The tax rebate program for 2008 involved sending out checks for about $100 billion during the second quarter of 2008. That $100 billion in 2008 would have been equivalent to about $74 billion in 2000 prices.

Here are the components of consumer expenditure for the first three quarters of 2008.

One simple estimate of the effect of the tax rebate is the difference between the actual consumption in the second quarter and interpolated value for the second quarter based upon the first and third quarter values; i.e., the average of the levels in the first and third quarter. The diagrams below show what is involved both for increasing increasing and decreasing consumption.

Those values for the estimated impact based upon the Bureau of Economic Analysis of the U.S. Department of Commerce data on the National Income Accounts in the year 2000 prices are:

The computations indicate that the impact of the $74 billion ($2000) tax rebates was an increase in consumer purchases of about $58 billion. Of the total, $33.6 billion came in consumer nondurable purchases and about $20 in consumer durable purchases. The was also an increase of $4.35 billion in consumer purchases of services. The increase in consumer purchases of $58 billion for an increase in consumer disposable income of $74 billion. This is a marginal propensity to consume out of disposable income of about 0.78.

However the effect on the net inventory investment was a decrease of 30.7 billion 2000 valued dollars. Thus consumers increased their purchases but the stores sold off their inventory and did not replace a substantial share (about half). On a positive side the impact was not an increase in imports but instead a decrease of almost $10 billion. This resulted in a net increase in aggregate demand. Altogether then the tax rebate increase aggregate demand by about $37 billion, an amount equal to one half of the abount of the tax rebate.

The more detailed estimates of the impacts of the tax rebate are:

The method of estimation of the impacts is simplistic, but the results are reasonable and in agreement with what one would expect the impact would be of consumers getting a $500 unexpected increasse in disposable income. The largest impact is in purchases of household equipment which would include television sets and computers as well as furniture. The second largest impact is on food purchases and the third on clothing. The magnitude of the rebate was too small to have much of an impact on motor vehicle purchases.

The careful reader might note that the sum of the detailed impacts is $62.75 billion, whereas in the previous table the total impact was given as $57.65. This is due to an intrinsic problem with making seasonal and price-level adjustments to the separate items in a total and separately making such adjustments to the total itself. When the estimation method is applied to the level of real consumer purchases the result for the impact of the rebate is $52.95 billion. If the total figure is equal to the sum of the separate components there would be no discrepancy but such is not the case.

The reported figure for consumer purchases in 2000 value dollars for the second quarter of 2008 is $8,341.3 billion. There are however figures reported for the separate levels of durable goods purchases, nondurable goods purchases and services. These figures total $8,361 billion, a difference of $19.8 billion from the reported figure for the total of the three. Presumably the total for the three components in current values and not seasonally adjusted match the total reported. But the separate adjustments for season and price change result in components which do add up to adjusted total figure. The same problem prevails concerning the components of the components. The reported figure for durable goods purchases for 2008II is $1,228.3 but the sum of the separate components of durable goods purchases is $1,267.6, a difference of $39.3 billion. For nondurable purchases the reported figure for the total is $2,420.7 where as the sum of the components is $2,46.7, a difference of $26.0 billion. For services there is not much of a difference. The reported figure for consumer purchases of services in 2008II is $4,712.1 whereas the sum of the components is $4,711.7, a difference of only $0.4 billion.

(To be continued.)