The Macroeconomic Effects of MicroSaving on the Unbanked

Transcription

1 The Macroeconomic Effects of MicroSaving on the Unbanked Very Preliminary Version Fan Liu March 1, 2016 Abstract This paper focuses on U.S. microsaving programs, especially programs directed at individuals who save to invest in small businesses. Aggregate data on Individual Development Accounts (IDAs) is used to theoretically and quantitatively explore the effects of microsaving programs on occupational choice, firm size, and income inequality. By using a general equilibrium model with heterogeneous agents, this paper incorporates the minimum balance requirements imposed by the banking sector and introduces a microsaving program for the low asset individuals. Due to high regulation costs, microsaving programs partner with traditional banks to serve unbanked individuals. The paper shows that microsaving programs have positive effects on economic development and the unbanked. Government subsidies to microsaving programs and deregulation of the bank sector are also evaluated. fan-liu-1@uiowa.edu 1

2 1 Introduction Surprisingly, in developed countries like U.S. many people remain unbanked or under banked. Unbanked individuals do not have bank accounts. Under banked individuals have bank accounts, but also use alternative financial services (AFS) outside of the banking system. According to the Federal Deposit Insurance Corporation (FDIC) Household Survey, 9.6 million households (7.7%) in the U.S. were unbanked in 2013 and 24.8 million households (20%) were under banked. In addition, 25 million people have no credit score, which makes them invisible to the mainstream U.S. financial system. 1 Microsaving is a branch of microfinance that is growing fast. This financial service is directed at lower-income or unbanked individuals to enable them to save small amounts of money so that they may protect themselves against negative shocks, pay for higher education, or operate small businesses. Unbanked people tends to come from lower-income households (39.1% of households with family income below $30, 000), non-asian minorities (20.5% of African American and 17.9% of Hispanic), women (about 30% of women), recent immigrants (22.7% of foreign-born noncitizens), lower educated, and working-age disabled households. Among the reasons people report for being unbanked, the most common are, Do not have enough money or Account fees are high or unpredictable (Figure 1). This is mainly due to banks requirements for minimum balances, which are described in detail in section 2. For example, banks such as Citibank require savers to keep at least a $1500 balance in Basic Banking Package to avoid maintenance fees. Figure 1: 2013 FDIC National Survey of Unbanked and Underbanked Households World Bank research shows that more than half of the total adult population in the world has no access to regular financial intermediaries services, especially people who are poor, have low income, or live in rural areas (CGAP). Microfinance, directed at small businesses 1 See: 2

3 that lack access to traditional banking and related services, were introduced to the poor as an economic experiment in the late 1970s and exploded into an industry in the 2000s. Currently, this is a $70 billion industry with 200 million clients (CGAP), affecting 533 million people including both borrowers and their households (Buera, Kaboski and Shin (2015)). Microsaving programs in the U.S. were introduced in late 1990s along with Individual Development Accounts (IDAs). Microsaving programs partner with banks and offer IDAs and other small savings accounts. These programs serve low-income people, minorities, recent immigrants, women, disabled people and those who lack access to traditional deposit services for other reasons. For example, a microsaving provider, EARN, has a $21, 000 average annual household income at enrollment for all EARN accounts; 71% of clients are women and 90% of savers self-identify as a person of color. An IDA is a special savings account for low-income people. Individuals who save in an IDA receive another dollar (match) or more for every dollar saved. The matching money is from donations and subsidies. Both savings and match money can only be used to purchase a first house, pay for post-secondary education, or invest in small businesses (Community Affairs Department 2005). IDAs were created by U.S. federal legislation, specifically the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 (National Association of Social Workers 1996), and IDAs are now available in more than 40 U.S. states (Center for Social Development 2010). Banks partner with local non-profit organizations, including organizations that provide microsavings, to offer IDAs and financial training courses to clients. In the last decade, more than 500 IDA programs were launched, with more than 85,000 accounts opened. This resulted in 9,400 new homeowners, 7,200 educational purchases and 6,400 small business start-ups and expansions (CFED). Since microsaving and IDAs overlap in many respects (serving similar groups of people, having partnership between banks and non-profit organizations, and offering small savings accounts), I combine them together in the model. There are two main strategies to study the impact of microfinance on the macroeconomy (Morduch 2012). Empirically, Demirguc-Kunt and Levine (2009) use cross-country data to show a positive correlation between financial expansion and the reduction of inequality, but they did not focus on microfinance. Hermes (2014) shows that higher levels of microfinance participation decrease income inequality using a macro level dataset for 70 developing countries. On the other hand, Ahlin and Jiang (2008) extend Banerjee and Newman (1993) s occupational choice model to include group lending. They conclude that microfinance helps people escape poverty by increasing income, which allows them to become self-employed. The model has no unbanked people and the saving decision and interest rates are exogenous. Buera, Kaboski and Shin (2015) theoretically and quantitatively focus on the effects of microfinance on the macroeconomy, where microfinance is introduced as fixed small-sized loans with the same interest rate as traditional banks loans. All individuals can save in traditional banks, saving decisions are endogenous, and individual lending standards are applied. Microsaving programs in developing countries are described and evaluated in detail as evidence for demand for savings by the poor (see Armendariz and Morduch (2010) on SafeSave in Bangladesh, Bank Rakyat Indonesia and BAAC in Tahiland; Collins, Morduch, Rutherford and Ruthven (2009) on RoSCAs in South Asia and ASCAs in SouthAfrica; Dowla and Barua (2006) on Grameen GPS in Bangladesh). The Financial Diaries (Collins, 2005; Rutherford, 2002; and Ruthven et al, 2002) are strong-empirical examples of such demand studies (Devaney 2006). However, most of the studies focus on microcredit instead of mi- 3

