RESTRICTING EMPLOYMENT OF LOW-PAID IMMIGRANTS: A GENERAL EQUILIBRIUM ASSESSMENT OF THE SOCIAL WELFARE IMPLICATIONS FOR LEGAL U.S.

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1 RESTRICTING EMPLOYMENT OF LOW-PAID IMMIGRANTS: A GENERAL EQUILIBRIUM ASSESSMENT OF THE SOCIAL WELFARE IMPLICATIONS FOR LEGAL U.S. WAGE-EARNERS PETER B. DIXON, MAUREEN T. RIMMER and BRYAN W. ROBERTS This paper builds on earlier work that used a general-equilibrium model to show that reducing employment of unauthorized immigrants in the United States through a tighter border-security policy lowers the average income of legal residents. Here we exploit further the detail available in the general-equilibrium model to look at distributional effects, recognizing that the policy increases wage rates for low-paid legal workers. We assess the social welfare effect on legal workers using a constant elasticity of substitution social welfare function. We contrast our general-equilibrium approach to immigration analysis with the more commonly used partial-equilibrium, econometric approach. (JEL D63, J61, C68) I. INTRODUCTION Most quantitative work on the economics of immigration in the United States has used partial-equilibrium econometric frameworks. In an earlier paper in this journal (Dixon, Johnson, and Rimmer 2011) we used a dynamic, computable general equilibrium (CGE) model to simulate the effects on the United States of reducing employment of unauthorized immigrants. The CGE method captures mechanisms that are not available in partial-equilibrium frameworks and produces results for the effects of immigration on a wide range of variables including wage rates by occupation, outputs by industry, exports and imports by commodity, and a complete array of macroeconomic variables. In our earlier paper, we concentrated on average effects. We found that policies to restrict unauthorized immigration reduce the average real income of legal U.S. residents. Here we exploit further the detail available in our CGE model to look at the welfare effects for legal Dixon: Centre of Policy Studies, Monash University, Wellington Road, Clayton, Victoria 3800, Australia. Phone , Fax , peter.dixon@monash.edu Rimmer: Centre of Policy Studies, Monash University, Wellington Road, Clayton, Victoria 3800, Australia. Phone , Fax , maureen.rimmer@monash.edu Roberts: Econometrica, Inc., 4416 East West Highway, Suite 215, Bethesda, MD Phone , Fax , broberts@econometricainc.com residents of restricting unauthorized immigration taking account not only of the average effect on wage rates but also distributional effects. Distributional effects are potentially important for welfare because restricting unauthorized employment raises the wage rates of some very low-paid U.S. workers (e.g., Miscellaneous agricultural workers) who compete with unauthorized immigrants while at the same time it lowers the wage rates of high-paid U.S. workers. The paper is organized as follows. In Section II, we start with a general introduction to our CGE model, USAGE. Then we provide a detailed description of the specification in USAGE of the markets for legal and unauthorized workers. In the final part of Section II we show how the CGE approach to immigration can broaden and deepen insights available from the econometric approach. We do this by reference to econometric work by Borjas, Grogger, and Hanson (2010) on the effects of low-skilled immigration on low-skilled wage rates in the United States. The first part of Section III describes USAGE results for the effects of restricting unauthorized employment on the occupational wage rates of legal workers. Then, we apply a social welfare function to these occupational wage results to compute welfare ABBREVIATIONS CES: Constant Elasticity of Substitution CGE: Computable General Equilibrium Contemporary Economic Policy (ISSN ) Vol. 32, No. 3, July 2014, Online Early publication February 25, doi: /coep Western Economic Association International

2 640 CONTEMPORARY ECONOMIC POLICY effects for legal residents. By using a social welfare function we take account of effects on wage rates across all occupations, not just the effect on the average wage rate. Finally in Section III we investigate the sensitivity of our welfare results to variations in key parameters. Concluding remarks are in Section IV. II. AN INTRODUCTION TO USAGE AND THE CGE APPROACH TO IMMIGRATION A. The USAGE Model USAGE is a dynamic CGE model of the U.S. economy. 1 A USAGE simulation of the effects of a shock to the economy (e.g., a change in immigration policy) requires two runs of the model: a baseline run and a perturbation run. The baseline is intended to be a plausible forecast while the perturbation run generates deviations away from the baseline caused by the shocks under consideration. As in all CGE models, optimizing behavior governs decision-making by firms and households. Industries minimize costs subject to given input prices and constant-returns-to-scale production functions. Households maximize utility subject to their budget constraint. Domestic and imported goods are treated as imperfect substitutes. Export demands for U.S. commodities are modeled as inversely related to their foreigncurrency prices. Explicit recognition is given to tax, transport, and other margins that separate purchaser prices from producer prices. The model can be run at various levels of aggregation. For this paper we adopted a version with 38 industries and 50 occupations. USAGE has three types of dynamic mechanisms: capital accumulation, liability accumulation, and lagged adjustment processes. An industry s capital stock at the start of year t + 1 is its capital at the start of year t plus its investment during year t minus depreciation. Investment during year t is determined as a positive function of the expected rate of return on the industry s capital. Liability accumulation is specified for the public sector and for the foreign accounts. Public sector liability at the start of t + 1 is public sector liability at the start of t plus the public sector deficit incurred during t. 1. USAGE was developed at the Centre of Policy Studies, Monash University in collaboration with the U.S. International Trade Commission. Its theoretical structure is similar to that of Australia s MONASH model, Dixon and Rimmer (2002). Net foreign liabilities at the start of t + 1are specified as net foreign liabilities at the start of t plus the current account deficit in t plus the effects of revaluations of assets and liabilities caused by changes in price levels and the exchange rate. As described in the next subsection, lagged adjustment processes are specified in USAGE for labor market variables. B. The Labor Market in the USAGE Model There are six ingredients in the USAGE labor-market specification. Here we provide a non-technical overview. The mathematical details are in Dixon and Rimmer (2010). The first ingredient is the division