Intertemporal substitution, risk aversion, and private savings in Mexico

Policy, Research, and External Affairs L WORKING PAPERS Debt and International Finance International Economics Department The World Bank Mey 1991 WPS 682 Intertemporal Substitution, Risk Aversion, and Private Savings in Mexico Patricio Arrau and Sweder van Wijnbergen Private savings in Mexico have fallen dramatically since 1982. The drop could be linked to a substantial increase in public savings, more thani to uncertainity or real interest rate develop- mlelnts. The lolicy, Resa rch. and 1:xicmaM Affairs ('onpleox distnhbites 'R E U'orking Papcrs todisseminate thc fiidungs of t f )rk in progress and to Cencourage Ihc exchange of ides among 13ank staff and all others intercsted in des clopmcnt Lsties. hese papers cdrr) the namecs of the authors, wiflect only their vtcsS, and should he used and cited accordingly. Ihc findings, inicrpreiatturvs. and conclusions are thc authors own The) should nut be attribuIed to thc World Blank, its lIoard of Dirc,tors, its manageiment, oir anl) of iLS member counincst .  -I 4 oly, Research, and External Afl3irs Debt and International Finance WPS 682 T'his paper - a product of the Debt and International Finance Division, International Economics Department - is part ol' a larger effort in PRE to study the links between external and domestic finance Copies are available free from tie World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Sheilah King-Watson, room S8-040, extension 31047 (28 pages). The decline in private savings since 1982 is * The results imply rejection of the traditional, arguably the most iilporlatilt probleiim inl highi- expected-utility approacih. debt couitries. A reversatl of the trend is essen- tial if gi ;vth is to be restored. Understanding * Risk aversion is signiificant but lower than the determinants of private savings behavior is many have argued from analysis of static ver- thus of more thIain academic interest. sions of the Capital Asset Pricing model. Three factors predominate: (1) the extent of' * Results on ;he intertemporal substitution intertemporal substitution, (2) attitudes toward elasticity are much weaker. risk, and (3) private/public savings interaction. These factors lie at the core of Arrau and van * Domestic bonds issued by the government Wijnbergen's researcih. It tests the issue of debt probably are considered as part of private wealth, neutrality - whether future taxes are recognized although significantly Icss than one for one, thus as an offset for the value of any government debt rejecting debt neutrality. held - and the response of private savings to real interest rates and uncertainty. The results suggest that the large increase in volatility of asset returns has lowered the risk- The authors estimated two configurations of adjusted rate of retuni on savings and may a joint portfolio-choice/savings model. First therefore havc lowered private savings. Tlhis they included equity, domestic bonds, and flight effect must, howcver, have been offset to some capital. In the second configuration they elimi- extent by the sharp increasc in real rates of nated flight capital. intercst. The second configuration, whichi eliminated The authors theln suggest that some of thc the possibility of double counting of assets, decline in private savings could more plausibly yielded substantially better, more intuitive be related to the substantial increase in public results. Among the authors' conclusions: savings that took place during the period. * The intertemporal approach to consumption is supported by the data. The PRE Working Paper Scries disserninates the findings of work under way in thc Bank's Policy, Research, and External i AffairsComplex. An objectivc of thc scries is 1o gCt these findings out quickly, even if presentations arc less Lhan fuill\ polished. Thc findings, intcrpretations, and conclusions in thcse papers do not necessarily represent official Bank policy. Produced hy thc PRE Dissemination Center  Intertemporal Substitution, Risk Aversion, c.nd Private Savings in Mexico by Patricio Arrau and Sweder van Wijnbergen* Table of Contents 1. Introduction 1 2. The Model: Consumption, Uncertainty, and Assets Returns 3 3. Estimation 8 3.1 Data 10 3.2 Results 10 4. Conclusions 13 References 15 Appendix A: Econometric Methodology 18 Appendix B: Data Sources 19 Appendix C: Individual Optimization when RRA = 1 21 Figures 23 Tables 27 * We are indebted to Donaciano Quintero of the Banco de Mexico for providing the data for this study, and to Stijn Claessens for helpful comments on an earlier version. Appendices covering estimation methodology, data definitions, and the data are available from the authors.  