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Do interest rates lead real sales and inventories? A spectral analysis approach.

This paper uses spectral analysis to study aggregate sales, inventories, and interest rates from a macroeconomic perspective. We assume countercyclical Federal Reserve policy acts on economic growth, sales, and inventories with a time lag of unknown duration. Interest rate changes affect sales first, and through sales, they indirectly influence inventories. Viewed from this perspective, changes in interest rates may be expected to have a leading long-run negative statistical association with sales. In addition, attempts to maintain proportionality between inventories and sales may explain a cyclical lead by sales on inventories and a positive correlation between these two variables. In turn, the lagged response of sales to interest rates and the co-movement of sales and inventories may explain, albeit indirectly, why a moderate long-run negative statistical association of inventories to interest rates may also be expected.


Forecasting business conditions is a critical function of many business economists, and there is a continuing quest for better tools to do this. This paper uses spectral analysis techniques to analyze nominal interest rates, real sales, and inventories from a macroeconomic perspective. Its primary purpose is to identify leads and lags between these three major and interrelated business cycle variables. A secondary outcome bears on the relative importance attached to inventories as compared to sales in business cycle analysis. In our view, the empirical role of inventories in recessions would be more complete if there were consideration of possible predictive leads by sales, which would make it easier for business to anticipate inventory behavior.

Spectral analysis is a statistical procedure that appears promising in business cycle analysis because it estimates cycles, correlations, lags, and turning points. It provides valuable diagnostics and complements other time series techniques. Its main objective is the decomposition of time series into their component frequencies. The analysis seeks to identify statistically significant cycles and lead-lag relationships that could be useful to applied economists.

Interest rate changes act on the economy with a time lag whose duration is to be determined. In turn, economic growth and changes in output are closely associated with changes in real sales, (1) and the latter are related to real inventories. There are two basic explanations for inventory behavior. One is known as the production-smoothing model. This theory asserts that the firm would be able to decrease costs if it meets temporarily high demand by smoothing production over several periods. This model makes three predictions: sales are negatively correlated to inventory investment over the short run, inventories are negatively correlated to interest rates, and sales are more variable than production. The other explanation for inventory behavior is based on accelerator models first proposed by Metzler (1941). In this view, if sales growth exceeds inventory growth there would be an ensuing inventory build-up to restore proportionality to the sales-inventory ratio. If, instead, sales growth were to be lower than inventory growth, then inventories would be liquidated, thus once again restoring proportionality. The model predicts that sales are positively correlated to inventories over the long run. Metzler's accelerator view was found to be important because it could generate business cycles in Keynesian models.

The results from this paper indicate that changes in interest rates have a leading long-run negative statistical association with sales growth. Furthermore, the results also indicate that sales appear to be positively correlated to, and lead, inventories. In turn, the lagged response of sales to interest rates and the likely co-movement of sales and inventories may help explain, albeit indirectly, why a moderate long-run negative statistical association of inventories to interest rates is to be expected. Though the actual relationship of sales to inventories is controversial, our results are consistent with the sales-inventory accelerator perspective, whereby sales and inventories are kept proportional to each other.

Our results are tentative on two counts. One count is usual: more studies are needed to confirm results. The second count is more serious: there is no agreement on uniform methods to estimate leads and lags with spectral analysis or even on whether such estimation is possible. However, in this paper we show that it is possible to make tentative estimates of lags. Thus, our application of spectral techniques indicates that interest rates are negatively correlated with sales and lead them by nearly twenty months. The inverse correlation presumably reflects the long-term effects of interest rate changes on economic activity. This would seem to imply that interest rates may be a leading indicator of real sales. Similarly, business sales appear to lead inventories by an average of ten months, which may lend some support to lagged accelerator models of inventory behavior.

Since our focus is on lead-lag relationships, the paper presents an overview of inventories, of sales, and the role of interest rates in the next three sections. Univariate spectral analysis follows in the fifth section, and cross-spectral analysis in the sixth. The concluding section presents some ideas on what the results imply.

Inventories and the Business Cycle

There have been ten recessions in the United States since World War II, and arguably all ten recessions have been caused by inventory adjustments. Inventories are characterized by their volatility and their sheer size. In the year 2000, the stock of real inventories amounted to $14 trillion, while real manufacturing and trade sales and real GDP were $11 and $9 trillion respectively. With sales and inventories at 120 and 155 percent of GDP, respectively, it is clear that changes in these variables affect expansions and contractions. For example, in recessions since 1945, decreases in inventory investment have accounted for eighty to ninety percent of the decrease in U.S. real GDP.

