extfieldsofstudy: Economics Medicine

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Can lower remittance costs improve human capital accumulation in Africa?

To evaluate gains in human capital accumulation from reduction in remittance prices, this study constructs a general equilibrium model in which the choices to invest in human capital and to migrate are endogenous. The model is calibrated for a group of eight African economies which offer student loans, and the effect on human capital accumulation of decreasing the remittance price to the level recommended by the United Nations (3%) is numerically derived. It is found that reduction in remittance prices alters the decisions of households, leading in the aggregate to a decrease in interest rates, a curbing of the desire to migrate, and an increase human capital. Hence, the study offers the policy prescription that governments, both in nations where remittances originate and in those to which funds are sent, must continue to lower remittance prices, by, for example, improving access to mobile banking, especially since such policies are relatively immune to economic shocks.

Introduction
International labor migration from developing to developed countries has increased three-fold over the past 40 years. Skilled labor emigration has been rising at an even faster rate (Docquier & Rapoport, 2012). In 2000, immigrants with tertiary education constituted 31.4% of African immigrants, 27.6% of Latin American immigrants, and 43f.5% of Asian immigrants (Docquier & Marfouk, 2004). 1 This level of skilled migration can be alarming given that the proportion of highly skilled workers in the labor force was only 3.6% in African countries and 6% and 11.8% in Asian and Latin and Caribbean countries, respectively. The emigration of skilled labor from developing economies is typically labeled brain drain and can raise vital concerns for governments in developing countries as they design programs that finance higher education. Factors that alleviate the problem of brain drain are remittances and brain gain (when workers acquire more education in hopes of migration to a higher wage labor market). This study demonstrates that policymakers can mitigate the negative impact of brain drain and extract more benefit from brain gain by lowering the price of remittances, aligning it with the UN's Sustainable Development Goals.
A general equilibrium model is built in which a worker can choose to migrate and then send remittances home if the utility from migration to a labor market with higher wages exceeds that from staying. However, of those who desire to migrate, only a fraction succeeds (brain drain). Those whose migration plans do not materialize accumulate more human capital, earn higher incomes, and accrue more savings, than they would have in the absence of migration possibilities (brain gain). Remittances further increase the incomes and savings of stayers. However, there is the possibility of a harmful secondary effect: as individuals borrow to finance their education, aggregate borrowing increases, which puts upward pressure on interest rates, making it prohibitive to invest in higher education. The model is calibrated for a set of eight African countries for which some data on student loans is available, and numerical results derived. It is shown that if policymakers successfully reduce the price of remittances, the harm from the secondary effect is mitigated, and the brain gain channel is strengthened, skilled migration rates fall, and human capital increases.
This study builds on earlier research by Beine, Docquier, and Rapoport (2008); Galor and Zeira (1993); Cai (2020); Djadjic, Docquier, and Michael (2019); Mesnard (2004) and Antunes, Cavalcanti, and Villamil (2008), that documents the impact of migration on human capital accumulation and investment while taking into account credit market dynamics. However, this work is novel in that it calculates the benefits of a reduction in remittance prices explicitly while taking into account the effect of this reduction on interest rates and migration decision.
Remittance prices are the transfer costs migrants must pay in order to send funds home, calculated as the transaction fee relative to the value sent. The World Bank estimates that with a reduction in the remittance price to 5%, developing countries would receive over $16 billion additional funds a year. 2 Given the importance of remittances for the receiving economies, one of the UN Sustainable Development Goals is the reduction of remittance prices from its worldwide average of 7% to less than 3% and the elimination of remittance corridors with costs higher than 5%. The importance of reducing remittance prices has been recognized by policymakers for over a decade. Leaders at the 2009 G-8 meeting and the 2014 G-20 meeting pledged to reduce remittance prices as well. Increasing access to banking services, particularly mobile banking, increasing competition between money transfer agencies, and improving information for migrants on costs at these agencies, are simple steps to reduce the costs of transferring funds (Yang, 2011). Additionally, governments can reevaluate their range of regulations to improve transparency of international transaction if these increase migrants' costs of transferring money home (Beck & Peria, 2011).
The remainder of the paper is organized as follows. The next section describes the related literature. The sections that follow introduce the model and describe the equilibrium. It is succeeded by discussion of the calibration strategy and presentation of the numerical findings. The last two sections respectively, discuss the policy implications of the findings and present the study's conclusion.

Related literature
Early literature on brain drain suggested that the migration of skilled labor made those left behind worse off (Bhagwati and Hamada, 1974;Miyagiwa, 1991;Wong and Yip, 1999), leading some economist to advocate taxing emigrants. However, later literature concluded that when workers are faced with a probability of migration to a labor market with a higher wage than prevalent at home, they accumulate more human capital levels than in the absence of migration so that the unsuccessful migrants boost the nation's stock of human capital in net (Stark, Helmenstein, & Prskawetz, 1998;Vidal, 1998). 3 The positive effect that the prospect of migration can have on human capital accumulation is typically labeled "brain gain". Empirically, evidence of brain gain is mixed. Beine, Docquier, and Rapoport (2001) and Beine et al. (2008) find evidence of brain gain effect whereas Faini (2003) fails to find such an effect.
Migration can also increase human capital through the effect of remittances. The impact of remittances on human and physical capital, and, in turn, growth, typically depends on the extent to which households use these funds for investment versus consumption. Many studies find that remittances are used for human capital investment: Adams and Cuecuecha (2013) find evidence of this in Ghana, Yang (2008) finds similar patterns for the Philippines, and Hines and Simpson (2019) find the same for Kenya. Also, evidence of the use of that remittances for physical capital investment has been document by Adams (1998) for rural Pakistan, Jena (2018) for Kenya, and Taylor, Rozelle, and de Brauw (2003)) for China. 4 Although some studies have found that remittances are spent on consumption smoothing rather than investment, there is ample evidence of the contribution of remittances to economic growth and productivity (Annen, Batu, & Kosempel, 2016;Gupta, Pattillo, & Wagh, 2009;Imai, Gaiha, Ali, & Kaicker, 2014;Kapri & Ghimire, 2020), which points to their importance in financing investment. 5 3 Mountford (1997) and Stark and Zakharenko (2012) go on to show that the migration possibilities of particular skilled workers can improve productivity, and Katz and Rapoport (2005) show that with migration, higher variance in the home country's return to education compared to that of the foreign country increases human capital. 4 Some work on the effect of remittances on human capital has focused on the educational attainment of the children left behind (see Amuedo-Dorantes and Pozo (2010); Jamal Bouoiyour (2015), and Salas (2014); Bansak and Chezum (2009), and Edwards and Ureta (2003). 5 Additionally, Abbas, Masood, and Sakhawat, (2017)) and Opperman and Adjasi (2019) show that loans can substitute for remittances. This study is also related to papers that have explored the forces that can shape the brain gain effect. For example, Chen (2009) incorporates fertility choice in an endogenous growth model and shows that while an increase in skilled migrants' probability of successful migration leads to brain drain in the long run, an increase in the probability of migration of low skilled migrants can lead to brain gain. Stark, Helmenstein, and Prskawetz (1997) and Chau and Stark (1999) identify return migration as a channel through which migration can lead to brain gain.
This study demonstrates that brain gain can be strengthened by the lowering of remittance prices, and that this lowering can lead households to invest more in human capital, save more, and migrate less.

