nach oben

Erschienen in:

2014 | OriginalPaper | Buchkapitel

3. Spatial Panel Data Models

verfasst von : J. Paul Elhorst

Erschienen in: Spatial Econometrics

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This chapter provides a survey of the specification and estimation of spatial panel data models. Five panel data models commonly used in applied research are considered: the fixed effects model, the random effects model, the fixed coefficients model, the random coefficients model, and the multilevel model. Today a (spatial) econometric researcher has the choice of many models. First, he should ask himself whether or not, and, if so, which type of spatial interaction effects should be accounted for. Second, he should ask himself whether or not spatial-specific and/or time-specific effects should be accounted for and, if so, whether they should be treated as fixed or as random effects. A selection framework is demonstrated to determine which of the first two types of spatial panel data models considered in this chapter best describes the data. The well-known Baltagi and Li (2004) panel dataset, explaining cigarette demand for 46 US states over the period 1963 to 1992, is used to illustrate this framework in an empirical setting.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Linear Spatial Dependence Models for Cross-Section Data

Nächstes Kapitel Dynamic Spatial Panels: Models, Methods and Inferences

Baltagi et al. (2003) are the first to consider the testing of spatial interaction effects in a spatial panel data model. They derive a joint LM test which tests for spatial error autocorrelation and spatial random effects, as well as two conditional tests which test for one of these extensions assuming the presence of the other.

\( \phi = 1 \) implies \( \sigma_{\mu}^{2} = 0 \), since \( \sigma_{\mu}^{2} \) may be calculated from \( \phi \) by \( \sigma_{\mu}^{2} = \frac{{1 - \phi^{2}}}{{\phi^{2}}}\frac{{\sigma^{2}}}{T} \).

Note that \( \varphi = {{\sigma_{\mu}^{2}} \mathord{\left/{\vphantom {{\sigma_{\mu}^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}} \) is different from \( \phi \) in the non-spatial random effects model and in the random effects spatial lag model.

Note that the matrix Z ₀ in Baltagi et al. (2007, pp. 39–40) has been replaced by \( \varvec{Z}_{0} = \left({T\sigma_{\mu}^{2} \varvec{I}_{N} + \sigma^{2} \left({\varvec{B}^{'} \varvec{B}} \right)^{- 1}} \right)^{- 1} =\, \frac{1}{{\sigma^{2}}}\left({T\varphi \varvec{I}_{N} + (\varvec{B}^{'} \varvec{B})^{- 1}} \right)^{- 1} =\, \frac{1}{{\sigma^{2}}}\varvec{V}^{- 1} \).

This remark through Balestra and Nerlove is striking especially since they are the devisers of the random effects model (Balestra and Nerlove 1966).

Mutl and Pfaffermayr (2011) derive the Hausman test when the fixed and random effects models are estimated by 2SLS instead of ML.

Software programs, such as Spacestat and Geoda, have built-in routines that automatically report the results of these tests. Matlab routines have been made available at http://oak.cats.ohiou.edu/~lacombe/research.html by Donald Lacombe and at www.regroningen.nl by Paul Elhorst.

See the routine “sar” posted at LeSage's website <www.spatial-econometrics.com>.

Note that the test results satisfy the condition that LM spatial lag + robust LM spatial error = LM spatial error + robust LM spatial lag (Anselin et al. 1996).

These tests are based on the log-likelihood function values of the different models. Table 3.2 shows that these values are positive, even though the log-likelihood functions only contain terms with a minus sign. However, since σ² < 1, we have –log(σ²) > 0. Furthermore, since this positive term dominates the negative terms in the log-likelihood function, we eventually have LogL > 0.

One application of this model in the literature is of Sampson et al. (1999), but this paper does not describe the estimation procedure in detail.

Bowden and Turkington start from the regression equation \( \varvec{Y} = \varvec{X\beta} +\varvec{\mu} \), where \( {\text{E}}\left({\varvec{\mu \mu}^{\text{T}}} \right) =\varvec{\Upomega} \), and some of the X variables are endogenous. Let Z denote the set of instrumental variables. Then, the GLS analog instrumental variables estimator is \( \varvec{b} = \left({\varvec{X}^{pT}\varvec{\Upomega}^{- 1} \varvec{X}^{P}} \right)^{- 1} \varvec{X}^{pT}\varvec{\Upomega}^{- 1} \varvec{Y} \), where \( \varvec{X}^{p} = \varvec{Z}(\varvec{Z}^{T}\varvec{\Upomega}^{- 1} \varvec{Z})^{- 1} \varvec{Z}^{T}\varvec{\Upomega}^{- 1} \varvec{X} \).

