Analysing the Households Portfolios of Liabilities: Formal and. Informal Debt *

Transcription

1 Analysing the Households Portfolios of Liabilities: Formal and Informal Debt * Carlos Aller Summary This paper studies the determinants of the different portfolios of households liabilities. Two kind of debts are considered depending on the lender: formal (banks and financial institutions) and informal (friends and relatives).a simple two-period model where the household decides to borrow from one (or both) of these sources is developed. Under both altruism and better monitoring technology of informal lenders, the theory predicts that high credit demand and low credit quality households borrow from their network of relatives and friends, since financing from formal credit market is rationed, scarce or expensive. These predictions are tested using a survey of Italian households in which the type of debt held by families is observed. Results suggest that those households with both kinds of debts have less income and wealth than those that are financed only by banks, but more than those that only borrow from informal sources. These latter households have, moreover, differentiated characteristics in age, employment and marital status that suggest that these funds are intergenerational loans given to households in great necessity. Keywords: Informal debt; formal debt; credit rationing. * I gratefully acknowledge the advice from Mario Padula and the valuable comments of Lorenzo Ductor. Departamento de Fundamentos del Análisis Económico, Universidad de Alicante, Campus de San Vicente, Alicante, Spain. caller@ua.es, caller1980@gmail.com.

2 1. INTRODUCTION Why some households borrow from friends and relatives as well as from banks and financial institutions? Why some others borrow only from the former (informal lenders) or only from the latter (formal lenders)? Which households do not have any kind of debt? This article investigates these questions both from a theoretical and empirical perspective, using a survey of Italian households (Survey of Households Income and Wealth, SHIW) in which they are asked about their portfolio of assets and liabilities. Informal arrangements present very different characteristics than formal. While loans with banks or financial institutions are always formally settled, it is very common that those loans with friends and relatives are not under a contract. Informal loans have clear advantages in the sense that lenders have a better monitoring technology with which make repayment more feasible and they are subject to less informational asymmetries than formal. 1 What is more, informal lending might be based on mutual trust and altruism and exchange of favours appear as important reasons for its realization. These facts imply a reduction in red-lining and interest rates on informal loans with respect to formal. 1 The concept of loan monitoring we have in mind is similar to the one described by Stiglitz (1990) when he states one of the advantages of local moneylenders over the formal institutions: "...they can monitor the borrowers more effectively, making sure that the funds are used productively and thus lowering the default rate". In fact, in a number of developing economies, informal lenders are commonly hired by microfinance institutions to monitor the borrowers. Some examples are Grameen Bank in Bangladesh, Banco Sol in Bolivia and Bank Rakyat in Indonesia. 1

3 However, the limited nature of informal funds and their stigma effects make that a low percentage of the population hold this kind of debts. It is well known that there exist a great variety of debt instruments in the credit market (for a nice explanation, see Bertola and Hochguertel, 2007). As well, the conditions under which informal loans are settled may vary noticeably. However, the differences between formal and informal loans stated above are important enough to group them in these two different categories. Several papers have dealt with private transfers or informal loans between households. While Barro (1974) and Becker (1974) proposed models of family transfers based on altruism, Cox (1987) tests alternative hypotheses about motivation (altruism and exchange) for inter vivos transfers that do not include loans. He uses Italian data and concludes in favour of the exchange motivation, a similar result as the one obtained by Cox and Rank (1992). Cox and Jappelli (1990) study the connection between credit rationing and private intergenerational transfers: they find a clear positive correlation among them, although those transfers rarely help to overcome liquidity constrained problems of households. Their definition of transfers includes gifts, financial support from relatives or friends and inheritances. Guiso and Jappelli (1991) show that these transfers help to ease households' borrowing constraints but a substantial number of liquidity constrained households remain after transfers have been made. 2 Although these papers propose similar questions to the ones posed here, it is important to note that their definition of transfers is different to the concept of loans we 2 For a detailed discussion of microeconomic models of private transfers and their motives, see Laferrère and Wolff (2006). 2

