Private Saving in Mexico,

Transcription

1 Sepember 3, 998 Privae Saving in Mexico, Craig Burnside The World Bank * Sepember 998 Absrac This paper analyzes he behavior of privae saving in Mexico from 98 o 995 using quarerly daa. Simple regressions sugges ha privae saving o a large exen offses changes in he governmen s budge balance. This is confirmed by vecor auoregressions in which ax shocks are found o be he primary deerminans of he raio of privae savings o GDP. Oher imporan deerminans of saving in Mexico are he shocks o he world oil price and o he level of oupu in he Unied Saes. A second goal of he paper is o undersand his behavior of saving using a heoreical model. A simple moneary exension of a neoclassical small open economy model can raionalize many of he empirical findings in he paper, alhough here are several puzzles remaining. * This draf was compleed while I was on leave from he World Bank and a Naional Fellow a he Hoover Insiuion, Sanford Universiy. I hank Jorge Roldos and various seminar paricipans for commens on an earlier draf of his paper.

2 This paper explores he behavior of privae saving in Mexico from 98 o 995. The paper examines privae saving using wo approaches, one purely empirical and he oher more heoreical. The empirical secion of he paper begins by analyzing he correlaion of he privae savings wih various macroeconomic series. This reveals wo ineresing aspecs of he daa. Firs, privae saving is srongly negaively correlaed wih he fiscal balance of he governmen. A second, and relaed fac, is ha privae saving is much more highly correlaed wih he level of privae disposable income, which has significan cyclical componens, han i is wih GNP. This suggess ha saving, raher han consumpion, mops up ransiory movemens in income. The paper hen proceeds o a regression analysis in which he level of privae saving is projeced on a number of poenial explanaory variables, such as income, he governmen s budge balance, he real ineres rae, and indicaors of fiscal and moneary policy. While such regressions canno idenify a srucural savings funcion, because he righ-hand side variables are all reasonably hough of as endogenous, hey do reveal one key fac: movemens in he governmen s budge balance are subsanially offse by changes in privae saving, so ha naional saving would remain roughly unaffeced. This is a fairly robus finding, because i does no depend very sensiively on which oher variables are enered ino he regression. Finally, he empirical secion proceeds o a more srucural analysis using vecor auoregressions (VARs) o ry o idenify he exogenous shocks which ulimaely deermine he Mexican savings rae. The analysis assumes ha here are exernal facors, such as he world price of oil, demand condiions derived from he sae of he Unied Saes economy, and US ineres raes, which drive some of he economic flucuaions in Mexico, and ulimaely affec he savings rae. I also assumes ha here are inernal facors such as echnology shocks and innovaions o ax, spending and moneary policy. The key findings of his secion are ha, in suppor of he previous analysis, shocks o ax policy, which would drive he budge defici holding spending consan, are he key deerminans of he privae savings rae. Oher imporan deerminans are he world oil

3 price (presumably hrough a wealh effec) and shocks o he level of US oupu oher han hose due o moneary policy. The second par of he paper oulines a heoreical framework for gaining insigh ino changes in privae saving. This framework is based on models used by Roldós (995) and, more closely, Rebelo and Végh (995), which are essenially moneary exensions of neoclassical small open economy models. While Rebelo and Végh s model used wo secors (radables and nonradables) o ry o explain secoral aspecs of he effecs of moneary sabilizaion programs, here a one secor model suffices. While assuming Ricardian equivalence, he model allows us o examine he effecs of shocks o domesic produciviy, governmen purchases, Mexican exchange rae policy, foreign ineres raes, and exernal wealh, by compuing impulse response funcions of savings o exogenous shocks o hese variables. The model is capable of explaining he qualiaive aspecs of several of he empirical findings, bu i does no perfecly mimic he dynamic paerns in saving ha we see in he daa. The firs secion of he paper discusses issues concerning he measuremen of saving. I also discusses he sources of he daa used in he empirical secion. The second secion of he paper derives he empirical resuls described above. The hird secion describes he heoreical model, and uses a calibraed version of i o explain he findings of he second secion. Conclusions follow. Daa and Measuremen. Naional Accouns Based Daa The main source of daa for he empirical par of he paper is he quarerly informaion on naional accouns aggregaes prepared by INEGI. Given he hisorical naure of he sudy, and he fac ha boh nominal and real aggregaes were needed, I chose o use only daa from 98 hrough mid-995 ha are based on raw figures provided by INEGI using he now superseded base year of 98. INEGI s newer published figures, which use 993 as 2

4 a base year, did no include nominal aggregaes a he he empirical resuls were obained for his draf. The Mexican naional accouns permi he separaion of GDP ino various componens. Consumpion purchases are spli beween he privae and public secors, while privae purchases can be furher subdivided ino services, nondurables and durables. My measure of privae consumpion is he sum of he official measures of services, nondurables and durables. A more ideal measure of privae consumpion would exclude privae durables purchases since hese represen an addiion o he sock of consumer durables, a form of physical capial. Furhermore, an ideal measure would include a consumpion service flow derived from he sock of consumer durables. However, lacking daa on durables socks, I chose o follow he simpler approach of including durables purchases in he consumpion measure. My measure of privae invesmen is he sum of privae gross fixed invesmen and invenory invesmen. My measure of public secor invesmen is aken direcly from he naional accouns measure. Impors and expors are obained direcly from he naional accouns. In order o obain he difference beween GDP and GNP, dollar-denominaed measures of ne foreign ineres and oher income, and ne foreign ransfers were obained from quarerly figures in he Inernaional Financial Saisics (IFS). These were convered o new pesos using he period average dollar exchange rae, also repored in he IFS. INEGI publishes real and nominal versions of each of he series described above excep he ne foreign income ha makes up he difference beween GDP and GNP. To conver hese flows o real erms I used he GDP deflaor. The raw quarerly daa from he naional accouns are highly seasonal. As a resul, a simple deseasonalizing filer ha is a varian of Census X was applied o all series..2 Governmen Budgeary Daa 3

