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An indirect way for measuring the underground economy.

BECAUSE measurement of the underground economy is both elusive and important for an accurate portrayal of the Nation's economy, it is worth experimenting with a variety of approaches to measurement. This article describes a new, indirect technique for measuring underground income and applies it to the possible understatement of the growth of national income in the United States from 1949 to 1982.

The basic idea underlying the new indirect technique is that although there is little agreement about the size of the underground economy, there is widespread agreement about the industries in which much underground activity takes place. Working "off the books," underreporting tips, and similar activities do not take place in the steel industry or the telephone industry; they are thought to take place in the services, construction, and a few other industries. If, as is sometimes alleged, official estimates of national income have been missing a growing portion of the "suspect" industries because of the underground economy, then certain indicators for these industries ought to be declining relative to the same indicators for "well-measured" industries.

The first section of the article discusses the classification of industries into suspect, well measured, and intermediate. The second section develops a framework and proposes a set of indicators for comparing suspect, well-measured, and intermediate industries. The third section reports regression results for 56 industries over 34 years. The section concludes with an estimate--subject to considerable uncertainty--that the underground economy caused the growth of national income in private domestic industries to be understated by an average of one-quarter of 1 percent per year from 1949 to 1982. The final section appraises this new estimate of understatement.

I. Classification of Industries

The underground economy refers to activities such as working "off the books," padding expense accounts, shoplifting, underreporting tips, or skimming (pocketing some part of cash register receipts). It also includes provision of prohibited goods and services through such activities as prostitution or narcotics dealing.

The new indirect technique will be used to estimate only a portion of the 1949-82 growth of income derived from underground activities. The technique will not be used to estimate income that is excluded by definition from the national income and product accounts (NIPA's)--for example, income from the production of prohibited goods and services. Nor will it be used to estimate income that is missing from tax returns but that is included in current estimates of the NIPA's because of (a) use of source data other than tax returns and (b) current adjustments for misreporting where tax returns are used. What it will be used to measure is the growth of income that belongs in the NIPA's, that is not included in the current estimates, and that is concentrated in suspect industries.

Three sources of information are in close agreement as to the industries in which underground activities are concentrated. The first is journalistic accounts of underground activities. Underground activities, according to these accounts, are heavily concentrated by industry in construction, agriculture, retail trade, and services. By type of firm, they are concentrated in small unincorporated enterprises. Occasionally, manufacturing and mining industries with a concentration of small enterprises, such as apparel manufacturing, are mentioned in this source.

The second source of information is the results by industry (unpublished) of Internal Revenue Service audits of a random sample of tax returns--the Taxpayer Compliance Measurement Program (TCMP) results for 1976. More than 80 percent of the understatement of either business receipts or profits detected by these audits was in the construction, retail trade, and services industries.

The third source of information, less direct than the first two, is NIPA estimates of employee compensation in noncorporate and corporate enterprises, by industry. The assumptions underlying the use of this source are (1) that the importance of noncorporate enterprises in an industry is correlated with the likelihood of underground activity, and (2) that employee compensation for such enterprises is measured more accurately than other income components such as proprietors' income. These assumptions, supported by the first two sources, imply that the ratio of noncorporate employee compensation to total employee compensation in an industry should be an indicator of the likelihood of underground activity. Ratios were examined for 1968 and 1984, and they generally pointed to the same "suspect" industries as the first two sources.

The division of industries into three groups was based solely on the third source, because this source was more detailed and available for more years than the other sources and gives similar results. The industries that this source was used to classify are those shown for the most detailed annual estimates published in section 6 of the NIPA tables. They follow approximately two-digit standard industrial classification detail. There are 21 manufacturing industries and 39 other private domestic industries. Income originating in government and rest of the world was omitted from the analysis. Three industries in which a large and variable portion of national income is imputed--banking, credit agencies, and real estate--were omitted from the analysis because the imputations greatly affect certain of the comparisons to be presented below for reasons that have no relation to the underground economy. One other industry, holding companies and other investment companies, was omitted because its negative national income in a number of years is difficult to interpret in the framework of this article.