4 are working with. Guiso et al. (2004), however, use informal loans in strict sense to study the effect of social capital on households' reliance on informal lending. 3 They also use SHIW data and conclude that this type of credit is more widespread in low trust areas of Italy. Grant and Padula (2006), using the same data and definition of informal loans, investigate whether the availability of family and friends' financial help makes borrower default more, or less, likely. As stated above, this paper's definition of informal arrangements excludes gifts, bequests, inheritances and all other transfers that are not pure loans. I focus on explaining the 'debt category' of the households. By 'debt category' or 'debt status' I mean whether the household holds no debt, formal debt, informal or both kinds of debts. Are informal debt just transfers from parents to kids (or vice versa)? What distinguishes those households that hold just formal debt from those that, besides, have loans with their network of relatives and friends? Is it because they have been red-lined in the credit market? Or rather they lower the burden and price of the debt with the bank by borrowing a fraction from the informal sector? What are the characteristics of the households that just borrow from friends and relatives? Are they wealthier or poorer than those pertaining to the other 'debt categories'? I try to address these questions both from a theoretical and empirical perspective. The theoretical model identifies those households that are somehow credit constrained in the formal sector and those who are not. This permits me to test whether credit rationing influences the probability of borrowing from friends and relatives. Based on the altruism and better monitoring technology of the informal sector, the model suggests that credit rationing is relevant in explaining the different 'debt categories' of the 3 More specifically, they define social capital as the degree of trust that Italians have in their compatriots. 3

5 households. As well, the prices of the loans in the credit market and the household's propensity to borrow are positively correlated with the probability of borrowing from the network of friends and relatives. These theoretical predictions are tested using a survey of Italian households: the Survey of Household Income and Wealth. This survey is going on since late 70 s and I only consider recent waves of it. Households are classified into different categories on the basis of the kind of portfolio of liabilities held. I estimate the determinants of being in one of these categories to conclude that high-credit-quality households avoid borrowing from their network of friends and relatives, something that I identify with stigma considerations. The group of households that borrow both from formal and informal sources has, on the average, a higher level of debt but a lower level of assets than the ones that only hold formal funds. Estimation results confirm that those households with both kinds of debts have less income and wealth than those that are financed only by banks and financial institutions. However, they are much more similar in characteristics than with respect to those households that just borrow from friends or relatives. Statistics show that, on average, these households have significant less income and wealth and hold less debt than those that borrow from formal and informal sources. This survey, as well, permits to test whether being credit rationed in the formal credit market is relevant in explaining the debt status of the households. The remainder of the paper is organised as follows. In Section 2 I develop a simple two-period model of the households formal and informal credit market. Section 3 describes the estimation strategy in order to test the implications of the theoretical model. In Section 4 results are presented while Section 5 concludes. 2. THE MODEL 4

6 I consider a credit market with households and banks. Households live for two periods and can either be borrowers or lenders. The former wants to smooth consumption over time so borrow from financial institutions and from other households that do not need to borrow. Utility of the borrowers, hence, depends on consumption: Ui = log( ci 1) + βilog( c i 2) I assume an iso-elastic utility function that it is time-additive. Borrowers earn no income at the first period. At the second, they earn a high wage with probability p w h and a low wage w l with probability (1-p). The credit is provided in the first period and repayment is made in the second. For simplicity, following Lawrance (1995), I assume that banks can only claim in excess of w l and that there is no additional cost of bankruptcy. This reflects the usual banks inability to collect from default-debtors. However, based on a better monitoring technology and mutual trust, even in the bad state of nature the informal lender will manage to recover her debt from the borrower. For this reason, they are, in principle, indifferent between lending to a high or a low credit risk friend or relative. Altruism is, after all, the motivation for this kind of loans. Hence, we assume that they charge an interest rate equal to the fix interest rate on deposits r : these lenders do not want to make profits from a friend or a relative. The maximization problem that the borrower faces is the following 4 max EU = log( F + I) + βp log( w FR I r) + β(1 p)log( w I r) FIR,, f i h f l, 4 As well, this perfect enforcement of debts may dissuade some households to ask for informal loans. 5

