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Economic Review Federal Reserve Bank of Dallas May 1987 1 Enforcing Sanctions against Employers of Illegal Aliens john K. Hill and james E. Pearce The 1986 immigration reform law will reduce employment of illegal aliens in some sectors of the economy but not in others. Small budgets will force authorities to enforce sanctions selectively. Worksites with numerous jobs that can be filled by illegals will be attractive targets. But such worksites account for only 30-50 percent of the jobs performable by illegals. By far, the majority of the attractive targets are in manufacturing, which on average employs eight times as many illegals per establishment as non manufacturing. The effectiveness of sanctions will be further diluted by leakage. About half of the illegals initially displaced by sanctions will move to employment in sectors where enforcement is weak. Thus, sanctions will reduce nonagricultural employment of illegals by 15-25 percent. In the first year, the percentage may be larger. Small employers are likely to avoid hiring iIlegals until they become familiar with the law and the enforcement pattern. 17 Estimating the Inflationary Consequences of Discretionary Central Bank Behavior Kenneth j. Robinson There is fairly widespread agreement that, especially over the long run, the central bank possesses the ultimate responsibility for maintaining price stability. The model of Federal Reserve behavior derived in this article assumes both benefits and costs are associated with inflation. Empirical results from a policy reaction function presented here indicate that benefits~in the form of seigniorage-and costs~as represented by deviations of unemployment from its natural rate-are significant factors in explaining observed inflation rates. Further, Federal Reserve behavior appears to be influenced by fiscal policy considerations but not by election-year constraints. This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org) Economic Review Federal Reserve Bank of Dallas May 1987 President Robert H. Boykin first Vice President William H _ Wallace Senior Vice President and Director of Research Harvey Rosenblum Assistant Vice President and Senior Economist Leroy 0 Laney Eugenie D . Short Economists National/International W . Michael Cox Gerald P_ O'Driscoll. Jr. John K Hill Robert T Clair Cara S. Lown Kenneth J. Robinson Regional/Energy Stephen P A Brown William C Gruben Ronald H . Schmidt Hilary H Smith William T Long III Jeffery W Gunther Keith R. Phillips Editorial Virginia M Rogers Elizabeth R. Turpin Graphics and Typesetting Graphic Arts Department The Economic Review is published by the Federal Reserve Bank of Dallas and will be issued six times in 1987 (January. March, May, July, September. and November) The views expressed are those of the authors and do not necessarily reflect the positions of the Federal Reserve Bank of Dallas or th e Federal Reserve System Subscriptions are available free of charge Please send requests for single- and multiple-copy subscriptions. back issues, and address changes to the Public Affairs Department, Federa l Reserve Bank of Dallas, Station K, Dallas, Texas 75222 (214/651-6289) Articles may be reprinted on the condition that the source is credited and that the Research Department is provided with a copy of the publication containing the reprinted material. Enforcing Sanctions against Employers of Illegal Aliens John K. Hill James E. Pearce Senior Economist Vice President and Director of Research Federal Reserve Bank of Dallas Federal Home Loan Bank of Atlanta The Immigration Reform and Control Act of 1986 introduced sanctions, or penalties, against employers convicted of knowingly hiring illegal aliens. 1 The sanctions were included in the legislation in the belief that potential illegal immigrants would be discouraged from crossing the border if jobs became more difficult to find. This confidence may be justified, but a prerequisite is that employers comply with the law. Compliance cannot be taken for granted. In Hong Kong, Canada, and several European countries, many illegal aliens hold jobs despite the presence of sanctions to deter their employment. Immigration control staff in these countries claim that sanctions do help reduce illegal immigration, but only if resources are devoted to discovering and punishing violators of the law. 2 The sanctions in the new u.s. law apply to all of the nation's more than four and one-half million business, household, and nonprofit employers. 3 According to news reports, authorities plan to employ between 1,500 and 3,000 agents to enforce sanctions. 4 The number of agents seems tiny compared with the number of employers, but the comparison exaggerates the magnitude of the task. Economic Review - May 1987 The research reported in this article finds that about three-fourths of all illegals are employed in industries accounting for only one and one-half million establishments. Within this group of industries, manufacturing firms employ over one-half the illegals in less than one-tenth of the establishments. Thus, the enforcement effort can be made manageable by concentrating on particular types of employers. A small budget and the uneven distribution of illegals combine to make selective enforcement almost inevitable. Obviously, an important part of such a strategy lies in choosing the targets for enforcement. Worksites with the potential for employing large numbers of illegals would certainly be attractive candidates. A few agents could monitor many jobs performable by illegals if they focused most of their attention on large employers. Indeed, employer size is likely to be incorporated into the strategy when enforcement of sanctions begins in June. With most laws, however, selective enforcement is actually less effective than it appears to be. The reduction in violations where enforcement is strong is at least partially offset by a rise in violations where surveillance is less thorough. An example is the recent experience with efforts to eliminate the cultivation of marijuana. Production has declined in West Coast states, where enforcement has been concentrated, but it has risen in Southeastern states, where authorities have been less vigilant. 5 In the case of employer sanctions, some illegal aliens initially displaced are likely to find new jobs in lightly enforced sectors of the economy. The research reported in this article examines the effects of sanctions when targets for enforcement are selected exclusively on the basis of the number of jobs performable by illegals at each worksite. Under this criterion, manufacturing contains most of the leading candidates for enforcement. Manufacturing establishments tend to be large and to rely heavily on low-skilled labor. Conspicuously absent from the list of attractive targets are the restaurant and construction industries. Although many illegals do work in these industries, they are thinly dispersed over a large number of establishments. The net reduction in employment of illegal aliens will depend on the number of illegals working in the heavily enforced sectors and on "Ieakage"-the percentage of illegals initially displaced who find new jobs in the United States. With targets based on potential illegals per establishment, heavy enforcement would be limited to employers initially accounting for 30-50 percent of the jobs held by illegal aliens. With this enforcement coverage, the analysis indicates that leakage would be about 50 percent. Consequently, sanctions would reduce the employment of illegal aliens by 15-25 percent. Determinants of the enforcement level In the introduction, the expectation that enforcement will be selective is based on a comparison of the likely number of inspectors and the number of employers. On the other Figure 1 EXPENDITURES hand, one might claim that the insufficiency of inspectors is a temporary condition. Over the longer term, the number of inspectors might be increased enough to achieve nearly complete enforcement. But that line of reasoning overlooks the controversy surrounding immigration reform . With so many people and interest groups opposing sanctions, widespread support for a large enforcement budget will be difficult to obtain, even if increases would result in a much higher compliance. 6 This suggests that the budget for enforcement is subject to a ceiling. It also shows that the relationship between the amount elected officials are willing to spend and the removal of illegals has the shape of the EE curve in Figure 1. If the budget is indeed effectively subject to a ceiling, the long-run level of enforcement will depend on how many of the jobs that can be performed by illegals can be monitored with the resources available. Although that point cannot be determined precisely, the present study provides a rough idea about whether and where diminishing returns to additional enforcement become evident. This information makes possible an educated guess about where costs are likely to approach the appropriation ceiling. The relationship between the enforcement budget and the reduction in illegal employment made possible by that budget is portrayed by the CC curve in Figure 1. The relationship is a cost function, and it is drawn to exhibit properties that are basic and common to cost functions. Eventually a point is reached where increases in output are achievable only with very large increases in costs. The key questions become whether enforcement costs have this property and where the marginal costs begin to rise. The subsequent sections of this article address these questions . The evidence indicates that successive reductions in employment of illegals do require increasingly higher expenditures. As the amount of enforcement is increased, the number of establishments to be monitored soon begins to rise faster than removals of illegals. The enforcement appropriation probably will be exhausted before half of the jobs performable by illegals can be monitored for compliance. Enforcement strategy and the distribution of iIIegals ILLEGAL ALIENS REMOVED 2 The activity that consumes the most resources in enforcement is monitoring. In the case of immigration law, worksites where jobs can be done by illegals must be inspected. The cost of monitoring increases with the dispersion of these jobs. If all such jobs are concentrated in large establishments in a limited number of cities, monitoring costs will be low and increase at a constant rate. But if only so me illegals are con centrated in this way, costs will Federal Reserve Bank of Dallas Table 1 MAJOR EMPLOYERS OF ILLEGAL ALIENS IN THE UNITED STATES Industry Percentage of all illegal alien employees Crop farming .. 6.46 Agricultural services . 0.87 Horticulture 0.93 Construction . . . . .. " 6.46 Meat products ............ .. . 1.40 Canned fruits and vegetables 1.79 Grain and bakery products . 2.03 Beverages and miscellaneous food products 0.83 Textiles .. 1.66 Apparel .. 10.59 Paper and allied products 1.00 Chemical and allied products 1.26 Rubber and plastics ........ . 1.26 leather and footwear ......... . 1.66 lumber and wood products 100 Furniture and fixtures 1 86 Primary metals 1 .39 Fabricated metals 2.53 Electronic computing equipment .. 0.73 Electrical machinery .. 3.06 Transportation equipment . 2.40 Miscellaneous manufacturing 2.26 Wholesale grocers . . . . .. .. 1 33 Department stores ....... . 0.80 Retail grocers 1.40 Eating and drinking places .. 7.39 Real estate and services to dwellings ... . 1 20 Auto repair ....... . 1.00 Private households 1.80 Hotels and motels 193 Cleaners 0.93 Hospitals . 1.53 Educational institutions 2.26 Total 7851 Percentage of total employees with less than 12 years of schooling 48.90 39.14 38.54 34.74 39.42 51.71 33.14 27.80 50.32 48.22 29.36 2037 32.40 52.15 45 .08 41 .20 3052 34.61 12.08 23.39 25.84 37.22 31 .18 23 .84 34.46 44.26 22.66 41 .11 57.74 36.45 43 .57 1544 10.41 30.03 SOURCE OF PRIMARY DATA: Public·Use Sample from the 1980 Census of Population Economic Review - May 1987 rise at an increasing rate. Thus, in a general way, the shape of the cost function facing the authorities can be inferred by examining the geographic and industrial distribution of illegals. In addition, data on the sizes of establishments in industries employing large numbers of illegals will be useful. Determining the exact industrial distribution of illegals is, of course, not possible. Data on illegal aliens are not of the same quality as data on the rest of the U.S. population. The 1980 Census of Population has become a widely used source, and it will be employed here. Analysts at the Census Bureau have combined the Census data with other sources to produce estimates of the number and geographic distribution of illegal aliens. They estimate the number of illegal aliens to be between 3 million and 5.5 million. 