# Effect of interest rate on consumption under alternative expectations hypotheses: evidence from Pakistan.

I. Introduction

The effect of the interest rate on consumption behavior has been subject to controversy. Before Keynes (1936), the interest rate was considered to be the prime determinant of savings. Keynes demonstrated that fluctuations in the short run interest rate had no significant effect on spending decisions. Kuznets (1946) reported that the savings rate remained stable over the long run. However, in Modigliani's (1953) life cycle hypothesis (LCH), the interest rate played an important part in measuring the consumer's expected future earnings and net worth which, in turn, influenced consumption behavior. In Friedman's (1957) permanent income hypothesis (PIH), the rate of interest became a major determinant of the marginal propensity to consume out of permanent income.

More recently, Wright (1967) and Heien (1972) estimated a negative and significant relationship between the interest rate and consumption expenditure. In contrast, Weber (1970) and Springer (1975) reported a positive and significant effect of the interest rate on consumption. Also, Boskin (1978) estimated a substantial interest elasticity of savings. Feldstein (1970) demonstrated that studies using the nominal instead of the real interest rate were subject to a serious specification bias. Carlino (1982) employing four different interest rates estimated contradictory signs for the interest rate coefficients and rejected the hypothesis that variations in the real interest rate altered consumption decisions. Likewise, Blinder and Deaton (1985) and Campbell and Mankiw (1989) estimated an insignificant effect of the real interest rate on consumption.

In this paper, we examine the effect of the real interest rate on consumption behavior in Pakistan, taking into consideration the presence of money market imperfections. Thus, alternative proxies for the opportunity cost of holding real balances are considered to test the sensitivity of the consumption function to the changing money market conditions. Section II discusses issues related to estimating the consumption function and to the structural characteristics of money markets in the developing countries. Section III outlines the theory of consumption function. Section IV presents the empirical results and Section V includes the concluding remarks.

II. Relevant Issues

Development of the theory of consumption function has been fascinating but controversial. For a long time, both the theoretical derivation and the econometric framework of the aggregate consumption function were considered settled. Most economists adhered to one of two ways of putting Fisher's theory of intertemporal optimization into cooperation: the PIH or LCH. Since each variant had sound theoretical construct, and since they had similar econometric forms that could explain the data well and had similar policy implications, there was not a great deal of controversy about. However, development in economic research have raised fundamental questions about the theory of consumption function. Some recent theoretical development included the Barro's equivalence hypothesis (1974), Lucas' critique (1976), Hall's random walk hypothesis (RWH) (1978), as well as flexible approaches by Giovannini (1985) and Blinder and Deaton.

Hence, a complementary goal of our investigation of the relationship between consumption and the real interest rate is to test the fit of the standard consumption models against that of their recent challenges to Pakistan's data. For a secondary issue as such, it may be suffice to focus on only two alternative formulations of the consumption function, for example, PIH and RWH that quarrel about the nature of income expectations.

Another important issue is the meaningfulness of the observed interest rate in the developing countries. In general, the observed interest rate may not correctly reflect the cost of holding money since there exist: (1) institutional rigidities and regulations which set the interest and discount rates; (2) unorganized money markets which yield substantially higher interest rates; (3) and immature financial markets which offer a limited range of alternative assets to the wealth holders. Under such conditions, physical assets represent the most common form of wealth holding. If readily liquidable, they constitute close substitutes for real balances. Thus, the expected rate of inflation, instead of the rate of interest, becomes an appropriate indicator of the rate of return on assets (see e.g. Nugent, and Glezakos, 1979).

In general though, the effect of unanticipated and variable inflation on the consumer demand is ambiguous. Workers, who expect their nominal incomes fail to keep up with inflation, try to spend less. To the extent that they treat higher inflation as a sign of hard times to come, inflationary expectations cause consumption expenditure to decline. However, expectations of higher inflation may have the opposite effect. Higher prices translated into reduced purchasing powers increase the level of aggregate demand as consumers spend more rapidly. They may decide to buy before prices rise. If the "purchasing power" effect predominates the "hard times" effect, then expectations of accelerating inflation will stimulate, rather than depress, the aggregate demand (see e.g., Dolan, 1980, 134-).

