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A non-linear Keynesian Goodwin-type endogenous model of the cycle: Bayesian evidence for the USA

  • Theodore Mariolis , Konstantinos N. Konstantakis , Panayotis G. Michaelides EMAIL logo and Efthymios G. Tsionas


This paper incorporates the so-called Bhaduri-Marglin accumulation function in Goodwin’s original growth cycle model and econometrically estimates the proposed model for the case of the US economy in the time period 1960–2012, using a modern Bayesian sequential Monte Carlo method. Based on our findings, the US economy follows an exhilarationist regime throughout our investigation period with the sole exception of an underconsumption regime for the time period 1974–1978. In general, the results suggest that the proposed approach is an appropriate vehicle for expanding and improving traditional Goodwin-type models.

JEL Classification: B51; C11; C62; E32

Technical Appendix

Sequential Monte Carlo

Chopin (2002) proposed a sequential PF for static models. Given a target posterior p(θ | Y): = p(θ | Y1:T), a particle system is a sequence {θj, wj} such that E(h(θ)|Y):=h(θ)p(θ|Y)dθlimJj=1Jwjh(θj)j=1Jwj, almost surely, for any measurable function h, provided the expectation exists. We consider the sequence of posterior distributions pt: = p(θ | Yt). The PF algorithm is as follows:

  1. Reweight: update the weights wjwjpt+1(θj)pt(θj),j=1,...,J.

  2. Resampling: resample {θj,wjJj=1H{θjr,1}j=1J}

  3. Move: draw θjmKt+1(θjr),j=1,...,J, where Kt+1 is any transition kernel whose stationary distribution is pt+1.

  4. Loop: tt+1,{θj,wj}j=1J{θjm,1}j=1J and return to Step 1.

Chopin (2002) recommends the independence Metropolis algorithm to select the kernel, which requires a source distribution. A possible choice, if we sampled from pn (n < T), with respect to pn+s is N(E^n+s,V^n+s) where


The strategy can be parallelized easily. If K processors are available, we can partition the particle system into K subsets, say Sk, k = 1, …, K), and implement computations for particles of Sk in processor k. The algorithm can deal with new data at a nearly geometric rate and, therefore, the frequency of exchanging information between processors (after reweighting) decreases at a rate exponential to n, which is highly efficient.

Resampling, according to θjmKt(θjr,.), reduces particle degeneracy (Gilks and Berzuini 2001) since identical replicates of a single particle are replaced by new ones, without altering the stationary distribution. For this application, using J = 212 particles gave a mean squared error in posterior means of 10–5 over 100 runs.

Chopin (2004) introduces a variation of MSC in which the observation dates at which each cycle terminates (say t1, …, tL) and the parameters involved in specifying the Metropolis updates (say λ1, …, λL) are specified. Therefore, 0 = t0 < t1 < … < tL = T and we have the following scheme (we rely heavily on Durham and Geweke 2014).

  1. Initialize l = 0 and θjn(l)p(θ),jJ, nN.

  2. For l = 1, …, L:

    1. Correction phase:

      1. wjn(tl–1) = 1, jJ, nN

      2. For s = tl–1 + 1, …, tl

      3. wjn(l1):=wjn(tl),jJ,nN.

    2. Selection phase, applied independently to each group jJ : Using multinomial or residual sampling based on {wjn(l),nN}, select


      from {θjn(l1),nN}.

    3. Mutation phase, applied independently across jJ, nN :


      where the drawings are independent and the pdf above satisfies the invariance condition:

  3. θjn:=θjn(l),jJ,nN.

At the end of every cycle, the particles θjn(l) have the same distribution p(θ|y1:tl). The amount of dependence, within each group, depends upon the success of the Mutation phase, which avoids degeneracy.


Amadeo, E. J. 1986. “The Role of Capacity Utilization in Long-Period Analysis.” Political Economy 2 (2): 147–185.Search in Google Scholar

Andronov, A. A., A. A. Vitt, and S. E. Khaikin. 1987. Theory of Oscillators. New York: Dover.Search in Google Scholar

Barbosa-Filho, N. 2015. “Elasticity of Substitution and Social Conflict: A Structuralist Note on Piketty’s Capital in the Twenty-First Century.” Cambridge Journal of Economics 40 (4): 1167–1183.10.1093/cje/bev042Search in Google Scholar

Barbosa-Filho, N. H., and L. Taylor. 2006. “Distributive and Demand Cycles in the U.S. Economy – A Structuralist Goodwin Model.” Metroeconomica 57 (3): 389–411.10.1111/j.1467-999X.2006.00250.xSearch in Google Scholar

