The Globalization of Household Production *

Transcription

1 Te Globalization of ouseold Production * Micael Kremer Stanley att ork in progress Please do not cite Marc 29, 2005 Abstract Immigration restrictions are arguably te largest distortion in te world economy and te most costly to te world s poor. Yet, tese restrictions seem firmly in place due to fears in ric countries tat immigration would exacerbate inequality among natives, fiscally drain te welfare state, and cange native culture. Many new ric countries are creating a new form of immigration tat may not encounter tese obstacles. Foreign private ouseold workers, primarily female, constitute more tan 6% of te labor force in Barain, Kuwait, ong Kong, Singapore, and Saudi Arabia, and about % in Taiwan, Greece, and Israel. Providing temporary visas for tese workers can potentially allow ig-skilled native women to enter te market labor force. Tis increased labor supply by native ig-skilled workers can increase te wages of low-skilled natives and provide a fiscal benefit by correcting distortions toward ome production created by income taxes. alibration suggests welfare gains to natives from a ong Kong style program may be equivalent to tose from a % increase income. e argue tat tere will be a Pareto improving level of migration from an ex ante perspective, but tat tis migration may noneteless be inconsistent wit etical norms in old ric countries ex post, at least in societies were membersip is based on lengt of residence. Programs wit temporary, non-renewable visas may be more acceptable in tese countries. * e are grateful to Abijit Banerjee, Davin or, Patricia ortes, Racel Glennerster, Elanan elpman, Ayesa Imtaz, Panwadee Kananusapkul, Maria Petrova, Matew Rabin, Alan inters, and Dan ood for comments.

2 . Introduction Migration restrictions are arguably te most important distortion in te world economy and te most armful to te world s poor. Klein and Ventura (2004 estimate tat te removal of immigration restrictions in OED countries could increase world output by up to 72%. Tey assume tat capital is mobile and tat immigrants can take advantage of OED levels of total factor productivity. Even witout tese favorable assumptions, almsley and inters (2003 estimate tat an increase of 3% of labor supply in immigration in developed countries could raise world welfare by 0.6%, alf of te gains associated wit complete trade liberalization. illiamson (996 argues tat 9 t entury mass migration led to income convergence across today s ric countries by directly raising te wages of te migrants and by reducing labor supply in te sending countries. Free migration can also provide a ceck against oppression. Te trigger for te collapse of communism may well ave been est Germany s openness to migration from te East. Yet despite occasional calls for freer mobility (peraps, most notably from Mexico s President Fox te elimination of immigration restrictions is not under consideration in ric countries. ig-income countries limit migration due to concerns tat immigration of low-skilled workers would ( exacerbate inequality among natives, (2 create a burden on te welfare state, (3 cange native culture, and (4 increase crime. In tis context, it seems wort examining a new form of immigration tat, as we discuss in section 2, is becoming widespread in countries tat ave become prosperous recently, from Saudi Arabia to ong Kong to Greece. In tis new type of immigration, foreigners,

3 women in particular, are employed as private ouseold workers eiter on temporary visas or under te table. e argue tat tis type of immigration may potentially address eac of te obstacles to migration cited above. It can potentially ( equalize wages among natives, (2 provide a fiscal benefit, (3 limit te impact of immigration on culture, and (4 make it arder for anti-immigration advocates to raise fears of a potential rise in crime. To see te logic, note tat in standard models, suc as Borjas (995, migration by low-skilled immigrants exacerbates inequality among natives. Te welfare gains for te ost country are arberger triangles and are small compared to distributional effects. Borjas (995 writes tat te relatively small size of te immigration surplus particularly wen compared to te very large wealt transfers caused by immigration probably explains wy te debate over immigration policy as usually focused on te potentially armful labor market impacts rater tan te overall increase in native income. In fact, Mayda (2004 finds tat in ric countries low-skilled natives are particularly likely to oppose immigration. In te US, for example, 28.8% of ig scool graduates support immigration as opposed to 45.7% of people wit college education. 2 en foreign workers perform services previously done witin ouseolds, suc as cooking, cleaning, and care for cildren, te sick, and te elderly, new effects arise. Immigrants involved in tese industries arguably displace pre-existing non-market labor. Since ig-skilled natives wit a iger opportunity cost of time are more likely to 2 Tese results come from te orld Value Survey wic asked te following ow about people from oter countries coming ere to work. ic one of te following do you tink te government sould do? (a et anyone come wo wants to? (b et people come as long as tere are jobs available? (c Place strict limits on te number of foreigners wo can come ere? (d Proibit people coming ere from oter countries? (e Don t know People supporting immigration were defined to be tose wo answered eiter (a or (b out of te entire sample wo answered eiter (a, (b, (c, or (d. 2

4 purcase tese services, native ig-skilled workers, women in particular, will spend more time working in te labor market. To te extent tat foreign private ouseold workers lead to increases in ig-skilled labor supply, tey create a new effect beyond tose analyzed in standard models suc as Borjas (995. By freeing up ig-skilled labor for market production, immigrant private ouseold workers can reduce wage inequality, since te increase in labor supply of ig-skilled workers leads to a decline in teir relative wage, and increase in te relative wage of complementary low-skill native labor. Moreover, wen ig-skilled women ire immigrant private ouseold workers and transfer teir labor from ome production to market work, teir output becomes taxable, providing a fiscal benefit for te population, even witout considering te taxes paid by te migrants, temselves. Te impact of foreign private ouseold workers on native culture is limited, since immigrant private ouseold workers are typically not allowed to bring families wit tem on teir visas. Tese workers are typically female, and crime is, terefore, less likely to be perceived as a problem. e construct a simple model designed to illustrate te possibility of tese effects. A very roug calibration of tis model suggests te benefits of tis type of migration could be substantial. it taxes at U.S. rates, immigration of 5% of te native labor force is estimated to increase welfare of low-skilled natives by te equivalent of a.6% increase in income. It increases welfare of te ig-skilled by te equivalent of a 0.3% cange in income. Total welfare accruing to natives increases by approximately 00 times te amount found by Borjas (999. 3