7 Some information on the origins and residences of illegal aliens is displayed in Charts 1 and 2. These charts are derived from the Census Bureau's calculations. They indicate that most illegals are Hispanic and that they are heavily concentrated in a few areas of the United States. About three-quarters have migrated from Mexico or elsewhere in latin America. Of the illegals, 60 percent live in California or Texas, and another 16 percent live in New York City and Chicago. los Angeles County has almost one-third of the illegal aliens, so that the nation's three largest metropolitan areas contain about half of the illegals. To assess the distribution of illegals across industries, we did our own analysis of the Public-Use Sample from the 1980 Census. Because the Census data do not identify any individual's legal status, one must approach the analysis of illegal populations indirectly. The Census questionnaire contained questions on each individual's country of birth and ability to speak English. Individuals born outside of the United States who lack a working knowledge of English constitute a good proxy group for illegal immigrants. Because members of the proxy group and actual illegals have similar skills and handicaps, the industrial distribution of the proxy group is probably representative of the distribution for illegals. 8 The industries that employ most of this proxy group's members are listed in Table 1. These workers are highly concentrated. Four industries-agriculture, apparel manufacturing, construction, and the restaurant industry-employ 30 percent of them. The extent to which these industries rely on low-skilled labor is indicated by the percentages of their workers who have not completed high school. For many of the industries, the percentage of lowskilled workers is high, but in a few cases, the percentage is below the average for the rest of the economy (which is about 20 percent). 3 Chart 1 Origin of Undocumented Aliens Counted in the 1980 Census OTHER LATIN AMERICA (22 PERCENT) MEXICO (55 PERCENT) ASIA (10 PERCENT) SOURCE OF PRIMARY DATA: Jeffrey S Passel and Karen A Woodrow, "Geographic Distribution of Undocumented Immigrants Estimates of Undocumented Aliens Counted in the 1980 Census by State," International Migration Review 18 (Fall 1984)' 642-71 Chart 2 Illegal Aliens Residing in the United States CALIFORNIA (49.8 PERCENT) FLORIDA (3.9 PERCENT) N.J., VA., MD., ARIZ., WASH. (7.3 PERCENT) ALL OTHERS (11.9 PERCENT) SOURCE OF PRIMARY DATA: Jeffrey S Passel and Karen A Woodrow, "Geographic Distribution of Undocumented Immigrants: Estimates of Undocumented Aliens Counted in the 1980 Census by State," International Migration Review 18 (Fall 1984): 642-71 4 Federal Reserve Bank of Dallas Table 2 SIZES OF NONAGRICULTURAL EMPLOYERS OF IllEGAL ALIENS Industry Manufacturing Meat products . Canned fruits and vegetables Grain and bakery products . Beverages and miscellaneous food products Textiles .......... . Apparel Paper and allied products Chemical and allied products Rubber and plastics Leather and footwear Lumber and wood products Furniture and fixtures Primary metals .......... . Fabricated metals Electronic computing equipment Electrical machinery . Transportation equipment ........... . Miscellaneous manufacturing ........ . Nonmanufacturing ........ . Construction Wholesale grocers Department stores Retail grocers . Eating and drinking places Real estate and services to dwelling Auto repair ........ . Private households Hotels and motels .. . .... . Cleaners Hospitals Educational institutions . Employees per establishment Illegal aliens per hundred employees' Illegal aliens per establishment' Percentage of illegal aliens in nonagricultural industries 61.42 87.69 12 .80 19.43 7.86 17.04 42 .61 1 .54 104.92 35.95 37.72 1 .97 65.16 21 .23 13.84 2.23 53.24 108.21 48.75 6.91 10.20 39.16 3.68 11.04 19.09 0.92 1 .83 11.64 9491 7.25 6 .88 1 .10 73 .32 50.69 73.05 6.38 8.16 36.64 4.67 4.14 26.77 1.39 1.39 1 .83 17.48 7.62 1.33 1.10 43 .59 120.96 41 .05 18.81 7.18 7.63 8.20 8.69 3.13 2.05 1 .53 2.79 194.31 116.36 9.53 7.04 18.52 8.19 0 .81 3.37 169 .00 6 .61 11 .16 2.64 24.11 20.73 9.36 17.49 151.83 15.81 26.02 4.58 6.64 8.69 2.32 3.03 6.27 0 .95 0.62 1 52 3.52 0.48 2.49 30.82 7 .10 1.46 0 .88 1 .54 14.59 6.97 1.02 8.13 1693 4.12 1.52 30.72 8.07 514.21 9.76 12.05 52.19 7.89 11.56 1 .60 1 .65 0 .50 0.79 2.42 0 .93 8.22 1.32 1.10 1 .98 2.12 1 .02 1 68 183.18 1.41 2.58 2.49 1 Computed as the number of illegal alien workers divided by the total number of employees . The estimates of illegal workers were obtained by multiplYing an estimate of the size of the illegal nonagricultural labor force by the industry's share of all proxy·group members engaged in nonagricultural employment 2 Column 3 equals column 1 times column 2, divided by 100. SOURCES OF PRIMARY DATA: 1982 Censuses of US Industries (for data on total employees and number of business establishments) . Public·Use Sample from the 1980 Census of Population (for industry distribution of alien proxy·group members) Economic Review - May 1987 5 Table 3 GEOGRAPHIC DIFFERENCES IN ILLEGAL ALIENS PER ESTABLISHMENT Illegal aliens per establishment' Industry Manufacturing Nonmanufacturing California Texas, New York, Illinois. Florida Other 45 states 22 .20 2.90 12.45 1 64 305 036 1 The number of illegal aliens employed in a given industry and region is computed by multiplying an estimate of the size of the illegal nonagricultural labor force by the fraction of all nonagricultural proxy-group workers employed In that industry and region The industries Included are those listed in Table 2 SOURCES OF PRIMARY DATA 1982 Censuses of U S Industries Public-Use Sample from the 1980 Census of Population The distribution of illegals across establishments of different sizes is shown in Table 2. 9 This distribution is determined from the industrial distribution of the proxy group and separate data on workers and establishments in the indicated industries. The entries in the third column have been scaled by an estimate of the number of illegal workers in the United 10 States. With this scaling, the computations produce approximations to the numbers of iIIegals per establishment. The wide range in the number of illegals per establishment is apparent in the third column. Consider the three nonagricultural industries employing the most illegals. Apparel employs almost 20 illegals per establishment, while construction and restaurants employ about 1. In general, manufacturing industries employ more illegals per establishment than do services or construction. The difference, which is very large, is attributable to a combination of larger establishments and more aliens per hundred workers in manufacturing. The geographic variation in illegals per establishment is shown in Table 3. California, which has one-half of the illegal population, has a much larger number of illegals per worksite than do other parts of the country. When combined, the four states ranking immediately below California have half as many illegals and twice as many worksites. 11legals are even more widely scattered in the remaining states. Indeed, California's service sector has almost as large a concentration of aliens as manufacturing does in the 45 lightly penetrated states. The estimated distribution of illegal aliens implies that monitoring and inspection efforts should cover hospitals and most of the manufacturing industries listed in Table 2. 6 large hotels, schools, and department stores also might be included. If budgets are low, enforcement will have to stop there. With a somewhat larger budget, enforcement could be expanded to the larger remaining service-sector employers, particularly in California. Outside of these cases, the number of additional worksites that would have to be inspected in order to monitor a given number of additional jobs becomes very high. Consequently, a very large budget would be necessary to cover fully the non manufacturing sector listed in the tables. One might think that enforcement could be confined to the five states singled out in Table 3. But if enforcement is too selective geographically, factories will migrate to states where enforcement is weak. (This is what happened in the marijuana case.) Thus, some geographic dispersion is necessary. Removal of iIIegals with incomplete enforcement Two issues must be addressed in order to estimate how many of the illegals displaced by selectively enforced sanctions would actually leave the country. The first issue is the response of employers in the unenforced sector, in which employment of illegals is subject to penalties but in which violations are rarely detected. The question is whether employers can be expected to obey the law even if it is not enforced. The second issue is the response of the aliens themselves. The introduction of sanctions will produce a decline in the demand for their labor, and this decline will reduce the advantage to i1legals of working in the United States as opposed to their returning home. The issue is what Federal Reserve Bank of Dallas Illegal Alie n Worke rs in the Texas Econo m y Illegal aliens are more Important to the Texas economy tnan they are to the national economy. Texas accounts for 6.8 percent of total U.S. employment. But based on information from the 1980 Census, the state employs 10.5 percent of all Illegais working In the United States. That a relatively high percentage of Texas Walkers are illegalll"l itself makes the Stale a prime target fOI close supervision by the Immigration authorities. However, illegal wOlkers are mOle widely dl5persed acros:> Individual business establishments In Texas than they are in other states. This will make enforcement more e)(J)ensive to carry out Within the state. Shown in the table ale the 2Q nonagricultural industries tnat employ the largest numbers of l11egal aliens in Texas. The industrie5 are ranked according to the average number of iIIegals that work at an Individual establishment. Following the discussion In the text, mdustries with a large number of illegals pel establishment are likely to be monitored especially closely. The nature of the ranking for industries in Texas is very similar to that nationwide. Apparel and food processing are at the top of the list, as they are in the national figu res. And more generally, manufacturing industries agam make the best targets for inspection. Of the 10 industries with at least 5 megals per establishment, 7 are in manufactunng. One Important difference between Texas and the nation, however, is that a smaller percentage Or the illegals Il'I Texas are employed in manufacturing industries. Manufacturing employs 48.0 percent of the illegal workforce nationwide, but only 31.4 percent of the illegal workers in Texas. This is largely a reflection of the more important role that construction plays as an employer of illegal aliens in Texas. Manufacturing, however, is the industry group with the highest concentration of illegal workers at the individual worksite. Outside of manufacturing. illegals are widely scattered ac ross establishments. This means that the monitonng of potential employers of illegal aliens will be relatively expensive in Texas. 1/ enforcement efforts are correspondingly less effective in Texas, this Will soften the impact that the new Immigration law will have on the state's economy. Economic Review- May 1987 INDUSTRY DISTRIBUTION OF IllEGAL ALIEN WORKERS IN TEXAS P~.u·nt~lIe 01 ,ll ea~1 ~henS Indun", Canned fruits and vegetables Apparel Meat products Primary metals Beverages and miscellaneous food Hospitals Electrical machinery Transport equipment Educational institutions Hotels and motels Services to dwellings Wholesale grocers lumber and wood products Fabricated metals Construction Private households Eating and drinking places Auto repair Retail grocers Oil and gas extraction ...lS Pl" t"ldbl .. hml'nl 11I"~~ 1 ~h In non~ g ,,~u!tu.al 'nduSI"es 1 .51 8 .73 82.74 40.32 24.10 17.01 147 145 9.74 9.61 8.22 8.04 1 42 1 .31 1 .79 1 .22 .'0 5.16 2.92 2.57 2.41 2.34 4.57 450 1&0 1.17 1 .74 18.88 2.&& 1.59 0,81 0.58 7.87 1 .36 1 .57 0.27 1 41 3.80 2.91 2.17 SOURC ES OF PR IMARV DATA 1982 Censuses 01 U S IfI(!uSl'oel,. Pubhc·U~ S.mple foam the 1!16O Cens .... of Pop ... laI,on , determines how many will remain working in the United States. Compliance without enforcement? The response of employers can, to some degree, be predicted by examining how employers' costs depend on enforcement. In economic models of illegal activity, individuals weigh the expected gain from taking an illegal action against the expected cost. The expected cost includes the expected penalty imposed upon detection and the probability of detection. This model of behavior has a mixed record for explaining illegal activity, but it does provide a useful framework for exploring the factors to be weighed by potential employers of illegals. 11 The penalty structure established in the new law is likely to encourage compliance among employers who suspect they are being monitored. 