Dual Job Search and Migration Christine Braun UC Santa Barbara E. Charlie Nusbaum UC Santa Barbara February 14, 2017 Peter Rupert UC Santa Barbara Abstract From 1964-1990, the aggregate intercounty migration rate remained largely unchanged, after which it began to decrease. During this same period, however, the intercounty migration rate of married couples steadily declined while the migration rate of single individuals concurrently increased. These differential trends suggest important differences in how multi-member households and individuals make decisions. This paper builds on the extensive demography and labor literature by asking how much of the decline in the mobility of married couples can be accounted for by the rapid increase in female labor force participation from 1960 to 2000? DRAFT: NOT FOR DISTRIBUTION Department of Economics, UC Santa Barbara, 2127 North Hall, Santa Barbara, CA. cbraun@umail.ucsb.edu. Department of Economics, UC Santa Barbara, 2127 North Hall, Santa Barbara, CA. enusbaum@umail.ucsb.edu. Department of Economics, UC Santa Barbara, 2127 North Hall, Santa Barbara, CA. peter.rupert@ucsb.edu. 1
1 Introduction The idea that households make decisions based on total family gains instead of personal gains has long been recognized in economics - a principle was first introduced to the migration decisions of households by Mincer (1978). Since then, the collocation problem of couples when searching for jobs has garnered significant attention. We build on the extensive demography and labor literature by asking how much of the decline in the mobility of married couples can be accounted for by the rapid increase in female labor force participation from 1960 to 2000? We estimate the effect of being a dual searcher household on the intercounty migration rate of married couples and develop a model of joint job search with multiple locations to analyze intercounty migration trends of married couples. From 1964-1990, the aggregate intercounty migration rate remained largely unchanged, after which it began to decrease. Once the migration rate is decomposed by marital status, however, a different trend emerges. We show that during this same period, the intercounty migration rate of married couples steadily declined while the migration rate of single individuals concurrently increased. These differential trends suggest important differences in how multimember households and individuals make decisions. Indeed, by disaggregating the migration rate of married couples by type of searchers - single searcher or dual searchers- we show that the migration rate of dual searcher households was approximately 4.8% from 1964 to 2000, whereas that of single searcher households was 6.2%. Over the same period, it is well documented that female labor force participation rate rapidly increased. We show that this increase was even more rapid for married women and that the percent of dual searcher households increased from 35% in 1960 to 75% in 2000. Motivated by these labor market trends and intercounty migration rates, we use household level data from the Current Population Survey to test the effect of the collocation problem on a household s migration decisions. We find that households in which both members are employed are 1.1 percentage points less likely to move than their single searching counterparts - a decrease of 17%. Furthermore, we show that among all households that moved, the relative probability that a household with both spouses employed moves for job related reasons than for other reasons is 34% lower than for households in which only one spouse is employed and the other is out of the labor force. These results are similar to previous studies that show the collocation problem faced by couples has significant a impact on migration decisions (Gemici, 2016; Costa and Kahn, 2000; Mincer, 1978). Our empirical results stand in contrast to those presented in Kaplan and Schulhofer-Whol 2
(2012). They argue that the decline in migration is due to the increasing similarities of locations in terms of returns to skill and an increase in available information regarding location amenities, rather than the demographic changes we propose. This paper differs in two key respects. First, our period of interest is 1960-2000 whereas Kaplan and Schulhofer-Whol (2012) focus on 1990-2011. Second, we focus on intercounty migration rates while the aforementioned authors focus on interstate migration rates. While we acknowledge the fact that some who make intercounty moves may in fact have not changed jobs, we believe that focusing on interstate migration rates misses a significant fraction of job-related moves. Furthermore, we address potential concerns of overestimating the mechanism we propose in section 2. We model the decisions of dual searcher households as in Guler et al. (2012). We add to the model by allowing both individuals to receive local and foreign offers while unemployed and employed, and interpret the acceptance of any foreign offer as a move. Once a move has taken place, only the spouse receiving the foreign offer remains employed. The interaction between mobility and on the job search has several implications on the reservation wages of individuals. First, if both spouses are employed, the foreign wage offers for which a household is willing to move is symmetric and increasing in both spouses