5 e also explore an extension to te model in an appendix in wic some natives would send teir cildren to cildcare centers staffed by natives in te absence of migration. Te qualitative results are similar to te basic model if we assume cildcare center services are as skill intensive as te economy as a wole, wic seems to be true empirically, and parents can obtain more ours of cildcare from foreign private ouseold workers tan from cildcare centers. Te model still abstracts from a number of key factors affecting te impact of immigration. A back of te envelope calculation taking into account tese factors, suggests a similar or possibly even sligtly larger impact of foreign private ouseold workers, but a somewat smaller impact on relative wages. Yet, if immigration by foreign private ouseold workers avoids many of te political economy obstacles to oter forms of migration, it may be seen as inconsistent wit etical norms in some countries. Tis may elp explain wy foreign private ouseold worker programs ave been instituted on a muc wider scale in new ric countries tan among te istorically ric. Restricting people wo ave lived in a country for twenty or tirty years to private ouseold work and preventing tem from bringing teir families may well be considered inconsistent wit etical norms in societies were membersip is based in part on lengt of residence. Yet, tis creates a paradox. Under etical norms tat place little obligations on society to tose born overseas regardless of time spent in te ost country, foreign domestic elpers may be admitted, making tem and te ost society better off. Under etical norms tat place low value on foreigners as long as tey stay overseas but tat consider foreigners entitled to better treatment given enoug time in te ost country, 4

6 societies may be unwilling to admit foreigners, potentially making everyone worse off. Tis represents a basic time consistency problem inerent to societies in wic membersip is based on lengt of residence. Programs wit temporary non-renewable visas migt make introducing foreign private domestic workers more palatable, reducing tis time consistency problem. ost societies can also structure policies in ways advantageous to foreign private ouseold workers. One important step would be to make canging employers easier. Te rest of te paper is structured as follows: Section 2 documents basic facts on foreign private ouseold workers immigration in new ric countries. Section 3 lays out a simple model designed to illustrate te potentially new effects of foreign private ouseold workers on wages and welfare in te ost country. Section 4 calibrates te model, reviews its limitations, and ten goes troug a back of te envelope calculation suggesting tat results would be similar in a somewat more realistic model. Section 5 discusses etical issues, and section 6 concludes. 2. Basic Facts Old ric and new ric countries are pursuing immigration policies wit very different implications for te developing world, and in particular for te poor in te developing world. Old ric countries are increasingly focusing on attracting ig-skilled immigrants in a global competition for talent. Kapur (2004 describes ow Australia, Germany, anada, te UK, and to a lesser extent te US are canging immigration systems to favor skilled workers. e argues tat te costs associated wit tis brain drain for developing countries are great, altoug oters like ommander, Kangasniemi, and inters (2003 5

7 argue tat tese costs may be mitigated by increased incentives to invest in uman capital and return migration. In contrast, many newly ric economies admit substantial numbers of foreign domestic elpers. Table sows tat in Barain, Kuwait, and Saudi Arabia around 0% of te labor force or more are foreign workers in private ouseolds. In ong Kong and Singapore, two of te tree countries oter tan Puerto Rico to ave joined te ranks of te world s ricest 25 countries in te last 40 years, about 6.8% and 7.0% of te total labor force, respectively, are foreign domestic elpers. 3 Among countries tat ave not quite reaced tis income category, many also ave substantial numbers of foreigners working as domestics, altoug te numbers are not as dramatic. Foreign domestic elpers make up at least 0.8% of te labor force in Taiwan, and immigrant workers in private ouseolds are at least 0.8% of te labor force in Israel. Non-Greek, non-eu employees in private ouseolds constitute about % of te labor force in Greece. Tese figures exclude illegal workers. Anecdotal evidence suggests tat substantial numbers of foreign women work illegally as ouseold employees. Autorities find it arder to enforce laws against iring illegal workers wen private ouseolds, rater tan firms, are doing te iring. ile, Italy and Israel are all reported to ave significant numbers of foreigners working illegally as private ouseold workers. Statistics on te number of foreign private ouseold workers are not readily available for ile, but 4.7% of te labor force is occupied in domestic service, and anecdotal evidence suggests substantial numbers of tese workers are Bolivian and Paraguayan 3 Only ong Kong, Singapore, Puerto Rico, and Korea ave entered te ranks of te world s 25 ricest economies as measured by real GDP per capita between 960 and Source: DI 6

