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A test for the presence of precautionary saving
Economics Letters North-Holland
471
37 (1991) 471-475
A test for the presence of precautionary saving Michael
Kuehlwein
Pomona College, Claremont, CA 91711, USA Received Accepted
22 July 1991 3 October 1991
This paper tests for precautionary saving by deriving an explicit measure of consumer uncertainty: the expectational errors from a consumption Euler equation. Using data from the Panel Study of Income Dynamics, I estimate these errors and find, contrary to the theory, a negative correlation between consumer uncertainty and consumption growth.
1. Introduction
The notion that income and other forms of uncertainty could encourage consumers to save was formalized originally by Leland (1968). Since then, several studies have argued that the presence of precautionary savings has important macroeconomic implications. Barsky et al (1986) show that such considerations can lead to a violation of Ricardian equivalence. Skinner (1988) contends that precautionary savings may constitute 56% of total life cycle savings. And Kimball and Mankiw (1989) demonstrate that announced future tax cuts can boost current consumption by reducing future income uncertainty. Despite these studies, little research has been done to confirm the presence of such saving. Skinner (1988) found that workers in risky occupations, such as self-employment and sales, actually saved significantly less than other workers, a rejection of the theory. One limitation of his study is that occupation may be a less than perfect index of consumer uncertainty. In this paper, I provide a more direct measure of consumer uncertainty: the expectational errors from a consumption Euler equation. In section 3, I use estimates of these errors to test for a correlation between uncertainty and consumption growth. Section 4 summarizes the results.
2. The theoretical model The familiar Euler equation function is: Ei,t[(l
0165-1765/91/%03.50
+
for an additively separable constant relative risk aversion utility
ri.l+t)tci,,,,/ci,~)-“]
0 1991 - Elsevier
=
Science
Publishers
l + 67 B.V. All rights reserved
472
M. Kuehlwein / A test for the presence of precautionary saving
where r is the after-tax real interest rate, A the coefficient of relative risk aversion, rate, and all variables are subscripted by individual, i, and time, t. Let:
Ei,t(xi,t+l)
Then
assume
Invoking
(2)
= (1 +Ti,t+l)/(Ci,r/Ci,r+I)-A.
X,t+,
=
’
+
xi,t+l
-LN
xi,t+t
E
log-normally:
where
ln(x,,,+,)
the assumption exp(pi
(3)
s.
X is distributed
+ ui2/2)
6 the discount
E(X,,,+,) N
N(Pi,
of rational
(4)
=exp(pi+u12/2),
(5)
(Ti2).
expectations,
eq. (3) gives us,
(6)
= 1 + 6,
pi = In( 1 + 6) - ui2/2,
(7)
Ei,t( Xi,,+ i) = In( 1 + 6) - u12/2.
(8)
Therefore,
Substituting
=ln(l+6)
xi,t+
1
ei,t+
1 -
(9)
-f$/2+ei,,+,,
(10)
N(0, ui2).
in for x~,~+ 1 and rearranging: ln(Ci,,+i/Ci,,)
= -(l/A) -(l/A)ei,t+l.
ln(1 + 6) + (l/A)fl?/2
+ (l/A)
ln(1 +
‘i,t+l)
(11)
The variance term on the right-hand side represents the effect of precautionary saving. It derives from the variance of the error term. Hence, the same uncertainty that produces Euler equation errors depresses current consumption and elevates future consumption, boosting consumption growth. This equivalence enables us to estimate the precautionary savings variable and to gauge its impact on consumption.
3. Data and estimation Annual data were provided by the Panel Study of Income Dynamics (PSID) for the years 1971-1972 and 1975-1982. The only consumption data recorded in the PSID are food expenditures. Though not ideal, they constitute 50% of consumer spending on nondurable goods, so they represent an important component of total consumption. Nominal household food expenditures were deflated by the appropriate Consumer Price Indices and adjusted for the number and ages of household members. Real ex-post after-tax interest rates
M. Kuehlwein / A test for the presence of precautionary saving Table 1 Estimates
of the elasticity
of intertemporal
Regressor A. Entire
l/A.
substitution, A ln(l+
sample
B. Unconstrained
sample
Two-stage
least squares.