5 The governmen budge balance figures (economic, financial and primary balances) were obained by calculaing quarerly averages of monhly figures provided o he World Bank by he Mexican auhoriies. Toal ax revenues were obained in he same manner. Budgeary figures are measured as nominal flows. To conver nominal flows o real flows I used he GDP deflaor. However, budgeary daa, unlike naional accouns daa, ypically include large ne ineres flows from he governmen o he nongovernmen secor. During a period of rapid inflaion a large fracion of hese ineres flows does no represen real income o he recipiens nor a real cos o he governmen. To ake his inflaion effec ino accoun, he Mexican governmen produces is own measure of he inflaion-adjused budge balance on an annual, bu no quarerly, frequency. As a resul, here I perform concepually equivalen inflaion adjusmens based on he following mehodology. An ideal measure of he budge balance should be measured as he decline in he real financial deb of he public secor: * P B P = B P, where * is he ideal measure of he nominal budge balance,p is he price level, andb is ne ousanding public deb a he end of period. Given his concep of he real budge balance, he ideal measure of he nominal budge balance is whereπ = P / P is he inflaion rae. [ B ( π ) B ], * = + Sandard measures of he budge balance correspond o ( B B ) =. The difference beween he ideal and sandard measures is * = π B. Since sandard measures of he defici measure a financial flow, his discussion only concerns how ha financial flow can bes be adjused o ake inflaionary effecs ino accoun. This discussion also assumes ha he governmen only issues deb denominaed in local currency, and does no index he face value of he deb o he price level. The discussion is based on ha presened by Barro (993). 4

6 From his discussion i becomes clear ha if he governmen has a subsanial quaniy of ousanding deb, measures of is budge balance will depend grealy on wheher inflaion adjusmens are applied o hem. Since symmeric adjusmens should be applied o privae secor income, measures of privae secor income may also be quie sensiive o wheher inflaion adjusmens are made or no. Since Mexico experienced rapid inflaion over much of he period examined in his paper, he daa will be adjused for inflaion. If he governmen issues deb denominaed in foreign currency, he required adjusmens are more complex. However, he reasons for he adjusmens are he same. If here is a single ype of foreign currency in which public deb is somes issued, hen he ideal measure of he public secor balance is ( π ) * = + π B + d e B f where e is he nominal exchange rae, d is he rae of depreciaion of domesic currency versus foreign currency beween - and, B is he ne domesic deb of he public secor a he end of period, and B f is he ne foreign deb of he public secor (measured in foreign currency) a he end of period. 2.3 Measuring Privae Saving and Income In order o measure privae saving, I sar from a naional accouns based measure of naional saving. From an accouning perspecive I define naional saving simply o be he porion of naional produc plus ne foreign ransfers which is no consumed domesically. So naional saving can be defined as S N =GNP+NFT-C=I+NX+NFI, where NFT is ne foreign ransfers from abroad, C is oal (privae and public secor) consumpion, I is gross domesic invesmen, NX is ne expors of goods and services and NFI is ne income from abroad, including ransfers. In order o discuss he behavior of privae saving we need o decompose naional saving ino is wo componens, privae and public saving. One way o do his is o obain 5

7 privae saving, S P, residually from he ideniy, S P =S N -S G, using he naional accouns measures of naional saving and some measure of public secor saving, S G. A series on naional saving can easily be compued using he naional accouns measure of GDP published by INEGI, he official Mexican saisical agency, and using measures of ne foreign income and ransfers from IFS. The imporan second sep is o measure public secor saving. This is radiionally done by summing some measure of he public secor budge balance,, and a measure of public secor invesmen, I G. Tha is, S G = + I G. To implemen his measuremen sraegy one mus choose a paricular concep of he public secor budge balance. For Mexico, a number of choices are available. These include:. he financial balance of he consolidaed public secor, which consiss of he cenral governmen, is agencies, public secor enerprises and public secor financial inermediaries, 3 2. he economic balance, which drops he financial inermediaries from he definiion of he public secor, and 3. he primary balance, which is he economic balance minus ne ineres paymens. The benchmark public balance concep used here is he inflaion-adjused version of he financial balance. The main reason for using he financial balance is ha i is based on he mos complee definiion of he public secor. The reasons for he inflaion adjusmen were given above. Once he measure of privae saving is obained residually from naional and public secor saving as S P =S N -S G i is hen possible o compue a measure of privae disposable income, as simply he sum of privae saving and privae consumpion: Y P =S P +C P. A measure of privae consumpion, C P, can be obained direcly from he naional accouns..4 Implemening he Inflaion Adjusmen o he Financial Balance 2 Again, his discussion assumes ha only nominal deb, eiher in domesic or foreign currency, is issued by he governmen. Indexed deb is ruled ou by assumpion. 3 Deailed daa on he finances of sae governmens are no available for Mexico. Therefore, sae governmens are implicily being excluded from he public secor. 6