8 women (Stefoni, In te US 35% of women illegal immigrants reported tat teir first job was working in a private ouseold (ortes ompared to new ric countries, te sare of te labor force in old ric countries composed of foreigners performing domestic work is muc smaller. For example, foreign workers in private ouseolds constitute only around 0.3% of te working population in te US 4. To te extent tat some illegal workers are not captured in te census, tis percentage migt be raised somewat, but it is unlikely to cange te conclusion tat te U.S. as a muc smaller proportion of foreign private ouseold workers tan many new ric countries. Not only is te sare of foreign private ouseold workers small in old ric countries, but private ouseold work in general is small. In te US, only around % of te entire employed population (including natives and non-natives are employed in te personal services private ouseold industries. In te UK in 990, only 0.05% of te working population was employed as domestic ousekeepers, altoug tis is a narrower definition of private ouseold workers tan we ave typically been using. Foreign private ouseold worker programs ave expanded rapidly among new ric countries. For example, from 987 to 996, te percentage of ouseolds employing domestic servants in ong Kong more tan doubled from 2.5% to 6.%. 5 In Singapore in 980 less tan 0.3% of te working population were foreign private 4 Tis figure is taken from te Marc 998 PS were te total number of non-citizens in te industry category Personal Services Private ouseolds is divided by te total number of people reporting to be working in an industry. Te PS supposedly contains data collected from illegal immigrants. 5 Tese figures come from various ong Kong Special Topics Report. 7

9 ouseold workers wereas today one in seven ouseolds employ a live-in elper (Kolesnikov-Jessop, Te data suggest tat ig-skilled natives are most likely to employ domestic workers. In 990 almost 8% of university educated moters in Singapore ired domestic workers wile only 5% of polytecnic educated moters, 2% of secondary educated moters and less tan % of primary scool educated moters ired domestic workers (Singapore ensus of Population 990. Table 2 sows labor force participation and fertility rates for a number of countries. One problem is tat labor force participation statistics for some countries include foreign private ouseold workers. e ope to obtain better data in te future, but it is wort noting tat data for Barain does not include foreigners. onsistent wit te idea tat foreign domestic workers can increase female labor force participation, ong Kong and Singapore bot ave ig rates of female labor force participation, muc iger tan in Korea and even iger tan tat of te US and UK (see Table 2. Female labor force participation was not ig in tese countries in te 970 s before large numbers of domestic workers from abroad began to enter te labor force, casting doubt on purely cultural explanations. Fertility rates for ong Kong and Singapore are muc lower and ave fallen more quickly tan in comparable countries, consistent wit te view tat women freed up from ouseold work to participate in te labor market ave fewer cildren. It is wort noting tat immigration of foreign private ouseold workers will only raise wages for low-skilled workers and provide fiscal benefits to te extent tat te time 6 4,23 Singaporean non-residents were employed in domestic service out of a total working population of,077,090 in 980 (Singaporean ensus of Population

10 of native women released from ome production is devoted towards market production rater tan eiter leisure or increased production of cildren. Te extent to wic tis occurs may depend on social norms. Trends in female labor force participation in ong Kong and Singapore are consistent wit te ypotesis tat foreign domestic elpers ave freed ig-skilled women to enter te labor force (altoug of course it is also possible tat ig female labor force participation as driven policy decision to admit foreign domestic elpers.. In te gulf, female labor force participation is low relative to oter countries wit comparable income, altoug female labor force participation as increased rapidly and fertility as fallen. If foreign private ouseold workers free up time tat natives devote to leisure or simply lead to more ouseold work being done tan would be done oterwise, relative wages between different classes of native workers will be unaffected. If foreign private ouseold workers lead to iger fertility among ig-skilled natives, long-run income distribution among natives may be equalized. First, iger fertility could increase te long-run supply of ig-skill labor, at least to te extent tat ig-skilled parents can transmit education to teir cildren. Second, to te extent tat greater fertility among ig-skill workers leads tem to split teir bequests and attention among more cildren te distribution of wealt will be equalized. e ope to consider more general cases in te future. 3. Model e present a model designed to illustrate te potentially new effects of foreign private ouseold worker migration beyond tose from te standard models. For simplicity, we present a very basic model tat illustrates te key ingredients necessary to derive tese 9

11 results. Subsection 3. sets up te model by describing ouseolds and producers. Subsection 3.2 solves te model wit zero immigration. Subsection 3.3 analyzes te equilibrium wit immigration Subsection 3.4 sows tat tere always exists a Paretoimproving level of immigration. Section 4 discusses several factors tat are abstracted away from in tis simple model. 3.. ouseolds and Producers ouseolds in our model consume two types of private consumption goods, a general good and a domestic good like cooking, cleaning, or cildcare. Te domestic good can eiter be purcased from te market, wic we term outside iring, or produced at ome. An identical utility function governs all ouseolds: U A ( + + v( g were A is te amount of te general good consumed, is tat amount of domestic good consumed from outside iring, is te amount of time invested in ome production of te domestic good, g is a public good provided by te government, and v( is an increasing, concave function. ouseolds inelastically supply one unit of labor and face te budget constraint: ( τ ( P A P, were i is te wage of te consumer i A + ( i {,, I} wic we describe later, P A is te price of good A, P is te price of good, te domestic good, ired from te outside and τ is te tax rate on labor income. Because we assume tat te outside and ome produced domestic goods are perfect substitutes, ouseolds will eiter ome produce or buy outside from te market all consumption of te domestic good. If prices are suc tat consumers are indifferent between ome production and outside iring, any combination of outside iring and ome production will be feasible. Te assumption of perfect substitutability is made for 0