4 crosavings. Limited field experiments in developing countries show evidence that individuals are more likely to increase consumption, income, investment in health and reduce vulnerability to illness and other negative shocks if they have access to savings accounts or informal savings (Dupas and Robinson (2009, 2011), Ashraf et al (2010)). In terms of research on microsavings in the U.S., Rademacher et. al (2010) study the impact of IDAs. They construct a dataset based on administrative records of 831 individuals in 17 states who purchased homes using IDAs between 1999 and IDA homebuyers obtained significantly preferable mortgage loan terms and were two to three times less likely to face foreclosure compared to other low-income homebuyers who purchased homes in the same communities and over the same time period. Overall, the evidence on microsavings is small and further evaluation is needed. This paper presents a model of the unbanked and microsaving programs in the U.S. The paper is related most directly to Buera, Kaboski and Shin (2015) and Liu and Villamil (2015). Liu and Villamil (2015) study the impact of U.S. microfinance programs on economic development, where the representative microfinance institution (MFI) lends to individuals but does not offer a saving program. The loan funding base is mainly donations, government subsidies, and loan and principal interest repayment. Agents have access to traditional banks to deposit their wealth. From the loan supply side, traditional banks require minimum loan sizes and agents can borrow a flexible amount from MFIs. In this paper access to microsaving/ida programs permit individuals to save small amounts with low or no fees and also borrow for small businesses with collateral. Banks operate both traditional lending and microlending. Because of the high cost of managing small savings accounts, traditional banks do not accept savings of less than a certain amount. Therefore, a large portion of poor people lack access to saving services and are unbanked. In order to provide saving services to the poor, banks partner with microsaving programs, and receive government subsidies and donations to cover the match money and extra transaction costs on small deposit accounts. 2 This paper focuses on the following questions: What are the effects of microsaving on developed countries occupational choices, firm sizes and income inequality? Does microsaving help the unbanked population? What are the effects of government deregulation designed to lower intermediation costs? Alternatively, what if governments increase subsidies to help savings programs? The results show that microsaving programs in the U.S. have a positive effect on the percentage of entrepreneurs, firm size, output, wages, and the credit to output ratio. The main reason is that with government and donors support, microsaving programs allow low bequest individuals to save, and provide matching money to micro-savers. These two aspects give micro-savers opportunities to become entrepreneurs by having the ability to borrow with collateral. As a consequence, more entrepreneurs and less workers induce a higher wage. Higher wage payments reduce the capital stock and profits by high-productivity firms, and this effect dominates the increase in the number of micro-enterprises, which have smaller profits compared with large firms. Therefore, the entrepreneurs income Gini index 2 If the saving service is provided by microfinance banks that transformed from traditional banks, we consider the fixed cost as a downscaling cost, which includes opening special branches, advanced risk management, market research, changing the organizational structure and financial methodology, increasing human resources, and adjusting the policy environment (Bounouala and Rihane (2014)). Non-profit organizations that partner with banks can avoid this cost. 4

5 decreases with microsaving programs. On the other hand, microsaving impacts on low income individuals borrowing activities dominates the effect on high-productivity firms borrowing activities, which leads to a higher credit to output ratio. Microsaving programs also help the unbanked population. By the nature of the program, individuals with low initial wealth are able to save in the program and receive matching money to either consume or invest in their businesses. Low wealth people have the opportunity to become entrepreneurs by borrowing with collateral via microsavings. The wage increases as a results of having more entrepreneurs and less workers. As a consequence, microsaving programs help unbanked workers directly through saving products and match money, and also help them indirectly through this wage effect. In addition, policy targets are sensitive to policy changes regarding government subsidies. Government subsidies provide banks with resources to cover the extra costs of managing small size deposits and matching money. However, a higher government subsidy also leads to a higher wage tax, which transfers a small amount of capital from workers to micro-savers or firm-owners who become entrepreneurs due to the microsaving programs. The positive effect of microsaving on the wage due to the smaller supply of workers promotes a higher after-tax wage. Overall, an increase in the government subsidy to microsaving programs will increase output, the percentage of entrepreneurs, and the aggregate payoff for all individuals. In the remainder, section 2 lists stylized facts. Sections 3 presents the model, with the bank s problem and an entrepreneur s problem, and also introduces microsaving programs and specifies an individual s occupational choice decision. Section 4 calibrates the model, using data from IDA and a microsaving program called EARN, to match U.S. data and discusses model fit. Section 5 analyzes the effects of microsaving and shows the quantitative experiments on policy targets. Section 6 concludes. 2 Stylized Facts about Microsavings The goal is to build a model that is consistent with several stylized facts from microsaving programs in the U.S. This section summarizes facts about U.S. microsaving/ida programs. Fact 1: Banks require a minimum balance Most banks charge maintenance fees or restrict individuals from opening an account unless they keep a minimum balance in their deposit account. For instance, Citibank requires $1,500 or more in the prior calendar month of combined average balances in either Basic Checking or linked Savings Plus accounts. Bank of America requires an average daily balance of $1,500 or more. US Bank requires either a $300 daily balance or $1, 000 average monthly balance to avoid fees. Banks require minimum amounts because banks have to pay overhead costs to keep branches running and labor to monitor accounts and provide customer services. Banks also must pay taxes and comply with costly regulations, which is explained in detail in Fact 3, in order to operate saving programs. In addition to regulation costs, banks pay a higher transaction cost per dollar for small deposits than for large deposits. Therefore, a high minimum balance requirement is common in the U.S. For low-income households, finding a financial intermediary to save a small amount can be difficult. Fact 2: People remain unbanked largely due to an inability to maintain the 5

