Increasing returns to scale and regions: a multilevel model for Brazil

Keywords: productivity, Verdoorn, increasing returns, regional externalities, Brazil


The paper proposes and tests an alternative way to incorporate a spatial dimension to the Verdoorn Law using multilevel models, tailored to deal with nested data. This methodology allows extending the Verdoorn equation, incorporating elements from Urban Economics to Post-Keynesian growth analysis. The estimations used firm-level data from the Brazilian manufacturing industry from 1996 to 2002. The results showed that, after controlling for firms’ characteristics, the spatial dimension is crucial to explain rates of labour productivity and output growth. Moreover, the estimations showed that substantial knowledge spillovers and urbanisation externalities are beneficial to firms’ growth, whereas localisation externalities tend to be harmful. 


Download data is not yet available.


Abramovitz, M. (1986). Catching Up, Forging Ahead, and Falling Behind. The Journal of Economic History, 46(2), 385-406.

Anas, A. (2001). Book review: The spatial economy. Regional Science and Urban Economics, 31, 601-615.

Angeriz, A., McCombie, J. S. L., & Roberts, M. (2006). Some New Estimates of Returns to Scale for EU Regional Manufacturing, 1986-2002. CCEPP Working Paper, Land Economy Department, WP03-06.

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

Becker, G. S. (1962). Investment in Human Capital: A Theoretical Analysis. The Journal of Political Economy, 70(5), 9-49.

Cardoso, A. R. (1999). Firms' Wage Policies and the Rise in Labor Market Inequality: The Case of Portugal. Industrial and Labor Relations Review, 53(1), 87-102.

Cardoso, A. R. (2000). Wage differentials across firms: an application of multilevel modelling. Journal of Applied Econometrics, 15(4), 343-354.

David, P. A. (1999). Krugman's economic geography of development: NEGs, POGs, and naked models in space. International Regional Science Review, 22(2), 162.

Dosi, G. (1988). Technical change and economic theory. London: Printer.

Dosi, G., Pavitt, K., & Soete, L. (1990). The economics of technical change and international trade: Harvester Wheatsheaf.

Dymski, G. A. (1996). On Krugman's model of economic geography. Geoforum, 27(4), 439-452.

Fingleton, B. (2000). Spatial econometrics, economic geography, dynamics and equilibrium: a ‘third way’. Environment and Planning A, 32(8), 1481-1498.

Fingleton, B. (2001a). Equilibrium and Economic Growth: Spatial Econometric Models and Simulations. Journal of Regional Science, 41(1), 117-147.

Fingleton, B. (2001b). Theoretical economic geography and spatial econometrics: dynamic perspectives. Journal of Economic Geography, 1(2), 201.

Fingleton, B. (2003a). Externalities, Economic Geography, And Spatial Econometrics: Conceptual And Modelling Developments. International Regional Science Review, 26(2), 197-207.

Fingleton, B. (2003b). Increasing returns: evidence from local wage rates in Great Britain. Oxford Economic Papers, 55(4), 716-739.

Fingleton, B. (2005). Towards applied geographical economics: modelling relative wage rates, incomes and prices for the regions of Great Britain. Applied Economics, 37(21), 2417-2428.

Fingleton, B., & McCombie, J. S. L. (1998). Increasing returns and economic growth: some evidence for manufacturing from the European Union regions. Oxford Economic Papers, 50(1), 89-105.

Fujita, M., Venables, A. J., & Krugman, P. (1999). The Spatial Economy: cities, regions, and international trade. London, England.: MIT Press.

Glaeser, E. L. (1999). Learning in Cities. Journal of Urban Economics, 46(2), 254-277.

Glaeser, E. L., Kallal, H. D., Scheinkman, J. A., & Shleifer, A. (1992). Growth in Cities. The Journal of Political Economy, 100(6), 1126-1152.

Glaeser, E. L., & Maré, D. C. (2001). Cities and Skills. Journal of Labor Economics, 19(2), 316-342.

Goldstein, H. (1995). Multilevel Statistical Models. London: Edward Arnold.

Henderson, V. (1986). Efficiency of resource usage and city size. Journal of Urban Economics, 19(1), 47-70.

Henderson, V., Kuncoro, A., & Turner, M. (1995). Industrial Development in Cities. Journal of Political Economy, 103(5), 1067-1090.

Hox, J. J. (1995). Applied Multilevel Analysis: TT-Publikaties Amsterdam.

Jacobs, J. (1969). The Economy of Cities New York: Vintage Books.

Kaldor, N. (1975). Economic Growth and the Verdoorn Law - A Comment on Mr. Rowthorn's Article. The Economic Journal, 85, 891-896.

Lösch, A. (1954). The economics of location (W. Woglom & W. Stolper, Trans.). New Haven: Yale University Press.

Marshall, A. (1890). Principles of Economics. London: Macmillan and Co.

Martin, R. (1999). The new ‘geographical turn’ in economics: some critical reflections. Cambridge Journal of Economics, 23(1), 65-91.

Martin, R., & Sunley, P. (1996). Paul Krugman's Geographical Economics and Its Implications for Regional Development Theory: A Critical Assessment. Economic Geography, 72(3).

McCombie, J. S. L., Pugno, M., & Soro, B. (2002). Productivity Growth and Economic Performance: Essays on Verdoorn's Law: Palgrave Macmillan.

Mincer, J. (1974). Schooling, Earnings, and Experience: New York: Columbia University Press.

Moerbeek, M., van Breukelen, G. J. P., & Berger, M. P. F. (2003). A comparison between traditional methods and multilevel regression for the analysis of multicenter intervention studies. Journal of Clinical Epidemiology, 56(4), 341-350.

Neary, J. P. (2001). Of Hype and Hyperbolas: Introducing the New Economic Geography. Journal of Economic Literature, 39(2), 536-561.

Pickett, K. E., & Pearl, M. (2001). Multilevel analyses of neighbourhood socioeconomic context and health outcomes: a critical review. Journal of Epidemiology and Community Health, 55(2), 111-122.

Pons-Novell, J., & Viladecans-Marsal, E. (1999). Kaldor's Laws and Spatial Dependence: Evidence for the European Regions. Regional Studies, 33, 443-451.

Raudenbush, S. W. (1988). Educational Applications of Hierarchical Linear Models: A Review. Journal of Educational Statistics, 13(2), 85-116.

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: applications and data analysis methods: Sage Publications Inc.

Raudenbush, S. W., & Kasim, R. M. (1998). Cognitive Skill and Economic Inequality: Findings from the National Adult Literacy Survey. Harvard Educational Review, 68(1), 33-79.

Sampson, R. J., Raudenbush, S. W., & Earls, F. (1997). Neighborhoods and violent crime: a multilevel study of collective efficacy. Science, 277(5328), 918-924.

Schumpeter, J. A. (1939). Business Cycles. New York: McGraw Hill.

Steenbergen, M. R., & Jones, B. S. (2002). Modeling Multilevel Data Structures. American Journal of Political Science, 46(1), 218-237.

Verspagen, B. (1993). Uneven Growth Between Interdependent Economies: An Evolutionary View on Technology Gaps, Trade, and Growth. Aldershot: Avebury.

Weber, A. (1929). Theory of the Location of Industries. Chicago: The University of Chicago Press Chicago.

How to Cite
Britto, G., & McCombie, J. S. (2015). Increasing returns to scale and regions: a multilevel model for Brazil. Brazilian Keynesian Review, 1(2), 118-134.