Barrales, J., and R. von Arnim. 2017. “Longer-Run Distributive Cycles: Wavelet Decompositions for the US, 1948–2011.” Review of Keynesian Economics 5 (2): 196–217.10.4337/roke.2017.02.04Search in Google Scholar

Bhaduri, A. 2008. “On the Dynamics of Profit-Led and Wage-Led Growth.” Cambridge Journal of Economics 32 (1): 147–160.10.1093/cje/bem012Search in Google Scholar

Bhaduri, A., and S. Marglin. 1990. “Unemployment and the Real Wage Rate: The Economic Basis for Contesting Political Ideologies.” Cambridge Journal of Economics 14 (4): 375–393.10.1093/oxfordjournals.cje.a035141Search in Google Scholar

Blecker, R. A. 1989. “International Competition, Income Distribution and Economic Growth.” Cambridge Journal of Economics 13 (3): 395–412.Search in Google Scholar

Blecker, R. A. 2016. “Wage-Led Versus Profit-Led Demand Regimes: The Long and The Short of It.” Review of Keynesian Economics 4 (4): 373–390.10.4337/roke.2016.04.02Search in Google Scholar

Bowles, S., and R. Boyer. 1988. “Labor Discipline and Aggregate Demand: A Macroeconomic Model.” American Economic Review 78 (2): 395–400.Search in Google Scholar

Canry, N. 2005. “Wage-Led Regime, Profit-Led Regime and Cycles: A Model.” Économie Appliquée 58 (1): 143–163.10.3406/ecoap.2005.3749Search in Google Scholar

Chopin, N. 2002. “A Sequential Particle Filter Method for Static Models.” Biometrika 89 (3): 539–551.10.1093/biomet/89.3.539Search in Google Scholar

Chopin, N. 2004. “Central Limit Theorem for Sequential Monte Carlo Methods and Its Application to Bayesian Inference.” Annals of Statistics 32 (6): 2385–2411.10.1214/009053604000000698Search in Google Scholar

Chou, N.-T., A. Izyumov, and J. Vahaly. 2016. “Rates of Return on Capital Across the World: are They Converging?” Cambridge Journal of Economics 40 (4): 1149–1166.10.1093/cje/bev065Search in Google Scholar

David, P. A. 1991. Computer and Dynamo: The Modern Productivity Paradox in a Not-Too-Distant Mirror, in OECD, Technology and Productivity. The Challenge for Economic Policy. Paris: OECD.Search in Google Scholar

Dumenil, G., and D. Levy. 2001. “Periodizing Capitalism: Technology, Institutions and Relations of Production.” In Phases of Capitalism Development edited by R. Albritton, M. Itoh, R. Westra and A. Zuege, 141–162, London: Palgrave.10.1057/9781403900081_9Search in Google Scholar

Durham, G., and J. Geweke. 2014. “Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments.” Advances in Econometrics 34: 1–44.10.1108/S0731-905320140000034003Search in Google Scholar

Dutt, A. K. 1990. Growth, Distribution and Uneven Development. Cambridge: Cambridge University Press.Search in Google Scholar

Eugeni, S. 2016. “Global Imbalances in the XIX, XX and the XXI Centuries.” Economics Letters 145: 69–72.10.1016/j.econlet.2016.05.018Search in Google Scholar

Flaschel, P., and S. Luchtenberg. 2012. Roads to Social Capitalism. Theory, Evidence and Policy. Cheltenham: Edward Elgar.10.4337/9781781951392Search in Google Scholar

Flaschel, P., G. Groh, G. Kauermann, and T. Teuber. 2009. “The Classical Growth Cycle After Fifteen Years of New Observations.” In Mathematical Economics and the Dynamics of Capitalism, edited by, P. Flaschel and M. Landesmann. London: Routledge.Search in Google Scholar

Foley, D. K. 2003. “Endogenous Technical Change with Externalities in a Classical Growth Model.” Journal of Economic Behavior and Organization 52 (2): 167–189.10.1016/S0167-2681(03)00020-9Search in Google Scholar

Freeman, C. 1987. “Information Technology and the Change in Techno-Economic Paradigm.” In Technical Change and Full Employment, edited by, C. Freeman and L. Soete. Oxford: Basil Blackwell.Search in Google Scholar

Gilks, W. R., and C. Berzuini. 2001. “Following a Moving Target: Monte Carlo Inference for Dynamic Bayesian Models.” Journal of the Royal Statistical Society B 63 (1): 127–146.10.1111/1467-9868.00280Search in Google Scholar

Goldstein, J. P. 1996. “The Empirical Relevance of the Cyclical Profit Squeeze: a Reassertion.” Review of Radical Political Economics 28 (4): 55–92.10.1177/048661349602800403Search in Google Scholar