Also, the degree of credit restraint may be a proxy for the interest rate as there exist certain links between the organized and unorganized money markets, and since borrowing is still a means of financing transactions. Due to the negligibility of the speculative money demand and pegging of the interest rate, the observable interest rates cease to be the key linkage between holding money and interest bearing assets. Instead, interest rates in the unorganized markets, although unobservable, reflect the degree of credit restraint in an economy. Wong (1977) suggested that, in the developing countries, where interest rates are inoperative, the degree of credit restraint can approximate the opportunity cost of holding real balances. His experimentation with various measures of the degree of credit restraint used in the demand for money function demonstrated that the negative of domestic credit to income ratio and one less the ratio of domestic credit to income are generally applicable.

In our empirical examination, thee PIH and RWH consumption models are estimated to determine the effect of the observed real interest rate or its proxy variables on consumption.

III. Consumption Model

In the PIH, permanent consumption is proportional to permanent income. (1) [Mathematical Expression Omitted] where, the factor of proportionality depends on the real rate of interest r ([Delta]k/[Delta]r<0), the ratio of human to nonhuman capital w ([Delta]k/[Delta]w<0), and consumer taste u for current consumption or savings and hence for future consumption. Permanent income and consumption are unobservable and therefore correspondence must be established between them and measured income and consumption, (2) [Mathematical Expression Omitted] (3) [Mathematical Expression Omitted] Transitory income and transitory consumption are random components of measured income and consumption [Mathematical Expression Omitted]. There is expected to be no correlation between permanent and transitory income, permanent and transitory consumption, and transitory income and transitory consumption, (4) [Rho] ([Y.sup.P], [Y.sub.T]) = [Rho] ([C.sup.P], [C.sup.T]) = [Rho] ([Y.sup.T], [C.sup.T] = 0 In particular, zero correlation between transitory income and transitory consumption implies that transitory income is saved to form capital or is spent on consumer durables. In the "strict" form of the PIH, all of the consumption increase is explained by the increase in permanent income. In the "modified" PIH, the marginal propensity to consume out of transitory income is positive, but smaller than the marginal propensity to consume out of permanent income [e.g., Laumas and Laumas (1976)]. Accordingly, consumption is a function of both permanent and transitory income, (5) [Mathematical Expression Omitted]

To investigate the effect of the interest rate on consumption behavior, Carlino expresses the marginal propensity to consume out of permanent income as a linear function of the real interest rate, (6) [k.sup.P] = a + [br.sub.t] Substitute (6) in (5), the consumption function becomes (7) [Mathematical Expression Omitted] Carlino's sensitivity test of (7) consists of the comparison between estimation results of (7) with those from a regression in which the real interest rate directly affects consumption, (8) [Mathematical Expression Omitted]

Since the PIH places great importance on the current period expectations of future income, the process of expectations formation plays a central role in the analysis of consumption behavior. Originally, the adaptive expectations hypothesis is used to generate values for unobservable permanent and transitory income by estimating income weights from a geometrically declining distributed lag function of past levels of the observed income (see Friedman).