12 convenience and is not critical for arriving at our main results. Given obb-douglas utility and Kun-Tucker conditions, consumers spend sare a of teir income on good ( τ i A: A. If P < ( τ i, consumers will purcase all domestic good P A ( ( τ i consumption from te market and set and 0. If P > ( τ i, P and 0. Finally, if P ( τ i, ouseolds will be indifferent between and ome-producing and [ 0, ] and. Producers can ire tree types of labor: native ig-skilled workers, native lowskilled workers and immigrants. e normalize te native population to one and assume tat a fraction are ig-skilled leaving te fraction of low-skilled natives. et m denote te population of immigrants making te total population in te ost country + m. Te production function for good A is A + ϕ ϕ / ϕ ( + ( ( θi were is ig-skilled native labor, is low-skilled native labor, I is immigrant labor, and θ <. 0 < < and 0 < φ <, were iger represent tecnologies tat use ig-skilled labor more intensively and η /( φ is te elasticity of substitution between igskilled and low-skilled labor. Immigrants imperfectly substitute for native low-skilled labor and complement native ig-skilled labor in production of A. Good is produced wit a linear production tecnology in te labor of any type: δ * abor. owever, because consumers generally tend to prefer teir own cooking, cleaning, and cildcare, and get utility from at least some aspects of tis work, we assume tat domestic good production ired from te outside is less efficient tan ome domestic

13 good production and so δ <. e assume all workers are equally effective in producing good, but tis assumption could be weakened. Te assumption tat immigrants and low-skilled natives are not perfect substitutes and tat immigrants ave a comparative advantage at producing te domestic good is necessary for our results. Imperfect substitutability of immigrants and native low-skilled workers may arise due to eiter differences in skills between tese workers or to government policies tat restrict certain immigrants ability to work outside te domestic sector, as in te ong Kong foreign domestic elpers program or te US and UK Au Pair programs. Some evidence tat immigrants ave a comparative advantage in domestic work is provided by te fact tat in 998 in te US, non-citizens were almost five times more likely to work in personal service private ouseold category as citizens. 3.6% of non-citizens were employed in tose occupations as opposed to 0.7% of US citizens. 7 In order to abstract from debates about weter immigrants pay more in taxes tan tey receive from te government in social services, we assume tat immigrants are neiter taxed nor enjoy te benefits of te government good. Terefore, our welfare analysis will remain largely agnostic about te direct net contribution of immigrants to te public sector. Te government taxes te labor income of all natives at tax rate,τ, and spends all tax revenue on a public good tat is only enjoyed by natives. In order to focus on te worst case scenario for te ost country, we consider te case in wic immigrants extract all surplus associated wit producing te domestic good. Te opposite assumption would be tat employers of private ouseold workers 7 Tese figures are from te autors calculations from te PS Marc 998. Private ouseold - personal service industry is defined to include private ouseolds wo employ workers tat are cooks, laundresses, maids, sitters, butlers, personal secretaries, managers of personal affairs; and outside workers, suc as gardeners, caretakers and oter maintenance workers as defined by OSA US Department of abor. 2

14 old all te bargaining power and are able to negotiate wages tat are equal to te reservation utility of te immigrant. As discussed in section 5., te split of surplus is likely to depend on legal institutions. e ope to generalize tis in future work. e conjecture tat for alternative saring rules te impact on relative wages and tax collected will be qualitatively similar, but native employers of foreign private ouseold workers will be better off Equilibrium witout Immigration e first focus on te case were ig-skilled workers earn more tan low-skilled workers and were tere are no private ouseold workers in te absence of immigration. Appendix explores an extension to our basic model were some natives send teir cildren to cildcare centers staffed by natives as part of teir domestic good consumption. Qualitative results are similar to te basic model if we assume tat cildcare center services are, at least, as skill intensive as te economy overall, wic seems to be true empirically, and if ouseolds can obtain more ours of cildcare from iring a private ouseold worker tan from cildcare centers. All firms in sector A and sector operate in competitive markets. e first solve for te sector A firms zero profit condition and find an expression for wages (Kun- Tucker conditions: P A or ϕ 0 if P ( A ϕ + ( ( + θi > ϕ ( ϕ ϕ (ϕ / ϕ + ( ( + θi ϕ (ϕ / ϕ ( 3

15 P A ( ( + θi or 0 if P A ϕ ( ϕ > ( ( + θi + ( ( + θi ϕ ( ϕ ϕ (ϕ / ϕ + ( ( + θi ϕ (ϕ / ϕ (2 Tese expressions must be satisfied in equilibrium. Te interior solution gives ( + θi / η wic is equal to ( / η / η in te absence of immigration. Under te assumption tat ig-skilled workers do not employ private ouseold workers in te absence of immigration, we ave, and ( wic implies ( / η. Tis assumption olds if P > ( τ. e next focus on te production of good to find P. Because all types are equally efficient at producing good, firms producing good will only ire types wit te lowest wages. Given tis production function and te firm zero profit condition, min(, P. δ To proceed, we need te following simplifying assumptions. First, to ensure tat ig-skilled wage is iger tan low-skilled wage, we need to assume tat >. Second, to guarantee tat tere are no private ouseold workers in te absence of immigration, we assume tat δ > ( τ. Tese two inequalities can be rewritten as < and > ( τ δ. Since ( / η, we can summarize tese conditions in te following assumptions: 4

16 Assumption A: η ( δ ( τ η ( + ( δ ( τ η η ( δ ( τ < < min η ( θ ( + ( δ ( τ η η, η η ( + Te first inequality guarantees tat ig-skilled workers do not earn so muc tat tey employ private ouseold workers in te absence of immigration wile te second inequality guarantees tat te ig-skilled earn iger wages tan low-skilled natives witout immigration, η <. η η + ( Te following proposition follows from te previous discussion. Proposition : Under assumption A, te ratio of low-skilled wages to ig-skilled wages is ( / η. etting te price of good A be te numeraire, under assumption A ( ϕ + ( ( ϕ ( ϕ (ϕ / ϕ (ϕ / ϕ ϕ ϕ + ( ( and ϕ. Assumption A means tat native workers are never formally employed in te domestic sector. Below we caracterize te no immigration equilibrium wen some natives perform domestic work for oters Equilibrium wit Immigration In order to examine te impact of immigration on te ost economy, we first determine te local effects around te no immigration equilibrium. In tis subsection we analyze te effects of immigration wen assumption A olds, and no native workers are ired to perform domestic work for oters. In te next subsection we analyze te equilibrium under assumption A2. 5