Suspect industries were defined as industries for which the ratio of noncorporate employee compensation to total employee compensation was more than 0.1 in either 1968 or 1981, or for which noncorporate employee compensation was more than 1 percent of economywide noncorporate employee compensation in either 1968 or 1981. These cutoffs were chosen so as to be consistent with the TCMP results and the journalistic accounts. The industries are: Farms Agricultural services, forestry, and fisheries Construction Lumber and wood products (manufacturing) Trucking and warehousing Wholesale trade Retail trade Security, commodity brokers, and services Insurance agents, brokers, and services Hotels and other lodging places Personal services Business services Auto repair, services, and garages Miscellaneous repair services Motion pictures Amusements and recreation services Health services Legal services Educational services Social services and membership organizations Miscellaneous professional services Private households

Intermediate industries were defined as those with ratios of noncorporate employee compensation to total employee compensation from 0.03 to 0.10 in either 1968 or 1981, except for those already classified as suspect (for example, an industry with a ratio of 0.095 in 1968 and 0.105 in 1981). These cutoffs were chosen so as to include as intermediate industries those occasionally, but not frequently, singled out in journalistic accounts. The industries are: Metal mining Coal mining Oil and gas extraction Nonmetallic minerals, except fuels Furniture and fixtures Food and kindred products Apparel and other textile products Printing and publishing miscellaneous manufacturing industries Local and interurban passenger transit Transportation services Electric, gas, and sanitary services

The remaining industries were classified as well measured. These industries are: Stone, clay, and glass products Primary metal industries Fabricated metal products Machinery, except electrical Electric and electronic equipment Motor vehicles and equipment Other transportation equipment Instruments and related products Tobacco manufacturers Textile mill products Paper and allied products Chemicals and allied products Petroleum and coal products Rubber and miscellaneous plastic products Leather and leather products Railroad transportation Water transportation Transportation by air Pipelines, except natural gas Telephone and telegraph Radio and television broadcasting Insurance carriers

In all, there are 22 industries in the well-measured group, 22 in the suspect group, and 12 in the intermediate group. In 1968, well-measured industries accounted for 35 percent of the published national income of all industries included in this analysis; intermediate industries accounted for 13 percent; and suspect industries accounted for 52 percent.

II. Framework of the Analysis

Decomposition of national income

The indicators to be compared among industries in the three groups are related to national income through the following identity, in which NI is national income, E is total employment, FTE is full-time equivalent employment, and C is employee compensation:

National income originating in each industry is expressed in this indentity as the product of four factors: Total employment, the ratio of full-time equivalent employment to total employment, employee compensation per full-time equivalent employee, and the ratio of total national income to compensation. If the growth of national income in an industry is understated, then the growth of at least one of these four factors must be understated. The next subsection will explain why only three of these four factors are used as indicators of understatement of income growth.

The four panels of chart 6 plot the four factors from 1949 through 1982 for well-measured, intermediate, and suspect industries in total. Table 1 shows average growth rates of the four factors for the three groups of industries. The chart and table offer a preliminary look at the data in summary form, although they do not reveal any of the industry detail or the timepaths of any of the other variables that will enter the regression analysis. For employment, the chart makes clear that suspect industries as a group have grwon much more rapidly than the other groups of industries--the opposite of what might be expected if growth in underground activities were large and heavily affected measured employment. For the other three factors, the chart indicates that suspect industries as a group have risen less, or declined more, than well-measured industries as a group. The regression analysis will provide a more refined estimate of this relative understatement by taking account, industry by industry, of influences on the three factors other than the possible growth of underground activity.

Omission of employment

Employment will be omitted from the regression analysis because it is not feasible to take systematic account of all the diverse forces that affect industry employment trends. These factors include changes in income and relative prices, foreign competition, and changes in input costs, competitive structure, and technology--as well as, perhaps, the underground economy. The omission of employment means that if surveys of employment are in fact increasingly understated, then the indirect measure in this article is also understated.

Evidence outside the framework of this article has been cited to indicate that underreported employment is an important source of growth in the underground economy, but the evidence is not convincing. One argument is that employment reported by business establishments, which comes from the same source as important components of national income, has grown less rapidly than employment reported in sample surveys of households tied to Census estimates of total population. From 1970 to 1980, however, the difference in growth between these two estimates of employment can be entirely accounted for by the Census Bureau's own estimate of the higher degree of coverage in the 1980 than in the 1970 Census of Population. Another argument is that the declining labor force participation rate of males over the last two decades (in contrast to females) is attributable to increasing concealment of employment. One student of these trends, however, finds that changes in Federal disability insurance provisions probably account for much of the decline. A third argument is that illegal activities are increasing and that persons engaged in such activities may fail to report that they are employed. Illegal activities, however, are outside the scope of the NIPA's.

