On Estimating the Size of the Shadow Economy

As long as it is employed cautiously enough, the model approach is a useful tool to estimate simultaneously the size and the development of the shadow economy in several countries. However, a second method is necessary to calibrate the model. The currency demand approach can lead to highly implausible results; the size of the shadow economy might be largely overestimated. An alternative is the survey method. For real tests of whether a variable has an impact, procedures are necessary that do not use the same variables as those used to construct the indicator. Thus, to make progress in analysing the shadow economy, the model approach has a role to play, but it has to be complemented by other methods employing different data. The currency demand approach cannot be used as long as it employs the same variables for its constructions.     

Estimation of the greenhouse gas externality with uncertainty

The shadow price of carbon dioxide is the value of the external damage caused by an emission. A shadow price model for calculating the present value of the external damage of a carbon dioxide emission is derived explicitly. Sixteen experts provided subjective high, low and most likely parameter estimates because correct values for the eight model parameters are uncertain. The estimation procedure retains parameter uncertainty while generating the main result, which is a distribution of shadow price estimates. Major assumptions made in the estimation identify the basis for the results. Of the eight model parameters, the discount rate dominates the determination of the shadow price. For comparison, expert estimates of the shadow price itself provide a second distribution of shadow price estimates.     

Measuring the size and dynamics of U.S. state-level shadow economies using a dynamic general equilibrium model with trends

We use a two-sector dynamic deterministic general equilibrium model that specifically accounts for trends among time-series variables to estimate the size of the shadow economy for the 50 U.S. states from 1999 to 2019, following Solis-Garcia and Xie (2018, 2022). This paper improves on existing measures of the state-level shadow economy (such as the multiple indicators, multiple causes (MIMIC) methodology by Wiseman (2013a)). In particular, this new measure is based on theoretical foundations, extends the previous measure to include the Great Recession, includes dollar value estimates of the shadow economy, and produces considerably more variation over time and across states. Furthermore, we explore determinants of this new shadow economy measure using a panel vector autoregressive model and find that, on average, states with higher levels of economic freedom, lower regulatory barriers, and larger real GDP have smaller shadow economies. States with bigger governments, on average, have larger shadow economies, and the effect of corruption on shadow economic activity is non-linear, with a positive initial and subsequent negative impact.     

Improvement of a Bio-Economic Mathematical Programming Model in the Case of On-Farm Source Inputs and Outputs

We present a two-step process for solving nonlinear farm activity models inside a linear framework under the assumption that market prices approximate the shadow prices of the model’s constraints. In the event of market imperfections or missing prices (for example non-marketed outputs), the previous assumption is not justified and the derived solution is not optimal. To circumvent this problem and to avoid nonlinear algorithms that may prove unwieldy for large models, we propose an iterative computation method, based on the re-estimation of shadow prices in each step until a converging solution is found. The method is applied to the bio-economic model AROPAj, which consists of a number of linear programming (LP) farm sub-models representing different farming systems across the European Union. For most of LPs producing non-marketed outputs a converging solution is obtained in two iterations, while the remaining LPs lead to periodic solutions of very low amplitude.

     

Shadow prices of $$\hbox {CO}_{2}$$ emissions at US electric utilities: a random-coefficient,random-directional-vector directional output distance function approach

We estimate the shadow prices of \(\hbox {CO}_{2}\) emissions of electric utilities in the US over the period from 2001 to 2014, using a random-coefficient, random-directional-vector directional output distance function (DODF) model. The main feature of this model is that both its coefficients and directional vector are allowed to vary across firms, thus allowing different firms to have different production technologies and to follow different growth paths. Our Bayes factor analysis indicates that this model is strongly favored over the commonly used fixed-coefficient DODF model. Our results obtained from this model suggest that the average annual shadow price of \(\hbox {CO}_{2}\) emissions ranges from $61.62 to $105.72 (in 2001 dollars) with an average of $83.12. The results also suggest that the firm-specific average shadow price differs significantly across electric utilities. In addition, our estimates of the shadow price of \(\hbox {CO}_{2}\) emissions show an upward trend for both the sample electric utilities as a whole and the majority of the individual sample electric utilities.     

Valuing environmental factors in cost-benefit analysis using data envelopment analysis

Environmental cost-benefit analysis (ECBA) is used for the social evaluation of investment projects and policies that involve significant environmental impacts. Economic valuation of environmental impacts forms one of the critical steps of ECBA. We develop a new method for this purpose, which does not require price estimation for environmental impacts using stated or revealed preference methods. Our approach is based on data envelopment analysis (DEA), which is modified to ECBA by using absolute shadow prices instead of relative prices. We also discuss how the method can be used for sensitive analysis in ECBA. We illustrate the method by means of a hypothetical numerical example.     

