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VIENNA47th International Atlantic Economic ConferenceMarch 17-22, 1999.

INCOME MEASUREMENT AND COMPARISONS

by

Ignacio Mauleón* and Jordi Sardá**.

(*) Universidad de Salamanca.(**)Universidad de Tarragona.

Abstract

The purpose of this paper is to provide a way for a better measurement of acountry's global income when official statistics fail to take into account theexistence of a thriving underground, or black economy. A second purpose of theresearch is to discuss adequate ways to perform international comparisons ofincome, and income per head, and to correct for depreciation. Besides the generalinterest of this problem there are two more specific reasons behind this work: theallocation of development funds by international agencies -for example, thestructural funds in the EMS-, are conditioned on this measure; and, second, themeasurement of unemployment may be totally distorted by failing to take accountof the hidden economy.

JEL classification code: C8.Keywords: Income per capita, underground economy, equilibrium exchange rate.

Corresponding author: Prof.Dr.Ignacio Mauleón.Dpto. de Economía e Historia.Fac. de Economía y Empresa (edif. FES).Campus Miguel de UnamunoUniversidad de Salamanca.37008 SALAMANCA(Spain)

Phone: 34 - 23 - 294640Fax : 34 - 23 - 294686Email: imaul@gugu.usal.es

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1. Introduction.1

The purpose of this paper is to discuss ways for a better measurement of acountry's global income when official statistics fail to take into account severalshortcomings. Among them, one that features prominently is, for some countries,the existence of a thriving underground, or black economy. A second purpose ofthe research is to discuss and provide improved ways to perform internationalcomparisons of income, and income per head, over existing ones. One importantapplication of the result of this work would be a proper analysis of theconvergence problem in growth analysis. The common wisdom is that countriesfar off the technical frontier grow faster, but the rate of growth diminishes as thelevel of income, or income per head, converges. Besides the undergroundeconomy, there are at least three other problems relevant for the measurement ofnational income, as discussed by an international agency specialised on this matter,like the Organization for Economic Cooperation and Development (OECD): 1) themeasurement of depreciation, 2) the conversion rate between different nationalcurrencies -i.e., the exchange rate -, and, 3) the unaccounted cost in terms ofnatural resources - i.e, pollution of several kinds, for example -. According to theOECD these rank among the highest problems in the measurement of nationalincome.

The paper proceeds by applying this methodology to the Spanish case,which we consider of general interest for at least three specific reasons: theallocation of development funds by international agencies -for example, thestructural funds in the EEC-, are conditioned on this measure; second, themeasurement of unemployment, which is rather high according to official data,may be totally distorted by failing to take account of the hidden economy; andthird, it is of great interest to check if the spanish economy is converging toEuropean averages, and if this is not the case, why: this could shed light on policyeconomic analysis for countries that are willing to join the EEC and share somesimilarities with the spanish case, specially those coming from the former easternblock – they had previously an autocratic political regime, and their level ofdevelopment lies below european averages, both features shared by Spain, prior tojoining the European Community -.

2. Methodological issues on income measurement.

One of the major international agencies concerned with aggregate incomemeasurement at the national level, is the OECD. The main concern is to establish aset of accounting standards that yield comparable results, on which to performinternational economic policy analysis. The main focus of the system of accountsdeveloped by this organisation is economic production, which relates to bothgoods and services. In measuring this concept, a number of methodological issuesarise, not all of them easy to solve. Some of the most relevant, always according to 1 This paper has benefited from the comments of the participants at the 47th IAER conference inVienna, 1999, specially those of Michael Pickhardt from Wuppertal University. Financial supportfrom the Dgcyt under project SEC98-1112, and the Junta C. y L under project SA29/99 isacknowledged. The comments of the participants at the AEA conference on Public deficits, 1997 inRome are also acknowledged. The authors are soley respnsible for any remaining errors.

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the OECD, are the following four: 1) illegal activities; 2) the depreciation of theoverall capital stock; 3) international comparisons of GDP, and, 4) theenvironment as a natural resource. We discuss them in turn in the next paragraphs.

