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Econometric Aspects of Convergence: A Survey

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Abstract

The literature on convergence in per-capita income across countries has not converged on a common concept of convergence. It may be within a country towards its own steady state or between countries. Between country convergence may be absolute convergence to the same steady state; conditional convergence to country specific steady states, functions of observed variables; or club convergence to different steady states. It may be measured by beta convergence; sigma convergence; or the presence of a common trend. This paper surveys the econometric issues involved in estimating the rate of convergence; testing for convergence; and specifying the unobserved steady state. The survey suggests that rather than there being different ways to measure a single concept, convergence, the different measures are measuring different things.

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Data Availability

No datasets were generated or analysed during the current study.

Notes

  1. The focus of the distributional literature has been on whether there is bi-modality, "twin-peaks". However, the 2010 distribution presented by JP appears to show three modes, though this may be a product of the smoothing.

  2. For convenience, the intercept has here been included in the steady state, but this means that if \(\beta _{it}=0,\) the expected growth rate is zero, which is not a desirable feature.

  3. Sen thanks Frank Hahn, Robin Mathews, Luigi Pasinetti, Joan Robinson and Robert Solow for comments on an earlier draft of the introduction, saying "Their suggestions, often contradictory but always useful, have helped me a great deal to prepare the final version."

  4. This included a different Sato (1966).

References

  • Acemoglu D, Molina CA (2021). Converging to converge? a comment. NBER working paper 28992

  • Acemoglu D, Naidu S, Restrepo P, Robinson JA (2019) Democracy does cause growth. J Polit Econ 127:47–100

    Article  Google Scholar 

  • Barro RJ (1991) Economic growth in a cross section of countries. Quart J Econ 106:407–44

    Article  ADS  Google Scholar 

  • Barro RJ (2015) Convergence and modernisation. Econ J 125:911–942

    Article  Google Scholar 

  • Barro RJ, Sala-i-Martin X (1992) Convergence. J Polit Econ 100:223–251

    Article  Google Scholar 

  • Baumol WJ (1986) Productivity growth, convergence, and welfare: What the long-run data show. Am Econ Rev 76:1072–1085

    Google Scholar 

  • Baumol WJ, Wolff EN (1988) Productivity growth, convergence, and welfare: Reply. Am Econ Rev 78:1155–1159

    Google Scholar 

  • Bernard AB, Durlauf S (1995) Convergence in international output. J Appl Economet 10:97–108

    Article  Google Scholar 

  • Bernard AB, Durlauf S (1996) Interpreting tests of the convergence hypothesis. J Econ 71:161–73

    Article  MathSciNet  Google Scholar 

  • Bianchi M (1997) testing for convergence: Evidence from non-parametric multimodality tests. J Appl Economet 12:393–409

    Article  Google Scholar 

  • Chen S, Chernozhukov V, Fernández-Val I (2019) Mastering panel metrics: Causal impact of democracy on growth. AEA Papers and Proceedings 109:77–82

    Article  Google Scholar 

  • Christiano LJ, Eichenbaum M (1990) Unit roots in real GNP: Do we know and do we care? Carn Roch Conf Ser Public Policy 31:7–62

    Article  Google Scholar 

  • Chudik A, Pesaran MH (2015) Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors. J Econ 188:393–420

    Article  MathSciNet  Google Scholar 

  • DeLong JB (1988) Productivity growth, convergence, and welfare: Comment. Am Econ Rev 78:1138–54

    Google Scholar 

  • De Visscher S, Eberhardt M, Everaert G (2020) Estimating and testing the multicountry endogenous growth model. J Int Econ 125:1–13

    Article  Google Scholar 

  • Dube A, Girardi D, Jordà Ò, Taylor AM (2023) A local projections approach to difference-in-differences event studies. NBER Working Paper No. 31184

  • Durlauf S (2009) The rise and fall of cross country growth regressions. History of Political Economy 41(annual supplement)315-333

  • Fernández-Villaverde J, Ohanian LE, Yao W (2023) The neoclassical growth of China. NBER Working Paper 31351

  • Friedman M (1992) Do old fallacies ever die? J Econ Lit 30:2129–32

    Google Scholar 

  • Galor O (1996) Convergence? inferences from theoretical models. Econ J 106:1056–1069

    Article  Google Scholar 

  • Hahn FH, Matthews RCO (1964) The theory of economic growth: A survey. Econ J 74:779–902

    Article  Google Scholar 

  • Harrod RF (1939) An essay in dynamic theory. Econ J 49:14–33

    Article  Google Scholar 

  • Hayakawa K, Pesaran MH, Smith LV (2023) Short T dynamic panel data models with individual, time and interactive effects. J Appl Econ forthcoming

  • Im KS, Pesaran MH, Shin Y (2003) Testing for unit roots in heterogeneous panels. J Econ 115:53–74

    Article  MathSciNet  Google Scholar 

  • Johnson P, Papageorgiou C (2020) What remains of cross-country convergence. J Econ Lit 58:129–175

    Article  Google Scholar 

  • Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root. J Econ 54:159–178

    Article  Google Scholar 

  • Kremer M, Willis J, You Y (2022) Converging to convergence. NBER Macroecon Annu 36:337–412

    Article  Google Scholar 

  • Lee K, Pesaran MH, Smith RP (1997) Growth and convergence in a multi-country empirical stochastic Solow model. J Appl Economet 12:357–392

