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Money demand and the shadow economy: empirical evidence from OECD countries

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Abstract

In this article, we analyze whether shadow economic activity has had a measurable influence on the demand for M1 and currency in a cross section of OECD countries since the 1970s. Since shadow economic activity is not directly observable, we use several indicator variables that are positively related to shadow economic activity. We find that, indeed, some of these variables have had a significant influence on M1 money and currency demand in OECD countries over the last decades. Our results indicate that the omission of unofficial activities leads to a considerable overestimation of the income elasticity and the interest semi-elasticity of M1 and currency demand. Measuring accurately the size of shadow economic activity is therefore an important task for central banks to determine the optimal stock of money.

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Notes

  1. Notice, for example, that in Germany (Spain), in 2010, the weight of currency in M1 was 33.7 % (25.4 %), and in M2, it was 19.6 % (15.8 %).

  2. However, in the empirical part of the paper, we allow for a more general nonlinear relationship between non-observed income and the indicator variables.

  3. In accordance with the measurement of the variables \(y\), \(r\), and \(\pi \), we will measure these indicators either in natural logarithms or as percentage shares such that the parameter estimates can be interpreted as elasticities or semi-elasticities, respectively.

  4. Notice that \( log(1+s)=s+O(s^{2})\) for \(|s|<1\). As the size of the shadow economy is supposed to be lower than official GDP, \(|s|<1\) is fulfilled in our case.

  5. Our country selection is determined by data availability for the time period and variables under study.

  6. Other indicators of shadow economic activity that display few time variation and that are commonly used to explain country-specific shadow economy quotes, as for example tax moral, do not deserve explicit consideration in the analysis since they are likely captured by the country fixed effects.

  7. We have tested the null hypothesis of no-cointegration in balanced panels excluding the variables TAX and SELF. The evidence in favor of cointegration is uniformly strong when using the residual-based approach in Kao (1999). Applying residual-based tests as introduced in (Pedroni 1999, 2004), the null hypothesis of no- cointegration cannot be rejected with conventional significance. ECM- based cointegration tests (Westerlund 2007) obtain mixed results on significant error-correction dynamics and hence mirror the sluggish speed of adjustment that we will discuss below in Sect. 5. Interestingly, aggregating the p values of country-specific ML-based cointegration diagnostics (Johansen 1991) by means of the Fisher criterion hints at the presence of multiple equilibria. From an economic perspective, the variables in our system might be used to formalize the stationarity of the real interest rate, or some implicit relation between indicators of unofficial economic activity and the real GDP. In light of scarce sample information, we refrain from analyzing a cross section of vector systems.

    Table 2 Unit root diagnostics for level data and first differences. The considered test statistics are the homogeneous panel unit root test proposed by Levin et al. (2002). Moreover, tests against the heterogeneous alternative introduced by Im et al. (2003) and Fisher tests (see Maddala and Wu (1999)) are shown with \(p\) values in parentheses.
    Full size table

  8. Unit root diagnostics indicate that most time series considered can be regarded as integrated of order one, i.e., stationary after taking first differences.

  9. We use the optimum routine as implemented in Gauss. The numerical optimization is initiated with estimation results obtained from static regressions. To check alternative estimation outcomes for distinct initial settings, we multiply the static regression estimates with independent Gaussian random variables with mean 1 and standard error 0.1. Then, we run 10,000 optimizations and report results for the most favorable outcomes in terms of overall maximization of the concentrated log-likelihood function.

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Acknowledgments

We are grateful to the constructive comments obtained from three anonymous referees. We thank Yabibal M. Walle for the provision of ECM-based cointegration tests. Bernd Theilen and Jordi Sardà acknowledge financial support from the Spanish ‘Ministerio de Ciencia e Innovación’ under Project ECO2013-42884-P.

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Authors and Affiliations

  1. Department of Economics, Georg-August-University Göttingen, Göttingen, Germany

    Helmut Herwartz

  2. Departament d’Economia and CREIP, Universitat Rovira i Virgili, Tarragona, Spain

    Jordi Sardà & Bernd Theilen

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  1. Helmut Herwartz
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  2. Jordi Sardà
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Correspondence to Bernd Theilen.

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Herwartz, H., Sardà, J. & Theilen, B. Money demand and the shadow economy: empirical evidence from OECD countries. Empir Econ 50, 1627–1645 (2016). https://doi.org/10.1007/s00181-015-0970-7

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