I. Review of Previous Studies of Household Savings in China

Like many other economic subjects, modern theories and models of saving and consumption originated in studies of saving behavior in the Western, developed, market economies. Among well-known models of saving in this context are the Keynesian absolute-income hypothesis; Duesenberry’s relative-income hypothesis; Friedman’s permanent-income hypothesis: the Modigliani-Brumberg life-cycle hypothesis, and the asset-adjustment models associated with, among others, Houthak-ker and Taylor and Leff and Sato. Later on, these models have been applied to the developing market economies, as seen in the surveys by Mikesell and Zinser (1973) and Snyder (1974). More recently, some studies of the exceptionally high savings rate in Japan have focused on aspects not included in traditional theories. In Horioka (1985) the role of target savings for housing and education was singled out, while Haya-shi (1986) drew special attention to the role of bequests.

Since the late 1970s, there have been quite a few studies of saving behavior in centrally planned economies, mainly of Eastern European countries and the U.S.S.R. One approach is to apply the above-cited models directly to those economies (for example, Pickersgill (1976, 1980)), ignoring the potential disequilibrium between the intention and realization of current household consumption and saving, which is believed by many authors to persist in such economies. Another approach takes this potential disequilibrium directly into account (for example, Portes and Winter (1980)).

Empirical studies on household saving behavior in China—a developing, centrally planned economy—did not start until 1982. Four studies prior to the present paper are noteworthy: De Wulf and Goldstein (1983, 1985); Naughton (1986); Feltenstein, Lebow, and van Wijnbergen (1986); and Armitage (1986).

The studies by De Wulf and Goldstein and Naughton shared common methods in estimating savings functions for China by applying time-series data to the traditional linear models cited above. Naughton (1986) used aggregate nominal data, whereas De Wulf and Goldstein (1983) applied per capita, real data, and they further separated the rural sector from the urban sector in their later paper (1985). Both studies found very low Durbin-Watson (DW) statistics in the estimation, indicating mis-specification, and that the estimated marginal propensity to save (MPS) varies, depending on the time period selected. In neither study, however, was the model respecified for further testing.

To avoid the misspecification problems arising with time-series data, Armitage (1986) instead used rural and urban household sample survey data of recent years to estimate separately the savings function in each sector. Constrained by the availability of data (for the rural sector, 1982–84 data from 28 provinces; for the urban sector, 1983 data from 29 cities), Armitage was only able to estimate a Keynesian savings model for each year from 1982 through 1984 for the rural sector and for 1983 for the urban sector, and Friedman’s permanent-income model for the rural sector in 1984. She found a substantial difference in household saving behavior between the rural and urban sectors, a result that is consistent with the common observation. Her estimation favored the permanent-income model over the absolute-income model for the rural sector in 1984, which is the only year for which the comparison can be made. Although the separation of the rural and urban sectors is justifiable, the results may not be reliable, especially because the urban sector data covered only one year.

Stressing the potential disequilibrium in the Chinese economy, Feltenstein, Lebow, and van Wijnbergen (1986) approached the problem quite differently. Instead of using the official price index as a deflator, they adopted what they called the “virtual price,” defined as that price level which would induce the observed quantity of consumption and savings in the absence of rationing. The approximation of the virtual price, p, in terms of observables was defined as p/P = (M/PR)^a, where P is the official price index, M is the money supply, PR is total retail sales, and a is a parameter, a constant. By using P instead of P as a deflator (where money supply is defined as M2), they found that only two out of five specifications give very low DW statistics and, for the permanent-income model, that the DW increased from 0.8 to 1.86; and that, by defining “real virtual interest rate” as 1 + r = (1 + i) x p/P ₊₁ where i is the official nominal interest rate, they were able to estimate a significant value of the elasticity of consumption with respect to the real virtual interest rate, on the order of about -0.20. They concluded that there was no regime shift in household saving behavior, as long as potential disequilibrium is allowed. The implication of their model is that the higher savings in recent years reflect the excessive monetary expansion and the increased degree of repressed inflation in the economy, and hence represent forced saving.

Although the theoretical derivation of the Feltenstein-Lebow-van Wijnbergen model itself is interesting, the selection and interpretation of the data in the time period remain a problem. First, their results are sensitive to the monetary aggregate selected: when they used Ml (defined as total cash in circulation) instead of M2 (total cash plus total savings deposits), the DW statistic was reduced from 1.86 to 1.27. The reasons for this are obvious: by including P = P (M / PR)^a in the regression, one expects to have a higher DW because M/PR is correlated with the rapid increase in savings, and the correlation is stronger if M includes savings itself, as when M2 is used. Second, their significant estimation of interest elasticity depends crucially on their assumption about expectations: consumers face rationing in a given year and expect rationing to be eliminated in the next year (remember that 1 + r— (1 + i) x p/P₊₁). It is doubtful, however, that this kind of expectation could survive every year for more than thirty years. If consumers expect rationing to continue in the coming year, then 1 + r = (1 + i) x p/p₊₁ = (1 + i), and the estimated results may not hold.

II. Factors Shaping the Chinese Economy and Influencing Household Behavior

The following factors are considered important in shaping the contemporary Chinese economy and in influencing household behavior—in the present case, household saving behavior.