The model
The model employed is a heterogenous-agent overlapping generations model with each individual living for three periods. In the first period individuals choose whether they will borrow to finance human capital as in the work by Croix and Michel (2007); in the second period individuals make their migration choices as in the work by Faini (1996). However, not everyone is successful in their attempt to migrate as in the work by Stark et al. (1997) and Beine et al. (2001). The probability of actually migrating is given by 0 < l < 1. The inclusion of uncertainty in an individual's migration outcome in the model is motivated by real-world features such as border restrictions and visa procedures set by receiving countries.
Those who do migrate work abroad at a higher wage and do not return. Those who stay home work at the prevailing domestic wage, pay back their loans and make their savings decision. In the last period agents retire and consume savings.

Households ability and home preference distribution
Individuals are heterogeneous along two dimensions, ability denoted by z and indexed by j and preference for staying at home denoted by θ and indexed by i. Heterogeneity in ability (represented by z j ) is uniformly distributed between [0,1] following Mayr and Peri (2008). 6 And following Faini (1996), preference for living in the home country (represented by θ i ) is distributed according to a Pareto function such that, where ε is a parameter of the Pareto distribution. If an individual lives at home, their utility is augmented by an idiosyncratic θ i > 1, but they receive no such augmentation if they migrate. The lower utility of living abroad represents social and psychological costs that come with adapting to a new environment (Faini, 1996).

Human capital evolution
Individual (i, j) is born in t−1, borrows b ij,t−1 , and accumulate human capital h ij,t . Human capital accumulated by each individual depends on their borrowing b ij,t−1 and on the aggregate level of the previous generation's human capital, H t −1 , and is governed by the following function as in the paper by Croix and Michel (2007), where 0 < λ < 1 determines the elasticity of human capital to borrowing.

Household types
Individuals with high enough ability z j invest in human capital. Individuals with high enough θ i stay at home, earn returns on their human capital at home and invest their savings at home; individuals with low enough θ i plan to migrate. After the migration outcome is revealed, the individual, in period t, decides on his optimal savings for retirement in period. The threshold of z j above which households invest in education is derived in section (4.3), and the threshold of θ above which individuals will stay home is derived in Appendix A.
Therefore, three types of individuals exist in each generation: stayers who invest in human capital, those who wish to migrate, and those who do not invest in human capital. The optimization problems and optimal levels of human capital, borrowing, and savings for those types are derived next.

Household type I: stayers
An individual (i,j) living in the origin country (o) who does not wish to migrate but invests in human capital is referred to as a stayer. Stayers maximize the following utility function, subject to human capital accumulation function (2) and the following budget constraints, where δ is the discount rate, and R t −1 and R t are the relevant interest rates. Ability (z j ) augments earning from human capital so that if two workers have the same level of human capital, the higher ability worker with higher z j would earn a higher income. s o 1 ij,t is savings for stayers who invest in human capital and The optimal levels of borrowing, human capital, and savings implied by the above maximization problem are, Stayers' human capital is negatively related to interest charged on debt, and their savings are a constant fraction of income. Using optimal levels of borrowing and human capital for stayers given by (6) and (7), the life-cycle income can be rewritten as (1 − λ) z j h o ij,t . Hence, the indirect utility of the individual staying in the origin country is given by, 3.3.2. Household type II: those who desire to migrate An individual (i, j) who wishes to migrate and live in the destination country (d) is referred to as a possible migrant. Before knowing whether he will successfully migrate or not, the possible migrant enters into a remittances contract with other possible migrants of the same type with whom he has familial ties. This contract dictates that those who successfully migrate remit a portion of their income back to those who remain behind. The remittances contract is discussed in more detail in section 3.3.3.
Possible migrants choose how much to borrow and invest in human capital (b d ij,t−1 and h d ij,t−1 ), and how much to save if they migrate or if they stay home (s d ij,t and s o 2 ij,t ) to maximize the following expected utility function, subject to the human capital accumulation function (2) and the following budget constraints, where x > 1 represents the higher earnings abroad and R d represents the foreign interest rate, which is unchanged by migration. 0 < τ < 1 is the portion of income a migrant remits to other family members, while T is the amount of remittances received and p is the remittance price defined as the cost of sending funds home. Note that migrants default on debt when they leave their country of origin. To motivate this assumption, it is observed that bankers in small countries have expressed reluctance to make student loans given the uncertainty of debt repayment in light of the established patterns of skilled emigration (Khraiche, 2011). 8 Similarly, Kenya, which does provide students loans to cover public and private education, has historically faced difficulty in collecting repayment partly because of emigration and poor record keeping and enforcement (Otieno, 2004). The phenomenon of debtors leaving a country and avoiding debt repayment was also a serious concern in Dubai in 2009, as indebted expatriates made unemployed by the financial crisis began leaving the country, debts unpaid (Worth, 2009). 9 To find an analytical solution, φ is defined as the portion of migrant income accruing to a single individual at home. Since remittances by a single individual can be distributed over several family members who stay, it is possible that τ / = φ. 10 In this case, T in terms of ϕ is defined as, On average, if the family size is F, then lF fraction of the family migrates, and (1 − l)F stays. Therefore, remittances sent by migrant family members of type (θ i , z j ) equal lF (τxz j h d ij,t ), which would be distributed over (1 − l)F stayers and each receives The solution to the maximization problem of possible migrants yields, where b d ij,t , h d ij,t , and s d ij,t are the optimal levels of borrowing, human capital accumulation, and savings of an individual who wish to migrate but fails. K = (1 − l + lλ) and Φ = 1 + (1 − p) φl are defined for simplicity of exposition and also because these two expression summarize the effect of the possibility of migration and remittances on human capital decisions of those who stay.
A comparison of the expressions for the human capital of stayers and migrants given, respectively, by (7) and (17), makes clear that those who wish to migrate accumulate more human capital There are two reason for the higher level of human capital accumulated by migrants. First, the possibility of migrating to a labor market with higher wages and defaulting on repayment augments human capital accumulation by a factor of 1 The second reason is the presence of remittances, which augments human capital by a factor of (Φ) λ 1−λ >1. A person who wanted to migrate and default, and now has to pay back the debt and stay home, can use remittances to pay back some of the debt and therefore accumulates more human capital to begin with (compared to the case where the worker receives no remittances). Therefore, migration boosts some individuals' human capital (brain gain). However, aggregate human can rise or fall depending the fraction of the population that migrates and no longer works at home (brain drain). 9 Despite including the assumption of defaulting migrants, a positive relationship between human capital accumulation and migration is still found. 10 For example, if there are two family members, one migrates while the other stays, then. On the other hand, if there are 3 family members, one migrates and two stay, then.
Eq. (19), describes the savings rates for possible migrants who fail to migrate. These individuals save a fraction δ 1+δ 1 + (1 − p) Φ − λ Φ K of their income. Remittances boost savings of possible migrants who stay by increasing the fraction saved.
If a possible migrant successfully migrates, then the indirect utility of the migrant can be obtained by substituting (17) and (18) into the budget constraints, yielding If a possible migrant stays home instead of migrating, then the indirect utility of the migrant can then be obtained by substituting (17) and (19) into the budget constraints, yielding

