David Andolfatto again brought up the model he had used some time ago to criticize nominal GDP level targeting. The shock in his model is a decrease in the expected productivity of capital. If these expectations are correct, then the output of consumer goods will be lower during the next period.
In his model, the lower expected productivity of capital goods leads young people to accumulate money/government bonds. This decrease in the demand for capital goods and increase in the demand for money "appears" to be a decrease in aggregate demand.
In comments on his blog, I reviewed what I take to be some of the ABC's of saving and investment. He insisted that interest rates and inflation are policy variables, but I presume he was speaking of his model.
My "model" is the supply of saving and demand for investment. Saving is positively related to the interest rate and investment is negatively related. At the natural interest rate, saving and investment are equal. That part of income not spent on consumer goods is saved. Investment is spending on capital goods. With saving equal to investment, that part of income not spent on consumer goods is instead spent on capital goods. Income is here potential output, the productive capacity of the economy.
If the interest rate is below the natural interest rate, saving is less than investment. Spending on consumer goods plus spending on capital goods outstrips the productive capacity of the economy. If the interest rate is above the natural interest rate, investment is less than saving, and spending on consumer goods plus spending on capital goods is less than the productive capacity of the economy.
Andolfatto's shock using my simple model is a shift of the investment demand curve to the left. At the initial natural interest rate, investment is less than saving and the sum of consumption and investment is less than the productive capacity of the economy.
If we consider the market interest rate adjusting from the initial natural interest rate to the new natural interest rate, as it falls, the quantity of investment demanded rises. While the demand for capital goods initially fell, it partly recovers due to the lower interest rate. The quantity of saving supplied decreases. This is the same thing as an increase in spending on consumer goods.
At the new natural interest rate, saving and investment are again equal, and the sum of investment and consumption equal the productive capacity of the economy. However, the amount saved and invested are both lower and spending on consumer goods is higher.
There is no impact on total spending on output now. Nominal GDP would remain on target. There is no impact on the price level. The prices of consumer goods might rise, but the prices of capital goods would fall. (If consumer prices are targeted, which is not unrealistic, then it might be necessary to reduce spending on output and slightly depress the overall price level, further lowering the prices of the capital goods.)
What could go wrong? Suppose there is a central bank targeting the nominal interest rate. Sadly, this is is a very realistic assumption, and one that Aldofatto includes in his model. The decrease in investment demand implies a lower natural interest rate, but should the market interest rate begin to fall, this pushes it below the central bank's target. If necessary, it sells off some of the assets it holds and contracts the quantity of money enough to prevent the interest rate from falling. If the demand to hold money is rising, then failing to expand the quantity of money enough to match the growing demand will also keep the market interest rate from falling.
Because the market interest rate fails to fall with the natural interest rate, investment falls below saving and the sum of consumption and investment is less than the potential output. As their sales fall, firms cut back production, causing output and income to fall below potential.
This decrease in spending on output and income is inconsistent with nominal GDP targeting. Of course, these decreases could be relative to what nominal GDP would have been, and so amount to a smaller than usual increase. A central bank targeting nominal GDP needs to expand the quantity of money and decrease its target for the interest rate.
While firms are likely to respond to the decrease in spending by producing less, they also will likely lower their prices, though this could be solely a matter of lowering them relative to where they would have been. In an inflationary environment, this amounts to raising their prices more slowly. A central bank targeting the price level (perhaps a growth path for the price level) or inflation also needs to expand the quantity of money and lower its target for the interest rate.
Suppose the central bank doesn't target interest rates at all, but rather targets some measure of the quantity of money. In that situation, the central bank takes no action to manipulate the quantity of money as the decrease in investment demand results in a lower market interest rate. If money bears interest, and the interest rate paid on money falls with other market interest rates, then a money supply target would allow all market rates to adjust to the new natural interest rate.
Aldofatto, however, assumes that the both the yield on money and its quantity remains fixed. A central bank following such a policy could keep the market interest rate from falling, and result in reduced investment expenditure, aggregate expenditures, production, and employment. A central bank targeting the price level or nominal GDP would need to lower the interest rate paid on money or else increase the quantity of money or both.
The implications of nominal GDP level targeting, price level targeting, and inflation targeting are all very similar. The market interest rate should be allowed to fall enough to match the new natural interest rate. Nominal GDP, the price level, and inflation should all remain unchanged.
What if the central bank fails to make the proper adjustment in its interest rate target and the quantity of money? In the likely scenario where at least some prices are flexible, then the decrease in spending on output will be matched by a less than proportional decrease in the price level. The central bank must return both spending on output and the price level to target.
With inflation targeting, however, the change in the price level due to the adjustment of the flexible prices is allowed to persist. The flexible prices can only increase again as the other, less flexible prices, especially including nominal wages, also adjust downward.
What about the future?
In the future, the smaller increase in the capital stock, and a perhaps realized reduction in the productivity of capital, will tend to result in a smaller than otherwise increase in real output. The reduced saving and the lower interest rate on accumulated wealth will reduce the claims on that output.
With price level targeting, spending on output must grow more slowly to reflect the smaller expansion in output. Since this effect is predictable, the result would be the same with inflation targeting.
However, with nominal GDP level targeting, spending on output in the future will continue growing as usual. The smaller increase in production will result transitional inflation. The price level will move to a higher growth path.
The smaller capital stock in the future would tend to result in lower real wages. Any decrease in the growth path of nominal wages made necessary by the change in the growth path of the capital stock would be dampened by the increase in the growth path of the price level. If wages are especially sticky, then this is a benefit of nominal GDP level targeting.
Because the inflationary implication of nominal GDP targeting can be expected, the nominal interest rate in the first period will fall by less than the real interest rate. It is possible that the nominal rate would remain unchanged or even rise. This effect of nominal GDP level targeting implies there is less chance of the reduction in the expected productivity of capital causing the nominal interest rate to fall to zero.
Andolfatto's model is different. There are overlapping generations. The young choose to use their endowment of output to produce capital goods or else sell it to old people in exchange for money/government bonds. When they are old, then consume the output of their capital goods or "spend" the money/government bonds on the output that belongs to the next generation of young people. The base line model has the quantity of money/government bonds and the nominal interest rate paid on them fixed. The way the government stabilizes nominal GDP is to vary the nominal interest rate, lowering it when expected capital productivity is low, to maintain the demand for capital goods.
As far as I could tell, a reduction in the expected productivity of capital results in the current old generation receiving a bonanza of cheap consumer goods from the current young people. Those young people try to obtain more money/government bonds but their quantity is fixed. And more importantly, what the young people get from them when they are old is simply the tax payment of the next generation of young people. That doesn't increase when the productivity of capital is low. So, the current young people get less consumption when they are old and the current old people get a bonanza of extra consumption. It seems to me that from the point of view of the current young people, the best strategy is to invest all of current output other than an infinitely small amount to exchange for all of the money/government bonds.
But really, I don't think these specialized, highly unrealistic assumptions really add much to the basic supply of saving and demand for investment approach.