7 where F and I are the amount of formal and informal debt respectively. r is the fixed interest rate on deposits. Under the assumption of free entry, the participation constraint of the bank is as follows: Fr = pfr f (1) so the interest rate charged on loans is R f r =. Rate sorting, thus, is allowed to occur in p this simplistic model. The following condition is the borrower's incentive compatibility constraint (ICC): log( w FR Ir) log( w ( w w) Ir) (2) h f h h l This condition requires that the utility from repayment is higher than that from strategic default. For simplicity, this model assumes that the income in the bad state of w l nature is as well the lower bound below which the bank can not extract earnings to the default borrower in order to recover the debt. This assumption makes the derivation of the model easier but incorporates as well the idea that friends and relatives have a better monitoring technology than banks. This better monitoring gives them the chance of recovering the debt even in the bad state of nature: they can extract rents below. Hence, in the good state of nature, a borrower will have incentives to default whenever wh FRf w l < (3) w l This is why the ICC takes the above form. The model needs to be completed with the participation constraint of the informal sector. These kind of loans are released whenever the potential informal lenders' utility U L gains from lending to a friend or relative who is in need of funds. As it is explained in the appendix, altruism arises as a determinant part of the realisation of these loans. 6

8 For this section purposes, it is enough to state the participation constraint of informal borrowers as follows: I U L >0 (4) Equation (4) suggests that a household needs to gain utility from lending for the informal loan to be released. The justification of this is explained in the appendix and it is based on the fact that whenever a household lends to a friend or a relative, its optimal intertemporal allocation of funds is no longer achieved, so the decision to lend depends on the improvement on their utility because of the improvement on the borrower s (altruism). In solving the maximization problem, I assume that the agent has unlimited funds from friends and relatives to borrow. As well, the financial institution does not observe whether or not the household holds informal debt and, in principle, does not ration credit. Taking derivatives with respect to F and I, I obtain the optimal level of both kinds of debts. The amount of informal debt desired by the borrower is * wl(1 + β p) whβ p I = 0 (1 + β ) r Observe that we need to impose the condition that this loan is bigger or equal than wl zero. The inequality holds whenever p <, that is, the lower is the probability ( w w) β h of being at the good state of nature (p) and the higher is the credit demand (inverse of β). The resultant level of formal debt is: * p( wh wl) F = r l 7

9 Proposition 1 When the probability of involuntary default and the credit demand are big enough, households will choose to borrow from both formal and informal sources. Observe that formal debt increases with p (the probability of being at the good state of nature). The opposite happens with the informal. This latter decreases with β, which can be viewed as the tendency to borrowing: the smaller is β, the higher the amount applied for. In this model, from the borrowers point of view, informal debt has the advantage of being cheap and the disadvantage of being perfectly enforceable by lenders. Both characteristics lead households whose credit quality is high enough (pay lower prices for formal debt) and whose credit demand is low enough not to rely on informal debt and viceversa. We have to take into consideration the limited nature of informal debt. That is, * the level of informal debt may not be the optimal I. Hence, the maximum value of the informal debt will be given by the participation constraint of this sector. But, assume that this maximum value is I. Hence, the optimal value of informal debt for the * borrower will be I max { I, I} =. following: Whenever I = I the optimal value of formal debt for the borrower will be the F = wh Ir(1 + β ) 1 r( β + ) p wl When p, the household will choose not to borrow from friends or ( w w) β h l ** relatives ( I = 0 ). The optimal level of formal debt is, hence, achieved by maximizing the following utility function: 8

10 max EUi = log( F) + β p log( wh FR f ) + β (1 p)log( w l ) FIR,, f The resulting level of formal debt is: F ** w h = 1 r( β + ) p Now we test the effect of being credit rationed in the formal sector on the 'debt status' of the household. For this purpose, I assume that, in principle, households go to the formal sector in order to borrow. Once the household is granted by a certain amount of formal debt at some cost, I will check whether it is profitable or not for them to ask for loans to relatives and friends. When the ICC is not binding the household will not be rationed, yielding the following level of debt and interest rate: R n f r = (5) p F n wh = 1 r( β + ) p (6) By substituting these two expressions into the ICC, we obtain the condition under which the borrower's promise to repay is credible: wl p ( w w) β h l (7) Whenever this condition is not satisfied, the household will be credit rationed. The optimal level of formal debt will be found by substituting the interest rate into the ICC 5 : R r f r = (8) p p r ( w ) h w l F = (9) r 5 This is similar to Fabbri and Padula (2003). 9