12 It is somewhat lenient on firsttime offenders, though. The fines vary with the number of illegals employed and the number of previous offenses. First offenses carry a fine ranging from $250 to $2,000 per alien (except during the first year of enforcement, when first-time violators will receive a warning). Fines for second offenses are higher, and third offenses carry fines ranging from $3,000 to $10,000 per alien. Employers convicted of pattern or practice violations are subject to criminal penalties. This penalty structure will tend to reinforce the effect that different monitoring intensities will have on the expected cost of employing illegals. Employers with prior convictions will be closely monitored and will face large fines for any future detected violations. Employers who are not closely monitored are unlikely to have had prior convictions and will, therefore, be subject to small fines if their violations are discovered. In such an environment, sanctions provide a strong deterrent to hiring illegals for some employers and a weak deterrent for many others. Because fines are set on a per-alien basis, sanctions are analogous to a tax on the employment of illegals. This analogy is particularly useful if the employers know the enforcement pattern and have no ethical or moral reservations about disobeying the law. Where the probability of detection is high (near 1), the tax rate is the likely amount of the fine to be imposed upon detection. Here, the advantage of employing illegals, which is assumed to be a lower wage, would be be offset by the penalties of being caught. Sectors with somewhat higher costs of monitoring compliance would have somewhat lower probabilities of detection. In these sectors, the tax rate would then be the expected amount of the fine times the probability of detection. Sanctions would be a less powerful deterrent here. In sectors in which high monitoring costs make probabilities of detection very low, the tax rate would be negligible, and 8 sanctions would provide little deterrence to the employment of illegals. The economic model implies that employers in sectors where monitoring costs are high will continue to employ illegals. This conclusion rests on two assumptions-that employers know the enforcement pattern and that they not be overly averse to risk. Behavior with respect to other laws, such as income tax codes and speed limits, is consistent with the assumption that people are aware of patterns of enforcement and that they are willing to take some risks where the odds appear to be in their favor. But the issue of risk raises a question about what enforcement strategy the authorities will adopt. An emerging line of research indicates that uncertainty about the probability of detection, even if low, serves as a deterrent. 13 Consequently, one strategy the authorities could adopt would be unpredictability. Experience, as well as the plans of the Immigration and Naturalization Service as reported in testimony before Congress, suggests that the INS will not behave unpredictably.14 Law enforcement agencies, from the Internal Revenue Service to the local police, display a strong tendency toward predictable emphasis on specific targets. 15 This research on how unpredictable enforcement patterns affect compliance has an important implication for compliance with the immigration law, however. Because knowledge about the enforcement strategy is likely to be scant when the new law first goes into effect, compliance is likely to be high initially. Recent media coverage, revealing that employers were dismissing illegals soon after the law was passed, supports this conclusion. 16 Once information about detection probabilities becomes widely available, however, compliance is likely to fall into a pattern. The research reported here thus applies better to an equilibrium achieved after the law has been in effect for a year or two. labor market adjustment. The effect of selectively enforced sanctions on employment of illegals can be explored through a standard supply-demand analysis of the market for illegal labor. How the policy is likely to affect the wages of illegal workers and the location of their employment is shown in Figure 2. The domestic economy has two sectors. Sector A consists of industries subject to inspection by the authorities and for which sanctions effectively operate as a tax on illegal labor. Sector B comprises all other industries, with enforcement in these industries considered negligible. The supply of illegal workers and the demand for these workers from industries in Sector B are shown in the left panel in Figure 2. These relationships are used to derive the excess supply schedule shown in the right panel. The market for illegal immigrant labor is in equilibrium when the Federal Reserve Bank of Dallas Figure 2 Effect of Employer Sanctions on the Market for Illegal Immigrant Labor WAGE WAGE S· Ds S w w w' w' 0A ' Ds j IB I' B I' QUANTITY excess supply from Sector B equals the demand from industries in Sector A. Sanctions reduce the demand for illegal labor in Sector A. This drives down the net immigrant wage from w to w'. Given the expected penalty, the cost of illegal labor is still higher for industries in Sector A. As a result, fA - 1/ workers are displaced, and I - I' of these withdraw from the national market. The remaining Is' - Is find employment in Sector B. The single-market model outlined above can be used to uncover the economic parameters that bear crUCially on the way the displaced workers are allocated between countries. A simple equation expresses the number of illegal workers leaving the national labor market as a fraction of the total number of workers displaced from the enforced sector: The value of dl/dlA is seen to depend upon three parameters: the elasticity of supply of illegal labor (1/), the share of illegal workers employed in the unenforced sector (As), and the elasticity of demand for illegal labor (8). The direction of influence each parameter has on the solution is straightforward: The more responsive the supply of immigrant labor to a decline in wages, the greater the share of the displaced workers who withdraw from the U.S. labor market. On the other hand, if a large fraction of illegal workers are employed in the unenforced sector and the capacity of that sector to absorb additional workers is high (as measured by a large elasticity of demand), then more of the workers who leave the enforced sector will find jobs in the unenforced sector. Economic Review - May 1987 I'A IA QUANTITY Quantifying the effects of sanctions Simulation runs performed with a small model of the U.S economy are discussed in this section. In having the simulations portray the effects of sanctions under varying levels of enforcement, three alternative enforcement schemes are analyzed. Industries are ranked according to the number of illegal aliens per establishment. Enforcement is assumed to start with the industry having the highest value and, in stages, to displace all illegals from industries having eight or more illegals per establishment (low enforcement coverage), then from two or more (medium coverage), and finally from all the industries listed in Table 2 (high coverage). The first enforcement level covers hospitals and nearly all manufacturing-industries that employ about one-third of the nonagricultural illegals. The second level extends coverage to about half of these illegals. The third level covers almost three-fourths of the illegals. Assumptions. Several simplifying assumptions were necessary to make the computations feasible. 1 ? The economy is divided into two sectors-one in which compliance with sanctions is complete and another with sanctions ignored.18 Production in each sector is a function of four factors: illegal immigrants, legal low-skilled labor, high-skilled labor (all presumed to be legaD, and capital. All markets are competitive, and production is governed by constant returns to scale. Assumptions about the various elasticities of substitution, demand, and supply are taken from the available empirical literature. For two key parameters, the simulations have been conducted over a range of values. 9 Table 4 EFFECT OF SANCTIONS ON EMPLOYMENT OF ILLEGAL ALIENS Enforcem e nt level Measure Number of establishments in enforced sector (in thousands) ... Percentage of illegal aliens initially employed in enforced sector Fraction of initially displaced illegal aliens leaving the United States Using favorable elasticities (11=1.0. €=1.0) Using intermediate elasticities (11=1 .0. €=1 .5) Using unfavorable elasticities (11= .5. €=1 .5) Percentage reduction in employment of illegal aliens Using favorable elasticities (11=1 .0. F1 .0) Using intermediate elasticities (11=1.0, €=1.5) Using unfavorable elasticities (11= .5, €=1 .5) One of these parameters is the elastiCity of immigrant supply (1'/ in the equation). Recall from Figure 2 that downward pressure on the wage of illegals is what motivates illegals to return to their native country. The supply elasticity reflects the magnitude of this response. The simulation runs used elasticities of 0.5 and 1.0. With these values, each 1.0-percent reduction in the illegal wage reduces the illegal workforce by 0.5 and 1.0 percent. The choice of this range is based on the results reported in the empirical literature, which indicate that the elasticity falls between 0.5 and 2.0.19 The values adopted are in the lower portion of the range for two reasons. First, the simulations here attempt to capture the effect of large changes in wages, whereas the estimates reported in the literature are point estimates of responses to small changes. They will therefore tend to overstate the response to large wage reductions. Secondly, the simulations do not directly incorporate the effect that immigration reform might have on the labor market in Mexico. Using low values indirectly cap10 Low Medium Hi gh 99 275 1.516 33 49 73 61 65 .79 .48 .55 .71 .33 .39 .56 20 32 58 16 27 52 11 19 41 tures the possibility that wages of illegals will decline in their home country as well as in the United States. Another parameter of importance is the sensitivity of the demand for illegals to their wage ( t: in the equation). This elasticity measures the unenforced sector's ability to absorb displaced illegals. The simulations assume values of 1.5 and 1.0. The literature suggests that the demand elasticity for low-wage labor in general is about 1/° a value that should be considered a lower bound for illegals. Normally, demand is more elastic for an individual member of a family of goods than for the entire family. For example, demand for a specific brand of soft drink is more sensitive to a change in its price (when prices of other brands are held constant) than is demand for all soft drinks as a group. Thus, estimating the effect with a higher elasticity of 1.5 is useful. Results. The simulation results are shown in Table 4. The figures in the first two rows reflect how coverage varies across the three enforcement regimes. The top row contains the number of establishments in the industries inFederal Reserve Bank of Dallas c1uded in the enforced sector. The entries in the second row are the percentages of illegal aliens that are employed in the enforced industries before sanctions are applied. Under the assumptions of the simulation model, these are also the percentages of illegals initially displaced by the introduction of sanctions. The third through the fifth rows show the extent to which iIIegals initially displaced actually leave the country. Leakage-the fraction of those displaced who become employed in the unenforced sector-can be computed by subtracting these values from 1. Each row shows the values under different supply and demand elasticities. The bottom three rows show the reduction in the employment of illegals after allowing for leakage. Results with different elasticities are shown to illustrate the range of likely effects. The elasticities used for the third and sixth rows, labeled "favorable," show the maximum likely effectiveness of sanctions for each level of coverage. The fifth and eighth rows, computed under "unfavorable" elasticities, reflect the minimal likely effectiveness. What the simulations reveal about differences in the enforcement level can be seen by looking across the rows. Higher enforcement levels naturally lead to larger reductions in employment of illegals. With intermediate supply and demand elasticities, employment of iIIegals will fall by 16 percent when enforcement is low and 52 percent when enforcement is high. The obvious contributor to this relationship is the larger number of illegals initially displaced when enforcement coverage expands; initial displacement in the simulations rises from 33 percent to 73 percent. Also contributing, however, is an increase in the fraction of those displaced who actually leave the country. With intermediate elasticities, the fraction rises from about one-half to about seven-tenths. This pattern reflects the smaller unenforced sector and the greater downward pressure on wages of illegals when enforcement coverage is higher. The importance of the supply and demand elasticities can be seen by comparing the appropriate rows. With medium coverage, the reduction in employment of illegals will be 32 percent if the elasticities are favorable and 19 percent if they are unfavorable. This difference is entirely attributable to greater leakage when demand for immigrant labor is more elastic and immigrant supply is less elastic. With medium enforcement and favorable elasticities, only 