First, China is a low-income developing country, with the majority of its population living in rural areas. At the persistently low level of incomes and of assets, for many years households were essentially struggling to meet basic needs. Saving was then considered a kind of “luxury good,” and not a realistic option when income was below a certain level. Borrowing in general was constrained either by the lack of a credit market or by traditional conservative attitudes toward borrowing. Under these circumstances, one cannot imagine that a consumer with a yearly disposable income of US$100 would have the same marginal propensity to save as one with $1,000 a year. This basic and simple notion leads us to suspect the application of a linear savings function to China in the thirty-year period (1955–85), during much of which most households were concerned with meeting their basic needs.

Second, China is a centrally planned economy, with most enterprises owned and controlled by the government. Before 1979, China followed a development path similar to that of other centrally planned economies—that is, one in which government policy actions were directed toward high accumulation, stable and low wages, full employment, and a high standard of social welfare (at least in the urban areas). On the one hand, with economic uncertainty reduced and the income flow smoothed, for a given level of income a household’s motives to save were considerably reduced: housing, education, pension, nursery, and medical services were all provided by the government. On the other hand, the persistent shortage of consumer goods may have forced such households to save the amount that they otherwise may have wished to spend in the absence of shortages. During this period, neither the government nor most economists viewed household savings as being a part of accumulation; rather, they thought currency and savings deposits held by households were unrealized purchasing power and were potential destabilizing influences for the consumer-goods market. Other things being equal, excess monetary expansion relative to the real growth of consumer goods output lead to either inflation or forced saving if the price level is controlled. The counterpart of the monetarist’s statement that “inflation is a monetary phenomenon” in the present context is that “excess savings are a monetary phenomenon.” Before 1979, the authorities were able, with some exceptions, to control monetary expansion in order to avoid either inflation or the rapid accumulation of household savings. Hence, the low and stable savings rate of the household sector before 1979, other things being equal, is the consequence of the institutional arrangement.

Third, economic reform has been under way in China since 1979. The main feature of the reform has been the decentralization of decision making to enterprises (in the case of urban reform), and to households (in the case of rural reform). One of the results of economic reform has been the sharp increase in both household disposable income and savings, with the measured MPS higher than ever before, especially in the rural sector, where per capita income nearly tripled during the past eight years. The emergence of household farms in rural areas and free and parallel markets in urban areas has increased the demand for money, since the economy has become more monetized. In the urban sector, income—now consisting of wages and bonuses, and possible extra money from various sources—is more volatile than before, and most consumers feel less certain about future income. In addition, reform itself increases uncertainty. For example, the impact on uncertainty of prospective price reforms is not insignificant.

Finally, China’s economy is also shaped by a number of unique factors—among them its huge size, immense population, and history. Traditional ideas about saving and the virtues of thrift, and the past thirty years’ experience of low income, may now contribute to a strong motive to save as a precautionary measure.

The above four factors are important in explaining recent high household savings in China. Specifically, the identity vM/PQ = s is postulated as a generalized form of money equation, where M is the money supply, P is the price level, Q is real output, and v is the equilibrium velocity of money. In the traditional theory of money, s is always set equal to unity, so that v is the observed velocity of money. As interpreted here, s is an index of the degree of disequilibrium in the economy; in particular, when s > 1, s is the index of shortage or repressed inflation. In the traditional theory with s = 1 and with v and Q fixed, the increase in M will lead to an increase in P; that is, to inflation. Now, as the possibility of disequilibrium is explicitly introduced, the increase in M, other things being equal, will result either in an increase in s or, most often in a centrally planned economy, in an increase in s, with P kept constant.

What happened in China during the past few years was the simultaneous increase in M, P, Q, and M/PQ. This leads to one possible hypothesis of the increase in s, assuming that v is constant. This is the assumption implicitly made by Feltenstein, Lebow, and van Wijnbergen (1986), under which they were able to explain the increased savings, maintaining the constancy of household saving behavior, especially the MPS, over time. This paper makes an alternative assumption. If s is assumed to be constant over time, the money equation is still valid if v decreases as M/PQ increases. This situation is quite possible, given the recent process of monetization in China. Hence, another hypothesis emerges: with s fixed, the increase in M/PQ is balanced by the decrease of v; that is, an increase in the demand for money. This paper shows, among other things, that the increased savings in recent years can be equally well explained under the latter hypothesis, if the possible shift of household saving behavior—especially the MPS—over time is allowed.

III. Motives for Saving: Urban Versus Rural

To examine saving behavior in China, it is essential to separate the rural and urban sectors because, as it will be seen below, different institutions and motives apply in each case. According to the definition before 1984, the rural population is about 80 percent of the total population, with the remaining 20 percent urban residents. Unlike other developing countries, in China population movement from the countryside to cities has been strictly controlled, so that the per capita income of urban residents was kept two times higher than that of rural residents for nearly thirty years. Farmers in rural areas and wage earners in urban areas experience different institutional environments. It is also evident that the two sectors experienced quite different economic development paths during the recent years of reform.

Urban wage earners have stable incomes and are extensively covered by the state or enterprise welfare plan. Saving for retirement is not necessary, since a retired worker will receive a pension of between 60 percent and 80 percent (in the case of a “model worker,” up to 100 percent) of his or her final wages. Nobody in urban areas saves for housing because houses are provided by the “employing unit” at very low rent. But there is a strong motive to save for consumer durables (television sets, washing machines, refrigerators, and the like). In addition, saving for children’s marriages is not uncommon.

