Market consumption and hidden consumption. A test for substitutability

Abstract

In this paper an empirical analysis is performed on the relationship between private consumption and underground economy for the Italian case. It is found that private market consumption and underground (or hidden) consumption may be defined as ‘complementary goods’: an increase in underground consumption tends to increase family market consumption and increase its marginal utility. An implication of this result is that the nonmarket sector does not offer hedging opportunities to the consumer-worker as stressed by Busato and Chiarini's (2004) artificial economy. Moreover, wealth effects associated with a change in underground consumption are negative. A statistical model confirms this structural interpretation.

Notes

¹ Here, we refer to those activities which are not taxed or registered. There exists a vast literature on this issue. See also Thomas (1992), Feige (1994), Lubell (1991), and the papers in The Economic Journal symposium (1999) among others. The methods of estimating the size of the underground economy have recently been surveyed by Schneider and Enste (2000). For some interesting criticisms, based on stationarity issues, of the monetary macroeconomic estimates of the underground economy see also Atkins (1999).

² The relationship between measured regular output and underground output over the business cycle has been investigated using econometric techniques similar to those adopted in this paper for the consumption series. Several interesting issues have been pointed out by Giles (1999) and Giles et al. (2002).

³ In the subsequent econometric analysis we will assume that the underground economy only produces consumption goods, and, mostly, that underground revenues are only employed to buy consumption goods. The consequence is that underground consumption can be either defined as consumption goods produced in the underground sector or as consumption goods which are bought using underground revenue.

⁴ We follow Barro (1989) and Christiano and Eichenbaum (1992) who define a relationship between consumption services and public consumption, and generalize the expected lifetime utility function (1) adding an extra-term where φ is a concave function. With , the consumer does not necessarily feel worse off when is increased. Notice that enters separably in (1) and, therefore, this term has no bearing on consumers' choices of consumption: is modelled as an exogenous variable. See also Aschauer (1985) and Karras (1994).

⁵ Here ϕ (.) is the linearly homogeneous aggregator of the two consumption goods.

⁶ See also Bovi and Castellucci (1998). Two additional methods for estimating the underground economy based on the labour market statistics are reported in Castellucci and Bovi (1999). Chiarini and Marzano (2004) estimate a time series using a modified version of the Tanzi's approach, in which the characteristics of nonstationarity of the basic series are exploited through cointegration techniques to generate a quarterly estimation of the Italian size of the underground economy (1975–1999). Some of the results of this paper are confirmed using these last series.

⁷ In general, the lack of micro-data on the features of the underground economy is a well-known problem, and very few studies are available (see for instance Lemieux et al. 1994; Fortin et al. 2000.).

⁸ See Schneider and Enste (2000) and the works quoted therein. A recent empirical investigation for North Cyprus (Besim and Jenkins, 2005) also estimates the size of the underreported income through data on the household consumption expenditure.

⁹ The ADF test for Private Consumption is −2.17 whereas, for the Underground Consumption data, the ADF statistic is −1.1348. Critical values at 1% and 5% are, respectively, −3.72 and −2.985.

¹⁰ See, among others, Davidson and MacKinnon (1993).

¹¹ Regressions with quarterly data estimated by Chiarini and Marzano (2004) produce a negative range of estimates for λ, between 0.2 and 0.6, even though they are less reliable due to rejection of the null hypothesis of normally distributed errors.

¹² See the papers in Gallie and Paugam (2000) and the works quoted therein.

¹³ Maximum likelihood assumes that the errors are multivariate normal. The Jarque–Bera statistic does not reject the hypothesis of normal distribution for the two equations of the model: for the equation the statistic is 0.262, with a p-values of 0.877 (with a kurtosis value of 3.2) while for the equation, the JB is 0.29 (0.864) and the kurtosis value is 2.62. The first equation yields an adjusted R ² = 0.855 and a standard error of regression S.E. = 0.029. The second equation yields, respectively, R ² = 0.811 and S.E. = 0.081.

¹⁴ As a consequence of the unit root in the model the impulse response function does not return to zero. The estimated responses of private consumption in first differences taper off to their initial level. See Lutkepohl (1993).

¹⁵ Notice that wealth may fall and utility may rise because of the φ (.) term. See footnote 4 and Barro (1989).

¹⁶ For this issue, see for instance, Cochrane (1991).