There is, in short, no solid evidence that employment in activities covered by the NIPA's is increasingly understated. A rapidly growing underground economy, however, can exist without any understatement of employment; journalistic examples abound in which hours of work or receipts are underreported, but employment is correctly reported.

Inclusion of other factors

For the three factors other than employment, it is possible by means of regression analysis to determine whether, holding other variables constant, suspect and intermediate industries tend to have lower rates of growth than well-measured industries. After this determination, the understatements of the various factors can be combined to provide an overall estimate of the understatement of the growth of national income.

To understand the implications of the regression analysis, it is important to be clear about what the new measure is and is not designed to detect. What the measure is designed to detect is income unreported or underreported because of such activities as working "off the books," skimming, and the like. As mentioned earlier, the measure is not designed to detect income from the production of prohibited goods and services, nor is it designed to detect underground activities already included in the NIPA's because of use of source data other than tax returns or because of adjustments for underreporting where tax return data are used. Thus, the measure will clearly not reflect the large volume of activity unreported on tax returns but included in the NIPA's. Finally, the new technique is designed to detect only those underground activities that are concentrated in suspect industries. Padding of expense accounts is an example of an underground activity unlikely to be concentrated in suspect industries, and therefore not detected by the new technique.

III. Regression Analysis

The regression analysis is based on 56 industry observations for each year from 1949 through 1982, or 1,904 observations in all. The regressions weight observations for each industry by that industry's proportion of national income in 1972, so that the effect of an industry on the estimated coefficients depends on its size.

There are three dependent variables: the logarithms of the ratio of full-time equivalent employment to total employment, the ratio of employee compensation to full-time equivalent employment, and the ratio of national income to employee compensation. Lagarithms of the ratios rather than the ratios themselves are the dependent variables because (a) estimated understatements of the ratios due to the underground economy can them simply be added rather than combined in a more complex way, and (b) for one ratio, compensation per full-time equivalent employee, specifying influences on rates of growth (implicit in a logarithmic specification) makes more sense than specifying influences on absolute changes.

Each dependent variable is related to (a) time trends, and (b) other influences that vary from one dependent variable to another. The time trends include one that takes on values of 1, 2, 3, etc., in successive years for each industry; a second that takes on these values only for industries in the intermediate group (it equals zero for all years for other industries); and a third that takes on these values only for industries in the suspect group (it equals zero for all years for other industries). The coefficients of the last two time trends indicate whether intermediate and suspect industries have grown at faster or slower rates than well-measured industries. Positive coefficients indicate faster growth than well-measured industries; negative coefficients, slower growth. The standard errors of these coefficients indicate whether the growth rate differentials depart significantly from what might be expected from a purely random assignment of industries into three groups.

The ratio of full-time equivalent employment to total employment

The first dependent variable is the logarithm of the ratio of full-time equivalent employment to total employment. It measures the importance of part-time work; the lower the variable, the more important part-time work. It will be sensitive to underground activity if such activity takes the form of underreporting the hours of part-time workers, or of misreporting full-time workers as part-time workers.

The independent variables in the regression include variables to measure differentials in both level and growth between suspect and well-measured industries and between intermediate and well-measured industries. Coefficients of a dummy variable equal to 1.0 for suspect industries and zero for other industries, and a similar variable for intermediate industries, measure average differences in levels between these industries and well-measured industries, after allowing for the other factors in the regression. Coefficients of time trends for suspect industries and for intermediate industries, described earlier, measure average differences in rates of growth between suspect and intermediate industries on the one hand and well-measured industries on the other, again after allowing for the influence of the other variable in the regression.

Apart from the underground economy, an important influence on employers in setting average hours is the state of demand for their output. When demand falls, employers will want to reduce labor input; and part of the reduction, especially if the reduction is viewed as temporary, will take the form of fewer hours per employee. The variable used to represent cyclical influences is the change from the previous year in the logarithm of total employment in each industry. Of several cyclical variables tested, this one was most consistently significant with coefficients of plausible magnitude.

Beyond this cyclical influence, employers will have to balance a number of influences on unit costs. For jobs that require a lot of job-specific knowledge and training--managerial jobs or complex technical jobs, for example--it will be advantageous to have full-time employees even if their hourly compensation is higher than that of competent part-time employees. The attractiveness to employers of using part-time employees probably varies substantially by industry; for example, petroleum refining, with its highly skilled work force, is probably much less suited to part-time employment than retail trade.