of the workforce into categories at start of year t reflecting workforce function in year t 1as well as birth-place and legal status. There are 160 categories in the version of the model used in this paper. They consist of: working in one of 50 occupations in the United States in year t 1 by three birth-place/ legal-status characteristics (U.S-born/authorized, foreign/authorized and foreign/unauthorized); short-term unemployed and long-term unemployed in the United States in year t 1 by three birth-place/legal-status characteristics; working outside the United States in year t 1 in a pool of potential unauthorized immigrants to the United States (all people in this category are classified as foreign/unauthorized); and new entrant to the workforce (no workforce activity in year t 1) by three birth-place/legalstatus characteristics. The second ingredient is the identification of workforce activities, that is what people do during the year. There are 157 of these corresponding to each of the categories except new entrant. Notice that working in occupation o as a foreign/unauthorized person is a different activity to working in occupation o as U.S.-born/ authorized person or as foreign/authorized person. The third ingredient is the determination of labor supply to each activity. This is done in USAGE by assuming that people in each category determine their labor supplies to activities by solving a constrained utility maximization problem in which the arguments are potential earnings in different occupations and the constraint reflects the total amount of labor that can be offered by people in the category. The

3 DIXON, RIMMER & ROBERTS: LOW-PAID IMMIGRANTS 641 parameters of the utility functions are chosen to ensure: (a) that people in each category supply their labor to activities that are compatible with their skills and birthplace/legal-status characteristics; and (b) that the overall elasticities of labor supply to activities are consistent with available evidence. On (a), the utility specifications ensure that people in a category with birthplace b and legal status s make offers only to activities with these characteristics. Thus, people in the category U.S.-born/authorized construction laborer can offer only to activities with the U.S-born and authorized characteristics. Most of these people offer to the activity U.S.-born/authorized construction laborer, that is, they offer to continue their employment of last year. However, some will offer to change occupation in response to changes in relative wages and a few will offer to unemployment. Some people in the category foreign/unauthorized working outside the United States will offer to foreign/unauthorized occupations in the United States, that is, they will seek to enter the United States as unauthorized immigrants, and some people in foreign/unauthorized categories operating in the United States will make offers to the activity foreign/unauthorized working outside the United States, that is they will offer to return home. Through the utility functions we capture the idea that people in these foreign/unauthorized categories decide their movements into and out of the United States by comparing wages in their home countries with wages for foreign/unauthorized occupations in the United States. On (b), we set the parameter, ε, that controls the willingness of people to switch occupations so that the overall long-run elasticity of supply of legal labor to any particular occupation is about In choosing this number we had in mind low-skilled occupations which are the main focus of our study. Evidence on occupational labor-supply elasticities is scanty, but for one important lowskilled occupation, Agricultural worker, supply responses have been studied relatively intensively. For these workers 2.2 seems a reasonable long-run elasticity value. 3 However, in view of 2. The parameter (ε) is the elasticity of substitution for members of a category between a dollar earned in different occupations. In our central simulation ε = 3 for all categories, leading to simulated long-run supply elasticities of legal labor to occupations of about Supply elasticities of legal workers to agriculture have been studied in connection with the end of the Bracero program in Wise (1974) suggested an elasticity of about 3. Later estimates by Duffield (1990) suggest lower numbers, between 0.71 and the high level of uncertainty, we report in Subsection III.A the sensitivity of our main results to variation in this elasticity. The fourth ingredient is the determination of demands for labor in U.S. industries. Each industry s overall demand for labor (a labor composite) in year t is specified along conventional CGE lines as a function of: the industry s capital stock; the overall real before-tax wage rate to the industry; and technology and price variables. Within industry j s overall labor input, the demand for labor by birthplace, legal status, and occupation is determined by a nested constant elasticity of substitution (CES) cost minimization problem. We assume that there are low substitution possibilities between occupations such as Cooks, Grounds maintenance workers, etc., and high substitution possibilities between foreign-legal and U.S.-born workers of the same occupation. Neither of these assumptions is controversial or important for the analysis in Section III concerning the welfare effects on legal workers of changes in the supply of unauthorized workers. However, a substitution elasticity that is of some importance is that between legal and unauthorized workers in the same occupation (denoted as σ in Subsection III.A). Unfortunately the econometrics literature does not give us any direct estimates for this elasticity. Ottaviano and Peri (2006) estimate 7.5 for the elasticity of substitution between U.S.-born and foreign legal workers. Guided by this number we set the substitution elasticity between legal and unauthorized workers in the same occupation at a somewhat lower value, namely 5. From the point of view of employers, legality is likely to be an important characteristic. For many employers who do not currently use unauthorized workers, a considerable reduction in the unauthorized/legal wage ratio may be required to tempt them to switch to unauthorized workers. The effects on our main results of varying the legal/unauthorized substitution elasticity are reported in Section III. The fifth ingredient is wage adjustment reflecting demand and supply. We assume that if a policy causes tightening in year t relative to baseline in the (b,s,o) market (the market for workers of birth place b, legal status s in occupation o), then there will be an increase between years t 1 and t in the deviation in the (b,s,o) real wage rate from its baseline path. In other words, in periods in which a policy has elevated (b,s,o) demand relative to supply, the (b,s,o) wage rate will grow relative to its baseline value.

