The Role of Firm Size in Training Provision Decisions: evidence from Spain

Transcription

1 The Role of Firm ize i Traiig Provisio Decisios: evidece from pai By aia Castay Uiversitat de Barceloa. AQR Research Group IREA. Avda Diagoal 690, Barceloa. lcastay@ub.edu Tel: FA: Abstract.: The level of traiig provided by small firms to their employees is below that provided by their larger couterparts. The provisio of firm-related traiig is believed to be associated to certai characteristics of the firm. I this paper we argue that small firms provide fewer traiig opportuities as they are less likely to be associated with these characteristics tha large firms. The suitability of estimatig traiig decisios as a double-decisio process is examied here: first, a firm has to decide whether to provide traiig or ot ad, secod, havig decided to do so, the amout of traiig to provide. The differeces i traiig provisio betwee small ad large firms are decomposed i order to aalyse the idividual cotributio of these characteristics to explaiig the gap. The results show that small firms face greater obstacles i accessig traiig ad that the mai reasos for that are related to their techological activity ad the geographical scope of the market i which they operate. Keywords: Cotiuous traiig; Firm size; Iovative activity; JE codes: J21, 11, M53, 25 I am grateful to Hessel Oosterbeek for his suggestios ad discussio of the results reported here, to Erique ópez-bazo for his supervisio ad support ad to Elisabet Motelló for her advice o Yu s methodology. 1

2 1. Itroductio Although the stadards of educatio attaied by the paish labour force have improved cosiderably over the last three decades, pai still lags behid other advaced ecoomies i this respect. However, employees qualificatio does ot deped solely o their schoolig (formal educatio), but also o the quality of their life-log learig, icludig cotiuous ad occupatioal traiig. The Natioal Reform Programme for pai (2005), developed withi the framework of the isbo Ageda, stresses the importace of cotiuous traiig for already occupied workers as a meas of acquirig additioal kowledge ad skills applicable to their preset ad future posts. Cotiuous traiig esures that workers skills ca be adapted to the costatly evolvig requiremets of the workplace, which ehaces their competitive positio. As workers become more productive, their employers i tur improve their performace. Yet, i 2004, oly 5.2% of the paish populatio received cotiuous traiig, while the EU- 15 average stood at 10.7% ad the EU-25 average at 9.9%. 1 Workers i small ad medium-sized eterprises (MEs) are less likely to receive cotiuous traiig. Give that the paish ecoomy is characterised by a smaller umber of large firms ad a smaller average firm size tha other advaced ecoomies, the difficulties faced by MEs may costitute a limitatio for the ecoomy as a whole. I this paper, the reasos as to why small firms may be facig greater difficulties i accessig cotiuous traiig are aalysed. Based o the evidece that traiig is geerally associated with certai types of firm ad employees, the hypothesis propouded here is that large firms are more likely to be associated with these characteristics, or at least, to be associated with them more itesely, tha their smaller couterparts. This, we argue, explais i part why small ad large firms take differet decisios regardig their traiig provisio. A empirical study coducted by Black et al. (1999) examies the relatioship betwee differet traiig measures ad firm size for a sample of U firms ad fids that large firms ivest more heavily i traiig. They argue that such firms have scale ecoomies i the provisio of formal ad iformal traiig ad provide more opportuities for udertakig co-worker traiig. Baldwi et al. (1995) coted that as large firms might ejoy a higher pay-off from their ivestmet i traiig, they are ecouraged to ivest more. Holtma ad Idso (1991) maitai that large firms face 1 The Natioal Reform Programme seeks to raise the percetage i receipt of such traiig to 10% by 2008 ad 12.5% by

3 lower ivestmet risks as they ca pool these risks. Barro et al. (1987) argue that there is a higher probability of shirkig i large firms: as employees work cooperatively to produce a commo output, it is more difficult to disetagle the participatio of each idividual worker. Thus, they claim, as large firms face higher moitorig costs, oe way to reduce these, is providig traiig to their employees. Accordig to Hashimoto (1979), large firms have access to cheaper capital for fiacig traiig. I the case of pai, Rigby (2004) reports that small firms typically have access to traiig plas that do ot reflect the specific eeds of employers ad are promoted actively by social parters idepedetly of employers. Aother strad of the literature is dedicated to examiig the reasos why firms decide to trai their workers ad the amout of traiig they provide. Empirical studies of iterest iclude Bartel (1989), Baldwi et al. (1995), Black ad ych (1998) ad Bludell et al. (1999). Evidece regardig the situatio i pai is reported i Alba- Ramírez (1994), Peraita (2005) ad Albert et al. (2005a). These studies estimate the impact of certai characteristics of firms (determiats) that are believed to affect traiig decisios. I what follows, the role of these determiats ad how they might vary with firm size are discussed. To start with, traiig will ted to be provided to those who have previously show a aptitude for formal educatio as they will beefit most from a firm s expediture o traiig (Black ad ych, 1998; Alba-Ramírez, 1994). Thus, firms that employ more qualified workers are more likely to provide traiig. O the role of firm size i this relatioship, Evas ad eighto (1989) report evidece of some sortig o ability characteristics across firm sizes (with better educated workers beig employed i larger firms) while Zábojík ad Berhardt (2001) propose a model where workers i larger firms ad idustries acquire more huma capital. Techological chages are itroduced at high speed ad require the cotiuous upgradig of the labour force. This use of advaced, specialized techology requires specific kowledge ad skills that are ot readily available i the labour market ad so traiig is a way of acquirig such skills (Baldwi et al., 1995; Korpi ad Mertes, 2004). The empirical evidece suggests that techological chage leads to workers receivig more traiig (upskillig) (see Osterma, 1995). Additioally, firms that lauch ew products may eed to trai sales or techical staff, while those that implemet process iovatios may eed to provide their productio workers with techical traiig (Alba-Ramírez, 1994; i et al., 2006). imilarly, the specific 3