6 minimum balance or high account fees. Johnston and Morduch (2008) define the unbanked as people who do not have a bank account. More commonly, unbanked refers to those who do not have deposit accounts of any type (Sherraden (2005 Chapter 8 Caskey)). The FDIC (2011, 2012) indicates that unbanked households are those that lack any kind of deposit account at an insured depository institution. The majority of unbanked are those who have low income and lack the minimum balance to open checking and saving accounts (Hamilton 2007). 3 Cull, Demirguc-Kunt and Morduch (2013 Chapter 2) cite a joint McKinsey-NYU study, where about half of the world s adult population lacked a bank account in 2005 based on Honohan s (2008) 2003 household level survey data. The Global Findex data show that the share of adults who are banked in high-income countries is more than twice the level in developing countries (Demiguc-Kunt and Klapper (2013)). According to the Federal Deposit Insurance Corporation (FDIC) Household Survey, 9.6 million households (7.7%) in the U.S. were unbanked in Rhine and Greene (2006) find that immigrants with less education, poverty-level income, or a larger family are more likely to be unbanked in the U.S., but immigrants with greater net worth or higher income are not. Mexican and other Latin American immigrants have the highest rates of being unbanked compared to other immigrants (a large portion of microfinance clients in the U.S. are immigrants). It is important for the poor to have access to loans in order to reduce credit market imperfections, but access to savings is also crucial for reducing savings imperfections. Robinson (2001, 21) claims that deposit services are more valuable than credit services for poorer households. Lack of access to formal financial services causes people to rely on their own assets. They need to use informal savings to pay for education or invest in small businesses. The limitation on having access to saving services can contribute to income inequality and slower economic growth (Demirguc-Kunt and Klapper (2013)). Fact 3: Microsaving programs partner with banks to avoid high regulation costs. Globally, some microfinance institutions (MFIs) provide microsavings accounts that are designed for lower income individuals who have an incentive to store funds for future use. Minimum balance requirements are often waived, or are very low. However, it is very expensive to have such savings programs due to regulations. Christen, Lyman and Rosenberg (2003) show that formal financial institutions all face regulations such as rules of governing their operations, minimum capital requirements, consumer protection, fraud prevention, establishing credit information services, secured transactions, interest rate limits, foreign ownership limitations, taxes and accounting issues. In order to serve clients with saving programs, MFIs need to hire expensive experts to handle the legal and reporting requirements. According to Ledgerwood and White (2006), transformation from a credit-focused MFI to a regulated financial intermediary with savings programs tends to cost between $700, 000 and $1.5 million. The costs differ depending on the country and most of the transformations need donor or government support. 4 3 Minimum balances in saving accounts are a constraint for the unbanked. They are similar to the minimum loan size that traditional banks require. The reason that traditional banks have minimum size requirements is to avoid high operation and monitoring costs on small accounts. 4 Also by regulation, Grameen Bank is the only MFI in Bangladesh that can use clients savings freely. 6

7 Due to the high cost of regulations, U.S. microsaving programs partner with banks instead of microfinance institutions to develop their own programs. Microsaving programs are sponsors who recruit participants and provide financial education, and banks have access to all of the micro deposits. Therefore, microsaving is treated as a product of banks in this model. Fact 4: Programs offer a match rate, often 1:1. dollar amount are not matched. Deposits over a certain Individual Development Accounts (IDA) are designed to distribute matching money for each dollar that clients save. Many IDA programs offer a 1:1 match rate, where for each dollar deposited in an IDA the account holder receives an additional dollar as match money to help achieve one of three goals: purchase a first house, pay for post-secondary education, or invest in a small businesses. Matching rates vary depending on the program (CFED 2009). For example, a non-profit organization called EARN was founded in California in 2001 by a group of individuals and organizations including a State Senator, government officers, and a foundation. They partnered with banks to provide microsaving products to help low income and unbanked households. Once clients reach the saving goals of $2000 in a certain period, they receive $4000 in match money (the matching rate is 1:2). Their clients, on average, have a household income below $21, 000, 71% are women and 91% identify themselves as a person of color. EARN s total deposit are $6.8 million, and they launched 775 microenterprises. Individuals can deposit as much as they want, but deposits will be matched only up to a certain amount, for example $500 in many programs, and $2000 in EARN. In this model, the minimum balance captures this feature. A one-to-one matching rate is used in the benchmark model and the policy experiment examines the effects of different matching rates on the economy. Fact 5: The extra transaction costs for small deposits and matching money is funded by governments and donors. The transaction cost per dollar transacted is higher for collecting small deposits than large deposits. Richardson (2003) cites evidence that many banks claim that it is impossible to profit on deposit accounts smaller than $500. Therefore, banks will have an incentive to manage small deposit accounts if the extra transaction costs for small saving accounts can be covered by government subsidies and donations. Currently, the largest provider of matching funds for IDA programs is the federal government s Assets for Independence (AFI) program. AFI applicants are required to raise non-federal funds in an amount equal to or greater than their AFI project grant. Grantees may use 15% of the grant for operating costs. In addition, IDA programs receive funds from many states governments and programs also borrow from investors. Any individual, organization or business can donate match dollars to IDAs and donors can get tax deductions for contributions to IDAs (CFED). Fact 6: Low-income individuals benefit from microsaving programs There is no clear regulation on whether non-government organizations (NGOs) can or cannot hold deposits, which causes many NGOs to hold back and concentrate on small-business lending (Collins, Morduch, Rutherford and Ruthven (2009)). 7