4 642 CONTEMPORARY ECONOMIC POLICY Because U.S. employment markets do not clear under the lagged wage-adjustment mechanism, it is necessary to specify which offers to employment are accepted and what activities are undertaken by those whose offers are not accepted. This is the sixth ingredient of the USAGE labor-market specification. The key concept here is vacancies. For every year, the model calculates vacancies in each (b,s,o) activity as the number of jobs in the activity minus the number filled by incumbents [people in (b,s,o) in the previous year]. Then, in proportion to the number of offers they make (b,s,o) vacancies go to the unemployed, new workforce entrants and people changing jobs. Employed people who miss out on their preferred vacancies stay in their existing jobs. Unsuccessful new entrants go to short-term unemployment and unsuccessful unemployed people go to longterm unemployment. C. CGE Versus Partial Equilibrium in the Analysis of Immigration Issues The quantitative literature on the economics of immigration issues in the United States is dominated by partial-equilibrium econometric studies. This literature deals with the causes of authorized and unauthorized immigration flows (Hanson and McIntosh 2007; Hanson 2006, 872); the performance of immigrants in the U.S. economy (e.g., the survey by Borjas 1994); the effects of immigrants on the economy (Borjas 1999, 2003; Borjas, Grogger, and Hanson 2008; Card 2005; Ottaviano and Peri 2006); the effects on unauthorized flows of policy intervention such as heightened border security (Espenshade 1994; Hanson and Spilimbergo 1999, 2001; Kossoudji 1992; Reyes 2004); and the public sector budgetary implications of unauthorized immigrants (Rector and Kim 2007; Strayhorn 2006). A recent example of the partial-equilibrium econometric approach is the study by Borjas, Grogger, and Hanson (2010) on the effects of immigration on wage rates for the incumbent workforce. They fit regression equations of the form (1) w ext = FE ext +β m ext where w ext is the growth in wage rates of people with educational attainment e (high-school dropout, high school graduate, some college, college graduate) and work experience x (0 5 years, 5 10, etc.) in period t (1960 to 1970, 1970 to 1980, 1980 to 1990 and 1990 to 2000); m ext is the ratio of the increase in immigrant labor of type (e, x) to employment of (e, x)- people; and FE ext is a vector of fixed-effect terms that allow for differences between time periods in overall wage growth and for trends favoring or penalizing particular educational and experience characteristics. Borjas, Grogger, and Hanson obtained negative values for the regression coefficient β, implying that an increased flow of immigrants to an (e, x) group has a negative effect on wage rates for that group. Quantitatively their results indicated that an influx of immigrants that raises the supply of (e, x) people by 10% reduces their wages by 3% to 5%. With the immigrant inflow in recent decades concentrated in the high-school dropout group, they concluded that immigration is an important driver of wage inequality. We do not dispute the 3% to 5% result. The USAGE CGE framework contains specifications that are consistent with Borjas, Grogger, and Hanson s econometric evidence that low-skilled immigration depresses wage rates for low-wage occupations in the United States. 4 This is the fifth ingredient in the USAGE labor market specification described in the previous subsection. However, this does not mean that cutting low-skilled immigration would have a positive effect on the welfare of legal U.S. workers, even when welfare is measured by a function that gives heavy weight to increases in the wage of low-paid workers. By using a CGE model we capture welfare effects that go well beyond those that can be gleaned by time-series econometrics. Chief among these in the context of unauthorized immigration is what we have called the occupation-mix effect (Dixon, Johnson, and Rimmer 2011). Unauthorized immigrants take jobs mainly in low-skilled, low-paid occupations. Restricting unauthorized immigration opens up vacancies for U.S. workers in these occupations. At the same time, it makes the economy smaller thereby reducing vacancies for U.S. workers in high-skilled, high-paid occupations. Eventually, as captured by the sixth 4. We are unconvinced by the theoretical underpinnings of their equation (1). The apparent assumption by Borjas, Grogger, and Hanson that employers treat people in different (e,x) groups as non-substitutes justifying the exclusion of non-(e,x) wage rates from the right-hand side of (1) seems unrealistic.