In the rural sector, in contrast, incomes (especially since the reforms) are less stable, depending on the weather, the market, and management of production. Housing and pension funds are provided by the farmers themselves. As mentioned earlier, farmers face investment opportunities too, which are not available for urban residents. Many of the motives common to saving behavior in market economies have become relevant for Chinese farmers in recent years.

Consumer durables in urban areas and housing in rural areas have accounted for the bulk of the increase in Chinese household savings in recent years. These two motives for saving can be attributed to (1) very low initial stocks, (2) the absence of rental markets, and, probably most important, (3) the ownership premium. One policy implication from this analysis is the effectiveness of introducing housing as a potential savings instrument in the urban areas for maintaining the household savings rate.

IV. Alternative Savings Models

This section describes in general terms the four models of saving that are used to obtain estimation results in Sections V and VI. In what follows, S is real per capita household savings and Y is real per capita disposable income.

Permanent-Income Model

As opposed to the absolute-income hypothesis, this model relates current savings to permanent income, which can be thought of as the steady rate of consumption a person could maintain for the rest of his life, given the present level of wealth and income earned now and in the future. The linear version of the model that has been widely used in empirical studies is

$S_t=a+b{Y}_t\mathrm{.}$

where

View Expanded

and are permanent income and transitory income in year t, respectively. To determine the permanent income, this paper follows the method used by Williamson (1968) which uses as a proxy for permanent income a three-year moving average of actual income; that is, = ⅓(Y_t + Y_t-1 + Y_t-2)_. Other methods of specifying permanent income involve hypotheses concerning the formation of expectations about future income; examples include the adaptive and rational expectations models (see the consumption model below).

V. Empirical Results for Urban Household Savings

This section describes the data used, and the results obtained, for the urban sector.

Data

Ideally, total disposable income (including income in kind) and total savings (including acquisition of consumer durables) should be used in the empirical analysis. Because of limited data, money income (excluding income in kind) and financial savings (excluding consumer durables) are used instead. The construction of time-series data is based on the following identity (household borrowing is negligible):¹

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Urban Per Capita Household Income, Consumption, and Savings in China, 1953–85

(In yuan, 1950 prices)

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A003

Source: China, Statistical Yearbook of China (various issues).

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household money income = household expenditure

+ household financial savings,

where

household expenditure = household expenditure on commodities

+ household expenditure on services

and

household financial savings = change of household cash holdings

+ change of household savings deposits

+ change of household bond

holdings.

Figure 1 plots the time series of urban household per capita real money income, financial savings, and consumption expenditure.

Urban income and savings are then expressed in real per capita terms by using data on the general retail price index and urban population. Data up to 1983 on urban population are cited directly from the Yearbook; estimates for 1984 and 1985 are derived by extrapolation using trend growth rates (the rapid increase in urban population on the basis of the official series reflects a redefinition of urban areas).

Two final remarks are in order about the data for 1984 and 1985. Savings in 1984 were exceptionally high, reflecting an unusual increase in wage bonuses in the last quarter of that year, and it would be inappropriate to select 1984 as the last year of observation. Data for 1985 were estimated by the author on the basis of partial information.

Empirical Results

It is worthwhile to plot savings/consumption against income before making any estimations. In Figure 2, panels A and C show real financial savings and real consumption in relation to real income. With permanent income taken as the past three years’ average income and transitory income as the difference between current and permanent income, panels B and D show the relation between savings and permanent and transitory incomes, respectively. Panels A and B show clearly the nonlinearity of the plotted functions, suggesting that any attempt to fit a linear equation to these data will not yield satisfactory results. Panels C and D, in contrast, show possible linear relationships in underlying variables.

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Urban Per Capita Household Savings/Consumption Versus Income in China, 1953–85

(In yuan, 1950 prices)

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A003

Source: China, Statistical Yearbook of China (various issues).

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To capture the idea of regime shifts in household saving behavior over time discussed in Section II, switching regression models are used in which two distinct regimes are explicitly recognized and the switching date between the two regimes will be estimated, not predetermined. The switching regression model, which is a special case of a more general time-varying parameter model, allows a simple discrete switch on the values of parameters, with the switching date determined according to the criterion of maximum likelihood. The results of least-squares estimation of the switching regression models as well as the ordinary linear regression models are presented in Tables 4–7. Interest rates were first included in the regressions but were later dropped because they were insignificant in all cases.

Table 4.

Absolute-income Model

(Urban)

Note: Equations are as follows:

$\begin{array}{cc}{S}_t^{*}=r\Delta Y_t\mathrm{.}& \left(5\right)\end{array}$

where D = 1 when t< 1979 and D = 0 when t ≥ 1979, and

$\begin{array}{cc}{S}_t=c+a{Y}_t\mathrm{.}& \left(4.2\right)\end{array}$

DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares; LLF is the log-likelihood function. Numbers in parentheses are t-statistics. See the text for definitions of variables.

Table 4.