Illegal activities in the national accounts are those which are usually legal,but which become illegal when carried out by unauthorised producers (forexample, unlicensed medical practitioners, or avoiding the payment of the VAT).Incomes from illegal production can be spent on purchasing legal goods andservices and, conversely, illegal goods and services can be purchased usingincomes derived from legal sources. Both sides of such transactions need to berecorded within the national accounts framework if discrepancies are to beavoided. In practice, however, it is difficult to make reliable estimates, and mostcountries omit this component of income entirely in the end. But perhaps moreimportantly, beyond avoiding discrepancies in the system of accounts, it is the totalvolume of GDP that may be grossly underestimated in some cases, if thiscomponent is omitted. Therefore, and however crude the estimate of the hiddeneconomy may be, it seems unavoidable the need for some kind of correction.

The estimate of overall production which also takes into account the factthat capital is being used up into the course of production is net domestic product,or NDP. While NDP provides a purer measure of production than GDP, placing avalue on consumption of fixed capital is a difficult process. In practice,consumption of fixed capital is not calculated on a consistent basis betweencountries, and so GDP is frequently used as the summary measure of a country'seconomic performance.

International comparisons of GDP depend on two conditions being met.The first is that the basis for GDP calculations are consistent for the countriesunder comparison. The second is that the unit in which GDP is expressed, iscomparable. The simplest way of comparing GDP of two different countries is toconvert each amount to a common currency using official exchange rates.However, this is widely recognised as inadequate, since official exchange rates donot adequately reflect the comparative purchasing power of local currencies intheir own markets. The concept of purchasing power parity (PPP), was developedto provied an alternative conversion factor for GDP, so that internationallycomparable price and volume comparisons of GDP could be established. PPPs arethe rates of currency conversion which equalise the purchasing power of differentcurrencies. This means that a given sum of money, when converted into differentcurrencies at the PPP rates, will buy the same basket of goods and services in allcountries. In other words, PPPs are the rates of currency conversion whicheliminate the differences in price and levels between countries. Thus, whenexpenditures on GDP for different countries are converted into a common currencyby means of PPPs, they are expressed in effect, at the same set of internationalprices, so that comparisons between countries reflect just differences in the volumeof goods and services purchases. PPPs appear also in international trade theory, butthose calculated by the OECD, as such, refer to the entire range of final goods andservices which make up GDP, as a whole including many items, such asconstructions and government services, which are not considered in internationaltrade.

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Finally, the impact of economic activity on the environment, is anotheraspect that in principle should be considered in the national accounts. A majordifficulty in doing so is that, because those activities are not part of the market in acountry, it is impossible to directly put a monetary value on them. The OECDsuggests producing estimates in the form of satellite accounts, not fullyincorporated in the basic system of national accounts (SNA)

Of these methodological issues, we take up the first three, and proposesolutions that will lead to better estimates of the overall economic activity, or atleast that will be complementary to existing ones. We discuss them in turn, in whatfollows.

2.1. The hidden economy.

The methodology suggested in order to estimate the hidden orunderground, as sometimes is also denominated, economy is based upon the socalled currency demand approach, first put forward, and applied in a number ofpapers by Gutmann (1977), Feige (1979), and Tanzi (1980, 1982, 1983), and laterdeveloped by other authors like Matthews (1982), Isachsen et.al. (1982) and Smith(1981). Recent applications can be found in Barthelemy (1988), Feige (1989) andLagenfeldt (1989). An informal presentation of the consequences of theunderground economy can be found in Quirk (1997), and estimation results for thewestern economies in Schneider (1997). The fundamental hypothesis in all thesepapers, is that the underground economy requires means of payment fiscallyopaque, so that abnormal changes in the currency in circulation, are assumed to bethe result of changes in the size of the underground economy. It is, therefore, anindirect estimation procedure.