5 DIXON, RIMMER & ROBERTS: LOW-PAID IMMIGRANTS 643 ingredient in the USAGE labor-market specification, the occupational mix of U.S. workers shifts in way that leaves them with a lowerskilled occupational mix of employment. This effect (in the opposite direction) will be familiar to students of the history of U.S. immigration. As described by Griswold (2002, 13), the inflow of low-skilled immigrants early in the twentieth century increased the size of the U.S. economy creating vacancies for U.S. workers at the high end of the occupational ladder while closing them off at the low end. This induced nativeborn U.S. residents to complete their education and move up the occupational ladder. Other CGE mechanisms captured in USAGE that are relevant in estimating the implications for the welfare of legal workers of reductions in the supply of unauthorized workers are: the unauthorized wage effect; the conventional terms-of-trade effect; the capital effect; and the public-sector budget effect. The unauthorized wage effect refers to the increase in the wage rates 5 of the remaining unauthorized workers after there is a reduction in their supply. From the point of view of the legal residents of the United States, this is akin to a reduction in the terms of trade: U.S. residents are paying more for imported low-skilled labor. As with other reductions in the terms of trade, an increase in the price of imported low-skilled labor leads to a reduction in the overall real wage rate of legal U.S. workers. 6 Going in the opposite direction, a cut in the supply of unauthorized workers increases the conventionally defined U.S. terms of trade. By making the U.S. economy smaller, the cut reduces U.S. imports with downward pressure on their price. Consequently there is a reduction in the volume of U.S. exports required to pay for imports. This works through the exchange rate and causes an upward movement along foreign 5. In USAGE calculations of welfare effects on legal residents, the relevant wage rates for unauthorized workers are post-tax. It is post-tax wage rates that measure the cost to the U.S. economy of employing these workers. 6. The connection between sustainable real wage rates and the terms of trade is intuitively clear: a terms-of-trade deterioration reduces the value of what workers can produce relative to the value of what they consume. More rigorously, let the marginal product of labor be x. Then the real wage rate from the point of view of workers is pg*x/pc where pg is the price of domestically produced goods and pc is the price of consumer goods. A reduction in the terms of trade will normally reduce the real wage rate because it reduces pg (which includes export prices but not import prices) relative to pc (which includes import prices but not export prices). demand curves for U.S. products. The reduction in the price of imports and an increase in the price of exports (a terms-of-trade improvement) is a source of wage gain for U.S. workers. Reducing unauthorized employment causes the United States to have a smaller capital stock in the long run than it otherwise would have had. As a first guess we might think that this would have little effect on the welfare of legal U.S. residents. At the margin, capital in the United States is supplied by foreigners. Thus if there is less capital in the United States then foreigners own less U.S. capital and earn less capital income from the United States. However, foreigners do not earn the full marginal product on their U.S. capital: they leave behind taxes paid to the U.S. Treasury. Thus, less capital in the United States means less tax collection by the Treasury from foreign owners of U.S. capital. This capital effect reduces the real aftertax wage of legal U.S. workers. 7 Against this, with a reduction in the number of unauthorized immigrants working in the United States, the public sector would cut expenditures made for their benefit, particularly expenditures on elementary education, emergency health care, and correctional services. This would allow either cuts in taxes or increased provision of public services to U.S. households. In our earlier paper (Dixon, Johnson, and Rimmer 2011), we quantified all of these effects in a USAGE calculation of the long-run implication for the welfare of legal residents of a 28.6% reduction in the employment of unauthorized immigrants caused by tighter border security. 8 We generated the 28.6% reduction by shocking variables in the utility functions of workers contemplating unauthorized entry to the United States Literally, these shocks introduced a preference shift against earning income in unauthorized U.S. employment. The shocks represent the effects on supply by unauthorized entrants that would flow from increased costs of entry associated with deterrent activity by U.S. authorities. A truncated version of the results is shown in Table 1. In total, we found that the assumed cut in unauthorized immigration reduces longrun welfare of U.S. households by 0.52%. In 7. Alternatively, it reduces the ability of the U.S. government to provide public goods has no particular significance. It represents a reduction in the unauthorized share of U.S. employment from a projected long-run level of 7% to 5%.