35 percent (100 x [1 - 0.65]) of the initially displaced illegals find jobs in the unenforced sector. This leakage is over 60 percent (100 x [1 - 0.39]) when the elasticities are unfavorable. The simulations allow the effects of sanctions to vary over a wide range. This range can be narrowed somewhat by examining the costs of enforcement. Throughout the range of enforcement considered in Table 4, marginal costs rise Economic Review - May 1987 with reductions in employment of illegals. Expanding from low to medium coverage increases the number of illegals removed by 60-75 percent, but the number of establishments monitored rises by 175 percent. Expanding to high coverage about doubles the removal of illegals, but it increases the number of establishments to be monitored by 450 percent. Reaching the high level thus requires that Congress be willing to add a large amount to the enforcement budget for a relatively small gain in compliance. Consequently, enforcement at the high level is unlikely. If one is willing to accept that enforcement will be somewhere in the low to medium range, then sanctions can be expected to reduce the employment of illegals by one-tenth to one-third. The range of possible effects can be further narrowed by adopting the intermediate assumptions about supply and demand elasticities. Then the simulations predict that employment of illegals would drop by one-sixth to one-fourth. Conclusions The analysis presented here produces some straightforward conclusions: • That enforcement of sanctions will be selective and that worksites with numerous jobs that can be filled by illegals are the most attractive targets; • That effective enforcement will be limited to 30-50 percent of the jobs performable by illegals and that the vast majority of these jobs will be in manufacturing, particularly in California; and • That about 50 percent of the illegals displaced by enforcement of sanctions will find employment in industries where enforcement is negligible. Thus, a forecast that sanctions will reduce the employment of illegals by 15-25 percent is consistent with this analysis. This prediction applies to the environment expected to develop after sanctions have been enforced for a year or so. In the initial period of enforcement, sanctions may be more effective because ignorance about the pattern of enforcement will make employers more cautious about hiring illegals. Whether an effect of this magnitude is deemed to be satisfactory will depend on the beholder. Up to now, the debate has been confined largely to whether sanctions are "good" or "bad." Enforcement has tended to be discussed as an all-or-nothing question. In this light, a 20-percent reduction in the employment of illegals might not seem very impressive. But such a reduction could represent one 11 million people, a number that is difficult to dismiss as inconsequential. 1. See The House Committee on the Judiciary, The "Immigration Reform and Control Act of 1986" (P.L. 99-603): A Summary and Explanation, 99th Con g., 2d sess., December 1986 (Washington, D.C.: Government Printing Office, 1986). For background coverage of the various issues related to the present topic, see the list of references at the end of this article. 2. See U.S. General Accounting Office, Illegal Aliens: Information on Selected Countries' Employment Prohibition Laws, Briefing Report to the Chairman of the Subcommittee on Immigration, Refugees, and Internationallaw, House Committee on the Judiciary (Washington, D.C.: Government Printing Office, October 1985). This document reports the results of a survey of Hong Kong and nine countries (Austria, Canada, Denmark, Federal Republic of Germany, France, Italy, Spain, Sweden, and Switzerland). Although most countries reported that sanctions reduced the number of illegal aliens, none provided any evidence supporting that claim. Thus, the extent to which sanctions are effective has not been rigorously analyzed . 3. This figure is based on 1982 data. It probably understates the number of employers in existence in 1987. See the footnotes to Table 2 for sources. 4. Enforcement responsibilities are divided between the Department of labor and the Immigration and Naturalization Service. The number of enforcement agents has not been determined because funding has yet to be authorized. Newspapers have reported that the INS will assign 1,632 investigators (see Gilbert Bailon, "Funds to enforce alien law debated: Critics say more needed to avert 'nightmare,'" The Dallas Morning News, 11 February 1987, lA, 14A) and that the agencies combined will employ 2,700 agents (see Dudley Althaus, "Reform act may hinder u.s. growth," The Dallas Times Herald, 23 March 1987, A-l, A-ll). 5. See Kenneth R. Weiss, "Shift From West: Marijuana Growers Taking Root In Southeast," Sarasota (Fla.) Herald-Tribune, 15 March 1987 6. Opposition arises from a variety of sources. For presentations of views from several perspectives, see Senate Committee on the Judiciary, Immigration Reform and Control Act of 1985: Hearings, On S. 1200, A Bill to Amend the Immigration and Nationality Act to Eflectively Control Unauthorized Immigration to the United States and for Other Purposes, 17, 18, 24 June 1985, Before the Subcommittee on Immigration and Refugee Policy, 99th Cong., 1st sess, S. Hrg. 99-273, Serial J-99-35 (Washington, D c.: Government Printing Office, 1985) Also, see William F. Shughart, Robert T. Tollison, and Mwangi S. Kimenyi, "The Political Economy of Immigration Restrictions," Yale Journal of Regulation 4 (Fall 1986): 79-97, for an analYSis of how the opposing positions of business and organized labor have been reconciled to produce small budgets for border enforcement that have varied over time. 7 12 See Jeffrey S. Passel, "Estimating the Number of Undocumented Aliens," Monthly Labor Review 109 (September 1986): 33. In his article "How Many Illegal Aliens?" (in The Journal of the Institute of Socioeconomic Studies 10 [Winter 1986J: 13-20), Courtenay Slater provides a good, nontechnical summary of research on the number of illegals. The article contains a history of the methods used to obtain the estimates, as well as many references . 8. Evidence supporting the use of this group as a proxy for illegal immigrants is presented in James E. Pearce and Jeffery W. Gunther, "Immigration from Mexico: Effects on the Texas Economy," Economic Review, Federal Reserve Bank of Dallas, September 1985, 1-14 . Kevin F. McCarthy and R. BurCiaga Valdez, in Current and Future Eflects of Mexican Immigration in California (Santa Monica, Calif.: The Rand Corporation, May 1986), also use this approach to approximate the distribution of illegals. 9. Crop farming is excluded from the list because the reform legislation contains two special provisions for meeting the fruit and vegetable growers' seasonal demand for labor with immigrant workers. The first provides for employment of guest workers allowed in the country temporarily to harvest perishable crops. The second provides for legalization of illegals who worked in seasonal agriculture in the year ending May 1986. These workers are required to work in agriculture for 90 days for three years after their legal status has been adjusted . The law also provides for additional workers to be legalized in a similar fashion if the supply of initially legalized agricultural workers is exhausted . 10. The value used is 4 million . It was derived by assuming a population of 6 million illegals, from which allowances are made for those not working, those working in agriculture, and those eligible for amnesty. The resulting estimate is probably too high, but because the error affects all industries equally, the ranking is preserved. 11 . The seminal articles in this endeavor are Gary S. Becker, "Crime and Punishment: An Economic Approach," Journal of Political Economy 76 (March/April 1968): 169-217; and Isaac Ehrlich, "Participation in illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy 81 (May-June 1973): 521-65, The model has been applied extensively to compliance with tax laws. For surveys and assessments of this literature, see Ann D, Witte and Diane F, Woodbury, "What We Know About the Factors Affecting Compliance with the Tax laws," in Income Tax Compliance, A Report of the ABA Section of Taxation, Invitational Conference on Income Tax Compliance (American Bar Association, 1983), 133-48; and Michael W . Spicer, "Civilization at a Discount: The Problem of Tax Evasion," National Tax Journal 39 (March 1986): 13-20. For a more general survey, see chap. 9 of Peter Schmidt and Ann D. Witte, An Economic Analysis of Crime and Justice: Theory, Methods, and ApplicatiOns (Orlando, Fla: Academic Press, Inc., 1984). 12 See The "Immigration Relorm and Control Act of 1986" (P.L. 99-603) . 13 See lawrence W. Sherman, "Uncertain Risks, Uneasy Criminals," Wall Street Journal, 11 September 1986, Southwest ed ., 34 Spicer also mentions that uncertainty about the probability of detection can serve as a deterrent This idea also relates to strategies for monitoring employees . Guillermo A. Calvo and Stanislaw Wellisz, in "Supervision, loss of Control, and the Optimum Size of the Firm," Journal 01 Political Economy 86 (October 1978): 943-52, discuss the efficiency of discontinuous, but unpredictable, monitoring to discourage employees from shirking. 14 INS Commissioner Nelson testified that plans for enforcing employer sanctions involve targeting specific employers for intensive monitoring See Alan C. Nelson, "Statement by Alan C. Nelson, CommiSSioner, Immigration and Naturalization Service," in Hearings, On H.R 1510, Immigration Relorm and Control Act 011983,1,2,9,10,14, and 16 March 1983, Before the Subcommittee on Immigration, Refugees, and Internationallaw, House Committee on the Judiciary, 98th Cong, 1st sess" Serial 2 (Washington, D,C: Government Printing Office, 1983) Federal Reserve Bank of Dallas 15. See Sherman's article in the Wall Street Journal. 16. See recent coverage by Maria E. Recio, Julie Flynn, Aaron Bernstein, and Staff, "Reform Breeds Its Own Crisis: The New Immigration law Causes Headaches All Over: Business Week, 30 March 1987, 26-27. 17. See John K. Hill and James E. Pearce, "The Incidence of Sanctions against Employers of Illegal Aliens: Working Paper, Federal Reserve Bank of Dallas, April 1987, for a complete discussion of the model. In addition to quantifying the removal of iIIegals, the model produces estimates of the changes in wages of legal workers and changes in output in both sectors. Economic Review - May 1987 18. The model assumes that employment of all nonagricultural illegal aliens not eligible for amnesty is sanctionable. The law, however, exempts illegals who were hired before 6 November 1986. But this assumption will not result in misleading data if turnover among iIIegals is high, a condition likely to be met. 19. See P. Krugman and]. N. Bhagwati, "The Decision to Migrate: A Survey: in The Brain Drain and Taxation : Theory and Empirical Analysis, edited by]. N. Bhagwati (Amsterdam: North Holland, 1976). 20. See A. Zucker, "Minimum Wages and the long Run Elasticity of Demand for low Wage labor: Quarterly Journal of Economics 87 (May 1973): 267-77; and P. Cotterill, "The Elasticity of Demand for low Wage labor: Southern Economic Journal 41 Oanuary 1975): 520-25. 13 References Althaus, Dudley. "Reform act may hinder u.s. growth." Dallas Times Herald, 23 March 1987, A-l, A-ll. Ashenfelter, Orley, and Robert S. Smith. "Compliance with the Minimum Wage Law." Journal of Political Economy 87 (April 1979): 333-50. Bailon, Gilbert. "Funds to enforce alien law debated: Critics say more needed to avert 'nightmare."' The Dallas Morning News, 11 February 1987, lA, 14A. Becker, Gary S. "Crime and Punishment: An Economic Approach." Journal of Political Economy 76 (March/April 1968): 169-217. Calvo, Guillermo A., and Stanislaw Wellisz. "Supervision, Loss of Control, and the Optimum Size of the Firm." Journal of Political Economy 86 (October 1978): 943-52. Clotfelter, Charles T. "Tax Evasion and Tax Rates: An Analysis of Individual Returns." The Review of Economics and Statistics 65 (August 1983): 363-73. Cotterill, P. "The Elasticity of Demand for Low Wage Labor." Southern Economic Journal 41 (January 1975): 520-25. Ehrlich, Isaac. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation." Journal of Political Economy 81 (May-June 1973): 521-65. Graetz, Michael J., and Louis L. Wilde. "The Economics of Tax Compliance: Fact and Fantasy." Paper from National Tax Association-Tax Institute of American Symposium. Emerging Issues in Tax Policy. Washington, D.C., 20, 21 May 1985. National Tax Journal 38 (September 1985): 355-63. Hill, John K., and James E. Pearce. "The Incidence of Sanctions against Employers of Illegal Aliens." Working Paper. Federal Reserve Bank of Dallas, April 1987. Krugman, P., and J. N. Bhagwati. "The Decision to Migrate: A Survey." In The Brain Drain and Taxation: Theory and Empirical Analysis, edited by j. N. Bhagwati. Amsterdam: North Holland,1976. McCarthy, Kevin F., and R. Burciaga Valdez. Current and Future Effects of Mexican Immigration in California. Santa Monica, Calif.: The Rand Corporation, May 1986. Nelson, Alan C. "Statement by Alan C. Nelson, Commissioner, Immigration and Naturalization Service." Hearings. On H.R. 1510, Immigration Reform and Control Act of 1983. Before the 14 Subcommittee on Immigration, Refugees, and International Law, House Committee on the Judiciary, 1, 2, 9, 10, 14, and 16 March 1983. 