8 Unbanked people receive no interest from saving and lack access to business loans because they lack collateral. Microsavings offer lower income individuals a channel to keep assets safely, earn interest, receive match money on saving, and access to business loans if needed. Overall, the facts show that U.S. microsaving programs partner with banks and receive government subsidies and donations to fund the extra cost of small saving accounts and provide match money. We now construct a model that is consistent with these facts. 3 Model Microsaving programs in the U.S. help low income people save to cover negative shocks and bring unbanked individuals into the financial mainstream. Typically, life-cycle models are used to study the effect of savings on consumption smoothing. However, my occupational choice model focuses on bringing unbanked people into the financial system. I use the model to study whether microsaving programs have an effect on occupational choice, wages and firm size, when banks have minimum deposit balance requirements. Consider an economy with a continuum of measure one individuals. Each individual lives for one period and reproduces another so population is constant. Time is discrete and infinite. A single good can be used for consumption or production, or left to the next generation as a bequest. 3.1 Preferences, endowments and technology Individuals care about their own consumption and a bequest to the next generation. The utility function for a representative individual in period t is U = (c t ) γ (z t+1 ) 1 γ, γ (0, 1) (1) where c t and z t+1 denote consumptions and bequests. Each individual is endowed with initial wealth b t, which is a bequest from the previous generation, and managerial talent x which is drawn from a continuous cumulative probability distribution function Γ(x) where x [0, 1]. Individuals choose their occupation, either a worker or an entrepreneur. Entrepreneurs can only operate one project which has a technology that uses capital k and labor n to produce a single consumption good y, which is represented by y = xk α n β, α, β > 0, and α + β < 1 (2) Capital fully depreciates between periods. Entrepreneurs employ workers and capital. 3.2 The capital market and microsaving programs Banks have a requirement on minimum deposit balance b and lend to individuals up to a limit 0 < l < l( ) as long as they have collateral. Individuals can do the following to invest initial wealth: b > b 8

9 Competitively rent capital to a bank and earn interest rate i D, or Use their own capital to fund a business. They may borrow additional capital from banks at interest rate i L. b < b with microsaving (Consistent with Fact 6) Competitively rent capital to a bank and earn interest rate i D and matching money s = ηb, where η is the matching rate, or Use their own capital to fund a business. They may borrow additional capital from banks at interest rate i L. b < b without microsaving - unbanked Keep capital at home and remain unbanked or Use their own capital to fund a business. They are not eligible for loans due to a lack of collateral. Bank: The representative bank issues business loans to borrowers who have collateral in the bank, and sets a minimum balance requirement b for savings accounts. Banks receive deposits D = D ms D 2, where D 1 represents the total deposits from savers with an initial bequest that is above the minimum balance. D 2 denotes the total deposits from individuals who do not meet the minimum balance bequest and can only save through microsaving programs. Consistent with Fact 5, the bank accepts donations S D and government subsidies S G in order to offer a microsaving program 5 and disburse match money s for micro savers. S is the aggregate match money for all micro savers with bequests below the minimum requirement, which captures Fact 3 where deposits above b will not be matched. Therefore, the representative bank s problem is the following: 6 5 When microsaving programs partner with banks, they avoid the fixed cost to develop a savings program. The extra transaction costs ec for small saving accounts are covered by donations and subsidies. Overhead and intermediation costs on loans are equivalent to the costs on deposits since D = L in equilibrium. Therefore, the problem is considered from the perspective of managing savings accounts. 6 No Microsavings: max (1 + i L )L (1 + i D )D 1 (ovc + τ)d 1 i L s.t. D = D 1 = bυ t (db) b (3) With Microsavings: max (1 + i L )L (1 + i D )D (ovc + τ)d 1 (ovc + τ + ec)d 2 S + (S D + S G ) i L b s.t. D = D 1 + D 2 = bυ t (db) + bυ t (db) b 0 (4) S D + S G = S + ecd 2 S = ηd2 9

