DRD DLSCUSSION PAPER Report Noo DRD243 -------------------·------------------------------------- SAVINGS, COHHODITY :1ARKET RAT luNING AND THE REAL RATE OF INTEREST IN CdlNA by Andrew Feltenstein University of Kansas David Lebm.v Princeton University and Sweder van Wijnbergen World Bank -·----------------------------------------- Dev8lopment Research Department Economics and Research Staff World Bank T!lt::.> tvorld Bank does not accept responsibility for tne views expressed herein which ar~ those of the author(s) and should not be attributed to the World Bank or to its affiliated organizationso The findings, interpretations, and con~.~lus ions dre the results of research supported by the Bank; they do not necessarily represent ofLi.cial policy of the Banko The designations employed, the prGsentation of material, and any maps used in this document are solely for tht~ convenience of the reader and do not imply the expression of any i.on whatsoPver on the p.1rt of the World Bank or its affiliates concerning thP l status of any country, territory, city, area, or of its authorities, or 12~Hh~(~rning the delimi.tations of its boundaries, or national affiliationo SAVINGS, COMMODITY MARKET RATIONING AND THE REAL RATE OF INTEREST IN CHINA by Andrew Feltenstein University of Kansas and World Bank David Lebow Princeton University Sweder van Wijnbergen World Bank, CEPR and NBER January 1987 The World Bank does not accept responsibility for the views expressed herein which are those of the author(s) and should not be attributed to the World Bank or to its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerning the legal status of any country, territory, city, area, or of its authorities, or concerning the delimitation of its boundaries, or national affiliation. Savings, Commodity Market Rationing and the Real Rate of Interest in China ABSTRACT This paper uses an intertemporal, disequilibrium framework to analyze the rapid increase in personal savings that has taken place in China since 1979. A theoretical model of savings behavior under rationing is developed, and a specification of a "virtual" price index is derived. The virtual price index is then used to estimate certain savings functions, and is found to explain the data better than official price indices. When savings are allowed to depend on real interest rates, defined in terms of the virtual price index, a negative and significant interest rate effect on consumption 1s foundo Using official pr1ces these results no longer hold. Andrew Feltenstein David Lebow Sweder van Wijnbergen University of Kansas Princeton University World Bank Lawrence, KS Princeton, NJ 08544 1818 H Street, N.W. (913) 864-3501 (609) 452-3999 Washington, D.C. 20433 (202) 473-1048 - 1 - SAVINGS, COMMODITY MARKET RATIONING AND THE REAL RATE OF INTEREST n4 CHINA by Andrew Feltenstein, David Lebow and Sweder van Wijnbergen 1. INTRODUCTION Developing adequate theories to describe household savings behavior has been a major element in modern economics. In this paper we attempt to develop such a theory for a highly non-market economy, and apply the resulting model to China, a country where private saving has undergone dramatic changes over the past thirty five years. China is of particular interest for a variety of reasons. First, because prior to the reforms carried out in 1979, it represented an extreme example of a repressed economy. Second, because it is now undergoing a series of economic reforms that are quite possibly the most far-reaching ever undertaken by a socialist country; one of the first indicators of the impact of these reforms has come in the dramatic increase 1n the volume of savings. Finally, because the analysis of private savings allows one to derive an empirical measure of the degree to which markets are repressed in China. Our results also refute the commonly stated notion that in planned economies such as China, consumers are subject to too many regime shifts to exhibit stable behavior characteristics. A recent article by Chow (1985) demonstrates that it 1s, indeed, We thank Morris Goldstein, Mohsin Khan, Francis Ng, Richard Portes and an anonymous referee for helpful comments. The views expressed in this article are those of the authors, a.nd do not necessarily represent the opinions of the World Bank. - 2 - possible to estimate stable behavioral relationships in the Chinese economy, in this case a version of the permanent income hypothesis. Chow's article, however, makes an assumption that we wish to avoid, namely, that official price data indeed reflect the costs that people perceive themselves as facing. This is an especially important assumption in a model that attempts to explain savings, since in an economy with significant price controls the official rate of jnflation may distort the relative cost of present and future consumption. Our general assertion is that the Chinese consumer finds himself in a world in which goods markets do not, at least temporarily, clear because of government price controls8 He has two possible views or the future; in one of these he expects markets to clear when prices eventually adjust, while in the other he expects markets to remain repressed indefinitely. In either of these circumstances the consumer's perception of the future purchasing power of his savings will be different than if he believed that he could satisfy his goods demands at existing official prices. We demonstrate that ignoring non-market clearing phenomena in China causes false qualitative conclusions to be drawn about savings behavior. We will show, for example, that use of the official rate of inflation series leads one to conclude that there has been a regime shift affecting household savings. Using the measure of repressed inflation that we shall develop, however, we find that there have been no regime shifts. We will also demonstrate that a number of neo-classical theories of savings are supported by our disequilibrium estimates and, perhaps more surprising, that household savings are responsive to real interest rates, if these rates are defined in terms of "virtual", or repressed, inflation rates. - 3 - There have been numerous studies of savings behavior in centrally planned economies (CPEs) ~/ with approaches to the problem falling essentially in one of two categories. In the first (e.g., Fortes and Winter, 1978; Fickersgill, 1976, 1980), there is no allowance made for the potential disequilibrium - the analysis assumes equilibrium and proceeds as if the CPEs were market oriented economies. This is clearly inappropriate 1n the presence of substantial repressed inflation, as observed quantities will not be on the consumption demand curve. The estimation is quite simple, however, and may yield reasonable results if the macroeconomic disequilibrium is not "too" pervasive. The second approach (e.g., Portes and Winter, 1980; Fodkaminer, 1982), involves explicit disequilibrium econometric techniques, ~/ which attempt to disentangle supply and demand schedules using a min-condition and discrete switching. The methodology is valid, although difficult to implement, and it requires specification of a supply equatipn in addition to demand. J/ This paper presents a third approach, that of "virtual prices."!!_/ The virtual price level is defined as that which would induce the observed 1/ Fortes (1986) provides a survey of this literature. 2/ The methodology is described in Fair and Jaffee (1972) and 1n Quandt (1982). 