98th Cong., 1st sess. Serial 2. Washington, D.C: Government Printing Office, 1983. Passel, Jeffrey S. "Estimating the Number of Undocumented Aliens." Monthly Labor Review 109 (September 1986): 33. - - - , and Karen A. Woodrow. "Geographic Distribution of Undocumented Immigrants: Estimates of Undocumented Aliens Counted in the 1980 Census by State." International Migration Review 18 (Fall 1984): 642-71. Pearce, James E., and Jeffery W. Gunther. "Immigration from Mexico: Effects on the Texas Economy." Economic Review, Federal Reserve Bank of Dallas, September 1985, 1-14. Schmidt, Peter, and Ann D. Witte. An Economic Analysis of Crime and Justice: Theory, Methods, and Applications. Orlando, Fla.: Academic Press, Inc., 1984. Recio, Maria E.; Julie Flynn; Aaron Bernstein; and Staff. "Reform Breeds Its Own Crisis: The New Immigration Law Causes Headaches All Over." Business Week, 30 March 1987, 26-27. Sherman, Lawrence W. "Uncertain Risks, Uneasy Criminals." Wall Street Journal, 11 September 1986, Southwest ed., 34. Shughart, William F.; Robert T. Tollison; and Mwangi S. Kimenyi. "The Political Economy of Immigration Restrictions." Yale Journal of Regulation 4 (Fall 1986): 79-97. Slater, Courtenay. "How Many Illegal Aliens?" The Journal of the Institute for Socioeconomic Studies 10 (Winter 1986): 23-32. Spicer, Michael W . "Civilization at a Discount: The Problem of Tax Evasion." National Tax Journal 39 (March 1986): 13-20. Stigler, George j. "The Optimum Enforcement of Laws." Journal of Political Economy 78 (May/June 1970): 526-36. Tulacz, Gary, Esq. How to Comply With the Tough New Immigration Law. Personnel Management, Labor Relations, Bull. 1, sec. 2, January 1987. Paramus, N.J.: Prentice-Hall Information Services, 1987. U.S. Congress. House. Committee on the Judiciary. Hearings. On H.R. 1510, Immigration Reform and Control Act of 1983. Before the Subcommittee on Immigration, Refugees, and International Law, 2, 9, 10, 14, and 16 March 1983. 98th Cong., 1st sess. Serial 2. Washington, D.C.: Government Printing Office, 1983. Federal Reserve Bank of Dallas References (Continued) - - -. The "Immigration Reform and Control Act of 1986" (P.L. 99-603): A Summary and Explanation. 99th Cong., 2d sess., Report to the Chairman, Subcommittee on Immigration, Refugees, and International Law, House Committee on the Judiciary, October 1985, GAO/GGD-86-17BR. Washington, D.C.: Government Printing Office, 1986. December 1986. Washington, D.C.: Government Printing Office, 1986. - - - . Senate. Committee on the Judiciary. Immigration Reform and Control Act of 1985: Hearings. On S. 1200, A Bill to Amend the Immigration and Nationality Act to Effectively Control Unauthorized Immigration to the United States and for Other Purposes. Before the Subcommittee on Immigration and Refugee Policy, 17, 18, 24 June 1985. 99th Cong., 1st sess. S. Hrg. 99-273. Serial 9-99-35. Washington, D.c.: Government Printing Office, 1985. u.s. Department of Commerce, Bureau of the Census. 1980 Census of Population and Housing. Washington, D.C.: Gov- ernment Printing Office, March 1982. - - -. Five-Year Censuses of u.s. Industries. Washington, D.C., 1982. (Censuses used include those for Manufactures, Construction Industries, Service Industries, Wholesale Trade, Retail Trade, and Mineral Industries.) u.s. General Accounting Office. Illegal Aliens: Information on Selected Countries' Employment Prohibition Laws. Briefing Economic Review - May 1987 - - - . Illegal Aliens: Umited Research Suggests Illegal Aliens May Displace Native Workers . Briefing Report to Congressional Requesters, April 1986, GAO/PEMD-86-9BR. D.C.: General Accounting Office, 1986. Washington, Weiss, Kenneth R. "Shift From West: Marijuana Growers Taking Root In Southeast." Sarasota (Fla.) Herald-Tribune, 15 March 1987. Witte, Ann D., and Diane F. Woodbury. "What We Know About the Factors Affecting Compliance with the Tax Laws." In Income Tax Compliance . A Report of the ABA Section of Taxation, Invitational Conference on Income Tax Compliance, American Bar Association, Reston, Va., 16-19 March 1983. American Bar Association, 1983. Zucker, A. "Minimum Wages and the Long Run Elasticity of Demand for Low Wage Labor." Quarterly Journal of Economics 87 (May 1973): 267-77. 15 Estimating the Inflationary Consequences of Discretionary Central Bank Behavior Kenneth J. Robinson Economist Federal Reserve Bank of Dallas Traditional examinations of central bank behavior assume the Federal Reserve conducts monetary policy in an attempt to achieve various macroeconomic goals, such as full employment and price stability. It has been hypothesized, however, that the central bank's objectives include not only macroeconomic goals and constraints but political goals and constraints as welL 1 Viewed in this manner, policy outcomes are the result of a series of trade-offs emanating from an attempt to balance the perceived benefits and costs (both economic and political) accruing to the Fed. Unlike previously estimated models of central bank behavior, the following analysis utilizes this benefits-costs approach. A Federal Reserve reaction function is derived in an attempt to explain why a central bank might allow or even pursue an inflationary monetary policy. That is, a certain mode of behavior on the part of the central bank is hypothesized to exist. The Fed is assumed to conduct policy based on the goals implied by the model of central bank behavior developed and the constraints under which the policymaker is assumed to operate. The model is built on the assumption that the central bank values implicit revenue from both money creation and the reduction in real federal debt outstanding. In addition, the policymaker faces certain constraints, particularly deviations of unemployEconomic Review - May 1987 ment from its "natural" rate and the costs associated with following an inflationary monetary policy. The empirical results indicate that seigniorage is a significant factor in explaining observed inflation rates. Moreover, the effect of this source of revenue on inflation varies with fiscal policy considerations. These findings lead to a certain amount of skepticism regarding central bank autonomy. Unemployment deviations are also significant factors behind central bank behavior but are not affected by election-year considerations. Thus, the evidence regarding central bank independence appears mixed. Considerations of the policymaker In its conduct of monetary policy, the central bank considers certain goals or objectives. The objectives assumed in this model are achieved through manipulation of inflation rates over time. That is, revenue from both money creation and depreciating federal debt outstanding is available through variations in the inflation rate. The macroeconomic constraints under which the Fed operates-namely, unemployment deviations and the costs of an inflationary policy-are also related to the central bank's policy outcome of inflation. 17 Revenue. A central bank that can create money has at its disposal a relatively easy means of obtaining revenue. For every dollar the central bank prints, it creates that many extra dollars for use by government to finance its spending. Given that the inflation rate is positively related to growth in the money supply, inflation amounts to a tax (implicit) on holdings of money. Revenue, in real terms, from the inflation tax is composed of two parts: the base of the tax, which is the level of real cash balances held by the public, and the rate of the tax, which is the rate of depreciation in the real value of money. If growth in the money supply is constant, the rate of inflation that yields maximum revenue occurs when the elasticity of demand for real cash balances equals - 1. When allowing for economic growth, there are two sources of revenue available to government: the proceeds of the tax on existing cash balances and further revenue from providing additional cash balances demanded by the public as income rises. Inflation, especially when unanticipated, favors some groups over others as it reduces the repayment burden of debtors and may encourage various types of investments. Since government is a large debtor, it stands to gain from the redistribution that favors debtors at the expense of creditors. The process by which this redistribution is accomplished stems from the fact that government commits itself to repay a fixed number of dollars when redeeming its securities and paying interest on them. "Unanticipated inflation reduces the amount of real resources embodied in this commitment. Hence, inflation captures, from those who purchased bonds, resources which otherwise either would not be available for Governmental use or distribution or would have to be financed with other taxes.,,2 Macroeconomic goals. The assumption that the Fed conducts monetary policy only with the consideration of extracting revenue imputes a rather narrow, bureaucratic mode of behavior to the central bank. Ample evidence exists, however, that the Federal Reserve, in its conduct of policy, is guided by macroeconomic goal variables. Federal Reserve reaction functions are estimated in an attempt to capture the effect on monetary policy of departures of certain macroeconomic targets from their "desired" levels. Reaction functions differ in what is assumed to be the policy variable (or dependent variable). These functions also differ in the definition of the actual targets and of the levels deemed optimal by the central bank. 3 Regardless of the policy instrument considered, though, evidence is presented indicating a strong, consistent response by the monetary authorities to departures of unemployment from the target rate. Departures of other goal variables from their targets-such as inflation, balance of 18 payments surplus, and real gross national product (GNP)exhibited a less systematic response by the Fed in the models estimated. Therefore, unemployment deviations are assumed to be the macroeconomic goal representing the Federal Reserve's concern about economic performance. Consequences of inflation. Evidence from more traditional views of central bank policymaking also indicates a concern on the part of the Fed about the ramifications of sustained inflation. An inflationary monetary policy imposes costs upon the economy that the Fed considers in its conduct of policy. For instance, unanticipated inflation hinders effective economic planning. Inflation, even when antiCipated, also inflicts welfare costs on the economy resulting from reductions in the amount of real money balances demanded. This decline in the use of money leads to costs in the form of loss of convenience, increasingly awkward barter arrangements, and so on. Fischer and Modigliani provide a descriptive analysis of the costs of anticipated and unanticipated inflation. 4 In addition, Fischer derives estimates of the effects of inflation on returns to capital and savings that amount to as much as 2 to 3 percent of GNP. Fischer concludes, "While the evidence and numbers cited ... are far from definitive, they support the notion that the welfare costs of high inflation, even if the inflation is expected, are large in the current United States economy."s Given the assumed objectives, it is possible to formulate a model of Federal Reserve policymaking. Such a formulation facilitates empirical testing of whether these considerations provide any inSights into explaining observed inflation rates. A model of central bank behavior In developing the model, it is hypothesized that the Fed considers both the benefits it derives and the costs incurred when conducting monetary policy. The central bank controls its instruments to achieve its policy target (ostensibly, money growth) in an attempt to attain the goal of maximizing its objective function. The objective function contains as arguments: seigniorage, redistribution effects (here, those associated with redUCing the value of government debt), deviations of unemployment from a preferred rate or goal, and regard for the costs associated with inflation . The Fed values, or derives certain benefits from, seigniorage, as it reduces the need for government to resort to more conventional, overt methods of taxation in the financing of public expenditures. Further, the Fed values certain redistribution effects associated with inflation, particularly with regard to debtors versus creditors. As the Federal Government is a large issuer of debt, the reasoning Federal Reserve Bank of Dallas is analogous to that of the first assumption. Underlying these two assumptions is an element of doubt regarding the complete independence of the central bank. That is, the Fed may be motivated at times to use inflation to extract revenue if it perceives such action to be of value to either the executive or the legislative branch of government. 