8 Denoing he public-secor financial balance as, he inflaion-adjused measure of he public-secor financial balance is given by * = + π B whereπ is he rae of inflaion of he GDP deflaor, andb corresponds o he end-ofperiod peso value of he consolidaed domesic public deb (economica amplia) published by he Bank of Mexico in he Informe Anual. This measure of he public deb considers he public secor o be he federal governmen, parasaal organizaions and enerprises, plus official financial inermediaries, and hus corresponds o he definiion of he public secor used o consruc he financial balance. I chose no o make furher adjusmens o he financial balance o ake ino accoun he exisence of foreign deb. This is jusified whenever purchasing power pariy approximaely holds or when foreign deb is relaively small compared o domesic deb. A furher problem arises if some of he domesic public deb is held by foreigners. In his case, no only should he public secor balance and public saving be adjused for inflaion, bu so should he measure of ne foreign ineres ha is included in GNP. This porion of GNP should also be inflaion adjused if privae deb denominaed in pesos is held abroad. And, as menioned above, sricly speaking, here are inflaion adjusmens which apply o foreign currency denominaed deb as well. Since he deailed daa on he holding of deb ha would be needed o perform hese calculaions are no available, I did no ry o make any of hese furher adjusmens. The hope is ha hey are relaively insignifican compared o he adjusmens made for domesic public deb.,.5 Oher Time Series Oher variables used in he analysis below include he depreciaion rae of he peso, he domesic 3-monh reasury bill rae, he domesic inflaion rae, he 3-monh reasury bill rae in he Unied Saes, he inflaion rae in he Unied Saes, gross domesic produc in he Unied Saes, he world price of oil, he moneary base, privae domesic credi, and he populaion of Mexico. 7

9 The depreciaion rae of he peso was measured as he percenage change, a an annual rae, beween successive end-of-quarer values of he peso-dollar exchange rae obained from he IFS. The reasury bill rae was obained from he IFS as he quarer-average nominal ineres rae on Mexican Treasury bills, while he domesic inflaion rae was aken o be he annualized rae of change of he GDP deflaor. The 3-monh Treasury bill rae in he Unied Saes was obained from he Chicago Fed s online daabase. The inflaion rae was measured as he annualized quarerly percenage change in he GDP deflaor, which along wih GDP was obained from he S. Louis Fed s online daabase. The world price of oil was obained from he IFS and was expressed in US dollars per barrel. Finally, he moneary base and he level of privae domesic credi were obained from he IFS. I also convered quaniies ino per capia measures. A quarerly series on he populaion was inerpolaed using he annual figures from he World Bank daabase. The mehod used assumed consan growh raes wihin each year. This is he opimal filer o use if he underlying rue daa follow a random walk wih drif. 2 Empirical Findings In his secion I explore he daa in four ways. Firs, I presens chars of series for various macroeconomic aggregaes in Mexico from 98 hrough mid 995. Second, I examine he paern of cross correlaion beween privae savings and oher variables of ineres. Third, I perform regression analysis, which is simply a way of compuing parial correlaions beween privae savings and he oher variables. I inerpre hese findings in ways which are only valid under he assumpion ha he regression equaion idenifies a srucural relaionship among he variables. Since a saic regression using quarerly daa is unlikely o acually idenify a srucural saving funcion, as an alernaive, in he fourh secion I use vecor 8

10 auoregressions o examine he dynamic responses of privae saving o a vecor of shocks ha may have a reasonable srucural inerpreaion. 2. A Look a he Daa Figure plos quarerly series for Mexico over he period 98Q-995Q2. The chars are drawn for he main macroeconomic aggregaes. They show ha GNP peaked in early 982, and hen, in associaion wih he deb crisis and he subsequen economic urmoil, i fell unil 987. This was followed by a period of sabilizaion in which GNP, consumpion and invesmen all rose a a fairly modes rae. Hisorically he curren accoun in Mexico was in defici, and i peaked in he leadup o he deb crisis. In he subsequen period i narrowed subsanially and was acually in surplus. However, under he sabilizaion plan he curren accoun again moved owards a defici. 4 Figure 2 illusraes some -series which are disaggregaed ino public and privae componens. These indicae several hings. Firs, privae consumpion srongly co-moved wih GNP over he period. Second, governmen consumpion expendiure displayed lile variaion over he period wih a sligh, and apparenly permanen, decline associaed wih he sabilizaion program of early 988. Third, privae invesmen has also srongly co-moved wih oupu, bu has been subsanially more volaile. I dropped dramaically in he wake of he deb crisis and by 994, unlike consumpion, had no reached is peak value of 982. Finally, public secor invesmen has fallen dramically over, especially in he pos deb crisis period. By 994 i was only one quarer of is peak level in 98. Figure 3 shows daa on he public secor budge balance and privae saving. The chars show ha when he budge daa are no adjused for he inflaion effecs described earlier, a srong negaive correlaion beween he budge balance and privae saving resuls. However, despie he fac ha his correlaion appears weaker when he daa are inflaion-adjused i acually remains quie srong. Anoher ineresing feaure of he daa 9