Applications based on the multilevel approach in regional economic research are Jones (1991), Ward and Dale (1992), Gould and Fieldhouse (1997), McCall (1998), Elhorst and Zeilstra (2007), Chasco and Lopez (2009), and Zeilstra and Elhorst (2012).

The linear expenditure system in its basic form is linear in the variables but nonlinear in the parameters. However, Barnum and Squire (1979) have shown that it can be rewritten in such a way that linear estimation techniques can still be used to estimate the parameters. Since the linear expenditure system extended to include interaction effects is also nonlinear in its variables, linear estimation techniques can no longer be used. The same applies to the techniques spelled out in Anselin (1988), which are partially linear.

Aaberge R, Langørgen A (2003) Fiscal and spending behavior of local governments: identification of price effects when prices are not observed. Public Choice 117:125–61

Allers MA, Elhorst JP (2011) A simultaneous equations model of fiscal policy interactions. J Reg Sci 51:271–291

Anselin L (1988) Spatial econometrics: Methods and models. Kluwer, Dordrecht

Anselin L (2010) Thirty years of spatial econometrics. Papers Reg Sci 89:3–25

Anselin L, Bera A (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Ullah A, Giles D (eds) Handbook of applied economics statistics. Marcel Dekker, New York, pp 237–289

Anselin L, Hudak S (1992) Spatial econometrics in practice: a review of software options. Reg Sci Urban Econ 22(3):509–536

Anselin L, Bera AK, Florax R, Yoon MJ (1996) Simple diagnostic tests for spatial dependence. Reg Sci Urban Econ 26(1):77–104

Anselin L, Le Gallo J, Jayet H (2006) Spatial panel econometrics. In: Matyas L, Sevestre P (eds) The econometrics of panel data, fundamentals and recent developments in theory and practice, 3rd edn. Kluwer, Dordrecht, pp 901–969

Arbia G, Fingleton B (2008) New spatial econometric techniques and applications in regional science. Papers in Regional Science 87:311–317

Arrelano M (2003) Panel data econometrics. Oxford University Press, Oxford

Balestra P, Negassi S (1992) A random coefficient simultaneous equation system with an application to direct foreign investment by French firms. Empir Econ 17:205–220

Balestra P, Nerlove M (1966) Pooling cross-section and time-series data in the estimation of a dynamic model: the demand for natural gas. Econometrica 34(3):585–612

Baltagi BH (2005) Econometric analysis of panel data, 3rd edn. Wiley, Chichester

Baltagi BH (2006) Random effects and spatial autocorrelation with equal weights. Econom Theory 22(5):973–984

Baltagi BH, Bresson G (2011) Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors. An application to hedonic housing prices in Paris. J Urban Econ 69:24–42

Baltagi BH, Levin D (1986) Estimating dynamic demand for cigarettes using panel data: the effects of bootlegging, taxation and advertising reconsidered. The Review of Economics and Statistics 48:148–155

Baltagi BH, Levin D (1992) Cigarette taxation: raising revenues and reducing consumption. Struct Change Econ Dyn 3(2):321–335

Baltagi BH, Li D (2004) Prediction in the panel data model with spatial autocorrelation. In: Anselin L, Florax RJGM, Rey SJ (eds) Advances in spatial econometrics: Methodology, tools, and applications. Springer, Berlin Heidelberg New York, pp 283–295

Baltagi BH, Liu L (2011) Instrumental variable estimation of a spatial autoregressive panel model with random effects. Econ Lett 111:135–137

Baltagi BH, Pirotte A (2010) Panel data inference under spatial dependence. Econ Model 27:1368–1381

Baltagi BH, Pirotte A (2011) Seemingly unrelated regressions with spatial error components. Empir Econ 40:5–49

Baltagi BH, Griffin JM, Xiong W (2000) To pool or not to pool: Homogeneous versus heterogeneous estimators applied to cigarette demand. Rev Econ Stat 82:117–126

Baltagi BH, Song SH, Koh W (2003) Testing panel data models with spatial error correlation. J Econom 117(1):123–150

Baltagi BH, Song SH, Jung BC, Koh W (2007) Testing for serial correlation, spatial autocorrelation and random effects using panel data. J Econom 140(1):5–51

Baltagi BH, Egger P, Pfaffermayr M (2012) A generalized spatial panel data model with random effects. CESifo Working Paper Series No. 3930. Available at SSRN: http://ssrn.com/abstract=2145816

Barnum HW, Squire L (1979) An econometric application of the theory of the farm-household. J Dev Econ 6:79–102

