DO COUNTRIES CONVERGE TO THEIR STEADY STATES AT DIFFERENT RATES?��Kian Ong�University of Nottingham Ningbo China

Dec 7^th, 2023

9^th WAMS, Asia School of Business, KL

NO CONSENSUS ON A DEFINITION OF CONVERGENCE IN INCOME

• Neoclassical growth model predicts economic convergence (in GDP per person) because poor countries catch up and rich countries slow down
• Unconditional convergence since the 2000s

- “[d]ocument a trend towards unconditional convergence since 1990 and convergence since 2000, driven by both faster catch-up growth and slower growth of the frontier.” (Kremer, Willis and You, 2022)

• Conditional convergence with fixed effects

- “[o]ur reanalysis finds that these results are driven by the lack of country fixed effects controlling for unobserved determinants of GDP per capita across countries. We show theoretically and empirically that failure to include country fixed effects will create a bias in convergence coefficients towards zero.” (Acemoglu and Molina, 2022)

• Two percent iron law of convergence (Barro, 2015)

- “In a country panel since 1960, the estimated annual convergence rate for GDP is 1.7%, conditional on time-varying explanatory variables. With country fixed effects, the estimated convergence rate is misleadingly high. With data starting in 1870, country fixed effects are reasonable and the estimated convergence rate is 2.6%. Combining the two estimates suggests conditional convergence close to the ‘iron-law’ rate of 2%.”

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NO CONSENSUS ON A DEFINITION OF CONVERGENCE IN INCOME

• We expect economic convergence (in GDP per person) from theory

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• Unconditional convergence since the 2000s

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• Conditional convergence with fixed effects

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• Two percent iron law of convergence (Barro, 2015)

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• This paper questions whether convergence rates differ across countries

- Using GDP per capita for 108 countries over 58 years (1960-2017), the Bayesian Information Criteria selects the heterogeneous model where countries converge to their steady states—a function of the U.S.—at different rates. This is also true for a shorter span (1990-2017).

- We show empirically that failure to allow for heterogeneous rates of convergence will create a bias in convergence coefficients towards zero. 

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WE DO NOT KNOW THE DATA-GENERATING PROCESS, DIFFERENT APPROACHES POSING DIFFERENT QUESTIONS

• The lack of data in growth and convergence means that the data generating processes is generally not visible suggesting that the true value is unknown. 

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• Smith (2023) suggests different econometric approaches measure different parameters which helps to think about convergence.

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• Kremer et al. (2022) and Acemoglu and Molina (2022) rely on data spanning several decades, Müller et al. (2022, p.1) similarly rely on data, spanning more than a century, concluding that “growth paths exhibit very wide uncertainty”. 

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• The evidence on balance fails to disclose the data-generating process even when we have more information. There is no way of knowing which model of convergence is correct. 

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WHAT WE DO

• Start from a heterogeneous model / linear adjustment model (Smith, 2023), allowing both convergence and long-run elasticity to the steady state to be heterogeneous across countries.
• We use Bayesian Information Criteria (model fit vs. parameters) to consider models where:  
• The steady states are the U.S., the world average and country-specific trends.
• The degree of heterogeneity of convergence paths varies from the mean group, pooled mean group, fixed effects and the pooled models.
• We compare convergence in incomes with convergence in growth.
• We also compare with the case of no convergence: growth is an independent process.

MAIN FINDINGS

• The evidence for heterogeneous rates of convergence is strong in full- and short-span.

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• We use the U.S. as the steady state countries are converging to. The data prefers the heterogeneous model where the long-run elasticities to the U.S. and convergence rates differ across countries. 

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• Acemoglu and Molina (2022) argue that convergence biases towards zero in the absence of fixed effects. We show that the fixed effects estimator is also biased towards zero because countries are restricted to converge at the same rate. This bias is present in full- and short-span data.

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• The long-run elasticity to the U.S.—another parameter of interest—associates positively (0.79) with countries’ average growth. Countries that learn from the technological frontier also grow faster.