4 kowledge that the ew process or product requires may ot be easily foud i the labour market. I lie with chumpeter (1942), various authors have argued that large firms ejoy a advatage over small compaies i terms of iovatio ad the evidece from pai seems to cofirm this (Huergo ad Jaumadreu, 2004). The same argumet holds for a more itese use of advaced techologies i large firms. Firms exposed to more competitive markets may ivest more i traiig programmes as a strategy to ehace the competitiveess of their employees (see, for istace, Bartel, 1989). There are reasos to believe that both small ad large firms are willig to provide traiig to icrease their competitiveess: the former, because of their vulerability to highly competitive markets; the latter, because they place themselves i such competitive markets, such as iteratioal markets. Other studies argue that foreig-owed firms are more likely to provide traiig for their workers (Görg ad trobl, 2005; Hughes et al., 2004). Typically, such compaies are multiatioal firms, characterised by maagerial efficiecy, the recruitmet of more qualified workers ad a more positive attitude regardig workers skills tha that of domestic firms. Fially, firms with a high proportio of temporary workers are assumed to ivest less i traiig. This state of affairs might be particularly importat i the case of the paish labour market, which has a high degree of temporary employmet (Alba- Ramírez, 1994; Albert et al., 2005b). Firms will ot be iterested i providig traiig for workers that may leave their employmet i the short term as they will be uable to recover the returs from their ivestmet. Furthermore, temporary workers lack icetives to acquire firm-specific huma capital as they are ulikely to stay with the firm. Oi (1983) fids that large firms have less rotatio because of iteral labour markets. 2 To aalyse these questios, we use data draw from the Ecuesta sobre Estrategias Empresariales (EEE). This survey gathers iformatio from a sample of paish idustrial firms with at least 10 employees, which has bee widely used i empirical idustrial orgaisatio. This study aligs itself iitially with that strad of literature that estimates the determiats of firm-related traiig. What is iovative, however, about this study is its cosideratio of the decisio to provide traiig as a 2 There are determiats of traiig for which we caot cotrol: the degree of uioizatio i the firm (Wagar, 1997), the persoal characteristics of workers (Oosterbeek, 1996) ad the workplace ad persoel practices (Black ad ych, 2004). 4

5 double-decisio process: firms first decide whether they will provide traiig or ot ad, oce a affirmative decisio has bee take, they decide the amout they wat to provide. To aalyse the traiig differetial betwee small ad large firms, this paper decomposes this differetial usig the Oaxaca-Blider methodology. This allows us to evaluate the idividual cotributio of each variable to this gap ad to distiguish betwee differeces due to firms characteristics ad differeces due to the impact of these determiats o traiig. I ectio 2, the appropriateess of usig a two-part model for estimatig firms decisios regardig the provisio of traiig is discussed. ectio 3 offers evidece that small firms sped less o traiig ad that this is related to firms characteristics. ectio 4 provides the results of the estimatio ad ectio 5 decomposes the traiig gap. ectio 6 cocludes. 2. Methodological questios ad empirical model It is commo practice to estimate a probit model to aalyse the factors that determie whether firms provide traiig to their employees or ot. ikewise, i aalysig the determiats of firms expediture o traiig, it is a fairly commo approach to estimate a tobit model, which takes ito accout the fact that the depedet variable is cesored at zero as, by ature, it ca oly take oegative values (Alba-Ramírez, 1994; Black ad ych, 1998; Black et al., 1999). Estimatig the specificatio by Ordiary east quares (O) istead, would provide icosistet estimates, as it assumes that the depedet variable ca take both positive ad egative values. Moreover, as the logarithm of zero does ot exist, a commo solutio is to add a small positive costat; but this costat is set arbitrarily. The mai limitatio of the tobit model is that it does ot cosider decisios regardig the provisio of traiig as a double-decisio process: first, firms decide whether they will ivest i traiig or ot (participatio decisio), ad oce the decisio has bee take, they decide the amout they wish to ivest (quatity decisio). This is particularly true whe the two decisios are motivated by differet determiats. For istace, whe the decisio as to whether to provide traiig ivolves icurrig fixed costs, such as desigig a traiig pla. The, these fixed costs determie the decisio as to whether to sped a sum of moey or ot, but they do ot ecessarily affect the decisio regardig the quatity. Eve i the case that the two decisios are depedet o the same factors, the depedet variable may iclude observatios that take a zero 5

6 value with high frequecy ad this mass of zeros might respod i a differet way to covariates tha observatios with positive values. Whe this occurs, there are reasos to model the decisio of traiig as two separate mechaisms, which ca be see as a geeralisatio of the tobit model. These models, heceforth referred to as two-part models, add flexibility i the sese that they allow zeros ad o-zeros to be geerated from differet processes (Camero ad Trivedi, 2005). Two approaches to these flexible models ca be adopted: the sample selectio model ad the two-part model itself. The mai differece betwee them is that the former takes the sample selectio effect ito accout, which, whe omitted, ca cause biased estimatios. The most popular sample selectio model is the bivariate sample selectio model studied by Heckma (1979). The so-called Heckit model comprises a participatio equatio that determies the sample selectio: * ' dtri 1i 1 1 i (1) where dtr * i is a cesorig latet variable that reflects whether each i-firm is willig to provide traiig, 1i is a vector of variables that determies this decisio ad 1i is the error term. The willigess of firms to provide traiig caot be observed, but we ca observe whether the firm speds moey o it. Defie dtr i as the cesorig observed variable, which is a biary idicator that takes value 1 if we observe that the firm * dedicates some amout of moey to traiig. Thus, dtr i = 1 if dtr i > 0 ad dtr i = 0 otherwise. Defie TR i as the firms expediture o traiig ad ltr i as its logarithm, which is determied by a vector of variables 2i. The quatity equatio ca be expressed as: l ' TRi 2i 2 2i (2) where 2i is the error term. Assumig that the error terms 1i ad 2i follow a bivariate ormal distributio with zero meas, stadard deviatio 1 ad 2, covariace 12 ad correlatio : E(lTR i dtr i ) ' 2 ' (3) i ' ' ' where ) ( ) ( ) is defied as the iverse Mills ratio, is the i ( 1i 1 1i 1 1i 1 stadard ormal desity fuctio ad is the stadard ormal cumulative distributio fuctio. i 1i 1 6