current wages. Second, if only the wife is employed, the unemployed spouse s reservation wage is decreasing in the wife s current wage. This results from the idea that the couple becomes tied" to a location. That is, as the employed spouse s wage increases, both will be less likely to receive acceptable foreign offers, thereby making local offers more attractive and decreasing the reservation wage for the second spouse. Other studies related to this paper include the following. Chen and Rosenthal (2008) and Nosal and Rupert (2007) study whether or not individuals move for job related reasons or for local amenities from 1970-2000. We focus on the collocation problem rather than local amenities. Flabbi and Mabli (2012) also extend the model presented in Guler et al. (2012) to investigate whether or not modeling households as a unit of decision making has important implications for estimated gender wage differentials and lifetime welfare inequality. We focus primarily on household migration decisions. Lastly, Kennan and Walker (2011) estimate a structural model to investigate the impact of expected income on migration decisions and estimate the cost of moving. Our model abstracts from one time moving costs, which we discuss in section 3. 3
2 Data 2.1 Trends in Female Labor Force Participation and Mobility It is a well known fact that female labor force participation increased rapidly after the end of World War II, nearly doubling from 33% in 1950 to 60% in 2001. Since we are interested in the migration decisions of married households, we decompose the labor force participation rate of women by marital status. Figure 1 shows that both the number of married and single women entering the labor force over this time increased substantially, and that labor force participation rate of married women nearly doubled from 1960 to 2000. Not shown is the labor force participation rate of married men, which decreased from 86% in 1962 to 76% in 2000. However, Figure 2 shows that the percent of dual searcher households, defined as married households in which both spouses are in the labor force, increased from 28% in 1962 to 46% in 2000. Figure 1: Female Labor Force Participation by Marital Status 70 60 Percent (%) 50 40 Married Single 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 Notes: The figure shows the percent of women, age 16 or older, that are in the labor force by marital status. The data comes from the basic monthly files of the Current Population Survey. The migration data come from the March sample of the Current Population Survey (CPS). The variable of interest is the one year mobility question in which respondents were asked if they had changed residence since March of the previous year. Movers are divided into five categories: those who had moved within the same county (intracounty); those who had crossed county lines but stayed in the same state (intercounty - intrastate); those who had resided in a different state (interstate); and those who had migrated from abroad. 4
Figure 2: Dual Searcher Households 70 Percent (%) 60 50 40 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Notes: Plotted is the percent of households in which the head of household is in the labor force that have a spouse who is also in the labor force. Households in which the head of household is not married are included in the sample and the percent of dual earner households is calculated as: (# of married households with both spouses in the labor force)/(total # of married households). The data comes from the basic monthly files of the Current Population Survey. We are ultimately interested in moves that occurred due job related reasons. Starting in 1999, the CPS asked individuals who moved for a primary reason for moving. However, since a majority of the increase in female labor force participation occurs prior to 1999, see Figure 1, we can not distinguish a job related move and a move related to other reasons during the time of rapid entrance of women into the labor force. As a proxy we focus on intercounty moves since they are more likely related to job changes. Figure 3 shows the percent of civilian households that moved each year from 1964 to 2015 by marital status of the head of households. The figure reveals that the trends in intercounty mobility are very different across marital status. While the percent of single movers increased from 4% in 1964 to 6.4% in 1984, the percent of married movers decrease from 5.5% to 5% over the same time period. By 1998 the percent of married movers decrease to about 4%. Since the fraction of dual searching households has stayed relatively constant since late the 1990 s, the increase in female labor force participation cannot explain the rapid decrease in the mobility rate of married couples after 2000. However, Figure 3 suggests that a structural change may explain the decrease that occurred after 2000 since both single and married mobility decrease rapidly. To ensure that the decrease in married household mobility is not coming from changes in 5