3/ A methodology which does not fit into either approach is that of Howard (1976}. See Portes and Winter (1980) for a discussion of the limitations of hi·s approach. 4/ The concept of virtual prices is introduced and analyzed extensively in Neary and Roberts (1980). Feltenstein and Farhadian (1986) uses virtual prices to explain money demand in China, and van Wijnbergen (1985) uses virtual prices to analyze the intertemporal consequences of commodity market rationing. - 4 - quantity of consumption (and savings) in the absence of price controls. By specifying the relationship between virtual and official prices, we may use the (unobserved) virtual prices to estimate a demand schedule as if we were in equilibrium. This methodology thus takes the potential disequilibrum into accou~~ while maintaining the simplicity and clarity of the first methodology above. The next section will give a brief overview of certain relevant aspects of recent Chinese economic history, while Section 3 develops a theoretical disequilibrum model suitable for our analysis. Section 4 presents estimation results for a number of standard specifications of savings behavior. Section 5 estimates a neo-classical specification of savings based on real interest rates, while Section 6 is a summary and conclus~on. 2. INSTITUTIONAL CHANGES AND THE BEHAVIOR OF HOUSEHOLD SAVINGS IN CHINA As indicated by Chart 1, household savings 1n China, after being a fairly stable fraction of national income for 25 years, ro~e sharply following the economic reforms instituted in 1979. These reforms are described in de Wulf (198Sa,b) and De Wulf and Goldsborough (1986), while their monetary implications are discussed in Feltenstein and Farhadian (1986), as well as 1n Chow (1986a) and Partes and Santorum (1986). We will summar1ze here those aspects of the Chinese economic system, both pre- and post- reform, that are relevant for our analysise Prior to 1979, the Chinese system did not view private sav1ngs as being a source of investment funds. Rather, lending for investment came from the budget and was interest free. Banks did offer low interest rates on - 5 - Char'.: 1 ---- ,..., ....... - \:C - I- \oj I - --'""~ """' ..J"-' r-"! ........ ''-'.........,_, ....-. ' ~.t~ ~ :-- ~= : :'-"' \.._; f"t.J:-1 Of SAVINGS - - - - -'. ••• t ..... ~:NE:':' :J£·:9: _ :"!2~ s~'-::s ..,0. ::1"::-::::::L· SJ.J - ..... ,..... ~ ....... .....i I f 45.0 I r- .::s.:J 40.0 ( 40.0 I I 35.0 (l I J- 35.:::1 30.0 30.0 I 25.0 i I I .t 25.0 I 20.0 I I / 20.0 I I 15.01 / 15.0 t / I I 10.0 I lO.Cl 5.0 -- S.Q 0.0 ·- -·--·- O.Cl -5.0 -s.o -10.0 -10.0 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 - 6 - deposits, and used these depostts to make short term loans to enterprises. Households, in turn, received wage payments in currency and although they were free to use their cash balances as they wished, the absence of financial assets forced them to distribute their income between current expenditure and savings deposits. The government, in turn, used a "cash plan" to attempt to determine the quantity of money held by households. It was felt that this quantity of money could have inflationary pressures if it grew too rapidly and was not channelled into savings. "If social purchasing power much exceeds commodity supplies, then part of the purchasing power will not be realized and will become excess currency circulation on the market which will influence the stability of the market and currency. Of course, if it is the purchasing power of the urban and rural population that is not realized then currency will accumulate in their hands, or in the form of savings deposits." ]:_/ At various periods, the Chinese authorities have experienced major failures 1n controlling monetary expansion, with immediat~ implications for savings behavior. During the period of the Great Leap Forward (1958-59) credit policy became, "Give as many loans as are needed whenever they are needed."~/ Currency in circulation thus rose by 140 percent between 1957 and 1961. The degree of repressed inflation rose steadily, and by 1961 could no longer be contained, with prices rising 16 percent, or about 8 times the previous average rate of inflation. Consumers responded in a neo-classical fashion by reducing their banks deposits by 50 percent between 1959 and 1/ Liu (1980), p. 169, quoted 1n Peebles (1983), p. 86. 2/ Li Chengrui (1981). - 7 - 1962. A similar situation occurred during the Cultural Revolution, particularly during 1966-69 and 1974-76. Since 1979, considerable autonomy has been granted to enterprises in wage determination; in addition) they are being permitted to retain profits, which they were previously required to remit to the government. The price system has not, however, been liberalized as rapidly as wages, and the result has been the rapid rise in savings. In addition, banks have been given greater autonomy with respect to interest rates, among other things. "Banks may make use of methods such as extending or refusing loans, •••• , raising or lowering :nterest rates, rewarding the good and penalizing the bad." ll As an attempt to control the rapid expense in liquidity, and fearing the growing volume of saving deposits was, "a tiger in a cage," the Chinese government in 1982 introduced the sale of Treasury bills to individuals, although the current volume of these sales is still quite low. We will now develop a model that allows us to predict ex ante the rate of inflation in the virtual pr.ice index corresponding to a particular level of market disequilibium. In addition, we will estimate the responsiveness of household savings to interest rates, shedding light on the effectiveness of one aspect of government macroeconomic policy. Finally, our estimates will indicate that Chinese consumers have not responded to market shortages by simply involuntarily saving excess wages, but that anticipation of future market conditions has also played a role. 1/ "Strive to Implement the 1985 Credit Plan," Zhongguo Jinrong (1985). - 8 - 3. A SIMPLE MODEL OF GOODS MARKET RATIONING AND SAVINGS BEHAVIOR The purpose of this section is to derive a simple equation describing private savings behavior in the presence of commodity market rationing. In the process we also discuss the measurement of wealth when market pr1ces do not represent the marginal cost of the goods concerned. We first present a simple theoretical analysis of goods market rationing, intertemporal trade and macroeconomic policy. The model is designed with empirical application in mind. We first present a market clearing version of the basic model, and then proceed to introduce commodity market rationing. 3.1 An Equilibrium Model of Price determination and Savings Behavior Consider a simple two period, one co~modity per period world. Since we intend to focus on savings behavior rather than the intertemporal allocation of production through investment, we will assume output to be fixed in each period, at level X in period one and at level x in period 2. 1/ In addition, we will suppose that that the economy is closed. Some of the output goes towards government expenditure. By assumption, the government is never rationed. G (g) is government expenditure in period one (two). We set g equal to zero for notational convenience. ~/ 1/ We will use upper case letters for first period variables and lower case letters for second period variables. 