11 is ha he marked and gradual decline in privae saving in he lae 98s urns ou o be an arifac of he unadjused figures. 2.2 Cross Correlaions of Consumpion and Saving Table provides he dynamic cross-correlaions beween privae saving and he oher variables o be used in he regression analysis. The cyclical componens of he income measures are hose implied by he Hodrick and Presco (997) (HP) filer. The mos sriking finding from he correlaion marix is he srong negaive conemporaneous correlaion beween privae saving and he governmen budge balance. Alhough his correlaion is no as srong a leads and lags, his finding hins a he possibiliy of approximae Ricardian equivalence. Anoher ineresing feaure of he daa is ha here is a much sronger correlaion beween privae savings and privae disposable income han here is beween privae savings and GNP. To he exen ha GNP reflecs movemens in permanen income more han privae disposable income does, his finding would be consisen wih a permanen income ype heory. Furher evidence ha hins a a permanen income ype heory comes from he fac ha he correlaion beween privae savings and he cyclical componen of privae income is abou he same as he correlaion beween privae savings and privae income as a whole. This suggess ha he imporan movemens in privae savings are a cyclical frequencies, and ha hese comove srongly wih emporary flucuaions in income. In dynamic correlaions asymmeries are ofen aken o be an indicaion of a leadlag relaionship beween wo variables. For example, were privae savings more highly correlaed wih pas income han fuure income, hen we migh say ha income leads savings. There is lile in he way of his sor of asymmery in he daa. The simple correlaions beween privae saving, he nominal ineres rae, he inflaion rae, he depreciaion rae of he peso and he level of governmen consumpion 4 In fac, in nominal erms, he curren accoun defici became quie wide by 994. This is no refleced by real figures because of he subsanially differen behavior of he deflaors for impors and expors during

12 purchases are all quie small. Governmen purchases as a whole, raher han jus purchases of consumables, are more highly correlaed wih privae savings. This may reflec comovemen beween public and privae invesmen. We will see in he nex secion ha he parial correlaions uncovered by regression analysis are quie differen han he simple correlaions presened here. 2.3 Regression Analysis This subsecion presens resuls of regressions which seek o explain variaion in privae saving. These regressions should be inerpreed cauiously. They do no idenify causal links, since some of he righ hand side variables are likely o be simulaneously deermined. They are mean o be informaive abou wha he sources of variaion in he savings rae migh be, and abou he comovemens beween privae savings and oher macroeconomic variables. The dependen variable in each of he regressions is he level of inflaion-adjused privae savings (SP). 5 The righ-hand side variables in he benchmark regressions presened here were chosen from among GNP (Y), he rend in GNP (GNPTR) as defined by he HP filer, he cyclical componen of GNP (GNPCY) as defined by he HP filer privae disposable income (PDY), he rend in privae disposable income (PDYTR) as defined by he HP filer, he cyclical componen of privae disposable income (PDYTR) as defined by he HP filer he ex-ane real ineres rae on Mexican reasury bills (R), purchases of goods and services by he governmen (PURG), purchases of consumpion goods and services by he governmen (CG), his period. 5 All quaniy variables in he equaions are measured in real per capia erms, excep he moneary base and privae domesic credi which were measured in nominal per capia erms.

13 he inflaion-adjused financial balance of he public secor (GBAL), he depreciaion rae of he peso (D), he annualized growh rae of he moneary base (MBG), he annualized growh rae of privae domesic credi (PDCG), Ideally he specificaion would be based on a heoreical relaionship expressing privae saving as some funcion of relevan exogenous and endogenous sae variables. In a small open economy model, hese would ypically include he level of physical capial, he level of ne foreign asses, he real rae of ineres, he depreciaion rae of he currency (or he growh rae of he money supply if his were he relevan moneary policy variable), governmen purchases of goods and services, and, possibly, various variables relaed o governmen budge financing. Since no all of hese variables are available for Mexico, cerain compromises mus be made. The rends and cyclical componens in GNP and privae disposable income are inroduced as possible ways of disenangling he effecs of permanen versus ransiory income from one anoher. However, he HP filer-defined rends may be very imperfec proxies for permanen income or wealh. The moivaion for he real ineres rae variable, R, is simply ha saving or borrowing decisions are likely o be a funcion of he real ineres rae. In a small open economy model, invesmen, consumpion, he curren accoun and subsequenly saving, are all affeced by he real ineres rae. The ex-ane real ineres rae was measured by he difference beween he nominal ineres rae on Mexican reasury bills and he expeced rae of inflaion compued as he fied values from a regression of he curren inflaion rae on pas inflaion, he pas nominal ineres rae and he pas depreciaion rae of he peso. I deemed his o be he appropriae real ineres rae o use o explain privae saving behavior. Public secor purchases of goods and services (PURG), or alernaively public secor consumpion purchases (CG), are included in he regression as hese represen physical resources exraced by he governmen from real GNP. These are resources unavailable for privae consumpion, and permanenly increased governmen purchases represen a decline in privae wealh. Furhermore, a es of wheher governmen 2

14 financing decisions maer requires governmen purchases o be enered as an explanaory variable. The disincion beween consumpion purchases and overall purchases may be necessary because overall purchases include public secor invesmen, which presumably, may augmen he sock of physical capial used o produce privae income. The public secor budge balance, GBAL, is irrelevan for privae consumpion and GNP under he null hypohesis of Ricardian equivalence. So, everyhing else held equal, if he governmen chooses, in a nondisorionary way, o run a higher budge defici, say for example by lowering lump-sum axes and increasing privae income, privae saving should compleely offse ha higher defici by absorbing any addiional privae income i generaes. So he coefficien on he budge balance should be - under Ricardian equivalence. 6 The depreciaion rae of he peso, D, is also included in he regressions. Flucuaions in he rae a which he peso depreciaes can have effecs because hey affec he real reurn o holding peso balances. More rapid depreciaion acs as a higher ax on peso balances. To he exen ha hese balances are useful in reducing ransacions coss, his higher ax will have real consequences for consumpion, invesmen, saving and oupu. The depreciaion rae is also included in ha i is an indicaor of moneary policy. As alernaive measures of moneary policy I consider wo oher variables, he growh rae of he moneary base, MBG, and he growh rae of privae domesic credi, PDCG. Boh of hese variables are problemaic as measures of policy because of major changes in Mexico s financial sysem during his period. I is ofen argued ha he growh of credi in Mexico in he early 99s led o a consumpion boom, and ulimaely o he peso crisis of lae 994. I will be of ineres o examine he impac of credi expansion on saving. The resuls of he regressions are presened in Table 2. The regressions use levels of he variables for wo reasons. Firs, i is arguable ha mos of he quaniy variables used in he regressions are saionary. There was lile real per capia growh in Mexico 6 For he regression o correcly idenify he exen o which pure nondisorionary financing decisions maer, all disorions mus be aken ino accoun on he righ-hand side. Wihou deailed informaionon marginal ax raes his is effecively impossible. 3