the demographic composition of married households we adjust the data to control for such changes. Figure 4 plots the unadjusted and adjusted percent of married households that moved across county lines within the year. The adjusted series controls for changes in the age, sex, race, and education of both the head of household and spouse, total real family income, number of family members living in the household and the age, race and education of the spouse. The figure shows that holding constant the composition of these factors at their 1964 levels does not change the trend in migration of married households and therefore changes in the demographic composition of married households alone cannot explain the decrease in mobility. Figure 3: Intercounty Mobility by Marital Status 7 Percent (%) 6 5 4 3 2 Married Single 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 Notes: The 1-year geographic mobility question was not asked between 1972 to 1975, 1977 to 1980, 1985 and 1995. The figure shows the percent of civilian households that moved across county lines within the previous year by marital status. Since the we are interested in the extent to which the increase in female labor force participation decreased the mobility rate of married couples we decompose the mobility rate of married couples by type of households. The two types of households we are interested in are dual searcher households, those with both spouses in the labor force, and single searcher households, those with only one spouse in the labor force. Figure 5 plots the mobility rates for both types of households from 1964 to 2015. The figure shows that the mobility rate for both types of households was fairly constant until the late 1990 s and that the mobility rate for dual searching households was lower than that of single searching households. The average mobility rate for single searcher households from 1964 to 2000 was 6.2% whereas the average mobility rate for dual searcher households was 4.9% over the same period. Figure 5 gives some 6
Figure 4: Intercounty Mobility of Married Households 6 5 Percent (%) 4 3 Unadjusted Adjusted 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 Notes: The figure shows the unadjusted and adjusted percent of married civilian households that moved within the previous year. The adjusted series is the sum of the percent of married households that moved in 1964 and the coefficients on the time dummies of a linear regression of the one year mobility status on time dummies, age, sex, race and education of the head of household and spouse, family size and total real family income. Figure 5: Intercounty Mobility of Marred Households by Household Type 7 6 Percent (%) 5 4 3 2 Dual Searcher Single Searcher 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 Notes: The 1-year geographic mobility question was not asked between 1972 to 1975, 1977 to 1980, 1985 and 1995. The figure shows the percent of married households that moved across county lines within the pervious year by household type. Dual searching households are those in which both spouses are in the labor force and single searching households are those in which only the head of household is in the labor force. empirical support for the mechanism driving the decline in the mobility of married couples. In the next section we analyze the difference in mobility rates across household types using 7
household level data from the March CPS. 2.2 Household-level Analysis In this section we use the household level data from the March CPS in order to determine whether households in which both spouses are in the labor force are less likely to move across county lines and for job related reasons. Since the primary reason for moving was only asked post 1999 we restrict the data to the year 1999 through 2015. Although this is not our primary time period of interest we use this section as evidence of the mechanism we propose in the model. We restrict the sample of households to civilian households in which the head of household is between the ages of 16 and 65. We create 3 samples of households: (1) Married-Total, all households in which the head of household is married, (2) Married-Living Together, all households in which the head of household is married and the spouse is present in the home and (3) Cohabitating, all households in the Married-Living Together sample plus households that include unmarried partners. Our variables of interest are the labor force and employment status of both spouses, so we divide the households into 6 subgroups: (1) EE, both spouses are employed (2) EO, one spouse is employed and the other is out of the labor force (3) EU, ones spouse is employed and the other is unemployed (4)UO, one spouse is unemployed and the other is out of the labor force (5) UU, both spouses are unemployed and (6) OO both spouses are out of the labor force. Table 1 gives summary statistics of the head of household and spouse characteristics, real family income and home ownership rates for the Married-Total sample and each subsample. Households across the samples a similar with respect to education attainment and race, they differ slightly with respect to age, with OO households about 10 years older on average than the other households. This is not surprising since people in these households are more likely to be retired. Households with both spouses employed have the highest total family income and highest homeownership rates. Summary statistics for the Married-Living Together and Cohabitating samples are similar and can be found in the appendix in Table A.1 and Table A.2. We use the data to answer two questions regarding the moving and work decisions of married households: First we ask if households in which both spouses are in the labor force are less likely to move across county lines than households in which only one spouse is in the labor force. Second, we restrict our analysis to only households that moved within the year and ask if households with both spouses in the labor force are less likely to move for job related reasons 8