2/ Government expenditure plays no important role in our theoretical analysis. It is introduced only as a counterpart to positive net private savings. Alternatively, we could have used an open economy model, allowing for a nonzero current account. - 9 - Consumer behavior is suwmarized through an expenditure function E. E represents the minimum discounted value of current and future expenditure needed to achieve utility level U, given current and future prices: P (p) represents the current (future) pr1ce level. ~N is the discount factor: ~N =1/(l+i) where i is the nominal rate of interest. The derivatives of E with respect to any price give the Hicksian demand function for the corresponding good (cf Dixit and Norman (1980)). Therefore commodity market clearing requires: (2) 1 stands for aE/aP, and where E we have used the fact that the Hicksian demand function is homogenous of degree zero in prices. A similar equation holds for second period goods market clearing, but can be eliminated through Walras' law. Under the simplifying assumption that there are no first period taxes and no second period government expenditure, the government budget constraint equals: G = ~t (3) - 10 - where t 1s a second period non-distortionary tax and o the real discount factor, o = poN/P. Similarly, the private sector faces a budget constraint: x + ox - at = E (1, o; u) (4) The mechanics of intertemporal trade are very simple since the asset choice is limited. Consumers can either hoard commodities, an opportunity which we will have to ignore for lack of relevant data, or deposit any income not spent in time deposit accounts in a bank. We ignore investment, so the only demand for bank loans comes from the government: since it raises no revenue through taxes in period one, it has to fund all its current expenditure through domestic credit to the banking sector. We assume, realistically, that consumers hold no interest bearing government paper other than through the indirect channel we just sketched. We also assume, in accordance with the facts, that consumer loans are negligible. Banks face no reserve requirements and hold no reserves. Therefore the only component of the monetary base is currency held by the public. For simplicity, we assume 1n the theoretical analysis that the economy starts out with a stock of monetary base to which nothing is added over time. Consumers' demand for money 1s derived from a straightforward transaction technology: consumers need to accumulate money balances equal to the exact amount of any purchase before being able to make that purchase (a cash in advance constraint). Therefore money market equilibrium requires: - 11 - M (m) is the first (second) period money stock. For convenience we assume M = m, although nothing hinges on that assumption. The mechanics of the model can be described as follows. Through (5), the money stock determines the price level in each period. Commodity market clearing then requires a nominal interest rate that, in combination with the current and future prices from (5), implies a real rate that makes (2) hold. The commodity market clearing equation (2) in conjunction with the private and public sector budget constraints (3) and (4) imply that in equilibrium, private savings equal public dissaving. This of course reflects our assumptions of no capital accumulation and a closed economy. 3.2 Commodity Market Rationing, Virtual Prices and the Real Rate of Interest Consider now the possibility of rationing in goods markets. We will only introduce temporary (period one) rationing, but will comment on the intertemporal aspects of permanent rationing later. In China, both prices and interest rates are still to a large extent administratively determined. We will therefore assume that prices and monetary policy are set up in such a way that excess demand results: M/P = E1 (l,o; U) > X- G (6) or, when current pr1ces (or real interest rates) are "too" low, there is excess demand for current goods. We can now define a "virtual" real discount factor 8 (or virtual price P, where &= oNp/P), defined as the real discount factor at which consumers would willingly consume the volume of goods available to them at official prices: - 12 - X- G= E (1, 6; u) ( 7) 1 The notion that agents 1n a repressed economy act as if they face the virtual price level rather than the official price level may be understood 1n a definitional way and need not be taken literally. Alternatively, we can imagine that rationed consumers really do face certain costs, such as a cost of queuing, which raise the effective price they face above the official pr1ce, and p reflects these costs. Of course, virtual pr1ces are not observable; we will therefore derive an approximation formula that expresses P in terms of observable variables. Define, for convenience of notation, R = X-G as the volume of goods available to the public. Note that M/P - R = E (1, o; U) - E (1, 6; U) (8) 1 1 or M/(PR) - 1 = (E 1 (1, o: U) - E (1, 8; u))/R 1 (8a) A first order Taylor expansion of (8a) yields: M/(PR) - 1 ~ (8E /R)(o - 8)/8 12 = a (o - 8)/6 where a 1s the elasticity of real consumption with respect to the real dis~ount factor (one over one plus the real interest rate). This can be written as an equation in virtual and actual prices, for given nominal interest rates and future prices: - 13 - (P - P)/P ~ 1/cr (M/(PR) - 1) (9) ~ = oP/P gives the link between P and 6. By definition, In our empirical work we use a logarithmic approximation to (9): logP - logP ~ 1/cr log(M/(PR)) (10) Also, the transaction period is not necessarily equal to the calendar year unit over which our data are available. Assume the ratio between the two is fixed and equal to k. k equals the inverse of the income velocity of money. Equation (10) then becomes: log P - log P ~ 1/cr(log (M/PR) - log k) (lOa) which is the formula actually used in the next two sections. If we furthermore assume homothetic preferences, we can rewrite the demand function for current goods as: E (P, oNp; u) = E1 (1, 6; u) (11) 1 =c (~) E (1, o; u) where c[6] 1s a share term independent of utility. Now E (P, oNp; U) equals the discounted value of wealth at virtual prices, something we cannot measure (even if we could measure wealth at actual prices). We know, however, that the intertemporal budget constraint holds at actual, not at virtual prices, since actual transactions take place at posted prices: - 14 - PR + oNpr = PE 1 (P, oNp; u) + oNpE2 (P, oNp; u) = E (P, u) u) N oNp; + (P - P)E 1 (1, 0; or PR + o pr N =E (P, oNp; u) or R + (oNp/P) r = E (1, 6; u) (12) Combining this with (11) leads to the equation: R = c (6) (R + 6 r) (13a) or, in terms of net discounted future expenditure (savings plus discounted future income), (13b) (13a) and (13b) are the equations underlying the empirical analysis presented 1n the next two sections. If intertemporal preferences are Cobb-Douglas, (1 - c(6)) is a constant; section 4 proceeds from that assumption. In section S, we relax that assumption and estimate functional forms that allow for interest sensitive expenditure shares in wealth. One further issue cannot be addressed in our two period theoretical model, but needs to be resolved before (13a,b) can be tested ag~inst actual data: the 1ssue of how long rationing is expected to last. Clearly nobody expects rationing to last ad infinitum, hence our assumption of period two goods market clearing. Permanent rationing would have no effect on the real interest rate, since it would affect future prices as much as current prices; - 15 - the relative price of future goods in terms of current goods would therefore not be affected and neither would savings behavior. But in practical terms, how long is period