15 over he period being considered. Second, using levels preserves he equivalence of he unis of measure of savings, income, and he various expendiure variables. The benchmark regression is in column A and uses GNP as he income concep. The coefficien on GNP indicaes ha as GNP rises savings rises bu much less han onefor-one wih GNP. So holding he oher variables equal, while savings rises wih income, privae savings as a fracion of GNP falls. The real ineres rae is insignfican in he regression, and remains so hroughou all he regressions presened in Table 2, which may indicae ha subsiuion and income effecs associaed wih ineres rae changes have a endency o cancel one anoher ou. Governmen purchases ener srongly and negaively ino he regression. The regression hold GNP and he budge balance consan, so a rise in governmen purchases in hose circumsances would coincide wih a rise in axes and, as a consequence, a decline in privae disposable income. A decline in savings migh be he expeced resul, if privae households smooh consumpion and he rise in governmen expendiure and axes is aken o be ransiory. The governmen s budge balance eners ino he regression wih a coefficien of approximaely -. This is srongly suggesive of Ricardian equivalence. If governmen purchases and GNP are held consan, he mos likely example of an improvemen in he budge balance is an increase in axes ha is relaively nondisoring (hence he lack of any effec on GNP). These axes would lower privae disposable income, bu since any rise in axes now, wih no change in governmen spending, would coincide wih a laer decline in axes, consumpion smoohing would imply ha he privae saving would absorb he enire decline in income. 7 Finally, more rapid depreciaion of he peso appears o lead o a rise in privae saving. This could be explained in he following way. Suppose ha peso balances are useful for making consumpion purchases, say because holding hem reduces shopping or ransacions coss. When he peso depreciaes more rapidly, perhaps in an unanicipaed way, his pus a ax on holding money and on consumpion purchases. If he 4

16 period of more rapid depreciaion is viewed as emporary, hen consumers will ineremporally subsiue higher consumpion in he fuure for lower consumpion now. If income does no decline, his implies an increase in curren saving. Column B indicaes ha he basic findings in column A are robus o using privae income raher han GNP as he income concep. Flucuaions in he governmen s budge balance are no longer offse one-for-one by privae saving, bu hey are largely (9 percen) offse. Columns C and D spli he income conceps ino heir rend and cyclical componens. As expeced more cyclical flucuaions in income have a posiive impac on privae saving, while movemens in he rends in income appear o have lile impac on privae saving. Column E uses govermen consumpion purchases in place of oal governmen purchases as he measure of fiscal policy, and reurns o using GNP as he income concep, so esimaes should be compared o hose in column A. Ineresingly, he coefficien on GNP changes sign, indicaing ha increases in income lead o small decreases in privae saving. The coefficien on governmen purchases iself is similar in magniude o he coefficien in column A, bu is esimaed very imprecisely. The coefficien on he governmen budge balance is significanly differen han -, and indicaes ha privae saving offses abou 75 percen of movemens in he budge balance. The depreciaion rae of he peso is neiher quaniaively nor saisically significan in he regression. And finally, he fi of he equaion is considerably poorer, indicaing ha governmen invesmen purchases have subsanial explanaory power for privae saving. In column F, he growh rae of base money is subsiued for he depreciaion rae of he peso as he indicaor of moneary policy. More rapid money growh, like more rapid depreciaion of he peso ended o coincide wih higher levels of privae saving, perhaps for similar reasons. Finally, in column G, in which he growh rae of privae domesic credi was used as he indicaor of moneary policy, we also find ha rapid credi growh was associaed 7 Sricly speaking he regression doesn hold fuure governmen purchases consan, only curren ones. This poins o a generic problem in he inerpreaion of coefficiens in saic regressions such as he ones 5

17 wih higher levels of privae saving. This is conrary o he noion ha rapid credi expansion led o a decline in privae saving in he 99s. A his poin, a furher discussion of he evidence regarding he Ricardian proposiion is warraned. The resuls in Table 2 consisenly sugges ha privae saving behavior offse he budgeary policies of he public secor in he 98s and early 99s in Mexico. However, here is a srong possibiliy ha his resul is driven by measuremen error. For example, suppose our measure of naional saving is correc, bu ha he measured budge balance, S *, is measured wih a whie-noise classical measuremen * * error. This will imply ha S = + ε where * is he rue budge balance and ε is a whie noise error erm uncorrelaed wih *. Since naional saving is measured correcly, his will imply ha privae saving is given by S * = S ε. In a simple regression of P P privae saving on he budge balance he coefficien esimae would be given by * * * ( P S ) Cov( S P ε + ε ) * * ( ) Var( + ε ) * * * ( P, ) Var( 2 ) σ ε * * 2 * ( ) Var( ) + σ ε Var( ) * Var( 2 ) σ ε. * 2 * 2 ( ) + σ ε Var( ) + σ ε * * ( P ) * ( ) + Cov S,, Cov S, β = = = Var S Var Cov S = Var = β * Var The noisier he budge balance daa are, he furher negaive he bias in he regression coefficien. To check wheher his was he source of my finding I smoohed he budge balance daa, and compued privae saving using hese smoohed daa and he original daa on naional saving. The very srong negaive correlaion beween privae saving and he budge balance remains. Finally, i should be poined ou ha he regressions canno ruly be given a srucural inerpreaion. They describe a purely saic relaionship among he variables, and hey do no idenify he response of privae saving o exogenous shocks o he Mexican economy. Mos of he righ-hand side variables in he equaions could easily be hough of as simulaneously deermined by a large number of common srucural shocks. + σ 2 ε σ σ 2 ε 2 ε presened in Table 2. 6