Table 1: Summary Statistics: Married-Total Households EE EO EU UO UU OO Moved, different county 0.03 0.04 0.05 0.07 0.09 0.04 Real Family Income 85,230.35 63,269.08 58,779.46 34,667.61 38,911.50 33,575.72 Own Home 0.85 0.74 0.68 0.57 0.53 0.77 Head of Household Characteristics Age 43.16 43.92 42.15 42.67 40.98 53.94 White 0.86 0.83 0.80 0.80 0.78 0.79 Black 0.07 0.07 0.11 0.11 0.12 0.11 One race - Other 0.06 0.08 0.08 0.08 0.09 0.08 Multiple races 0.01 0.01 0.02 0.02 0.02 0.02 Less than High School 0.02 0.07 0.05 0.12 0.12 0.09 High School 0.31 0.39 0.43 0.53 0.50 0.49 Some College 0.12 0.08 0.10 0.07 0.07 0.07 College 0.24 0.19 0.16 0.09 0.10 0.12 Advanced Degree 0.13 0.10 0.08 0.04 0.04 0.07 Spouse Characteristics Age 43.27 44.48 42.27 43.61 41.15 56.89 White 0.86 0.80 0.80 0.73 0.78 0.73 Black 0.07 0.06 0.11 0.08 0.12 0.10 One race - Other 0.06 0.07 0.08 0.07 0.09 0.07 Multiple races 0.01 0.01 0.02 0.02 0.02 0.01 Less than High School 0.02 0.07 0.05 0.11 0.12 0.09 High School 0.31 0.37 0.43 0.47 0.50 0.44 Some College 0.11 0.08 0.10 0.06 0.07 0.06 College 0.24 0.18 0.16 0.08 0.10 0.11 Advanced Degree 0.13 0.15 0.08 0.14 0.04 0.16 Observations 732,428 369,097 51,815 16,224 4,006 77,513 than households with only one spouse in the labor force. We answer the first question using a probit model on an indicator variable that takes on the value 1 if the household moved across county lines within the last year. Specifically we run, P(move i = 1) = Φ( β 0 + β 1 EE i + β 2 EU i + β 3 UU i + β 4 UO i + β 5 OO i + X i γ + η t + ε i ) (1) where EE i is an indicator for both spouses in household i being employed, EU i is an indicator for one spouse being employed and the other being unemployed, UU i is an indicator for both spouses being unemployed, UO i is and indicator for one spouse being unemployed and the other being out of the labor force and OO i is an indicator for both spouses being out of the labor force. X i is the set of household covariates which include: age, age squared, race, and education for both the head of household and the spouse, an indicator for homeownership, real total family income and an indicator which takes on the value 1 if a child is present in the home. η t are year fixed effects and Φ( ) is the c.d.f. of the normal distribution. 9
Table 2 gives the estimated coefficients on the labor market indicators. The sign of β 1 indicates that the probability of moving when both spouses are employed is less than that when one is employed and one is out of the labor force, as expected. The sign of β 3 and β 4 are as expected if the arrival rate of both foreign and local job offers is higher when unemployed. The sign of β 2 warrants some discussion since there are two competing effects which leave the direction of the effect ambiguous. First, because both members of the household are in the labor force and may be receiving job offers in other areas, they may be more likely to move relative to EO households. However, if the unemployed spouse receives a job offer in another area they may be less likely to move than EO households since the employed spouse may likely become unemployed following a move. The estimated coefficient on EU shows that the first effect dominates and thus EU households are more likely to move across county lines than EO couples. Table 3 gives the marginal effects of the labor market indicators for a household in which both spouse are white, 40 years old, with a college degree, own a home and have a child present in the home in the year 2000. Focusing on the Total" column of Table 3 shows that the probability of moving when both spouses are employed is 1.1 percentage points lower than when a single spouse is employed and the other is out of the labor force. Given that the average probability of moving across county lines across the entire sample of married households is 3.1%, this effect is quite large. Moreover, the probability of moving when at least one spouse is unemployed is greater than when one spouse is employed and the other is out of the labor force. This suggests that job arrival rates are higher when unemployed than when employed. Next we use the reason for moving response to ask if households with both spouses in the labor force are less likely to move for job related reasons. There are 19 categories for the reason for moving variable which we regroup into 4 broader categories. Our main category of interest is New job or transfer" which includes only households that indicated that a new job or job transfer as their primary reason for moving. Our second category is Other job reasons", this category includes all households that indicated: to look for work or lost job, for easier commute, retired, or other job-related reason as their primary reason for moving. Our third category is Family" which includes all households that indicated: change in marital status, to establish own household, or other family reason as their primary reason for moving. Our fourth category is Other" all remaining reasons for moving.1 Table 4 gives a summary of the reasons 1The remaining reasons for moving are: wanted own home - not rent, wanted new or better housing, wanted better neighborhood, for cheaper housing, other housing reason, attend/leave college, change of climate, health reasons, other reasons, natural disaster, and foreclosure or eviction. 10