one? The issue matters for our empirical measure of permanent income y = W/y where wealth W = R + ~ r, andy= 1/(1-o). p Consider then a multiperiod world. Assume for simplicity that real income in periods with rationing equals y, and 1n non-rationing periods y. If rationing is expected to last until period T, wealth equals: (14) This can be written as: 00 00 W= E o 1 y+ E o1 (y - y) (15) i=O T 00 = YY + oT E oi(y - y) 0 So if there is no rationing, or rationing 1s expected to last for a negligible period, W = yy; if rationing lasts forever, W= yy. In section 4, these two extremes are tested against each other. Note that even if T is small and hence W ~ yy, there may still be strong substitution effects; these operate through ~' not through W. - 16 - 4. VIRTUAL PRICES AND COMMON SAVINGS FUNCTIONS In this section, we estimate a number of common savings functions under the assumption that consumers respond to virtual prices, and show that this yields superior results to the same functions estimated using official pr1ces. The saving equations in this section are based on the assumption of Cobb-Douglas intertemporal preferences, so that savings will depend on wealth only, not on intertemporal substitution effects. 4.1 Specification of the Empirical Model The model consists of two equations: a virtual pr1ce level equation and a sav1ngs equation. The virtual pr1ce level is derived in equation (10): }:_/ ln P = lnP + a ln (M/PR) (16) where R is real retail sales, M is the stock of money and a = 1/a. The specification has a very natural "money chases goods" interpretation. If M and PR increase at the same rate, there is no additional divergence between the official and virtual price levels. When a =0 (the intertemporal substitution elasticity is infinite) the virtual price level collapses to the official price level. 1/ Feltenstein and Farhadian (1986) used a different specification for P. In our estimation, the variables P and M/PR were normalized to equal unity 1n the year 1953. This latter normalization corresponds to the inclusion of the constant kin equation (lOa). - 17 - We employ several common savings specifications, all involving real per capita disposable income as an explanatory variable for real per capita savings. The virtual price level is used to deflate nominal savings. The following specifications are tested: S/P = b0 + b Ip + b It 1 2 (17) (18) (19) S/P = b0 + b I 1 (20) where S is per capita nominal savings and I is per capita real disposable income (divided into permanent and transitory components IP and It). Equation (17) is a permanent income model, equ~tion (18) an asset adjustment model, equation (19) a general distributed lag model, and equation (20) an absolute income model. We define permanent income (IP) as a 3 year moving average of I, l and t~ansitory income (It) is defined by It = I - IP. It is not our intention to propose any one saving~ specification appropriate for China; rather, we test a number of common specifications to demonstr~te that deflating savings by the virtual price index is more reasonable than deflating by the official price index. 1/ Results will be presented for two definitions of IP: backward-looking, where IP = 1/3 (I + I_ 1 + I_ 2 ) and forward-looking, where IP = 1/3 (I+l + I + I_ 1 ). - 18 - Substituting for P from equation (16), equations (17) to (20) become S/P = (~ PR )a (b o + b IP + b2It) 1 (21) S/P = (~ PR )a (b 0 + b1(%J-1 + b2(I-I_1)) (22) S/P = (~R)a (bo + bli + b2 I_l + b3I-2) (23) S/P = (~ PR )a (b o + b I) 1 (24) Again, note that when a = o, these equations reduce to the usual equations based on the official price level. Hence our hypotheses are nested, with no rationing (a = 0) being a testable restrictione !/ 4.2 The Data Monetary data are taken from Byrd (1983) and from International Financial Statistics~ Income, sales and price data are taken from Chinese Statistical Yearbook (1984). Household savings is taken to be the change in urban and rural savings deposits over the year. As there is no disposable income series, we construct one using retail sales as a proxy for consumption, plus the savings variable. We employ two alternative definitions of real disposable income: one normalized by the official price index, the other by the virtual price index: 1/ The importance of allowing disequilibrium 1n the maintained hypothesis was stressed by Portes and Winter (1980). - 19 - r 1 =R + S/P r2 = R + S/P. Retail sales are measured in real units, so in both cases, reported nominal retail sales are normalized by the official pr1ce index to obtain R. Regarding the nominal savings component, however, it is less clear which is the more appropriate deflator, and we employ both. As argued in sectiou 3, the choice of deflator should relate to the length of time the rationing 1s expected to last. Specifically, if rationing is expected to cease after 1 period, r 1 is the appropriate real income definition, and if rationing 1s expected to last forever, r 2 is the more appropriate definition. We use a monetary aggregate coresponding to M2, equal to the sum of currency 1n circulation plus savings deposits. !/ We take the consumer price index, an average of retail and service price indices, as our official price index. 2 1 All data are listed in Appendix A. ll 4.3 Empirical Results Equations (21) to (24) were estimated by the nonlinear max1mum likelihood technique of Berndt, Hall, Hall and Hausman, on yearly data over the period 1955 to 1983. The model was similarly estimated under the constraint a = 0, that is, the official price level is used to deflate nominal savings rather than the virtual price level. The results for the case 1/ In appendix B, we present selected results using currency in circulation as our definition of money. 2/ Results using the retail price index are similar to these presented here. 3/ For further information on Chinese data, see Chow (1986b). - 20 - of one period expected rationing (income normalized by the official price level) are presented in Table 1. For all savings specifications, estimates for a are highly significant, as is clear from the t-statistics. Indeed a likelihood ratio test decisively rejects the hypothesis a = 0 in all specifications, as the 2 . . X stat1st1cs 8 range f rom 7 • 4 to 22 •• The .99 value of lS 6.63. This in itself is strong evidence in support of our virtual price level specification, since the models are nested and the estimates of a are quite stable across savings specifications. The hypothesis that the highest value of a (1.796) is equal to the lowest value (.729) cannot be rejected (the t-statistic on the difference is 1.8q). Further, in the official pr1ce model (i.e., when a is constrained to equal zero), with the exception of the asset adjustment specification, which contains a lagged dependent variable, the Durbin Watson statistic easily rejects the null hypothesis of zero first order serial correlation at a 1 percent confidence level. In the virtual price model, (when a is unconstrained) only the absolute income specification and the forward-looking permanent income specification display serially correlated errors; for the other specifications, zero first order serial correlation cannot be rejected at a 5 percent confidence level. The high degree of serial correlation in the offical price residuals leads one to suspect the existence of a spurious correlation and is, in addition to the highly significant estimate of a, sufficient grounds for rejecting the model. With regard to the parameter estimates, in all cases savings propensities out of income are much larger in the offici~l price model than in the virtual price model. For example, in the backward-looking permanent income specification, the savings propensities out of transitory and permanent - 21 - Table 1 Equation Period a b R2 ow 0 (x10- 3 ) bl b2 b3 LLF (a = 0) (H) a 1955.... i9d3 I .427 -.510 .009 .082 166.7 .9494 I .86 (2.99) (-.71) (.96} (2.97) 20.4 0 -5.767 .081 .209 156.5 .8973 0.87 {-7.27} (8.32) (4.40) b 1955-1982 1.346 -1 .519 0.23 .064 153.9 .8931 I .05 (2.62) (-1 .44) (I .64) (I .63) 11.8 0 -6.709 .096 .084 148.0 .8355 0.61 ( -8. 