The methodology is based upon the so called currency demand approach.Since the methodology assumes that the underground economy requires a fiscallyopaque payment system, and assuming that we can derive an estimate for theamount of currency demanded by the legal economy, we can subtract it from thetotal amount in circulation, thereby deriving an estimate of the amount of currencydemanded by the underground economy, as well. This suggestion is detailed next.We start by considering first, a standard demand for money - currency, in thecurrent context -, that we make it depend on the usual variables, that is, prices, P,income, - observed, or legal – YL , and the nominal interest rate, R. Since we wantto capture the impact of the underground economy, we have to add a measure offiscal pressure, c, as well. In the present paper, such measure has been taken to bethe average effective rate of the Social Security contributions - that is, totalproceeds by this concept, over accounted GDP -. The reason behind this choice isthat neither indirect taxes, nor other direct measures of fiscal pressure - like theincome tax rate - seemed able to capture adequately any effect in the demand forcurrency. On the other hand, and since the bulk of the underground economy canbe safely assumed to be made up by entrepreneurial activities, this is a reasonablechoice .

The demand for money is specified in log linear terms, following thestandard procedure, that is,

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log(Et) = α0 + α1.log(YLt) + α2.log(Pt) + α3.ct + α4.Rt + ut (1)

The equation, without the logarithmic transformation looks like follows,

Et = α0.YLtα1.Pt

α2.exp(α3.ct+α4.Rt+ut) (2)

The basic assumption is that taxes capture the effect of the omitted, orunderground, economy: therefore, we can assume that the demand for moneyattributable to total income, underground, YS, and observed, YL, will be given bythe next expression,

Et = α0.(YLt+YSt)α1.Ptα2.exp(α4.Rt+ut) (3)

Equating the last two expressions, (2) and (3), and after some cancellations,we arrive at,

YLtα1.exp(α3.ct) = (YLt + YSt)α1 (4)

From here, and by means of straightforward manipulations, one finallyobtains the expression,

YSt/YLt = exp(α3.ct/α1) – 1 ≈ α3.ct/α1 (5)

which explains the proportion of the underground economy over the totaleconomy, as a function of the fiscal pressure, as measured by ct. Note, also, thatthe approximation in the second line of (5) is valid, as long as ct takes on valuesless than 1 in absolute value, which is precisely the case. On the other hand, andsince α1 and α3, are estimated parameters, the estimation of the proportion of theunderground economy will itself be a random variable, with a standard error easilycomputable, by means of standard procedures - given the variance-covariancematrix of the estimated parameters, α1 and α3-.

The methodology just described is implemented in Mauleón et. al.(1992,1998), and estimates for the size of the hidden economy in Spain arederived, drawing on the empirical estimation of equation (1) – an early suggestionalong this line for the spanish case, first appeared in Mauleón (1988) -. The resultsreported in those two papers are used in the comparisons of section 3 – the moneydemand framework of Mauleón and Sardá (1999), could provide the basis for theapplication of the methodology at the European level -.

2.2.The depreciation of physical assets.

The methodology implemented to estimate depreciation rates, varies widelyacross countries. Besides, it is usually based on some accounting methodology,combined with hypothesis about the theoretical rate of depreciation for physicalassets. One possible way to homogenise the estimation methodology, that is bothcoherent with economic theory and statistical techniques is described next - thismethodology has been applied to some problems; see Nadiri et. al. (1993), andMauleón et. al. (1997) -. The basic idea consists of estimating the rate of

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depreciation as an additional parameter in the production function. That is,suppose that we write a simple production function as given by,

Y t = f(Kt, Lt) (6)

where Y is output, K is the stock of capital, and L is labour. But K must be net ofdepreciations so that

Kt = Kt-1 (1-d) + It = Σ0

t-1 It-s (1-δ)s + K0.(1-δ)t

= k( It, It-1, ... , I1 , δ, K0) (7)

It being gross investment (observable), and δ the rate of depreciation(unobservable). If we consider (δ,K0) as further parameters to be estimatedeconometrically, along with the remaining parameters of the production function,we arrive at a non linear, but otherwise (almost) standard model, that can beestimated with appropriate available techniques – the fact that Kt depends on allpast values of investment, although non standard itself, can be dealt with withstandard econometric packages; see Nadiri et.al (1993) -.

The implementation of this procedure yields reasonable estimates - seeNadiri et. al. (1993) and Mauleón (1997)-, and could be extended to othercountries.