Absolute-income Model

(Urban)

Period and Equation		c	d	a	a1	a2	DW		RSS	LLF
1955–83
	(4.1)	-74.2	68.2		0.29	0.04
		(-3.7)	(3.4)		(4.8)	(3.6)	1.125	0.931	103.8	-59.64
	(4.2)	-22.1		0.12			0.489	0.716	461.6	-81.28
		(-6.5)		(8.5)
1955–85
	(4.1)	-61.7	55.7		0.256	0.04
		(-10.12)	(8.2)		(15.3)	(2.9)	1.67	0.967	176.2	-70.92
	(4.2)	-33.4		0.17			0.398	0.833	961.0	-97.21
		(-9.3)		(12.3)

Note: Equations are as follows:

$\begin{array}{cc}{S}_t^{*}=r\Delta Y_t\mathrm{.}& \left(5\right)\end{array}$

where D = 1 when t< 1979 and D = 0 when t ≥ 1979, and

$\begin{array}{cc}{S}_t=c+a{Y}_t\mathrm{.}& \left(4.2\right)\end{array}$

DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares; LLF is the log-likelihood function. Numbers in parentheses are t-statistics. See the text for definitions of variables.

View Table

Table 4.

Absolute-income Model

(Urban)

Period and Equation		c	d	a	a1	a2	DW		RSS	LLF
1955–83
	(4.1)	-74.2	68.2		0.29	0.04
		(-3.7)	(3.4)		(4.8)	(3.6)	1.125	0.931	103.8	-59.64
	(4.2)	-22.1		0.12			0.489	0.716	461.6	-81.28
		(-6.5)		(8.5)
1955–85
	(4.1)	-61.7	55.7		0.256	0.04
		(-10.12)	(8.2)		(15.3)	(2.9)	1.67	0.967	176.2	-70.92
	(4.2)	-33.4		0.17			0.398	0.833	961.0	-97.21
		(-9.3)		(12.3)

Note: Equations are as follows:

$\begin{array}{cc}{S}_t^{*}=r\Delta Y_t\mathrm{.}& \left(5\right)\end{array}$

where D = 1 when t< 1979 and D = 0 when t ≥ 1979, and

$\begin{array}{cc}{S}_t=c+a{Y}_t\mathrm{.}& \left(4.2\right)\end{array}$

DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares; LLF is the log-likelihood function. Numbers in parentheses are t-statistics. See the text for definitions of variables.

Table 5.

Permanent-Income Model

(Urban)

Note: Equations are as follows:

$\begin{array}{cc}{S}_t=c+\mathit{dD}+a_1{Y}_t^p(1-D)+a_2{Y}_t^{p}D+\mathit{b}{Y}_t^t& \left(5.1\right)\end{array}$

$\begin{array}{cc}{S}_t=c+a{Y}_t^p+\mathit{b}{Y}_t^t& \left(5.2\right)\end{array}$

$\begin{array}{cc}{S}_t=c+\mathit{dD}+{\mathit{a}}_1{Y}_t^p(1-D)+a_2{Y}_t^{p}D+b_1{Y}_t^t(1-D)+b_2{Y}_t^{t}D& \left(5.3\right)\end{array}$

$\begin{array}{cc}{S}_t=c+\mathit{dD}+a{Y}_t^p+b_1{Y}_t^t(1-D)+b_2{Y}_t^{t}D,& \left(5.4\right)\end{array}$

where D = 1 when t < 1979 and D = 0 when t ≥1979. DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares; LFF is the log-likelihood function. Numbers in parentheses are t-statistics. See the text for definitions of variables.

Table 5.

Permanent-Income Model

(Urban)

Period and Equation		c	d	a1	a1	a2	b	b1	b2	DW		RSS	LLF
1955–83
	(5.1)	-63.7	62.6		0.26	0.011	0.25			1.64	0.94	87.1	-57.09
		(-3.4)	(3.3)		(4.3)	(0.75)	(4.34)
	(5.2)	-20.2		0.11			0.21			0.48	0.71	451.9	-80.97
		(-4.7)		(5.0)			(1.7)
	(5.3)	-70.0	68.0		0.27	0.02		0.36	0.20	1.47	0.94	80.8	-56.01
		(-3.7)	(3.5)		(4.5)	(1.1)		(3.5)	(3.0)
	(5.4)	7.0	-11.6	0.03				0.28	0.16	1.12	0.90	14.7	-64.15
		(1.1	(-3.3)	(1.7)				(2.1)	(1–9)
1955–85
	(5.1)	-64.8	63.6		0.27	0.01	0.24			2.00	0.97	157.5	-69.18
		(-4.4)	(4.5)		(5–4)	(0.67)	(4.28)
	(5.2)	-19.5		0.10			0.44			0.76	0.88	654.6	-91.26
		(-4.0)		(4.2)			(5.8)
	(5–3)	-59.1	57.1		0.25	0.02		0.27	0.20	1.93	0.97	1.554	-68.97
		(-3.3)	(3.2)		(4.1)	(0.9)		(3.6)	(2.3)
	(5.4)	1.97	-7.9	0.04				0.49	0.14	1.30	0.95	237.3	-75.54
		(0.3)	(-2.7)	(1.7)				(10.1)	(1.4)

Note: Equations are as follows:

$\begin{array}{cc}{S}_t=c+\mathit{dD}+a_1{Y}_t^p(1-D)+a_2{Y}_t^{p}D+\mathit{b}{Y}_t^t& \left(5.1\right)\end{array}$

$\begin{array}{cc}{S}_t=c+a{Y}_t^p+\mathit{b}{Y}_t^t& \left(5.2\right)\end{array}$

$\begin{array}{cc}{S}_t=c+\mathit{dD}+{\mathit{a}}_1{Y}_t^p(1-D)+a_2{Y}_t^{p}D+b_1{Y}_t^t(1-D)+b_2{Y}_t^{t}D& \left(5.3\right)\end{array}$

$\begin{array}{cc}{S}_t=c+\mathit{dD}+a{Y}_t^p+b_1{Y}_t^t(1-D)+b_2{Y}_t^{t}D,& \left(5.4\right)\end{array}$

where D = 1 when t < 1979 and D = 0 when t ≥1979. DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares; LFF is the log-likelihood function. Numbers in parentheses are t-statistics. See the text for definitions of variables.