Table 2: Probit Estimation Results Married Total Living Together Cohabitating EE 0.126 0.125 0.108 (0.00922) (0.00924) (0.00850) EU 0.0994 0.0981 0.104 (0.0183) (0.0184) (0.0158) UU 0.279 0.276 0.262 (0.0544) (0.0549) (0.0446) UO 0.197 0.197 0.177 (0.0313) (0.0314) (0.0272) OO 0.114 0.109 0.118 (0.0192) (0.0193) (0.0177) N 424,718 423,910 466,950 Robust standard errors in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 Table 3: Probit Marginal Effects Married Total Living Together Cohabitating EE -0.0110-0.0109-0.00973 (0.000904) (0.000902) (0.000837) EU 0.00867 0.00852 0.00936 (0.00164) (0.00163) (0.00147) UU 0.0243 0.0240 0.0236 (0.00483) (0.00485) (0.00410) UO 0.0172 0.0171 0.0159 (0.00281) (0.00281) (0.00252) OO 0.00992 0.00946 0.0106 (0.00173) (0.00173) (0.00165) N 424,718 423,910 466,950 Marginal effects evaluated for a household in which both spouse are white, 40 years old, with a college degree, own a home and have a child present in the home in the year 2000. Robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001 for moving by labor force status for the Married-Total sample. For all subgroups, Other" is the largest reason for moving and New job or transfer" is the second largest for all subgroups 11
Table 4: Reasons for Moving: Married-Total Households EE EO EU UO UU OO New job or transfer 26.8 33.7 30.2 10.3 10.5 5.2 Other job reasons 11.6 12.4 15.4 19.3 24.8 17.7 Family 22.5 19.9 20.7 28.3 28.6 28.5 Other 39.1 34.0 33.6 42.1 36.1 48.7 Total 100.0 100.0 100.0 100.0 100.0 100.0 Observations 9,718 6,376 1,220 399 133 1,086 in which at least one spouse is employed. For households in which one spouse is employed and the other is out of the labor force, the percent of households that moved for New job or transfer" reasons, 33.7%, is almost the same as the percent of households that moved for other reasons, 34%. The summary tables for reasons for moving for the other two samples, Married-Living Together and Cohabitating, can be found in the appendix in tables Table A.3 and Table A.4. We use the 4 broader categories to estimate the probability that a household with both spouses in the labor force will move for job related reasons. Specifically we model the probability that a move occurred for reason j {New job or transfer, Other job reasons, Family, Other} = K as, P(whymove i = j) = e ( β 0j+β 1j EE i +β 2j EU i +β 3j UU i +β 4j UO i +β 5j OO i +X i γ j +η t j +ε i ) 1 + k K e ( β 0k +β 1k EE i +β 2k EU i +β 3k UU i +β 4k UO i +β 5k OO i +X i γ j +η tk +ε i ) (2) where the variables are define as in the probit estimation. Table 5 gives the estimated coefficients on the labor market indicators, the base case is Other so all probabilities are relative to moving for other reasons. Again focusing on the Total column, we find that the coefficient on EE is negative and statistically significant for both the new job or transfer and other job related reasons for moving. The estimated coefficients imply that the relative probability a household with both spouses employed moves for a new job or transfer is 34% lower than for a household with one spouse employed and the other out of the labor force and the relative probability an EE household moves for other job related reasons is 19% lower than and EO household2. The coefficients for households with both spouses unemployed or one spouse unemployed and the other out of the labor force are both negative and statistically significant for the new job or transfer reasons for moving. Although one might 2The relative probabilities of the multinomial logit are exp( β j ). 12
Table 5: Multinomial Logit Results Married Total Living Together Cohabitating New job or transfer EE -0.412-0.415-0.352 (0.0502) (0.0503) (0.0466) EU -0.00530-0.0113-0.0384 (0.0980) (0.0984) (0.0843) UU -1.339-1.301-1.422 (0.400) (0.402) (0.349) UO -1.040-1.029-0.987 (0.211) (0.211) (0.182) OO -1.612-1.600-1.659 (0.177) (0.178) (0.163) Other job related reason EE -0.208-0.214-0.132 (0.0659) (0.0660) (0.0601) EU 0.187 0.196 0.161 (0.120) (0.120) (0.102) UU 0.690 0.748 0.631 (0.257) (0.260) (0.213) UO 0.0306 0.0373 0.0111 (0.178) (0.178) (0.155) OO -0.0187-0.0357-0.130 (0.122) (0.122) (0.113) Family EE 0.00135-0.00200 0.00665 (0.0552) (0.0553) (0.0488) EU 0.00242 0.00309 0.0347 (0.108) (0.109) (0.0858) UU 0.0579 0.117 0.115 (0.266) (0.269) (0.203) UO -0.0291-0.0318-0.115 (0.155) (0.156) (0.131) OO -0.00365-0.00139-0.0828 (0.108) (0.108) (0.0954) N 13,514 13,467 17,054 Robust standard errors in parentheses. Base case is other reason for moving. * p < 0.05, **p < 0.01, *** p < 0.001 13