Hall argues that empirical research on the LCH and PIH is seriously weakened by failing to take proper account of the endogeneity of income, which is the major independent variable in these consumption functions. Begg (1982) formulates the rational expectations RWH consumption behavior by assuming that households lend or borrow at a constant real rate of interest [Delta]. Denoting [W.sub.t] as the current period real wealth and [Mathematical Expression Omitted] as rational expectations of future incomes conditional on current information, permanent income is defined as (9) [Mathematical Expression Omitted] Considering that households at the time (t - 1) form expectations conditional on information available at this time, expectations of permanent income is (10) [Mathematical Expression Omitted] By definition of permanent income as a constant stream that households envisage over the planning horizon, it must be true that (11) [Mathematical Expression Omitted] Substitute (11) in (10) and subtract that from (9), (12) [Mathematical Expression Omitted] Noting that each and every term in the right hand side is a pure rational expectations forecast error, rewrite (12) as (13) [Mathematical Expression Omitted] Where [u.sub.t] is a white noise random variable. Equation (13) implies that individuals ought not to expect their permanent income to change, for if it did, this knowledge should already have been used to reassess permanent income.

To derive the RWH consumption function, lag (1) by one period, subtract that from (1) and then apply (13), (14) [C.sub.t] = [C.sub.t-1] + [V.sub.t] where [v.sub.t] = [ku.sub.t] is also white noise random variable. Accordingly, consumption follows a random walk behavior, implying that the best guess about future consumption is the current period consumption because it is based on the latest assessment of permanent income, which embodies all available information at the time of forming expectations. In the random walk test of consumption behavior, up to four period lagged values of variables such as consumption expenditure, observed income, or the real interest rate are added to (14), (15) [Mathematical Expression Omitted] (16) [Mathematical Expression Omitted] (17) [Mathematical Expression Omitted] Hypothesis testing of the presence of irrelevant variables (t-test) and joint test on several regression coefficient (F-test) are performed [Pindyck and Rubinfeld (1981: 130-131 and 117-119)]. The random walk behavior is observed if the estimated coefficient of one period lagged consumption does not vary significantly from one, while coefficients of other lagged variables included in (15)-(17) do not significantly vary from zero.

IV. Empirical Results

Data include annual observations on private consumption expenditure and disposable personal income expressed in 1960 prices and per capita values for the 1953-84 period. The long run government bonds interest rate is deflated to represent the real interest rate. The rate of inflation is computed as the percentage change of the implicit GNP deflator over its previous period. Main sources of data included Statistical Yearbook for Asia and Pacific, Pakistan Economic Survey, Report on Currency and Finance, and various reports of State Bank of Pakistan and 20 Years of Pakistan in Statistics (for more detailed explanation see Ghouri, 1986).

The observe variables in the consumption function models are:

C: Consumption expenditure

Y: Disposable personal income

r:Interest rate

i: Inflation rate The measure of credit constraint, as suggested by Wong, does not seem to be appropriate and, therefore, is not considered. The degree of credit restraint is likely to be exogenous. In particular, the level of domestic credit itself is highly influenced by the GNP and other macroeconomic variables. Hence, the negative domestic credit-income ratio, for instance, will not accurately measure the opportunity cost of holding money and may generate biased estimates.

The adaptive expectations PIH consumption functions (5), (7), and (8) are estimated by first or second degree serial correlation procedures, whenever necessary. The Almon procedure is used to estimate the appropriate weights in generating values for the unobservable permanent and transitory incomes and expected inflation rate. Best weights are obtained from a polynomial distributed lag model with degree one and length three subject to a tail restriction.(1) Table 1 presents the estimation results. In all equations, the autonomous consumption is insignificant, indicating the existence of a long-run consumption relationship. Coefficients of both permanent and transitory income variables are significantly different from zero and one. But, the marginal propensity to consume out of permanent income is close to unity and larger than that of transitory income. This result supports the "modified" PIH in which some of the transitory income is consumed. The estimate coefficient of the real interest rate (r) or expected inflation rate ([i.sup.e]) on consumption is insignificant. This result indicates that the "purchasing power" and "hard time" effects of inflation offset each other, generating no significant net impact on the level of aggregate demand. [Tabular Data 1 Omitted]