View Table

Table 5.

Permanent-Income Model

(Urban)

Period and Equation		c	d	a1	a1	a2	b	b1	b2	DW		RSS	LLF
1955–83
	(5.1)	-63.7	62.6		0.26	0.011	0.25			1.64	0.94	87.1	-57.09
		(-3.4)	(3.3)		(4.3)	(0.75)	(4.34)
	(5.2)	-20.2		0.11			0.21			0.48	0.71	451.9	-80.97
		(-4.7)		(5.0)			(1.7)
	(5.3)	-70.0	68.0		0.27	0.02		0.36	0.20	1.47	0.94	80.8	-56.01
		(-3.7)	(3.5)		(4.5)	(1.1)		(3.5)	(3.0)
	(5.4)	7.0	-11.6	0.03				0.28	0.16	1.12	0.90	14.7	-64.15
		(1.1	(-3.3)	(1.7)				(2.1)	(1–9)
1955–85
	(5.1)	-64.8	63.6		0.27	0.01	0.24			2.00	0.97	157.5	-69.18
		(-4.4)	(4.5)		(5–4)	(0.67)	(4.28)
	(5.2)	-19.5		0.10			0.44			0.76	0.88	654.6	-91.26
		(-4.0)		(4.2)			(5.8)
	(5–3)	-59.1	57.1		0.25	0.02		0.27	0.20	1.93	0.97	1.554	-68.97
		(-3.3)	(3.2)		(4.1)	(0.9)		(3.6)	(2.3)
	(5.4)	1.97	-7.9	0.04				0.49	0.14	1.30	0.95	237.3	-75.54
		(0.3)	(-2.7)	(1.7)				(10.1)	(1.4)

Note: Equations are as follows:

$\begin{array}{cc}{S}_t=c+\mathit{dD}+a_1{Y}_t^p(1-D)+a_2{Y}_t^{p}D+\mathit{b}{Y}_t^t& \left(5.1\right)\end{array}$

$\begin{array}{cc}{S}_t=c+a{Y}_t^p+\mathit{b}{Y}_t^t& \left(5.2\right)\end{array}$

$\begin{array}{cc}{S}_t=c+\mathit{dD}+{\mathit{a}}_1{Y}_t^p(1-D)+a_2{Y}_t^{p}D+b_1{Y}_t^t(1-D)+b_2{Y}_t^{t}D& \left(5.3\right)\end{array}$

$\begin{array}{cc}{S}_t=c+\mathit{dD}+a{Y}_t^p+b_1{Y}_t^t(1-D)+b_2{Y}_t^{t}D,& \left(5.4\right)\end{array}$

where D = 1 when t < 1979 and D = 0 when t ≥1979. DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares; LFF is the log-likelihood function. Numbers in parentheses are t-statistics. See the text for definitions of variables.

Table 6.

Asset-Adjustment Model

(Urban)

Note: Equations are as follows:

$S_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2{\mathrm{\Delta }Y}_{t}D& \left(6.1\right)$

$\begin{array}{cc}{S}_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t& \left(6.2\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2\mathrm{\Delta }\mathrm{}{Y}_{t}D& \left(6.3\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b\mathrm{\Delta }{Y}_t,& \left(6.4\right)\end{array}$

where D = 1 when t < T and D =0 when t > T.H is the Durbin-Watson H -statistic; is the adjusted coefficient of determination: RSS is the residual sum of squares; LLF is the log-likelihood function. Numbers in parentheses are t -statistics. See the text for definitions of variables.

Table 6.

Asset-Adjustment Model

(Urban)

Period and Equation		a	a1	a2	b	b1	b2	T	H		RSS	LLF
1955–83
	(6.1)		0.86	0.51		0.31	0.14	1978	2.00	0.91	134.9	-63.4
			(10.1)	(2.7)		(5.2)	(2.3)
	(6.2)		0.95	0.34	0.22			1977	2.02	0.90	155.0	-65.45
			(12.2)	(1.9)	(4.8)
	(6.3)	0.81				0.34	0.08	1978	1.97	0.90	151.2	-65.1
		(9.8)				(5.4)	(1–5)
	(6.4)	0.92			0.17				1.53/125	231.8	-71.3
		(9.9)			(3.2)
	1955–85
	(6.1)		0.79	0.53		0.26	0.14	1978	1.81	0.93	352.0	-81.65
		(6.1)	(1.8)		(3.8)	(1.4)
	(6.2)		0.86	0.35	0.22			1977	1.97	0.94	363.5	-82.2
			(7.7)	(1.4)	(3.8)
	(6.3)	0.75				0.28	0.09	1978	1.77	0.94	360.9	-82.0
		(6.2)				(4.3)	(1.2)
	(6.4)	0.86			0.21				1.83/0.33	0.93	627.4	-84.7
		(7.2)			(3.4)