Of the two explanations for inventory behavior, the predictions of the production-smoothing model are the least successful. Yet, in spite of its predictive shortcomings, some investigators, such as Blinder and Maccini (1991), consider it important to business cycle research. This is because much macroeconomic literature on inventories has used this model as its micro-foundation. (2)

The Role of Sales

It is possible that the view of inventories as a major force in the propagation of recessions could be enhanced and made more complete. This could come about by assigning a more prominent role to sales in the dynamics of the business cycle than heretofore. A step in this direction would be evidence that shows sales as anticipating inventory changes. The two major inventory views are based on a close relationship of sales and inventories, but empirical work has, by and large, found sales to be less variable than production. It is possible, therefore, that researchers have found sales to be a less interesting topic. Yet Fair (1989) has shown the opposite, that production is less variable than sales in a variety of industries. This was the case for sectors where sales and production could be measured in physical units versus deflated dollars. Fair concludes that some of the work showing production as more variable than sales may be due to inadequate data. In a similar vein, McConnell and Perez-Quiros (2000) fin d that the volatility of durable goods sales can he divided into two periods. Prior to the early 1980s, production is considerably more volatile than sales. However, for the period since then, the variability of production dampens to a level apparently comparable to that of sales. So, it may be that volatility is not necessarily fixed for either production or sales and seems to shift over time. This makes sales more interesting.

There are two distinct sales categories. One is "final sales," defined as GDP less inventory investment. Final sales, however, include service sector sales that, while large, also are the least volatile and do not have associated inventories. The other category is "manufacturing and trade sales," including the wholesale and retail sectors. This study uses manufacturing and trade sales, since they are associated with comparable inventory groupings.

Nominal and Real Interest Rates

Theory suggests that changes in interest rates affect (and therefore anticipate) many macroeconomic series -- a basic premise of monetary policy. This is borne out by several studies that concur in stating real and nominal rates "are leading indicators of future output." (3) The hypothesis that interest rates are negatively related to future economic growth and operate with a lag is empirically supported by Fiorito and Kollintzas (1994), who find real interest rates for the G7 countries lead real GDP by four quarters, albeit at low correlations; by Chiari, Christiano, and Eichenbaum (1995), who find the nominal Federal Funds rate has its highest correlations with real GDP at leads of four to six quarters; and by King and Watson (1996), who find nominal rates have a higher correlation and a longer lead (five to six quarters) than real rates. (4) The latter are found to have a substantially lower correlation and a shorter lead on output (three to four quarters). Boldrin, Christiano, and Fisher (2001) show simil ar results and concur with King and Watson that these properties of real and nominal interest rates confirm that monetary policy considerations play an important role in explaining the dynamics of the business cycle.

One difference between the above studies and this one is that the role of interest rates is not especially singled out, as would be done in leading indicator analysis. It is only one set of many statistical associations pertinent to business cycles that are studied and analyzed. Additionally, the reported interest rate results are based primarily on simple correlations using the level of interest rates and real GDP or industrial production. One difference in our analysis from others is that we focus on changes in the nominal interest rate, (5) as contrasted to its level. A second difference is that we attempt to relate the leading indicator property of changes in interest rates to changes in sales and inventories, rather than to GDP or other output measures. The change unit used covers twelve-month spans from 1970 to 2000 (i.e., June 1998/June 1999, then July 1998/July 1999, etc.). Sales and inventories are reported monthly and include total sales of durables and retail sales. A third difference between this study and others is that the techniques used here are in the frequency-domain and thus enable a decomposition of variation across frequencies, which may provide fresh insights. A final difference is the graphical nature of spectral analysis. This helps make the results visually intuitive and also allows for comparisons with the leading indicator charts used to portray such series by The Conference Board.

Univariate Spectral Analysis of Sales, Inventories, and Interest Rates

The term "spectral" leads to the following analogy found in Statsoft (1995). Suppose you analyze a beam of white sunlight for the first time. It appears to be uninteresting. If viewed through a prism, however, there is a decomposition of the light into the colors of the spectrum, each with different wavelengths. In similar fashion, spectral techniques are capable of finding underlying cycles that are either hidden in the data or not readily apparent to visual inspection. In essence, performing spectral analysis on a time series is like putting the series through a prism in order to uncover cyclical patterns and identify component wavelengths and their relative importance.