The rational expectation RWH consumption functions (14)--(17) are estimated to test a joint null hypothesis claiming that the coefficient of one period lagged consumption is one, while coefficients of all other variables lagged are equal to zero. Table 2 presents the estimation results. No evidence of serial correlation is present as indicated by values of the Durbin-h statistic. In all regression equations, the estimated coefficient of the one period lagged consumption is close to unity and the null hypothesis that this coefficient is equal to one cannot be rejected. Coefficients of additional lagged consumption or income are significant, indicating that consumption follows a random walk behavior. Once again, the estimated coefficient of the real rate of interest or the expected rate of inflation is statistically insignificant. These alternative measures of the cost of holding money are viewed as irrelevant variables in the RWH consumption function.(2) The efficiency loss from the inclusion of these irrelevant variables does not greatly influence the significance of the one period lagged consumption parameter. In the joint test involving coefficients of the additional variables, the null hypothesis that their coefficients equal to zero is accepted as values of the computed F-statistic are all smaller than their critical values. [Tabular Data 2 Omitted]

V. Conclusion

Our complementary findings are that both the adaptive expectations PIH and rational expectations RWH fit our data equally well and that the replacement of the real interest rate by the expected rate of inflation does not alter the empirical results.

Our estimation results of the consumption function present evidence that the real rate of interest has no effect on consumption behavior in Pakistan. This finding has important implications for domestic capital formation and income growth. An interest-insensitive consumption function in a low-income country such as Pakistan indicates that individuals are unwilling or unable to alter significantly their projected consumption path to take advantage of higher rates of return on interest bearing assets. No increase in the volume of domestic savings may occur and no additional resources may be released for investment in response to variations in the real interest rate. The likely response of the current account is thus, other things equal, a deficit due to the low savings-GNP ratio. Also, limited domestic capital formation hinders income growth in the absence of external financing to fill in the savings-investment gap. such an interest-insensitivity is crucial in the case where the economy faces constraints on international indebtedness should the international lending institutions require higher real interest rates to increase savings of domestic residents and stimulate capital formation.

Notes

(1)The adaptive expectations hypothesis is used to generate predictions for income and inflation rate variables from polynomial distributed lag models of degree one and minimum lag length of three years with tail restrictions. Time-series on permanent income include the predicted values of the measured income and transitory income series are the residuals and time-series on expected inflation rate consist of the predicted values of actual inflation rates. (2)Coefficients of the fourth lagged real interest rate, as well as inflation rate are close to zero and thus not reported in Table 2.

Bibliography

Begg, D. K. H. The Rational Expectations Revolution in Macroeconomics: Theories and Evidence, Oxford: Philip Allan Publishers, 1982. Blinder, A. S. and A. Denton. "The Time Series Consumption Function Revisited," Brooking Papers on Economic Activity, 35(2), 188, 316-335. Boskin, M. J., "Taxation, Saving, and the Rate of Interest," Journal of Political Economy, 88(2), S3-S27. Campbell, J. Y. and N. G. Mankiw, "Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence," in O. J. Blanchard and S. Fisher (eds.) NBER Macroeconomics Annual 1989, Cambridge, MA: MIT Press, 1989, 185-216. Carlino, G. A. "Interest Rate Effects and Intertemporal Consumption," Journal of Monetary Economics, 9, 1982, 223-234. Dolan, E. G., Basic Macroeconomics, Hinsdale, IL: The Dryden Press, 1980. Feldstein, M. "Inflation, Specification Bias, and the Impact of Interest Rates," Journal of Political Economy, 78(6), 1970, 1325-1339. Friedman, M. A. Theory of Consumption Function, Princeton: Princeton University Press, 1957. Ghouri, S. S., Testing Consumption Behavior Under Alternative Income Hypothesis for Pakistan, MA Thesis, University of Waterloo, 1986. Giovanni, A. "Saving and the Real Interest Rate in LDCs," Journal of Development Economics, 18, 1985, 197-217. Hall, R. E. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, 86(6), 1978, 971-987. Heien, D. M. "Demographic Effects and Multiperiod Consumption Function," Journal of Political Economy, 80(1), 1972, 125-188. Keynes, J. M. The General Theory of Employment, Interest and Money, London: MacMillan, 1936. Kuznets, S. S. National Product Since 1869, New York: National Bureau of Economic Research, 1946. Laumas, P. and G. Laumas. "The Permanent Income Hypothesis in an Underdeveloped Economy," Journal of Development Economics, 3(3), 1976, 289-297. Modigliani, F. and R. E. Brumberg. "Utility Analysis and the Aggregate Consumption Function. "Mimeo, 1953. Nugent, J. B. and C. Glezakos, "A Model of Inflation and Expectations in Latin America," Journal of Development Economics, 6 September 1979, 431-446. Pindyck, R. S. and D. L. Rubinfeld. Econometrics Models and Economics Forecasts, New York: McGraw-Hill, 1981. Springer, W. L. "Did the 1968 Surcharge Really Work?" American Economic Review, 83(3), 1975, 664-659. Weber, W. E. "The Effects of Interest Rates on Aggregate Consumption," American Economic Review, LX(4), 1970, 591-600. Wong, C., "Demand for Money in Developing Countries: Some Theoretical and Empirical Results, "Journal of Monetary Economics, 3 1977, 59-86. (*)This research is drawn from Salman Saif Ghouri's graduate thesis at the University of Waterloo. He is indebted to Professors D. A. Wilton, S. K. Ghosh, and L. P. Fletcher under whose supervision the thesis was completed. Abbas Pourgerami, California State University at Bakersfield. Salman Saif Ghouri, Colorado School of Mines at Golden.