11 I check whether holding additional debt from friends and relatives is profitable for both kinds of households, rationed and non rationed, in formal credit market: Proposition 2 A household that is not credit rationed in the formal credit market does not have incentives to borrow from friends and relatives. Proof See appendix. Proposition 3 A household that is credit rationed in the formal credit market has incentives to borrow from friends and relatives. Proof See appendix. If we assume that, below some level of p, say p, banks and institutions fully ration credit, we will find the explanation for the existence of households that just borrow from friends and relatives. This is what is called the 'informal status'. Proposition 4 A household that is fully credit rationed in the formal credit market will have the strongest incentives to borrow from friends and relatives. Proof See appendix. The intuition behind propositions 2-4 is clear: informal markets are usually used as an alternative to formal for a number of reasons, like the limited nature of informal funds (that may not fulfil all the financing necessities) or the stigma considerations of having a debt with a friend or a relative. All these results help to explain what we observe in the data: credit rationing is fundamental in explaining the informal debt, something in line with the results obtained 10

12 by Cox and Jappelli (1990). Credit rationing is significantly more relevant in order to explain the 'informal status' than 'formal-informal' one. However, credit rationing appears to be not the only relevant variable in explaining the different status of the households, what suggest that some households do not take the informal debt as an alternative to the formal. Rather, they consider both kind of debts as a portfolio of liabilities and they want to set the optimal allocation. 3 DATA I use data from four waves of the Survey of Household Income and Wealth (SHIW): 2002, 2004, 2006 and The SHIW is conducted by the Bank of Italy and provides detailed information about, among other things, income, consumption, debt and a set of characteristics of a representative sample of Italian households. To avoid the influence of outliers, I excluded those households whose income is below the 1st percentile or above the 99th percentile of the income sampling distribution. I finally use a total of 31,081 observations, whose main characteristics are summarized in Table 1. An explanation of the variables is provided in the appendix. We observe that just 7,282 (23.43%) hold any kind of debt. SHIW is a rich dataset regarding households debt held with banks or financial institutions. In particular, I can observe the kind of loans (house, car, valuables and other durables purchases, non-durable consumption), and the outstanding balance of each loan at the end of the year. As well, it provides the amount of debt owed to friends and relatives in that moment. I group the loans provided by banks or financial institutions in one category, Formal Debt, while those funds owed to the network of friends and relatives are going to be the Informal Debt. 6 6 SHIW also provides information about the interest rate charged on mortgages, but not for the rest of loans. 11

13 An increasing tendency in holding informal debt throughout the years considered in this paper is observed: from 0.9% that borrowed from friends and relatives in 2002 to 3.1% in The percentage of household holding formal debt has also increased from 19.6% to 23.1% during those years. Figure 1 illustrates all this information. Among those indebted households, just a small proportion of them borrow from friends and relatives, exclusively (5.2% on average) or jointly borrowing from banks and financial institutions as well (3.2%). Table 2 reports characteristics of the households in function of their debt status. Statistics reported in Table 2 suggest that borrowing from friends and relatives is characteristic of the less wealthy households. However, those that borrow from banks and financial institutions attain a higher level of income, wealth or education than those who do not borrow or borrow from friends and relatives exclusively. What is more, among those that hold formal debt, we observe important differences between those that solely borrow from banks and financial institutions and those that, besides, borrow from friends and relatives. The latter have less income, less real assets and attain a lower level of education as a proxy for future income. However, they hold, on average, a higher level of formal debt. This fact leads us to think in informal debt as a way of lowering the burden and cost of formal. In Table 1 it is reported the percentage of households that were credit market participants during the last twelve months, that is, those that applied for a loan or refused to do so because they thought they might be turned down (discouraged households). These latter, jointly with those whose applications where partially or totally rejected by the bank, are the rationed households. Table 3 shows the percentage of rationed households across the four debt-categories. 12