think such households would be more likely to move for new jobs, they, by definition, will never move for a job transfer as they are not currently employed. We take the sign of these estimated coefficients to reflect this fact. However, the relative probability a household in which both spouses are unemployed moves for other job related reasons is double that of a household in which one spouse is employed and the other out of the labor force, which is in line with the fact that such households may move to look for new work. We have documented the fact that mobility rates have declined for married couples from 1960 to 2000 while concurrently female labor force participation and the fraction of dual searcher households rapidly increased and thus suggest that the need for two jobs has played a role in decreasing the fraction of married couples that choose to move. We have presented some empirical evidence of this mechanism using household level data from the Current Population Survey showing that dual searching households are less likely to move across county lines and for job related reasons than their single searching counterparts. In the following section we model this mechanism using a model of dual labor search and try to quantify the extent to which search frictions and an increase in the fraction of dual searching households contributed to the observed decrease in mobility. 3 Model We are interested in modeling the job search problem for married couples under two different circumstances. First, the single searcher household, in which only one spouse is actively searching and receiving job offers while the other enjoys some utility from being out side the labor force and second, the duals searcher household, in which both spouses are actively searching and receiving job offers. The key feature of our model is that searchers can receive either local job offers or foreign job offers. 3.1 Environment Consider a world in which households search for jobs and enjoy utility over pooled income similar to Guler et al. (2012). There are two types of households, single searcher households and dual searcher households. Within the dual searcher households individuals are ex ante identical and both receive job offers, in the single searcher household individuals differ as only one is searching for jobs. Since we take the increase in female labor force participation as given we do not model the household s decision of becoming either a single searching household or 14
dual searching household. Individuals who are out of the labor force receive flow utility b O and do not receive job offers. Individuals who are in the labor force but unemployed receive flow utility b I and can receive either local or foreign job offers. They receive local offers at wage w drawn from the c.d.f. F(w) at exogenous poisson rate α u l and foreign offers at wage w drawn from the same c.d.f. at exogenous poisson rate α u f. Individuals also search for jobs while employed and can again receive local or foreign offers at wage w drawn from the same c.d.f. at rate αl e and α e f. All jobs separate at exogenous rate δ and households discount utility at rate r. If an individual receives a foreign offer he or she must move locations, however we abstract from moving costs since we are ultimately interested in the difference between moving rates for single searcher and dual searcher households and if monetary moving costs do not differ across these households, they will not change the relative 3.2 Single Searcher Household A single searcher household is composed of two individuals, one which is out of the labor force and the other is in the labor force and searching for jobs. Such a household can be in one of two states: employed-out of the labor force with value function EO(w) or unemployed-out of the labor force with value function UO. The value function are: ruo = b O + b I + α u l max{eo(w) UO,0} df(w) + α u f max{eo(w) UO, 0} df(w) (3) reo(w) = b O + w + αl e + α e f w w EO(w ) EO(w) df(w ) EO(w ) EO(w) df(w ) (4) In either state the household receives flow utility b I from the spouse that is out of the labor force and foreign or local offers. Since there is no cost to moving, the reservation wage for both local and foreign offers is the same. Let R s be the reservation wage such that EO(R s ) = UO. The reservation wage is given by the implicit equation, R s b I = (α u l + α u f αe l αe f ) 1 F(w) R s r + δ + (αl e + dw. (5) αe )[1 F(w)] f 15
The steady state unemployment rate, u s, and steady state distribution of households employed at wage less than or equal to w, G(w), are G(w) = u s = δ δ + (α u l + α u f )[1 F(R s)] δ[f(w) F(R s )] {δ + (α e f + αe l )[1 F(w)]}[1 F(R s)] (6) (7) Each are derived as in Burdett and Mortensen (1998). The migration rate for single searcher households is the sum of the migration rate of the unemployed plus the migration rate of the employed. The migration rate of the unemployed is: α u f [1 F(R s)]. The rate at which workers employed at wage w migrate is α e f [1 F(w)] therefore the aggregate migration rate for single searcher households, M s, is: M s = δα u f [1 F(R s)] δ + (α u f + αu l )[1 F(R s)] + αe f R s 1 F(w) dg(w). (8) 3.3 Dual Searcher Household A dual searcher household is composed of two individuals both of whom are searching for jobs. Such a household can me in one of three states: employed-employed with value function EE(w,w ), employed-unemployed with value function EU(w) and unemployed-unemployed with value function UU. Just as in the single searcher household, since there are no moving costs, the reservation wage for accepting jobs while in the unemployed-unemployed state is the same for both local and foreign offers. Since individuals within the household are identical while unemployed the reservation wage will also be the same across member of the household. Let R 1 be the reservation wage for individuals when both members of the household are unemployed. Then the corresponding value function is: ruu = 2b I + 2(α u l + α u f ) EU(w ) UU df(w ). (9) R 1 If one member of the household is employed, several decisions about accepting jobs offers need to be made. First if the unemployed spouse receives a local job offer, he may take that offer if the value of joint employment exceeds the value of single employment. If for example, the wife is employed at wage w the husband will accept any local offer w such that EE(w,w ) EU(w). Let R 2 (w) be the reservation wage for the second spouse, defined as EE(w, R 2 (w)) = 16