Shadow pricing of labour and capital in an economy with unemployed labour

This paper derives the shadow prices of labour and capital to be used in the public sector in a situation of unemployment. The setting considered is that of a three-good, two-period general equilibrium model. Then shadow prices are compared to their corresponding market prices and shown to closely depend on own and cross-elasticities of supply and demand for labour and investment. In the first part, a rigid wage rate is the sole source of distortion; then, a tax on capital income is introduced so that our formula for the social rate of discount can be contrasted with that of Harberger, Sandmo and Drèze.     

Estimating the size of the shadow economy in Spain: a structural model with latent variables

There has recently been a revival of international interest in measuring the size of the shadow economy. The current study adopts an approach to the Spanish case that is based on the theory of unobservable variables. This methodology involves the estimation of structural models (MIMIC) which analyses a set of causes of the shadow economy while simultaneously taking into account its influence upon a series of indicators. The proposed model permits the determination of a relative evolution over time of the size of the shadow economy, which requires the calibration of the model with an exogenous estimation in order to obtain real values. The exogenous estimation employed is that obtained by a monetary method based on a money demand function. The results show a considerable shadow economy, measuring between 8 and 18.8% of GDP in the period 1976–2002, and demonstrate that the shadow economy is significantly influenced by the tax burden, the degree of regulation and unit labour costs. A positive correlation is obtained between GDP, money demand and the level of the shadow economy.     

Financial development and the shadow economy: A panel VAR analysis

This paper examines the dynamic relationship between financial development and the shadow economy using data for 161 countries over the period 1960–2009. Specifically, we use a panel vector autoregression model to construct impulse response functions that illustrate the time path of one variable (e.g., the shadow economy) following an orthogonal shock to another variable (e.g., financial development). We find that financial development reduces the size of the shadow economy. Moreover, there is some evidence of reverse causality between these variables; namely, a shock to shadow economy inhibits financial development.     

The Shadow Economy in German Regions: An Empirical Assessment

Despite the increasing number of contributions to the literature, regional variations of the shadow economy have been hardly studied. This article analyses the determinants and derives the size of the shadow economy on the district level in Germany. I find that an inferior local labour market and the burden of taxation significantly contribute to the existence of the shadow economy, while a better enforcement of tax rules and regulations has the potential to deter such activities. Districts in the affluent south of Germany experience on average smaller shadow economies.     

Do the catholic and protestant countries differ by their tax morale?

Does the tax morale differ between various countries? The paper introduces a model of tax evasion. The equilibrium shadow production is determined by consumers’ and entrepreneurs’ tax morale, affected by the inherited culture or religion. The model suggests that in the conditions of the prisoners’ dilemma, shadow economies tend to be large once a moral code is violated. The implications of the model are tested in the OECD data on groups of countries with different religious denominations in two regimes, 1979–1992 and 1992–2003. We find evidence on a link between tax morale and shadow market activities, but none to support the view that tax morale differs between the catholic south and protestant north in Europe.     

US shadow economies: a state-level study

Recent studies of shadow economies focus primarily on cross-country comparisons. Few have examined regional or state-level variations in underground economic activity. This paper presents estimates of the shadow economy for 50 US states over the period 1997–2008. Results suggest that tax and social welfare burdens, labor market regulations, and intensity of regulation enforcement are important determinants of the underground economy. Among the states, Delaware, on average, maintains the smallest shadow economy at 7.28 % of GDP; Oregon, on average, has the second smallest shadow economy at 7.41 % of GDP; followed by Colorado, averaging 7.52 % of GDP, rounding out the three smallest shadow economies in the US West Virginia and Mississippi, on average, have the largest shadow economies in the US as a percent of GDP (9.32 and 9.54 %, respectively).     

A model selection approach for multiple indicators multiple causes model

This study proposes a model selection approach for determining the inclusion or exclusion of a latent variable when two exogenous and two endogenous variables are provided. The models compared are the multivariate regression model without latent variables (MR model) and the multiple indicators multiple causes model (MIMIC model). The inclusion of a latent variable in the MR model yields the MIMIC model. In the proposed approach, an information criterion is used to select the best model of the two. The efficacy of the proposed approach is examined through two types of simulation studies and empirical analyses of the shadow economy and the fiscal illusion.     

Exploring the dynamics of the shadow economy across US states

This article examines the dynamics of the shadow economy using data for 50 US states over the period 1998–2008. Using a panel VAR model, we analyse the impulse response of the shadow economy to an orthogonal shock in capital tax rates, educational attainment, union participation and gross state product. We find evidence of significant dynamics underlying the relationship between the shadow economy and its determinants. The results remain robust to alternate measures of the determinants of the shadow economy, alternate causal ordering of the variables in the system and conditioning on the level of income in each state.     