2.3. The currency conversion rate.

The main problem at this point, is to differentiate between the equilibriumexchange rate compatible with current account equilibrium, and the exchange rateappropriate for income comparisons. Both are strikingly different in manysituations, and can lead to disparate conclusions. The current account equilibriumexchange rate is based on the assumption that in the long run the exchange rate hasto adjust so that, on average, the current account is in equilibrium - i.e., equal tozero -. Therefore, one possible way to calculate an equilibrium conversion rate ofchange between two currencies would proceed in two steps: 1) calculate the longrun value, by taking the average of the real exchange rate over a sufficiently longtime period, and, 2) correct this measure multiplying it by relative prices, in orderto obtain the current conversion rate of change. Alternatively, the directcomparison of the purchasing power parity of two currencies, is derived by acomparison of the price in national units, of a similar basket of good and servicesin both countries. As such, this measure compares directly the purchasing power ofmoney, and is, therefore, adequate to perform income comparisons. Thiscalculation is conducted periodically for a given year in time, usually - every yearwould be unnecessarily costly -. The current conversion rate between the twocurrencies can be obtained now as before, that is, multiplying the purchasingpower rate of change by relative prices every year.

In the spanish case both rates are not too different, according to OECDestimates, though. However, they are so, indeed, for many of the remainingeuropean countries, resulting in a large difference, when the spanish income iscompared to the european average – see Mauleón (1996a, 1996b), for the current

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account equilibrium exchange rate in the spanish case -. The explanation for thelarge difference is, simply, that not all goods are traded: the equilibrium exchangerate is adequate for current account analysis, and the purchasing power rate, asmeasured by comparing representative basket prices, is more appropriate forincome comparisons.

3. Results for the Spanish economy.

We shall focus on two related points: 1) the comparison of income per headbetween Spain and average Europe, as a measure of relative welfare at a givenmoment in time, and, 2) the convergence of this measure along time, or lackthereof.

We have chosen to present our main results by means of comparative tablesand graphs. The data in each table is given as a percentage rate of thecorresponding variable compared to the European average. The graphs given nextdepict alternative measures of income per head, or per working person, which wedeem to be fairly informative:

FIGURE 1Income per head at equilibrium exchange rates.

40

50

60

70

80

79 81 83 85 87 89 91 93 95 97Year

%

FIGURE 2Income per head, at Purchasing Power Parity, exchange rates.

687072747678

79 81 83 85 87 89 91 93 95 97

Year

%

8

FIGURE 3figure 2, adding the hidden economy.

74767880828486

79 81 83 85 87 89 91 93 95

Year

%

FIGURE 4figure 2, according to net income - rather than gross -.

65

70

75

80

85

79 81 83 85 87 89 91 93 95

Year

%

FIGURE 5figure 2, measuring income per worker - rather than per head -.

7580859095

100105

79 81 83 85 87 89 91 93

Year

%

9

FIGURE 6figure 2, adding the hidden economy, and using net income.

70

75

80

85

90

79 81 83 85 87 89 91 93 95Year

%

FIGURE 7figure 6, measuring income per worker.

80859095

100105110115

79 81 83 85 87 89 91 93Year

%

FIGURE 8comparisons of growth rates, Spanish versus European average.

-2

0

2

4

6

79 81 83 85 87 89 91 93 95 97

Year

%

Spain U.E.

The message conveyed by these graphs is interpreted next. Fisrt, andaccording to figures 1 and 2, there is almost no convergence in a period ofapproximately twenty years. This results is smoothed somewhat, when we considernet rather than gross income - see figure 4 -, but still, the basic result of none orlittle convergence holds. Taking account of the hidden economy does not change

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the basic picture in any significant way, either - see figure 3-. This is ratherstriking, and might point to some structural weakness of the spanish economy. Andindeed, this is the case to some extent, when we consider the comparison ofincome per working person, rather than per head - see figure 5 -. In this latter case,the convergence is pronounced, by contrast, pointing to the root of the problem: alack of physical, and possibly human, capital. In other words, while there has beena marked convergence in productivity levels, this has been achieved by reducingtotal employment, rather than by increasing investment and the level of capital ofall kinds thereby.