The effect of the interest rate on consumption behavior has been subject to controversy. Before Keynes (1936), the interest rate was considered to be the prime determinant of savings. Keynes demonstrated that fluctuations in the short run interest rate had no significant effect on spending decisions. Kuznets (1946) reported that the savings rate remained stable over the long run. However, in Modigliani's (1953) life cycle hypothesis (LCH), the interest rate played an important part in measuring the consumer's expected future earnings and net worth which, in turn, influenced consumption behavior. In Friedman's (1957) permanent income hypothesis (PIH), the rate of interest became a major determinant of the marginal propensity to consume out of permanent income.

More recently, Wright (1967) and Heien (1972) estimated a negative and significant relationship between the interest rate and consumption expenditure. In contrast, Weber (1970) and Springer (1975) reported a positive and significant effect of the interest rate on consumption. Also, Boskin (1978) estimated a substantial interest elasticity of savings. Feldstein (1970) demonstrated that studies using the nominal instead of the real interest rate were subject to a serious specification bias. Carlino (1982) employing four different interest rates estimated contradictory signs for the interest rate coefficients and rejected the hypothesis that variations in the real interest rate altered consumption decisions. Likewise, Blinder and Deaton (1985) and Campbell and Mankiw (1989) estimated an insignificant effect of the real interest rate on consumption.

In this paper, we examine the effect of the real interest rate on consumption behavior in Pakistan, taking into consideration the presence of money market imperfections. Thus, alternative proxies for the opportunity cost of holding real balances are considered to test the sensitivity of the consumption function to the changing money market conditions. Section II discusses issues related to estimating the consumption function and to the structural characteristics of money markets in the developing countries. Section III outlines the theory of consumption function. Section IV presents the empirical results and Section V includes the concluding remarks.

II. Relevant Issues

Development of the theory of consumption function has been fascinating but controversial. For a long time, both the theoretical derivation and the econometric framework of the aggregate consumption function were considered settled. Most economists adhered to one of two ways of putting Fisher's theory of intertemporal optimization into cooperation: the PIH or LCH. Since each variant had sound theoretical construct, and since they had similar econometric forms that could explain the data well and had similar policy implications, there was not a great deal of controversy about. However, development in economic research have raised fundamental questions about the theory of consumption function. Some recent theoretical development included the Barro's equivalence hypothesis (1974), Lucas' critique (1976), Hall's random walk hypothesis (RWH) (1978), as well as flexible approaches by Giovannini (1985) and Blinder and Deaton.