7 P The coefficiets 1 are obtaied by a first-step probit regressio of dtr o 1 : ' dtr ( ) 1 1 i 1. The Heckit model augmets the O regressio o the quatity of traiig by the iverse Mills ratio ad the uses the positive values of TR to estimate the model by O. The estimate of 2 is cosistet, as it takes the sample selectio bias ito accout. 3 By itroducig the iverse Mills ratio, this model corrects for possible sample selectio effects. ample selectio appears whe the error terms of the two equatios are ot idepedet, ad thus the covariace of the error terms, 12, is differet from zero. Whe 12 equals zero, the Heckit model simplifies to the two-part model, which simply uses the positive values of TR to estimate the model by O, obtaiig cosistet estimates of the 2 parameters. The two-part model was first proposed by Cragg (1971) ad was specifically desiged for data o expediture that cotais a large umber of zeros ad a right-skewed distributio. The two-part model also starts from a participatio ad a quatity equatio ad equatio (3) simplifies to: E(lTR i dtr i 1) (4) I this paper, the followig quatity equatios, correspodig to the Heckit ad the two-part models respectively, are estimated. For dtr=1: ltr ' 2 ' ' 2i 2 1i vi i i 2 12i 1 l TRi ' 2 i 2 2i (5) (6) 3. The dataset ad descriptive aalysis For the empirical aalysis, I use a sample of paish idustrial firms draw from the Ecuesta sobre Estrategias Empresariales (EEE), carried out by the Fudació Empresa Pública (FUNEP). This survey is a ubalaced pael that covers the period ad gathers iformatio o the strategic decisios ad behaviour of firms. The referece populatio of the EEE is firms with 10 or more employees dedicated to oe of the activities correspodig to divisios 15 to 37 from the CNAE-93, excludig divisio 23 (activities related to refiemet of oil ad fuel treatmet). I the base time period, all firms with more tha 200 employees were required to participate (of which 70% actually did). The firms with 10 to 200 employees were sampled radomly by 3 The bivariate sample selectio model ca also be estimated by M although this would impose stroger assumptios o the distributio of the error terms. 7

8 idustry ad four size strata, retaiig about 5%, so that represetativity for every idustry ad firm size was guarateed. 4 I the preset paper, we use iformatio correspodig to years 2001 ad 2002, 5 i which data is available for 1,515 ad 1,505 firms respectively, of which 30% are large. The variables used i this aalysis are defied as follows: - Traiig is measured as a discrete variable (accordig to whether the firm provides cotiuous traiig or ot) ad as a cotiuous variable (the log of the real expediture o cotiuous traiig per worker). Cotiuous traiig is measured as the exteral expeses o traiig per worker, icludig five differet types of traiig: computatio ad iformatio techologies, foreig laguages, sales ad marketig, egieerig ad techical traiig ad other issues. - Firm size is defied as the total umber of employees, takig ito cosideratio full time ad part time employees as well as temporary employees. - The percetage of white collars i the firm is the proportio of egieers, graduates, middle level egieers, experts ad qualified assistats o the total umber of employees. 6 - The itesity of use of advaced techologies is measured by a set of three dummy variables labelled as low, medium ad high, whe firms use 0-1, 2-3 or 4-5 advaced techologies respectively. The EEE cosiders these techologies as beig: Computer Numerically Cotrolled (CNC) machies ad tools, Robots, Computer-Aided Desig (CAD), a combiatio of the previous systems by cetral computer (CAM, flexible maufacturig systems, etc) ad ocal Area Network (AN) for factory use. - Iovatio is defied as a dummy variable that takes value 1 if the firm has itroduced a product or a process iovatio. - The geographical scope of the market where the firm operates is defied by a dummy that takes values 1 whe the firm operates i a iteratioal market ad zero otherwise. - The participatio of foreig capital is defied as the percetage of foreig-owed capital i the firm. 4 For further details o the dataset, see Fariñas ad Jaumadreu (1999). 5 The iformatio o the firms provisio of cotiuous traiig i the EEE is oly available for 2001 ad This variable eters the equatios with oe lag. Data o white collar workers are ot available for 2000 ad 2001 as they are ot assumed to chage substatially from oe year to the ext. We therefore iterpolate the percetage of white collars, assumig that they chage liearly. 8