6 It is also argued that Federal Reserve policymakers consider the costs associated with their actions. With this in mind, it is hypothesized that the Fed is constrained by a performance trade-off, especially in the case of unemployment. In addition, costs associated with an inflationary monetary policy represent a further constraint on Federal Reserve behavior. Thus, the central bank is allowed to possess different interests (or some independence) from elected officials, particularly with regard to the consequences of its policymaking. Given these assumptions, a formal model of central bank behavior is developed fully in Appendix A to determine the extent to which observed inflation rates are the result of an attempt to balance the hypothesized benefits and costs that monetary policymakers face. The significance of these factors in explaining inflation provides insights into the degree of autonomy enjoyed by the central bank. That is, a truly autonomous central bank, attempting to achieve traditional macroeconomic goals, such as full employment and price stability, would resist any pressures placed on it to provide government with revenue. The reaction function is then modified to allow for detection of possible outside influences affecting monetary policy-namely, fiscal policy effects and election-year considerations. Such a specification provides further evidence regarding the degree of central bank independence. Benefits. Seigniorage is defined formally as the extra dollars created by the central bank in any time period. In real terms, then, seigniorage is the change in the money supply divided by the current price level. The public's demand for real money balances plays an important role in the amount of revenue that can be collected. The more inflation people expect, the less money they are willing to hold. In effect, the public's holdings of money are inversely related to expected inflation. If the Fed prints too much money, people come to expect more inflation. Consequently, revenue could actually decline if the public rapidly reduces its demand for real money balances. Under a fractional-reserve banking system, the central bank receives as seigniorage only a portion of the actual money supply. The Fed supplies the monetary base, and the actual money supply is some multiple of the base. Therefore, the amount of seigniorage the central bank collects is related to the money supply multiplier. If the multiplier exEconomic Review - May 1987 ceeds unity, the Fed shares a portion of the revenue with the banking system. If the multiplier is reduced, the portion of inflationary finance accruing to the central bank is increased. 7 The national accounts in the federal budget treat the Federal Reserve System as though it were a private corporation. Therefore, the transfer of revenue from the Fed to the U.S. Treasury is classified as a tax on corporate profits. s The percentage of total federal taxes on corporate profits that these Federal Reserve payments account for is shown in Chart 1. Over the 1951-85 period, these transfers have made up an increasing proportion of the collected tax on corporate profits. As Chart 2 demonstrates, however, Federal Reserve payments to the Treasury have remained a relatively small part of total Federal Government receipts. Redistribution effects associated with reducing the value of nominal federal debt outstanding also generate revenue for government. This revenue is obtained by depreciating the repayment burden borne by government and is accomplished by increases in the current price level. 9 In a manner analogous to that associated with seigniorage, this redistribution depends on the public's holdings of federal debt. It is reasonable to assume that the demand for government debt depends on its expected real return, defined as the nominal return less the expected inflation rate. Therefore, if people expect more inflation, either the nominal return on government debt must increase or the demand for this debt will decrease. In either occurrence, revenue collected depends ultimately on the amount of debt the public is willing to hold. According to Bach and Stephenson, households have consistently been substantial net creditors, while government has been the main offsetting debtor. "Thus, since World War II inflation has apparently caused a massive transfer of wealth from households, as the major net creditors, to the federal government, as the major net debtor."'o The Fed may be motivated to provide seigniorage and to depreciate federal debt because of the gains accruing to government. If the Fed is a quasi-independent agency, it may derive certain benefits from following such a policy. The benefits are assumed to rise one for one with these two sources of government revenue. Costs. The Federal Reserve is hypothesized to be concerned about the consequences of its actions. This concern stems from inflation's effect on unemployment and, also, any other costs inflation imposes on the economy. Unanticipated changes in the inflation rate are assumed to result in movements in the unemployment rate in the opposite direction." The Fed is assumed to view deviations, in either direction, of unemployment from the natural rate 19 Chart 1 Federal Reserve Payments to Treasury as a Share of Corporate Profits Tax Accruals PERCENT 35r-----------------------------------------, 30 25 20 15 10 5 '51 '54 '57 '60 '63 '66 '69 '72 '75 '78 '81 '84 SOURCES OF PRIMARY DATA: Board of Governors of the Federal Reserve System, 72nd Annual Report, 1985 Economic Report of the PresIdent, January 1987 Chart 2 Federal Reserve Payments to Treasury as a Share of Total Federal Government Receipts PERCENT 2.5~------------------------------------------_. 2.0 1.5 1.0 .5 o~~~~~~~~~~~~~~~~~~~~~~~ '51 '54 '57 '60 '63 '66 '69 '72 '75 '78 '81 '84 SOURCES OF PRIMARY DATA: Board of Governors of the Federal Reserve System, 72nd Annual Report, 1985_ Economic Report of the President, January 1987 20 Federal Reserve Bank of Dallas as generating costs. Unemployment rates below the natural rate are possible only by continuous, unanticipated increases in inflation. This occurrence is considered costly to the extent that it results in expectations of accelerating inflation. Monetary policymakers desire to avoid such adverse effects on expectations because it then becomes more difficult both to extract revenue and to exploit an inflationunemployment trade-off in the future. Increases in unemployment above the natural rate are also assumed to generate costs in the form of obvious factors, such as forgone output and human suffering. In effect, a simple quadratic loss function is used, which implies that these costs increase at an increasing rate with departures of unemployment from its preferred level. Departures of inflation from zero are also assumed to generate costs of the type implied in the section on consequences of inflation. Further, these costs are assumed to increase at an increasing rate with departures of inflation from zero. Federal Reserve objective function If the Federal Reserve attempts to maximize net benefits associated with monetary policy, then, from the results in Appendix A, this leads to the following objective function: (1) Nt = P1tRmt + P2tRgt - n (P3tf2)(Ut - Ut )2 - (P4tf2)(TI t)2 . The Fed chooses its policy target, the money growth rate, to achieve its ultimate goal of maximizing the expected value of equation 1. Since the Federal Reserve System has never bound itself to any monetary rule, it is assumed that the Fed is a discretionary policymaker. Discretion implies no possibilities for prior constraints or commitments that would restrict subsequent choices of money growth rates. Further, a discretionary policymaker takes expectations as given. 12 This is due to the fact that, under discretion, the central bank's choice of money growth this period in no way constrains its choice of money growth next period. That is, current money growth supplies no additional information about the objectives or technology of the policymaker. It is reasonable to assume that expectations of future inflation are a function of expectations of future money growth rates. Thus, expectations of inflation are assumed given to the Fed only if the choice of current money growth has no implications for expectations of future money growth rates (and therefore no implications for expectations of future inflation), which is the essence of discretionary policymaking. In particular, this concentration on the presEconomic Review - May 1987 ent does not derive from myopia on the part of the policymaker. With given expectations, the policymaker has no way at date t to influence future values of the objective function. Therefore, a discretionary policymaker chooses the money growth rate to maximize the current expected value of equation 1, given expectations. After substituting for the expressions found in Appendix A for Rmt, Rgt, and Uu to solve for the inflation rate, the assumption is made that E(Ut - Uf) equals (Ut - Uf). This implies that the Fed's forecast of the gap between unemployment and its natural rate equals the actual gap. Such an assumption suggests perfect foresight on the part of the policymaker,13 leading to the following reaction function: (2) TIt = (P1tfP4t)[(1/m t)(Mt- 1/Pt)] + (P2tfP4t)(G t- 1 /Pt) + Z[(P3t/P4t)(Ut - ut)] . Interpreting equation 2 as a reaction function employs the pivotal assumption that the Fed is capable of controlling the inflation rate. The signs attached to the coefficients of the reaction function reflect the assumed preferences of the policymaker exhibited in equation 1 and, also, the assumption that in the central bank's view, increases in the inflation rate raise revenue and reduce deviations of unemployment above its target. If unemployment is below its desired level, decreases in the inflation rate occur. Equation 2 represents the (equilibrium) rate of inflation that results when the policy maker maximizes the expected value of his objective function, taking as given the formation of expectations. Further, equation 2 represents a rational expectations equilibrium in the sense that the inflation rate is sufficiently high, such that the marginal benefits of a hypothetical unit of surprise inflation just balance the marginal costs involved. In effect, systematic surprises do not occur in equilibrium. The presence of the unemployment variable may seem surprising, given that equation 2 implies that no systematic surprises in the inflation rate may occur in equilibrium. Barro and Gordon provide an explanation: Some people have argued that policymakers do not face a "cruel choice" between inflation and unemployment in a natural rate environment. This argument is misleading in a context where monetary institutions do not allow for policy choice to be committed .... [Plolicymakers do optimize in each period subject to the appropriate givens, which include the formation of expectations. Given these expectations, the choice of TIt does influence the unemployment rate "right now"-that is, for date t. The social 21 trade-off between unemployment and inflation ... is central to the policymaker's decision. 14 Empirical results To assess the importance of the variables of the reaction function as determinants of observed inflation rates, it is necessary to estimate equation 2. In an effort to determine whether the hypothesized benefits and costs are significant determinants of Federal Reserve behavior, the following modification of the reaction function is undertaken to facilitate empirical estimation and testing: (3) ANNUAL = 0: 0 + 0:1*SEIGN + 0:2*RLDEBT + 0:3*(UNEMP - NA TUN) + et, where ANNUAL = annual rate of inflation per quarter SEIGN = (1/m t)*(Mt- 1/Pt) RLDEBT = (GH/Pt) UNEMP =z*Ut NATUN = z*Ur 0: 0 = intercept 0: 1 = /31tl/34t 0: 2 = /32tl/34t 0: 3 = /33J /34t et = random disturbance. Since inflation influences as well as is influenced by SEIGN, RLDEBT, and deviations of the unemployment rate that are deemed acceptable by the Fed, the technique of instrumental variables- or two-stage least squares-is employed to resolve the Simultaneity present in equation 3. For SEIGN and RLDEBT the reverse causation flows through the current price level, Pt. A change in Pt alters ANNUAL and will, by definition, alter SEIGN and RLDEBT. The Simultaneity associated with unemployment operates through a usual Phillips curve mechanism. Increases in the inflation rate may decrease unemployment, and vice versa. The instruments generated attempt to capture the variables that explain SEIGN, RLDEBT, and (UNEMP - NATUN) and are also exogenous with respect to the current inflation rate. Since SEIGN is a function of the amount of the medium of exchange demanded, lags of personal income appear to represent a scale variable common in money demand functions. Lags of interest rates are included to capture the opportunity cost of money holdings. Finally, lags of the regressor itself are used. Similar considerations were employed in the construction of the other instrumental variables. 15 Using these instruments, consistent estimates of the parameters of equation 3 are then derived. 