To differentiate between industries not suited to part-time work and others, and additional dummy variable and a time trends were used in the regression. The dummy variable was set equal to 1.0 for all industries with a 1949 ratio of full-time equivalent employment to total employment of 0.95 or greater, and set equal to zero for all other industries. A 1949 ratio of 0.95 or greater was thus taken to indicate an industry not suited to part-time work. The time trend is equal to 1, 2, 3, etc. for successive years in each industry with a high 1949 ratio, and zero for all years in other industries. The coefficient of this variable measures the greater growth, or smaller decline, in the hours ratio for industries not suited to part-time work.

If the high-hours industries were all in the well-measured group and the low-hours industries in the suspect group, then it would not be possible to separate the effect of high hours from the effect of the underground economy. Fortunately, the suspect group includes both industries in the high-hours group (construction, for example) and industries in the low-hours group (retail trade, for example).

Preferences of employees as well as employers affect hours of work. Employee preference for part-time work clearly varies with household status. Primary earners in central age groups generally have a stronger preference for full-time work than secondary earners with child-care responsibilities or than students. To represent the influence of household status, the initial regression analysis included the proportion of the total labor force accounted for by males from ages 25 through 54, on the grounds that this is a group with an especially high preference for full-time work. However, the coefficient of this variable was either negative or insignificant in alternative specifications of the regression. It was therefore dropped from the analysis.

Institutional arrangements that bear on the choice of hours worked include the practice, partly due to legislation, of restricting certain fringe benefits to those who work full time or nearly full time. The importance of this practice has grown as fringe benefits have become a larger fraction of labor compensation. The regression does not include a variable measuring this factor specifically; its influence will affect the coefficient of the time trend for all observations.

To recapitulate: the independent variables in the regression include a constant term for all industries and constant terms for intermediate industries and for suspect industries; a time trend for all industries and time trends for intermediate industries and for suspect industries; the change in the logarithm of employment; and a constant term and a time trend for industries with high hours in 1949. The dependent variable is the logarithm of the ratio of full-time equivalent employment to total employment.

The regression results are shown in the first column of table 2. The constant term and constant-term differentials shown in the table have no implications for the estimated growth of underground activity and therefore will not be discussed for this regression or the others. The negative coefficient of the time trend for all industries reflects a slight downward trend in average hours since 1949. The coefficients of the time-trend differentials, especially that for suspect industries, are indicators of the missing growth of national income. The coefficient for suspect industries indicates missing growth of just over 0.1 percent per year, and the coefficient for intermediate industries is still smaller. Both coefficients, however, have t-ratios of 2.0 or greater (in absolute value), indicating that their negative values are unlikely to be due to chance.

Coefficients of other variables are plausible. The positive coefficient for the change-in-employment variable, CHLE, indicates a pro-cyclical movement of average hours. The positive coefficients for the dummy variable and time trend for industries with high hours in 1949 indicate that these industries have higher average hours and a smaller rate of decline in average hours than other industries.

Constant-dollar employee compensation per full-time equivalent employee

The second dependent variable is the logarithm of employee compensation per full-time equivalent employee divided by a price index for gross domestic business product. Dividing by a price index converts the variable to a measure of real compensation, but does not affect the differentials among industries. One reason for incorporating the price variable into the analysis in this way, rather than including it among the independent variables, is the high correlation of the price index with other indenpendent variables in the analysis. In the discussion that follows, the dependent variable is referred to as "real compensation per employee". It will be sensitive to underground activity if such activity takes the form of underreporting of wages or fringe benefits.

Independent variables include dummy variables and trends to measure differentials in levels and growth rates among the three industry groups. These variables are the same as the ones used in the previous regression.

Prominent among influences on real compensation per employee are cyclical fluctuations in economic activity, which cause parallel changes in real compensation per employee. Cyclical influences are again represented by the change from the previous year in the logarithm of total employment.

For employers, the trend of productivity is also an important influence. The coefficient of a time trend for all observations reflects the average growth of productivity from 1949 to 1982, but not its deceleration. To reflect the deceleration of productivity, a variable was constructed that is equal to zero until 1968 and then equal to 1, 2, etc. in succeeding years.