9 - The percetage of temporary workers over the total employees is measured at the ed of the year. Whe the firm reports that the umber of temporary employees has chaged cosiderably, it is calculated as a mea of every quarter. - Fially, the cotrol variables are: the use of the productive capacity (percetage), a dummy reflectig whether the firm is part of a group, a set of 20 sector dummies, a set of 17 regioal dummies ad year dummies. Table 1 presets a descriptive aalysis of traiig, both for the discrete variable (dtr) ad for the expediture per worker (TR) accordig to the above-metioed characteristics. First, the data show that aroud 40% of the firms i the sample provide traiig. I terms of the firms characteristics, we see that firms with a percetage of white collar above the media (labelled high % of white collars ), iovative firms, firms that make a itese use of advaced techologies, 7 firms that operate i iteratioal markets, those that have a higher participatio of foreig capital ad those with a percetage of temporary workers below the media provide more traiig. Moreover, the differeces betwee firms with these characteristics ad without them are sigificat at 1%. This evidece supports the belief that traiig is associated with certai characteristics of the firm. [Isert Table 1 about here] As this study focuses o differeces by firm-size, we divide the sample ito two subsamples of small ad large firms. Aroud 25% of small ad 75% of large firms provide some traiig, while the average real expediture per worker is 42 euros ad 141 euros respectively. Thus, large firms provide more traiig ad the differeces are sigificat at 1%. As Table 2 shows, amog the firms with a percetage of white collars above the media, large firms provide sigificatly more traiig tha their smaller couterparts. imilarly, amog the firms with a percetage of white collars below the media, large firms also provide sigificatly more traiig. Aalogue results are obtaied for all the other firm characteristics cosidered here (sigificace at 1%). I additio, the statistics of the tests of equality of proportios ad meas that compare the provisio of traiig i small ad large firms are smaller for the group of firms with a high level of qualified workers tha for the group with a low level. This idicates that differeces betwee small ad large firms reduce for firms with more 7 Firms that make a high use of these techologies provide more traiig tha firms with medium use, ad firms that make medium use of advaced techologies provide more traiig tha firms with low use. 9

10 huma capital. Thus, havig a high percetage of white collars seems to slightly mitigate the differeces i traiig provisio decisios betwee small ad large firms. This result is obtaied for all the other characteristics (except for temporary workers). Therefore, the results suggest that the presece of certai characteristics makes small firms behave as large oes with respect to the provisio of traiig; evertheless, the differeces betwee the two groups remai otable. [Isert Table 2 about here] The objective here is to determie whether small ad large firms preset differet patters i their traiig decisios i relatio to the characteristics of the firm. The hypothesis is that the difficulties faced by small firms i accessig traiig are related to the fact that they are ot associated with the above-metioed characteristics (or ot associated with the same itesity as large firms). Table 3 cofirms this reasoig: large firms employ more high-skilled workers, iovate more ad use advaced techology with a itermediate ad high itesity more tha small firms do; they also operate more i iteratioal markets ad they have a greater participatio of foreig capital. As for small firms, they use advaced techology with low itesity more tha large firms do ad they have more temporary workers tha large firms. The differeces i these characteristics betwee the two groups are sigificat at 1%. These results suggest that large firms may provide more traiig because they are more associated with these characteristics. I the ext sectio, we perform a regressio aalysis to study whether such characteristics are drivig the traiig decisios ad whether they have differet impact o small ad large firms. [Isert Table 3 about here] 4. Estimatio 4.1. The Heckit ad the two-part model As commeted above, aroud 60% of the observatios of the depedet variable TR take value zero. This percetage idicates the existece of a high degree of cesorig ad, thus, the eed to cosider the possibility that the zeros ad positive observatios are geerated by differet processes. 8 I this ectio, we discuss whether it is more 8 The distributio of expediture o traiig per worker is clearly right skewed. The media is 90 per worker i 2001 ad 109 per worker i 2002, while the average is 171 ad 186 respectively. The skewess coefficiet is 7 i 2001 ad 5.3 i

11 appropriate to model firms traiig decisios as a two-part model with sample selectio or ot. The estimatio of expressios (5) ad (6) is show i Table 4. The first ad secod colums show, respectively, the margial effects ad coefficiets of the participatio equatio (which is the same i the Heckit ad the two-part model). The third ad fourth colums show the coefficiets of the quatity equatio i the Heckit model i the twopart model. 9 I the participatio equatio, all the variables of iterest are sigificat (except for the percetage of temporary workers) ad have the expected sig. I the quatity equatio, the percetage of white collars, the iovative activity, the participatio of foreig capital ad the percetage of temporary workers are clearly sigificat. I the Heckit model, the itesive use of advaced techologies ad operatig i a iteratioal market also icrease firms expediture o traiig sigificatly. [Isert Table 4 about here] The choice betwee the two models is a cotroversial questio ad has led to itese debate i recet years (Dow ad Norto, 2003). First, the type of depedet variable to be modelled must be give careful cosideratio. To put it simply: whe aalysig traiig expediture with a large proportio of zeros, do we observe potetial traiig-providers that for some reaso decided ot to provide traiig? Or do we observe firms that do ot wish to provide traiig (observed outcome)? Dow ad Norto (2003) argue that whe the observed zeros do ot represet zero values for the potetial outcome the a sample selectio bias might appear. ych (1993) argues that, i small firms, fixed costs of traiig are distributed across a smaller umber of employees: for istace, the productio losses associated with a worker beig away from his or her workplace or the desig of a firm s traiig pla ca be more costly i a small tha i a large firm. We argue that, i the presece of fixed costs, some firms caot afford to provide traiig ad we observe a zero i the variable measurig the expediture o traiig. If these fixed costs were smaller, these firms would decide to provide traiig ad we would observe a positive value. ee i this light, fixed costs might be hidig a latet potetial traiig provisio. Here, we are 9 Notice that the two sets of coefficiets of the quatity equatio caot be directly compared: while i the two-part model, the coefficiets are equal to the coditioal margial effects, i the Heckit, they are oly part of the coditioal margial effect. For further details, see Camero ad Trivedi (2005). 11