10 max i L (1 + i L )L (1 + i D )D (ovc + τ)d 1 1 ms (ovc + τ + ec)d 2 1 ms S + 1 ms (S D + S G ) b s.t. L = D = D ms D 2 = bυ t (db) + 1 ms bυ t (db) 1 ms [S D + S G = S + ecd 2 ] b 1 ms [S = ηd2] 0 (5) The zero profit condition implies that i L = i D + τ + ovc (6) τ reflects transaction costs such as financial sector taxes (e.g. taxes on financial transactions, bank profits or inflation), or bank regulation (e.g. reserve and liquidity requirements). ovc is bank overhead costs to operate the institution such as labor and utility costs. 3.3 Optimal behavior and Competitive Equilibrium Entrepreneurs Given the frictions on both saving and lending markets, the entrepreneur s problem is similar to the problem in Antunes, Cavalcanti and Villamil (2008). Individuals who decide to become entrepreneurs choose the level of capital and the number of employees to maximize profit subject to a technological constraint and a credit market incentive constraint. Given k and w, an entrepreneur solves the problem: π(k, x; w) = max xk α n β wn (7) n Let a be the amount of self-financed capital (or, equivalently, the part of the loan that is fully collateralized by the agent s personal assets) and l be the amount borrowed from a bank (or, equivalently, the amount of the loan that is not collateralized). Unconstrained problem: An entrepreneur who does not need credit (b > a and l = 0) solves 7 max k 0 π(k, x; w) (1 + i D)k (8) Deposit interest rate i D is the opportunity cost of investing one s own funds in the firm. Constrained problem: The probelm of a higher-income entrepreneur is different from the problem of a lower-income individual. b b: If the entrepreneur has an initial bequest above the minimum balance, the individual has free access to the banking system. To borrow from the bank, the loan contract must be self-enforcing because the entrepreneur cannot commit to repay, so 7 Use the optimal π(n) to solve for k. φπ(a + l, x; w) (1 + i D + ovc + τ)l 10

11 The incentive constraint guarantees ex ante repayment and can be written as: l(b, x; w, r) φ 1 + i D + ovc + τ π(k(b, x; w, i D), x; w) = l(b, x; w, i D ) (9) l is the maximum amount that an entrepreneur can borrow from a bank, which is increasing in the entrepreneur s bequest and managerial ability, b and x. If an entrepreneur with a high enough initial bequest borrows from a bank, then the problem is to maximize net income: V (b, x; w, i D ) = max π(a + l, x; w) (1 + i D)a (1 + i L )l a 0, l 0 st. 0 l a b φ π(k(b, x; w, i D ), x; w) 1 + i L feasibility (10) In equilibrium, 1 + i L = 1 + i D + ovc + τ. Optimal policy functions a(b, x; w, i D ) and l(b, x; w, i D ) define the size of each firm: k(b, x; w, i D ) = a(b, x; w, i D ) + l(b, x; w, i D ). b < b: Banks do not offer loan packages to borrowers who do not have collateral/savings in the bank. Therefore, microsaving programs play an important role for lowerincome borrowers. When microsaving programs exist, lower-income entrepreneurs can selffinance their initial bequest (or equivalently, the part of the loan that is fully collateralized by the agent s personal assets), receive match money s (which agents can also invest into their business), and borrow the remaining capital from a bank. However, without microsaving programs, constrained borrowers have to give up being an entrepreneur and become workers due to lack of capital to reach their optimal capital level. In other words, an individual becomes an entrepreneur only if b k when there are no microsaving programs. This occurs because banks will not lend to these people if they have no collateral in the bank. 8 An entrepreneur without a high enough initial bequest faces the following problem: V h (b, x; w, i D, 1 ms s) = st. max π(a + 1 ms(l + s), x; w) (1 + 1 ms i D )a a 0, l 0 0 l a b 1 ms s 1 ms (1 + i L )l φ π(k(b, x; w, i D, 1 ms s), x; w) 1 + i L feasibility (11) Optimal policy functions a(b, x; w, i D ) and l j (b, x; w, i D, 1 ms s) define the size of each firm: k(b, x; w, i D, 1 ms s) = a(b, x; w, i D ) + l j (b, x; w, i D, 1 ms s), where j = MS or NoMS. 8 For b < b, no microsaving gives With microsaving, the problem becomes: V = max xa α n β wn max π(a + l + s, x; w) (1 + i D )b s (1 + i L )l For b b, the solution of entrepreneure s problem is the same as ACV(2008) 11

12 3.3.2 Occupational choice The occupational choice for each individual is derived from maximizing the agent s life time income. Define Ω = [0, ] [x, x]. For any w, i D > 0, an individual described by the pair (b, x) will choose to be an entrepreneur 9 if (b, x) E(w, i D ), where { {(b, x) Ω : V (b, x; w, i D ) (1 τ w )w} if b b E(w, i D ) = (13) {(b, x) Ω : V (b, x; w, i D, 1 ms s) (1 τ w )w} if b < b The complement of E(w, i D ) in Ω is E c (w, i D ). If (b, x) E c (w, i D ), then individuals are workers. Lemma 3.1 Define b e (x; w, i D ) as the curve in Ω where V (b, x; w, i D ) = (1 τ w )w. Then there exists an x (w, i D ) such that be(x;w,i D) < 0 for x x (w, i x D ), and be(x;w,i D) = for x x = x (w, i D ) with microsavings. In addition: 1. If b < b e (x; w, i D ), then (b, x) E c (w, i D ) x (the agent is a worker) 2. If b b e (x; w, i D ), then (b, x) E(w, i D ) x (the agent is an enterpreneur) Proof The proof follows the standard proof of Lemma 2 in Antunes et al. (2008). Figure 2 indicates that agents are workers when their managerial ability is low, i.e. x < x (w, i D ), or initial bequest is low, i.e. b < b. For x x (w, i D ) and b > b, agents may become entrepreneurs, depending on whether or not they are credit constrained. If bequests are very low, unless agents optimal capital is below their initial bequest, agents are workers although their managerial ability is higher than x (w, i D ) due to no collateral to borrow from financial institutions. Microsaving programs provide better options to individuals who have very low bequest but high managerial ability to become entrepreneurs, see figure 3. Same as Antunes, Cavalcanti and Villamil (2008), the negatively sloped b curve indicates that some high ability agents may be credit constrained. 3.4 Consumers First of all, individual s life income is defined as: { max{(1 τ w )w, V (b t, x t ; w t, i td )} + (1 + i D )b t Y t = max{(1 τ w )w, V (b t, x t ; w t, i td, 1 ms s t )} + (1 + 1 ms i td )b t + 1 ms s t if b b if b < b (14) 9 In previous literatures, occupational choice is determined by the entrepreneur and worker value functions. This is because their lifetime wealth has the same extra term (1+i D )b since everyone can save. In this paper, occupational choice is determined by their lifetime wealth. Both methods lead to the same solution. { {(b, x) Ω : V (b, x; w, i D ) + (1 + i D )b (1 τ w )w w + (1 + i D )b} E(w, i D ) = {(b, x) Ω : V (b, x; w, i D, 1 ms s) + (1 + 1 ms i D )b + 1 ms s (1 τ w )w + (1 + 1 ms i D )b + 1 ms s} (12) if b b if b < b 12