    Article  Google Scholar 

  • Lucas RE (1988) On the mehanics of economic development. J Monet Econ 22:3–42

    Article  Google Scholar 

  • Maddison A (1982) Phases of capitalist development. Oxford University Press, New York

    Google Scholar 

  • Mankiw NG, Romer D, Weil DN (1992) A contribution to the empirics of economic growth. Quart J Econ 107:407–37

    Article  Google Scholar 

  • Mountford A (2023) Economic growth analysis when balanced growth paths may be time varying. MPRA 119938

  • Müller UK, Stock JH, Watson MW (2022) An econometric model of international growth dynamics for long-horizon forecasting. Rev Econ Stat 104:857–876

    Article  Google Scholar 

  • Nickel S (1981) Biases in dynamic models with fixed effects. Econometrica 49:1417–1426

    Article  MathSciNet  Google Scholar 

  • Patel D, Sandefur J, Subramanian A (2021) The new era of unconditional convergence. J Dev Econ 152:102687

    Article  Google Scholar 

  • Pesaran MH (2006) Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74:967–1012

    Article  MathSciNet  Google Scholar 

  • Pesaran MH (2007a) A pair-wise approach to testing for output and growth convergence. J Econ 138:312–355

    Article  MathSciNet  Google Scholar 

  • Pesaran MH (2007b) A Simple panel unit root test in the presence of cross section dependence. J Appl Economet 22:265–312

    Article  MathSciNet  Google Scholar 

  • Pesaran MH, Shin Y, Smith RP (1999) Pooled mean group estimation of dynamic heterogeneous panels. J Am Stat Assoc 94:621–634

    Article  MathSciNet  Google Scholar 

  • Pesaran MH, Smith RP (1995) Estimation of long-run relationships from dynamic heterogeneous panels. J Econ 68:79–114

    Article  Google Scholar 

  • Pesaran MH, Smith RP, Yamataga T, Hvozdyk L (2009) Pairwise tests of purchasing power parity. Economet Rev 28:1–27

    Article  MathSciNet  Google Scholar 

  • Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75:335–346

    Article  MathSciNet  Google Scholar 

  • Phillips PCB, Sul D (2007) Bias in dynamic panel estimation with fixed effects incidental trends and cross-section dependence. J Econ 137:162–188

    Article  MathSciNet  Google Scholar 

  • Phillips PCB, Sul D (2009) Economic transition and growth. J Appl Economet 24:1153–85

    Article  MathSciNet  Google Scholar 

  • Prasad ES (2023) Has China’s growth gone from miracle to malady? NBER Working Paper 31151

  • Quah D (1993) Galton’s fallacy and tests of the convergence hypothesis. Scand J Econ 95:427–43

    Article  Google Scholar 

  • Quah D (1996) Empirics for economic growth and convergence. Eur Econ Rev 40:1353–75

    Article  Google Scholar 

  • Rodrik D (2013) Unconditional convergence in manufacturing. Quart J Econ 128:165–204

    Article  Google Scholar 

  • Romer PM (1986) Increasing returns and long-run growth. J Polit Econ 94:1002–37

    Article  Google Scholar 

  • Sala-i-Martin X (1997) I just ran four million regressions. NBER Working Paper 6252

  • Sato K (1966) On the adjustment time in neo-classical growth models. Rev Econ Stud 33:263–68

    Article  Google Scholar 

  • Sato R (1963) Fiscal policy in a neo-classical growth model: An analysis of time required for equilibrating adjustment. Rev Econ Stud 30:16–23

    Article  Google Scholar 

  • Sen A (ed) (1970) Growth Economics. Penguin modern economics readings, Penguin Books, Harmondsworth

  • Smith RP (2021) The Challenge of identification and the value of descriptive evidence, Chapter 35, p 917-940, of The Palgrave Handbook of Comparative Economics, Edited by Elodie Douarin and Oleh Havrylyshyn, Palgrave Macmillan

  • Solow RM (1956) A contribution to the theory of economic growth. Quart J Econ 70:65–94

    Article  Google Scholar 

  • Summers R, Heston A (1988) A new set of international comparisons of real product and price levels: Estimates for 130 countries. Rev Income Wealth 34:1–25

    Article  Google Scholar 

  • Sutton J (1997) Gibrat’s legacy. J Econ Lit 35:40–59

    Google Scholar 

  • Swan TW (1956) Economic growth and capital accumulation. Econ Rec 32:334–361

    Article  Google Scholar 

  • Weill L (2013) Bank competition in the EU: How has it evolved? J Int Finan Markets Inst Money 25:100–112

    Article  ADS  Google Scholar 

  • Westerlund J, Karabiyik H, Narayan PK, Narayan S (2022) Estimating the speed of adjustment of leverage in the presence of interactive effects. J Financ Economet 20:942–960

    Article  Google Scholar 

Download references

Acknowledgements

I am grateful to Kian Howe Ong for his encouragement in writing this paper and for useful comments from participants at a Nottinghan Ningbo workshop in September 2023 and from an anonymous referee.

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  1. Birkbeck. University of London, London, England

    Ron P. Smith

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Smith, R.P. Econometric Aspects of Convergence: A Survey. Open Econ Rev (2024). https://doi.org/10.1007/s11079-024-09753-w

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