most simila egion in tems o sectoal composition 24 and the magins om the National and the Regional Accounts. Once that a ull set o 18 SRIO tables was obtained, also by means o the RAS pocedue, all the tables wee hamonised to the Regional Accounts o the magins, and then, cell by cell, with the 1995 National Input-Output. Thus, peious to the estimation o the Inte-egional IO Table, a ull hamonised set o SRIO was obtained o all the egions with a common sectoal classiication and an optimum eeence to the inte-sectoal stuctues aailable om the new and old SRIO tables aailable. This is the set o homogeneous SRIO tables that hae been used in this pape. Finally, once that the 18 SRIO tables wee estimated, the inteconnection o all o them was obtained thoughout a paallel database on inteegional tade lows by poducts (Llano, 2004b). The commodity lows wee estimated using detailed statistics on tanspot lows by tanspot modes and egional pices by poducts. The inte-egional lows o taded seices wee obtained using gaity models based on actual data on poduction/consumption by secto/egion and the intensity o inteegional commodity lows, as a poxy o inte-egional integation. 24 Mucia, La Rioja, Cantabia, Castille-La Mancha, Baleaic Islands (at this time) and Ceuta and Melilla. 27
Table A.1. Spanish egions SPAIN ANDALUCIA ARAGON ASTURIAS BALEARIC ISLANDS BASQUE COUNTRY CANARY ISLANDS CANTABRIA CASTILLE-LEON CASTILLE- LA MANCHA CATALONIA EXTREMADURA GALICIA MADRID MURCIA NAVARRA (LA) RIOJA VALENCIAN REGION stands o egions excluded in peious eseach due to lack o indiidual egional IO tables 28
Table A.2. Secto categoies SECTOR NACE Re 1 (R93) BBVA R-20 AGRICULTURE, HUNTING, FORESTRY AND FISHING 010205 1 ENERGY AND WATER 101112234041 2 FOOD, DRINKS AND TOBACCO 1516 3 TEXTILES, APPAREL, FOOTWEAR, 171819 4 LEATHER WOOD AND CORK PRODUCTS; 2036 5 MISC. MFG. PAPER, PRINTING, AND 2122 6 PUBLISHING CHEMICAL 24 7 RUBBER AND PLASTIC 25 8 NONMETALLIC MINERALS AND 14 26 9 RELATED MANUFACTURES METAL MINERALS AND IRON AND 13 27 28 10 STEEL MFG. AND METALLIC PRODUCTS AGRICULTURAL AND INDUSTRIAL 29 11 MACHINERY OFFICE MACHINERY, ELECTRIC 30313233 12 AND ELECTRONIC PRODUCTS TRANSPORT EQUIPMENT 3435 13 CONSTRUCTION 45 14 RETAIL SERVICES, REPARATION, 505152 69 to 74 15 OTHER MARKET SERVICES NEC 92 HOTELS AND RESTAURANTS 55 16 TRANSPORT SERVICES AND POST AND 60 to 64 17 TELECOMMUNICATION SERVICES BANKING AND INSURANCE 656667 18 SERVICES REAL STATE ACTIVITIES 68 19 NON-MARKET SERVICES 75 80 to 91 93 20 29
TABLES Table 1. Estimated egional acto poductiity dieences acoss egions Hicks-Neutal (HN) estimation Facto Augmenting Industy Neutal (FAIN) estimation Physical capital (K) High-educ. labou (H) Low-educ. labou (L) () s.e. R 2 (,) s.e. R 2 (,) s.e. R 2 (,) s.e. R 2 Andalucia 0.78 0.03 0.93 0.75 0.02 0.93 0.70 0.02 0.78 0.76 0.03 0.89 Aagon 0.80 0.02 0.96 0.77 0.01 0.96 0.63 0.01 0.90 0.81 0.02 0.96 Astuias 0.88 0.04 0.89 0.83 0.02 0.89 0.80 0.03 0.86 0.75 0.03 0.86 Baleaic Islands 0.70 0.03 0.92 0.71 0.01 0.71 1.04 0.03 0.85 1.02 0.02 0.61 Canay Islands 1.10 0.03 0.95 1.09 0.03 0.95 1.06 0.04 0.88 1.01 