12 specifically iterested i this potetial outcome ad so the Heckit model appears to be more appropriate. ecodly, the Heckit model may have problems of idetificatio whe the same regressors are icluded i the two equatios, while i the case of the two-part model this is ot a limitatio. Although the Heckit model with ormal errors is theoretically idetified without exclusio restrictios o ay regressor, whe the same regressors are icluded i the two equatios, this model is close to uidetified. Camero ad Trivedi (2005) explai that sometimes it ca be very difficult to make defesible exclusio restrictios. I our case, it seems difficult to fid at least oe regressor that determies the decisio as to whether or ot to provide traiig, but which does ot determie the quatity of traiig provided. A t-test o the coefficiet of the iverse Mills ratio ca be used to test the ull hypothesis that the two-part model is correct agaist the alterative hypothesis that the Heckit is correct. 10 However, uder colliearity betwee the covariates ad the iverse Mills ratio, the power of the test is limited ad this test caot be used as a criterio to select betwee the two models; with low colliearity, the test is reliable. Accordig to eug ad Yu (1996), imposig o exclusio restrictios is a mai source of multicolliearity. These authors recommed usig the coditio umber to check for multicolliearity betwee the iverse Mills ratio ad the covariates i the quatity equatio. Based o Mote Carlo experimets, Belsley et al. (1980) suggest that a coditio umber beyod 30 is idicative of colliearity problems. For the total sample, the coditio umber for the covariates is 26.9, ad after icludig the iverse Mills ratio it takes a value of As suggested i Camero ad Trivedi (2005), although the coditio umber icludig the iverse Mills ratio takes a value above 30, the icrease whe icludig this regressor is very small, for which multicolliearity problems ca ot be cosidered as severe. The, the test o the iverse Mills ratio ca be cosidered a useful tool for selectig betwee the two models. Table 4 shows that the coefficiet of the iverse Mills ratio takes a value of 0.57 ad is ot statistically sigificat; thus, the ull that the two-part model is correct caot be rejected. Fially, usig statistical criteria to select betwee the two models, Dow ad Norto (2003) recommed the test proposed by Toro-Vizcarrodo ad Wallace (1968), which 10 Dow ad Norto (2003) stress that if the coefficiet of the iverse Mills ratio is zero, the Heckit reduces exactly to the two-part model, but the two-part model does ot require the coefficiet to be equal to zero. The two models simply make differet implicit distributioal assumptios ad they are oly partially ested. 12

13 they ame a empirical mea squared error (EME) test. The origial test statistic was derived for O models, but the ituitio ca be exteded to the Heckit ad two-part models. This test ivolves calculatig the EME of both estimators, uder the assumptio that oe model is cosistet ad correct. The, the estimator with the lower EME is chose. For most of the variables i the empirical specificatio (with the sole exceptio of the variable o temporary workers), the EME for the two-part model is smaller tha the EME for the Heckit model, idicatig that the former seems more appropriate. As for the cotrol variables, the same result is obtaied, with the exceptio of some regioal dummies. 11 Uder the two assumptios, the results are similar, idicatig the robustess of the results. Therefore, although from a theoretical poit of view it ca be argued that sample selectio might exist, a sigificace test o the iverse Mills ratio ad the EME test suggest that i practice it seems more appropriate to estimate a two-part model to model firms traiig provisio. I the case of the subsamples of small ad large firms similar results are obtaied The two-part model with radom effects Empirical studies that use firm-level datasets reveal a high degree of heterogeeity amog firms with similar observed characteristics. This particularity of the data requires estimatig a model that takes firm-specific effects ito accout. If there are sigificat uobserved time-ivariat, firm-specific effects that are correlated with the explaatory variables, the simple pooled regressio may produce biased ad icosistet estimates. I the case of micro-databases, where firms i the sample are selected radomly from a larger populatio, it is quite commo to estimate a radom effects model, rather tha a fixed effects model. 12 The participatio equatio is estimated by meas of a radom effects probit model, which assumes a ormal distributio for the radom effects. The model is estimated by maximum likelihood (Guilkey ad Murphy, 1993). 13 As for the quatity 11 Due to limitatios of space, the results for the EME test have ot bee icluded here. However, they are available from the author upo request. 12 ee for istace Groot ad Maasse va de Brik (2003), Barrios et al. (2003), Máñez et al. (2004) or icadro et al. (2004). 13 The itegral i the likelihood fuctio is approximated with the o-adaptive Gauss-Hermite quadrature. The quadrature formula requires that the itegrated formula is well approximated by a polyomial. As the pael size icreases, the quadrature approximatio becomes less accurate. If the results of the estimatio chage whe the umber of quadrature poits chages, the results should be dismissed. We verified the magitude of these chages ad foud that, for most variables, the relative 13