Note: Equations are as follows:

$S_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2{\mathrm{\Delta }Y}_{t}D& \left(6.1\right)$

$\begin{array}{cc}{S}_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t& \left(6.2\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2\mathrm{\Delta }\mathrm{}{Y}_{t}D& \left(6.3\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b\mathrm{\Delta }{Y}_t,& \left(6.4\right)\end{array}$

where D = 1 when t < T and D =0 when t > T.H is the Durbin-Watson H -statistic; is the adjusted coefficient of determination: RSS is the residual sum of squares; LLF is the log-likelihood function. Numbers in parentheses are t -statistics. See the text for definitions of variables.

View Table

Table 6.

Asset-Adjustment Model

(Urban)

Period and Equation		a	a1	a2	b	b1	b2	T	H		RSS	LLF
1955–83
	(6.1)		0.86	0.51		0.31	0.14	1978	2.00	0.91	134.9	-63.4
			(10.1)	(2.7)		(5.2)	(2.3)
	(6.2)		0.95	0.34	0.22			1977	2.02	0.90	155.0	-65.45
			(12.2)	(1.9)	(4.8)
	(6.3)	0.81				0.34	0.08	1978	1.97	0.90	151.2	-65.1
		(9.8)				(5.4)	(1–5)
	(6.4)	0.92			0.17				1.53/125	231.8	-71.3
		(9.9)			(3.2)
	1955–85
	(6.1)		0.79	0.53		0.26	0.14	1978	1.81	0.93	352.0	-81.65
		(6.1)	(1.8)		(3.8)	(1.4)
	(6.2)		0.86	0.35	0.22			1977	1.97	0.94	363.5	-82.2
			(7.7)	(1.4)	(3.8)
	(6.3)	0.75				0.28	0.09	1978	1.77	0.94	360.9	-82.0
		(6.2)				(4.3)	(1.2)
	(6.4)	0.86			0.21				1.83/0.33	0.93	627.4	-84.7
		(7.2)			(3.4)

Note: Equations are as follows:

$S_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2{\mathrm{\Delta }Y}_{t}D& \left(6.1\right)$

$\begin{array}{cc}{S}_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t& \left(6.2\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2\mathrm{\Delta }\mathrm{}{Y}_{t}D& \left(6.3\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b\mathrm{\Delta }{Y}_t,& \left(6.4\right)\end{array}$

where D = 1 when t < T and D =0 when t > T.H is the Durbin-Watson H -statistic; is the adjusted coefficient of determination: RSS is the residual sum of squares; LLF is the log-likelihood function. Numbers in parentheses are t -statistics. See the text for definitions of variables.

Table 7.

Consumption Model

(Urban)

Note: DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares. Numbers in parentheses are (-statistics. See the text for definitions of variables.

Table 7.

Consumption Model

(Urban)

Period	Equation	DW		RSS
1955–83	(7.1) Ct= -0.73 + 1.03 Ct-1 (-0.07) (22.98)	1.95	0.95	3,265
1957–83	(7.2) Ct= -4.6 + 1.09 C-.-0.24 Ct-2 (-0.38) (5.4) (-0.82) + 0.35 Ct-3 - 0.15 C,-4 (1.17) (-0.68)	1.83	0.95	2,751
1955–83	(7.3) Ct= 4.7 + 0.71 Ct-1 + 0.29 Y,., (0.3) (1.21) (0.54)	1.90	0.95	3,229
1957–83	(7.4) Ct = 0.08 + 0.84 Ct-1, + 0.32 Yt-1 (0.005) (1.38) (0.57) -0.34 Yt-2 + 0.31 Yt-3, - 0.12 Yt-4 (-1.19) (1.09) (-0.56)	1.98	0.95	2,706
1955–83	(7.5) Ct= 5.1 + 0.75 Ct-1 + 0.24 Yt (0.46) (1.96) (4.7)	1.92	0.97	1,754
(Instruments: Ct-1, St-1)
1955–85	(7.1) Ct= -23.5 + 1.14 Ct-1 (-2.19)(24.0)	1.36	0.95	5,709
1957–85	(7.2) Ct = 25.6 + 1.42 C,-, - 0.53 Ct-2, (1.9) (6.2) (-1.48) + 0.23 Ct-3 + 0.02 Ct-4 (0.62) (0.08)	1.67	0.95	4,742
1955–85	(7.3) Ct= 15.1 - 0.29 Ct-1, + 1.2 Y,-\ (1.05) (-0.7) (3.6)	1.54	0.96	3,905
1957–85	(7.4)Ct = 8.3 - 0.03 Ct-1, + 1.2 F,., (0.5) (-0.07) (3.3) -0.45 Y.-2 + 0.27 yt-3, - 0.05 yt-4 (-1.5) (0,91) (-0.21)	1.82	0.96	3,280
1955–85	(7.5) Ct= 10.1 + 0.42 Ct-1, + 0.53 Y, (1.7) (4.8) (8.3)	1.6	0.99	742
(Instruments = C,-i, S,-i)

Note: DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares. Numbers in parentheses are (-statistics. See the text for definitions of variables.