Hence, a complementary goal of our investigation of the relationship between consumption and the real interest rate is to test the fit of the standard consumption models against that of their recent challenges to Pakistan's data. For a secondary issue as such, it may be suffice to focus on only two alternative formulations of the consumption function, for example, PIH and RWH that quarrel about the nature of income expectations.

Another important issue is the meaningfulness of the observed interest rate in the developing countries. In general, the observed interest rate may not correctly reflect the cost of holding money since there exist: (1) institutional rigidities and regulations which set the interest and discount rates; (2) unorganized money markets which yield substantially higher interest rates; (3) and immature financial markets which offer a limited range of alternative assets to the wealth holders. Under such conditions, physical assets represent the most common form of wealth holding. If readily liquidable, they constitute close substitutes for real balances. Thus, the expected rate of inflation, instead of the rate of interest, becomes an appropriate indicator of the rate of return on assets (see e.g. Nugent, and Glezakos, 1979).

In general though, the effect of unanticipated and variable inflation on the consumer demand is ambiguous. Workers, who expect their nominal incomes fail to keep up with inflation, try to spend less. To the extent that they treat higher inflation as a sign of hard times to come, inflationary expectations cause consumption expenditure to decline. However, expectations of higher inflation may have the opposite effect. Higher prices translated into reduced purchasing powers increase the level of aggregate demand as consumers spend more rapidly. They may decide to buy before prices rise. If the "purchasing power" effect predominates the "hard times" effect, then expectations of accelerating inflation will stimulate, rather than depress, the aggregate demand (see e.g., Dolan, 1980, 134-).

Also, the degree of credit restraint may be a proxy for the interest rate as there exist certain links between the organized and unorganized money markets, and since borrowing is still a means of financing transactions. Due to the negligibility of the speculative money demand and pegging of the interest rate, the observable interest rates cease to be the key linkage between holding money and interest bearing assets. Instead, interest rates in the unorganized markets, although unobservable, reflect the degree of credit restraint in an economy. Wong (1977) suggested that, in the developing countries, where interest rates are inoperative, the degree of credit restraint can approximate the opportunity cost of holding real balances. His experimentation with various measures of the degree of credit restraint used in the demand for money function demonstrated that the negative of domestic credit to income ratio and one less the ratio of domestic credit to income are generally applicable.

In our empirical examination, thee PIH and RWH consumption models are estimated to determine the effect of the observed real interest rate or its proxy variables on consumption.

III. Consumption Model

In the PIH, permanent consumption is proportional to permanent income. (1) [Mathematical Expression Omitted] where, the factor of proportionality depends on the real rate of interest r ([Delta]k/[Delta]r<0), the ratio of human to nonhuman capital w ([Delta]k/[Delta]w<0), and consumer taste u for current consumption or savings and hence for future consumption. Permanent income and consumption are unobservable and therefore correspondence must be established between them and measured income and consumption, (2) [Mathematical Expression Omitted] (3) [Mathematical Expression Omitted] Transitory income and transitory consumption are random components of measured income and consumption [Mathematical Expression Omitted]. There is expected to be no correlation between permanent and transitory income, permanent and transitory consumption, and transitory income and transitory consumption, (4) [Rho] ([Y.sup.P], [Y.sub.T]) = [Rho] ([C.sup.P], [C.sup.T]) = [Rho] ([Y.sup.T], [C.sup.T] = 0 In particular, zero correlation between transitory income and transitory consumption implies that transitory income is saved to form capital or is spent on consumer durables. In the "strict" form of the PIH, all of the consumption increase is explained by the increase in permanent income. In the "modified" PIH, the marginal propensity to consume out of transitory income is positive, but smaller than the marginal propensity to consume out of permanent income [e.g., Laumas and Laumas (1976)]. Accordingly, consumption is a function of both permanent and transitory income, (5) [Mathematical Expression Omitted]