14 equatio, a stadard regressio model icludig radom effects is estimated by geeralized least squares. Table 5 offers the results of the two-part model icludig firm-specific effects, for the total sample ad for the subsamples of small ad large firms. I the case of the total sample (first set of colums i Table 5), the results are similar to those i Table 4: the same variables are sigificat ad they show the same sig. Although the results are similar to the model without the iclusio of radom effects, the tests reject the ull hypothesis that firm-specific effects are zero. I the case of the participatio equatio, whe the pael-level variace compoet is uimportat, the pael estimator is ot sigificatly differet from the pooled estimator. The test rejects the ull that the paellevel variace compoet is equal to zero at 1%. As for the quatity equatio, the Breusch ad Paga agrage-multiplier test rejects the ull hypothesis at 1%. imilar coclusios from the tests are obtaied for the subsamples of small ad large firms. Therefore, the two-part model with radom effects was chose to carry out the rest of the aalysis. [Isert Table 5 about here] I geeral, the results obtaied here cofirm the fidigs of previous empirical studies. ee for istace, Bartel (1989), Alba-Ramírez (1994), Baldwi et al. (1995), Black ad ych (1998) ad Hughes et al. (2004). More specifically, i the case of the total sample, the effect of firm size is positive ad sigificat i the participatio equatio idicatig the presece of effects associated with large firms eve after cotrollig for the set of possible traiig determiats. I particular, icreasig the firm size by oe poit icreases the probability of firms providig traiig by 0.2. The fact that firm size is sigificatly positive i the participatio equatio, eve after cotrollig for other variables ad firm-specific effects, suggests the existece of scale ecoomies i the provisio of traiig as well as other effects associated with firm size. Apart from this direct effect of firm size, the other covariates may have differet effects i the subsamples of small ad large firms, as suggested by the descriptive aalysis i ectio 3. For example, does a icrease i the participatio of skilled workers lead to a higher probability of traiig (or higher expediture) i both small ad large firms? Is this effect larger i magitude i either group? To further aalyse this questio, the same equatios are estimated for the subsamples of small ad large differece betwee the coefficiets usig differet quadrature poits was smaller tha 0.01%. o, the results of the probit radom effects model estimated here are reliable. 14

15 firms. Give that small firms are ackowledged to have more difficulties i accessig traiig, we are iterested i aalysig the impact of these variables o traiig decisios ad whether they play differet roles i firms of differet size classes. The secod ad third sets of Colums i Table 5 show the results for the estimatio of the empirical specificatio for the subsamples of small ad large firms respectively. Results suggest the existece of certai differeces betwee small ad large firms i their traiig provisio decisios. pecifically, firm size has a egative effect o traiig expediture per worker i small firms, while this is ot the case with large firms. This could be explaied by the high fixed costs of traiig, especially for the smallest firms. I the case of the degree of qualificatio of the labour force, this factor does ot determie whether large firms will decide to provide traiig, although it does have a impact o the amout of traiig provided. I small firms, however, the degree of qualificatio of the labour force is a determiat of both decisios. This result ca be explaied by the fact that large firms employ a wide rage of employees, ad so, ceteris paribus, there is a higher probability that they will provide traiig to at least oe employee. The variables related to techology appear to be importat determiats of a firm s decisio to provide traiig, both for small ad large firms. However, i the case of the latter, the effects seem to be slightly smaller i magitude tha i the case of small firms. Moreover, i shiftig from beig a o-iovative to a iovative large firms icrease their expediture o traiig per worker by almost 22%, whereas i the case of small firms, this variable does ot have a sigificat effect. These results suggest a relatioship betwee size, techological activities ad the traiig per worker. As we discuss below, techological activities appear to explai i part why large firms provide more traiig per worker. I the case of small firms, competig i a iteratioal market ad havig foreig capital participatio affect the two traiig decisios. This ca be explaied by the fact that small firms with these characteristics may decide to provide traiig as a way of guarateeig success i their competitive eviromet. However, the impact of the geographical scope of the market o the decisio as to whether to provide traiig is much larger i large firms tha i their smaller couterparts. Fially, the coefficiet of the variable for temporary employmet is oly sigificat (presetig a egative sig) i the decisio regardig the quatity of traiig i large 15

16 firms. As before, give that large firms employ a wide rage of workers, it does ot affect their probability of providig traiig but rather the quatity of it. With regards to the cotrol variables o the group ad the use of productive capacity, small ad large firms do ot differ i their respective behaviour. However, the sets of dummy variables o regio ad sector show differeces betwee the two groups. Overall, the techological activities ad the geographical scope of the market appear to be importat determiats of firms traiig decisios. I additio, there are certai differeces betwee small ad large firms that may explai why small firms provide less traiig per employee tha their larger couterparts. I the ext ectio, the traiig provisio gap betwee small ad large firms is decomposed to ivestigate further the cotributio of these variables. 5. Decompositio of the traiig gap betwee small ad large firms 5.1. The Oaxaca-Blider decompositio i the two-part model The Oaxaca-Blider methodology is applied here to decompose the traiig provisio differetial betwee large ad small firms. 14 It allows us to decompose the differeces i the participatio decisio ad i the amout of traiig ito two compoets: differeces i the levels of the determiats of traiig (firm characteristics) ad differeces i the impact of these determiats. The former reflects the fact that small ad large firms have differet characteristics, which are associated with differet traiig levels. The latter reflects the differeces by firm size i the impact of such characteristics o the traiig provisio. For example, supposig that small ad large firms had the same percetage of qualified workers, would they show a similar propesity to ivest i traiig? tartig from two auxiliary regressios for the sub-samples of small ad large firms: T T F( ' F( ' ) ) (7) 14 The Oaxaca-Blider decompositio methodology has bee widely used to study wage gaps associated with differeces i workers characteristics ad discrimiatio by geder or race (Oaxaca, 1973 ad Blider, 1973). To the best of our kowledge, mith et al. (2004) ad Castay et al. (2007) are the oly papers that have applied this method to aalyse differeces betwee firms. 16