6 644 CONTEMPORARY ECONOMIC POLICY TABLE 1 Long-Run Percentage Effect on the Real Income of U.S. Households of Reducing Unauthorized Employment by 28.6% Through Tighter Border Security Occupation-mix effect 0.31 Unauthorized wage effect 0.29 Capital effect 0.24 Public expenditure effect 0.17 Conventional terms-of-trade and other macro effects 0.15 Welfare of U.S. households (% increase in 0.52 sustainable consumption) making this calculation, we took no account of distributional issues. In effect we adopted a Utilitarian stance in which a dollar increase in the income of any household, rich or poor, makes the same contribution to overall welfare. However, USAGE simulations show that policies to restrict unauthorized immigration have distributional effects that most economists would view as positive. In the next section we use a social welfare function to look at the welfare effects for legal workers of restricting unauthorized immigration taking account not only of the average effect on wage rates but also of the distributional effect. 9 III. WELFARE EFFECTS OF UNAUTHORIZED IMMIGRATION ON LEGAL U.S. WAGE-EARNERS A. Effects on Occupational Employment and Wage Rates of Residents Table 2 gives long-run labor-market results for the USAGE simulation outlined in Section II. Column 1 shows baseline relative wage rates for legal workers, from the lowest-paid occupation, Miscellaneous agricultural workers with a wage rate of 1, through to the highest-paid occupation, Construction supervisors with a wage of Column 2 shows baseline percentages of full-time-equivalent jobs of legal workers. The bulk of legal employment is in one occupation, Services other, which accounts for 9. Our approach to evaluating welfare impacts for legal workers is similar to that in Muller s (1999) study of the effects of unskilled immigration and protection on the welfare of native-born Swiss. 10. The baseline wage relativities in column 1 reflect those implied in the Bureau of Labor Statistics Table I-1 at (downloaded April 1, 2006). Technical documentation of how these data were used in the USAGE model are in Dixon and Rimmer (2006) % of baseline legal jobs. This lop-sided distribution of employment results from our decision to use an occupational classification that gives maximum detail on employment of unauthorized workers. About 90% of unauthorized employment is in the 49 occupations shown in Table 2 excluding Services other. Column 3 shows percentages of occupational wage bills accounted for by unauthorized workers. Because we assume that unauthorized occupational wage rates are lower than those for legal workers, the percentages in column 3 are indicative of unauthorized employment percentages, but are a little lower. Columns 4 and 5 show wage rates and employment for legal workers in the policy situation, that is with the implementation of the 28.6% cut in unauthorized employment. Columns 6 and 7 show the percentage deviations in wage rates and employment for legal workers caused by the policy. As can be seen from columns 6 and 7, there are large increases in wages (over 2.5%) and employment (over 5%) for legal workers in the following 16 occupations: Miscellaneous agricultural worker; Dishwasher; Housekeeping and cleaning; Grounds maintenance; Transport packer; Production helper; Butcher; Packing machine operator; Construction helper; Construction laborer; Painter; Carpet installer; Roofer; Concrete mason; Dry wall installer; and Brick mason. Unauthorized workers are a significant share of employment in all of these occupations (see column 3). In accordance with popular perceptions, most of these occupations command low wages. However, the last 6 of the 16 occupations have higher than average wage rates. These occupations are concentrated in construction in which wages are high and there is a heavy reliance on unauthorized workers. The last three rows of Table 2 show totals and averages. Column 3 shows the baseline share of unauthorized workers in the total U.S. wage bill as 3.6%. The share for low-paid occupations (those with wage rates less than 4.474, the average in column 1) is much larger than that for high-paid occupations: 10.8% compared with 1.8%. This confirms that legal workers in lowpaid occupations face much more severe competition from unauthorized workers than is the case for legal workers in high-paid occupations. Comparing the averages at the foot of column 4 with those at the foot of column 1, we see that the policy (reducing unauthorized employment by 28.6%) increases the average wage rate for low-paid workers from to (i.e.,

7 DIXON, RIMMER & ROBERTS: LOW-PAID IMMIGRANTS 645 TABLE 2 Long-Run Real Wage and Employment Levels, and Effects of a 28.6% Reduction in Unauthorized Employment Wage Rate, (Index) Baseline Percent of Jobs Unauthorized % of Occ. Wage Bill Policy (28.6% Reduction in Unauthorized Employment) Wage Rate, (Index) Percent of Jobs Policy-Induced Percentage Deviations Wage Rate, Employment, Occupations (1) (2) (3) (4) (5) (6) (7) Misc. agriculture worker Personal care Child care Food serving Dishwasher Misc. food preparation Waiter Food preparation worker House keeping and cleaning Grounds maintenance Laundry Cashier Cooks Nursing Janitor and building cleaner Transport packer Sewing machine operator Transport, cleaner Stock clerk Transport laborer Retail sales Farm-food clean other Supervisor food preparation Production helper Repair helper Shipping clerk Butcher Packing machine operator Industrial truck operator Other production worker Production misc. assistant Automotive repairs Maintenance and repairs Transport driver Construction helper Welder Construction laborer Production other Painter Transport other Construction other Carpet installer Roofer Concrete mason Services other Carpenter