Beck N (2001) Time-series-cross-section data: What have we learned in the past few years? Ann Rev Polit Sci 4:271–293

Beenstock M, Felsenstein D (2007) Spatial vector autoregressions. Spat Econ Anal 2(2):167–196

Bowden RJ, Turkington DA (1984) Instrumental variables. Cambridge University Press, Cambridge

Breusch TS (1987) Maximum likelihood estimation of random effects models. J Econom 36(3):383–389

Brueckner JK (2003) Strategic interaction among local governments: An overview of empirical studies. International Regional Science Review 26(2):175–188

Burridge P (1980) On the Cliff-Ord test for spatial autocorrelation. J R Stat Soc B 42:107–108

Burridge P (1981) Testing for a common factor in a spatial autoregression model. Environ Plann A 13(7):795–400

Chasco C, López AM (2009) Multilevel models: an application to the beta-convergence model. Région et Développement 30:35–58

Corrado L, Fingleton B (2012) Where is the economics in spatial econometrics? J Reg Sci 52(2):210–239

Cressie NAC (1993) Statistics for spatial data. Wiley, New York

Debarsy N, Ertur C (2010) Testing for spatial autocorrelation in a fixed effects panel data model. Reg Sci Urban Econ 40:453–470

Debarsy N, Ertur C, LeSage JP (2012) Interpreting dynamic space-time panel data models. Stat Methodol 9(1–2):158–171

Driscoll JC, Kraay AC (1998) Consistent covariance matrix estimation with spatially dependent panel data. Rev Econ Stat 80:549–560

Egger P, Pfaffermayr M (2004) Distance, trade and FDI: a Hausman-Taylor SUR approach. J Appl Econom 16:227–246

Elhorst JP (2003) Specification and estimation of spatial panel data models. Int Reg Sci Rev 26(3):244–268

Elhorst JP (2005) Unconditional maximum likelihood estimation of linear and log-linear dynamic models for spatial panels. Geograph Anal 37(1):62–83

Elhorst JP (2008a) Serial and spatial autocorrelation. Econ Lett 100(3):422–424

Elhorst JP (2008b) A spatiotemporal analysis of aggregate labour force behaviour by sex and age across the European Union. J Geogr Syst 10(2):167–190

Elhorst JP (2010a) Applied spatial econometrics: raising the bar. Spat Econ Anal 5(1):9–28

Elhorst JP (2010b) Spatial panel data models. In: Fischer MM, Getis A (eds) Handbook of applied spatial analysis. Springer, Berlin, pp 377–407

Elhorst JP (2012) Matlab software for spatial panels. Int Reg Sci Rev. doi:10.1177/0160017612452429

Elhorst JP (2013) Spatial panel models. In: Handbook of Regional Science, Ch. 82. Springer, Berlin (Forthcoming)

Elhorst JP, Zeilstra AS (2007) Labour force participation rates at the regional and national levels of the European Union: an integrated analysis. Papers Reg Sci 86:525–549

Frees EW (2004) Longitudinal and panel data. Cambridge, Cambridge University Press

Fiebig DG (2001) Seemingly unrelated regression. In: Baltagi BH (ed) A companion to theoretical econometrics. Blackwell, Malden, pp 101–121

Fingleton B (2001) Theoretical economic geography and spatial econometrics: dynamic perspectives. J Econ Geogr 1:201–225

Fingleton B (2007) Multi-equation spatial econometric model, with application to EU manufacturing productivity growth. J Geogr Syst 9:119–144

Florax RJGM, Folmer H, Rey SJ (2003) Specification searches in spatial econometrics: the relevance of Hendry’s methodology. Reg Sci Urban Econ 33(5):557–579

Froot KA (1989) Consistent covariance matrix estimation with cross-sectional dependence and heteroskedasticity in financial data. J Fin Anal 24:333–355

Goldstein H (1995) Multilevel statistical models, 2nd edn. Arnold (Oxford University Press), London

Gould MI, Fieldhouse E (1997) Using the 1991 census SAR in a multilevel analysis of male unemployment. Environ Plan A 29:611–628

Greene WH (2008) Econometric analysis, 6th edn. Pearson, New Jersey

Griffith DA (1988) Advanced spatial statistics. Kluwer, Dordrecht

Griffith DA, Lagona F (1998) On the quality of likelihood-based estimators in spatial autoregressive models when the data dependence structure is misspecified. J Stat Plan Infer 69(1):153–174

Halleck Vega S, Elhorst JP (2012) On spatial econometric models, spillover effects, and W. University of Groningen, Working paper

Hausman JA (1975) An instrumental variables approach to full information estimators for linear and certain nonlinear econometric models. Econometrica 43:727–738