19) II .20) ( .82) c 1955-1983 I. 796 .103 .560 .034 166.0 .9468 2.32 (3.79) (I • 44) (4.04) (2.27) (-1 .84) 10.4 0 .017 .924 .120 160.8 .9237 2.07 ( .07) (I 2 .20) (3.62) (-Q.22) d 1955-1983 1.598 -.271 .044 -.002 -.036 168.0 .9536 I .86 (3.07) (-.48~ (2.33) (-.15) (-2.69) 22.8 0 (-5.719 .159 -.024 -.055 156.6 .8977 0.85 (-6.96) (4.23) (-.39) (-1.28) e 1955-1983 .729 -2.933 .044 157.4 .9039 0.85 (2. 18) (-2.21) (2.47) 7.4 0 -6.831 .098 153.7 .8754 0.64 (-9.68) (13.77) (a) S/P = b + b Ip + b It Permanent I ncome1 (Backward- Iook i ng) 0 1 2 (b) S/P = b0 + b1IP + b 2 It where Ip =~ (I+ 1 +I + I_ ) Permanent Income (Forward-looking> , 1 (c) S/P = b0 + b 1 (s/P)_ 1 2 + b (~- I_ ) Asset Adjustment 1 (d) S/P = b0 + b1I + b2I-1 + b3I-2 General Distributed Lag (e) S/P = bo + b1 I Current income - 22 - 1ncomes are, respectively, .082 and .009 in the virtual price model, and .209 and .081 in the official price model. In both models, as we would expect, the propensity to save out of transitory income is much higher than that out of p~rmanent income. However, only in the virtual price model do we fail to reject the theoretically attractive hypothesis that savings out of permanment 1ncome 1s zero. Next, we show that 1n the official pr1ce level model, the parameter estimates are unstable. We employ a d11mrny variable which takes a value of unity from 1979-1983, the period of liberalization, and check for a change in slope during this period. In the permanent income model, we check the slope of transitory 1ncome. In the asset adjustment model, we check the slope of the change in 1ncome. In the distributed lag and current income models, we check the slope of current income. Results are presented in Table 2. In the virtual price model, only the absolute income specification yields a dummy parameter which is significantly different from zero at 5 percent. In the official price model, however, in four of the five specifications the dummy is significant, indicating a change in the slope during the liberalization period. Further, the inclusion of these slope dummies brings the parameters in the official price specifications closer to those estimated in the virtual price model. In the backward-looking permanent income specification, for example, the coefficient on savings out of transitory income declines from .209 to .148, whereas in the virtual price model the coefficient was estimated to be .082. By no means does adjustment for the regime change eliminate the problems of the official price model; serial correlation is not eliminated and, in two of the specifications, the estimate of alpha is still significant. The result that the virtual price - 23 - Table 2 Equation Period a b bl Dummy LLF R2 DW 0 (xl0- 3 ) b2 b3 (H) a 1955-1983 1.234 -.554 .010 .075 .039 168.5 .9552 I. 79 (2.65) (-.75) (I .03) (3. 10) (1.29) 0 -4.183 .061 .148 .191 159.9 .9188 0.95 (-4.41) (5.23) (3.01) (2.57) b 1955-1982 1.647 -1.076 .017 .034 .149 155.9 .9077 1.00 (2.71) (-1 .20) ( 1.38) ( .99) (1.57) 0 -6.645 .095 .066 .364 148.3 .8391 0.56 (-7.99) (10.87) ( .63) (0.74) c 1955-1983 .989 .144 .588 .040 .061 169.4 .9579 2.25 ( I •63) ( I • 39) (4.31) (2.08) (1.26) (-I .28) 0 .149 .753 .067 .181 168.0 .9536 2.15 ( .81) ( 10.22) (2.28) (4.01) (-.45) d 1955-1983 .925 -.151 .056 -.008 -.042 .009 171 .8 .9644 1.91 (1.90) (-.21) (.2. 75) (-.40) (-2. 77) (I .45) 0 - -1 .655 0.95 -.013 -.053 .032 167.6 .9521 1.61 (-1 .71) (3.27) (-.31) (-1. 78) (5.22) e 1955-1983 .249 _, .918 .033 .024 163.4 .9364 I .13 ( .80) (-1 .62) (:2. 11) (2.23) 0 -2.490 .042 .034 163.0 .9345 I. 16 (-2.40) (3.30} (4.84) (a) S/P = b0 + b IP + b2 It + b d I t DUM where I p = J 1 (I + r_l + I_2) 1 2 (b) S/P = b0 + bliP+ b2It+ b2d It DUM 1 (I where I p = - 1 + I + I_l) 3 +1 {c) S/P = b 0 + b1 (s/P)_ 1 + b2 (I- I_ ) + b d (I - I_ ) DUM 1 2 1 (d) S/P = b 0 + bli + b2I_ 1 + b3r_ + bld I DUM 2 (e) S/P = b0 + bli + bld I DUM - 24 - model is stable over the same period ~hat the official price model indicates a reg1me shift is further evidence in favor of the virtual price model. We now turn to the length of time that rationing is expected to continue. The above results were presented for the case in which rationing is expected to last for a negligible period of time. We similarly estimated the model under the assumption that rationing is expected to last forever: that is, nominal income is deflated by virtual pr1ces. Qualitative results were similar, and we present only the values of the respective log likelihood functions in Table 3. Table 3. Log Likelihood Values Under Temporary and Permanent Rationing Equation Temporary Rationing Permanent Rationing Permanent Income (Backward-Looking) 166.7 164.0 Permanent Income (Forward-Looking) 153.9 152.7 Asset Adjustment 166.0 163.0 Distributed Lag 168.0 165.3 Current Income 157.4 156 .. 6 - 25 - As the two income variables are highly collinear, it is not possible to imbed these in the same model and estimate the expected duration of rationing explicitly. 1/ Nevertheless, in all cases the temporary rationing model leads to a higher likelihood value than does the permanent rationing model, which gives reason to believe that rationing was indeed expected to be temporary. A final issue concerns our assumption of constant velocity. In appendix B we test for interest sensitivity of the velocity factor k within the context of the model of this section. Interest sensitivity turns out to be insignificant both when we use M2 and when we use a more narrow concept, currency in circulation. This 1s perhaps not surprising given the absence of alternative assets in China. It maybe of interest to exam1ne the ratio of virtual to official price indices over time. Chart II therefore plots p/p, using a as estimated in table 1, equation (a). We notice that there 1s a gradual increase 1n this measure of repressed inflation until 1978, when the economic liberalization began. From this point, p/p rises rapidly, as one might expect. Thus the wedge between virtual and official 190% in 1979, rose to about 600% in 1984. 1/ Ideally one would like to allow consumers to update their expectation on duration of rationing each period, incorporating the new information about rationing in that period. Data availability precludes estimation of such learning models. - 26 - 5. SAVINGS AND THE REAL RATE OF INTEREST In this section we move beyond the specifications of section 4 and allow savings to depend on real interest rates in addition to wealth& The real interest rate (p) is given by 1 + P = (1 + i)/(1 + rr) = (1 + i) P/p = 1/o 1n the market clearing model, or by 1 + p = (1 + i)P/p = 1/& (25) in the rationing model, where variables are defined as in section 3. Rationing this period which is expected to stop next period implies a lower "virtual" inflation rate (as current virtual prices are higher than current official prices) and hence a higher "virtual" real interest rate than would be the case if the current official price level were market clearing. This higher real interest rate induces people to save more in the rationing regime than in the market clearing regime for given values of the official price level and interest rate. Our empirical specification is derived from equation (13a) in section 2. 