22 Table 1 INITIAL RESULTS OF FEDERAL RESERVE REACTION FUNCTION CORRECTED FOR SERIAL CORRHA TlON CoeffiCient Standard error -16.7900* 4.6890 SEIGN 30.8576* 4.7602 RLDEBT (UNEMP - NA TUN) -1.4351 ** .1203* Variable Intercept .7085 0452 * Signiiicant at the l·percent level .. Significant at the 5·percent level NOn- R' = 7202 Estimates of the extent of the response of unemployment to inflation surprises, z, are obtained from results found in Barro and Rush. 16 Their study examines the effect of unanticipated money growth on the unemployment rate based on both annual and quarterly data. It is estimated that a 1-percentage-point increase in unanticipated money growth reduces the unemployment rate by a proportion of 3.5 to 5.8 percent. Assuming that unanticipated money growth results in unanticipated inflation, these estimates may be employed for the z parameter in equation 3. Finally, values for the money supply multiplier are derived by dividing real money balances by the monetary base. Results are reported in Table 1 for z equals 4.5, approximately the midpoint of the Barro-Rush range, using quarterly data for the 1951-83 period. The estimates are obtained after correcting for the presence of serial correlation indicated by the Breusch-Godfrey test. 17 In order to purge the data of autocorrelation, the Cochrane-Orcutt process is used to estimate the first-order autocorrelation coefficient, along with the Prais-Winsten modification to account for the first observation. The estimated value of rho, the autocorrelation coefficient, is 0.383. Using this value, the data are transformed to obtain weighted least squares estimates. The results indicate that seigniorage collected by the Fed and deviations of unemployment from the Fed's target possess the hypothesized sign and are significant at the 1-percent level. RLDEBT, however, possesses the wrong sign and is significant at the 5-percent level. The reaction function estimated assumes that Fed behavior is stable. It is possible, though, that Federal Reserve policy shifts from one goal to another, erratically or otherwise. If so, then emFederal Reserve Bank of Dallas ploying a random coefficients specification results in mote efficient parameter estimates. When the parameters are allowed to enter as random variables, the coefficient on RLOEBT is still negative but not significant at the 5-percent level. The other coefficients retain their hypothesized, significant signs. Table 2 ESTIMATES OF FEDERAL RESERVE REACTION FUNCTION FOR FISCAL POLICY AND ELECTION-YEAR EFFECTS Variable Federal Reserve independence The degree to which policy actions undertaken by the Federal Reserve System are independent of any political considerations has long been a source of debate. 18 Results from Table 1 provide some evidence regarding the independent status of the Federal Reserve. A truly autonomous central bank would not respond to pressures that may exist to extract revenue from money holdings. An additional test for central bank independence is available from certain implications that follow from the reaction function. If the Fed perceives an increased need for revenue, then the rate of inflation should rise. This need might be acute in periods when alternative sources of revenue give rise to greater welfare losses at the margin or when government expenditures increase sharply. An attempt to capture these influences on Federal Reserve behavior is made by modifying the estimation equation (3) to include two additional variables: Intercept . SEIGN RLDEBT . .... . Coefficient -16.9046* 3.6935 15.9615* 5.8409 -.5756 .4409 (UNEMP - NA TUN) (TAX/PI)*SEIGN (DEF/GNP)* RLDEBT DUM*(UNEMP - NA TUN) Standard error .2065* .0447 94.9179* 18 .1066 -20.2121 * 4.5719 -.0670 .0687 • Significant at the 1-percent level NOTE R' = .6690 tual inflation. Therefore, the response by the central bank to the last term in the estimation equation is assumed to depend on a dummy variable whose value is 1 if in a presidential election year and 0 otherwise. (6) (4) and (5) First, the desire to collect seigniorage is assumed to depend on (TAX/PJ), personal tax and nontax payments expressed as a percentage of personal income. This variable attempts to capture the extent of the increasing burden of conventional taxation. Increases in this variable are hypothesized to result in an increase in seigniorage. In addition, (OEF/GNP) is the federal budget deficit as a percentage of GNP, accounting for periods when government spending increases sharply. In such circumstances, the central bank may be more motivated to depreciate outstanding federal debt. 19 This modification gives insight into fiscal policy pressures that might confront monetary policymakers. The degree to which the Fed responds to these pressures provides a rough test of the extent of central bank independence. 2o Further, if unemployment exceeds the natural rate, the extent of the response of inflation depends on (1(3' the costs of unemployment deviations relative to how costly the Fed perceives inflation. The rate of inflation should increase if the costs of the unemployment gap exceed the cost of acEconomic Review - May 1987 This variable attempts to capture the possibility that the Fed may view increases in unemployment as more costly in a presidential election year. If so, additional evidence is provided regarding the degree of central bank independence. 21 Substituting these specifications into the version of the reaction function used for estimation purposes gives the following: (7) ANNUAL = (1(0 + a10*SEIGN + a20*RLDEBT + a30*(UNEMP - NA TUN) + a11( TAX/PI)*SElGN + a22*(DEF/GNP)*RLDEBT + a33*OUM*(UNEMP - NA TUN) + 8t . Estimates of equation 7 are found in Table 2. The results indicate that the effect of SEIGN on observed inflation rates depends strongly on the variable (TAX/PI). That is, the higher are personal tax payments as a percentage of income, the more the Fed attempts to extract implicit revenue through seigniorage. The data indicate that the Federal Reserve is not influenced by political considerations in its reaction to unemployment deviations. Finally, the ef23 fect on observed rates of inflation from reducing the value of nominal federal debt is insignificant, while the interaction term associated with this variable indicates a negative effect on inflation. It appears as though the Fed tends to "tighten" in light of expansionary fiscal policy, possibly to prevent unemployment from falling below its natural rate. (April 1980): 199-211; George Macesich, The Politics of Monetarism: Its Historical and Institutional Development (Totowa, N.J.: Rowan & Allanheld, 1984); and John T. Woolley, Monetary Politics: The Federal Reserve and the Politics 01 Monetary Policy (Cambridge: Cambridge University Press, 1984). 2- Charlotte E. Ruebling, "Financing Government Through Monetary Expansion and Inflation," Federal Reserve Bank of St. Louis Review, February 1975, 21 Conclusions Recently, models of Federal Reserve policymaking have been formulated to attempt to analyze hypothesized tradeoffs the central bank faces. The model of central bank behavior developed in the analysis here utilizes this framework. It is argued that Fed policy is guided by trade-offs that manifest themselves in revenue and unemployment. Under this assumption, a reaction function is derived to explore the degree to which seigniorage, revenue from reducing the value of nominal federal debt outstanding, and deviations of unemployment from the natural rate prove to be significant variables in explaining observed inflation rates. Seigniorage is found to be an important determinant of inflation, leading one to question, to some extent, the degree of independence possessed by the Federal Reserve System. Further, the model exhibits a significant effect on inflation of deviations of unemployment from the natural rate. Next, the reaction function is modified to provide a further test for central bank autonomy. The effect of seigniorage on inflation depends on the proxy for the increasing burden of conventional taxation. Deviations of unemployment, however, are not significantly affected by the electoral cycle, making it more difficult to draw definitive conclusions regarding the independent status (or lack thereof) of the Federal Reserve. This model of central bank behavior only examines the stability of Fed policymaking with regard to fiscal policy effects and presidential elections. A useful extension of the model would be to examine its stability as a function of the tenure of various chairmen of the Board of Governors of the Federal Reserve System. That is, are periods with different chairmen meaningful subperiods in which to classify this model of monetary policymaking? Also, the extent to which the model developed is applicable to other countries can be investigated. The role revenue considerations and unemployment play in explaining observed inflation rates provides insights into the independence of foreign central banks. See, for example, Robert J Gordon, "The Demand for and Supply of Inflation," Journal 01 Law and Economics 18 (December 1975): 807-36; Edward J. Kane, "Politics and Fed Policymaking: The More Things Change the More They Remain the Same," lournal 01 Monetary Economics 6 24 3. For a summary of the literature on reaction functions, see James Barth, Robin Sickles, and Philip Wiest, "Assessing the Impact of Varying Economic Conditions on Federal Reserve Behavior," Journal 01 Macroeconomics 4 (Winter 1982): 47-70. 4_ Stanley Fischer and Franco Modigliani, "Towards an Understanding of the Real Effects and Costs of Inflation," Weltwirtschaltliches Archiv 114, nO . 4 (1978): 810-33 5. Stanley Fischer, "Towards an Understanding of the Costs of Inflation: II," in The Costs and Consequences 01 Inflation, Carnegie-Rochester Conference Series on Public Policy, ed. Karl Brunner and Allan H. Meltzer, vol 15 (Amsterdam: North-Holland Publishing Company, 1981), 36, The classic analysiS of the welfare cost is found in Martin J. Bailey, "The Welfare Cost of Inflationary Finance," Journal of Political Economy 64 (April 1956): 93-110 . 6. For an explanation of why the Fed might respond to these government branches, see Kane, "Politics and Fed Policymaking," and Edward J. Kane, "External Pressure and the Operations of the Fed," in Political Economy of International and Domestic Monetary Relations, ed _Raymond E. Lombra and Willard E. Witte (Ames: Iowa State University Press, 1982), 211-32. 7_ Estimates of the importance of seigniorage are found in Robert J. Barro, "Measuring the Fed's Revenue from Money Creation," Economics Letters 10 (1982): 327-32. In actuality, the U.s . Treasury does not simply regard newly created monetary base as current revenue . However, when the Fed permanently increases the base, it usually lends money indirectly to the Treasury by increasing its holdings of US Government securities_ While the Treasury pays the Fed interest, the Fed transfers its profits (composed mostly of these interest payments) back to the Treasury. See J. Huston McCulloch, Money and Inflation: A Monetarist Approach, 2d ed . (New York: Academic Press, 1982). Over the period from 1914 to 1983, Federal Reserve System payments to the Treasury totaled $128 billion, or almost 90 percent of the System's gross income (Verle B. Johnston, "The Formative Years," Federal Reserve Bank of San Francisco Weekly Letter, 9 November 1984). 8. Robert J Barro, Macroeconomics (New York: John Wiley & Sons, 1984), 302 n_ 1. 9_ If government debt is viewed as permanent and, thus, part of nominal net wealth, it has the same effect on inflation as increases in the money supply Such an occurrence makes it impossible to attribute inflation solely to the policy actions of the central bank. For evidence of this proposition, see W Michael Cox, "Inflation and Permanent Government Debt," Federal Reserve Bank of Dallas Economic Review, May 1985, 13-26, and the references cited therein. But according to Charles I Plosser, "Government Financing Decisions and Asset Returns," Journal 01 Monetary Economics 9 (1982): 325-52; Barro, Macroeconomics, 380; and Roger C. Kormendi and Philip Meguire, "Government Debt, Government Spending, and Private Sector Behavior: Reply," American EcoFederal Reserve Bank of Dallas nomic Review 76 (December 1986): 1180-87, it is not evident that government debt is part of nominal net wealth. 10. G. L. Bach and James B. Stephenson, "Inflation and the Redistribution of Wealth," Review of Economics and Statistics 56 (February 1974): 4. Additional redistribution effects associated with inflation that the Fed may consider in its policymaking are described in Basil J. Moore, "The Endogenous Money Stock," Journal of Post Keynesian Economics 2 (Fall 1979): 49-70; Alan S Blinder, "The Anatomy of Double-Digit Inflation in the 1970s," in Inflation: Causes and Effects, ed. Robert E. Hall (Chicago: University of Chicago Press for National Bureau of Economic Research, 1982), 261-82; Michael J. Mumper and Eric M . Uslaner, "The Bucks Stop Here: The Politics of Inflation in the United States," in The Politics of Inflation: A Comparative Analysis, ed . Richard Medley (New York: Pergamon Press, 1982), 104-26; and Kane, "External Pressure and the Operations of the Fed." See Fischer and Modigliani, "Towards an Understanding of the Real Effects and Costs of Inflation," for an explanation of the difficulties involved in considering these other effects. 