a Observations
rL.,+r)
0.258 (0.230)
9,607
0.868 * (0.440)
1,802
” Figures in parentheses are heteroskedasticity-consistent ,* Significant at the 5% level.
standard
473
errors.
were calculated using annual changes in food prices, the yields on one-year Tbills, and marginal tax rates estimated from reported federal income tax liabilities. Any observations involving changes in family composition were discarded, as were all C,+i/Ct observations outside the 0.25-4 range to control for extreme cases of measurement error. Family units headed by someone older than 65 were excluded. To generate estimates of the variance of the error term, eq. (11) was first-differenced:
A lW,,t+ 1/Ci,,> = (l/A) A 141 + rr,t+l) - (l/A) A’,,,+,.
(12)
To control for the correlation between the change in ex-post interest rates and the error term, I instrumented with the real ex-post interest rate and marginal tax rate dated t - 1, and with predictions of the real expost interest rate for time t using AR(4) forecasts of inflation from period I - 1 and the lagged marginal tax rate. The results, with heteroskedasticity-consistent standard errors, are reported in the first line of table 1. The estimated parameter on the interest rate variable suggests a coefficient of relative risk aversion roughly equal to 4. Though a plausible value, l/A is not significantly different from 0, and a 95% confidence interval stretches from negative numbers to 0.7. I chose therefore to work with a range of values for A: 0.5, 1, 2, 4, and 10. These roughly span the values obtained by other researchers [e.g. Hansen and Singleton (1983) and Mankiw (198511, and working with different risk aversion parameters should provide an indication of the robustness of the results. With an estimate of A, one can generate estimates of the error terms (plus a constant) in eq. (111, and hence compute estimates of household-specific error variances. ’ I limited the sample to those households with at least 4 years of data to minimize the measurement error in the variance estimates. For each assumed value of A, I then ran the regression: WG,,+l/CJ
-
(l/A)
141
+
Ti,t+~)
=Bo
+
BlGi2/2
+
Ei.r+l.
(13)
In theory, consumption growth will be positively related to the uncertainty variable. Because of measurement error in the right-hand side variable, I used the age of the household head, average household food needs, disposable income, and wealth from the first period of the sample, and the variance of household disposable income over the sample as instruments. The results, with heteroskedasticity-consistent standard errors, are displayed in the first tier of table 2. For every assumed level of risk aversion, uncertainty has a significant negative effect on consumption growth. The levels of significance range from 5% for A = 10, 4, and 2, to 1% for ’ Kuehlwein (1987) shows that this estimation in the consumption data.
procedure
is still valid in the presence
of a likely form of measurement
error
M. Kuehlwein /A
474 Table 2 Estimates
of the impact
Regressors
of income
uncertainty
test for the presence of precautionary saving
on consumption
growth.
Two-stage
Constant
$/2
0.087 (0.016) * *
- 0.445 (0.121) * *
2. A=1
0.057 (0.015) * *
- 0.341 (0.120) **
3.A=2
0.043 (0.015) * *
- 0.290 (0.120) *
4. A=4
0.036 (0.015) * *
- 0.264 to.1201 *
5. A = 10
0.032 (0.015) *
- 0.248 (0.120) *
0.065 (0.023)
- 0.275 (0.199)
2. A=1
0.039 (0.023)
-0.184 (0.201)
3. A=2
0.026 (0.023)
-0.140 (0.202)
4.A=4
0.020 (0.023)
-0.118 (0.204)
5. A = 10
0.026 (0.023)
-0.140 (0.202)
A. Entire sample 1. A = 0.5
B. Unconstrained 1. A = 0.5
least squares.
a
Observations 14,822
4,644
sample
are heteroskedasticity-consistent a Figures in parentheses * Significant at the 5% level. ** Significant at the 1% level.
standard
errors.