11 Taking a log-linear approximation yields: 1/ We use consumption rather than savings in this section as we wish to use the logarithmic specification and the flow of savings was negative for part of the sample. - 27 - with I a proxy for permanent 1ncome or, equivalently, wealth. Substituting from equations (16) and (25) yields Finally, allowing for differing responses to permanent and transitory income, obtain ln R (26) We estimate equation (26) using the same two permanent 1ncome specifications as in section 4 above. ll As current disposable income is correlated with current consumption, we instrument for this variable using two stage least squares. 3/ We similarly instrument for the unobserved future price. Instruments include all independent variables, a lagged dependent ·variable, and three additional variables thought to be correlated with income: government expenditure, fixed investment, and GNP in Japan (Japan being China's largest trading partner). Results are presented in Table 4. 1/ We present results only for the backward-looking permanent income specification. Results for the forward-looking specification are similar. 2/ Similarly, we technically should have instrumented for disposable income in section 4 above. However. as our equations in that section are highly nonlinear, in parameters as well as variables, we were not able to carry this out. Further, in this section omitting the instruments leads to only a negligible change in the estimated parameters, indicating that the omission in section 4 would not be expected to affect the qualitative conclusions. - 28 - Table 4: a b 0 bl b2 l-b3 LLF R2 x2 3 * a) .323 .0416 -.207 •733 0 97.20 .9991 6.83 (5.72) (6 .01) (-4.67) (23.42) b) .172 -.0640 -.193 .771 .033 99.05 .9992 4.41 (I .62) (-.98) (-4.45) (20.22) (I .62) c) 0 -.0108 -.005 .730 0 77.19 .9978 11.92 (-I. 98) (-.07} ( 12.33) d) I .57 .0174 -.040 .759 0 87.55 .9983 13.20 (.51) (2.71) (-.49) ( 16.58) Period: 1955-1983 *This tests the hypothesis that the residuals are white noise to three autocorrelation lags. x2 = 7.81 a) b3 =I 3, .95 x2 = 11.34 b) no restrictions 3, .99 c) b3 = 1· a = 0 I d) b 3 =I; i =0 t ln R = b + b 1n((l + i)P/P+l) + bl a ln(M/PR) + b .!__ + b31n rP 0 1 2 Pr - 29 - In row a we make the theoretically plausible assumption that the elasticity of consumption with respect te permanent income is unity. As we see from row b, this assumption is justified - we cannot reject a unitary coefficient on permanent income. We see that the estimate for a 1n row a 1s highly significant, although smaller than in section 4. The most striking result, however, is that the estimate of b 1 is negative and significant. That is, consumption declines (savings increases) in response to an increase in real interest rates. Given the difficulty researchers have had in finding a significant savings response to real interest rates 1n developing countries (see, e.g., Giovannini, 1985), or, for that matter, 1n developed countries, we take this result to be of some interest. As in section 4, when a is constrained to equal zero the errors di~~ serial correlation and, 1n addition, the significance of the real interest rate disappears. Again, the virtual price model far out-performs the official price model. We also estimate the model omitting the nominal interest rate - that is, b 1 now represents the consumption response to the inverse of the expected inflation rate. The results are presented in row d. In this equation b 1 is seen to be insignificant, indicating that the nominal interest rate is itdeed important in explaining consumption behavior. It might be thought that the correlation between savings and real interest rates need not represent causality. That is, perhaps the government adjusts nominal interest rates to accommodate observed savings patterns. In the context of our model, this would indicate that we have omitted an interest rate determination equation, of which savings would be an argument. We test this possibility by estimating equation (26) while instrumenting for the nominal interest rate. The U.S. T-Bill rate is added to the list of - 30 - instruments. This estimation y:elds results (presented in appendix B) very similar to those of Table 4; in particultlr, the estimate of b is still 1 negative and significant. This would indicate that real interest rates really do influence savings, and not the converse. 6. SUMMARY AND CONCLUSIONS China has seen a rapid increase in personal savings since the economic liberalization began 1979. We have attempted to explain this phenomenon in an intertemporal disequilibrium framework, using a virtual price technique. The virtual price level is defined as that price level which would induce the observed level of consumption in the absence of price controls. We first set out a simple theoretical model of sav1ngs behavior under rationing which, when combined with a cash in advance constraint, leads to a simple virtual price specification which links the virtual price to observable variables. We then use the virtual price level to estimate a number of common savings functions. We find that normalizing savings by virtual prices explains savings behavior far better than does normalizing by the official pr1ce ser1es. When official prices are used, that is, when equilibrium is imposed, the equations are found to be unstable and to indicate a regime shift during the liberalization. Allowing for disequilibrium by employing virtual pr1ces eliminates this problem. We next provide a test which lends support to the theory that rationing was perceived to be temporary, suggesting that intertemporal phenomena do play an important role in determining savings behavior. We therefore proceed to include real interest rates as a determinant of - 31 - sav1ngs. Using virtual pr1ces, we find a negative and significant real interest rate effect on consumption which, despite its intuitive appeal, has only rarely been empirically detected. As before, when we eliminate the virtual prices and assume equilibrium, the results deteriorate and we no longer detect a consumption response to real interest rates. This interest rate response indicates that savings does indeed respond to future market conditions, and is not simply an involuntary residual. Finally, we find that the nominal interest rate has considerable importance in influencing savings behavior, so that macroeconomic policy in China may be more effective than previously thought. We see two primary directions for future reaearch. First, the model should be extended to include open economy effects, as the balance of payments represents an alternative to savings as an outlet for excess monetary expansion. Finally, the relationship of the virtual price estimation technique to more traditional disequilibrium approaches could usefully be explored. - 32 - References Byrd, William A., 1983, China's Financial System, (Westview Press). Chinese Statisticsl Yearbook, 1984, (Beijing). Chow, Gregory, 1985, "A Model of Chinese National Income Determination," Journal of Political Economy, 93(4), 782-92. Chow, Gregory, 1986a, "Money and Price Level Determination in China," Econometric Research Program Research Monogram No. 327, Princeton