18 In he nex secion, I ake a small sep owards idenifying hese srucural shocks and he response of privae saving o hem. 2.4 The Dynamic Responses of Privae Saving o Shocks In his secion I use a VAR approach o modeling he response of privae saving o various shocks o he Mexican economy. The shocks I aemp o idenify are as follows: (i) wealh effecs arising from exogenous flucuaions in he world price of crude oil, (ii) demand shocks resuling from he Unied Saes business cycle, (iii) moneary policy shocks in he Unied Saes, (iv) echnology shocks in he Mexican economy, (v) exogenous innovaions in governmen purchases in Mexico, (vi) exogenous innovaions in ax financing in Mexico and (vii) exogenous changes in he rae of depreciaion of he peso. These are assumed o comprise a complee se of he shocks which ulimaely deermine he aggregae level of privae savings in Mexico. The specificaion of hree exogenous policy shocks (v)-(vii) is possible in an open economy, because he firs wo will deermine he governmen s financing requiremen. The laer will endogenously deermine he level of seignorage financing, leaving, as a residual, he level of deb finance required. To idenify he firs hree shocks I assume ha hey are deermined enirely exogenously wih respec o he Mexican economy. I specify a separae VAR for he logarihm of he world price of crude oil, he logarihm of per-capia GDP in he Unied Saes, and he 3-monh reasury bill in he Unied Saes. Suppose we denoe hese hree variables, in he same order, in vecor form as x. Ignoring he consan erm, I esimae a VAR of he form A x = A x + L + A x + u p p where A is assumed o be lower riangular wih ones on he diagonal, and u is assumed o be whie noise. The assumpion ha he variables ener in he order I have described above means ha shocks o he world oil price are deermined prior o US ineres rae policy, and prior o he deerminaion of oupu in he US. However, he Fed, in seing 7

19 ineres rae policy, is assumed o see he level of oupu (or is deerminans in he curren quarer). The lag lengh I used in pracice was p=4. Esimaing he VAR for x leads o a se of residuals$u ha we can hink of as esimaes of he shocks,u. In he second sep I assume ha Mexican daa on governmen purchases of goods and services, oupu, axes ne of ransfers and he depreciaion rae of he peso can be used o idenify he remaining shocks. I denoe hese variables as y. I assume ha he error in he governmen purchases equaion represens an exogenous shock o governmen purchases, ha he error in he oupu equaion represens an exogenous shock o echnology, ha he error in he ax equaion represens an exogenous financing shock, and ha he error in he depreciaion equaion represens an exogenous moneary policy shock. I choose he order of he variables in he VAR in order o reasonably argue ha he errors in he esimaed equaions can be given his inerpreaion. The VAR I esimae is of he form B y = B y + L + B y + C x + C x + L + C x + v p p p p where B is assumed o be lower riangular wih ones on he diagonal, and v is assumed o be whie noise and is orhogonal o u. I assume ha he realiies of fiscal policy are such ha when he governmen deermines is level of purchases of goods and services i does so absen knowledge abou he curren levels of echnology, he level of axes i may raise in he curren quarer and he sae of moneary policy. Second, I assume ha oupu is hen deermined by he level of echnology, all pas informaion and any of he curren shocks already discussed. Once oupu is deermined, he level of axes is deermined, so axes come afer oupu in he ordering. Finally, moneary policy, or he deerminaion of he exchange rae occurs once all hese oher shocks have been realized, so he depreciaion rae of he peso comes las in he ordering. Subjec o his ordering, he second VAR idenifies esimaes of he Mexican srucural shocks, v, which I denoe $v. Once he shocks have been idenified i is possible o deermine he impulse response funcion of a variable, z, no included in he VARs, o he various shocks, u 8

20 and v in a number of ways. Here I assume ha i is sufficien o specify an ARMA model for z of he form z = φ z + L + φ z + θ u + L + θ u + θ v + L + θ v, q p u un n v vn n in order o obain a good approximaion o he moving average represenaion of z. In pracice I assumed ha q=4 and ha n=. I worked wih wo models, one for he logarihm of real per capia privae savings, and anoher for he share of privae savings in GNP. The resuls I obained were qualiaively similar for he wo examples, so I used he model of he share of privae savings in GNP (I call his he privae savings rae) for beer inerpreabiliy. Figure 4 illusraes he esimaed impulse response funcions of he raio of privae savings o GNP wih respec o he 7 shocks I have described above. The graphs illusrae he change in he savings rae, in percenage poins, ha occurs when here is a shock of each ype. Each of he shocks has been normalized o be equal in size o he sandard deviaion of he relevan residual from he esimaed VARs. 8 The firs graph shows he response of privae savings o an increase in he world price of oil. The shock o he price of oil assumed is abou 2 percen, he sandard deviaion of he innovaion o he oil price in he esimaed VAR. Since an increase in he world price of oil, o Mexico, represens an increase in wealh, we migh expec he savings rae o drop as a resul. Indeed, we see ha by he quarer afer he shock, he privae savings rae drops by abou percenage poin. Afer ha here is a gradual reurn of privae savings o is previous value. The second graph shows he response of he privae savings rae o an innovaion in US oupu of abou one half of one percen of is GDP. I inerpre his innovaion as a shock o he demand for Mexican producs. When his occurs we also see a decline in he privae savings rae by jus over one percenage poin. Presumably, again, he increase in US demand leads o an increase in perceived wealh in Mexico. This increase in wealh 8 I is imporan o noe han in esimaing he equaion for he raio of privae savings o GNP, a perfec fi is no obained. In oher words, he privae savings rae canno be perfecly explained by he 7 shocks ha have been included in he VARs. We examine he unexplained componen below. 9