A = 1 and 0.5. These results contradict the theory of precautionary savings. For all plausible values of relative risk aversion, consumption growth is negatively, and significantly, correlated with consumer uncertainty. Several authors [e.g., Zeldes (1989)] have concluded that the presence of liquidity constraints interferes with the standard consumption Euler equation. To account for this, I discarded those observations for households with low levels of wealth. Asset holdings were estimated from reported asset income. Housing wealth was excluded due to its potential illiquidity. Households were classified as unconstrained if their estimated wealth exceeded one-sixth of their previous year’s income. Estimation of eq. (12) for unconstrained households is displayed in table 1. The estimate of l/A is significant at the 5% level and suggests a value of A approximately equal to 1. However, a 95% confidence interval again encompasses other plausible values of A, so I proceeded to work with the same range of risk aversion parameters. Estimates of eq. (13) are contained in table 2. Again, the estimated effect of consumer uncertainty on consumption growth is negative for all values of A. The coefficient on the uncertainty variable is no longer significantly different from 0 at conventional levels. However, these results again provide no evidence of precautionary saving.
M. Kuehlwein /A
test for the presence of precautionary saving
47.5
4. Conclusion
In this paper, I noted that the uncertainty that generates precautionary saving is reflected in the expectational errors of the consumption Euler equation. Under certain parametric assumptions, one is able to quantify that uncertainty and test for its impact on consumption growth. The results paradoxically indicated that greater consumption uncertainty engenders a flatter consumption trajectory. This agrees with Skinner’s (1988) finding that individuals in riskier occupations actually save less.
References Barsky, R., N.C. Mankiw, and S. Zeldes, 1986, Ricardian consumers with Keynesian propensities, American Economic Review 76, 676-691. Hansen, L.P. and K.J. Singleton, 1983, Stochastic consumption, risk aversion, and the temporal behavior of asset returns, Journal of Political Economy 91, 249-265. Kimball, M. and N.C. Mankiw, 1989, Precautionary saving and the timing of taxes, Journal of Political Economy 97, 863-879. Kuehlwein, M., 1987, Consumption in the presence of uncertainty, unpublished/doctoral dissertation, M.I.T. Leland, H.E., 1968, Savings and uncertainty: The precautionary demand for saving, Quarterly Journal of Economics 82, 465-473. Mankiw, N.G., 1985, Consumer durables and the real interest rate, Review of Economics and Statistics 67, 353-362. Skinner, J., 1988, Risky income, life cycle consumption, and precautionary savings, Journal of Monetary Economics 22, 237-255. Zeldes, S., 1989, Consumption and liquidity constraints: An empirical investigation, Journal of Political Economy 97, 305-346.
471
37 (1991) 471-475
A test for the presence of precautionary saving Michael
Kuehlwein
Pomona College, Claremont, CA 91711, USA Received Accepted
22 July 1991 3 October 1991
This paper tests for precautionary saving by deriving an explicit measure of consumer uncertainty: the expectational errors from a consumption Euler equation. Using data from the Panel Study of Income Dynamics, I estimate these errors and find, contrary to the theory, a negative correlation between consumer uncertainty and consumption growth.
1. Introduction
The notion that income and other forms of uncertainty could encourage consumers to save was formalized originally by Leland (1968). Since then, several studies have argued that the presence of precautionary savings has important macroeconomic implications. Barsky et al (1986) show that such considerations can lead to a violation of Ricardian equivalence. Skinner (1988) contends that precautionary savings may constitute 56% of total life cycle savings. And Kimball and Mankiw (1989) demonstrate that announced future tax cuts can boost current consumption by reducing future income uncertainty. Despite these studies, little research has been done to confirm the presence of such saving. Skinner (1988) found that workers in risky occupations, such as self-employment and sales, actually saved significantly less than other workers, a rejection of the theory. One limitation of his study is that occupation may be a less than perfect index of consumer uncertainty. In this paper, I provide a more direct measure of consumer uncertainty: the expectational errors from a consumption Euler equation. In section 3, I use estimates of these errors to test for a correlation between uncertainty and consumption growth. Section 4 summarizes the results.
2. The theoretical model The familiar Euler equation function is: Ei,t[(l
0165-1765/91/%03.50
+
for an additively separable constant relative risk aversion utility
ri.l+t)tci,,,,/ci,~)-“]
0 1991 - Elsevier
=
Science
Publishers
l + 67 B.V. All rights reserved
472
M. Kuehlwein / A test for the presence of precautionary saving
where r is the after-tax real interest rate, A the coefficient of relative risk aversion, rate, and all variables are subscripted by individual, i, and time, t. Let:
Ei,t(xi,t+l)
Then
assume
Invoking
(2)
= (1 +Ti,t+l)/(Ci,r/Ci,r+I)-A.