University. Chow, Gregory, 1986b, "Chinese Statistics," The American Statistician, 40(3) pp. 191-96. de Wulf, Luc, 1985a, "Economic Reform 1n China," Finance and Development, December, 19-22. de Wulf, Luc, 1985b, "Financial Reform in China," Finance and Development, March, 8-11. de Wulf, Luc, and David Goldsborough, 1986, "The Evolving Role of Monetary Policy in China," IMF Staff Papers, 33~ 209-242. Dixit, A. K. and V. Norman, 1980. Theory of International Trade (Cambridge University Press). Fair, R. C. and D. M. Jaffee, 1972. "Methods of Estimation for Markets 1n Disequilibrium", Econometrica, 40, 497-514. Feltenstein, A., and z. Farhadian, 1986, "Fiscal P~licy, Monetary Targets and the Price Level in a Centrally Planned Economy; An Application to the Case of China", Journal ?f Money, Credit and Banking, forthcoming. Giovannini, A., 1985, "Savings and the Real Interest Rate in LDCs," Journal of Development Economics, 18, 197-217. Howard, D. H., 1976. "The Disequilibrium Model in a Controlled Economy: An Empirical Test of the Barre-Grossman Model," American Economic Review, 66(5) 871-79. Li Chengrui, 1981, "The Balance of Finance and Credit," Ji!lgji Yanjiu (Economic Research), No. 3, 3-12. Liu, Hongru, 1980, Problems of Socialist Money and Banking (Peking: China · Finance and Economics Publishing House). Neary, J. P., and K. W. S. Roberts, 1980. "The Theory of Household Behavior under Rationing,'' European Economic Review, 13, 25-42. - 33 - Peebles, Gavin, 1983, "Inflation, Money and Banking in China: In Support of the Purchasing Power Approach," ACES BU;lletin, 25(2), 81-103. Pickersgill, J., 1976, "Soviet Household Saving Behavior", Review of Economics and Statistics", 18, 139-47. Pickersgill, J., 1980. "Recent Evidence on Soviet Household Saving Behavior,;( Review of Economics and Statistics, 62, 628-33. Podkaminer, L. 1982, "Estimates of the Disequilibria in Poland's Consumer Markets 1965-1978," Review of Economics and Statistics, 64, 423-31. Partes, R., 1986, "The Theory and Measurement of Macroeconomic Disequilibrium in Centrally Planned Economics," Centre for Economic Policy Research Discussion Paper No. 91. Partes, R., and D. Winter, 1978. "The Demand for Money and for Consumption Goods in Centrally Planned Economies," Review of Economics a~1d Statistics, 60, 8-18. Partes, R., and D. Winter, 1980. "Disequilibrum Estimates for Consumption Goods Markets in Centrally Planned Economics," Review of Economics Studies, 47, 137-159. Partes, R. and A. Santorum, 1986, "Money and the Consumption Goods Market 1n China," unpublished mimeo, University of London. Quandt, R. 1982, "Econometric Disequilibrium Models," Econometric Review, 1, 1-63. van Wijnbergen, Sweder, 1985, "Oil Price Shocks, Unemployment, Investment and the Current Account: An Intertemporal Disequilibrium Analysis," Review of Economic Studies, 52(4), 627-45. Zhongguo, Jinrong (Chinese Finance), 1.985, People's Bank of China, January. Appendix A AI I series are in billions of Yuan unless noted. ( 1) (2) (3) (4) (5) (6) {7) (8) (9) { 10) { 11) Investment in Real GNP Currency in Savings Population Interest Retai I fixed expen- Japan (billion circulation deposits Money Savings CPl (mi II ions) <%> sales diture assets Gover~ment 1980 yen) 1953 3.96 1.23 5.19 0.37 121 .4 587.96 0.1539 32.88 29077 1954 4.11 1.59 5.70 0.36 123.1 602.66 o. 1539 35.61 30776 1955 4.01 1.99 6.00 0.40 123.5 614.65 o. 1539 36.40 10.52 26.93 33496 1956 5.70 2.67 8.37 0.68 123.4 628.28 0.1539 42.40 16.08 30.57 35937 1957 5.27 3.52 8.79 0.85 126.6 646.53 o. 1539 44.16 15.12 30.42 38614 1958 6.75 5.52 12.27 2.00 125.2 659.94 0.1355 48.12 27.91 40.94 40781 w 1959 7.49 6.83 14.32 1.31 125.6 672.07 0.0560 55.65 36.80 55.29 44406 +:-- 1960 9.60 6.63 16.23 -0.20 128.8 662.06 0.0629 59.24 41.66 65.41 50327 1961 12.55 5.54 18.09 -1.09 149.6 658.59 0.0629 53.77 15.61 36 .. 70 57612 1962 10.65 4.11 14.76 -1.43 155.3 672.95 0.0629 54.37 8.73 30.53 61657 1963 8.97 4.57 13.54 0.46 146.1 691.72 0.0629 54 .. 48 11.67 33.96 68109 1964 8.01 5.55 13.56 0.98 140.7 704.99 0.0629 57.27 16.59 39.90 77060 1965 9.07 6.52 15.59 0.97 139.0 725.38 0.0497 59.01 21.69 46.63 68992 1966 10.81 7.23 18.04 0.71 137.3 745.42 0.0403 63.28 25.48 54.16 76325 1967 12.18 7.39 \9.57 o. \6 136.4 763.68 0.0403 67.91 18.77 44.19 84567 1968 13.40 7.83 21.23 0.44 136.5 785.34 0.0403 64.92 15.16 35.98 95319 1969 13.71 7.59 21.30 -0.24 137.8 806.71 0.0403 69.82 24.69 52.59 107035 1970 12.34 7.95 20.29 0.36 137.8 829.92 0.0403 72.88 36.81 64.94 117591 1971 13.61 9.03 22.64 1.08 137.7 852.29 0.0385 77.69 41.73 73.22 123104 1972 15.08 10.52 25.60 1.49 137.9 871.77 0.0329 85.35 41.28 76.64 134147 1973 16.61 12.12 28.73 1.60 138.0 892.11 0.0329 91.77 43.81 80.93 145977 1974 17.61 13.65 31.26 1.53 138.9 908.59 0.0329 96.74 46.32 79.08 144167 Appendix A (continued) ( 1) (2) (3) (4) (5) (6) (7) (8) (9) ( 10) ( 11) Currency in Savings Investment in Real GNP Population Interest Retai I fixed expen- circulation deposits Money Savings CPI Japan (billion (millions) <%> sales diture assets Government 1980 yen) 1975 18.25 14.96 33.21 1 .31 139.5 924.20 0.0329 104.64 1976 20.36 15.91 36.27 54.49 82.09 147655 0.95 139.9 937. 17 0.0329 109.90 1977 19.51 18.16 37.67 52.39 80.62 155502 2.25 143.7 949.74 0.0329 1978 21.20 117.43 54.83 84.35 21.06 42.26 2.90 144.7 962.59 163752 1979 26.77 0.0329 126.49 66.87 111.10 28.10 54.87 7.04 147.4 975.42 172133 1980 34.62 0.0385 147.60 69.94 127.39 39.95 74.57 11.85 158.5 987.05 181137 1981 0.0516 179.40 74.59 121.27 39.63 52.37 92.00 12.42 162.5 189787 1000.72 0.0554 200.25 66.75 1982 43.91 67.54 111.45 15.17 111.50 197462 165.8 1015.41 0.0582 218. 15 1983 52.98 83.75 136.73 84.53 115.33 204059 16.21 169.1 1024.95 0.0591 242.61 95.20 129.25 210903 w IJl (1) Source: International Financial Statistics (IFS) and Byrd, p. 138. (2) Source: I FS and Byrd, p. 157. (3) Currency in circulation plus savings deposits. (4) Change in savings deposits. (5) 1950 = 100. Source: IF$ and Chinese Statistical Yearbook (CSY), p. 425. (6) Source: CSY, p. 81. (7) Annual rate on one-year term individuals bank deposits. Source: Byrd, p. 154. (8) Source: CSY, p. 345. (9) Source: CSY, p. 301. (10) Source: CSY, p. 417. (11) Source: IFS. - 36 - Appendix B B.l Currency Rather than M2 as Definition of M This appendix contains additional results referred to in the text. We first present selected results using an alternative definition of money, currency in circulation. Table Bl presents the backward-looking permanent income equation of Section 4. Table B2 presents the corresponding equation (including interest rates) of Section 5. Table Bl 1 S/P = b + b Ip + b It where Ip - 3 (I + I_ + I_ ) 0 1 2 1 2 a. bo bl b2 LLF a2 DW 1.590 -2.396 .035 .095 160.1 .9202 1.27 (2.06) (-1.83) (2.03) (2.63) 0 -5.766 .081 .290 166.5 .8973 0.87 (-7.27) (8.31) (4.40) Period: 1955-1983 - 37 - Table B2 t ln R = b0 + b11n((l + i)P/P+l) + bl" ln (M/PR) + b2 ~p + b3 ln rP where Ip= !(I + I + I ) 3 -1 -2 bo b1 b2 l-b3 LLF R2 x2 .L 3 .455 .0358 -.203 .592 0 85~03 .9982 7.91 (3.70) (3.08) (-2.79) (lOoSft.) 