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OVERVIEW

1. DATA
2. THE HETEROGENEOUS MODEL AND MODELS CONSIDERED
3. RESULTS
4. CONCLUSION

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HETEROGENOUS MODEL

HETEROGENOUS MODEL

BAYESIAN INFORMATION CRITERION

RESULTS

1. WHAT DEGREE OF HETEROGENEITY?
2. NO CONVERGENCE?
3. DO THE LONG-RUN ELASTICITIES DIFFER FROM ONE?
4. DOES GLOBAL GROWTH DRIVE COUNTRIES’ GROWTH?
5. WHICH COUNTRIES CONVERGE TO THE U.S.? CHALLENGE THE IRON LAW OF CONVERGENCE
6. DO THE LONG-RUN ELASTICITIES TO THE U.S. DIFFER FROM ONE?

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2 WHAT DEGREE OF HETEROGENEITY?

The mean group is the best regardless of the steady state.

4 NO CONVERGENCE?

We extend Acemoglu and Molina’s argument by showing convergence biases towards zero relative to the homogeneous estimates of convergence.

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7 WHICH COUNTRIES CONVERGE TO THE U.S.? �

Convergence rates differ across countries, with some divergences. Challenge the iron law of convergence.

9 DO THE LONG-RUN ELASTICITIES DIFFER FROM ONE?

This shows why the data prefers the mean group over the pooled mean group models.

The correlation is 0.79 for 93 countries when we exclude 15 countries that either diverge or nearly do not converge.

11 COUNTRIES ARE CONVERGING TO A STEADY STATE THAT DIVERGES FROM THE U.S.

CONCLUSIONS

Renewed interest in convergence (Kremer et al., 2022), but no consensus on a definition of convergence.

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We proceed on the basis that we do not know the data-generating process, and different estimators measure different convergence concepts. 

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Do countries converge to their steady states at different rates?

Systematic investigation where we use BIC for the model selection

• Stronger evidence for convergence in growth than convergence in income in full-span, and the reverse is true in the short-span
• Convergence in levels: the evidence for heterogeneous rates of convergence is strong.

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CONCLUSIONS

Implications for convergence regressions

• Whilst Acemoglu and Molina (2022) argue against the pooled estimator of convergence, this paper argues against the fixed effects estimator of convergence. Where does the bias come from? Not all countries converge. And the rates are different. This is known as the heterogeneity bias. 

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Implications for economic theory

• The evidence for heterogeneous rates of convergence is strong. We use the same data as Kremer et al. and Acemoglu and Molina. This corroborates the study by Müller et al. (2022). This stylised fact challenges the iron law of convergence and corroborates growth models that explain heterogeneous convergence across countries. In the multi-country technological catch-up model, countries that learn from the technological frontier grow faster.

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Thank you for your attention

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NEXT STEPS

• The main focus of this paper is on unconditional convergence, which gives a big data set. Adding covariates reduces the data set.
• The choice of steady state: non-convergence to the U.S. is consistent with converging to something else.
• Müller, Stock, and Watson (2022 p858) highlight five features of the data apparent from a panel of 113 countries, 1900-2017, which echo previous findings. There is:
• "a common growth factor,
• persistent changes in long-term growth rates within countries,
• a temporally stable dispersion of the historical cross-sectional distribution,
• extremely persistent country-specific effects, and
• a possible group structure of cross-country correlations."

1 CONVERGENCE IN GROWTH OR INCOME?

3 WHICH STEADY STATE?

It is unclear, but we choose the U.S. as the steady state because it is the economic frontier.

5 DO THE LONG-RUN ELASTICITIES DIFFER FROM ONE?

6 DOES GLOBAL GROWTH DRIVE COUNTRIES’ GROWTH?

8 ARE WE SURE THAT THERE IS CONVERGENCE TO THE U.S.?

10 ARE WE SURE THAT THE LONG-RUN ELASTICITIES DIFFER FROM ONE?

11 COUNTRIES ARE CONVERGING TO A STEADY STATE THAT DIVERGES FROM THE U.S.

12 FULL- vs. SHORT-SPAN DATA