Publications   Empirical StudiesKYN - SLAMA: MACROECONOMIC CONSUMPTION FUNCTION FOR CZECHOSLOVAKIA

C. The Planners' Consumption Function

1

We have seen that consumer behavior, as suggested by the estimated consumers' consumption function, is trivial; people seem to consume a very high and almost fixed proportion of their disposable income, with no discernible time lag. We would not expect the planners consumption function to be as trivial. If the consumer does not think in terms of the future, the planner surely does. Surprisingly, the plot of consumption expenditures against national income in Diagram 2 suggests that in the specification of the equation (23) we can start again with the most simple linear form.

Click below to display Diagram 2
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(28)

  CSt = a0 + a1 Yt + ut

2

 

The following table showing the estimates of equation (28) supports this intuitive feeling.

Table 6

The Planer's Consumption Function 

Eq. (28)

No.

Method

Estimated Parameters

(standard errors)

ARC

R2

DW

Standard Error
of Regression

a0

a1

15.

OLSQ

10.288

(1.869)

.517

(.009)

.478

(.176)

.992

1.00

3.513

16.

CORC

9.453

(3.360)

.519

(.016)

.476

(.176)

.994

1.84

3.058

Immediately, however, we see three marked differences:

(a)

 The intercept is much larger and significantly different from zero. This implies that the average share of consumption in national income was larger than the marginal share, and was declining.

(b) 

Planners' "marginal propensity to consume a1 is only about .52 which is, of course, much lower than the propensity of consumers. In the long run, planners allocate 52 percent of the increment of national income to increase personal consumption while the remaining 48 percent is used for other purposes, including investment and public consumption.

(c) 

The low Durbin-Watson statistic and the large and significant autoregressive coefficient indicate that the specification of the consumption function is not fully satisfactory. In Diagram 2 we see peculiar fluctuations that were not detected in the consumers' consumption function. These fluctuations are even more apparent from the plot of residuals (Diagram 3).

Click below to display Diagram 3
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3

The Cochrane-Orcutt iterative procedure worked well in correcting for autocorrelation, but the cause of the cyclical fluctuations remains unexplained. One plausible explanation of observed fluctuations is that planners' behavior is similar to consumer behavior in a market economy as postulated by the permanent income hypothesis.

The planners' permanent income hypothesis assumes that planners have their own idea about the long-run normal growth path of the economy and that they consider the level of national income corresponding in each year to such a long-run normal path to be normal or "permanent" national income. The difference between actual national income and the "permanent income" can then be called the "planners' transitory income".

The normal or "permanent" national income is obviously not constant, and it is usually not equal to planned national income. Planners can and frequently do plan for faster or slower growth than the long-run normal growth rate.  

4

We can now formulate the planners' permanent income hypothesis as follows:

Planners' decisions about the final use of national income depend on the ratio between the transitory and permanent components of national income. Specifically, investment is positively and consumption is negatively related to this ratio; or, to put it differently, the share of investment is higher in transitory than in permanent income, while for the share of consumption the opposite is true.14

The motivation for this hypothesis came from empirical investigation of planners' investment and consumption decisions and in particular from the pioneering study of W. Schrettl (1974), who scrutinized the so called "shock-absorber hypothesis" according to which the "Soviet investment is much more stable than in Western market economies, this stability being achieved by curtailing consumption in case of insufficient national income".15 Schrettl estimated several variants of the macroeconomic investment function for the Soviet economy, among which the most interesting variants related aggregate investment or deviations of investment from their trend to fluctuations in the rates of growth of national income or to deviations of national income from its trend. He found that "investment is to a considerable degree affected by fluctuations of national income" and that "investment participates almost twice as much in increments of national income than is its average share";16 these findings led him to the conclusion that 

5

"the shock-absorber hypothesis... is wrong in its extreme form as well as in its moderate form. All regressions indicate that the opposite is true, namely that not the consumer but investment 'suffers'."17

Portes and Winter in their recent study18 tested a similar hypothesis by estimating the planners' (i.e. supply) consumption functions for Czechoslovakia, Poland, Hungary, and East Germany. They maintained that in their decisions about the supply of consumer goods planners respond differently to long-run factors (for which they took trend values of various macroeconomic indicators) than to short-run deviations and exogenous shocks. Their results led them to conclude that "planners exhibit stable resource allocation behavior19 and to reject "a common theme of the literature on CPEs" which considers "consumption to be a 'buffer' which absorbs all shocks"20. Specifically for Czechoslovakia they found that "the consumption-goods supply is completely protected from deviations from trend in total output".21

At first glance it may seem that the planners' permanent income hypothesis contradicts the traditionally assumed goal of planners, namely maximization of the rate of economic growth. However, Schrettl has recently demonstrated theoretically22 that planners' behavior may protect consumption from short-run fluctuations, provided that consumers can exert pressure on planners by withdrawing labor (or diminishing their efforts) if the real consumption planned for them is in their view inadequate.