The mix of full-time and part-time workers is also an important influence on real compensation per employee. The dependent variable in the first regression, the logarithm of the ratio of full-time equivalent employment to total employment, is a measure of this mix, but if the underground economy has affected the accuracy of this variable, then it is a biased measure. Instead of including this variable in the second regression, therefore, the determinants of the variable--the set of variables from the first regression--are included in the second regression--are included in the second regression. Most of the variables from the first regression are already included on other grounds; the only additions are the dummy variable and time trend for industries with high hour in 1949.

Among other influences on real compensation per employee, union membership and minimum wages are obvious possibilities. The regression does not, however, include variables representing these factors. In the case of union membership, the reason is that estimates of the distribution of union membership by industry are subject to large errors and are not available in any case for recent years. Rough calculations suggest that the influence of this variable cannot have been large.sup.12.. In the case of the minimum wage, several alternative specifications of a variable representing its level and coverage gave regression coefficients with signs opposite to expectations.

An important influence on the measurement of employee compensation is legal form of organization. In a noncorporate enterprise, remuneration of proprietors or partners is not counted as employee compensation, whereas in a corporation, remuneration of executives is. Because executives have remuneration far above the average, compensation per employee will tend to be higher for corporations than for noncorporate enterprises. It may be higher for other reasons as well--for example, if the corporate form tends to be associated with firms that pay high salaries. To represent legal form of organization, the variable used is the ratio of noncorporate employee compensation to total employee compensation. Of several possible variables, this one is least likely to be distorted by errors of measurement.sup.13.. A disadvantage of this variable is that it is the variable used to classify industries as well measured, intermediate, or suspect. It is possible that the growth of the variable is correlated with the growth of underground activity, and therefore might bias the regression results. For this reason, regression results omitting this variable will be compared with results including it.

A final institutional influence on real compensation per employee is the presence of underground activity itself. Off-the-books activity is often conducted at reduced rates of compensation, because taxes are not paid on the earnings. Where off-the-books activity is a significant part of an industry, competition may compel fully reporting enterprises in that industry to lower their employee compensation rates and other forms of income (or restrict increases in them). In such a situation, the approach to measuring the underground economy adopted in this paper will exaggerate the growth of underground activity. The differential growth rate for a suspect industry will reflect not only unreported employee compensation, but also reduced compensation in fully reporting enterprises due to competition from underground enterprises. There is no variable in the regression analysis to represent this indluence; it must simply be kept in mind as a possible source of overstatement in the estimated growth of underground income.

The results of the regression appear in the second column of table 2. The coefficients of the time trends for all observations indicates that real compensation per employee rose at an average rate of 2.65 percent until 1968, but only 0.77 percent (2.65 minus 1.88) afterwards. For intermediate and suspect industries, coefficients of time-trend differentials are negative and statistically significant. These coefficients suggest growing underground activity in the form of unreported real compensation per employee amounting to more than six-tenths of 1 percent per year for intermediate industries and one-quarter of 1 percent per year for suspect industries.

Other variables performed as expected. The coefficient of the ratio of noncorporate to corporate employee compensation, NCC, is negative and highly significant. The possibility that this variable is biasing the coefficients of time-trend differentials was discussed earlier. Rerunning the regression without this variable does change those coefficients. The alternative coefficients are closer to zero; -0.0040 instead of -0.0062 for intermediate industries and -0.0007 instead of -0.0025 for suspect industries. The alternative regression thus indicates less missing growth in employee compensation than does the regression shown in table 2. The implications of this alternative regression will be discussed after reporting on a similar alternative for the next dependent variable.

The ratio of national income to employee compensation

The third dependent variable is the logarithm of the ratio of national income to employee compensation. It measures the return to all factors of production relative to the return to employed labor. It will be sensitive to underground activity if underreporting of profits, proprietors' income, or other property income is greater, in percentage terms, than underreporting of employee compensation.

Once again, cyclical factors are an important influence on the behavior of the ratio, mainly because they have a greater percentage impact on profits than on employee compensation. The change from the previous year in the logarithm of employment therefore appears in this regression as well as in the first two.

An additional factor that influences the ratio of national income to employee compensation, as it does real compensation per employee, is legal form of organization. The influence arises because the denominator of the ratio, employee compensation, does not include the return to the labor of proprietors and partners, but does include the return to the labor of corporate executives. The result of this characteristic is that the ratio tends to be far higher for proprietorships and partnerships than for corporations. The variable selected to represent this factor, the ratio of noncorporate employee compensation to total employee compensation, is expected to have a positive coefficient in this regression, whereas its coefficient in the previous regression was (and was expected to be) negative.

