# Interest rates and aggregate inventory investment.

THIS article suggests a new view of how interest rates may effect
inventory demand, Specifically, it suggests that when real short-term
interest rates surpass previous peak levels, firms revise their
inventory management techniques; when interest rates recede from a peak,
the revamped management techniques remain in place, affecting inventory
holdings until a new peak in interest rates is recorded.

Using this new "ratchet" approach to incorporating the effect of interest rates leads to the following main findings:

* The interest rate variable is a statistically significant determinant of aggregate inventory investment. Many earlier studies failed to find a significant interest rate effect.

* The interest rate variable, along with expected sales and beginning stocks of inventories, explains aggregate inventory investment rather well.

* Discrepancies between desired and actual levels of inventories are removed slowly; it takes about three quarters to eliminate one-half of a given discrepancy.

* The relationship between inventory investment, on the one hand, and expected sales and the interest rate variable, on the other, appears to have been relatively stable over the 1952-84 period.

Interest rate ratchet

Many earlier investigtions failed to establish a significant effect of the rate of interest on inventory demand. This failure, in the face of the widespread theoretical conviction that cost considerations are an important determinant of inventory investment, suggests that the effect of interest rates may be more subtle than commonly supposed. Research on the demand for money suggests a plausible mechanism for incorporating interest rates in inventory investment equations.

Some analysts at the Federal Reserve have found that money demand equations perform better if an interest rate ratchet variable is included in the equation. A ratchet variable is a variable that moves in only one direction, usually upwards. Formally, a ratchet variable R that represents the real interest rate r may be defined as:

The rationale for including a ratchet variable in a demand for money equation is straightforward. When interest rates reach a new peak, the opportunity cost of holding money becomes high enough to trigger investment in new cash management techniques. When interest rates recede from the peak, the new management techniques are not jettisoned, but remain in place until a new interest rate peak is recorded.

The same rationale may be put forward to explain the effect of interest rates on inventories, by changing the "cost of holding money" to the "cost of holding inventories" and "new cash management techniques" to "new inventory management techniques." These new inventory management techniques may take a number of forms. They may entail consolidation of storage facilities, personnel training, the acquisition of new equipment (which may range from conveyor belts and for lift trucks to computers), etc. Effecting these changes may involve significant outlays over extended periods of time. These and other innovations in inventory management techniques would all have the same goal, namely to reduce the size of inventories relative to sales, thereby reducing the cost of holding inventories.

Model and data

The ratchet interest rate variable (R.sub.t) and the level of expected sales (XS.sub.t) are assumed to determine the optimal inventory stock (INV.sup.*.sub.t) according to the following specification:

By allowing expected sales to scale the ratchet variable, this specification implies, reasonably, that the effect of the interest rate ratchet increases as expected sales increase.

Equation (1) is used in conjunction with another equation, known as the stock-adjustment (or partial adjustment) model, which states that discrepancies between optimal and actual inventories are eliminated gradually:

The speed at which discrepancies are eliminated is given by [lambda]. If [lambda] = 0, the discrepancy is never reduced; if [lambda] = 1, the entire discrepancy is eliminated in the current period. The final term in equation (2), u.sub.t, incorporates all other factors that impinge on the change in inventories, the most obvious of which is unexpected sales, or "sales surprises" (SS.sub.t).

Sales surprises should be allowed to enter the estimating equation explicitly. Their effect on inventory change is a matter of interest in its own right for what it reveals about the bufferstock model of inventory investment. Moveover, failure to take explicit account of SS.sub.t could bias the estimated coefficients of the other variables in the equation.

Substituting equation (1) into equation (2), letting sales surprises enter explicitly, and defining the remaining "other factors= as u'.sub.t, yields: or

Clearly, equations (3) and (3a) are equivalent. The former explains the change in inventories (i.e., inventory investment) between the end of quarter t-1 and the end of quarter t; the latter explains the level of inventory at the end of quarter t.