To investigate the effect of the interest rate on consumption behavior, Carlino expresses the marginal propensity to consume out of permanent income as a linear function of the real interest rate, (6) [k.sup.P] = a + [br.sub.t] Substitute (6) in (5), the consumption function becomes (7) [Mathematical Expression Omitted] Carlino's sensitivity test of (7) consists of the comparison between estimation results of (7) with those from a regression in which the real interest rate directly affects consumption, (8) [Mathematical Expression Omitted]

Since the PIH places great importance on the current period expectations of future income, the process of expectations formation plays a central role in the analysis of consumption behavior. Originally, the adaptive expectations hypothesis is used to generate values for unobservable permanent and transitory income by estimating income weights from a geometrically declining distributed lag function of past levels of the observed income (see Friedman).

Hall argues that empirical research on the LCH and PIH is seriously weakened by failing to take proper account of the endogeneity of income, which is the major independent variable in these consumption functions. Begg (1982) formulates the rational expectations RWH consumption behavior by assuming that households lend or borrow at a constant real rate of interest [Delta]. Denoting [W.sub.t] as the current period real wealth and [Mathematical Expression Omitted] as rational expectations of future incomes conditional on current information, permanent income is defined as (9) [Mathematical Expression Omitted] Considering that households at the time (t - 1) form expectations conditional on information available at this time, expectations of permanent income is (10) [Mathematical Expression Omitted] By definition of permanent income as a constant stream that households envisage over the planning horizon, it must be true that (11) [Mathematical Expression Omitted] Substitute (11) in (10) and subtract that from (9), (12) [Mathematical Expression Omitted] Noting that each and every term in the right hand side is a pure rational expectations forecast error, rewrite (12) as (13) [Mathematical Expression Omitted] Where [u.sub.t] is a white noise random variable. Equation (13) implies that individuals ought not to expect their permanent income to change, for if it did, this knowledge should already have been used to reassess permanent income.

To derive the RWH consumption function, lag (1) by one period, subtract that from (1) and then apply (13), (14) [C.sub.t] = [C.sub.t-1] + [V.sub.t] where [v.sub.t] = [ku.sub.t] is also white noise random variable. Accordingly, consumption follows a random walk behavior, implying that the best guess about future consumption is the current period consumption because it is based on the latest assessment of permanent income, which embodies all available information at the time of forming expectations. In the random walk test of consumption behavior, up to four period lagged values of variables such as consumption expenditure, observed income, or the real interest rate are added to (14), (15) [Mathematical Expression Omitted] (16) [Mathematical Expression Omitted] (17) [Mathematical Expression Omitted] Hypothesis testing of the presence of irrelevant variables (t-test) and joint test on several regression coefficient (F-test) are performed [Pindyck and Rubinfeld (1981: 130-131 and 117-119)]. The random walk behavior is observed if the estimated coefficient of one period lagged consumption does not vary significantly from one, while coefficients of other lagged variables included in (15)-(17) do not significantly vary from zero.

IV. Empirical Results

Data include annual observations on private consumption expenditure and disposable personal income expressed in 1960 prices and per capita values for the 1953-84 period. The long run government bonds interest rate is deflated to represent the real interest rate. The rate of inflation is computed as the percentage change of the implicit GNP deflator over its previous period. Main sources of data included Statistical Yearbook for Asia and Pacific, Pakistan Economic Survey, Report on Currency and Finance, and various reports of State Bank of Pakistan and 20 Years of Pakistan in Statistics (for more detailed explanation see Ghouri, 1986).

The observe variables in the consumption function models are:

C: Consumption expenditure

Y: Disposable personal income

r:Interest rate

i: Inflation rate The measure of credit constraint, as suggested by Wong, does not seem to be appropriate and, therefore, is not considered. The degree of credit restraint is likely to be exogenous. In particular, the level of domestic credit itself is highly influenced by the GNP and other macroeconomic variables. Hence, the negative domestic credit-income ratio, for instance, will not accurately measure the opportunity cost of holding money and may generate biased estimates.