Hausman JA (1983) Specification and estimation of simultaneous equation models. In: Griliches Z, Intriligator MD (eds) Handbook of econometrics, vol 1. Elsevier, Amsterdam, pp 392–448

Hayashi F (2000) Econometrics. Princeton University Press, Princeton

Hepple LW (1997) Testing for spatial autocorrelation in simultaneous equation models. Computational, Environmental and Urban Systems 21(5):307–315

Hsiao C (1996) Random coefficients models. In Mátyás L, Sevestre P (eds) The econometrics of panel data, 2nd revised edn. Kluwer, Dordrecht, pp 77–99

Hsiao C (2003) Analysis of panel data, 2nd edn. Cambridge University Press, Cambridge

Hsiao C, Tahmiscioglu AK (1997) A panel analysis of liquidity constraints and firm investment. J Am Stat Assoc 92:455–465

Hunneman A, Bijmolt T, Elhorst JP (2007) Store location evaluation based on geographical consumer information. In: Paper presented at the marketing science conference, Singapore, 28–30 June 2007

Jackman R, Papadachi J (1981) Local authority education expenditure in England and Wales: why standards differ and the impact of government grants. Public Choice 36:425–439

Jenrich RI, Schluchter MD (1986) Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42:805–820

Jones K (1991) Multi-level models for geographical research. In: Concepts and techniques in modern geography, vol 54. University of East Anglia, Norwich.

Kapoor M, Kelejian HH, Prucha IR (2007) Panel data models with spatially correlated error components. Journal of Econometrics 140(1):97–130

Kapteyn A, Van de Geer S, Van de Stadt H, Wansbeek T (1997) Interdependent preferences: an econometric analysis. J Appl Econom 12:665–686

Kelejian HH (1974) Random parameters in simultaneous equations framework: Identification and estimation. Econometrica 42:517–527

Kelejian HH, Piras G (2012) Estimation of spatial models with endogenous weighting matrices and an application to a demand model for cigarettes. In: Paper presented at the 59th North American meetings of the RSAI, 2012, Ottawa, Canada

Kelejian HH, Prucha IR (1998) A generalized spatial two stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. J Real Estate Fin Econ 17(1):99–121

Kelejian HH, Prucha IR (2002) 2SLS and OLS in a spatial autoregressive model with equal spatial weights. Reg Sci Urban Econ 32(6):691–707

Kelejian HH, Prucha IR (2004) Estimation of simultaneous systems of spatially interrelated cross-sectional equations. J Econom 118:27–50

Kelejian HH, Prucha IR, Yuzefovich Y (2006) Estimation problems in models with spatial weighting matrices which have blocks of equal elements. J Reg Sci 46(3):507–515

Lahiri SN (2003) Central limit theorems for weighted sums of a spatial process under a class of stochastic and fixed designs. Sankhya 65:356–388

Lauridsen J, Bech M, López F, Maté M (2010) A spatiotemporal analysis of public pharmaceutical expenditures. Ann Reg Sci 44(2):299–314

Lee LF (2003) Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econom Rev 22(4):307–335

Lee LF (2004) Asymptotic distribution of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6):1899–1925

Lee LF, Yu J (2010a) Estimation of spatial autoregressive panel data models with fixed effects. J Econom 154(2):165–185

Lee LF, Yu J (2010b) Some recent developments in spatial panel data models. Reg Sci Urban Econ 40:255–271

Lee LF, Yu J (2012a) QML estimation of spatial dynamic panel data models with time varying spatial weights matrices. Spat Econ Anal 7(1):31–74

Lee LF, Yu J (2012b) Spatial panels: Random components versus fixed effects. Int Econ Rev 53:1369–1388

Lee LF, Liu X, Lin X (2010) Specification and estimation of social interaction models with network structures. Econom J 13(2):145–176

LeGallo J, Chasco C (2008) Spatial analysis of urban growth in Spain, 1900-2001. Empir Econ 34:59–80

LeSage JP (1999) Spatial econometrics. www.spatial-econometrics.com/html/sbook.pdf

LeSage JP, Pace RK (2009) Introduction to spatial econometrics. CRC Press Taylor & Francis Group, Boca Raton

Lindstrom MJ, Bates DM (1988) Newton-Raphson and EM algorithms for linear mixed-effects model for repeated-measures data. J Am Stat Assoc 83:1014–1022

Longford NT (1993) Random coefficient models. Clarendon Press, Oxford

Magnus JR (1982) Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood. J Econom 19(2):239–285