Second, we detect a significant degree of hidden economic activities, whichis far larger than in the remaining European countries - see figure 3; although notrecorded in the graphs or data given here, the size of the hidden economy relativeto the official one, has fluctuated between 12 and 16 per cent, according to someestimates (Mauleón and Sardá (1998)) -. Notwithstanding the variance of thismeasurement, the basic result is that income per head in Spain is significantlycloser to european averages than official statistics might conclude - it is worthpointing out, that other measurements based on direct surveys reach a similarconclusion, although the size of the hidden economy according to them issignificantly larger (around 22% of the corresponding officially recorded)-.

Third, there are no large differences when net, rather than gross income, isconsidered - see figure 4-. Nevertheless, it is worth pointing out that in this case,the relative position of the spanish income improves, and that the convergence ismore pronounced along time.

Fourth, as far as the exchange rate is concerned, we detect a largedifference when using the equilibrium exchange rate - figure 1 -, or exchange ratesbased upon the purchasing power of each currency; as noted before, this latterconcept seems more adequate for income comparisons.

4. Conclusions.

This paper has tackled the problem of national income measurement,focusing on three of the four main shortcomings in conventional measurements, asdiscussed by an specialised international agency on the topic, like the OECD.These are the following: 1) the underground, or hidden economy, 2) thedepreciation of the physical stock of capital, 3) the currency conversion rate, and,4) the impact of economic activity on the environment. Of these, we havediscussed the first three. The second general purpose of the paper has been toapply the methodology to a case that we deem of general interest in this respect,the spanish case, because of the following reasons: 1) the official unemploymentrate is very high, which might point to a thriving underground economy, and, 2)the convergency of income per head to european averages, or lack thereof, so as toassess the growth prospects for new members of the european economiccommunity, coming from the former eastern block.

The measurement of the underground economy has been attempted in theliterature by one of two ways: 1) indirect estimation, i.e. looking at a set ofappropriately chosen indicators of economic activity, such as energy consumption

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and the like, and, 2) by assessing its impact on money demand, and morespecifically, on currency demand. This latter approach assumes that the mainpurpose of hidden economic activities is tax evasion, and that leads to a higherdemand for means of payment difficult to track down by tax authorities, mainlycurrency. The approach proceeds by estimating a money demand equation for veryliquid assets, introducing an adequate tax variable as explanatory in the estimatingequation.

The measurement of depreciation of the capital stock depends heavily onaccounting standards, which vary widely from country to country. In this respect,we suggest a common ground, based on a new proposal which focuses on directestimation of the net capital stock by econometric methods.

International comparisons of income depend heavily on the chosencurrency conversion rate, that is, the exchange rate. Since in the short run it candeviate strongly from its "adequate" value, failure to take this into account may beseriously misleading. We discuss the relative merits of two exchange rates in thisrespect, and propose a methodology based on the Purchasing Power Parityconcept, as a first approximation; but this has to be corrected in every moment intime, in order to represent more adequately what the equilibrium exchange ratewould be. The paper suggests a new way to accomplish this.

We then go on to apply these corrected measurements to the spanisheconomy. For at least three specific reasons this may be of general interest: theallocation of development funds by international agencies -for example, thestructural funds in the EEC-, are conditioned on this measure; second, themeasurement of unemployment, which is rather high according to official data,may be totally distorted by failing to take account of the hidden economy; andthird, it is of great interest to check if the spanish economy is converging toeuropean averages, and if this is not the case, why: this could shed light on policyeconomic analysis for countries that are willing to join the EEC and share somesimilarities with the spanish case, specially those coming from the former easternblock.

The empirical results for the underground economy suggest that it might beas large as 20% of the legal, or officially recorded level of activity. This matchesresults of other researchers based on direct surveys. Secondly, the methodology tocalculate the right value for the exchange rate is applied to measure nationalincome, and to conduct an international comparison - more specifically, to the restof Europe -. These comparisons are carried out for the last fifteen years.