17 where T deotes traiig, both as a discrete (dtr) or cotiuous variable (ltr), is the matrix of the regressors, is the coformig vector of estimated coefficiets ad subscripts ad refer to large firms ad small firms respectively. 15 Notice that F( ) ca be both a liear fuctio quatity equatio or a oliear fuctio participatio equatio. The traditioal detailed Oaxaca-Blider decompositio ca be applied i liear models, but it is ot suitable for o-liear specificatios. Istead, for the latter we apply a recet proposal (Yu, 2004) to compute detailed decompositios for o-liear models that are liear i their argumets, such as the participatio equatio. 16 Accordig to the stadard Oaxaca-Blider decompositio, the differeces i the quatity of traiig betwee small ad large firms ca be decomposed as: lt R ' ' ' ltr (8) where the first term o the right-had side is the part of the traiig gap due to differeces i characteristics betwee the represetative small ad large firms ad the secod term o the right-had side is the cotributio of differeces i the impact betwee both types of firm. The stadard versio of the Oaxaca-Blider decompositio builds o the assumptio that oe of the two equatios is the atural model (for istace, i the case of the wage gap decompositio by geder, it may appear quite atural to assume that wome are the discrimiated group ad, thus, to aalyse what their wages would have bee if they had had the returs of me). Nevertheless, i the preset case there is o compellig reaso to calculate the differeces i firms edowmets assumig that all the firms had the coefficiets of either large or small firms. It is difficult at times to establish which is the atural model ad the results may ofte differ cosiderably. Oe strad of the literature suggests a variatio o the stadard decompositio that avoids havig to make this assumptio. Accordig to this approach, there exists a odiscrimiatory structure of coefficiets * i relatio to which oe group is 15 The Gardeazábal ad Ugidos (2004) trasformatio has bee applied i the estimatio of i order to distiguish the effects due to the differet sets of dummies. 16 As far as we kow Yu s detailed decompositio was applied for the first time by Motelló ad ópez- Bazo (2005) ad Heraz ad Toharia (2006). 17

18 18 discrimiated while the other is favoured (Oaxaca ad Rasom, 1994). 17 The, the traiig differetial ca be expressed as: TR R T ' ' ' ' l l * * * (9) where I ) ( * ad ) ' ' ( ) ' ( 1. The first term o the right- had side of (9) reflects traiig differeces due to differeces i firms characteristics. The secod ad third terms are estimates of the large firms advatage ad small firms disadvatage i relatio to the o-discrimiatory coefficiets structure. The two terms together are cosidered as differeces i the expediture o traiig by firm size associated with differeces i coefficiets without imposig a discrimiated group. As for the decompositio of the participatio equatio, the Yu s methodology cosists of fidig the cotributio of every -variable to the total differece. Usig the variatio suggested by Oaxaca ad Rasom (1994) for the Yu-Oaxaca-Blider decompositio of the participatio equatio, we have: ) ( ) ( ) ( ) ( ) ( ) ( * 1 * 1 * * 1 N disc N fav N W W W dtr dtr (10) where, is a stadard ormal cumulative distributio fuctio, W ad W are the weights for each -variable ad subscripts fav ad disc idicate that the weights correspod to the effect of large firms advatage ad small firms disadvatage i relatio to the o-discrimiatory coefficiets structure. The key questio is fidig proper weights for the variables. Yu (2004) suggests evaluatig the value of the fuctio usig mea characteristics ad the usig a first order Taylor expasio to liearize aroud, ad *. I this way, the weights ca be expressed as: * * ) ( ) ( W ; fav W ) ( ) ( * * ; disc W ) ( ) ( * * (11) The first term o the right-had side of equatio (10) reflects traiig differeces due to differeces i characteristics. This term is a estimate of the differetial i the probability of providig traiig betwee small ad large firms i the absece of differeces i the impact of these characteristics. The secod ad third terms are 17 It ca be easily proved that a cosistet estimate of * ca be obtaied by O i the whole sample of firms.

19 estimates of the differetial i probability of providig traiig due to differeces i the impact of firms characteristics. Together, they collect the effect of large firms advatage ad small firms disadvatage i relatio to the o-discrimiatory coefficiets structure Results of the decompositio of the traiig gaps I this ectio, we assess the idividual cotributio of firms characteristics i explaiig the traiig gap betwee small ad large firms i two ways: differeces i the level of the determiats of the traiig provisio ad differeces i their impact o the traiig provisio decisios. To perform this aalysis, the detailed decompositio described i expressios (9) ad (10) is applied. Table 6 shows the results of the Oaxaca-Blider decompositio based o the two-part model with ad without firm-specific effects. 18,19 The magitudes of the effects of each variable are similar uder the two models. The differetial i the probability of providig traiig betwee small ad large firms is 2.7. The decompositio for all the variables together shows that most of the gap is due to differeces i characteristics, while differeces i the impact of characteristics explai oly 5% of the gap (ad eve less i the model icludig firm-specific effects). However, we are especially iterested i the idividual decompositio for aalysig the cotributio of each variable. [Isert Table 6 about here] The fact that large firms employ more white-collar workers explais a very small part of the differetial of the probability of providig traiig both as differeces i characteristics ad as differeces i the impact of characteristics. I the case of the variables related to techological activities, the differeces i the itesity of their use explai aroud 20% of the gap, while the global impact of this variable has a very small effect. The differeces i iovative activity betwee small ad large firms explai about 10% of the differetial i the probability of providig traiig, while the global impact of this variable is also very small i magitude. The differeces i the variable related to the geographical scope of the firms market explai about 8% of the gap i the probability of traiig, while differeces i 18 I the RE model the trasformed residuals have zero mea, but ot the residuals from the origial specificatio. This prevets obtaiig a exact decompositio of the traiig gap based o the RE estimates of the coefficiets. 19 Table 6 shows the most relevat results of the decompositio. For more complete results, see Table A1 at the Appedix. 19