This article concentrates on the specification given by equation 3, because analysts usually are more interested in inventory investment than they are in the absolute level of inventories. Whichever variant is used for regression purposes, however, it should be noted that the estimated coefficient for the sales variable will be an estimate of the product of [lambda] and b.sub.1, and the estimated coefficient for the interest rate variable will be an estimate of the product of [lambda] and b.sub.2. As a result, the estimated coefficients will measure the immediate, or short-run, impact of a change in sales or interest rates. To obtain the eventual, or long-run, impact, the estimated coefficients must be divided by the estimate of the adjustment coefficient, [lambda].

In estimating equation (3), inventories and sales were taken from the national income and product accounts (NIPA's). NIPA table 5.11 presents aggregate end-of-quarter inventories (seasonally adjusted), in billions of 1972 dollars. The quarter-to-quarter change in these inventory stocks is used as the dependent variable in the regression.

NIPA table 5.11 also shows two measures of sales: business final sales and business final sales of goods and structures, both in billions of 1972 dollars. The use of either sales measure in an inventory demand equation can be justified. On the one hand, because it is goods that are held in inventory, it is natural to assume that the production (and sale) of goods (and, possibly, structures) far outweights the production of services as a determination of inventory demand. On the other hand, because inventories are held to support the activities of the entire economy, it is just as natural to assume that the inventory demand of the total (business) sales. There is no a priori reason for preferring one sales measure over the other, and regression results are much the same regardless of which is chosen. The regressions reported below use the total business final sales series. (Table 5.11 presents final sales as quarterly totals, but at monthly rates. For ease of interpreting the regression results, the final sales series has been converted to quarterly rates--i.e., has been multiplied by 3.)

Equation (3) uses expected sales and sales surprises. Many techniques are available for generating expected sales from actual sales. One of the simplest is to assume that expected sales in quarter t equal actual sales in quarter t-1. This technique has been used in many studies of inventory investment. Sales surprises, of course, are calculated as the difference between actual and expected sales.

The real short-term rate of interest is crudely approximated by subtracting an inflation rate from a nominal interest rate. The rate on commercial paper (4-6 months) serves as the nominal short-term interest rate. A price index for inventory stock is the obvious choice for the price variable; such a price index is not readily available, however. An implicit price deflator for inventory stocks is available, but it reflects both price changes and changes in the composition of inventories. In instances where compositional changes can safely be ignored, deflators may be adequate indicators of price movements; in the case of inventories--which have rapid turnover--it is not clear that compositional changes can be safely ignored. In the regressions reported below, the deflator for final sales (in which compositional changes are presumed to be less important) is used as the price variable. Quarter-to-quarter changes (at annual rates) in the deflator are subtracted from the nominal interest rate to obtain the real rate, which is expressed as a decimal (e.g., 4 percent = 0.04).

Construction of the interest rate ratchet variable is straightforward. When the real rate is below its previous peak level, the ratchet variable is equal to the previous peak level; when the real rate rises above its previous peak level, the ratchet variable is equal to the current real rate.

The real rate and the ratchet variable derived from it are shown in chart 1. The rachet varable shows very little variation--it changes only nine times--over the sample period, and it is certainly far different from the real rate itself.

Results

Ordinary least-squares estimation of equation 3 yields:

Figures in parentheses are absolute values of t-statistics; rho is the first order autocorrelation coefficient from A Cochrane-Orcutt correction.

The ratchet variable has the correct (negative) sign and is significant at the 5-percent level. The coefficients of expected sales and lagged inventory stock carry the correct signs and are highly significant. Sales surprises enter the equation with a negative (albeit very small and statistically insignificant) coefficient, as implied by the buffer-stock model of inventory investment.

The coefficient of the lagged inventory stock is of particular interest, because it is a measure of the speed with which discrepancies between optimal and actual inventories are removed. The estimated speed of 21 percent per quarter implies that it takes about three quarters to eliminate one-half of a given discrepancy. This speed is slower than might seem reasonable on a priori grounds, but it is quite consistent with the adjustment speeds found in many earlier studies.

The overall goodness of fit, as measured by R.sup.-2, is satisfactory. As chart 2 shows, the equation tracks actual inventory change quite well during the sample period--perhaps better than one might expect from an equation with an R.sup.-2 of 0.59.