Eight industries are omitted from this regression, for various reasons. National income consists entirely of employee compensation for one industry, private households, and consists very largely of employee compensation for two industries that include many nonprofit organizations, educational services and social services. These industries are omitted because their ratios of national income to employee compensation are always equal to, or are very close to, one. The other five omitted industries--farms, agricultural services, oil and gas extraction, jpetroleum refining, and electric and gas utilities--are so heavily influenced by large swings in farm and fuel prices that they are of little value in drawing inferences about other factors affecting the ratio of national income to employee compensation.

The results of the regression appear in the third column of table 2. The negative coefficient of the time trend for all observations reflects the declining share of profit-type income in national income since 1949. For intermediate industries, the coefficient of the time-trend differential is positive, indicating no understatement of the ratio. For suspect industries, the corresponding coefficient is negative, but it is small and not significant. The other two variables, CHLE and NCC, both have coefficients of expected sign and are highly significant.

The possibility that the presence of NCC biases the coefficients of differential time trends was discussed earlier. Omitting this variable alters these coefficients; for intermediate industries the coefficient is lowered from 0.0040 to 0.0036, and for suspect industries, it is lowered from -0.0004 to -0.0032. These alterations are roughly the opposite of the alterations due to omitting NCC from the regression for compensation per full-time equivalent employee. The alternative regression thus leaves the estimated total understatement about the same.

However, the regression reported in table 2 and the alternative regressions differ in their estimates of the composition of the understatement. According to the regressions in table 2, the understatement lies mainly in employee compensation; according to the alternative regressions, the understatement lies mainly in other forms of income. Direct evidence from tax audits and special surveys accords with the results of the alternative regressions in this respect.

The growth of underground income

The new estimate of understatement in the growth of national income in this study is based on the coefficients of differential time trends for suspects and intermediate industries. For suspect industries, the coefficients in the three regression are -0.0011, -0.0025, and -0.0004. Their sum, -0.0040, is an estimate of understated growth in suspect industries; the estimate suggests that growth in these industries was understated by an average of 0.40 percent per year during 1949-82. Because suspect industries account for a little over one-half of published national income of the industries in this study, the understatement of growth in total private domestic national income due to this understatement is 0.21 percent per year, or just over one-fifth of 1 percent.sup.14..

For intermediate industries, the corresponding three coefficients in table 2 are -0.0007, -0.0062, and 0.0040. Their sum implies that growth in the intermediate industries was understated by 0.29 percent per year, or a little less than three-tenths of 1 percent. The understatement of growth in total private domestic national income due to intermediate industries is only 0.04, or four one-hundredths of 1 percent, per year.

The estimated understatement due to both suspect and intermediate industries is 0.21 plus 0.04, or 0.25 percent per year. The standard error of the overall estimate is 0.08 percent, or one-third of the estimate itself.sup.15..

The estimate understatement is small compared to the average 1949-82 growth rate of published national income in private domestic industries. The understatement is one-thirtieth of the growth rate based on current-dollar national income, 7.41 percent per year. It is one-thirteenth of the growth rate based on constant-dollar national income, 3.30 percent per year (the latter comparison is meaningful if, as seems plausible, the understatement is in real growth and not in inflation).

IV. Appraisal

This section appraises the new indirect estimate of understatement of the growth of national income in three ways. First, it compares the estimate with a direct estimate of understatement recently reported in the SURVEY. Second, it compares the estimate and the procedures used to construct it with other indirect estimates. Finally, it discusses possible sources of understatement or overstatement in the new estimate.

Comparison with a direct estimate

A recent study has led to improved adjustments in 1977 for misreporting on the tax return information used in constructing the NIPA's. It is estimated that national income for that year should be adjusted upward by $58 billion, in addition to the adjustments for underreporting already incorporated in the published estimate.sup.16.. This upward adjustment covers essentially the same activities as the estimate in this article.

Comparison between this direct estimate and the indirect estimate in this article is difficult because the former is a dollar level and the latter is a rate of growth. To compare them, the latter can be converted into a dollar level by assuming a level of zero (no understatement) in 1949 and then cumulating understated growth from 1950 through 1977. Because of the zero assumption for 1949, this procedure gives a lower bound to the understatement in 1977.