14 Regarding the first category, No Debt, while I find reasonable explanations for the existence of rationed households (they have been fully rationed in the formal sector and have not been able to borrow from friends and relatives), it is more difficult to justify the existence of households that have not been credit rationed in the current year but lack of any kind of debt. One explanation might be that they have been granted a loan whose maturity is smaller than one year and the formal credit have been already repaid. The other explanation is misreporting. With respect to the third category, Informal Debt, I provide some justification for the existence of non-rationed households. I attribute it to the short maturity of the loan or to the possibility that these households, that were not denied credit by the bank or financial institution, chose the option of borrowing just from friends and relatives because they found it optimal. In any case, just 10 households are in this situation in the credit market participants' sample. 4. ESTIMATION The model developed in section 2 shows that credit rationed households are more prone to borrow from informal sources than the not rationed ones. The model suggests that high risk credit households and those with a higher demand of credit will be more likely to ask for loans to friends and relatives and, hence, more likely to receive those funds whenever they are available. In order to assess the plausibility of these theoretical results, two different analyses are performed. In the first one, I take the whole sample of households and consider four possible outcomes for each individual: (1) hold no debt; (2) hold both formal and informal debt; (3) hold just informal debt, or (4) hold just formal debt. The second part of the analysis focuses on determining to which extent being credit rationed by the formal sector is relevant in explaining the debt 13

15 status of the household. For this purpose, I will consider just those households that participate in the credit market as it is defined in the previous section. 4.1 METHODOLOGY In order to estimate a model with multiple discrete outcomes, I use a multinomial probit model (MNP), where the random utility error terms are assumed to be multivariate normally distributed. This model does not impose the Independence of Irrelevant Alternatives (IIA) since it allows the error terms to be correlated across alternatives. This is a great advantage with respect to the multinomial logit. In this particular context, imposing IIA would mean, for example, that the probability ratio of households choosing between holding only formal debt and holding only informal debt would not depend on the possibility of holding both kind of debts at the same time, which seems unrealistic. I apply a 4-choice MNP model, with utility of the jth choice given by where V = xβ. ij i j Uij = Vij + εij, j=1,2,3,4, The four choices are the ones described at the beginning of this section and the errors are joint normally distributed, with εi N[0, ] MNP model requires numerous assumptions about the covariance structure of the unobserved terms (see, for example, Cameron and Trivedi, 2005, p. 517). xi is a vector of households characteristics that includes the age of the household head and its square, total disposable income (in logs), real assets (in logs), years of education and dummy variables for the ownership of the residence and whether the household head is 14

16 unemployed or retired. I also include a set of dummies that collect information about the year of interview, location of the city of residence (that distinguish between north, centre and south of the country) and population size of that city. 4.2 RESULTS All Households Table 4 contains the multinomial probit results where each column represents a different outcome (holding no debt, formal and informal debt and just informal debt). The omitted outcome is holding just formal debt. We observe that having debts with a bank or financial institution is characteristic of the wealthiest households (real assets) and those with a highest income (all this variables present significant and negative coefficients). Moreover, having a debt with friends and relatives is typical of poorest households and those with a high necessity of funds (unemployed). Significance and sign of the variable age (negative) and its square (positive) in columns 2 (no debt) and 4 (informal debt) suggest, respectively: 1- that households follow a concave pattern in holding a debt with a financial institution or a bank. I attribute it to the higher tendency in holding a mortgage for middle-age households; 2- that informal loans are intergenerational loans from parents to children when these latter are young, and vice versa when parents are old. With respect the third column, Both Debts, I observe less significant variables. Log of income and assets are an example of them, but in a lesser extent that in the fourth column, what reinforces the idea that households ask friends and relatives for financing when they do not have access to credit markets. But this fact can be more properly tested in credit market participants. According to these results, living in couple reduces the probability of holding informal debt, which seems to be surprising since one could expect that a couple had a wider network of friends and relatives to borrow from. 15

17 However, it can also be argued that banks and financial institutions grant credit to more stable households, and a couple can be understood as good signal of it. Moreover, being self-employed have similar signs and significance, what I attribute to the higher financing necessities these people have that can not be fulfilled by the informal networks. As well, the sign and significance of the dummy "city size" (that takes the value 1 whenever the population size of the city where the household lives is bigger than 500,000) may imply that households with a higher demand of credit (those that live in big cities) go to both sectors, formal and informal, to be financed. The justification is twofold: on the one hand, households borrow from friends and relatives as well in order to lower the interest rate charged by the formal sector; on the other hand, some households borrow from friends and relatives when they have not been granted the amount of debt desired by the bank Credit Market Participants Table 5 contains the multinomial probit results of estimations made taking the subsample of credit market participants, without accounting for selection. 7 With respect to Table 4, an additional regressor is included: a variable that indicates whether the household has been credit rationed or not. The omitted outcome is holding only formal debt again. As we expected, being rationed is an important variable in this analysis. This variable helps to explain differences between those households that borrow from banks and financial institutions and those that have a different debt category. This fact 7 The reason of not performing a selection model is, by one hand, the impossibility of finding a valid exclusion restriction and, by other hand, if we permit that the identification relies solely on functional forms, it would be advisable to have the same variables in the selection and in the main equation, something that is not possible since the credit rationing variable must be included in the latter but can not be included in the former. 16