11. See Robert J. Barro and David B. Gordon, "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy 91 (August 1983): 589-610. The assumption is that only unanticipated monetary expansions lead to increases in real economic activity. Equivalently, these nominal shocks lower the unemployment rate below its natural rate. This hypothesis is consistent with rational expectations models used in Robert E. Lucas, Jr., "Some International Evidence on OutputInflation Tradeoffs," American Economic Review 63 (June 1973): 326-34, and in Robert J. Barro, "Rational Expectations and the Role of Monetary Policy," Journal of Monetary Economics 2 (January 1976): 1-32. 12. This analysis of discretionary policy follows the general line of argument presented in Robert J. Barro, "Inflationary Finance Under Discretion and Rules," Canadian Journal of Economics 16 (February 1983): 1-16, and in Robert J. Barro and David B. Gordon, "Rules, Discretion and Reputation in a Model of Monetary Policy," Journal of Monetary Economics 12 (July 1983): 101-21. The assumption of discretion on the part of the policymaker ignores the possibility that the central bank invests in its reputation or credibility. In reputational models of central bank behavior, it is assumed that current actions of the policymaker influence expectations regarding future actions. The link between current actions and expectations is the Fed's reputation or credibility. For a summary of the research to date on credibility, see Alex Cukierman, "Central Bank Behavior and Credibility: Some Recent Theoretical Developments," Federal Reserve Bank of St. Louis Review, May 1986, 5·17. 13. See William G. Dewald and Harry G. Johnson, "An Objective Analysis of the Objectives of American Monetary Policy, 1952·61," in Banking and Monetary Studies, ed. Deane Carson (Homewood, III.: Richard D Irwin, 1963), 171-89; Ann F Friedlaender, "Macro Policy Goals in the Postwar Period: A Study in Revealed Preference," Quarterly Journal of Economics 87 (February 1973): 25-43; and Thomas Havrilesky, "A Test of Monetary Policy Action," Journal of Political Economy 75 (June 1967): 299-304. Richard K Abrams, Richard Froyen, and Roger N. Waud, in "Monetary Policy Reaction Functions, Consistent Expectations, and the Burns Era," journal of Money, Credit, and Banking 12 (February 1980): instrumental-variable procedure to overcome the errors in variables. Judging the relative merits of the instruments in this case, however, is impossible. As these authors point out, "How efficient these estimates [instrumentsl will be depends on how high the correlation is between the actual forecasts and our measures of these forecasts ... . The unobservability of the true policymaker forecasts makes the measurement of these correlations impossible" (Abrams, Froyen, and Waud, p. 34 [emphasis added]). 14. Barro and Gordon, "A Positive Theory of Monetary Policy in a Natural Rate Model," 601 . 15. "Any instruments that fulfill the requirement of being un correlated with the stochastic term and correlated with the regressors will result in a consistent estimate of the parameters" (George G. Judge, William E. Griffiths, R. Carter Hill, and Tsoung-Chao Lee, The Theory and Practice of Econometrics [New York: John Wiley & Sons, 1980l, 533). Because lagged values are used to generate predicted values for the endogenous variables, the instruments are not affected by (are exogenous with respect to) the current rate of inflation and, hence, are "uncorrelated with the stochastic term ." This condition holds, however, only if the estimation equation is purged of any serial correlation. The first-stage regressions resulted in R2 values that exceeded 90 percent, thus fulfilling the second requirement for instrumental variables. This use of instrumental variables is consistent with that employed by John H. Wood, "A Model of Federal Reserve Behavior," in Monetary Process and Policy: A Symposium, ed . George Horwich (Homewood, III.: Richard D. Irwin, 1967),135-66; Richard T. Froyen, "A Test of the Endogeneity of Monetary Policy," journal of Econometrics 2 (July 1974): 175-88; and Abrams, Froyen, and Waud, "Monetary Policy Reaction Functions, Consistent Expectations, and the Burns Era." See Appendix B for a description of the data and instrumental variables used . 16. Robert J. Barro and Mark Rush, "Unanticipated Money and Economic Activity," in Rational Expectations and Economic Policy, ed. Stanley Fischer (Chicago: University of Chicago Press for National Bureau of Economic Research, 1980), 23-48. 17. As the Durbin·Watson statistic is inappropriate in the case of stochastic regressors, the test employed is that developed by T. S. Breusch, "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers 17 (December 1978): 334-55, and l. G. Godfrey, "Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables," Econometrica 46 (November 1978): 1303-10. This discussion assumes the absence of vector autocorrelation of the type described in David K Guilkey," Alternative Tests for a First·Order Vector Autoregressive Error Specification," journal of Econometrics 2 (May 1974): 95·104, That is, we assume the error terms of the first-stage regressions are serially uncorrelated and are uncorrelated with each other 18. See Woolley, Monetary Politics . 19. The variables (TAX/PI) and (OEF/GNP) can be thought of as proxy variables To the extent that these variables measure with error the increasing burden of conventional taxation and government spending, 30-42, argue that this assumption Introduces two sources of bias. First, simultaneous-equation bias is present if the dependent variable of the reaction function affects the explanatory variables within the period Second, an errors·in·variables problem exists because the policymaker's forecast differs from the actual outcome Therefore, inconsistent pa· rameter estimates are obtained We introduce instrumental variables underestimation or overestimation of the parameters is possible when two regressors are measured with error, making it difficult to correct for to resolve the first problem Abrams, Froyen, and Waud suggest an the inconsistency Economic Review - May 1987 respectively, there is an errors·in-variables problem . As such, the parameter estimates are inconsistent. G. S. Maddala, Econometrics (New York: McGraw-Hili Book Company, 1977), 158-62, argues that either 25 20. Such an approach is found in Richard C. K. Burdekin, ' Fiscal Pressure and Central Bank Policy Objectives," Federal Reserve Bank of Dallas Economic Review, May 1986, 1-9. tives of the Federal Reserve System," Quarterly Journal of Economics 92 21 . Similar arguments are found in Froyen, 'A Test of the Endogeneity of Monetary Policy'; Glenn T. Potts and Dudley G Luckett, 'Policy Objec- (August 1982): 415-45. 26 (August 1978): 525-34; and Nathaniel Beck, "Presidential Influence on the Federal Reserve in the 1970s," American Journal of Political Science 26 Federal Reserve Bank of Dallas Appendix A A Model of Central Bank Behavior Given the following: Mt = nominal money stock in period t C t = nominal stock of net federal debt Pt = the general price level n t = log(Pt{Pt-1) Ilt = log(Mt /Mt _ 1) nr+1 = expected inflation from t to t + 1 Rmt = seigniorage in period t Rgt = revenue obtainable from depreciating federal debt outstanding Yt = level of real income, where Ilt is the Fed's target variable; Cv nrH and Yt are exogenous variables; Mv Pt, and n t are endogenous variables; and Rmt and Rgt are arguments of the Fed's objective function. Seigniorage in period t is defined as (Al) Rmt = (Mt - Mt-1)JPt = MtlPt - (Mt-1/Pt-1)(Pt-1/Pt) . It is assumed that the demand for real money balances depends inversely on expected inflation and positively on real income: (A2) then The benefits the Fed derives are assumed to increase monotonically with these two sources of revenue: (A7) where P1t and P2t represent the Fed's benefit parameters. Given the following Phillips curve relationship: (A8) where Ut is the current unemployment rate and Up is the "natural" rate of unemployment, inflation surprises result in reductions in the unemployment rate. It is assumed the natural rate can shift over time because of autonomous real shocks, 6, and that these shocks generate a persisting influence on the unemployment rate: n (A9) Utn = lUr"_1 + (1 - l)U + 6 t , where 0::;; l ::;; 1 and Therefore, un is the long-run mean of Up.1 Then, seigniorage collected by the Fed is equal to (A3) Rmt = (l/m t ) [exp(aYt - bn~+1) The costs that the Fed confronts in its conduct of policy are assumed to include the following: (All) Revenue associated with reducing the value of outstanding federal debt is expressed as (A4) Rgt = (C t- 1/Pt- 1) - (C t- 1/Pt) . Assuming that holdings of government debt depend on the difference between the nominal rate of interest on such debt, iv and also on expectations of inflation: (AS) Economic Review - May 1987 The reaction function given by equation 1 in the text is differentiated using three conditions: (dnt/dll t ) Inr,nr+1) = 1, which follows from equation A2; (dnr+1/dllt) = 0; and E(6 t ) = O. Solving for the rate of inflation gives equation 2 in the text. 1. See Robert J. Barro and David B. Gordon, "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy 91 (August 1983): 589-610. 27 Appendix B Description of Data Set Quarterly data are available for all variables. The time period chosen for the analysis is 1951-83- the period following the U.S. Treasury-Federal Reserve accord of 1951-to assume a maximum amount of independence of the Federal Reserve System. The criteria used here for "independence" are described by Woolley: At a minimal level, a central bank can be considered to be independent if it can set policy instruments without approval from outside authorities, and if, for some minimal period of time, the instrument settings clearly differ from those preferred by the fiscal authority.l Data between the post-World War II period and 1951 exhibit the effects of the Fed's "pegging" operations as directed by the Treasury. From 1914 until the middle 1930s, the Comptroller of the Currency and the Secretary of the Treasury were members of the Board of Governors of the Federal Reserve System, rendering this time period questionable in meeting the definition of independence. Finally, the remaining years are excluded because of the distortions caused by the Great Depression and World War II. M, is defined as the narrow money stock, or Ml. This constitutes currency plus demand deposits plus other checkable deposits (available after 1980). The data for the series are not adjusted for seasonal variation as it is this amount from which the Fed's revenue accrues. P, is defined as the implicit price deflator for GNP (1972 = 100). U, is defined as the total unemployment rate-all civilian workers as a percentage of the civilian labor force, adjusted for seasonal variation. Data on M" P" and U, are found in U.S. Department of Commerce, Bureau of Economic Analysis, Business Statistics 1979 and Business Statistics: 1982 (supple- 28 ments to the Survey of Current Business) and also in various issues of the Federal Reserve Bulletin. The monetary base is defined as total reserves plus currency outside the U.S. Treasury, Federal Reserve Banks, and vaults of nonmember banks, not seasonally adjusted. Data for the base are found in Board of Governors of the Federal Reserve System, Annual Statistical Digest, 1970-1979, and Annual Statistical Digest, 1982, plus various issues of the Federal Reserve Bulletin. G, is defined as total gross public debt of the u.s. Government held by the public, excluding that held by U.S. Government agencies and trust funds and that held by Federal Reserve Banks. These data are available in various issues of the Federal Reserve Bulletin. Estimates of the natural rate of unemployment were obtained from Gordon.2 The following data were used to construct instrumental variables: personal income, seasonally adjusted totals at annual rates; Federal Government outlays, calendar years; the yield on three-month Treasury bills; the index of industrial production (1967 = 100), adjusted for seasonal variation; and estimated retail sales, adjusted for seasonal variation and trading-day differences, at all types of retail stores. Data for these variables are found in the 1979 and 1982 editions of Business Statistics and various issues of the Survey of Current Business. Data for personal tax and nontax payments, the federal budget deficit, and gross national product are found in Business Statistics: 1982 and subsequent issues of the Survey of Current Business. 1. John T. Woolley, "Central Banks and Inflation," in The Politics of Inflation and Economic Stagnation: Theoretical Approaches and International Case Studies, ed leon N. lindberg and Charles S. Maier (Washington, D.c.: Brookings Institution, 1985), 320 2. Robert J. Gordon, Macroeconomics, 3d ed . (Boston: little, Brown and Company, 1984), Table B-2. Federal Reserve Bank of Dallas