Remittances contract
An individual enters into a remittances contract in period t−1 only if, a priori, the expected lifetime indirect utility of paying remittances is bigger than or equal to the expected lifetime utility of not paying remittances. Formally, an individual will enter in an enforceable remittances contract if, where V d ij,t (given by Eq. (20)) is the lifetime utility of migrant in a remittances contract. And  (22) amounts to a participation constraint that defines a threshold level of,τ below which an individual would be better off participating in the remittances contract when he is still not sure whether he will migrate or not. Simplifying (22),τ is found as follows, Eq. (23) is not an explicit function of τ since φ and Φ vary with τ. However, Eq. (23) shows that there exists a positive level of remittances that would make the possible migrant enter into a remittances contract. It is assumed that the level of τ satisfies the constraint given by (23) and that all migrants enter into a remittances contract and honor their commitment.

Household type III: least skilled
The next worker whose problem is formalized is the one with very low ability z j , who finds it optimal not to invest in human capital and is labeled as least skilled. The least skilled earns an income a in period t, some of which is saved for period t + 1. The least skilled are excluded from the credit markets, and therefore do not receive a return on their savings. The implications of excluding the least skilled from capital markets are discussed in section (4). Therefore, an individual (i, j) living in the origin country (o) who does not wish to migrate or invest in human capital (referred to as a least skilled individual) maximizes the following utility function, subject to the following budget constraints, The solution to the least skilled optimization problem is the following optimal savings function and the indirect utility is given by,

Aggregation
Now that the decision processes of individuals have been formalized, the next section proceeds to find the fraction of the population that will invest in human capital. The fraction of the population that wants to migrate is derived in Appendix A. This is followed by derivations of aggregate human capital, savings, and borrowing levels.

Human capital investment decision threshold
Although it has been assumed that the least skilled will not migrate, 11 the decision to invest in human capital is endogenous for stayers. Those who do not wish to migrate will only invest in human capital if and only if V o 1 ij,t ≥ V n ij,t which implies that the utility of investing in human capital and staying home is larger than the utility of not investing in human capital and simply earning income a. This inequality gives rise to a threshold of ability, ẑ, above which the individual will invest in human capital. Formally, anyone with ability z i above the threshold ẑ given below will invest in human capital, 11 Mayr and Peri (2008) make a similar assumption when calibrating their model in order to guarantee that some population will remain home regardless of migration restrictions. This assumption is further discussed in the Appendix B.

Aggregate human capital
The fraction of the population that would like to migrate, since its preference for staying at home (θ i ) is low enough to ensure that its utility from migration is higher than that from staying, is defined as m t . The full expression for m t is in Appendix A. Since m t is the desired migration rate and only l migrate successfully, then lm t as the realized migration rate. Aggregate human capital for a generation is given by 12 From the expressions for the human capital of stayers and of those who would prefer to migrate, given respectively by (7) and (17), the aggregate level of human capital in the country of origin becomes, Note that remittance prices have an impact on aggregate human capital through their effect on individuals' human capital decision, their effect on interest rates, and their effect on migration decisions.

Aggregate borrowing and savings
The aggregate level of savings for a generation, S t , is given by, And aggregate borrowing is given by, The assumption of excluding the least skilled individuals from the credit markets does not change the expression for aggregate borrowing in the model. This is because borrowing is exclusively used for education. If the least skilled were able to invest their savings, the level of savings they would accumulate would still be given by δ 1+δ a, since they save a fraction of their income determined by the discount rate δ. Therefore, the aggregate savings function would be given where the first integral sums over the savings of those who accumulate human capital and the second integral sums over those who do not (the least skilled). Examining this expression reveals that the savings of the least skilled can only impact the aggregate savings function S t through changes in ẑ, since a and δ are constants. However, even without considering the savings of the least skilled, changes in ẑ are already taken into account as they change the aggregate savings of those who accumulate human capital (by changing the limits of the first integral).
For example, if a parameter (other than δ or a) change caused ẑ to increase, this would mean that a higher threshold of ability must be attained in order for a worker to invest in human capital, increasing the proportion of least skilled workers in the economy and decreasing the number of skilled workers. This in turn would increase the contributions of the least skilled to aggregate savings (if their savings were included in aggregate savings), but reduce the contributions of those who accumulate human capital. The key, however, is that those who accumulate human capital would have a higher level of savings than the least skilled, implying that aggregate savings would fall as threshold ẑ increased. Qualitatively, the model still predicts that aggregate savings would fall with a higher ẑ even if the least skilled were excluded from capital markets and their contributions to aggregate savings were ignored.