21 precedes he subsequen increase in Mexican GNP, so he increase in consumpion drives down savings iniially. The hird graph illusraes he response of privae savings o a US moneary policy shock in he form of an increase in he 3-monh US T-bill rae of abou 64 basis poins. I is less easy o provide inuiion for his finding. Higher ineres raes in he US ough o ranslae ino higher ineres raes in Mexico, oher hings equal, and his is usually hough of as an incenive o save. Assuming ha a higher T-bill rae in he US ranslaes ino a higher real cos of borrowing from abroad, here should be a negaive wealh effec associaed wih he shock. This should cause consumpion o fall, as well as invesmen, and a shor run improvemen in he curren accoun and savings. Evenually, his effec will be reversed as oupu declines, and savings falls in line wih he decline in invesmen. I is for his reason ha he finding here seems puzzling. The fourh graph illusraes he response of privae saving o an innovaion in governmen purchases of goods and services. The shock represens a roughly 2.5 percen increase in purchases. The privae savings rae rises by abou.5 percenage poins as a resul of he increase in governmen purchases, bu quickly reurns o is previous value. This resul can be reconciled wih our regression findings, which assumed ha he increase in governmen purchases was accompanied by no change in he governmen s budge balance, and herefore was accompanied by an increase in axes. If axes do no respond immediaely o an increase in governmen spending, hen privae income may be largely unaffeced by he increase in spending, whereas life wealh will have declined. In his case, a decline in privae consumpion and an increase in privae saving would no be surprising. The fifh graph illusraes he response of privae savings o a echnology shock in Mexico represening a.8 percen ouward shif in he producion possibiliies se. In neoclassical models, echnology shocks raise he rae of reurn o invesmen, and lead o an increase in life wealh. The consequen rise in consumpion would ousrip he shor-run increase in oupu and would cause privae individuals o borrow from abroad in order o finance heir consumpion and invesmen purchases. As a resul saving would fall in he shor run. This effec would evenually be reversed. The esimae impulse 2

22 response funcion is puzzling because i indicaes a very shor-run increase in saving followed by a decline in saving ha persiss over several quarers. Bu we will see, in he heoreical secion, ha inuiion abou he effecs of echnology shocks is highly sensiive o he degree of persisence one assumes hey have. The sixh graph illusraes he response of privae saving o a shock o he governmen s ax revenue. The shock represens a roughly 4 percen increase in revenue. Recall ha his is an increase in revenue ha is no prediced by any prior change in he level of governmen spending, so we may hink of i as an exogenous decision by he governmen o raise axes now, and eiher raise expendiure in he fuure or have lower axes in he fuure han would oherwise have been he case. I would appear ha since he privae savings rae falls subsanially in is response o he ax shock, a rise in axes now is aken o imply a decline in axes in he fuure. Consequenly life wealh, and privae consumpion remain unchanged, and privae savings falls (since income mus have fallen by he amoun of he axes). Finally, he sevenh graph illusraes he response of saving o an unanicipaed increase in he rae a which he peso depreciaes. The shock o he peso represens a depreciaion of 3 percen a annual raes. Afer a single period increase in he privae savings rae, i declines by abou.6 percenage poins and hen reurns o is previous level. In some moneary models, more rapid depreciaion of he peso can imply a negaive wealh effec, which we would expec o lead o a shor-run increase in saving. The impulse response funcions characerize he response of privae saving o differen kinds of shocks. We can decompose he variance of privae saving (as a fracion of GNP), a various forecasing horizons, ino componens deriving from each of he 7 shocks. This decomposiion is provided in Table 3. I illusraes ha abou a hird of he variance in privae saving a all horizons is due o he ax financing shock. In oher words, privae savings is largely driven by he governmen s exogenous decisions regarding financing. The second mos imporan shock is he one o US oupu. Flucuaions in US GDP ac like an exogenous shock o he demand for Mexican producs and clearly have an imporan impac on privae saving in Mexico. And he hird mos imporan shock is movemen in he world price of oil. Beween hem, hese hree shocks accoun for 6 o 2

23 7 percen of he variaion in privae savings in Mexico. Since beween 2 and 27 percen of he variaion in privae saving is simply unexplained, his leaves very lile o be accouned for by he oher 3 shocks. In he nex secion I presen a heoreical model which incorporaes he Ricardian proposiion direcly ino he heory. Thus, i can immediaely explain he imporance of governmen financing decision for privae saving. I will also be useful in gaining insigh ino how a modified neoclassical model can be used o ry o undersand he oher findings in his paper. 22