0 -Q0075 -.037 .685 0 76.85 .9978 8.55 (-1.28) (-.51) (10.34) Period: 1955-1983 We see that results are similar to those using the broader definition of money. In the Cobb-Douglas permanent income equation of Table Bl, the estimate of a 1s significant and the Durbin-Watson statistic is larger than when a is constrained. Similarly, in the interest rate model of 1able B2, a 1s highly significant, and b 1 is negative and significant, confirming the interest sensitivity of savings. As with the model in Table Bl, however, the inclusion of virtual prices (allowing a to differ from zero) does not eliminate the problems of serial correlation as readily as it does in the text where we used the broader monetary aggregate. Nevertheless, the basic results seem robust to the choice of monetary aggregate. B.2 Interest Sensitive Velocitl We now allow the velocity term (1/k) from equation (lOa) to depend on interest rates, rather than forcing it to be a constant. We specify - 38 - ln - = k0 - k 1 ln (1+i) where k 0 which gives ln P = ln P + a ln M (PR) (1+~ )k ] [PR M 0 1+10 1 (Bl) (B1) corresponds to the formula used in the text for k 1 = 0. The normalization described in footnote 1 of p. 16 corresponds to the (PR/M) 0 term. The subscript "o" refers to year 1953. A positive value for k indicates that velocity increases with the interest rate. We use this equation to estimate the backward looking permanent income equation, employing currency 1n circulation as our money definition as in section Bl of this appendix. As we have assumed that there exist no alternative assets to savings, we would not expect a positive interest elasticity of velocity when we use the broader monetary aggregate as 1n the text. - 39 - Table 83 S/P = b0 + b Ip + b It where rP 1 2 =! 3 (I + I -1 + I_ ) 2 ln P= ln p + a l n [M (PR) (l+1.· )kl] PR M: 0 l+1 0 kl a bo bl b2 LLF R2 ow 11.76 1.098 -9.243 .143 .378 165.6 .9461 1.87 (1.71) ( 1 •98) ( -1 •94) (2.06) (2.60) 0 1.590 -2.396 .035 0.95 160.1 .9202 1.27 (2.06) ( -1 •83) (2.03) (2.63) Period: 1955-1983. We see that the estimate of k 1 is positive but not significant. The estimate of a is smaller than in the constant velocity (k 1 = 0) case, but remains significant. The insignificance of k 1 gives support to our constant velocity assumption. B.3 Instrumental Variables Applied to Interest Rates We now present results for the interest rate model in which we instrument for nominal interest rates, and add the U.S. T-bill rate to the instrument list. Results are very similar to those of Table 4 in the text. - 40 - Table B4 t ln R = b0 + b1 ln((l + i)P/P+l) + bl a ln (M/PR) + b ~p + b ln rP 2 3 ct bo bl b2 1-b 3 LLF R2 x2 3 .343 .040 -.190 .739 0 97.16 .9991 8.66 (4.99) (5.48) (-4.03) (23.15) 0 -.009 -.011 .696 0 77.03 .9977 8.54 (-1.51) (-.15) (9.79) - 41 - Appendix C How Does the Model Perform on US Data? 1/ In the paper, we present a model based on the assumption of commodity market rationing. The empirical work reported for China strongly supported that assumption. Of course, there is a strong presumption that there is commodity market rationing in China. One's confidence in the approach employed would obviously increase if the same tests, when applied to the USA, where widespread commodity market rationing is implausible, would in fact reject the assumption of commodity market rationing. We perform two tests. In the first test, we use exactly the same data definitions as we used in the main body of the text for China. However, the assumption that increases in savings deposits capture a substantial part of private sav1ngs, while reasonable for China, clearly makes less sense for a country like the USA. Hence we present a second test where we use the difference between personal disposable income and private consumption as our measure of private savingss~/ The results of both tests are reported below. In this section we use exactly the same data definitions as used in the China regressions; we run the US equivalents of all the equations reported in Table 1 for China. 1/ The tests performed in this appendix were suggested to us by an anonymous referee. 2/ The data on personal disposable income and private consumption are taken from the Economic Report of the President 1985. All other U.S. data are from IFS. - 42 - Table C1 Equation Period Cl bo b1 b2 b3 LLF R2 ow (H) (d) 1959-1984 -1.10 -0.00 0.36 1.42 227.5 0.85 1.55 (2.07) ( 1.27) (2.10) (4. 15) (b) 1959-1983 0.03 -0.00 0.18 1.10 214.9 0.80 1.32 ( .03) (0.67) (1.31) (3.19) (c) 1959-1984 0.10 o.oo 0.58 0.69 229.7 0.87 1.47 (0.17} (2.59) (6.05) (3.78) ( 1.20) (d) 1959-1984 -1.10 -o.oo 1.10 -.41 -0.29 227.8 0.85 1.39 ( 1 .84) (1.22) (3.81) (3.53) (2.62) (e) 1959-1984 -3.34 -0.00 2.42 215.1 0.61 1.38 (4.31) (2.30) (2.44) where IP = l3 (I + I -1 + I -2 ) The results are unambiguous: every single equation either rejects the hypothesis of a different from zero, or, where it does not do so, a has the wrong sign. The model therefore clearly rejects the rationing hypothesis for the US, at least conditional on the data definitions used. The second set of regressions, reported below, tests the same hypothesis using a better measure of private savings. - 43 - Table C2 Equation Period a bo bl b2 b3 LLF R2 ow (H) (a) 1959-1984 .32 -.23 .091 .097 -119.3 0.79 0.93 (0.58) (0.60) (2.64) (0.61) (b) 1959-1983 .53 -.20 .082 .44 -112.9 0.82 0.85 ( 1• 13) (0.67) (3.07) (2. 13) (c) 1959-1984 -0.66 0.26 0.90 0.33 -113.8 0.86 2.32 ( 1.57) (0.94) (12.7) (2.42) (-1.01) (d) 1959-1984 0.36 ~0.23 0.035 0.16 -0.10 -118.6 0.80 1.19 (0.65) (0.63) (0.31) ( 1.03) (0.91) (e) 1959-1984 0.33 -0.22 0.090 -119.3 0.79 0.94 (0.69) (0.67) (2.97) (a) s/P = b0 + bl rP + b It + b d I t DUM where Ip 1 -3 (I + I_ + I_ ) 2 2 1 2 t p (b) S/P = b0 + bliP+ b It+ b d I DUM 2 2 where I = l3 (I +1 + I + I -1 ) (c) S/P = b0 + b 1 (s/P)_1 + b2 (I - I_ 1 ) + b d (I - I_ ) DUM 2 1 (d) S/P = b0 + bli + b2I-1 + b3I-2 + bld I DUM (e) S/P = b0 + bli + bld I DUM These results are clear also: again a is insignificant, or, where significant, has the wrong sign. These results therefore clearly reject the assumption of commodity market rationing in the US. Of course this is an implausible assumption for the US, hence this outcome should increase the confidence in the approach developed and employed in this paper. Some Recent DRD Discussion Papers 225. The Value-Added Tax: Revenue Inflation and the Foreign Trade Balance, by A.A. Tait. 226. VNr, Income Distribution, and Tax Incidence, by C.E. McLure. 227. The Value-Added Tax in the Cote d'Ivoire, by B. Heian. 228. Development of a Value Added Tax in Colombia, by G. Perry, A.L. 0. de Triana Hejia. 229. Strike and Lock-out Threats and Fiscal Policy, by A. Lindbeck and D. Snower. 230. An Intercountry Analysis of Employment and Returns to Labor in Agriculture, by Y. Kislev and P. Siegel. 231. Economic Reform, External Shocks and the Labor Market: Chile 1974-1983, by A.C. Edwards. 232. Labor Markets and the Choice of Technology in the Open Developing Economy, by J. Aizenman. 233. Exchange Rates and Domestic Inflation: A Study of Price/Wage Inflation in Eight Latin American Countries, 1946-85, by. S. Jorgensen and M. Paldam. 234. Terms of Trade, Exchange Rates and Labor Harkets Adjustment in Developing Countries, by S. Edwards. 235. The Argentinian Experience with the Value Added Tax, by O.H. Schenone. 2~6. Agricultural Settlement with Alternative Objectives and Constraints, by E. Feinerman and Y. Kislev. 237. Tax Reforms, Welfare, and Effective Tax Rates, by W. R. Thirsk. 238. Lessons from Value-Added Taxation for Developing Countries, by ~1. Gillis, C. Shoup and G.P. Sicat. 239. Adjustments to Policy Changes: The Case of Korea, 1960-1985, by R. Richardson and B.W. Kim. 240. Adopting a Value-Added Tax in a Developing Country, by. G.P. Sicat. 241. External Shocks and Policy Reforms in the Southern Cone: A Reassessment, by V. Corbo and J. de Melo. 242. Adjustment with a Fixed Exchange Rate: Cameroon, Cote d'Ivoire and Senegal, by S. Devarajan and J. de Melo.