Equilibrium
Equilibrium in the asset market requires that, which in turn determines the equilibrium interest rate in the origin country, R t −1 . Using the optimal levels of borrowing derived for individuals who live in the origin country and the expressions for aggregate savings and borrowing, the interest rate which clears the asset market is given by

Steady state
To find the origin country's steady state interest rate, the equalities R t −2 = R t −1 = R t = R and m t −1 = m t = m are imposed. This yields the following expression for the steady state interest rate, R: .
The existence of the equilibrium is discussed in Appendix D. Note that the interest rate is a function of remittances and remittance prices. More remittances and lower remittance prices increase savings directly as more funds arrive, and indirectly through their effect on human capital accumulation, borrowing, and desired migration (m). Next, numerical results are turned to in the next section to estimate the degree to which remittance price reduction can change the interest rate and the migration rate, and in turn, human capital.

Numerical results from policy experiment
In this section, the effects of reducing remittance prices upon the growth of human capital accumulation, interest rates, and desired migration rates, as implied by the model, are estimated. To do so, the model is calibrated to match data from developing countries from which emigrants depart, and developed economies, the migrants' destination.

Calibration strategy
First, the traditional parameters of the model are calibrated. The variable x, which captures the differences in productivity between developing and developed countries, is assumed to equal 2, as in the paper by Mayr and Peri (2008). The discount rate, δ, is set to 0.5. Eq. (15), which defines φ as T/ z j h d ij,t , where T is remittances received and z j h d ij,t is income earned, is used to calibrate ϕ. Therefore, the World Bank's estimates of remittances received by the host country as a percent of its GDP is taken for the value of φ.
Since detailed data on student loans in developing economies is not available, structural estimation of the nontraditional parameters of the model is not possible. Therefore, a simple calibration strategy is employed to calculate λ, l, and ε for a set of eight African countries for which data on student loan interest rates and borrowing levels are available for the year 2005. The countries are Burkina Faso, Ethiopia, Ghana, Kenya, Namibia, Nigeria, Rwanda, and South Africa. Their pertinent data are listed in Table 1. Although developing economies have historically offered free public education, this trend has seen changes as some countries have opted for cost sharing programs whereby some education expenses (such as boarding, program fees, tuition) are charged to students (Woodhall, 2007). As such cost sharing increased, student loans were introduced to help students deal with paying their share of the expenses. In 2003, after cost sharing was introduced, Ethiopia established a loan program in which students borrow to cover food, lodging and 15% of tuition cost. The loans required repayment to start a year after degree completion (Johnstone & Aemero, 2001;Yizengaw, 2007). Similarly, Ghana also offers students loans with a subsidized interest rate (Atuahene, 2008). Recently, Strathmore University (a private institution in Kenya), the World Banks' International Finance Corporation, and the Commercial Bank of Africa Ltd established a loan program for students enrolled in the University. Similarly, South Africa and Nigeria, have student loan programs. The First Bank of Nigeria Ltd offers student loans for those seeking private education. 13 The parameters, l, ε, and initial value of m, are simultaneously calibrated using three equations: the equilibrium interest rate equation given by (37), the equilibrium desired migration rate given by (40), and lm set equal to each country's emigration rate among those with tertiary education, retrieved from the IAB Brain Drain Dataset, published by the German Institute for Employment Research (Brucker, Capuano, & Marfouk, 2013). Using a value of R equal the student loan interest rates (listed in Table 1) and the aforementioned equations, a nonlinear equation solver enabled solving for l, ε, and m. The computed values of the parameters for each country are listed in Table 2.  To calculate λ for each of the eight countries, the fact that λ is the elasticity of human capital with respect to debt, and therefore, can be written as δH t−1 δb ij,t−1 b ij,t−1 H t−1 , is exploited. δH t−1 δb ij,t−1 is scaled so that the interest rate in the model lies between 0 and 1. Finally, interpretation of b ij,t −1 and H t −1 as the dollar amount borrowed and the dollar cost of education enables calculation of λ. Utilized data on the ratio of borrowing to the cost of education is listed in Table 1.
Finally, remittance prices for the sample of countries are retrieved from the World Bank's Remittance Prices Worldwide database. Table 3 shows the average transaction costs of sending remittances to these countries. The highest remittance price in the sample stands at over 19.5% for Namibia. Indeed, some African countries have the highest costs of sending funds home (KNOMAD, 2017). Even so, Africans are found to remit twice as much on average as migrants from other developing countries (Bollard, McKenzie, & Morten, 2010).

Policy experiment
This section documents the extent to which a decrease in remittance prices (p in the model) to 3% can affect human capital accumulation in developing economies experiencing brain drain. 3% is chosen since the UN Sustainable Development Goals is to reduce remittance prices to this percentage.

Computational method
To measure the impact of reduction in the remittance price to 3% upon human capital accumulation, the new desired migration rate and the interest rate that clears the asset market under the new remittance price are simultaneously calculated. 14 The subsequent change in human capital is calculated using Eq. (31). Some studies document that remittances respond to changes in costs. Freund and Spatafora (2008) find a negative correlation between remittance prices and remittances, and Ashraf, Aycinena, Martinez, and Yang (2010) demonstrate that this could be substantial for migrants from El Salvador. Similarly, using survey hypotheticals of Tongan migrants in New Zealand, Gibson, Mckenzie, and Rohorua (2006) estimate a high elasticity of remittances to changes in cost. The elasticity of remittances to their price for this study's sample of 8 African countries is calculated to be −0.13 based on taking each country's remittance rate and remittance price as individual points along a demand curve. Therefore, the simulations assume that the remittance rate increases by 0.13% for each 1% reduction in the remittance price.