20 the global impact of this variable are quite small. The differeces i the participatio of foreig capital ad the percetage of temporary workers show a small cotributio to explai the differeces i the probability of providig traiig. The differetial i the logarithm of the expediture o traiig per worker betwee small ad large firms is 0.4. The decompositio for all the variables together shows that differeces i firms characteristics explai aroud 65% of the differetial, while differeces i the impact of characteristics explai 35%. Agai, the percetage of white-collar workers has a almost egligible cotributio i explaiig the gap i the quatity of traiig. The use of advaced techologies explais more tha 15% of the differetial i the quatity of traiig (25% i the case of the RE model). Of this figure, aroud 5% of the differetial is due to differeces i the impact of usig advaced techologies, while the rest is due to differeces i characteristics (both i favour of large firms). The iovative activity also explais about 15% of the gap more tha 10% is due to differeces i characteristics ad the remaiig portio is due to differeces i the impact. Differeces i the geographical scope of firms markets explai more tha 16% of the traiig gap ad both differeces i characteristics ad differeces i the impact of these characteristics have a similar cotributio, both i favour of large firms. The participatio of foreig capital explais a fairly sizeable part of the differetial: aroud 14% is due to the fact that large firms ejoy a greater participatio of foreig capital. However, the impact of this variable is also quite large ad favours small firms, with values aroud 24%. I other words, uder equal impact of characteristics (i.e. coefficiets), the gap i the probability of providig traiig would be larger favourig large firms. Fially, the percetage of temporary workers makes a importat cotributio i explaiig the differetial i the quatity of traiig ad this is maily due to differeces i the impact of characteristics i favour of small firms, takig values of almost 40%. Thus, if small ad large firms recorded the same impact from the variable of temporary workers, ceteris paribus, the gap i the probability of providig traiig betwee small ad large firms would be eve wider. All i all, the variables that play the most relevat role i explaiig the gap betwee small ad large firms i terms of the probability of providig traiig are: the use of advaced techology, the iovative activity ad the iteratioal scope of the market i which firms operate. Together they explai about 40% of this gap ad their 20

21 effect is primarily due to differeces i characteristics. As for the quatity equatio, the variables that make the mai cotributio i explaiig the gap are the same as i the case above, explaiig more tha half of the gap. However, here this is due to differeces i characteristics as well as differeces i the impact of these characteristics. Additioally, the participatio of foreig capital i the firms ad the percetage of temporary workers seem to explai a large part of the effect, which is due i particular to differeces i the impact of these characteristics o the quatity of traiig i favour of small firms. 6. Coclusios This paper has sought to uderstad why small firms provide their employees with less traiig tha their larger couterparts. The iitial hypothesis holds that large firms provide more traiig opportuities because they are edowed with certai characteristics that permit them to exped greater efforts i traiig their workers. These iclude employig more white-collar workers ad egagig fewer temporary workers. Furthermore, the provisio made by large firms is greater because they are edowed with certai characteristics that, i their tur, require more traiig. These iclude their adoptio of more advaced techologies or iovative activity, operatig i more competitive markets (e.g. iteratioally) ad beig partially owed by foreig capital. The empirical evidece reviewed here seems to support the hypothesis that traiig provisio is ideed closely associated with these characteristics. Usig the EEE, we have preseted evidece that large paish idustrial firms ivest more traiig (per worker) ad that they are more closely associated with these characteristics tha their smaller couterparts. The paper has discussed the suitability of adoptig two-part models for aalysig traiig decisios, both from a theoretical ad applied perspective. Although the Heckit model seems to be more appropriate from a theoretical poit of view, o evidece of strog sample selectio was apparet i the case of pai s idustrial firms, suggestig that the two-part model might be more appropriate for modellig their traiig decisios. Based o previous evidece that small ad large firms follow differet patters i their traiig decisios, we estimated the two subsamples separately. 21

22 The results of these estimatios suggest that techological activities ad the geographical scope of the market are importat determiats of firms traiig decisios for both small ad large firms. Ideed, the effects of techological variables o the participatio decisio are larger i magitude i the case of small firms. ikewise, a large firm that switches from beig o-iovative to iovative will icrease its expediture o traiig cosiderably. I the case of the geographical scope of the market, this factor determies both decisios for small firms, while for large firms it has a greater effect o the probability of providig traiig. The decompositio of the traiig gap betwee small ad large firms allows us to assess the relative cotributio to the gap made by these firms characteristics. I the case of the decisio as to whether to provide traiig, the most importat cotributios are related to firms techological activity ad the geographical scope of the market i which they operate; these effects are maily due to differeces i characteristics i favour of large firms. I the case of the decisio regardig the quatity of traiig per worker, the variables related to techological activity ad market scope explai a sizeable part of the gap. Here the effects are due both to differeces i characteristics ad differeces i the impact of these characteristics i favour of large firms. I additio, the participatio of foreig capital ad temporary workers explai a large part of the gap, basically as differeces i the impact of characteristics i favour of small firms. Overall, this study cofirms the fidig that small firms face greater restrictios i gaiig access to traiig. The results suggest that the differeces i traiig provisio betwee small ad large firms are related to differeces i the firms requiremets to update the skills of their employees to esure that they acquire the specific kowledge to use ew techologies ad to make the firms more competitive i iteratioal markets. Ad these differeces i ecessity favour large firms. I other words, the differeces betwee small ad large firms do ot, i geeral, seem to be related to those characteristics that allow firms to provide more traiig (i.e. the fact of employig more qualified workers or o-temporary workers). This ca, perhaps, be see as a factor that impedes small firms from becomig more competitive because of a more restricted access to traiig, a tool that eables employees to upgrade their skills ad so become more competitive. Refereces 22