Decomposition of Net Final Values: Systemic Value Added and Residual Income

This paper proposes a model aiming at decomposing the Net Final Value of a project under certainty. It makes use of a systemic outlook: the investor's net worth is regarded as a dynamic system whose structure changes over time. On this basis, a profitability index is presented, here named Systemic Value Added (SVA), which lends itself to a periodic decomposition: the periodic shares formally translate the economic concept of residual income (or excess profit). While as an overall index the Systemic Value Added coincides with the Net Final Value (NFV) of an investment, the systemic partition of a SVA is shown to differ from the NFV decomposition model proposed by Peccati (1987, 1991, 1992), which in turn bears a strong resemblance to Stewart's (1991) EVA model. The SVA model and the NFV–based model bear interesting relations: by introducing the concept of a shadow project the SVA model can be re–shaped so that the decomposition of the SVA can be accomplished by applying Peccati's argument to the shadow project , or, which is the same, by computing the shadow project 's Economic Value Added. The paper then generalizes the approach allowing for a portfolio of projects, multiple debts and multiple synchronic opportunity costs of capital, for which a tetra–dimensional decomposition is easily obtained.     

An Exploration of the Greek Shadow Economy: Can Its Transfer into the Official Economy Provide Economic Relief Amid the Crisis?

We explore the determinants of the Greek shadow economy, its interaction with the official economy, and its relationship with corruption. In doing so, we undertake — for the first time — an interdisciplinary review of economic and political studies on the size and determinants of the shadow economy, tax evasion, undeclared work and, moreover, of their relation with corruption in Greece in order to reveal the extent and complexity of these phenomena. We estimate the size and determinants of the shadow economy via a multiple-indicators-multiple-causes (MIMIC) approach. Our findings indicate that the important determinants are factors related to macroeconomic conditions, such as unemployment and GDP growth, and institutional factors, such as tax morale and the rule of law. We also indicate that the shadow economy and corruption are complementary and that the official and the shadow economy substitute each other over the business cycle. An adoption of policy based on these findings would lead to a successful transfer of part of the shadow economy to the official economy, would boost government revenue, and would eventually lead the Greek economy out of the depression that emerged as a result of the sovereign debt crisis.     

The Impact of the Shadow Economy on Indirect Tax Revenues

This paper examines empirically the impact of the shadow economy on indirect tax revenues in an unbalanced panel of 125 countries for the period 1990–2011. The same analysis is conducted excluding at first and then including international trade tax revenues in (total) indirect tax revenues, as a way to disentangle any impact of trade liberalization. In both cases, the results suggest that the size of the shadow economy increases the ratio of indirect tax revenues to GDP, as long as informality does not exceed a cutoff value. When the size of the shadow economy exceeds that level, any further increase affects indirect taxation negatively. The findings are robust to a number of sensitivity tests and when addressing the problem of potential endogeneity. The empirical evidence is in line with the predictions provided by the theoretical framework of the paper.     

Can consumption of convenience products reveal the opportunity cost of time?

I examine how people’s consumption of time-saving products can be used to estimate the shadow value of time. I use a household production model to motivate an empirical approach that can be implemented using survey data.     

Shadow short rate and monetary policy in the Euro area

Empirical modelling of the monetary policy effects using conventional linear econometric models is put to a great test when interest rates approach the zero-lower bound. A possible remedy recently proposed in the literature is to introduce a shadow short rate (SSR) obtained from the yield curve model as an alternative monetary policy measure. This paper examines the usefulness of shadow rates as a policy stance measure for the Euro area. Moreover, the SSR can be used to study the country-specific monetary policy stance. We incorporate the shadow short rate in a standard vector autoregressive analysis to study the effects of monetary policy shocks both at the level of the Euro area and for two periphery EA countries, Italy and Spain, that endured significant financial stress during the crisis. Our analysis shows that monetary policy shocks identified form the SSR produce similar macro responses as shocks identified from the standard policy rate. The Euro area shocks can directly translate to a corresponding change in the country-specific financing conditions in the periphery, whereas the reverse effect is limited. The historical decomposition of the stochastic component of the SSR series shows that the unconventional policy measures were effective in stabilising the sovereign crisis in 2011, however, their relatively limited quantity provided only a weak stimulus to the economy.     

The shadow economy in three Mediterranean countries: France,Spain and Greece. A MIMIC approach

This paper offers estimations of the evolution of the shadow economy in three Mediterranean countries, namely France, Spain and Greece. A multiple indicators and multiple causes model based on the latent variable structural theory has been applied. As established by Giles (Working paper on monitoring the health of the tax system, 1995), filtered data to solve the non-stationary problems are used. The model includes the tax burden (both as a whole and disaggregated into direct taxes, indirect taxes and social security contributions), a proxy of regulation burden, theu nemployment rate and self-employment as causes of the shadow economy and the GDP growth rate, the labour force participation ratio and the currency ratio as indicators of the underground economy. The results confirm that unemployment, the fiscal burden and self-employment are the main causes of the shadow economy in these countries, and confirm that an inverse relationship exists between the official GDP growth rate and that of the unofficial economy. This paper has benefited from the comments and suggestions of the anonymous referees. The usual disclaimer applies. The paper was partly written when third author was visiting Real Colegio Complutense at Harvard University. The hospitality of this Institution is gratefully acknowledged.