Electronic Journal of Statistics

Innovation, growth and aggregate volatility from a Bayesian nonparametric perspective

Antonio Lijoi, Pietro Muliere, Igor Prünster, and Filippo Taddei

Full-text: Open access

Abstract

In this paper we consider the problem of uncertainty related to growth through innovations. We study a stylized, although rich, growth model, in which the stochastic innovations follow a Bayesian nonparametric model, and provide the full taxonomy of the asymptotic equilibria. In most cases the variability around the average aggregate behaviour does not vanish asymptotically: this requires to accompany usual macroeconomic mean predictions with some measure of uncertainty, which is readily yielded by the adopted Bayesian nonparametric approach. Moreover, we discover that the extent of the asymptotic variability is the result of the interaction between the rate at which the economy creates new sectors and the concavity of returns in sector specific technologies.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 2179-2203.

Dates
Received: November 2015
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1468954727

Digital Object Identifier
doi:10.1214/16-EJS1165

Mathematical Reviews number (MathSciNet)
MR3528712

Zentralblatt MATH identifier
1346.62060

Subjects
Primary: 62F15: Bayesian inference 60G57: Random measures 91B62: Growth models

Keywords
Bayesian nonparametrics aggregate volatility asymptotics economic growth Poisson-Dirichlet process

Citation

Lijoi, Antonio; Muliere, Pietro; Prünster, Igor; Taddei, Filippo. Innovation, growth and aggregate volatility from a Bayesian nonparametric perspective. Electron. J. Statist. 10 (2016), no. 2, 2179--2203. doi:10.1214/16-EJS1165. https://projecteuclid.org/euclid.ejs/1468954727