View Table

Table 7.

Consumption Model

(Urban)

Period	Equation	DW		RSS
1955–83	(7.1) Ct= -0.73 + 1.03 Ct-1 (-0.07) (22.98)	1.95	0.95	3,265
1957–83	(7.2) Ct= -4.6 + 1.09 C-.-0.24 Ct-2 (-0.38) (5.4) (-0.82) + 0.35 Ct-3 - 0.15 C,-4 (1.17) (-0.68)	1.83	0.95	2,751
1955–83	(7.3) Ct= 4.7 + 0.71 Ct-1 + 0.29 Y,., (0.3) (1.21) (0.54)	1.90	0.95	3,229
1957–83	(7.4) Ct = 0.08 + 0.84 Ct-1, + 0.32 Yt-1 (0.005) (1.38) (0.57) -0.34 Yt-2 + 0.31 Yt-3, - 0.12 Yt-4 (-1.19) (1.09) (-0.56)	1.98	0.95	2,706
1955–83	(7.5) Ct= 5.1 + 0.75 Ct-1 + 0.24 Yt (0.46) (1.96) (4.7)	1.92	0.97	1,754
(Instruments: Ct-1, St-1)
1955–85	(7.1) Ct= -23.5 + 1.14 Ct-1 (-2.19)(24.0)	1.36	0.95	5,709
1957–85	(7.2) Ct = 25.6 + 1.42 C,-, - 0.53 Ct-2, (1.9) (6.2) (-1.48) + 0.23 Ct-3 + 0.02 Ct-4 (0.62) (0.08)	1.67	0.95	4,742
1955–85	(7.3) Ct= 15.1 - 0.29 Ct-1, + 1.2 Y,-\ (1.05) (-0.7) (3.6)	1.54	0.96	3,905
1957–85	(7.4)Ct = 8.3 - 0.03 Ct-1, + 1.2 F,., (0.5) (-0.07) (3.3) -0.45 Y.-2 + 0.27 yt-3, - 0.05 yt-4 (-1.5) (0,91) (-0.21)	1.82	0.96	3,280
1955–85	(7.5) Ct= 10.1 + 0.42 Ct-1, + 0.53 Y, (1.7) (4.8) (8.3)	1.6	0.99	742
(Instruments = C,-i, S,-i)

Note: DW is the Durbin-Watson statistic; is the adjusted coefficient of determination; RSS is the residual sum of squares. Numbers in parentheses are (-statistics. See the text for definitions of variables.

For the absolute-income model (Table 4). the likelihood ratio (LR) test decisively rejects the hypothesis of no regime shift, where LR = 52.58 for 1955–85 (LR =43.28 for 1955–83). when the 0.99 value of is 6.63. The estimated year in which the shift occurs is 1979, coinciding with the beginning of reforms. When the shift is included. the DW statistic is increased from 0.398 to 1.67. indicating no serious autocorrelation (from 0.489 to 1.125, though. for 1955–83). The adjusted coefficient of determination () is also improved significantly. All of the indicators show strong support for the switching specification.

With regard to the parameters estimated, MPS now depends on the following regimes (from 1955–85 equation):

S_t=–6.0+0.04Y_t, when t < 1979

S_t=–6.0+0.26Y_t, when t ≥ 1979.

However, the estimate from the simple linear regression (from 1955–85 equation) is S_t = –33.4 + 0.17Y_t. Hence, the estimated MPS before (after) 1979 is lower (higher) than the estimate from the simple linear regression.

In estimating the permanent-income model (Table 5). the hypothesis of no shift in MPS out of permanent income is tested under two alternative assumptions: (Al) there is no shift in MPS of transitory income, and

(A2) there is a shift in MPS of transitory income. Log-likelihood ratios are presented below:

	Assumption Al	Assumption A2
1955–83	47.76	16.28
1955–85	44.16	13.14

View Table

	Assumption Al	Assumption A2
1955–83	47.76	16.28
1955–85	44.16	13.14

The original hypothesis is decisively rejected under either assumption because the 0.99 value of is 6.63. One may conclude that there is a shift in MPS of the permanent income. Next, the hypothesis that there is no shift in MPS out of transitory income is tested, given the shift in MPS out of permanent income. The log-likelihood ratio is 0.42 (or 2.16 for 1955—83). The hypothesis cannot be rejected, since the 0.90 value of is 2.71.

As in the absolute-income model, the estimated shifting year is 1979. Parameters estimated are:

$$\begin{gathered} S_t=-1.2+0.01Y_t^p+0.24Y_t^t,\mathrm{when}t<1979 \\ {S}_t=-64.8+0.27Y_t^p+0.24Y_t^t,\mathrm{when}t\ge 1979. \end{gathered}$$

The corresponding DW statistic is 1.996 (or 1.64 for 1955–83); the is 0.970 (or 0.940 for 1955–83).

There is one interesting finding from the estimation. Before 1979, propensities to save in relation to permanent income and transitory income differed greatly, with almost all savings being in response to the increase in transitory income. Since 1979, propensities to save from permanent income and from transitory income have been nearly identical. This contradicts Friedman’s permanent-income hypothesis, and at the same time, supports the Keynesian absolute-income model estimated previously, where MPS out of current income is 0.256, which is about the average of MPS out of permanent income and out of transitory income here. This result may be interpreted in the following way. Before 1979, household incomes were so low that households saved almost nothing out of permanent income; hence only transitory increments of income were saved. Since reforms began, as discussed in Section II, urban households have been saving such a significant amount from permanent income that they behave like Keynesian consumers.