18 reinforces the idea that those households whose loans applications are partially or totally rejected usually go to their network of friends and relatives in order to be financed. The rationing variable is as well important to distinguish "formal" from "no debt". Finally, the last column shows the differences from those households that, having applied for credit in the formal sector, borrow either from friends and relatives or from banks and financial institutions. As expected, rationing plays a crucial role, and the magnitude of this variable is higher than in the other two cases. Besides, we observe that the variables for income and years of education are negative (but a high level of significance in most cases), something in line with the theoretical results in the sense that the informal sector tends to provide more financial aid to low-income households regardless of their solvency. With respect to the rest of the covariates, results remain broadly the same to the ones obtained for all households. 5. CONCLUSIONS This paper proposes both a theoretical and an empirical explanation for the existence of different portfolios of households liabilities depending on the nature of the lender: formal (banks and financial institutions) and informal (relatives and friends). The different characteristics that are assumed the latter has with respect to the former (altruism, better monitoring technology and limited funds) help to understand what it is observed in the results: only a small percentage of households holds informal debt (lowincome households); in addition, some other wealthier households hold both formal and informal debt at the same time, something that I justify with their intention of diminishing the formal debt burden and, hence, lowering the interest rates charged by the formal lenders. Besides, the existence of informal loans is as well explained by the 17

19 fact that the household has been credit rationed in the formal credit market or is in a situation of great necessity, i.e., unemployed. These results show the importance of informal financing for households. However, the low percentage of families observed in this study that borrow from their network of friends and relatives joint with the high number of rationed households in the formal credit market that do not get informal funds, suggest the policy makers the necessity of making informal lending easier through, for example, tax benefits for the lenders. As well, banks and financial institutions are encouraged to streamline informal loans in order to alleviate financial problems of their customers. 18

20 REFERENCES Barro RJ Are government bonds net wealth? Journal of Political Economy 82: Becker GS A theory of social interactions. Journal of Political Economy 82: Bertola G, Hochguertel S Household debt and dredit: economic issues and data problems. Economic Notes 36(2): Cameron AC, Trivedi PK Microeconometrics: Methods and Applications. Cambridge, Cambridge University Press. Cox D Motives for private income transfers. Journal of Political Economy 95 3: Cox D, Jappelli T Credit Rationing and Private Transfers: Evidence from Survey Data. Review of Economics and Statistics 70: Cox D, Rank MR Inter vivos transfers and intergenerational exchange. Review of Economics and Statistics 74: Conning J Outreach, sustainability and leverage in monitored and peer-monitored lending. Journal of Development Economics 60: Diamond DW Financial Intermediation and Delegated Monitoring. Review of Economic Studies 51 (3): Fabbri, D, Padula M Does Poor Legal Enforcement Make Households Credit Constrained? Journal of Banking and Finance 28: Grant C, Padula M Bounds on repayment behaviour: evidence for the consumer credit market, mimeo. Guiso L, Jappelli T Intergenerational Transfers and Capital Market Imperfections. European Economic Review 35(1):

21 Guiso L, Sapienza P, Zingales L The role of social capital in financial development. American Economic Review 94: Jepsen C Multinomial Probit Estimates of College Completion at 2-year and 4- year Schools. Economics Letters 98: Laferrère A, Wolff FC Microeconomic Models of Family Transfers. In Handbook on the Economics of Giving, Reciprocity and Altruism, ed. Serge- Christophe Kolm and Jean Mercier Ythier, Amsterdam: Elsevier. Lawrance EC Consumer Default and the Life-Cycle Model. Journal of Money, Credit and Banking 27(4): Stiglitz J Peer Monitoring and Credit Markets. World Bank Economic Review. 4(3):