6

In this paper we shall test the implications of the planners' permanent income hypothesis for the planners' consumption function only.23 Because the "permanent national income" is unobservable and because it is not clear a priori exactly how planners' behavior is influenced by the ratio of transitory to permanent income, we shall estimate several alternatively specified variants of the planners' consumption function.

Let us begin with the widely used assumption that permanent income is formed in the process of adaptive expectations. This approach is known to lead to consumption functions with distributed lags. The Koyck transformation of the planners' consumption function with a geometrically distributed lag gave quite good results (Table 7). The addition of lagged consumption to the right-hand side of the equation (28) improved the fit as measured by R2 only slightly, but the autcorrelation disappeared and the lag coefficient l was significant at the 2 % level. The long-run MPC is .513, which is very close to a1 estimated from the consumption function without a lag. The estimated l = .489 implies a moderately long mean lag of .956 years.

Table 7

The Planner.' Consumption Function

(Koyck Transformation)

No.

Method

Estimated Coefficients

(standard errors)

R2

DW

SER

F

a0

a1

l

17

OLSQ

5.391

(2.444)

.276

(.099)

.489

(.197)

.994

1.78

3.16

1755.7

 

7

The consumption function with a polynomially distributed lag gave results similar to the Koyck transformation when the lag was distributed over 4 to 5 years, the degree of the polynomial was low, and the zero condition was imposed (Table 8 and Diagram 4 a).

Click below to display Table 8
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Click below to display Diagram 4a
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This version of the consumption function indicates a somewhat shorter mean lag of .5 to .75 of a year. The presence of autocorrelation suggests that the lag structure may not have been well specified.

8

The mean lag increased to 1.5 - 2.5 years, and the autocorrelation disappeared when the lag was distributed over longer periods of 8 - 9 years and the degree of the polynomial was increased (Table 9). However, the shape of the lag, as can be seen from Diagram 4b, is unreasonable and many of the lag coefficients are negative and/or insignificant.

Click below to display Table 9
in this windowin a new window
Click below to display Diagram 4b
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In the next step, we shall try to introduce the "permanent" income and the "transitory" income into the consumption function explicitly. As they are both unobservable, we have to find proxy variables for them. We suggest that a reasonable proxy variable for the planners' "permanent" income may be the fitted value of national income from the aggregate production function and the proxy for transitory income may be the deviation of the actual national income from its fitted value. The obvious reason for this suggestion is that the fitted value of production functions can be interpreted as a hypothetical national income which would have been produced under the normal (in the long-run sense) utilization of factors of production and with the normal growth of factor productivity.

For the purpose of this paper, it will suffice to use the Cobb-Douglas production function24 with constant returns to scale, preassigned capital and labor elasticities25, and disembodied technical change with a quadratic term in the exponent

(29)

 Yt = A0Kt.35Lt.65 exp(r0t + 1/2 r1t2)

Yt

is national Income

Kt 

is undepreciated stock of fixed capital

Lt

is employment.

9

The parameters estimated from the logarithmic transformation of (29) are shown in Table 10 and the fitted values Yt are shown in Table 3 in the Appendix.

Table 10

Trend in Total Factor Productivity 

Eq. (29)

No.

Method

Estimated parameters

(standard errors)

R2

DW

SER

F

logA0

r0

r1

31

OLSQ

-5.658

(.031)

.0654

(.0053)

-.0021

(.0004)

.974

.37

.049

429.4

 

As suggested by the planners' permanent income hypothesis we shall estimate the consumption function with the ratio of transitory to permanent income added to the right-hand side. Under our assumption, the permanent income is Yt and transitory income Yt - Yt so that we can define the new right-hand variable as follows:

(30)

 Et = (Yt - Yt )/Y

The new specification of the consumption function is

(31)

 CSt = a0 + dEt + a1 Yt + ut

10

According to our hypothesis we expect d to be negative. The estimates of equation (31), as shown in Table 11, are satisfactory. Compared with the results of Table 6, all the statistics improved while the estimated values of a0 and a1 remained virtually unchanged. The most important outcome of the new regression is that the coefficient d has the right sign and proved to be highly significant for the explanation of the short-run variations in the Czechoslovak consumption expenditures.

Table 11

 

The Planners' Consumption Function

with the Relative Transitory Income

Eq. (31)

No.

Method

Estimated parameters

(standard errors)

ARC

R2

DW

SER

F

a0

d

a1

32

OLSQ

9.665

(1.447)

-.490

(.117)

.267

(.193)

.267

(.193)

.996

1.46

2.71

2611.94

33

CORC

9.934

(2.068)

-.477

(.149)

.522

(.010)

.267

(.193)

.996

1.86

2.66

2486.90

 

 

 

 

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