8 646 CONTEMPORARY ECONOMIC POLICY Wage Rate, (Index) Baseline Percent of Jobs TABLE 2 Continued Unauthorized % of Occ. Wage Bill Policy (28.6% Reduction in Unauthorized Employment) Wage Rate, (Index) Percent of Jobs Policy-Induced Percentage Deviations Wage Rate, Employment, Occupations (1) (2) (3) (4) (5) (6) (7) Dry wall installer Plumber Brick mason Construction supervisor Totals or averages All occupations (0.114 a ) High-wage occupations ( a ) Low-wage occupations (0.763 a ) a Averages calculated with baseline wage-bill weights (weights based on column 2 times column 1) %, column 6). For high-paid workers the policy reduces the average wage rate from to (i.e., 0.031%). With such a tiny percentage reduction in the average wage rate for highpaid workers (0.031%), and a more significant percentage increase in the wage rate for lowpaid workers (0.578%), it is perhaps surprising that column 6 shows a reduction in the average wage rate for all occupations, a fall of 0.325%. The explanation is what we described earlier as the occupational-mix effect. All the averages to which we have referred are true averages calculated by looking at changes in wage bills per person. Such averages are affected not only by wage rates but also by movements of people between occupations with different wage rates. The policy reduces the true average wage rate of legal workers by changing the mix of their employment toward low-paid occupations. If we hold occupational shares in the total wage bill constant at their baseline levels (thereby removing the occupation-mix effect), then the weighted average of the percentage changes in occupational wage rates in column 6 is 0.114% rather 0.325%. Occupational-mix effects are also apparent within low-paid and high-paid occupations. Within the low-paid group, the occupationmix effect is noticeably unfavorable: holding constant the occupational composition of lowpaid legal employment gives a policy-induced increase in the average wage rate of 0.763%, compared with the true average increase of only 0.578%. Within the high-paid group, the occupation-mix effect is positive, though negligible: the baseline-weighted decrease in the average wage rate is slightly greater than the true average, 0.036% compared with 0.031%. We assume that changes in policies toward unauthorized immigrants do not affect the overall supply of legal labor or the long-run unemployment rate in any occupation. Nevertheless, as can be seen at the foot of column 7 there is a small reduction in aggregate employment for legal workers, 0.153%. This is because equilibrium unemployment rates are higher for lowskilled occupations than for high-skilled occupations. Consequently, aggregate employment of U.S. workers is reduced when the occupational mix of their employment shifts towards lowskilled occupations. For low-paid occupations, legal employment increases by 1.424% whereas for high-paid occupations it falls by 1.024%. B. Welfare Effects Assessed Through a CES Welfare Function Cutting unauthorized employment raises the wage rates of legal workers in low-paid occupations (e.g., Miscellaneous agricultural workers) who compete with unauthorized immigrants and lowers the wage rates for high-paid U.S. workers. Is this sufficient to generate an increase in social welfare for legal residents despite a reduction in their average wage rate over all occupations?

9 DIXON, RIMMER & ROBERTS: LOW-PAID IMMIGRANTS 647 TABLE 3 Reducing Unauthorized Employment by 28.6%: Percentage Welfare Effects for Utilitarian Rawlsian ρ sw1(ρ) sw2(ρ) Notes: sw1 shows the true percentage change in social welfare calculated with (2). sw2 shows the percentage change in social welfare excluding occupational-mix effects. sw2 is calculated from (2) with S i,p in the numerator replaced by S i,b. To answer this question we employ a CES social welfare function of the form ( ) 1 S i,p W ρ ρ i,p sw(ρ) = 100 i (2) ( ) 1 1 S i,b W ρ ρ i,b where sw(ρ) is the percentage change in social welfare caused by implementation of a policy; S i,j is the share of legal employment accounted for by occupation i in simulation j, j is baseline (b) orpolicy(p); W i,j is the after-tax real wage rate for legal workers in occupation i in simulation j; and ρ is a parameter whose value is less than or equal to 1 but not precisely zero. When ρ = 1, (2) reflects the Utilitarian position: social welfare is increased by x percent if and only if the true average wage rate increases by x percent irrespective of whether the wage increases are for high-paid or low-paid workers. At the other extreme, when ρ approaches, (2) reflects the Rawlsian position: social welfare is increased by x percent if and only if the lowest wage rate in the policy situation is x percent higher than the lowest wage rate in the baseline. Intermediate values of ρ accommodate ethical positions between Rawlsian and Utilitarian. With these intermediate values, a sufficiently large wage-rate decrease for a high-paid worker offsets a given smaller increase in the wage rate of a low-paid worker. Results from applying Equation (2) to the wage rates and employment shares in columns 4 and 5 (policy) and columns 1 and 2 (baseline) of Table 2 are given in the sw1 row of Table 3. When ρ = 1 (the Utilitarian case), the