Results
The results are presented in Fig. 1. It is found that for the sample countries, human capital increases following a remittance price reduction. The increases are detailed in Table 4.
The gains in human capital from reduction in the remittance price come mainly from lower interest rates and lower migration rates (see Figs. 2 and 3). The market clearing interest rate  decreases as the remittance price decrease since saving increases faster than borrowing. The increase in saving comes directly from the receipt of more remittances as their transaction cost decreases. The additional remitted funds also enable households to increase human capital (brain gain) without increasing borrowing, which enables them to earn more income and increase saving.
Also, as the interest rate decreases, the threshold of ability above which households invest in human capital (ẑ) decreases. So, with a reduction in the remittance price, households which would have ordinarily decided not to invest in human capital, reverse that decision.
Additionally, the desired migration rate (m) decreases as the remittance price falls. This implies that, as emigrated family members can send more funds home, fewer households desire to migrate. Therefore, reduction in the remittance price, by reducing migration, further increases human capital at home by curbing brain drain.
Human capital gains from the reduction in the remittance price are larger for countries with a high probability of success in migration (l). In other words, in economies in which it is easy to migrate, the increase in human capital from reducing the remittance price is more pronounced. One reason for this effect is that households plan their human capital accumulation decision before their migration outcome is revealed. A benefit of human capital accumulation is higher earnings and remittances sent home, upon successful emigration of a family member. A decrease in the price of remittances would increase this benefit, and it stands to reason that this increase shall be more pronounced the higher the probability of emigration. Unsurprisingly, reduction of remittance price to 3% tends to induce a bigger increase in human capital in countries in which this price was higher to begin with, as may be seen in Fig. 4.

Policy discussion
This study contends that the lowering of the prices of remittances is a potential policy tool for increasing brain gain and reducing brain drain towards raising the levels of human capital in developing economies. Beck and Peria (2011) hold that remittance prices may be reduced by such measures as improving access to bank, increasing competition between providers of remittance services, and reevaluating the level of regulation for governing these providers.
As is well known, the introduction of mobile banking has improved access to financial services in general, particularly in developing economies. Therefore, increasing access to mobile phones and investing in communication infrastructure may significantly lower remittance prices. Additionally, improving consumer information about the charges of the various providers can foster competition between them leading to lower costs. The World Bank has calculated the average cost of sending remittance via the cheapest service providers and has found that migrants often pay more than this. This suggests that dissemination of information about the lowest cost providers could bring down the cost.
Given these various means of bringing down the prices of remittances, lowering these to 3% may well be within reach. However, certain obstacles remain. U.S. regulations against moneylaundering have prevented many Western banks from dealing with African remittance providers, occasionally these providers fly banknotes on airplanes to their agents in Africa, a method severely interrupted by the coronavirus pandemic as planes were grounded in many locations (The Economist, 2020). In the interest of human capital accumulation, hence economic development, in developing economies, the U.S. might consider relaxing its international funds transfer regulations, per the argument of this paper.

Conclusion
In order evaluate gains in human capital accumulation from reduction in remittance prices, this study builds a general equilibrium model in which the choices to invest in human capital and migrate are endogenous. To decide whether or not to migrate, individuals weigh the gains from the chance to earn a higher lifetime income abroad and send remittances home against their idiosyncratic preferences for consumption at home. Their migration decision then affects their borrowing and savings in the asset market, and therefore, the domestic interest rate.
Since human capital is better rewarded abroad, those who wish to migrate borrow more to accumulate more human capital in preparation (brain gain). This increased borrowing puts upward pressure on the domestic interest rate in the origin country. On the other hand, more human capital accumulation by potential migrants leads to higher earnings at home and abroad and greater remittances home, all of which has the effect of lowering interest rates. The model in this study is calibrated for a group of eight African economies which has provision for student loans, and the effect upon human capital accumulation of decreasing remittance prices to 3% is numerically derived. It is found that interest rates decrease, the desire to migrate decreases, and human capital growth rate increases.
Policymakers have already directed efforts to reduce remittance costs in the past. This study's policy recommendation is that they continue to do so by for example, increasing access to mobile banking.

Appendix A. Migration decision and migration rate
An individual considering his option to migrate in time t will stay at home if his preference for living at home exceeds the thresholdθ t defined by the condition V o 1 ij,t = V d ij,t . Using this condition, the expression forθ t is derive as, Therefore, anyone with home preference (θ i ) aboveθ t , will have V o 1 ij,t > V d ij,t , and will decide to stay home.
The probability that an individual's θ i exceeds the aforementioned threshold in a generation will be equivalent to the portion of that generation staying home, which is denoted by 1 − m t , where m t is the generation's desired migration rate. Given that each θ i follows a Pareto distribution as in (1), then The fraction of the population who would like to stay for a given generation (1−m t ) is increasing in the interest rate differential on savings between the origin country and abroad R t R d . It is decreasing in the excess return on human capital abroad, x.   (1 − m) and an equilibrium exists. The equilibrium would be unique since f(m) is monotonic given that g(m) is monotonic. Therefore, a sufficient and necessary condition for an equilibrium characterized by 0 < m < 1 to exist is for f (0) = α ε 1+δ δ λ 1−λ εδ 1+δ < 1. A simple sketch of the proof can be seen in Figs. 5 and 6.


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Establishing and assessing adaptive parking prices in a city: Algorithms, software and examples

We propose ParkSage, a set of spatially-explicit algorithms for establishing parking prices that guarantee a predetermined occupancy rate over a city, and for evaluating the achieved reduction in parking search time. We apply ParkSage for establishing overnight parking prices that guarantee 85% occupation in the Israeli city of Bat Yam. Pricing by street links ensures high parking availability and close to zero cruising everywhere in the city, but is inconvenient for drivers. Establishing prices by the large and heterogeneous city quarters results in local mismatch between demand and supply, the emergence of areas with fully occupied on-street parking and a long search time for the drivers whose destinations are in these areas. We demonstrate that pricing by the medium sized Transportation Analysis Zones, which is easy enough for drivers to comprehend and abide by, is sufficient for eliminating cruising. The software for establishing and assessing performance parking prices is based on the standard municipal GIS layers of streets and parking lots and is available for free download from https://www.researchgame.net/profile/Nir_Fulman