1 1. ZTNDODUCTIOI The decline in private savings since 1982 is arguably the most important problem in high debt countries. This decline has significantly exacerbated the direct impact on growth of the reduction in net external transfers that has taken place slnce the debt crisis. A reversal of this trend is essential if growth is to be restored, since renewed external transfers at the scale customary before 1982 are unlikely for the foreseeable future. Understanding the determinants of private savings behavior is thus of much more than academic interest. Three factors seem predominant. First, many countries have seen periods of extremely high real interest rates. For example, ex post real interest rates in Mexico exceeded 40X for most of 1988 and 1989. Second, uncertainty has increased substantially. The continuing threat of balance of payment crises and attendant exchange rate response implied large potential relative price changes in the future; stock market returns often became much more variable; and finally, uncertainty about future debt service translates into uncertainty about future taxes. Third, from a pollcy point of view, the impact of public sector deficits on private sector savings is important. In the absence of debt neutrality, cutting public sector deficiLs is the most direct way of increasing national savings. If however the private sector offsets changes in public sector deficits one for one, as debt neutrality implies, fiscal deficits per se would have no impact on national savings. The three factors mentloned,. the extent of intertemporal substitution, attitude towards risk and private/public savings interaction, are at the core of the resear_.h presented below. There is an extensive llterature on the first and the last point. Traditional approaches, linking private consumption to measures of real income and interest rates have by and large produced inconclusive results. Early claims about the negative impact of real interest rates on private consumption tutrned out Lmpossible to replicate (Giovannini, 1983). Individual country exercises sometimes showed a significant negative impact of real interest rates on private consumption (e.g. van Wijnbergen (1982), using kerb market rates in Korea), but a comprehensive attempt by Giovannini (1985) failed to  2 establish a significant impact of real interest rates on private consumption.l/ More recently, the theoretical basis for such exercises has come under attack. As an alternative, empirical work based on estimation of equations derived from the first order conditions of a representative consumer's optimal consumption problem have been tried out. This research program has not been very successful. Typically, overidentifying restrictions implied by the theory were violated (e.g. Hansen and Singleton, 1982; Bernanke, 1985; Mankiw et. al., 1985). Some have argued that liquidity constraints are to blame for this (Hayashi, 1987; Campbell and Maiikiw, 1989). Others have reported success with an approach explicitly incorporating money into the framework (Arrau (1990), Koenig (1990)). But by and large attempts to test intertemporal theories of consumption behavior explicitly have not been successful. A new line of research has recently questioned the use of expected utility as a criterion by which consumers would rank different consumption streams (see in particular Epstein and Zin, 1989, 1991; Farmer, 1990; and Weil, 1990). Expected utility maximization implies a rigid inverse link between the elasticity of intertemporal substitution and risk aversion. But it is clearly -mnsatisfactory to impose such a link between er.tirely different attributes of consumer preferences by choice of utility fuuction, rather than establish any link there might be empirically. An axiomatic basis for a more general theory is provided by Kreps and Porteus (1978), who relax the indifference with respect to resolution of uncertainty about consumption streams implied by expected utility maximization. This approach has been implemented and applied empirically by Epstein and Zin (1989,1991), called henceforth EZ. The main attraction of this approach is the ability to separately address risk aversion and intertemporal substitution. Siace we just argued that both are likely to feature prominently in any explanation of the recent slowdown in private savings in many developing countries, we adopt the Epstein-Zin approach. This leaves the third factor, the link between private savings and public deficits. This too has spawned a large literature (cf Bernheim (1988) 1 See Balassa (1990) for a survey of the sensitivity of savings to the interest rate in developing economies.  3 for a critical survey plus extensions). Part of this literature is closely related to our concerns, and focuses on the impact of deficits on private consumption. If private consumption equations show equal coefficients, be- of opposite sign, on disposable income and deficits, income net of Government expenditure influences consumption. This is typically interpreted as support for Ricardian equivalence. Most studies reject strict Ricardian equivalence, although they fall short of supporting the strict Keynesian view that only after-tax income matters (cf for example van Wijnbergen (1986)). This literature must be considered suspect, however; if the conditions for Ricardian equivalence would hold, such consumption finctions, linking current consumption to measures of current income, would clearly not obtain, at least not for plausible processes generating income and aeset returns. In this paper, we propose an alternative approach, directly testing whether Government bonds are net wealth in the intertemporal optimization framework presented by Epstein and Zin. If they are, even partially, strict Ricardian equivalence must be rejected and Government deficits and more generally the timing of taxes may influence