24 3 A Model of Privae Saving in Mexico The previous secion presened empirical evidence ha suggesed ha in Mexico (i) privae saving is largely driven by, and offses, movemens in he governmen budge balance, and (ii) privae saving appears o decline when consumers are confroned by a posiive shock o heir wealh. This secion describes a model in which he firs finding holds exacly by assumpion (he governmen budge balance is irrelevan o privae consumpion). We will see wheher he second finding is prediced by he model, and, in fac, wha he model predics for he reacion of privae saving o several kinds of exogenous shocks o he economy. The model in his secion is derived from and is a simplificaion of he one presened by Rebelo and Végh (995). The model describes an economy in which here are forward looking consumers who gain uiliy from a single consumpion good and who suffer disuiliy from. In he version of model presened here, he labor marke clears, so ha he real wage is se equal o he marginal rae of subsiuion beween consumpion and leisure. Producion akes place in a single secor which produces a radable good using capial and labor. Capial is accumulaed using a sandard invesmen echnology which allows for adjusmen coss. The model reas Mexico as a small open economy, so ha boh he privae and public secors can borrow from he foreign secor a he world nominal ineres rae measured in foreign currency. This does no allow he model o capure hose aspecs of inernaional borrowing and lending relaing o risk. The exchange rae is reaed as an exogenous policy variable, whose rae of depreciaion is seleced by he governmen according o a rule. This makes he supply of money an endogenous variable, since money mus be allowed o adjus o susain any paricular value of he exchange rae. 9 Money eners he model hrough a sandard 9 The opposie case where he money supply follows a rule and he exchange rae is endogenously deermined can also be examined. 23

25 ransacions echnology. Purchases of consumpion and invesmen have associaed ransacions coss which are smaller he greaer are money balances. A deailed descripion of he model is provided in secion 3.. Secion 3.2 describes he numerical calibraion of his model o Mexican daa. Secion 3.3 describes he firs order condiions of he model, while secion 3.4 describes a mehod for solving he model. Then secion 3.5 analyzes how differen exogenous shocks would impac on privae saving if hey were fed hrough he mechanism of he model. The exen o which he model is useful for gaining an undersanding of savings behavior in Mexico is discussed. 3. The Model The model is a dynamic opimizing model of a small open economy in which households own capial which is rened o firms owned by he households. The model is a one secor simplificaion of he wo secor model of Rebelo and Végh (995). The Household Secor There is a represenaive household which maximizes he discouned sream of is uiliy which is given by ( ) E β U C, N, = where β<, C is consumpion and N is labor supplied. The uiliy funcion is assumed o be of he form ( ) ( ν C N ) ψ, N = U C / σ / σ where σ> is he ineremporal elasiciy of subsiuion, and ν deermines he labor supply elasiciy. This uiliy funcion, associaed wih Greenwood, Hercowiz and Huffman (988) miigaes problems associaed wih unrealisic wealh effecs on labor supply in dynamic opimizing models. The household maximizes is uiliy subjec o he budge consrain 24

26 e B + C P + I P + S P + M = * ( ) e B + r + M + W N + R K + Π Ω where e is he exchange rae in pesos per dollar, B is he households ne foreign asses in dollars, P is he price level, I is invesmen, S is real ransacions coss, M is ne money * holdings of he household secor, r is he dollar ineres rae a -, W is he nominal wage rae, R is he renal rae of capial, K - is he household s capial sock chosen a -, Π is profis of he firms, and Ω is ne lump-sum axes. Capial is accumulaed using a sandard adjusmen cos echnology where he adjusmen cos is a funcion of he size of invesmen relaive o he exising sock of echnology. So, where ϕ( δ ) = δ, ϕ ( δ ) K ' =, and ( ) I = K ϕ + K ( δ ) K ϕ'' δ = κ / δ, where κ δ is a free parameer. δ Transacions coss are associaed wih purchases of consumpion and invesmen goods. In his model hese coss are assumed o be charged o he budge of he households. The coss are an increasing funcion of he value of household purchases bu a decreasing funcion of he quaniy of money balances held by he household relaive o ha value. In paricular he real coss are given by S ( C I ) v M P / = ζ S + θ C + θi where v(x)=x 2 -X+ξ. The parameer θ denoes he fracion of invesmen purchases which are made less cosly by he holding of money. This allows, for example, he model o deal wih he fac ha some invesmen purchases are no made by privae households, bu are, in fac, made by he governmen. Firms Producers maximize profis given by α α Π = P ζ K N W N R K where ζ represens he level of TFP, K - is he quaniy of capial rened by producers a and N is he quaniy of labor hey hire. 25

27 Facor and oupu markes are assumed o be compeiive and marke clearing. The Public Secor The governmen makes exogenous decisions regarding is level of consumpion expendiure, is level of foreign borrowing, ne axes paid by he household secor, he ax rae and he rae of depreciaion of he peso. Given hese decisions he money supply mus adjus in order for he governmen s budge o balance according o * ( ) e F = e F + r + M M + Ω P G, where F is he governmen s ne foreign asses in dollar erms, and G is governmen purchases of consumable goods. Equilibrium Relaionships A rade surplus a any poin in is associaed wih an accumulaion of foreign asses so ha in equilibrium he real rade balance is given by * ( )( ). TB = B + F + r B + F This condiion can derived by aggregaing he household s and he public secor s budge consrains. Finally, I assume ha purchasing power pariy holds so ha he domesic price level is given by P = e P * where P * is he foreign price level. For simpliciy I assume ha P * = for all, so ha he foreign inflaion rae is zero, and he foreign nominal and real ineres raes are equivalen. 3.2 Calibraion of he Model s Parameers A number of choices mus be made vis-a-vis he model parameers. The model was calibraed so as o mach, as closely as possible, key feaures of he Mexican economy in he period The ineremporal elasiciy of subsiuion was se o σ=.2 a small value consisen wih he evidence on ineremporal subsiuion for developing counries provided by Ogaki, Osry and Reinhar (995). 26