percentage change in social welfare caused by the policy is This is the reduction in the average wage rate shown at the foot of column 6 in Table 2. When ρ = 60 (which is close to the i Rawlsian case), the percentage change in social welfare is This is close to the percentage change (4.55%) in the wage of the lowest paid occupation, Miscellaneous agricultural workers (first row, column 6, Table 2). The switch point where the social welfare result turns from negative to positive occurs at ρ = 1.7. To help understand the ethical position implied by various values of ρ, particularly ρ = 1.7, we have prepared Table 4. This shows in a two-person situation the losses sustained by the high-paid person that would just offset a gain of $1 by the low-paid person. In the Utilitarian column (ρ = 1) these losses are $1, irrespective of wage inequality. As we get close (ρ = 3) to the Rawlsian situation, the losses sustained by the high-wage person are huge. For example if the high wage is 10 times the low wage, then a gain of $1 to the low-wage person is just offset by a loss of $3,697.2 by the high-wage person. If ρ = 1.7, then a policy change that generated a $1 gain to a low-paid person would be social-welfare neutral if it simultaneously generated a $6.50 loss to a person whose wage was double that of the low-paid person. If our ethical stance is that a $6.50 loss more than offsets the $1 gain by the low-wage person, then the appropriate value for ρ is greater than 1.7. In this case, we would be satisfied that the results in the sw1 row of Table 3 imply that the policy of cutting unauthorized employment by 28.6% is welfare-reducing for legal workers. Many people in the immigration debate find it difficult to understand how a cut in unauthorized employment could be welfare-reducing for legal workers under any ethical position concerning wage inequality. We suspect this is because they do not take account of the occupation-mix effect. In the absence of this effect, the percentage changes in wages shown in column 6 of Table 2 would be welfare-increasing for legal workers under any value of ρ. This is demonstrated in the sw2 row of Table 3. In this row we have recalculated the percentage change in social

10 648 CONTEMPORARY ECONOMIC POLICY TABLE 4 Two-Person CES Social Welfare Function: $ Losses by the High-Paid Person that Offset a $1 Gain By the Low-Paid Person ρ Utilitarian Rawlsian Inequality a a Inequality is the ratio of the wage of the high-paid person to that of the low-paid person. TABLE 5 Reducing Unauthorized Employment by 28.6%: Percentage Welfare Effects Under Alternative Values for ρ, σ, and ε Utilitarian Rawlsian ρ σ = 5.0, ε = σ = 7.5, ε = σ = 5.0, ε = σ = 7.5, ε = Notes: ρ is the parameter in the CES welfare function given by Equation (2); σ controls the elasticity of demand for legal and unauthorized workers with respect to their wage rates. It is the elasticity of substitution in industry production functions between legal and unauthorized labor in the same occupation; ε is the elasticity of substitution for members of a category between a dollar earned in different occupations. Moving ε from 3 to 2.5 reduces simulated long-run supply elasticities for legal labor to occupations from about 2.2 to 1.6. welfare using the baseline structure of legal employment as the policy weighting scheme in (2), that is we have set S i,p equal to S i,b for all i. With the occupation-mix effect excluded in this way, the sw2 row has positive entries for all ρ: increasing from (the average percentage wage increase calculated with baseline wage-bill shares, see the foot of column 6 in Table 2) in the Utilitarian case to 4.55 (the percentage wage increase for Miscellaneous agricultural workers) in the Rawlsian case. 11 However, in our view the occupational-mix effect is a reality that should not be ignored. The relevant row in Table 3 is sw1, not sw A curious feature of Table 3 is that the sw2 calculations converge to the Rawlsian result (4.55) quicker than the sw1 calculations as ρ approaches. On analyzing this we found that occupational-mix effects (which damp the increase in social in welfare) remain non-negligible in the sw1 case even when ρ has reached 60. C. Sensitivity Analysis As mentioned in Section II.B, there is considerable uncertainty about the values of elasticity parameters on both the demand and supply sides of the markets for legal and unauthorized workers. Table 5 shows results generated under alternative assumptions for two critical parameters: σ on the demand side and ε on the supply side (defined in the foot of the table and discussed in Subsection II.B). The first row of results in Table 5 reproduces the sw1 results from Table 3. This is followed by three rows of results for sensitivity simulations. In each of the sensitivity simulations we adjust the preference shocks for workers contemplating unauthorized entry to maintain the 28.6% reduction in long-run unauthorized employment. The second row in Table 5 shows results generated with the same supply-side parameter