Turning to the asset-adjustment model (Table 6), four versions of the model, depending on the assumptions of shift in different parameters, were estimated (equation numbers refer to the table):

$S_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2{\mathrm{\Delta }Y}_{t}D& \left(6.1\right)$

$\begin{array}{cc}{S}_t=a_1{S}_{t-1}(1-D)+a_2{S}_{t-1}D+b_1\mathrm{\Delta }{Y}_t& \left(6.2\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b_1\mathrm{\Delta }{Y}_t(1-D)+b_2\mathrm{\Delta }\mathrm{}{Y}_{t}D& \left(6.3\right)\end{array}$

$\begin{array}{cc}{S}_t=a{S}_{t-1}+b\mathrm{\Delta }{Y}_t,& \left(6.4\right)\end{array}$

where D = 1 when t < T and D = 0 when t ≥ T. The log-likelihood ratios are given below for possible nested hypotheses:

	(6.4)	(6.4)	(6.2)	(6.3)
	Versus	Versus	Versus	Versus
	(6.2)	(6.3)	(6.1)	(6.1)
1955-83	11.68	12.40	4.02	3.30
1955-85	5.0	5.24	1.0	0.76

View Table

	(6.4)	(6.4)	(6.2)	(6.3)
	Versus	Versus	Versus	Versus
	(6.2)	(6.3)	(6.1)	(6.1)
1955-83	11.68	12.40	4.02	3.30
1955-85	5.0	5.24	1.0	0.76

Because the 0.99 value of is 6.63 and the 0.95 value of is 3.84, one may want to reject specifications (6.4) and (6.2) and choose (6.3); that is, there is a shift in the savings response to the change in income, without a shift in the current savings response to the lagged savings. The estimated time of shifting is 1978 in this model:

$$\begin{gathered} S_t=0.75S_{t-1}+0.09\mathrm{\Delta }{Y}_t,\text{when }t<1978 \\ {S}_t=0.75S_{t-1}+0.28\mathrm{\Delta }{Y}_t,\text{when }t\ge 1978 \end{gathered}$$

Using the formula presented in Section IV allows one to calculate structural parameters—in particular, the long-run savings-income ratio S/Y—under alternative interpretations. After 1978, according to the methodology of Houthakker and Taylor (1966), the MPS out of assets is

B = 2 x (0.75 – 1)/(0.75 + 1) = –0.29, and the MPS out of income is C = 2 x 0.28/(0.75 + 1) = 0.32.

The long-run savings rate consistent with the constant growth rate of income of 4 percent is S/Y = 0.32 x 0.04/(0.04 + 0.29) = 3.88 percent. Under the interpretation of Leff and Sato (1975), the adjustment parameter relating actual to desired savings is k =1 – 0.75 = 0.25, and the desired asset-income ratio is r = 0.28/0.25 = 1.12. With the constant income growth at 4 percent, the long-run savings rate under this interpretation is S/Y = 0.28 x 0.04/(0.04 + 0.25) = 3.86 percent, which is very close to the figure obtained by Houthakker and Taylor.

The analysis next attempts to estimate the structural equations of consumption (Table 7). The equations were estimated using C_t-1 and S_t-1 as instruments. This is equivalent to applying the method of two-stage least squares to simultaneous equations:

C_t = a + bC_t-1 + dY_t

$$\begin{gathered} S_t={\mathit{eS}}_{t-1}+f(Y_t-Y_{t-1}) \\ {Y}_t=C_t+S_t\mathrm{.} \end{gathered}$$

In contrast to Chow (1985), estimates of the coefficient of current income, d, are all significant, but this does not contradict the principal stochastic implications of the life-cycle permanent-income hypothesis of Hall (1978) mentioned in Section IV (that is, lagged income should not have predictive power for current consumption).

Hall’s random-walk hypothesis is formally tested by estimating a conditional expectation, E(C_t/C_t-1,X_t-1), and showing it is not a function of X_t-1. The weak version of the hypothesis takes X_t-1 as lagged consumption beyond C_t-1, whereas the strong version would include lagged income or any other lagged variables. Note that what is estimated is the conditional expectation, not the true structural relation between consumption and its determinants.

In Table 7, where equation (7.2) includes C_t-2, C_t-3, and C_t-4 in addition to C_t-1 as in equation (7.1), the F-statistic for the hypothesis that the coefficients of C_t-2, C_t-3, and C_t_₄ are all zero is 1.37 for 1955–83 (or 1.63 for 1955–85), well under the critical value of 2.96 at the 5 percent level. This implies that, by adding C_t-2, C_t-3, and C_t-2 into the regression, one adds no additional information. Hence the weak version of the hypothesis is supported.

The predictive power of the lagged levels of disposable income is tested next. Equation (7.3) of Table 7 incorporated a single lagged value of income, and equation (7.4) tried a four-year lag. For data up to 1983, F-statistics are 0.29 and 1.08, respectively. Therefore, the strong version of the hypothesis cannot be rejected at the 5 percent level. But for data extended to 1985, the values are 12.9 and 4.26, respectively, and the hypothesis can be rejected, although not decisively.