As was mentioned earlier, the estimated coefficients of the expected sales and interest rate ratchest variables represent the short-run impacts of these variables on inventory investment; the long-run coefficents are found by dividing the estimated coefficients by the estimated speed of adjustment (table 1).

Table 1 also shows the implied elasticity of inventory stocks with respect to expected sales and the interest rate ratchet. The long-run elasticity of stocks with respect to expected sales is 1.1; a 1-percent increase in expected sales induces, eventually, an approximately 1-percent increase in inventory stocks. The elasticity with respect to the interest rate ratchet variable is very small: below -0.1 in the long run. Nevertheless, such a value implies that a 1-percentage-point increase in the level of the ratchet from 4-1/2 percent to 5-1/2 percent would have led, eventually, to a reduction in inventory stocks of more than $5 billion (1972 dollars).

The deflator for final sales was used in constructing the ratchet variable shown in chart 1 and used in the regression. Ratchet variables were also constructed using several alternative price measures. Table 2 defines these alternatives ratchets and, in column 1, shows the t-statistic of each when it is scaled by expected sales and used in the regression. In an effort to determine whether scaling materially affects the results, column 2 of the table shows the t-statistics for each of the ratchets when it is not scaled by expected sales. Regardless of the precise specification, the ratchet does quite well; in all cases, it is significant at the 10-percent level or better.

Although there are difficulties in applying the F test for structural stability to regressions estimated with autocorrelation corrections, and although there are no obvious points at which to check for structural shifts, the test was conducted, with arbitrary breaks (alternatively) in the first midpoint of the sample period) and of 1981 (before the ratchet makes its F-statistic statistically significant. At the 5-percent level of significance, the critical value of the F-ratio--with 4 and 124 degrees of freedom--is approximately 2.45; the calculated F-ratios were 1.47 (for the break in the first quarter of 1968) and 1.74 (for the break in the first quarter of 1981). The null hypothesis of structural stability cannot be rejected, but because of the difficulties mentioned above, this finding can only be interpreted as suggestive, not conclusive.

Using this new "ratchet" approach to incorporating the effect of interest rates leads to the following main findings:

* The interest rate variable is a statistically significant determinant of aggregate inventory investment. Many earlier studies failed to find a significant interest rate effect.

* The interest rate variable, along with expected sales and beginning stocks of inventories, explains aggregate inventory investment rather well.

* Discrepancies between desired and actual levels of inventories are removed slowly; it takes about three quarters to eliminate one-half of a given discrepancy.

* The relationship between inventory investment, on the one hand, and expected sales and the interest rate variable, on the other, appears to have been relatively stable over the 1952-84 period.

Interest rate ratchet

Many earlier investigtions failed to establish a significant effect of the rate of interest on inventory demand. This failure, in the face of the widespread theoretical conviction that cost considerations are an important determinant of inventory investment, suggests that the effect of interest rates may be more subtle than commonly supposed. Research on the demand for money suggests a plausible mechanism for incorporating interest rates in inventory investment equations.

Some analysts at the Federal Reserve have found that money demand equations perform better if an interest rate ratchet variable is included in the equation. A ratchet variable is a variable that moves in only one direction, usually upwards. Formally, a ratchet variable R that represents the real interest rate r may be defined as:

The rationale for including a ratchet variable in a demand for money equation is straightforward. When interest rates reach a new peak, the opportunity cost of holding money becomes high enough to trigger investment in new cash management techniques. When interest rates recede from the peak, the new management techniques are not jettisoned, but remain in place until a new interest rate peak is recorded.

The same rationale may be put forward to explain the effect of interest rates on inventories, by changing the "cost of holding money" to the "cost of holding inventories" and "new cash management techniques" to "new inventory management techniques." These new inventory management techniques may take a number of forms. They may entail consolidation of storage facilities, personnel training, the acquisition of new equipment (which may range from conveyor belts and for lift trucks to computers), etc. Effecting these changes may involve significant outlays over extended periods of time. These and other innovations in inventory management techniques would all have the same goal, namely to reduce the size of inventories relative to sales, thereby reducing the cost of holding inventories.