EU(w). Second, both the employed and unemployed spouse may receive a foreign offer. If the foreign offer is received by the spouse that is currently employed, the household will be willing to move for any wage greater than the one it is currently receiving. We do not allow for the possibility that members of the household can live in separate locations or that the household can split up. Therefore, if the unemployed spouse receives a foreign offer, the employed spouse must quite her job and transitions into the unemployed state. Since individuals are identical within the household and households only value total income, which spouse is employed is irrelevant to the decision of employment, and thus the household is again willing to move for any wage offer greater than the one it is currently receiving if the unemployed spouse receives a foreign offer. The value function for the employed-unemployed state is: reu(w) = b I + w + (αl e + αe f + αu f ) EU(w ) EU(w) df(w ) + α u l R 2 (w) w EE(w,w ) EU(w) df(w ) + δ[uu EU(w)]. (10) If both members of the household are employed, each will accept local job offers above their current wage. If one receives a foreign offer, the household must decide whether or not to move. If the household chooses to move, the spouse who did not receive the offer transitions into the unemployed state and begins receiving flow utility b I. Let R 3 (w,w ) be the moving reservation wage defined as EE(w,w ) = EU(R 3 (w,w )) such that the household decided to move for all foreign offers above R 3 (w,w ) when one spouse is employed at w and the other is employed at w. The value function for the employed-employed state is: ree(w,w ) = w + w + αl e + αl e + 2α e f w EE(w,w ) EE(w,w ) df(w ) w EE(w,w ) EE(w,w ) df(w ) R 3 (w,w ) EU(w ) EE(w,w ) df(w ) + δ[eu(w) EE(w,w )] + δ[eu(w ) EE(w,w )]. (11) An steady state in the dual searcher household consists on three measures of households and two steady state distributions of households across jobs. Let uu d, eu d and ee d be the measure of households in the the unemployed-unemployed state, measure of households in the employedunemployed state and measure of households in the employed-employed state. Let T (w) be the measure of households in the employed-unemployed state that are employed at wage less than 17
Figure 6: Dual Searcher Flows uu d 2(α u l + α u f )[1 F(R 1)] δ eu d 2δ + 2α e f R 1 R 2 (w) 1 F[R 3(w,w )] d 2 H(w,w ) α u l R 1 1 F[R 2 (w)] dt (w) ee d or equal to w and let H(w,w ) be the measure of household in the employed-employed state in which one member is employed at wage less than or equal to w and the other is employed at wage less than or equal to w. Figure 6 depicts the flows into and out of each state. The equations that solve the steady state of the dual searcher problem can be found in Appendix B. The migration rate for dual searcher households is the sum of the migration rates of all three states. The migration rate of the unemployed-unemployed households is 2α u f [1 F(R 1)]. The migration rate for the employed-unemployed households is (α e f + α u f )[1 F(w)] and the migration rate for the employed-employed households is 2α e f [1 F(R 3(w,w ))]. Therefore the aggregate migration rate of dual searching households, M d, is: M d = 2α u f [1 F(R 1)]uu d + (α e f + αu f R ) 1 F(w) dt (w)]eu d 1 + [2α e f 1 F(R 3 (w,w ) d 2 H(w,w )]ee d. (12) References R 1 Burdett, Kenneth and Dale T Mortensen, Wage Differentials, Employer Size, and Unemployment, International Economic Review, May 1998, 39 (2), 257 273. Chen, Yong and Stuart S. Rosenthal, Local amenities and life-cycle migration: Do people move for jobs or fun?, Journal of Urban Economics, November 2008, 64 (3), 519 537. R 2 (w) 18
Costa, Dora L. and Matthew E. Kahn, Power Couples: Changes in the Locational Choice of the College Educated, 19401990, The Quarterly Journal of Economics, 2000, 115 (4), 1287 1315. Flabbi, Luca and James Mabli, Household Search or Individual Search: Does It Matter? Evidence from Lifetime Inequality Estimates, IZA Discussion Papers 6908, Institute for the Study of Labor (IZA) October 2012. Gemici, Ahu, Family Migration and Labor Market Outcomes, Working Paper, 2016. Guler, Bulent, Fatih Guvenen, and Giovanni L. Violante, Joint-search theory: New opportunities and new frictions, Journal of Monetary Economics, 2012, 59 (4), 352 369. Kaplan, G. and S. Schulhofer-Whol, Understanding the Long-Run Decline in Interstate Migration, NBER Working Paper Series, 2012, 59 (4), 352 369. kdfjl;ae, Braun, Family Migration and Labor Market Outcomes, Working Paper, 2016. Kennan, John and James R. Walker, The Effect of Expected Income on Individual Migration Decisions, Econometrica, 01 2011, 79 (1), 211 251. Mincer, Jacob, Family Migration Decisions, Journal of Political Economy, 1978, 86 (5), 749 773. Nosal, Ed and Peter Rupert, How Amenities Affect Job and Wage Choices Over the Life Cycle, Review of Economic Dynamics, July 2007, 10 (3), 424 443. A Tables 19