Introduction
Every city in the world has its own parking policy. In some cities, on-street parking is provided for free, whereas in most cities in the western world parking costs money. Typically, a large area centered around the CBD is priced uniformly throughout the day. However, demand for parking is determined by the attractiveness of single destination buildings and thus varies substantially in space and time. Underpriced parking in neighborhoods where demand exceeds supply entails long searches for parking, which increase traffic congestion. The associated external costs in terms of time, fuel and environmental degradation can be very high. Overpriced parking, on the other hand, deters drivers from visiting an area and may harm local economic activities (Arnott & Inci, 2006;Pierce & Shoup, 2013).
Studies suggest that keeping about 1 in 7 parking places vacant in each block, or 85% occupancy, would allow drivers to find parking quickly and at the same time be sufficient for maintaining economic activities in the area (Shoup, 2006, Levy et al., 2013. This view has become popular and in recent years, a number of cities around the world have initiated programs for enforcing a predefined level of parking occupation using prices as a control parameter (LADOT, 2019;SDOT, 2019;SFMTA, 2014;AT, 2019;CPA, 2017;City of Boston, 2018;DDOT, 2019;Parking Authority of Baltimore City, 2019;Berkeley Transportation Division, 2019). Parking prices in these programs vary by time of day and location, which, depending on the program, may be by street link or larger urban area. In each pricing unit, the prices are updated periodically until the occupancy rate converges to the desired range, typically between 60 -80%.
The straightforward way to ensure a uniform occupancy rate is to vary parking prices by small units and indeed, in most of the existing programs, performance prices are varied by street segments or block faces. The prominent example is San Francisco's SFpark pilot program (SFMTA, 2014), where smart sensors were used to measure parking occupancy and establish prices for each individual block. Pricing by block faces or street links is not free of shortcomings. Due to stochastic fluctuations in demand and the small number of spots, minimal parking availability in a unit is still not guaranteed at all times. This undermines the ability of drivers to plan where to park prior to arrival -drivers can decide to park at an affordably priced block face close to their destination, only to find on arrival that it is fully occupied. These drivers then face a complicated decision-making process of searching for parking in a heterogeneously priced parking space whilst under time pressure, which can lead to frustration and illegal behavior.
Prices established over larger areas are easier for drivers to comprehend and abide by. Despite the lack of research on the topic, the cities of Seattle (SDOT, 2019), Calgary (CPA, 2019) and Auckland (AT, 2019) followed this view and established performance parking price by zones that consist of several or more street segments with similar demand profiles. The risk associated with pricing by large units is the high chance for mismatch between local demand and supply, and the emergence of islands of under-and over-occupied parking within the unit.

ParkSage structure
ParkSage consists of three algorithms:  An algorithm for approximating the parking occupancy pattern given heterogeneous demand and supply patterns (Levy and Benenson, 2015; )  An algorithm for establishing a pattern of parking prices that guarantees a predefined occupation rate (Fulman and Benenson, 2018 b )  An algorithm for approximating parking search time based on parking occupancy  2.1 The algorithm for approximating parking occupancy Urban parking demand is mostly determined by building capacity and use for residential, commercial, office and other purposes. In addition, parking is necessary near non-building attractions such as parks, open-air markets and historical sites. The algorithm for approximating parking occupancy constructs a Maximally Dense Parking Pattern (MDPP) based on urban parking demand at resolution of a single building or attraction, referred to here as a "destination." Destination attributes, such as the floor area of a residential or office building, determine its attractiveness and consequently the number of drivers who arrive to the area and search for parking nearby.
Parking supply in the city is not less heterogeneous than demand, and varies by street links, surface lots and aboveground/underground garages that vary in their capacity, limitations and price. Typically, high-resolution data on demand and supply are available as part of standard municipal spatial databases, and can be converted into spatially explicit demand and supply maps. A building's use, footprint and height can serve for estimating the number of residents and employees and, accounting for car ownership in the area, is sufficient for estimating the demand for parking by hour of the day and day of the week. GIS layers of parking lots typically contain information on their capacity, which can be otherwise estimated based on their area. In case information about on-street parking is unavailable, curb parking spots can be constructed programmatically, 5 meters apart from each other on both sides of a two-way street link, and on the right side of a one-way link, with some shift from the junction. Parking regulations and restrictions, if available, can also be accounted for.
The MDPP algorithm generates a parking occupancy pattern based on spatially explicit highresolution demand and supply information. As reflected in its name, the MDPP supplies a parking pattern that is "maximally dense," whereas real drivers possibly exploit parking space less effectively. Informally, the MDPP algorithm manages parking in a city of autonomous vehicles that are governed by one control station possessing complete information on the destinations of all arriving vehicles, and all occupied and vacant parking places. When a vehicle arrives to the area, the system reserves the vacant parking spot that is most desirable to the driver in terms of price and walking time from parking place to destination. Vehicles are fully controlled by the system and, thus, a reserved spot can be occupied by the assigned vehicle only.
Formally, let A c,p (d) be the attractiveness of a parking spot p at a distance d from the driver's c destination, and F p be the parking price of p. We assume that A c,p (d) satisfies two conditions:  A c,p (d) decreases with the increase in distance d between p and the destination as 1/d α ,  Driver c is sensitive to the parking price F p only when F p is above a threshold "negligible" level f negligible > 0, and A c,p (d) depends on F p only when F p > f negligible . Formally, we express this as Based on parking studies in the field (Levy and Benenson, 2015), we assume that an acceptable walking distance d between parking spot and destination is limited to 500m aerial distance, d max < 500m.
We also assume that drivers whose parking options all have low attractiveness, may give up on parking. Let A c,best be the attractiveness of the best available parking spot for the driver c. The probability g(A c,best ) to give up on parking is calculated as: where γ is a parameter. In all examples below γ = 0.1.
Drivers who fail to find parking within distance d max from destination or forgo parking due to low attractiveness of the available spots, are assumed to park far away and use additional means of transportation to reach their destinations.

An algorithm for establishing demand-responsive parking prices
The Nearest Pocket for Prices Algorithm (NPPA) applies the MDPP in a recursive way for approximating parking prices. Let the target occupation level in the area be O threshold . The idea is to increase the price F u of each parking unit u (e.g. block face or neighborhood), where the average occupancy exceeds the threshold O threshold , from F u to F u (1 + ), and to redistribute the drivers who arrive to park in the area, by applying the MDPP with the new price pattern.
Increasing the parking price in a unit reduces the attractiveness of parking places in it, and drivers who are sensitive to the new price respond by preferring to park elsewhere, typically farther away from their destination, where parking is cheaper. The algorithm quits when the price of parking at each unit u reaches a level that guarantees an average occupancy rate O u ≤ O threshold . The NPPA's flow is as follows   Below we apply the NPPA algorithm with the  = 0.05. The typical number of iterations necessary for convergence to a steady price pattern is 50.