The adaptive expectations PIH consumption functions (5), (7), and (8) are estimated by first or second degree serial correlation procedures, whenever necessary. The Almon procedure is used to estimate the appropriate weights in generating values for the unobservable permanent and transitory incomes and expected inflation rate. Best weights are obtained from a polynomial distributed lag model with degree one and length three subject to a tail restriction.(1) Table 1 presents the estimation results. In all equations, the autonomous consumption is insignificant, indicating the existence of a long-run consumption relationship. Coefficients of both permanent and transitory income variables are significantly different from zero and one. But, the marginal propensity to consume out of permanent income is close to unity and larger than that of transitory income. This result supports the "modified" PIH in which some of the transitory income is consumed. The estimate coefficient of the real interest rate (r) or expected inflation rate ([i.sup.e]) on consumption is insignificant. This result indicates that the "purchasing power" and "hard time" effects of inflation offset each other, generating no significant net impact on the level of aggregate demand. [Tabular Data 1 Omitted]

The rational expectation RWH consumption functions (14)--(17) are estimated to test a joint null hypothesis claiming that the coefficient of one period lagged consumption is one, while coefficients of all other variables lagged are equal to zero. Table 2 presents the estimation results. No evidence of serial correlation is present as indicated by values of the Durbin-h statistic. In all regression equations, the estimated coefficient of the one period lagged consumption is close to unity and the null hypothesis that this coefficient is equal to one cannot be rejected. Coefficients of additional lagged consumption or income are significant, indicating that consumption follows a random walk behavior. Once again, the estimated coefficient of the real rate of interest or the expected rate of inflation is statistically insignificant. These alternative measures of the cost of holding money are viewed as irrelevant variables in the RWH consumption function.(2) The efficiency loss from the inclusion of these irrelevant variables does not greatly influence the significance of the one period lagged consumption parameter. In the joint test involving coefficients of the additional variables, the null hypothesis that their coefficients equal to zero is accepted as values of the computed F-statistic are all smaller than their critical values. [Tabular Data 2 Omitted]

V. Conclusion

Our complementary findings are that both the adaptive expectations PIH and rational expectations RWH fit our data equally well and that the replacement of the real interest rate by the expected rate of inflation does not alter the empirical results.

Our estimation results of the consumption function present evidence that the real rate of interest has no effect on consumption behavior in Pakistan. This finding has important implications for domestic capital formation and income growth. An interest-insensitive consumption function in a low-income country such as Pakistan indicates that individuals are unwilling or unable to alter significantly their projected consumption path to take advantage of higher rates of return on interest bearing assets. No increase in the volume of domestic savings may occur and no additional resources may be released for investment in response to variations in the real interest rate. The likely response of the current account is thus, other things equal, a deficit due to the low savings-GNP ratio. Also, limited domestic capital formation hinders income growth in the absence of external financing to fill in the savings-investment gap. such an interest-insensitivity is crucial in the case where the economy faces constraints on international indebtedness should the international lending institutions require higher real interest rates to increase savings of domestic residents and stimulate capital formation.

Notes

(1)The adaptive expectations hypothesis is used to generate predictions for income and inflation rate variables from polynomial distributed lag models of degree one and minimum lag length of three years with tail restrictions. Time-series on permanent income include the predicted values of the measured income and transitory income series are the residuals and time-series on expected inflation rate consist of the predicted values of actual inflation rates. (2)Coefficients of the fourth lagged real interest rate, as well as inflation rate are close to zero and thus not reported in Table 2.

Bibliography

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Author: | Pourgerami, Abbas; Ghouri, Salman Saif |
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Publication: | American Economist |

Date: | Sep 22, 1991 |

Words: | 3108 |

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