Wagner’s law versus displacement effect

ABSTRACT

The public sector has grown dramatically over the past few centuries in many developed countries. In this article, we use wavelet methods to distinguish between two leading explanations for this growth – Wagner’s law and the displacement effect. In doing so, we use the long-term data of 10 OECD countries for a maximum time span of 1800–2009. We find that the validity of Wagner’s law is likely to vary strongly over time for each country. A roughly similar feature in most of the countries is that the law is less valid in the earliest stage of economic development as well as in the advanced stages, with the validity tending to follow an inverted U-shaped pattern with economic development. Further, our results indicate that the long-run growth of government size cannot be adequately explained by Wagner’s law. On the other hand, the displacement effect appears to account for the bulk of the growth in most of the countries.

KEYWORDS:

• Size of public sector
• Wagner’s law
• economic development
• displacement effect
• wavelet

JEL CLASSIFICATIONS:

• E62
• H50
• N40

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Erratum

Acknowledgement

I would like to thank an anonymous referee, David Peel (the editor), and Kazuki Hiraga for their constructive comments that helped me improve the article. The usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ For example, trade openness, country size, ethnic fragmentation and income inequality are the other leading factors or determinants of government size. See, for example, Meltzer and Richard (1981), North and Wallis (1982) and Shelton (2007) for a detailed survey of the other leading hypotheses.

² The law was initially tested by Lall (1969) and then analysed by Mann (1980), Singh and Sahni (1984), and Abizadeh and Gray (1985). See, for example, Thornton (1999) for results of Europe, Iyare and Lorde (2004) for Caribbean countries and Akitoby et al. (2006) for the developing countries. Chow, Cotsomitis, and Kwan (2002) suggest that controlling for the effects of money supply is crucial for the validity of Wagner’s law. Brückner, Chong, and Gradstein (2012) use oil price shocks as an instrument variable and estimate the permanent income elasticity of government expenditure. While most earlier studies use national-level data, an exception is Narayan, Rath, and Narayan (2012), who investigate the law for Indian states.

³ Compared with the Wagner’s law literature, few studies, for example, Goff (1998) and Legrenzi (2004), test the displacement effect.

⁴ To test the law, Lamartina and Zaghini (2011), Durevall and Henrekson (2011), Kuckuck (2014), and many others adopt some cointegration analysis methods. Formal structural break tests using the cointegration approach require a certain sample size and might overlook minute breaks that occur frequently. On the other hand, our wavelet approach allows for a local time-varying relationship between government size and economic development and can detect breaks even if they repeat frequently. Kuckuck (2014) examines the structural changes of the law for previously divided subsample periods with each country’s stage of economic development, but we try to endogenously detect structural changes if any.

⁵ See, for example, Durevall and Henrekson (2011) for why this specification appears proper when testing the law.

⁶ The former data can be found on the website of International Monetary Fund (https://www.imf.org/external/pubs/cat/longres.aspx?sk=40222.0), and the latter, on Robert Barro’s website (http://rbarro.com/data-sets/).

⁷ Lall (1969) also focuses on development stages. While Kuckuck (2014) and this study rely on time series data, Lall (1969) analyses the cross-sectional 1962–1964 averages data for 46 developing countries using per capita GNP to divide the countries into three income groups.

⁸ Christiano and Fitzgerald (2003) and others consider business cycle frequencies as between 1.5 and 8 years. Hence, we define lower frequencies as long-run frequencies.

⁹ This is consistent with the findings of Chang, Liu, and Caudill (2004), who examine the causal relationship between income and government spending over the period 1951–1996 in Australia but find no evidence in favour of the law. As pointed out by Lamartina and Zaghini (2011) and Kuckuck (2014), such a structural change in phase difference indicates that the validity of the law is weakened in the advanced stage of development in Australia as well.

¹⁰ The results are consistent with Chang, Liu, and Caudill (2004), who examine the relationship between income and public expenditure in Canada for the more recent period from 1951 to 1996 and find no evidence of the law. On the other hand, our results do not support the findings of Ahsan, Kwan, and Sahni (1996), who limit the period to 1953–1988 and find that the law is valid in Canada. However, as stated by Chang, Liu, and Caudill (2004), this finding could be due to the fewer samples observed, and seems open to question.

¹¹ Our outcomes support Kuckuck’s (2014) findings of weak evidence of the law in the high income stage and provide more detailed description on the following aspects. First, our findings roughly support the law in the upper middle income stage (from 1908 to 1968), as suggested in Kuckuck (2014), and show that the validity changes over time even within the upper middle income stage in a precise sense. That is, from the present endogenously detected time span, the law is validated not from 1908, but from 1930. Second, weak evidence of the law is indicated not only in the high income stage, but also before 1930 and in the lower middle income stage.

¹² These results for the 8–16-year frequency band are important to understand Kuckuck’s (2014) indication that Wagner’s law is less validated in the high income stage from 1978.

¹³ These results support the well-cited paper of Mann (1980), who tests Wagner’s law for Mexico over a maximum period, from 1925 to 1976. As far as the Musgrave version is concerned (using GY and PCY), Mann provides stronger evidence of the law in the subsample period from 1941 to 1976 than for the full sample from 1925 to 1976. Considering the structural change around 1940, as mentioned earlier in the article, we can understand Mann’s findings. Moreover, Iniguez-Montiel (2010) suggests that the law is valid for more recent times from 1950 to 1999. This is consistent with our findings indicating strong validity of the law after the mid-1960s.

¹⁴ In addition to Kuckuck’s (2014) indication that Wagner’s law is less validated in the high income stage from 1969, the validity is also weak in the first half of the nineteenth century. This is consistent with Durevall and Henrekson (2011), who analyse long-term data from the early nineteenth century and find that the law holds only between roughly 1860 and the mid-1970s.

¹⁵ These findings support the positive evidence provided by Gyles (1991), Oxley (1994), Chang (2002) and Chang, Liu, and Caudill (2004), all of them using observations included in the upper middle income stage. We also confirm that Wagner’s law is less validated in the high income stage from 1973, as indicated in Kuckuck (2014), and find that the validity is also weak in the lower middle income stage. While our results agree with Durevall and Henrekson (2011) findings, which show that the law holds between roughly 1860 and the mid-1970s, we can extract more detailed evidence from the coherency. That is, the significant region of the coherency suggests that the law is particularly validated in more local periods spanning from the mid-1890s until 1960. This region spreads throughout the 8–32-year frequency band.

¹⁶ These results support the findings of Islam (2001), who limits the period to 1929–1996 and finds positive evidence of the law. During a large part of this period, the phase difference for the 8–16-year frequency band is between $-\pi /2$ and 0, and the effects are reflected in Islam’s results. However, our results also suggest the possibility that the time period covered by Islam leads to failure of the appropriate test. That is, the selected period includes a structural break around 1970 and picking a subsample that ends in 1970 seems appropriate for Islam’s analysis.