Export citation

References

  • [1] Acemoglu, D. (2009)., Introduction to Modern Economic Growth. Princeton University Press.
  • [2] Aghion, P. and Howitt, P. (1997). A Schumpeterian perspective on growth and competition. In, Advances in Economics and Econometrics (Kreps, D., ed.).
  • [3] Aoki, M. (2008). Thermodynamic limits of macroeconomic or financial models: one- and two-parameter Poisson-Dirichlet models., J. Econom. Dynam. Control 32, 66–84.
  • [4] Aoki, M. and Yoshikawa, H. (2012). Non–self–averaging in macroeconomic models: a criticism of modern micro–founded macroeconomics., J. Econ. Interact. Coord. 7, 1–22.
  • [5] Burda, M., Harding, M. and Hausman, J. (2008). A Bayesian mixed logit-probit model for multinomial choice., J. Econometrics 147, 232–246.
  • [6] Charalambides, C.A. (2005)., Combinatorial Methods in Discrete Distributions. Wiley, Hoboken, NJ.
  • [7] Cont, R. and Tankov, P. (2004)., Financial modelling with jump processes. Chapman & Hall/CRC, Boca Raton, FL.
  • [8] De Blasi, P., Favaro, S., Lijoi, A., Mena, R.H., Prünster, I. and Ruggiero, M. (2015). Are Gibbs-type priors the most natural generalization of the Dirichlet process?, IEEE Trans. Pattern Anal. Mach. Intell. 37, 212–229.
  • [9] De Blasi, P., James, L.F. and Lau, J.W. (2010). Bayesian nonparametric estimation and consistency of Mixed Multinomial Logit choice models., Bernoulli 16, 679–704.
  • [10] Devroye, L. (2009). Random variate generation for exponentially and polynomially tilted stable distributions., ACM Transactions on Modeling and Computer Simulation 19, N. 18.
  • [11] Ewens, W.J. (1972). The sampling theory of selectively neutral alleles., Theor. Popul. Biol. 3 87–112.
  • [12] Favaro, S., Lijoi A., Mena, R.H. and Prünster, I. (2009). Bayesian nonparametric inference for species variety with a two parameter Poisson-Dirichlet process prior., J. R. Stat. Soc. Ser. B 71, 993–1008.
  • [13] Ferguson, T.S. and Klass, M.J. (1972). A representation of independent increments processes without Gaussian components., Ann. Math. Statist. 43, 1634–1643.
  • [14] Ferguson, T.S. (1973). A Bayesian analysis of some nonparametric problems., Ann. Statist. 1, 209–230.
  • [15] Gancia, G. and Zilibotti, F. (2005). Horizontal Innovation in the Theory of Growth and Development. In, Handbook of Economic Growth (P. Aghion and S. Durlauf eds), vol. 1A, pp. 111–170, North Holland, Amsterdam.
  • [16] Gnedin, A. and Pitman, J. (2005). Exchangeable Gibbs partitions and Stirling triangles., Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 325, 83–102 (transl. in J. Math. Sci. (N.Y.) 138 (2006), 5674–5685).
  • [17] Griffin, J.E. (2011). The Ornstein-Uhlenbeck Dirichlet process and other time-varying processes for Bayesian nonparametric inference., J. Statist. Plann. Inference 141, 3648–3664.
  • [18] Griffin, J.E. and Steel, M.F.J. (2004). Semiparametric Bayesian inference for stochastic frontier models., J. Econometrics 123, 121–152.
  • [19] Griffin, J.E. and Steel, M.F.J. (2006). Order-based dependent Dirichlet processes., J. Amer. Statist. Assoc. 101, 179–194.
  • [20] Griffin, J.E. and Steel, M.F.J. (2011). Stick-Breaking Autoregressive Processes., J. Econometrics, 162, 383–396.
  • [21] Hirano, K. (2002). Semiparametric Bayesian inference in autoregressive panel data models., Econometrica 70, 781–799.
  • [22] Hjort, N.L., Holmes, C.C. Müller, P., Walker, S.G. (Eds.) (2010)., Bayesian Nonparametrics. Cambridge University Press, Cambridge.
  • [23] Lau, J.W. and Siu, T.K. (2008). On option pricing under a completely random measure via a generalized Esscher transform., Insurance Math. Econom. 43, 99–107.
  • [24] Lau, J.W. and Siu, T.K. (2008). Long-term investment returns via Bayesian infinite mixture time series models., Scand. Actuar. J. 4, 243–282.
  • [25] Lijoi, A., Mena, R.H. and Prünster, I. (2005). Hierarchical mixture modeling with normalized inverse-Gaussian priors., J. Amer. Statist. Assoc. 100, 1278–1291.
  • [26] Lijoi, A., Mena, R.H. and Prünster, I. (2007a). Controlling the reinforcement in Bayesian non-parametric mixture models., J. R. Stat. Soc. Ser. B 69, 715–740.
  • [27] Lijoi, A., Mena, R.H., and Prünster, I. (2007b). Bayesian nonparametric estimation of the probability of discovering a new species, Biometrika. 94 769–786.
  • [28] Lijoi, A., Prünster, I., and Walker, S.G. (2008). Bayesian nonparametric estimators derived from conditional Gibbs structures., Ann. Appl. Probab. 18, 1519–1547.
  • [29] Mena, R.H., Ruggiero, M. and Walker, S.G. (2011). Geometric stick-breaking processes for continuous-time Bayesian nonparametric modeling., J. Statist. Plann. Inference 141, 3217–3230.
  • [30] Mena, R.H. and Ruggiero, M. (2016). Dynamic density estimation with diffusive Dirichlet mixtures., Bernoulli 22, 901–926.
  • [31] Mena, R.H. and Walker, S.G. (2005). Stationary models via a Bayesian nonparametric approach., J. Time Ser. Anal. 26, 789–805.
  • [32] Pitman, J. (1995). Exchangeable and partially exchangeable random partitions., Probab. Theory Related Fields 102, 145–158.
  • [33] Pitman, J. (1996). Some developments of the Blackwell-MacQueen urn scheme., Statistics, probability and game theory. Papers in honor of David Blackwell (T.S. Ferguson, L.S. Shapley and J.B. MacQueen eds.), 245–267, IMS Lecture Notes Monogr. Ser., Hayward, CA.
  • [34] Pitman, J. (2006)., Combinatorial stochastic processes. Ecole d’Eté de Probabilités de Saint-Flour XXXII. Lecture Notes in Mathematics N. 1875. Springer, New York.
  • [35] Prünster, I. and Ruggiero, M. (2013). A Bayesian nonparametric approach to modeling market share dynamics., Bernoulli 19, 64–92.
  • [36] Romer, P. (1990). Endogeneous technological change., J. Politic. Econ. 98, S71–S102.
  • [37] Rosiński, J. (2007). Tempering stable processes., Stochastic Process. Appl. 117, 677–707.
  • [38] Solow, R. (1956). A contribution to the theory of economic growth., Quarterly Journal of Economics 70, 65–94.
  • [39] Yamato, H. and Sibuya, M. (2000). Moments of some statistics of Pitman sampling formula., Bull. Inform. Cybernet. 32, 1–10.