22 APPENDIX Proof of Proposition 2 n The amount granted and the interest rate charged are, respectively, F and R. I compute the derivative of the utility function with respect to the informal debt (computed at zero value of it). The utility function to be derived incorporates the informal debt: EU = log( F + I) + βp log( w FR I r) + β(1 p)log( w I r) i h f n The strategy is to substitute F and R by the expressions derived above, that is, when the household was not credit rationed, n f h h EUi = log( w + I) + βp log( wh w r I r) + β(1 p)log( w I r) 1 1 r( β ) r( β ) p l + + p p and derive the resulting expression with respect to I at I=0, l n f EU I i γ 1 1 r(1 p)[ β ( ) + ] γ p = w h wl where, for simplicity, γ =. w h This expression is less or equal than zero, what suggests that, according to the model, non-credit-rationed households do not have incentives to ask friends and relatives for loans. Proof of Proposition 3 21

23 The procedure is similar than in Proposition 2. Now, the amount granted and the r interest rate charged in the formal sector are, respectively, F and values in the same utility function of Proposition 2: r R f. Substituting these ( ) ( ) log( pw h w ) log( pw l h l EUi = + I + β p w w r h I r) + β(1 p)log( wl I r) r r p and deriving with respect to I at I=0, we get: EU I i 1 β r[ ] p(1 γ ) γ = w h This expression is greater or equal than zero. Thus, we show that credit rationed households do have incentives to ask for informal debt. Proof of Proposition 4 In this case, the household is fully rationed in the formal sector so F=0. The expression to be derived is the following: max EU = log( I) + β p log( w I r) + β(1 p)log( w I r) I i It is easy to see that the derivative of this expression evaluated at I=0 goes to infinity, so we conclude that fully credit rationed households would have the strongest incentives to borrow from friends and relatives. h l Participation constraint of the informal sector As it is stated in the beginning, altruism arises as the main cause of informal lending. The reason is that it is assumed that the price charged to this kind of loans is exactly the same as the fixed interest rate on deposits r. That is, informal lenders make no profit from borrowing to friends or relatives. 22

24 Consider the utility function of a household that is not credit rationed, regardless it applies for credit to the formal sector or not. Assume that maximizes its utility at * and : c L2 * c L1 U = U ( c ) + β U ( c ) * * L 1L L1 L 2L L2 Whenever this household is asked by a friend or a relative for some informal loan, automatically incorporates the utility of that friend or relative ( U L function ( ): U B ) into its utility U = U ( c, U ) + β U ( c ) L 1L L1 B L 2L L2 Under no altruism, that is, if the potential informal lender does not incorporate the utility function of the informal applier to hers, this informal lender finds no incentives to lend. The reason is that she will not improve the optimal consumption allocation. Under altruism, the utility of the informal applier is taken into account, as it is stated above. Assuming, for simplicity, that o o U ( c, U ) = U ( c ) + U ( U ), the 1L L1 B 1L L1 1L B utility of the informal lender results: cl 1 c L 2 o o U = U ( c ) + U ( U ) + β U ( c ), L 1L L1 1L B L 2L L2 where o o and are the non-optimal consumption allocation of the informal lender. Hence, it is easy to see that altruism is essential for the informal loan to be released ( ( ) U L U1 L U B > 0 and I >0). Otherwise, it will not occur. 23

25 DESCRIPTION OF VARIABLES Age: In years, age of the household head. City Size: Dummy variable that takes the value 1 whenever the population size of the city where the household lives is bigger than 500,000. Couple: Dummy variable that takes the value 1 if the household head is married. Credit Market Participation: Dummy variable that takes value 1 if the household applied for a loan to a bank or a financial institution (formal source) during the last 12 months or refused to do so because they thought they might be turned down. Debt: Total amount of outstanding debt at the end of the year (from both formal and informal sectors). Debt from friends and relatives: Total amount of outstanding debt to friends and relatives at the end of the year. House Owner: Dummy variable that takes the value 1 when the residence is owned by the household and zero, otherwise. Household Size: Number of the members of the household. Net Disposable Household Income: Includes payroll income, pensions and net transfers, property and net self-employment income. North, Centre, South: Dummy variables. North takes values 1 if the household resides in Piemonte, Val d' Aosta, Lombardy, Trentino-Alto Adige, Veneto, Friuli- Venezia, Liguria or Emilia-Romagna; Centre (Tuscany, Umbria, Marche or Lazio); South (Abruzzo, Molilse, Campania, Puglia, Basilicata, Calabria, Sicily or Sardania). 24