McCall L (1998) Spatial routes to gender wage (in) equality: regional restructuring and wage differentials by gender and education. Econ Geogr 74:379–404

Millo G, Piras G (2012) Splm: spatial panel data models in R. J Stat Softw 47(1):1–38

Millo G (2013) Maximum likelihood estimation of spatially and serially correlated panels with random effects. Comput Stat Data Anal http://dx.doi.org/10.1016/j.bbr.2011.03.031, Forthcoming in print

Montes-Rojas GV (2010) Testing for random effects and serial correlation in spatial autoregressive model. Journal of Statistical Planning and Inference 140:1013–1020

Mood AM, Graybill F, Boes DC (1974) Introduction to the theory of statistics, 3rd edn. McGraw-Hill, Tokyo

Moscone F, Tosetti E, Knapp M (2007) SUR model with spatial effects: an application to mental health expenditure. Health Econ 16:1403–1408

Mur J, Angulo A (2009) Model selection strategies in a spatial setting: Some additional results. Reg Sci Urban Econ 39:200–213

Mur J, López F, Herrera M (2010) Testing for spatial effects in seemingly unrelated regressions. Spat Econ Anal 5(4):399–440

Murphy KJ, Hofler RA (1984) Determinants of geographic unemployment rates: A selectively pooled-simultaneous model. Rev Econ Stat 66:216–223

Mutl J, Pfaffermayr M (2011) The Hausman test in a Cliff and Ord panel model. The Econometrics Journal 14:48–76

Nerlove M, Balestra P (1996) Formulation and estimation of econometric models for panel data. In Mátyás L, Sevestre P (eds) The econometrics of panel data, 2nd revised edn. Kluwer, Dordrecht, pp 3–22

Pace RK, Barry R (1997) Quick computation of spatial autoregressive estimators. Geographical Analysis 29(3):232–246

Parent O, LeSage JP (2010) A spatial dynamic panel model with random effects applied to commuting times. Transp Res Part B 44:633–645

Parent O, LeSage JP (2011) A space-time filter for panel data models containing random effects. Comput Stat Data Anal 55:475–490

Pfaffermayr M (2009) Maximum likelihood estimation of a general unbalanced spatial random effects model: a Monte Carlo study. Spat Econ Anal 4(4):467–483

Pollak RA, Wales TJ (1981) Demographic variables in demand analysis. Econometrica 49:1533–1551

Rey S, Montouri B (1999) US regional income convergence: a spatial econometrics perspective. Reg Stud 33:143–156

Sampson RJ, Morenoff JD, Earles F (1999) Beyond social capital: spatial dynamics of collective efficacy for children. American Sociological Review 64:633–660

Schubert U (1982) REMO – An interregional labor market model of Austria. Environ Plan A 14:1233–1249

Shiba T, Tsurumi H (1988) Bayesian and non-Bayesian tests of independence in seemingly unrelated regressions. Int Econ Rev 29:377–395

Shin C, Amemiya Y (1997) Algorithms for the likelihood-based estimation of the random coefficient model. Stat Probab Lett 32:189–199

Swamy PAVB (1970) Efficient inference in a random coefficient regression model. Econometrica 38:311–323

Swamy PAVB (1974) Linear models with random coefficients. In Zarembka P (ed) Frontiers in econometrics.Academic Press, New York, pp 143-168

Verbeek M (2000) A guide to modern econometrics. Wiley, Chichester

Wang X, Kockelman KM (2007) Specification and estimation of a spatially and temporally autocorrelated seemingly unrelated regression model: application to crash rates in China. Transportation 34:281–300

Wang W, Lee LF (2013) Estimation of spatial panel data models with randomly missing data in the dependent variable. Reg Sci Urban Econ. doi:10.1016/j.regsciurbeco.2013.02.001

Ward C, Dale A (1992) Geographical variation in female labour force participation: An application of multilevel modelling. Reg Stud 26:243–255

White EN, Hewings GJD (1982) Space-time employment modeling: Some results using seemingly unrelated regression estimators. J Reg Sci 22:283–302

Yang Z, Li C, Tse YK (2006) Functional form and spatial dependence in spatial panels. Econ Lett 91(1):138–145

Zeilstra AS, Elhorst JP (2012) An integrated analysis of regional and national unemployment differentials in the European Union. Reg Stud (Forthcoming). http://www.tandfonline.com/loi/cres20

Titel: Spatial Panel Data Models
verfasst von: J. Paul Elhorst
Verlag: Springer Berlin Heidelberg
Buch: Spatial Econometrics
Print ISBN: 978-3-642-40339-2

Electronic ISBN: 978-3-642-40340-8

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-642-40340-8_3

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"