An algorithm for estimating cruising time based on the occupation pattern
Parking search time increases with the increase in the occupation rate in the driver's search area. However, the average occupancy rate over a spatial unit does not directly translate to parking availability and cruising time, due to the spatial heterogeneity of demand and supply within the unit. Larger spatial units contain many street links and buildings and, given the average occupation rate O u over the entire unit is below the preferred O threshold , the number of links within it that are occupied at a level that exceeds O threshold , increases with the size of the unit. Since parking is impossible on fully occupied links, their occurrence within the destination's search neighborhood determines cruising time.
The algorithm for predicting parking search time distribution for the driver whose destination is n is based on the distribution of link occupancy within the destination's search neighborhood. It builds on two components: The MDPP-provided occupation rate p(l) for every link l  N(n) (Fulman and Benenson, 2018 a ) and experimentally discovered probability w(l, n) of including each link l  N(n) in a cruising path, depending on the distance between l and n (Fulman and Benenson, 2019). Given the patterns of w(l, n) and p(l) within N(n) , and assuming that a driver traverses one link per time unit, we are able to estimate probability q nopark to traverse a fully occupied link per time unit (Fulman and Benenson, 2018 a ): The probability Q(τ, n) to cruise longer than τ time units, for the driver whose destination is n, is: The flow chart of the algorithm for estimating cruising time is as follows (Fulman and Benenson, 2018 a ): The set of ParkSage algorithms is sufficient for establishing and evaluating the efficiency of various pricing schemes in a city. In what follows, we apply ParkSage for establishing overnight parking prices in the Israeli city of Bat Yam, comparing three methods of partitioning the city into priced units.

Establishing parking prices in the city of Bat Yam
We apply ParkSage for establishing overnight parking prices in Bat Yam, using data from 2010 (Martens et al., 2010). The total Bat Yam population in 2010 was ca. 130,000, car ownership 35,000, and the number of residential buildings 3,300 with 51,000 apartments. Residential buildings in Bat Yam provide their tenants a total of 17,500 dedicated parking places that we exclude from the demand and supply data.

Bat Yam demand and supply
Parking supply in Bat Yam data is given in two GIS layers -a layer of streets and a layer of offstreet parking facilities. Based on the layer of streets, 27,000 spots for curb parking were constructed automatically, 5 meters apart on both sides of two-way street links, and on the right side of one-way links, with a necessary gap from the junction. In addition, 1,500 spots are available for the city's residents in its parking lots, where Bat Yam residents can park in the evening free of charge. The average overnight demand/supply ratio is thus very low (35,000 -17,500) / (27,000 + 1,500) ≈ 0.61 car/parking spot. However, the distributions of demand and supply in Bat Yam are both highly heterogeneous, and the overnight demand in the center of Bat Yam significantly exceeds the supply there (Figure 4).

Arrivals and departures
In the experiments below, we consider evening (16:00 to 23:00) on-street parking by residents and their guests. We assume that all parking spots are vacant at 16:00 and residents arrive to the area between 16:00 and 18:00 and park until the end of the evening. Guests arrive and depart throughout the whole evening, and their parking time is uniformly distributed on the [ min ,  max ] interval, where  min = 1 hour and  max = 2 hours.
Drivers that aim at a destination n i are generated by a Poisson process with a per-hour average λ i based on the n i 's hourly demand d i by residents and guests. We assume that for each n i , residents comprise a constant fraction e < 1 of the total demand d i . During that time period, we set the hourly number of arrivals to each destination n i as  i = e*d i /2. We adjust the hourly arrival rate of guests, to guarantee that the average number of guests arriving to n i be equal to (1e)*d i . Accounting for the guests' average parking time ( min +  max )/2, their per hour arrival rate to a destination n i is λ i = 2*(1 -e)*d i /( min +  max ), and we assume that it remains constant throughout the evening.
At each 30 seconds model tick, the list of arriving and departing drivers is created, randomly reordered, and each driver acts in its turn, facing the parking pattern created by the actions of its predecessors. Average occupation rate in the city converges to equilibrium towards 20:00 and then fluctuates, very slightly, over time.

Cruising for parking in Bat Yam with the existing free of charge parking
Let us estimate evening cruising time in Bat Yam, assuming that the ratio between residents and guests seeking parking is 85:15, and that parking on-street and in public lots is free to residents of Bat Yam whereas outsiders are required to pay a yearly fee of 300 ILS for a parking permit. We consider the permit price as the negligible threshold of locals (see formula (2)) and establish f negligible per night as f negligible = 1 ILS, roughly equivalent to $0.3. In what follows, we refer to this price as the base price.
The patterns of supply and residential demand for overnight parking at a resolution of buildings, street links and lots, and the demand to supply ratio aggregated over Transport Analysis Zones (TAZ), are presented in Figure 4. Drivers aim to park as close as possible to their destinations. Where night parking is free, Bat Yam drivers clog up links within the residential blocks where demand exceeds supply and spill over to adjacent areas, worsening parking conditions there. As a result, in Bat Yam's center, parking in the evening becomes unavailable over large continuous areas. The resulting cruising time is long: The estimated average cruising time for most destinations in and around the city center is, on average, 2.5 minutes; and cruising for longer than 5 minutes becomes very common ( Figure 5). a b c Figure 5. The percentage of time that street segments are fully occupied (a); the average parking search times (b); and the probability to cruise for over 5 minutes (c) in Bat Yam.

Establishing parking prices that guarantee close-to-zero cruising time
We establish parking prices for the traditional threshold occupation O threshold = 85% (1 of 7 spots is vacant) in each street segment, commonly accepted as guaranteeing close-to-zero cruising (Shoup, 2006). In these model experiments we assume that the parking fee is charged once for the entire evening and parking durations are not influenced by the prices. We also assume that residents and guests are equally sensitive to prices, the distance-payment tradeoff coefficient in formula (1) is α = 0.5, the coefficient γ in formula (2) is γ = 0.1 and the minimal attractiveness threshold A threshold = 0.1.
Despite a global demand to supply ratio far below 1, demand in the center of Bat Yam is essentially higher than supply (see Figure 4 above). As a result, to maintain an average occupancy rate of 85%, prices in the busiest blocks should be 25-30 ILS, whereas at the periphery of the city the prices can remain at the base level ( Figure 6). Similar to the outcomes of the SFpark experiment (SFMTA, 2014), one can frequently observe a twofold difference between parking prices for two adjacent street links.
The established pattern of parking prices ensures that almost none of the street links is fully occupied for longer than an hour and clusters of two or more connected links that are fully occupied for longer than half an hour almost never emerge. With parking available on every link almost all of the time, cruising time is reduced nearly to zero. The average parking search time over all destinations is shorter than 60 seconds and less than 1% of drivers are expected to cruise for longer than 150 seconds. Figure 6. Equilibrium parking prices, in ILS, for 85% occupation threshold established by street links and parking lots as pricing units.