13 Figure 2: Occupational Choice in Economy without Microsavings Figure 3: Occupational Choice in Economy with Microsavings 13

14 Given life time wealth, the individual solves the following problem: max U = (c t ) γ (z t+1 ) 1 γ, γ (0, 1) c t,z t+1 s.t. c t + z t+1 = Y t (15) The optimal consumption and bequest are thus c t = c(y t ) and z t+1 = b(y t ) policy functions. The functional form of a consumer s preferences implies that individuals leave a proportion 1 γ of their lifetime wealth as a bequest. Bequests are non-negative since every individual can be a worker. 3.5 Competitive Equilibrium Let Γ t be the bequest distribution at period t, which is endogenously determined across periods. The initial bequest distribution Γ 0 and government spending g are exogenously given. In a competitive equilibrium, an individual optimally solves their problem as described before, and all markets clear. 1. Free entry into the bank sector (zero profits in equilibrium): i L i D = ovc + τ 2. The market clearing conditions for labor and capital are: n(x; w t, i td )Υ t (db)γ(dx) = Υ t (db)γ(dx) (16) z E(w t,i td ) z E c (w t,i td ) z E(w t,i td ) k(b, x; w t, i td )Υ t (db)γ(dx) = bυ t (db)γ(dx) b + (1 1 ms ) a(b, x; w t, i td )Υ t (db)γ(dx) z E(w t,i td ) b + 1 ms bυ t (db)γ(dx) + 1 ms sυ t (db)γ(dx) 0 b z E(w t,i td ) (17) 3. The government budget constraint given wage, tax τ w, intermediary tax or regulation cost τ, government subsidies to microsaving programs S G and government spending g: τ w wn(x; w t, i td )Υ t (db)γ(dx) + τd = g + S G (18) 4. Law of motion: Υ t+1 = P t (b, A)Υ t (db) (19) The law of motion for the distribution of bequests is provided to fully characterize the competitive equilibrium since the bequest is the only connection between periods. Define 14

15 P t (b t, A) = P r{z t+1 A b t } as a non-stationary transition probability function, which assigns a probability for a bequest in t + 1 for the descendant of an agent that has bequest b t. The quantitative exercises evaluate policy experiments where the real wage, interest rate and income distribution do not change significantly over time Calibration In order to study the quantitative effect of microsaving on entrepreneurship, wage, output, and other variables, we must assign values for the model parameters. We calibrate to match key statistics in the United States, where financial markets are well developed and intermediation costs in the banking sector are small. Later, policy experiments are conducted to study how government subsidy policy on microsaving programs and regulation costs affect the economy. The baseline model is calibrated so that the equilibrium matches some key statistics of the U.S. economy. Each person lives for one period in the model 11. Assume that the cumulative distribution of managerial ability is given by Γ(x) = x 1 ɛ and x [0, 1]. When ɛ is one, entrepreneurial talent is uniformly distributed in the population. When ɛ exceeds one, the talent distribution is concentrated among low talent agents. The following parameters must be determined: two for technology(α, β), one for utility (γ), and ten institutional and policy parameters (b, ovc, ec, η, φ, τ w, τ, S G, g, S D ). Following Gollin (2002), we set α and β so that in the entrepreneurial sector 55% of income is paid to labor, 35% is paid to capital, and 10% are profits. As in Antunes et. al (2014), intermediation costs are the sum of intermediary taxes/regulation costs and overhead costs. The tax/regulation cost as a percentage of total bank assets is 0.5% in the U.S. 12 and the overhead cost is measured as the total expenses of the financial institutions over its total assets. According to Beck and Demirguc-Kunt (2009), the magnitude is 2% in high income countries, which corresponds to banks overhead cost in this paper 13. The payroll tax τ w = 0.33 is set to match the average tax rate on labor income in the U.S.(Jones, Manuelli, and Rossi (1993)). Microsaving programs partner with banks. Program sponsors screen clients and offer financial training courses, for banks that provide small savings accounts and distribute match money. Many programs have a one-to-one matching rate and some programs have a one-totwo matching rate, such as EARN. This benchmark model uses a 1:1 matching rate (η = 1), and a policy experiment can be used to look at the effect of various match rate on individuals and the economy. Consistent with Fact 5, the largest provider of matching funds for IDA programs is the federal government s Assets for Independence (AFI) program. AFI applicants are required to raise non-federal funds in an amount equal to or greater than their AFI project grant. 10 Antunes et al. (2008) show that there exists a unique stationary equilirum with w > 0, r 1 < and for any initial bequest distribution Υ 0, it converges to an invariant bequest distribution Υ. 11 One period is chosen to be 35 years, which is the typical working years from 25 to 60 years old. 12 Previous literatures use this cost as the regulation costs on loans. Since deposits equal credit in the equilibrium, the data is used in this paper to measure the tax and regulation cost on deposits. 13 A model period corresponds to 35 years, thus the target overhead cost is ovc = ( ) 35 1 = 1, and the tax is τ = ( ) 35 1 =