17 Because immigrants are less efficient at producing good A tan te native lowskilled, immigrants will ave te lowest wage in te economy, wic implies tat, if any domestic goods are ired from te outside, tey will be produced by te immigrants. Recall tat m is te number of immigrants entering te ost country. Because ig-skilled natives ave te iger wage, tey will outbid te lowskilled for te ired domestic good services offered by immigrants. ig-skilled natives will pay no more tan ( - τ for tis service, since at tis price tey are indifferent between iring from te outside or ome producing. Tus, by being ired to produce te domestic good immigrants will earn a wage of δ( - τ, since we ave assumed tat te immigrants extract all surplus associated wit producing te domestic good. If good A is te numeraire, te sector A firms zero profit condition describes labor demand given wages. I / ϕ I θ θ ( η ( / ϕ or I θ 0 if I > θ. (3 e ave earlier asserted tat by assuming <, we guarantee tat entering immigrants will first work in te outside production of te domestic good. Proposition 3 sows ow < is sufficient for generating tis result. Proposition 3: If assumption A olds, as long as te number of immigrants is not too large, entering immigrants work exclusively in te good sector. Proof: Given te existing labor supplies of te ig and low-skilled natives, I η ( δ ( τ δ ( τ > θ if and only if <. If m is close to η η ( θ ( + ( δ ( τ zero, te wage of te immigrant in sector is strictly iger tan te marginal product of 6

18 te immigrant in sector A, and te immigrant s labor supply in sector A is I0. Tere is a level of immigration m > 0 suc tat all immigrants up to m enter te good sector. e note tat because δ <, immigrants ome produce teir own domestic good consumption so tat te amount of ired domestic good available to be purcased is δm. o Te propositions in tis section apply to levels of m < m suc tat all immigrants work in sector. Proposition 4: Under assumption A and under a level of immigration local to zero, te wages of low-skilled natives increase relative to native ig-skilled wages wit te level of immigration. Proof: By proposition 3 we know tat te immigrants produce domestic good only for te ig-skilled and do not work in sector A. Because immigrants only supply units of teir own labor to te labor force, ig-skilled natives only need to ome produce ( δm of te domestic good, allowing tem to supply + δm to te formal sector. ow-skilled natives still ome produce teir own domestic good and eac lowskilled ouseold supplies units of labor to te formal sector. Using te expressions given for wages in sector A, / η ( [ + δm]. Relative native low-skilled wages / η ( are increasing in te number of immigrants for η > 0.o etting P be te numeraire, ( ( + ϕ ( + δm ϕ (ϕ / ϕ and (ϕ / ϕ ϕ ( + δm + ( ϕ (. 7

19 Proposition 5: If assumption A olds, immigration increases taxes collected by te government and, tus, g. Proof: Total factor payments are equal to total production for ES production functions. Since no immigrants work in sector A, all income goes to individuals taxed at rate τ. Total production in sector A is increasing in ig-skilled labor, implying tat taxes increase wit immigration. o en market work is taxed more eavily tan ome production, taxation introduces a distortion as ouseolds do not ire from te outside enoug of te domestic good. en immigrants reduce te price of te ired production of te domestic good, tis distortion can be mitigated. For expositional purposes, we set tis issue aside for te time being, owever, by considering te case in wic te marginal utility of te public good is zero. Assuming tat te marginal utility of te public good is zero is a very strong assumption as natives essentially pay taxes to a wortless good. Proposition 6: en assumption A olds, immigration is local to zero, and te marginal utility of te public good is zero, welfare for ig-skilled types is decreasing in te number of immigrants. Proof: ig-skilled types provide + δm/ labor in sector A, at a rate net of taxes of (-τ. Tey pay δ(-τm/ for ired domestic good production, so tat ultimate net income is (-τ. Since is falling in m for η > 0, consumption of good A falls wit immigration. onsumption of good is constant. Togeter tese imply a fall in welfare for ig-skilled types.o Intuitively te increase in income of eac ig-skilled native from working more in sector A is spent paying for ired domestic good production. ollectively te ig- 8

20 skilled increase te supply of ig-skilled labor, causing teir wages to fall relative to no immigration. Proposition 7: en assumption A olds, immigration is local to zero, and te marginal benefit of te public good is zero, te welfare of native low-skilled is increasing in immigration. Proof: ow-skilled income is (-τ and is increasing in immigration. Immigration as not canged te consumption of te domestic good for te low-skilled but as increased absolute wages, implying a rise in welfare.o Finally, altoug we ave demonstrated tat te wages of te native low-skilled rise wit immigration and tat wage inequality as decreased, we ave not sown ow income (wage times labor supply inequality as canged wit immigration. Bot incomes are increasing in te number of immigrants. Relative income I I equals ( + δm /. Tis is proportional to ( + δm (η / η, implying income inequality rises if η >. Te empirical evidence supports an elasticity of substitution between igskilled and low-skilled labor of greater tan one, suggesting tat income inequality among natives increases even wen immigration is local to zero. (Katz and Murpy 992, Krusell et al. 997, eckman, et al Pareto Improving levels of Immigration it te furter infusion of additional migrants, te analysis of subsection 3.3 will continue to old for iger levels of immigration until te occurrence of one of te tree following outcomes occurs: ( native low-skilled wages rise suc tat low-skilled 9