Table A.1: Summary Statistics: Married-Living Together Households EE EO EU UO UU OO Real Family Income 85,317.15 64,452.80 58,895.15 35,503.86 39,052.42 34,346.51 Own Home 0.85 0.75 0.69 0.59 0.53 0.79 Head of Household Characteristics Age 43.17 44.09 42.17 43.21 41.00 54.99 White 0.86 0.84 0.80 0.81 0.78 0.80 Black 0.07 0.07 0.11 0.09 0.12 0.11 One race - Other 0.06 0.08 0.08 0.08 0.09 0.08 Multiple races 0.01 0.01 0.02 0.02 0.02 0.01 Less than High School 0.02 0.07 0.05 0.12 0.12 0.09 High School 0.31 0.39 0.43 0.53 0.49 0.49 Some College 0.12 0.08 0.10 0.07 0.07 0.07 College 0.24 0.19 0.16 0.09 0.10 0.12 Advanced Degree 0.13 0.10 0.08 0.04 0.04 0.07 Spouse Characteristics Age 43.28 44.49 42.29 43.65 41.19 56.90 White 0.86 0.84 0.80 0.81 0.78 0.80 Black 0.07 0.07 0.11 0.09 0.12 0.11 One race - Other 0.06 0.08 0.08 0.08 0.09 0.07 Multiple races 0.01 0.01 0.02 0.02 0.02 0.02 Less than High School 0.02 0.07 0.05 0.12 0.12 0.10 High School 0.31 0.39 0.43 0.53 0.49 0.48 Some College 0.11 0.08 0.10 0.07 0.07 0.07 College 0.24 0.19 0.16 0.09 0.10 0.12 Advanced Degree 0.14 0.11 0.08 0.04 0.04 0.08 Observations 731,160 348,425 516,66 145,13 3,985 70,675 20
Table A.2: Summary Statistics: Cohabitating Households EE EO EU UO UU OO Real Family Income 82,780.92 62,787.54 55,358.34 33,391.32 35,535.40 33,469.31 Own Home 0.83 0.74 0.65 0.56 0.49 0.78 Head of Household Characteristics Age 42.80 43.82 41.42 42.45 39.84 54.58 White 0.86 0.84 0.80 0.81 0.77 0.80 Black 0.07 0.07 0.11 0.10 0.12 0.11 One race - Other 0.06 0.08 0.07 0.07 0.09 0.08 Multiple races 0.01 0.01 0.02 0.02 0.02 0.02 Less than High School 0.02 0.07 0.05 0.11 0.11 0.09 High School 0.32 0.39 0.44 0.54 0.51 0.50 Some College 0.12 0.08 0.10 0.06 0.07 0.07 College 0.24 0.19 0.16 0.09 0.10 0.12 Advanced Degree 0.13 0.10 0.07 0.04 0.03 0.07 Spouse Characteristics Age 42.87 44.18 41.46 42.80 39.99 56.40 White 0.86 0.84 0.80 0.80 0.77 0.80 Black 0.07 0.07 0.11 0.10 0.12 0.11 One race - Other 0.06 0.08 0.07 0.08 0.09 0.08 Multiple races 0.01 0.01 0.02 0.02 0.02 0.02 Less than High School 0.02 0.07 0.05 0.11 0.11 0.10 High School 0.32 0.39 0.44 0.55 0.52 0.48 Some College 0.11 0.08 0.10 0.06 0.07 0.07 College 0.24 0.19 0.16 0.09 0.09 0.12 Advanced Degree 0.13 0.10 0.07 0.04 0.04 0.07 Observations 770,047 362,788 57,529 16,152 4,662 73,645 Table A.3: Reasons for Moving: Married-Living Together Households EE EO EU UO UU OO New job or transfer 26.9 33.7 30.3 10.4 10.8 5.2 Other job reasons 11.5 12.5 15.5 19.4 25.4 17.5 Family 22.4 19.9 20.7 28.0 28.5 28.6 Other 39.1 34.0 33.6 42.2 35.4 48.8 Observations 9,685 6,361 1,213 396 130 1,082 21
Table A.4: Reasons for Moving: Cohabitating Households EE EO EU UO UU OO New job or transfer 24.7 31.1 25.3 10.4 9.8 4.9 Other job reasons 11.7 12.3 15.2 17.7 22.3 16.1 Family 24.9 21.9 24.7 28.8 31.7 29.2 Other 38.7 34.8 34.8 43.1 36.2 49.8 Total 100.0 100.0 100.0 100.0 100.0 100.0 Observations 12,975 7,487 1,833 548 224 1,307 22
= [δ + (α e l + αe f + αu f )[1 F(w)] + αu l (1 F(R 2(w)))]T (w)eu d (15) B Steady State Equating the flow into and out of the unemployed-unemployed state gives flowing equation that must be satisfied in steady state: eu d = 2(αu l + α u f )(1 F(R 1)) uu d. (13) δ Equating the flow into and out of the employed-employed state gives the flowing equation that must be satisfied in steady state: [ ] α u l (1 F(R 2(w))) dt (w) eu d R 1 [ = 2δ + R 1 R 2 (w) ] 2α e f (1 F(R 3(w,w )))d 2 H(w,w ) ee d. (14) Since households must be in one of three states uu d + eu d + ee d = 1 must hold in steady state as well. Similarly the flow into and out of the measure of households employed at wage less than or equal to w must equate in steady state. The flow in is equal to unemployed households that receive a wage offer great than their reservation wage and less than or equal to w, plus the households in which both spouses are employed but they receive a foreign offer at less than or equal to w and choose to move. The flow out is equal to employed-unemployed households in which the unemployed member receives a wage offer above his reservation wage plus the households that loose their job. Therefore the following equation must be satisfied in steady state: 2(α u l + α u f )[F(w) F(R 1)]uu d + dh(w,w ) + 2δ dw dw + 2δH(w,w) w [ 2α e f max{f(w) F(R 3 (w,w )),0} d 2 H(w,w ) R 1 R 2 (w ) ] ee d The flow into and out of the measure of households in which one member is employed at less than or equal to w and the other is employed at less than or equal to w must equate in steady state. The flow in is equal to employed-unemployed households employed at wage less than or equal to w in which the other member receives a wage offer less than w but greater than his reservation wage and the flow out is equal to households that choose to move plus 23
those in which one member looses their job. Therefore the following equation must be satisfied in steady state: {α u l max{f(w ) F(R 2 (w)),0}[t (w) T (w ) 1(w > w )] + α u l max{f(w ) F(R 2 (w)),0}[t (w ) T (w) 1(w > w)]}eu d (16) = [α e l (1 F(w)) + αe l (1 F(w )) + 2(δ + α e f (1 F(R 3(w,w )))]H(w,w )ee d 24