Goodwin, R. M. 1967. “A Growth Cycle.” In Socialism, Capitalism and Economic Growth: Essays Presented to Maurice Dobb, edited by, C. H. Feinstein. London: Cambridge University Press.Search in Google Scholar

Goodwin, R. M. 1986. “Swinging Along the Turnpike with von Neumann and Sraffa.” Cambridge Journal of Economics 10 (3): 203–210.10.1093/oxfordjournals.cje.a034995Search in Google Scholar

Goodwin, R. M., and L. F. Punzo. 1987. The Dynamics of a Capitalist Economy: A Multi-Sectoral Approach. Cambridge: Polity Press.Search in Google Scholar

Gordon, D. M. 1995. “Growth, Distribution, and the Rules of the Game: Social Structuralist Macro Foundations for a Democratic Economic Policy.” In Macroeconomic Policy after the Conservative Era, edited by, G. A. Epstein and H. A. Gintis. Cambridge: Cambridge University Press.Search in Google Scholar

Julius, A. J. 2005. “Steady-State Growth and Distribution with an Endogenous Direction of Technical Change.” Metroeconomica 56 (1): 101–125.10.1111/j.1467-999X.2005.00209.xSearch in Google Scholar

Kaldor, N. 1961. “Capital Accumulation and Economic Growth.” In The Theory of Capital, edited by F. A. Lutz and D. C. Hague, 177–222. New York, USA: St. Martins Press.10.1007/978-1-349-08452-4_10Search in Google Scholar

Kiefer, D., and C. Rada. 2015. “Profit Maximising Goes Global: The Race to the Bottom.” Cambridge Journal of Economics 39 (5): 1333–1350.10.1093/cje/beu040Search in Google Scholar

Kurz, H. D. 1990. “Technical Change, Growth and Distribution: A Steady-State Approach to ‘Unsteady’ Growth.” In Capital, Distribution and Effective Demand. Studies in the ‘Classical’ Approach to Economic Theory, edited by, H. D. Kurz. Cambridge: Polity Press.10.1007/978-1-349-10947-0_24Search in Google Scholar

Kurz, H. D. 1994. “Growth and Distribution.” Review of Political Economy 6 (4): 393–420.10.1080/09538259400000019Search in Google Scholar

Lavoie, M. 1995. “The Kaleckian Model of Growth and Distribution and its neo-Ricardian and neo-Marxian Critiques.” Cambridge Journal of Economics 19 (6): 789–818.10.4337/9781802206951.00008Search in Google Scholar

Lorenz, H.–W. 1989. Nonlinear Dynamical Economics and Chaotic Motion. Berlin: Springer-Verlag.10.1007/978-3-662-22233-1Search in Google Scholar

Marglin, S. A., and A. Bhaduri. 1988. “Profit Squeeze and Keynesian Theory.” World Institute for Development Economics Research of the United Nations University, Working Paper 39, April 1988.Search in Google Scholar

Mariolis, T. 2013. “Goodwin’s Growth Cycle Model with the Bhaduri-Marglin Accumulation Function.” Evolutionary and Institutional Economics Review 10 (1): 131–144.10.14441/eier.A2013008Search in Google Scholar

Mohun, S. 2009. “Aggregate Capital Productivity in the US Economy, 1964–2001.” Cambridge Journal of Economics 33 (5): 1023–1046.10.1093/cje/ben045Search in Google Scholar

Nikiforos, M., and D. K. Foley. 2012. “Distribution and Capacity Utilization: Conceptual Issues and Empirical Evidence.” Metroeconomica 63 (1): 200–229.10.1111/j.1467-999X.2011.04145.xSearch in Google Scholar

Rodousakis, N. 2014. “The Stability Properties of Goodwin’s Growth Cycle Model with a Variable Elasticity of Substitution Production Function.” Studies in Microeconomics 2 (2): 213–223.10.1177/2321022214545249Search in Google Scholar

Rodousakis, N. 2015. “Goodwin’s Growth Cycle Model with the Bhaduri-Marglin Accumulation Function: A Note on the C.E.S. Case.” Evolutionary and Institutional Economics Review 12 (1): 105–114.10.1007/s40844-015-0004-3Search in Google Scholar

Rodrik, D. 2011. The Globalization Paradox. Why Global Market, States and Democracy Can’t Coexist. Oxford: Oxford University Press.Search in Google Scholar

Rowthorn, B. 1981. “Demand, Real Wages and Economic Growth.” Thames Papers in Political Economy 3: 1–39.Search in Google Scholar

Samuelson, P. A. 1971. “Generalized Predator-Prey Oscillations in Ecological and Economic Equilibrium.” Proceedings of the National Academy of Sciences USA 68 (5): 980–983.10.1073/pnas.68.5.980Search in Google Scholar PubMed PubMed Central