21 natives begin purcasing domestic good from te outside, (2 alternative wages to immigrants paid by sector A rise as more ig-skill natives work in te sector, and eventually immigrants begin working in sector A, or (3 immigrants fulfill all demand for market produced domestic good at P ( - τ, and P falls below tis level. ic outcome among te tree appens first will depend on parameters. Regardless of te timing of tese outcomes, owever, increased immigration as unambiguous effects on welfare and income, wic we sow below by considering all possible timings. Initially immigration frees up ig-skilled labor and reduces te relative wages of te ig-skilled, but eventually wit enoug immigration low-skilled labor will be expanded so tat relative wages will return to non-immigration levels wile more domestic goods will be available troug outside iring. Proposition : Under assumption A, tere always exists a Pareto-improving level of low-skilled immigration, m suc tat all natives are no worse off tan witout immigration. Informal Proof: More formal versions of te proofs of propositions and 2 are given in Appendix A and B. For expositional ease, we separate tis proof into two different cases. ase : Immigrants are relatively efficient in sector A: δ(-τ < θ emma : If δ(-τ < θ, low-skilled natives never ire from te outside production of te domestic good. Proof: Immigrants always ave te lowest wages in te economy since tey are θ < times as productive as te low-skilled. Because immigrants can always coose to work in good A production, immigrant wages can be no less tan θ. In order for te native 20

22 low-skilled to ire from te outside production of te domestic I θ good ( τ > P wic will never occur wen δ(-τ<θ. o δ δ In tis case low-skilled natives will never ire immigrants to produce te domestic good so outcome ( will never occur. As immigration increases eiter immigrants will first begin working in good A production, outcome (2, or P will first fall below (-τ, outcome (3. If immigrants satisfy demand for domestic goods at P ( - τ, P will fall below tis level, and all ig-skilled workers will supply teir full unit of labor to te outside labor force. ow-skilled native wages will be unaffected by furter immigration since low-skilled natives are neiter expanding teir labor supply by iring domestic good production from te outside (emma nor facing labor competition from te immigrants in sector A. Te ig-skilled, owever, will consume more domestic good since te price of iring domestic good production as fallen relative to teir wage, and welfare will be increasing wit furter drops in P brougt by more immigration. Eventually wit even more immigration, P and, tus, I will fall so muc suc tat immigrants will start working in te sector A. en entering immigrants work bot in sector A, outcome (2, and in producing te domestic good for oters, outcome (3, furter immigration reduces te wages of te native low-skilled but still increases te welfare of native ig-skilled types by increasing teir consumption of te domestic good. en te level of immigration reaces ( m ( ( + ( τ θ ( η m, low-skilled wages and welfare are equal to wages at zero immigration. ig-skilled welfare is iger since wages ave 2

23 been restored to te no immigration equilibrium, and ig-skilled types can afford to consume more of te domestic good. Above, we ad assumed tat te price of good fell, outcome (3, before immigrants began working in sector A, outcome (2. Noting would cange if tis were reversed and freed up ig-skill labor increases demand for immigrants in sector A enoug for at least some of tem to move to tat sector before wages fall in production of good. In tis case, new immigrants work bot in sector A and sector, but tey divide teir labor between te two sectors suc tat te labor tey free up for te ig-skilled exactly offsets te extra labor tat immigrants provide in sector A, i.e. remains +θi constant. Tus, wages for ig and low-skilled natives do not depend on immigration. And, welfare for natives does not cange as consumption of good remains constant at -. Eventually, increased immigration will result in so muc production of te domestic good tat ig-skilled demand will be exausted at P ( - τ. To see tis, note tat te ratio of ig-skilled to low-skilled labor remains constant in sector A, implying tat for ig enoug immigration, ig-skilled individuals eventually engage in no domestic goods production. At tis point, te analysis will proceed exactly as it did in te previous paragrap. ase 2: Immigrants are relatively inefficient in sector A: δ(-τ θ emma 2: If δ(-τ θ, immigrants will not work in sector A until all natives ave purcased from te outside all teir domestic good production. Proof: Because ig-skilled wages are iger tan low-skilled wages, low-skilled natives will not ire domestic good production until ig-skilled natives are outside iring. If low-skilled natives ave not outside ired all consumption of te domestic good, 22

24 immigrant wages paid in te ired production of te domestic good are δ ( τ. From equation (3 we know tat sector A firms will ire no immigrants if te marginal I product of immigrants are lower tan te wages, i.e. I > θ. Since δ(-τ θ, we know tat I δ ( τ θ and so sector A firms will ire no immigrants so long as all natives ave not outside ired all consumption of te domestic good. 8 o By lemma 2 we know tat immigrants will not work in sector A until all lowskilled workers ave outside ired all domestic good production, outcome (2 will occur last. e proceed as we did in te previous case by analyzing te effects wen outcome (3 supply ired domestic good production exausts demand at P ( τ precedes ( low-skilled wages rising sufficiently for low-skilled natives to demand outside iring for te domestic good and ten te reverse. Outcome (3 preceding outcome ( implies tat P < ( - τ and tat te low-skilled are not outside iring for te domestic good. ig-skilled natives supply a full unit of labor to te outside labor force, and low-skilled wages and welfare are not affected by furter immigration since low-skilled natives are neiter outside iring nor facing immigrant labor competition in sector A. ig-skilled welfare is increasing in te level of immigration, as increased immigration reduces P and increases ig-skilled consumption of te domestic good. it enoug immigration, eventually, P will fall suc tat low-skilled natives will outside ire te domestic good and outcome ( will be obtained. en outcome ( and (3 are obtained, low-skilled natives outside ire for te domestic good, and increased immigration frees up te low-skilled to enter te formal workforce. Tus, furter immigration reduces low-skilled wages and raises ig-skilled 8 e ave assumed tat in te knife edge case wereδ ( τ θ and low types are outside iring only part of teir domestic good consumption, sector A firms ire no immigrants. 23