26 Rationed: Dummy variable that takes the value 1 when the household was credit rationed in the last 12 months or refused to applied for a loan because of a high probability of rejecting. Real Assets: Stock of real assets of the household. Retiree: Dummy variable that takes the value 1 if the household head is retired. Self-employed: Dummy variable that takes the value 1 when the household head is a self-employed worker. Unemployed: Dummy variable that takes the value 1 if the household head is unemployed. Years of Education (household head): no education (0 years); primary school certificate (5 years); lower secondary school certificate / vocational secondary school diploma (8 years); upper secondary school diploma (13 years); completed university (18 years); graduate education (20 years). 25

27 Table 1. Descriptive statistics: 2002, 2004, 2006 and Variable Mean Std dev Minimum Maximum Age of household head Family size Household income a Real assets a Formal debt a,b Informal debt a,b Years of education Variable (%) Mean Variable (%) Mean Couple 60.9 Big city 8.6 Self-employed 11.5 Formal debt 22.2 Owner 70.2 Informal debt 2.0 Unemployment of head 2.4 Credit Market Participation 7.2 Retiree 43.5 Year North 38.0 Year Centre 19.1 Year South 42.9 Year Notes: Author's calculations based on data from the Survey of Household Income and Wealth. Data relate to 31,081 households observed at t, where t = 2002,2004,2006,2008. a : Expressed in 2005 prices using national consumer price index. b : Computed using the sample of households with any level of the debt greater than zero. Figure 1: Debt Status by year Percent Formal Debt Informal Debt Both Debts Sources: Author s calculations based on data from the Survey of Household Income and Wealth. 26

28 Table 2. Descriptive Statistics by Debt Status: (1) (2) (3) (4) No Debt Both Debts Informal Debt Formal Debt Variable Mean Age of household head Family size Household income a Real assets a Years of education Debt a Observations (1) (2) (3) (4) No Debt Both Debts Informal Debt Formal Debt Variable (%) Mean Couple Self-employed Owner Unemployment of head Retiree Big City Observations Notes: Author's calculations based on data from the Survey of Household Income and Wealth. Data relate to 31,081 households observed at t, where t = 2002,2004,2006,2008. a : Expressed in 2005 prices using national consumer price index. Table 3. Debt Status and Rationing. Credit Market Participants. (1) (2) (3) (4) No Debt Both Debts Informal Debt Formal Debt Observations Rationed (%) Notes: Data relate to 2,223 households observations that reported participation in credit market either asking for a loan in a bank or financial institution or as discouraged borrowers. These latter are rationed households jointly with those whose loan applications were partially or totally rejected by a bank or a financial institution. 27

29 Table 4. Results explaining households debt status. All households. No Debt Both Debts Informal Debt Independent variable Coefficient Standard error Coefficient Standard error Coefficient Standard error Age ( 10 ) * * Age 2 ( 100 ) 0.001* * Household income (logs) * * * Real Assets (logs) * * * Years of education Couple * * Self-employed * * Owner Family Size * Unemployment of head 0.457* * * Retiree 0.180* North Centre Big city * Intercept 4.431* * * Notes: The number of observations is 31,081. Estimations include year dummies and standard errors are clustered at the region level. Base outcome: Formal Debt. * Significant at 5%. 28

30 Table 5. Results explaining households debt status. Credit Market Participants. No Debt Both Debts Informal Debt Independent variable Coefficient Standard error Coefficient Standard error Coefficient Standard error Age ( 10 ) Age 2 ( 100 ) Household income (logs) * Real Assets (logs) * * * Years of education Couple * Self-employed * Owner Family Size Unemployment of head Retiree * North Centre Big city Rationed 1.361* * * Intercept * Notes: The number of observations is 2,223. Estimations include year dummies and standard errors are clustered at the region level. Base outcome: Formal Debt. * Significant at 5%. 29