private consumption decisions. One final point. There is special merit in testing tenets about private savings behavior in developing countries. Especially over-recent years, swings in interest rates and more generally asset prices have been much larger in say Mexico than in the US. Similarly, one can observe substantially large ings in public sector' deficits. With so much more variation in the relevant variables, one should expect more success in empirical testing. We have chosen Mexico with this point in mind; real interest rates went from minus 5X in 1987 to almost plus 45X in 1988 and around 30X in 1989; stock market returns showed a large variance in the eighties; and the public sector transformed a 7X of GDP non-interest deficit in 1981 into a 8.4 % of GDP surplus in 1989. The remainder of the paper is organized as follows. In section 2 we briefly review the formal theory and derive the equations estimated. Section 3 describes results, while Section 4 summarizes and discusses directions for future research. 2 ThE MODEL: CONSUMPTION, UNCERTAINTY AND ASSETS RETURNS The model used is the Epstein and Zin (1987) impLementation of the  4 preference structure laLd out in Kreps and Porteus (1978). Thus, consumers. maxi. .-e current utility, which is a non-linear function of current consumption and a certainty-equivalent measure of next period utility. Next eriod utillty, in turn, is a function of next period consumption and utility in the period beyond next period, and so on. This leads to the following recursion formula for utility (with a C.E.S aggregator): vt Ctot (1) where the "-" indicates the certainty equivalent value of next period utility Vt.. The certainty equivalent value, when defined using a value function of the Constant Relative Rate of Risk Aversion (CRRA) class, can be expressed as follows:2 V (E V1<)T for col (2a) 1o0(9) = zlog(V) for a=1 (2b) with E the expected value operator defined over the distribution of V. (1) is maximized subject co tne current budget constraint: At,* a (At- c.); 1 .1- (3) 2 Using a CRRA value function v (v(V) - V1'-) leads to the followinb certainty equivalent value: v * arg I v(x) - E v(V)) - v-1(E v(V)) - (E V1<i)Ta vh:.ch clarlfles why ve interpret a as the RRA parameter. By taking log and applying L'Hopital rule to evaluate the limit we can go from (2a) to (2b).  5 ct is private consumption in period t; At is the stock of wealth at the end of period t, Ri,t+l is return of asset i between end-of-period t and end-of-period t+l (n assets); es,t is the share of wealth in asset i at the end of period t. Since we use a representative consumer model, individual shares of assets equal market shares. Therefore the ma.'-et return is: FtM.t-IZ I .ei.t Ri't-1 (4) The timing conventions are as follows. At the end period t, the consumer receives the asset returns on the assets held over from the previous period. These returns bring hls wealth to At, of which he chooses to consume ct. The remainder, At - ct, is allocated over the n assets available to him. As already indicated, we label the share aliocated to asset i "fit". This allocation choice problem has to be solved befgre the returns on the n assets (Rit+l for l-l... n) are known (i.e. there is no safe asset). For a - 1, maximizing (2a) subject to (3) leads to the following set of Euler equations (Epstein, 1988; Epstein and Zin 1989): [ fV['1 1) (5) Et [ - Rlt.t)J *o for i-2....,n. where -y - (l-a)/p, and p is related to the lntertemporal elasticity of substitution o: a - l/(l-p). Si6ilarly, the coefficient of relative risk aversion equals a - 1 - p7. (5) is the Euler equation for consumption and ;6) the Euler equations for portfollo decisions. Notice that, as mentioned by Epstein and ZIn (1989) and Giovannini and Veil (1989), qnd unlike in the  6 static CAPH model, the path of future consumption affects today's portfolio decisions. Nultiplying equation (6) by che share of asset i, for all i, summing over i, and combining with (S), the n-equation system (5)-(6) can be expressed a. the n-equation system I7(P~(-1 ) Et f- ] t R - 1 ] 0 for i'l,...,n. Notice chat when the CRRA coefficient a is equal to the inverse of the intertemporal elasticity of substitution a (a - 1/a), then y - 1 and the system of equations (7) take the familiar form from "expected utility" theory. In system (7), the intertemporal elasticity a (function of p above) is not identified when a approaches 1 (7 goes to 0), as Epstein arid Zin (1991) point out. Since in the empirical application presented below we cannot reject the hypothesis a - 1, we are interested in finding the first ord.r conditions which relate asset returns and consumption for the restricted model with a - 1. These first order conditions are (see appendix C for the derivation): E [log( [Ct'l] RM )| G O ~~(8) Et [,R(t.l R.t.1) ]0 for i-2,...,n. (9) Unlike the case of a41 (cf equation (6) above), for a-1 portfolio decisions are lndependent of consumption (cf equation (9)). As noted by Giovannini and Weil (1989), the logarithmic case implies "rational myopia" in portfolio decisions, in the sense that the future does not matter for those decisions.  7 Multipl-ing equation (9) by the share of asset i, for all i, summing over i, and using (3b), allows us to express the portfolio decisions as Et [^At l]-1 for