16 Therefore, S D S G. Grantees may use 15% of the grant for operating costs 14. According to FDIC (2007), almost 60 percent of IDA programs that receive matching funds through the AFI, and the AFI has provided an average of $25 million in annual appropriations to fund IDA matches. I use this number to adjust government subsidies for the 35 year model period and normalize by $10 million to get S G = In addition, IDA programs receive funds from many state governments and they also borrow from investors. Any individual, organization or business can donate match dollars to IDAs and donors can get a tax deduction for contributions to IDAs (CFED). In the benchmark model, there is no microsaving programs. Given the government subsidy S G = 0, the intermediation cost on deposit τ = , and the wage tax τ w, the government spending g is simulated to be to balance the government budget using equation (18). Later on, during the policy experiment of introducing microsaving programs, the wage tax τ w is adjusted by using S G = 87.5, g = and τ = from the benchmark model. Banks also differ in the minimum balance they require (Fact 1). For example, Citibank requires $1,500 or more in the prior calendar month of combined average balances in either a Basic Checking or linked Savings Plus account. Bank of America and Chase both ask for an average daily balance of $1,500 or more. U.S. Bank has a policy of a $300 minimum daily ledger balance 17 or a $1, 000 average monthly collected balance 18. The benchmark economy takes $1, 500 as the minimum balance requirements. In addition, the transaction cost per dollar transacted is higher for collecting small deposits than large deposits. Since banks have an incentive to manage small deposit accounts if the extra transaction costs for small saving accounts can be covered by government subsidies and donations, I assume that S G + S D = S + ecd 2 holds, and the match money S = ηd 2. The match rate η is 1 in the benchmark economy, which means that microsaving programs match $1 for every dollar that clients saved in the program. The simulated total amount of small saving D 2 is the sum of saving among individuals whose bequest is below b. S G is given by the AFI data. The relationship between donations and government subsidies is calculated using the EARN 2012 financial statement data, where S D = 1.7S G 19. Since the data on donations is better than the data on the extra cost of managing a small savings account, the extra cost then is endogenously calculated using equation S G + S D = S + ecd 2, ec = = 6.7(ovc + τ) 20. Policy experiments will be conducted later to better explain 14 Three fourths of the government subsidy covering the match money is not used in the benchmark model, but this is varied in the policy experiments. 15 S G = [$25, 000, 000/10, 000, 000] 35 = % in a 35 year-period. 17 The daily ledger balance is the balance at the end of each business day, equal to the beginning balance for that day plus the current business day credits, and minus the current business day debits. (U.S. Bank Standard Saving Account) 18 The average monthly collected balance is calculated by adding the principal in the account for each calendar day in the statement period and dividing that figure by the total number of calendar days in the statement period. (U.S. Bank Standard Saving Account) 19 $833,351 $486,647 = Donations can also be endogenously calculated using given government subsidies, the match rate, small savings and the extra cost of managing a small savings account. The method of calculating the extra cost is to collect data on minimum balances and the maintenance fees from commercial banks. For example, clients need to keep $1000 on average monthly in their account in order to avoid a $5 fee. $25 is the minimum deposit to keep the account open. Therefore, I calculate the monthly extra managing cost on small loans as 16

17 the role of donations in microsavings. Moreover, according to the FDIC (2013) report, there are 7.7% of households that are unbanked, which is approximately 9.6 million households and 16.7 million adults. The working age population in the U.S. is calculated using the FRED 2013 data, and it is million, which leads to a 8.26% unbanked individuals in the economy. Three parameters remain to be determined: the fraction of total income left to the next generation, 1 γ, the investor protection or the strength of financial contract enforcement, φ, and the curvature of the entrepreneurial ability distribution, ɛ. These three parameters are chosen such that in the baseline model the percentage of the unbanked population is 8.26%; the percent of entrepreneurs over the total employed population in the U.S. is 12% according to definitions on entrepreneurship 21 and the Gini index of entrepreneurial earning is 67.5% from Tang (2014). Table 1 shows the value of each parameter. Table 1: Calibration, parameter values, baseline economy (No microsavings) Parameters Value Comment/Observations α 0.55 Capital share, Gollin (2002) β 0.35 Labor share, Gollin (2002) τ Tax/regulation cost, Demirguc-Kunt and Levine (2000) τ w 0.33 Payroll tax rate, Jones, Manuelli, and Rossi (1993) ovc 0.02 Bank overhead cost, Beck and Demirguc-Kunt(2009) η 1 Matching rate (cfed 2009) b $1,500 Minimum balance γ Calibrated to match the U.S. percentage of unbanked population (FDIC and FRED 2013) φ Calibrated to match the percent of entrepreneurs over the total population (about 12%) according to various definitions on entrepreneurship ɛ 4.2 Calibrated to match the entrepreneurial income Gini index of 67.5% based on Tang (2014) The calibrated value of γ = matches the percentage of the unbanked population in the U.S., which indicates that agents in general leave about 4.3% of lifetime wealth to the next generation. The ratio of bequests to labor earnings in the steady state of our model 1000 $5 25 b db = and the yearly cost is ec = The OECD reports entrepreneurs as a percentage of the total employed population at 7% during time period. Assah Meh (2002) reports 12%. Cagetti and De Nardi (2006) find that business owners or self-employed individuals as a percentage of total population is 16.7% and self-employed business owner as a percentage of total population is 7.6%. In Quadrini (1999), there are two definitions of entrepreneurs: one is defined as families that own a business or have a financial interest in some business enterprise. The entrepreneurs are identified as families in which the head is self-employed in their main job. The percentage of entrepreneurship is 14.9% under the first definition, and 17.9% in the latter one. Moreover, the Global Entrepreneurship Monitor (GEM) 2014 reports that the number is 14% among the U.S. working age population. Based on the various definitions and measurements with the range from 7% to 17.9%, I choose the percentage of entrepreneurs to be 12% as the target. 17