Model and data

The ratchet interest rate variable (R.sub.t) and the level of expected sales (XS.sub.t) are assumed to determine the optimal inventory stock (INV.sup.*.sub.t) according to the following specification:

By allowing expected sales to scale the ratchet variable, this specification implies, reasonably, that the effect of the interest rate ratchet increases as expected sales increase.

Equation (1) is used in conjunction with another equation, known as the stock-adjustment (or partial adjustment) model, which states that discrepancies between optimal and actual inventories are eliminated gradually:

The speed at which discrepancies are eliminated is given by [lambda]. If [lambda] = 0, the discrepancy is never reduced; if [lambda] = 1, the entire discrepancy is eliminated in the current period. The final term in equation (2), u.sub.t, incorporates all other factors that impinge on the change in inventories, the most obvious of which is unexpected sales, or "sales surprises" (SS.sub.t).

Sales surprises should be allowed to enter the estimating equation explicitly. Their effect on inventory change is a matter of interest in its own right for what it reveals about the bufferstock model of inventory investment. Moveover, failure to take explicit account of SS.sub.t could bias the estimated coefficients of the other variables in the equation.

Substituting equation (1) into equation (2), letting sales surprises enter explicitly, and defining the remaining "other factors= as u'.sub.t, yields: or

Clearly, equations (3) and (3a) are equivalent. The former explains the change in inventories (i.e., inventory investment) between the end of quarter t-1 and the end of quarter t; the latter explains the level of inventory at the end of quarter t.

This article concentrates on the specification given by equation 3, because analysts usually are more interested in inventory investment than they are in the absolute level of inventories. Whichever variant is used for regression purposes, however, it should be noted that the estimated coefficient for the sales variable will be an estimate of the product of [lambda] and b.sub.1, and the estimated coefficient for the interest rate variable will be an estimate of the product of [lambda] and b.sub.2. As a result, the estimated coefficients will measure the immediate, or short-run, impact of a change in sales or interest rates. To obtain the eventual, or long-run, impact, the estimated coefficients must be divided by the estimate of the adjustment coefficient, [lambda].

In estimating equation (3), inventories and sales were taken from the national income and product accounts (NIPA's). NIPA table 5.11 presents aggregate end-of-quarter inventories (seasonally adjusted), in billions of 1972 dollars. The quarter-to-quarter change in these inventory stocks is used as the dependent variable in the regression.

NIPA table 5.11 also shows two measures of sales: business final sales and business final sales of goods and structures, both in billions of 1972 dollars. The use of either sales measure in an inventory demand equation can be justified. On the one hand, because it is goods that are held in inventory, it is natural to assume that the production (and sale) of goods (and, possibly, structures) far outweights the production of services as a determination of inventory demand. On the other hand, because inventories are held to support the activities of the entire economy, it is just as natural to assume that the inventory demand of the total (business) sales. There is no a priori reason for preferring one sales measure over the other, and regression results are much the same regardless of which is chosen. The regressions reported below use the total business final sales series. (Table 5.11 presents final sales as quarterly totals, but at monthly rates. For ease of interpreting the regression results, the final sales series has been converted to quarterly rates--i.e., has been multiplied by 3.)

Equation (3) uses expected sales and sales surprises. Many techniques are available for generating expected sales from actual sales. One of the simplest is to assume that expected sales in quarter t equal actual sales in quarter t-1. This technique has been used in many studies of inventory investment. Sales surprises, of course, are calculated as the difference between actual and expected sales.

The real short-term rate of interest is crudely approximated by subtracting an inflation rate from a nominal interest rate. The rate on commercial paper (4-6 months) serves as the nominal short-term interest rate. A price index for inventory stock is the obvious choice for the price variable; such a price index is not readily available, however. An implicit price deflator for inventory stocks is available, but it reflects both price changes and changes in the composition of inventories. In instances where compositional changes can safely be ignored, deflators may be adequate indicators of price movements; in the case of inventories--which have rapid turnover--it is not clear that compositional changes can be safely ignored. In the regressions reported below, the deflator for final sales (in which compositional changes are presumed to be less important) is used as the price variable. Quarter-to-quarter changes (at annual rates) in the deflator are subtracted from the nominal interest rate to obtain the real rate, which is expressed as a decimal (e.g., 4 percent = 0.04).