25 wages. en ( ( m + δ (η / η m, eac low-skilled native supplies unit of labor to te outside labor force, and domestic good consumption is still exactly -. At tis point all natives are supplying one unit of labor to sector A, and te original wage equilibrium witout immigration obtains. Te native low-skilled are now indifferent to immigration at tis level and zero immigration, and te native ig-skilled are better off since tey can now consume more of te domestic good. Te analysis for letting outcome ( precede outcome (3 is similar.o Proposition 2: If assumption A olds, income inequality is non-decreasing wit immigration. Proof: Given in Appendix B. Our model as abstracted from te existence of cildcare centers. e extend te model by allowing for te existence of native cildcare centers in Appendix. Te main results of te model including proposition continue to old, if we assume tat cildcare center services are equally as skill intensive as te overall economy and if private ouseold workers can provide more ours of cildcare tan cildcare centers. 4. alibration Subsection 4. calibrates te model outlined in section 3. Subsection 4.2 discusses te limitations associated wit our calibration. Subsection 4.3 provides a roug back of te envelope calculation of te possible welfare effects, taking into account some factors not yet in te model. 24

26 4.. alibration of te Model e calibrate te model using data from ong Kong from around te year 2000 and from te U.S. e first attempt to find an estimate for, te utility parameter associated wit te general consumption good. If we believe our model of obb-douglas utility, we know tat - is te sare of time a ouseold spends on producing its own domestic good. Using te Multinational Time Use Study, Freeman and Scettkat (2004 estimate tat over te course of a seven day week, men aged 25 to 54 on average spend 44. ours in market work and 6. ours doing domestic work. omen aged 25 to 54 on average spend 28.7 ours per week in market work and 30. ours doing domestic work. Teir results come from a survey done in te US in 992. If we assume tat a ouseold consists of one man and one woman, we find tat on average an American ouseold spent 38.8% of its working time doing ouseold work. Tis gives us an estimate of 0.6 for. Te ong Kong ensus and Statistics Bureau conducted a time use survey of residents in 200 and In ong Kong, people spend approximately 0.68% of teir total time in market and ouseold work on market work. In our model low-skilled immigrants are generally imperfect substitutes for lowskilled natives in te production of te general consumption good. Te parameter θ < gives te relative efficiency of low-skilled immigrants relative to natives. owever, te foreign domestic worker program in ong Kong legally proibits domestic workers from working in any oter sector. Terefore, in practice θ 0 in ong Kong, and we make tis assumption for our calibration. 25

27 In te 996 ong Kong population census, 2.2 million people in te working population ad not completed a ig scool degree wic we define to be low-skilled in ong Kong and about 800,000 ad ig scool degrees and above. Tese figures, owever, include about 8,000 foreign domestic elpers of wic, according to a 996 survey of domestic elpers, 79% ad secondary scool educational attainment or below. 9 Since - in our model is te fraction of low-skilled natives, we adjust te census figures by subtracting te appropriate number of ig and low-skilled domestic elpers. e estimate in ong Kong to be around Katz and Murpy (992 estimate η,, te elasticity of substitution between igskilled and low-skilled workers, to be.4 using US data from 963 to 987. Krusell et al. (997 estimate te elasticity to be.3 using a US dataset expanded to 99 and an estimate of.67 from a model wit capital-skill complementarity. eckman, et al.(998 estimate te elasticity to be.44 using a model incorporating job training. For simplicity, we assume tat η is.5 for te purposes of our calibration. e use statistics of earnings by educational attainment in 993 from te US ensus Bureau to estimate, te factor intensity of ig-skilled workers (Kominski and Adams, 994. en tere are very few low-skilled immigrants in te domestic sector, / η (. If we caracterize ig-skilled workers in te United States as tose / η ( aving completed a college education, we find tat te ratio of low-skilled mean earnings to ig-skilled mean earnings is about e also find tat, of te total population of 9 Te data do not differentiate between secondary scool graduation and secondary scool matriculation. e make te assumption tat all domestic elpers in tis category only matriculated and did not graduate and, terefore, are considered low-skilled. Tis assumption makes marginal difference to our calibrations. 26