Pricing parking by large spatial units
We establish parking prices for coarse partitions that are convenient for drivers, starting with Bat Yam's 6 largest administrative units, referred to as quarters (Figure 7). Each quarter contains between 2700 and 5800 parking places, and their size varies between 0.7-1.4 square km. The application of ParkSage with O threshold = 85% results in upper-than-base prices in one quarter only -the core of the Bat Yam city, which is about 1 km 2 and contains over 3000 parking places. The parking price in this core quarter is 8.5 ILS (~$2.5). a b Figure 7. Six quarters of Bat Yam (a); and equilibrium parking prices, in ILS, for 85% occupation threshold estimated by city quarters as pricing units (b).
Priced parking in the central quarter drastically reduces cruising for almost all destinations there and for some external destinations close to its border. The difference between cruising time for the case of no pricing versus priced parking in the central quarter is close to 3 minutes on average and 75% of the drivers whose destinations are in this quarter cruise for less than 90 seconds.
Yet pricing the central quarter does not guarantee parking availability everywhere in it. Priced parking there pushes some drivers to park in adjacent quarters, while the occupation rate of some links within the core remains far above 85% (Figure 8). Similarly, in the quarters where prices aren't established, clusters of fully occupied links emerge around the locations where demand exceeds supply and, in addition, areas bordering on the central quarter ( Figure 9). The problem is thus partially displaced instead of being resolved. In Bat Yam, large and heterogeneous spatial units of 1 km 2 are inappropriate for pricing because the average occupancy rate does not adequately represent parking availability in the city. Let us investigate the consequences of pricing by the intermediately coarse partition of Bat Yam into 42 Transport Analysis Zones (TAZ). The average TAZ is 0.16 square km with an average parking capacity of 600 spots, making a TAZ substantially larger than a street link and smaller than a quarter. Figure 10 presents TAZ-based parking prices that guarantee 85% occupation rate. The prices are above the base level in 24 TAZ, all located in and around the center of the city, and prices range up to 17.5 ILS ($5).
Despite being essentially smaller than quarters, pricing by TAZ does not guarantee 85% occupation for every single link. In many links parking in the evening is still unavailable, and their average occupancy rate over the evening remains close to 100%. However, with TAZ-based pricing, overly-occupied links rarely form large spatial clusters and parking is always available one or two links away. As a result, the average search time does not exceed 2.5 minutes for any destination and the average cruising time for the 500 destinations around which visitors cruise the longest, is only 75 seconds ( Figure 11). a b c d Figure 11: Characteristics of Bat Yam TAZ-based pricing: Average occupancy rate by links (a); average parking search time (b); average difference in search times compared to non-priced parking (c); probability to cruise longer than 2.5 minutes (d).

The choice of optimal partition for demand-responsive pricing
In most cities around the globe, parking prices are controlled by law. Prices were generally established a long time ago and remain steady to avoid protest from car owners and politically costly public debate. As a result, a substantial fraction of drivers is exempt from paying, the others pay less than the situation requires, and all drivers suffer from long and exhausting searches for parking. Performance pricing of parking aims to balance parking demand and supply. The shift to market-defined prices is of dire importance, and establishing the minimal prices that would improve parking conditions demands solid guidelines since one design flaw may sabotage an otherwise smart policy. The use of ParkSage, a spatially explicit toolset for establishing demand-responsive parking prices, can assist in ensuring the reliability of performance pricing.
Practical experiments for establishing performance-defined pricing schemes have had only limited success (SFMTA, 2014;Pierce and Shoup, 2013;Chatman and Manville, 2014;Millard-Ball et al., 2014). It is hypothesized that the constraints placed upon these parking programs, including lax enforcement of illegal parking, free parking permits, abuse of disabled parking placards and price ceilings are to blame for this. Our work shows that unconstrained performance pricing should be able to reduce parking search substantially, if not end it completely.
The basic rule of thumb in performance pricing is to keep 15% of parking places vacant in each link or block, guaranteeing one of seven spots open on each block face. However, due to stochastic variations of demand, parking can never be guaranteed on every block all of the time. Searching for the ideal place when parking prices vary by the block is challenging, and may lead to frustration, prolonged cruising, and encourage illegal behavior. Pricing by units larger than street links is simpler to conduct and easier to convey to drivers. We show that pricing by medium sized units, such as Transport Analysis Zones, is sufficient for preserving an occupation level that prevents cruising for parking.
Using ParkSage for examining the effects of pricing by unit size in Bat Yam, we have demonstrated that pricing by the very large city quarters does not prevent substantial cruising by visitors. It also brought to light a potential caveat of confining performance pricing to neighborhoods notorious for long cruising, as done in the pilot areas in San Francisco's SFpark program (SFMTA, 2014) and Washington D.C.'s Chinatown and Penn Quarter (DDOT, 2019). In these pilot areas, drivers whose destinations are within a pricing unit yet close to its borders often search for cheaper parking beyond it and these spillovers worsen parking conditions in adjacent areas, introducing cruising for parking where it did not previously exist.
ParkSage can be applied not only for establishing optimal pricing partitions, but in several additional ways, one of which is assessment of parking constraints and permissions. To date, all performance pricing programs that we are aware of, including the prominent SFpark project, are constrained in one or more ways. Illegal parking, parking permits, disabled parking placards and other limitations can be modeled in ParkSage by taking into consideration drivers who are completely or partially insensitive to parking prices. Using ParkSage in this way, one can reveal where and when it is plausible to expect good results despite the constraints and permissions, and where they may render pricing ineffective.
Time-varying pricing, including time-varying pricing units, is another aspect of performance pricing that can be explored using ParkSage. Inclusion of time into the pricing policy demands an additional compromise: If the price remains uniform over a period of time that includes inherent variations in demand, the average occupancy rate over that period does not represent parking availability. On the other hand, very short time bands would be equally as frustrating for drivers as prices that vary by street links. We did not investigate time-varying prices in this paper, but it should be noted that given sufficient information about the daily variation of demand, ParkSage can be used for choosing the appropriate time bands, especially for establishing daily intervals of charged and free parking.