Construction of the interest rate ratchet variable is straightforward. When the real rate is below its previous peak level, the ratchet variable is equal to the previous peak level; when the real rate rises above its previous peak level, the ratchet variable is equal to the current real rate.

The real rate and the ratchet variable derived from it are shown in chart 1. The rachet varable shows very little variation--it changes only nine times--over the sample period, and it is certainly far different from the real rate itself.

Results

Ordinary least-squares estimation of equation 3 yields:

Figures in parentheses are absolute values of t-statistics; rho is the first order autocorrelation coefficient from A Cochrane-Orcutt correction.

The ratchet variable has the correct (negative) sign and is significant at the 5-percent level. The coefficients of expected sales and lagged inventory stock carry the correct signs and are highly significant. Sales surprises enter the equation with a negative (albeit very small and statistically insignificant) coefficient, as implied by the buffer-stock model of inventory investment.

The coefficient of the lagged inventory stock is of particular interest, because it is a measure of the speed with which discrepancies between optimal and actual inventories are removed. The estimated speed of 21 percent per quarter implies that it takes about three quarters to eliminate one-half of a given discrepancy. This speed is slower than might seem reasonable on a priori grounds, but it is quite consistent with the adjustment speeds found in many earlier studies.

The overall goodness of fit, as measured by R.sup.-2, is satisfactory. As chart 2 shows, the equation tracks actual inventory change quite well during the sample period--perhaps better than one might expect from an equation with an R.sup.-2 of 0.59.

As was mentioned earlier, the estimated coefficients of the expected sales and interest rate ratchest variables represent the short-run impacts of these variables on inventory investment; the long-run coefficents are found by dividing the estimated coefficients by the estimated speed of adjustment (table 1).

Table 1 also shows the implied elasticity of inventory stocks with respect to expected sales and the interest rate ratchet. The long-run elasticity of stocks with respect to expected sales is 1.1; a 1-percent increase in expected sales induces, eventually, an approximately 1-percent increase in inventory stocks. The elasticity with respect to the interest rate ratchet variable is very small: below -0.1 in the long run. Nevertheless, such a value implies that a 1-percentage-point increase in the level of the ratchet from 4-1/2 percent to 5-1/2 percent would have led, eventually, to a reduction in inventory stocks of more than $5 billion (1972 dollars).

The deflator for final sales was used in constructing the ratchet variable shown in chart 1 and used in the regression. Ratchet variables were also constructed using several alternative price measures. Table 2 defines these alternatives ratchets and, in column 1, shows the t-statistic of each when it is scaled by expected sales and used in the regression. In an effort to determine whether scaling materially affects the results, column 2 of the table shows the t-statistics for each of the ratchets when it is not scaled by expected sales. Regardless of the precise specification, the ratchet does quite well; in all cases, it is significant at the 10-percent level or better.

Although there are difficulties in applying the F test for structural stability to regressions estimated with autocorrelation corrections, and although there are no obvious points at which to check for structural shifts, the test was conducted, with arbitrary breaks (alternatively) in the first midpoint of the sample period) and of 1981 (before the ratchet makes its F-statistic statistically significant. At the 5-percent level of significance, the critical value of the F-ratio--with 4 and 124 degrees of freedom--is approximately 2.45; the calculated F-ratios were 1.47 (for the break in the first quarter of 1968) and 1.74 (for the break in the first quarter of 1981). The null hypothesis of structural stability cannot be rejected, but because of the difficulties mentioned above, this finding can only be interpreted as suggestive, not conclusive.

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Author: | Larkins, Daniel; Gill, Gurmukh S. |
---|---|

Publication: | Survey of Current Business |

Date: | Jun 1, 1985 |

Words: | 2050 |

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