X,t+,
=
’
+
xi,t+l
-LN
xi,t+t
E
log-normally:
where
ln(x,,,+,)
the assumption exp(pi
(3)
s.
X is distributed
+ ui2/2)
6 the discount
E(X,,,+,) N
N(Pi,
of rational
(4)
=exp(pi+u12/2),
(5)
(Ti2).
expectations,
eq. (3) gives us,
(6)
= 1 + 6,
pi = In( 1 + 6) - ui2/2,
(7)
Ei,t( Xi,,+ i) = In( 1 + 6) - u12/2.
(8)
Therefore,
Substituting
=ln(l+6)
xi,t+
1
ei,t+
1 -
(9)
-f$/2+ei,,+,,
(10)
N(0, ui2).
in for x~,~+ 1 and rearranging: ln(Ci,,+i/Ci,,)
= -(l/A) -(l/A)ei,t+l.
ln(1 + 6) + (l/A)fl?/2
+ (l/A)
ln(1 +
‘i,t+l)
(11)
The variance term on the right-hand side represents the effect of precautionary saving. It derives from the variance of the error term. Hence, the same uncertainty that produces Euler equation errors depresses current consumption and elevates future consumption, boosting consumption growth. This equivalence enables us to estimate the precautionary savings variable and to gauge its impact on consumption.
3. Data and estimation Annual data were provided by the Panel Study of Income Dynamics (PSID) for the years 1971-1972 and 1975-1982. The only consumption data recorded in the PSID are food expenditures. Though not ideal, they constitute 50% of consumer spending on nondurable goods, so they represent an important component of total consumption. Nominal household food expenditures were deflated by the appropriate Consumer Price Indices and adjusted for the number and ages of household members. Real ex-post after-tax interest rates
M. Kuehlwein / A test for the presence of precautionary saving Table 1 Estimates
of the elasticity
of intertemporal
Regressor A. Entire
l/A.
substitution, A ln(l+
sample
B. Unconstrained
sample
Two-stage
least squares.
a Observations
rL.,+r)
0.258 (0.230)
9,607
0.868 * (0.440)
1,802
” Figures in parentheses are heteroskedasticity-consistent ,* Significant at the 5% level.
standard
473
errors.
were calculated using annual changes in food prices, the yields on one-year Tbills, and marginal tax rates estimated from reported federal income tax liabilities. Any observations involving changes in family composition were discarded, as were all C,+i/Ct observations outside the 0.25-4 range to control for extreme cases of measurement error. Family units headed by someone older than 65 were excluded. To generate estimates of the variance of the error term, eq. (11) was first-differenced:
A lW,,t+ 1/Ci,,> = (l/A) A 141 + rr,t+l) - (l/A) A’,,,+,.
(12)
To control for the correlation between the change in ex-post interest rates and the error term, I instrumented with the real ex-post interest rate and marginal tax rate dated t - 1, and with predictions of the real expost interest rate for time t using AR(4) forecasts of inflation from period I - 1 and the lagged marginal tax rate. The results, with heteroskedasticity-consistent standard errors, are reported in the first line of table 1. The estimated parameter on the interest rate variable suggests a coefficient of relative risk aversion roughly equal to 4. Though a plausible value, l/A is not significantly different from 0, and a 95% confidence interval stretches from negative numbers to 0.7. I chose therefore to work with a range of values for A: 0.5, 1, 2, 4, and 10. These roughly span the values obtained by other researchers [e.g. Hansen and Singleton (1983) and Mankiw (198511, and working with different risk aversion parameters should provide an indication of the robustness of the results. With an estimate of A, one can generate estimates of the error terms (plus a constant) in eq. (111, and hence compute estimates of household-specific error variances. ’ I limited the sample to those households with at least 4 years of data to minimize the measurement error in the variance estimates. For each assumed value of A, I then ran the regression: WG,,+l/CJ
-
(l/A)
141
+
Ti,t+~)
=Bo
+
BlGi2/2
+
Ei.r+l.