18 is (1 γ)/(1 (1 γ)(1 + r)) = 0.045, which falls into the interval estimated by Gokhale and Kotlikoff (2000), where bequests account for 4-8% of labor compensation. The value of φ in the baseline economy is This value is lower than the value of 0.26 found in Antunes, Cavalcanti and Villamil (2008) and is consistent with the intution that lower bequest individuals cannot borrow without microsavings and borrows with collateral require less enforcement. Recall that φ is equivalent to an additive utility punishment that reflects the strength of contract enforcement. Table 2: Basic statistics, U.S. and baseline economy U.S. economy Baseline model Yearly real interest rate(%) Tax as a % of total bank assets(%) % of entrepreneurs(%) Entrepreneurs income Gini (%) Capital to output ratio Private credit to output ratio % of unbanked The model fits the U.S. economy fairly well. Besides the statistics that we calibrated, the capital to output ratio and the private credit to output ratio, which are not calibrated, also match well. Maddison (1995) shows that the U.S. capital to output ratio is about 2.55 and it is 2.73 in the model. The World Bank Development Indicators data shows that average total private credit as a share of income in the U.S. was 2.03 from 1993 to 2013, and it is 1.34 in the model since the benchmark economy restricts low wealth people from borrowing. The model does not match the income Gini of 40-44% in the data; the model predicts about 30%. This is a standard problem that occurs because workers in the model receive the same equilibrium wage, which should underestimate the real world income Gini. Furthermore, the unbanked based on FDIC 2013 report and FRED working age population data is 8.26% and it is 4.6% in the benchmark model. It is reasonable to underestimate the unbanked population because, in practice, there are individuals who choose to be unbanked due to other reasons such as having bank history problems, or concerns about privacy or tax evasion which are not modeled in the benchmark economy. 5 Quantitative Analysis Quantitative experiments are designed to explore how the equilibrium properties of the model change when microsaving programs are introduced in the economy and if there are changes in the subsidy for microsavings and regulation costs on banks. 5.1 Impact of microsavings The initial stationary equilibrium in the without microsavings model is calibrated. Individuals choose their occupation based on their initial ability and bequest. Now the experiments are conducted to assess the effects of microsavings by introducing the program into the benchmark economy. 18

19 Table 3: Baseline economy v.s. economy with microsavings Baseline model Model with Microsavings % of entrepreneurs (%) Wage Payroll tax rate (Government subsidy) (S G = 0) (S G = 87.5) After tax wage Entrepreneurs income Gini (%) Capital to output ratio Private credit to output ratio Compared to an economy without microsavings, introducing the program leads to a Higher percentage of entrepreneurs: one goal of the microsaving program is to help poorer individuals save and borrow and nascent micro-entrepreneurs to start micro businesses. Higher wage and after tax wage: By having more entrepreneurs, the demand for workers increases while the supply of workers decreases. The lack of workers in the economy increases the wage. However, the wage tax also rises in order to fund microsaving programs via government subsidies. Overall, the wage effect is bigger than the wage tax effect, which results in a higher after tax wage. Lower entrepreneur income Gini coefficient: among all entrepreneurs, there are more lower income micro entrepreneurs than without microsaving. However, the income for highly-productive firms drops due to the wage effect. The effects of microsaving on the income of highly-productive firms dominates the effects on micro firms, which leads to a small reduction in the entrepreneur Gini index. Higher credit to output ratio: Microsavings provide more working capital due to external donations and government directed credit; introducing saving products to the high ability and low resource individuals so that credit becomes available to them. However, a higher wage causes high-productivity firms to have less profits and borrow less to invest. The positive impact of microsavings on low bequest individuals borrowing activities dominates the negative impact of the wage on high-productivity firms borrowing activities. The net effect on credit is positive. Table 3 shows that the aggregate differences among variables are small with and without microsavings, which means that microsaving programs have a small influence on the U.S. macroeconomy in terms of occupational choice, income inequality and the credit to output ratio. In this model, microsavers are those individuals with initial bequests that are below the bank s minimum balance and their economic activities are at a very small scale. However, once they become microenterprises, which are businesses that have less than 5 employees, due to help from the microsaving programs, they contribute to the economy by enhancing income, creating and sustaining jobs, which are saved for future research projects. 19