28 8 year olds and older wo report earnings, 24.% are classified as ig-skilled under tis definition. Tis gives us an estimate of equal to Standard tax rates in 2002 in ong Kong were 5%, and employees were required to make social security contributions of 5%. Because te tax rate for ong Kong is so low, we also calibrate te model wit a iger tax rate. In 2003, te top tax rate in te United States was 35%. After including 5.3% payroll taxes (Social Security and Medicare and a state tax rate of 5.3% 0 ig-income taxpayers wo would be likely to ire personal ouseold workers face a marginal rate of around 5.6%. Finally, we need an estimate for δ, te relative efficiency of ired domestic good production. ouseolds will be on te margin of weter or not to ire foreign domestic elpers wen wages for te domestic worker are δ(-τ times te wage of te ouseold. e find tat in % of domestic elpers earned 3,750 ong Kong dollars a mont. (ong Kong General ouseold Survey 996. owever, tis figure does not include food and lodging wic we estimate to be equivalent to 55% of te take ome wage. 2 Tis implies tat total compensation to domestic elpers in 996 was around 5,84 ong Kong dollars a mont. From te same report, te rate of ouseolds employing domestic elpers jumps from 5.3% to.3% wen moving from a montly ouseold income bracket between 20,000 to 29,9999 to a bracket between 30,000 to 39,999 ong Kong dollars per mont. Tus, we interpret ouseolds wit montly 0 Tis is te state income tax rate in Massacusetts. In 996, te ong Kong dollar was pegged to te US dollar at a rate of 7.73 ong Kong dollars to one US dollar. 2 e know today tat foreign domestic elpers in ong Kong receive a minimum wage of 3,270 ong Kong dollars. If food is not provided by te employer, a mandatory food allowance of 300 K dollars is to be paid. Finally, troug conversations wit employers, we also estimate te value of lodging for a domestic elper to be around,500 ong Kong dollars. Tis implies tat non-wage compensation accounts for about 55% of te listed minimum wage today. 27

29 incomes of 35,000 to be te marginal ouseold. Assuming a 5% tax rate on native ouseold income 3 imply tat δ Tis estimate for δ may seem too low, as it suggests tat five private ouseold workers substitute for only one ig-skilled native. owever, δ captures bot efficiency and preference effects. Altoug private ouseold workers may be less efficient, a moter wo ires a ouseold worker to take care of er cild for five ours may still want to spend four ours wit er cild based on er own preferences. A ouseold wit a private ouseold worker may still prefer to prepare teir own meals. it regards to te public good, we assume tat te government keeps expenditure at a constant level. Tus, any increases in tax revenue brougt about by immigration will contribute to a lowering of te tax rate. To describe te distortionary effects of labor taxation troug costs like tax evasion, tax collection, and labor distortion, Browning (987 defines te marginal welfare cost as te cange in total welfare brougt about by a unit cange in tax revenue. e assume tat te marginal welfare cost is around.4 wic implies tat for every one fewer dollar of taxes collected, te increase in total welfare is equivalent to an increase of $.40. Te column labeled MF gives te alternative welfare effects, if we assume tat taxes are nondistortionary. Table 3 gives te results of our calibration. Te column labeled no tax assumes tat te tax rate is zero. olumns labeled MF.4 assume te marginal cost of raising $ in tax revenue as $.40. olumns labeled MF assume no distortion associated wit taxation. Te level of immigration is set suc tat immigrants are 3 Te Mandatory Provident Fund Scemes (Social Security for ong Kong was implemented in December of

30 equivalent to 5% of te native workforce. Because immigrants still spend - units of labor producing teir own domestic good, actual labor displaced is *δ* 5%. e first notice tat low-skill relative wages increase by 2.5% wit immigration. Tis corresponds rougly to te percentage increase in te ig-skill native labor supply we consider. Te welfare effects of immigration can be sizeable. e calculate welfare as te transfer of gross income before immigration required suc tat natives are indifferent between immigration and no immigration. elfare for ig-skilled natives decreases by.4% and for low-skilled natives increases by.0% wen we assume tat taxes are set at zero. Te welfare loss for ig-skilled natives may be exaggerated since we assume in our model tat ig-skilled natives receive no surplus associated wit iring foreign private ouseold workers. Te overall welfare gain is about 0.0% of GNP. Even after considering te tax benefits of immigrants, ig-skilled natives lose welfare, and lowskilled natives gain. it a 20% tax rate, ig-skilled workers lose te equivalent of 0.7% of income in welfare, low-skill workers gain te equivalent of.2% of income, and te overall welfare gain is 0.4% of GNP. elfare gains are iger for all types under te 5.6% tax rate, as a iger tax rate implies tat immigrant ouseold workers can reverse a larger preexisting distortion. ig-skilled workers gain te equivalent of 0.3% of income, low-skilled workers gain.6%, and te economy gains te equivalent of.0% of income. en we assume no distortions associated wit taxation, te welfare wit taxation and te public good unsurprisingly decreases, altoug te magnitude of tis effect is not large. 29

31 Borjas (999 estimates increases in national income accruing to natives under te standard model for te US. e finds tat wen immigrants account for 0% of te workforce, national income at most increases by 0.0% to 0.02%. 4 Assuming linearity, wen immigrants account for 5% of te US workforce, Borjas s figures sould be around.005% to.0%. Using te 5.6% tax rate and te MF.4, our estimated welfare effects are more tan 00 times larger tan Borjas s figures. Te estimate for m, te Pareto improving level of immigration if θ 0 and if tere are no fiscal effects associated wit immigration, is 400.9% of te native labor. By freeing up natives to enter te workforce, immigration sould ave an even stronger positive effect on measured GDP tan on welfare accruing to natives. In Table 3 we compute National Income, wic measures ow muc more gross income is generated by natives wit immigration, to be.5% imitations Te models and calibrations are subject to a number of limitations: To te extent tat private ouseold workers contribute to increased fertility or consumption of leisure, as may be te case in te Gulf States, our calibration will overestimate te ig-skilled labor response and will overestimate canges in wages and welfare. 2 Te model does not allow for capital. To te extent tat capital is mobile or oterwise adjusts over time, te estimates may be reasonable in te long run, but in te sort run, overall increases in output will not be as sarp. Te pattern in canges and 4 Borjas (999 estimates tese gains for a variety of different assumptions. e take te estimates from is tree factor model of production (capital, skilled and unskilled labor were te supply of capital is perfectly elastic. 30