Sasaki, H. 2013. “Cyclical Growth in a Goodwin-Kalecki-Marx Model.” Journal of Economics 108 (2): 145–171.10.1007/s00712-012-0278-4Search in Google Scholar

Shah, A., and M. Desai. 1981. “Growth Cycles with Induced Technical Change.” The Economic Journal 91 (364): 1006–1010.10.2307/2232506Search in Google Scholar

Skott, P. 2012. “Shortcomings of the Kaleckian Investment Function.” Metroeconomica 63 (1): 109–138.10.1111/j.1467-999X.2010.04111.xSearch in Google Scholar

Skov A. M. 2004. Oil and Gas Energy in US Economy, SPE Annual Technical Conference and Exhibition, 26–29 September, Houston, Texas. in Google Scholar

Sportelli, M. C. 1995. “A Kolmogoroff Generalized Predator-Prey Model of Goodwin’s Growth Cycle.” Journal of Economics 61 (1): 35–64.10.1007/BF01231483Search in Google Scholar

Stockhammer, E., and J. Michell. 2017. “Pseudo-Goodwin Cycles in a Minsky Model.” Cambridge Journal of Economics 41 (1): 105–125.10.1093/cje/bew008Search in Google Scholar

Tavani, D. 2012. “Wage Bargaining and Induced Technical Change in a Linear Economy: Model and Application to the US (1963–2003).” Structural Change and Economic Dynamics 23 (2): 117–126.10.1016/j.strueco.2011.11.001Search in Google Scholar

Tavani, D. 2013. “Bargaining Over Productivity and Wages when Technical Change is Induced: Implications for Growth, Distribution, and Employment.” Journal of Economics 109 (3): 207–244.10.1007/s00712-012-0287-3Search in Google Scholar

Tavani, D., and L. Zamparelli. 2015. “Endogenous Technical Change, Employment and Distribution in the Goodwin Model of the Growth Cycle.” Studies in Nonlinear Dynamics and Econometrics 19 (2): 209–226.10.1515/snde-2013-0117Search in Google Scholar

Tavani, D., and L. Zamparelli. 2017. “Endogenous Technical Change in Alternative Theories of Growth and Distribution.” Journal of Economic Surveys 31 (5): 1272–1303.10.1002/9781119483328.ch6Search in Google Scholar

Tavani, D., P. Flaschel, and L. Taylor. 2011. “Estimated Non-Linearities and Multiple Equilibria in a Model of Distributive-Demand Cycles.” International Review of Applied Economics 25 (5): 519–538.10.1080/02692171.2010.534441Search in Google Scholar

Veneziani, R. and S. Mohun. 2006. “Structural Stability and Goodwin’s Growth Cycle.” Structural Change and Economic Dynamics 17 (4): 437–451.10.1016/j.strueco.2006.08.003Search in Google Scholar

Vercelli, A. 1984. “Fluctuations and Growth: Keynes, Schumpeter, Marx and the Structural Instability of Capitalism.” In Nonlinear Models of Fluctuating Growth, edited by, R. M. Goodwin, M. Krüger and A. Vercelli. Berlin: Springer.10.1007/978-3-642-45572-8Search in Google Scholar

van der Ploeg, F. 1987. “Growth Cycles, Induced Technical Change, and Perpetual Conflict Over the Distribution of Income.” Journal of Macroeconomics 9 (1): 1–12.10.1016/S0164-0704(87)80002-2Search in Google Scholar

von Arnim, R., and J. Barrales. 2015. “Demand-Driven Goodwin Cycles with Kaldorian and Kaleckian Features.” Review of Keynesian Economics 3 (3): 351–373.10.4337/roke.2015.03.05Search in Google Scholar

von Arnim, R., D. Tavani, and L. Carvalho. 2014. “Redistribution in a Neo-Kaleckian Two-Country Model.” Metroeconomica 65 (3): 430–459.10.1111/meca.12047Search in Google Scholar

Wolff, E. N. 2006. “The Growth of Information Workers in the US Economy, 1950–2000: The Role of Technological Change, Computerization, and Structural Change.” Economic Systems Research 18 (3): 221–255.10.1080/09535310600844193Search in Google Scholar

Wolff, E. N. 2003. “What’s Behind the Rise in Profitability in the US in the 1980’s and in the 1990’s?” Cambridge Journal of Economics 27 (4): 479–499.10.1093/cje/27.4.479Search in Google Scholar

Zamparelli, L. 2015. “Induced Innovation, Endogenous Technical Change and Income Distribution in a Labor Constrained Model of Classical Growth.” Metroeconomica 66 (2): 243–262.10.1111/meca.12068Search in Google Scholar

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Published Online: 2018-07-03

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