11 DIXON, RIMMER & ROBERTS: LOW-PAID IMMIGRANTS 649 (ε) as in the first row but with the demandside parameter (σ) reset at 7.5. Comparing the two rows reveals that the welfare results for legal workers are less negative with the higher value of σ at all values for ρ. On inspecting the detailed wage results in columns (1) and (3) of Table 6, we see that with σ at 7.5 the wage outcome for legal workers in every occupation is better than in the central case in which σ was 5. With a higher σ, the elasticity of demand for unauthorized workers is increased. Thus, the 28.6% cut in supply produces a smaller increase in the wage paid to unauthorized workers. As explained earlier, from the point of view of legal residents, changes in the wage of unauthorized workers are akin to a change in the terms of trade brought about by a change in the price of an imported product (low-skilled labor). With a smaller increase in the price of unauthorized workers (equivalent to a smaller terms-oftrade deterioration), real wages for legal workers are higher. This applies to all occupations and reflects the macro-economic nature of the underlying terms-of-trade mechanism. The third row in Table 5 shows results generated with the same demand-side parameter (σ) as in the first row but with the supplyside parameter (ε) reset at 2.5. By comparing the entries in Table 6 at the foot of columns (5) and (1) ( compared with 0.325) we see that changing the supply-side parameter does not significantly affect the USAGE projection of the overall ability of the economy to pay legal workers. However it does affect the projected change in relative occupational wage rates: in column (5) the wage outcomes are more favorable for the predominantly low-paid occupations vacated by unauthorized workers and less favorable for the relatively high-paid occupation Services other. This produces the improved welfare outcomes that are apparent in Table 5 as we go from row 1 to row 3. With a lower value for ε, reflecting less flexibility in occupational choice by all categories of legal labor, greater changes in relative wages are needed to facilitate the change in the occupational mix of legal employment required to accommodate the assumed 28.6% reduction in unauthorized employment. The fourth row in Table 5 shows results generated with the demand-side parameter (σ) set at 7.5 and the supply-side parameter (ε) at 2.5. These results show that to a high degree of accuracy the effect of changing σ is independent of the value at which ε is set and the effect of changing ε is independent of the value at which σ is set. This means that the results in the fourth row can be understood as though they were generated by the equation (3) Row4(ρ) Row1(ρ) + [Row3(ρ) Row1(ρ)] + [Row2(ρ) Row1(ρ)] (effect of changing ε) (effect of changing σ) In Table 7, we use Table 4 to interpret and summarize Table 5. Subsection III.B explained that the negative effect on welfare of the reduction in the average real wage rate for legal workers associated with a cut in unauthorized employment could be offset by the positive distributional effect. One s view of the trade-off depends on one s ethical stance. For the central simulation (σ = 5.0, ε = 3.0) we found welfare neutrality under an ethical stance in which a $6.5 reduction in the income of a person earning 2X is offset by a $1 increase in the income of a person earning X. This is the north-west entry in Table 7. The other entries in Table 7 show the corresponding numbers for the three sensitivity simulations. Consistent with our discussion above, these entries imply that higher values for the demand-side parameter (σ) and lower values for the supply-side parameter (ε) increase the range of ethical stances under which the positive effect of distributional improvement would be judged to outweigh the negative effect of the reduction in the average real wage. IV. CONCLUDING REMARKS The presence of low-paid, unauthorized immigrants in the U.S. workforce makes the U.S. economy larger than it would be without them. While the immigrants close off vacancies at the low end of the labor market, they open up vacancies at the top end. This allows legal U.S. workers to take better paid jobs than they would in the absence of low-paid immigrants. Overall, unauthorized immigrants raise the average wage rate of legal workers. On the other hand, they reduce the wages that can be earned by U.S. workers in low-paid occupations. Thus, in working out the social welfare effects of reducing unauthorized employment, there is a trade off: the negative effect of a reduction in average wages versus the positive effect of a reduction in wage inequality. Under the Rawlsian assumption, the increase in wage rates for low-paid workers associated with restriction of unauthorized immigration

12 650 CONTEMPORARY ECONOMIC POLICY TABLE 6 Long-Run Percentage Effects on Wages and Employment of from a 28.6% Reduction in Unauthorized Employment σ = 5.0, ε = 3.0 σ = 7.5, ε = 3.0 σ = 5.0, ε = 2.5 σ = 7.5, ε = 2.5 Real Wage Rate Employment Real Wage Rate Employment Real Wage Rate Employment Real Wage Rate Employment Occupations (1) (2) (3) (4) (5) (6) (7) (8) Misc. agriculture worker Personal care Child care Food serving Dishwasher Misc. food preparation Waiter Food preparation worker Housekeeping and cleaning Grounds maintenance Laundry Cashier Cooks Nursing Janitor and building cleaner Transport packer Sewing machine operator Transport, cleaner Stock clerk Transport laborer Retail sales Farm-food clean other Supervisor food preparation Production helper Repair helper Shipping clerk Butcher Packing machine operator Industrial truck operator Other production worker Production misc. assistant Automotive repairs Maintenance and repairs Transport driver Construction helper Welder Construction laborer Production other Painter Transport other Construction other Carpet installer Roofer Concrete mason Services other Carpenter Dry wall installer Plumber Brick mason Construction supervisor All occupations