0.03 0.92 Cantabia 0.95 0.03 0.94 0.92 0.02 0.94 1.00 0.02 0.92 0.97 0.03 0.96 Castille-Leon 0.79 0.02 0.96 0.77 0.02 0.96 0.74 0.02 0.91 0.84 0.03 0.96 Castille-La Mancha 0.69 0.03 0.90 0.67 0.01 0.90 0.85 0.02 0.85 0.71 0.02 0.87 Catalonia 1.03 0.01 0.99 1.04 0.01 0.99 1.16 0.03 0.96 1.05 0.02 0.97 Valencian Region 0.85 0.01 0.97 0.85 0.01 0.97 0.91 0.03 0.95 0.85 0.01 0.98 Extemadua 0.60 0.05 0.68 0.57 0.01 0.68 0.68 0.02 0.50 0.58 0.02 0.77 Galicia 0.85 0.03 0.91 0.81 0.02 0.91 0.75 0.02 0.89 0.58 0.02 0.85 Madid 1.29 0.03 0.96 1.29 0.03 0.96 0.81 0.02 0.96 1.43 0.03 0.88 Mucia 0.88 0.03 0.95 0.85 0.01 0.61 1.11 0.02 0.78 0.81 0.01 0.47 Naaa 0.97 0.02 0.96 0.97 0.03 0.96 0.87 0.02 0.94 0.98 0.04 0.95 Basque County 1.00 0.03 0.90 1.07 0.03 0.90 1.00 0.03 0.92 1.11 0.05 0.92 Rioja 0.73 0.01 0.98 0.69 0.02 0.98 0.64 0.01 0.58 0.84 0.04 0.91 Note: The HN estimated coeicients ae om equation (7) in the main text, and the FAIN estimated coeicients ae om equation (8) in the main text. 30
Table 2. Results o tests on the HOV model s peomance I. Stict model 1.- The HOV Model 2.- The Paiwise HOV Model 3.- The Relatie HOV Model K H L Pooled K H L Pooled K/L K/H L/H Pooled Sign test 0.35 0.71 0.65 0.57 0.47 0.65 0.54 0.55 0.64 0.60 0.63 0.62 Vaiance test 0.54 0.81 0.37 0.55 0.59 0.81 0.23 0.55 0.72 0.55 0.71 0.66 Slope test -0.26 0.11-0.09 0.08-0.35 0.40 0.02 0.07 0.28 0.17 0.08 0.16 Standad eo 0.31 0.39 0.13 0.19 0.04 0.07 0.03 0.02 0.05 0.04 0.05 0.03 R-squaed 0.05 0.08 0.03 0.03 0.21 0.11 0.00 0.01 0.11 0.05 0.01 0.04 II. With Facto Poductiity Adjustments - Hicks Neutal (HN) 4.- HOV-HN Model 5.- The Paiwise HOV-HN Model 6.- The Relatie HOV-HN Model K H L Pooled K H L Pooled K/L K/H L/H Pooled Sign test 0.65 0.88 0.71 0.75 0.48 0.65 0.59 0.58 0.64 0.66 0.62 0.64 Vaiance test 0.87 0.93 0.90 0.90 0.91 0.85 0.79 0.86 0.86 0.67 0.81 0.78 Slope test 0.27 0.43 0.15 0.29 0.11 0.37 0.23 0.27 0.37 0.22 0.17 0.24 Standad eo 0.23 0.22 0.24 0.23 0.06 0.05 0.05 0.03 0.05 0.05 0.05 0.03 R-squaed 0.08 0.20 0.03 0.09 0.01 0.17 0.07 0.03 0.16 0.05 0.01 0.04 III. With Facto Poductiity Adjustments - Facto Augmenting Industy Neutal (FAIN) 7.- HOV-FAIN Model 8.- The Paiwise HOV-FAIN Model 9.- The Relatie HOV-FAIN Model K H L Pooled K H L Pooled K/L K/H L/H Pooled Sign test 0.65 0.82 0.70 0.71 0.48 0.63 0.57 0.57 0.63 0.63 0.61 0.62 Vaiance test 0.85 0.88 0.84 0.86 0.88 0.82 0.77 0.83 0.83 0.64 0.78 0.76 Slope test 0.26 0.30 0.13 0.20 0.09 0.32 0.21 0.21 0.33 0.21 0.14 0.22 Standad eo 0.22 0.19 0.19 0.19 0.05 0.04 0.04 0.03 0.05 0.04 0.05 0.03 R-squaed 0.08 0.14 0.02 0.11 0.01 0.12 0.05 0.00 0.11 0.03 0.00 0.03 Note: The HOV model uses 17 obseations pe acto and 51 obseations in the pooled analysis. The Paiwise HOV model uses 272 (17x16) obseations pe acto and 816 obseations in the pooled analysis. The Relatie HOV model uses 272 (17x16) obseations pe acto pai and 816 obseations in the pooled analysis. The sign test, aiance test and slope test ae explained in the main text. Thee ae thee poduction actos: physical capital (K), high-educated labou (H) and low-educated labou (L). 31