The result of this calculation is an estimate of $88 billion, or $30 billion more than the direct estimate. The difference between the two estimates is equal to roughly one standard deviation of the former estimate--a difference that could easily arise by chance due to the uncertainties of statistical estimation. The two methods thus do not give significantly different results, if income missing from the NIPA's was negligible in 1949. If income missing in 1949 was substantial, however, then the inderect estimate might imply significantly more missing income than the direct estimate for 1977.sup.17..

The direct estimate places most of the understatement of national income in proprietors' income. The indirect estimate based on the regression results in table 2 places most of the understatement in employee compensation; however, an estimate based on alternative regressions, mentioned earlier, would place most of the undestatement in other forms of income (including proprietors' income). The indirect method thus does not lead to any firm conclusion abot the distribution of the understatement.

Comparison with other indirect estimates

It is difficult to compare the estimate in this article with other published indirect estimates because it is quite unlikely that the various estimates are measuring the same thing. The estimate in this article, as noted earlier, refers to activities unreported or underreported in the NIPA's because of working off the books, skimming, and the like. It does not cover (a) prohibited activities excluded from the NIPA's, such as the production and distribution of illegal drugs, and (b) incomes unreported on tax returns, but included in the NIPA's.

The indirect estimates of Feige, Gutmann, and Tanzi--all of which are based on financial ratios--probably include both these categories. They should therefore be larger than the estimate in this article (and larger than appropriate for gauging possible understatement in the NIPA's). In fact, Gutmann's estimate is nearly twice as large, and Feige's estimate is four or five times as large. Tanzi's estimate, however, is about the same size.sup.18..

It is far from clear, however, that the excess of the Gutmann and Feige estimates over the one in this article is due to income from prohibited goods and services, or to income missing from tax returns but included in the NIPA's. The estimate in this article involve a careful attempt to correct for influences other than the growth of the underground economy. This correction is accomplished by examining differences between suspect and well-measured industries rather than movements in suspect industries alone, and by using a multiple regression procedure that takes account of important influences on the indicators other than the underground economy. The two larger of the three other indirect estimates do not attempt to correct carefully for other influences on the indicators they use. It is not possible to account systematically for the excess of their estimates over the one in this article.sup.19..

Sources of understatement and over statement of the new measure

Although the estimate in this article does not share some of the short-comings of other indirect estimates of the underground economy, it is subject to uncertainty for several reasons. It is appropriate to end this article with a brief summary of these sources of possible understatement or overstatement.

One sorce is the uncertainties of statistical estimation. The variation in the estimate that can be attributed to this source is summarized by the standard deviation of the estimate, equal to about one-third of the estimate itself.

A second source of uncertainty is the ommission, for reasons discussed earlier, of an analysis of employment differences among suspect, well-measured, and intermediate industries. While there is no convincing evidence that the growth of employment is understated, there is no way to be sure what a detailed analysis of employment growth would show.

A third source of uncertainty is due to the fact that the new estimate covers only those underground activities that are concentrated in suspect industries or intermediate industries and absent from well-measured industries. It does so because it is based on unexplained differences between these groups of industries. The covered activities probably inclde the great bulk of working "off the books" and skimming. They probably do not include padded expense accounts and employee theft, both of which take place in well-measred as well as suspect industries. This partial coverage is a factor that makes the new measure understate the level of underground activity. Partial coverage could make the new measure of understated growth either too low or too high, depending on how rapidly the uncovered activities have grown.sup.20..

A final source of uncertainty may cause the measure in this article to overstate both the level and the rate of growth of underground income. That factor, discussed earlir, is the impact of the underground economy on incomes in correctly reporting enterprises. Price competition from a growing underground sector in an industry may compel correctly reporting enterprises to limit increases in their incomes. The measure in this article reflects any such induced slowing of the growth of compensation, even though it is not itself a part of the underground economy.

Because of these sources of uncertainty, it is not possible to say whether the new measure understates or overstates the growth of underground income missing from national income. Nevertheless, in an area where quantitative information is extremely scarce, even an uncertain measure is of some help. It would be of interest to calculate the measure for other bodies of data, such as tax returns classified by industry of employment or national income by industry for other countries, and compare the results with those of the present study. It will also be of interest to recalculate the measure after the next benchmark revision of the NIPA's, because that revision will incorporate new adjustments for the underground economy.
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Author:de Leeuw, Frank
Publication:Survey of Current Business
Date:Apr 1, 1985
Previous Article:County and metropolitan area personal income, 1981-83.
Next Article:The business situation (corporate profits; first quarter 1985 and 1984)

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