The results point to the fact that the official figures for the spanish totalincome may grossly underestimate its true size; this would help explain, in turn,the very high official unemployment figure, - which is unlikely to be that highafter all -. Besides, the spanish income per head, when compared to the rest ofEurope, turns out to be substantially higher than official statistics would suggest -because of the adequate exchange rate, as well -. This is good news for the conductof economic policy associated with the democratic political system adoptedapproximately twenty years ago. The size of the hidden economy relative to theofficial one has fluctuated between 12 and 16 per cent, according to some

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estimates (Mauleón and Sardà (1998)) -. Notwithstanding the variance of thismeasurement, the basic result is that income per head in Spain is significantlycloser to european averages than official statistics might conclude - it is worthpointing out that other measurements based on direct surveys reach a similarconclusion, although the estimated size of the hidden economy is significantlylarger in this case (around 22% of the corresponding officially recorded)-.

Finally, another interesting result is that there is almost no convergence in aperiod of approximately twenty years. This result is smoothed somewhat when weconsider net, rather than gross income, but still, the basic result of none, or littleconvergence, holds. Taking account of the hidden economy does not change thebasic picture in any significant way, either. This is rather striking, and might pointto some structural weakness of the spanish economy. And indeed, this seems to bethe case to some extent, when we consider the comparison of income per workingperson, rather than per head. In this latter case, by contrast, the convergence ispronounced, pointing to the root of the problem: a lack of physical, and possiblyhuman, capital. In other words, while there has been a marked convergence inproductivity levels, this has been achieved by reducing total employment, ratherthan by an increase in investment and the level of capital of all kinds thereby. Alack of capital markets flexibility might go some way towards explaining thisresult.

Data Appendix.

Year A B C1979 73,1841622 80,7478884 85,94119651980 73,3157859 80,6637846 89,80662071981 72,9499756 80,2613114 91,31611611982 73,1426779 80,1666753 92,08075291983 73,161303 80,1870889 92,59427611984 72,3587994 78,9640542 94,46467741985 72,2146532 78,6153121 96,08228941986 72,2874033 78,6176562 95,46564281987 74,0164581 80,5768179 94,8639031988 74,8343773 81,4672324 94,19277681989 75,868498 82,6735513 93,06379651990 76,7083664 83,7106703 99,49651881991 76,4580878 83,6394717 98,35175891992 76,5294762 84,2395353 99,25263171993 76,2302179 84,0690927 100,7786641994 75,7870271 83,3430899 99,24229861995 75,9726441 82,9881361996 76,4809615 83,7048004

Year D E F1979 76,5464971 84,4577272 93,24777731980 74,6533577 82,1354131 94,49203961981 73,2011128 80,5376185 95,21299481982 73,473678 80,5294618 95,7821293

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1983 73,0776831 80,0954388 95,84633141984 71,9656579 78,5350248 96,65404081985 73,522064 80,0386038 100,1502631986 73,8014692 80,2643097 99,63640961987 76,2437786 83,0015543 99,54708871988 76,6495556 83,4432968 97,84793931989 77,8160152 84,7957518 96,80490521990 78,5308801 85,6995517 106,4766011991 80,1138331 87,6385857 108,0145071992 80,2340574 88,3173393 109,824441993 80,7182554 89,0186423 112,4278391994 79,881237 87,8454977 109,3647791995 80,6837124 88,1342354

The contents of the cols. is given next:

Column A: Income per head, at Purchasing Power Parity (PPP in what follows),exchange rates (as a percentage rate of the corresponding variable compared tototal European average -E.U.15-).Column B: Income per head (PPP) adding the hidden economy (as a percentagerate of the corresponding variable compared to total European average -E.U.15-).Column C: Income per worker (PPP) (as a percentage rate of the correspondingvariable compared to total European average -E.U.7. Spain, Germany, Belgium,France, Greece, Ireland and Italy-).Column D: Net Income per head (PPP)(as a percentage rate of the correspondingvariable compared to total European average -E.U.15-Column E: Net Income per head (PPP) adding the hidden economy (as apercentage rate of the corresponding variable compared to total European average-E.U.15-).Column F: Net Income per Worker (PPP) adding the hidden economy (as apercentage rate of the corresponding variable compared to total European average-E.U.7. Spain, Germany, Belgium, France, Greece, Ireland and Italy-).

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