(13)
In theory, consumption growth will be positively related to the uncertainty variable. Because of measurement error in the right-hand side variable, I used the age of the household head, average household food needs, disposable income, and wealth from the first period of the sample, and the variance of household disposable income over the sample as instruments. The results, with heteroskedasticity-consistent standard errors, are displayed in the first tier of table 2. For every assumed level of risk aversion, uncertainty has a significant negative effect on consumption growth. The levels of significance range from 5% for A = 10, 4, and 2, to 1% for ’ Kuehlwein (1987) shows that this estimation in the consumption data.
procedure
is still valid in the presence
of a likely form of measurement
error
M. Kuehlwein /A
474 Table 2 Estimates
of the impact
Regressors
of income
uncertainty
test for the presence of precautionary saving
on consumption
growth.
Two-stage
Constant
$/2
0.087 (0.016) * *
- 0.445 (0.121) * *
2. A=1
0.057 (0.015) * *
- 0.341 (0.120) **
3.A=2
0.043 (0.015) * *
- 0.290 (0.120) *
4. A=4
0.036 (0.015) * *
- 0.264 to.1201 *
5. A = 10
0.032 (0.015) *
- 0.248 (0.120) *
0.065 (0.023)
- 0.275 (0.199)
2. A=1
0.039 (0.023)
-0.184 (0.201)
3. A=2
0.026 (0.023)
-0.140 (0.202)
4.A=4
0.020 (0.023)
-0.118 (0.204)
5. A = 10
0.026 (0.023)
-0.140 (0.202)
A. Entire sample 1. A = 0.5
B. Unconstrained 1. A = 0.5
least squares.
a
Observations 14,822
4,644
sample
are heteroskedasticity-consistent a Figures in parentheses * Significant at the 5% level. ** Significant at the 1% level.
standard
errors.
A = 1 and 0.5. These results contradict the theory of precautionary savings. For all plausible values of relative risk aversion, consumption growth is negatively, and significantly, correlated with consumer uncertainty. Several authors [e.g., Zeldes (1989)] have concluded that the presence of liquidity constraints interferes with the standard consumption Euler equation. To account for this, I discarded those observations for households with low levels of wealth. Asset holdings were estimated from reported asset income. Housing wealth was excluded due to its potential illiquidity. Households were classified as unconstrained if their estimated wealth exceeded one-sixth of their previous year’s income. Estimation of eq. (12) for unconstrained households is displayed in table 1. The estimate of l/A is significant at the 5% level and suggests a value of A approximately equal to 1. However, a 95% confidence interval again encompasses other plausible values of A, so I proceeded to work with the same range of risk aversion parameters. Estimates of eq. (13) are contained in table 2. Again, the estimated effect of consumer uncertainty on consumption growth is negative for all values of A. The coefficient on the uncertainty variable is no longer significantly different from 0 at conventional levels. However, these results again provide no evidence of precautionary saving.
M. Kuehlwein /A
test for the presence of precautionary saving
47.5
4. Conclusion
In this paper, I noted that the uncertainty that generates precautionary saving is reflected in the expectational errors of the consumption Euler equation. Under certain parametric assumptions, one is able to quantify that uncertainty and test for its impact on consumption growth. The results paradoxically indicated that greater consumption uncertainty engenders a flatter consumption trajectory. This agrees with Skinner’s (1988) finding that individuals in riskier occupations actually save less.
References Barsky, R., N.C. Mankiw, and S. Zeldes, 1986, Ricardian consumers with Keynesian propensities, American Economic Review 76, 676-691. Hansen, L.P. and K.J. Singleton, 1983, Stochastic consumption, risk aversion, and the temporal behavior of asset returns, Journal of Political Economy 91, 249-265. Kimball, M. and N.C. Mankiw, 1989, Precautionary saving and the timing of taxes, Journal of Political Economy 97, 863-879. Kuehlwein, M., 1987, Consumption in the presence of uncertainty, unpublished/doctoral dissertation, M.I.T. Leland, H.E., 1968, Savings and uncertainty: The precautionary demand for saving, Quarterly Journal of Economics 82, 465-473. Mankiw, N.G., 1985, Consumer durables and the real interest rate, Review of Economics and Statistics 67, 353-362. Skinner, J., 1988, Risky income, life cycle consumption, and precautionary savings, Journal of Monetary Economics 22, 237-255. Zeldes, S., 1989, Consumption and liquidity constraints: An empirical investigation, Journal of Political Economy 97, 305-346.