Spectral analysis decomposes a variable into underlying sine and cosine functions of particular wavelengths or cycles. For example, spectral analysis identifies a recurring sixty-two-month cycle, with six of them contained in the 372-month data series, as the most important wavelike pattern of interest rates, real sales, and inventories. This particular "wave" or "frequency" (we use the terms interchangeably) is identified as most important because it accounts for a higher percentage of the total variance of the entire time series than any other frequency. This contribution is known statistically as a density value. Spectral analysis proceeds to identify other recurring cycles in the sales data in descending order of importance, as ranked by their densities. This is shown in Table 1, which displays the densities of the first fifteen frequencies for the T-bill, sales, and inventories. Technically, the number of frequencies in spectral analysis is half the total number of observations in the data set, which in our case is 372. Our data therefore have waves ranging from a low frequency of one cycle, to a maximum high frequency of 186 cycles. The complete set of all 186 waves is known as a power spectrum.

However, it should be emphasized spectral analysis is not deterministic but is instead a statistical procedure. It is therefore appropriate that the density values referred to above should be interpreted in terms of a probabilistic variance (sums of squares) of the data at the respective frequency. As with other statistical techniques, sampling errors can affect the parameters of the data spectrum, which are just estimates of true but unknown population data. The statistical methods do no more than assign weights to the various frequencies, such that these weights reflect the relative strength of each frequency in fitting the data. These weights, however, are not precise values. The randomness in the data tend to lead to a smearing effect across frequencies in the spectrum that is analogous to wide confidence bands on the coefficients of a regression.

Figure 1 depicts the shape of the power spectrums. For graphical convenience, the chart shows the first fifty frequencies of our three variables' spectrum, with the density highest around six, corresponding to cycles of 62 months' duration. The remaining 136 frequencies, which are not shown, are characterized by very low density values. King and Watson (1995) tell us that a conventional frequency domain definition of the business cycle is that these are frequencies between 24 and 128 months, roughly equivalent to the interval between the third and the fifteenth frequencies of Figure 1 and Table 1. The range of this domain definition derives from the duration of business cycles isolated by NBER researchers using the methods of Burns and Mitchell (1946). Applying this frequency range to our data we note that this business cycle interval contains the peak of the spectra and the bulk of the variance of the interest rate (sixty-nine percent), sales (seventy-one percent), and inventories (eighty percent). The hump shape of the power spectrum indicates there is substantial predictability (6) of the cyclical component of these growth rates (which is not the same as predictability of the variables).

The power spectrum of interest rates, sales, and inventories shown in Figure 1 is similar to the growth rate spectrum of a wide range of macroeconomic variables. (7) In particular, our growth rate spectrum shares the following broad features with the growth rate spectrum of other macroeconomic variables: the power spectrum is relatively low at low frequencies (a small number of cycles), rises to a peak at six cycles (62 months duration), then rapidly declines at higher frequencies of cycles. (8) The height of the spectrum indicates the extent of that frequency's contribution to the variance of the growth rate.

As shown in Figure 1, a spectral representation describes cycles in a frequency-amplitude domain. However, this representation can easily be converted to the amplitude-time domain characteristic of all time series. The time domain may at times lend itself more readily to visual interpretation. Accordingly, Figure 2 shows the fit between two time series: one is the single sixty-two-month cycle of Table 1 (repeated six times), the other is the actual twelve-month T-bill basis point changes. In all figures involving interest rates, the "inverted" T-bill interest rate is the T-bill rate multiplied by (-1) so that it co-moves with sales. This renders all upward sloping lines as showing a fall in the interest rate, and all downward sloping lines as showing a rise in the interest rate. Figure 3 also represents time series, and shows how closely the sum of the first fifteen frequencies of Table 1 approximates the actual T-bill twelve-month changes.

Cross-Spectral Analysis

So far, we have used univariate spectral analysis on sales, inventories, and the T-bill rates, and have observed that these three variables share their most important low frequency waves with each other. While spectral techniques decompose a single time series into a spectrum of frequencies of fixed-length cycles, cross-spectral analysis is the bivariate extension of spectral analysis and relates to pairs of time series. It measures the strength of the statistical association of waves of equal cycles corresponding to any two economic variables and also measures their respective leads or lags. This is possible because the spectral density matrix has real and imaginary mathematical components, which can be transformed into two cross-spectral statistics of direct relevance to cycle analysis. The first is coherence, which defines the association between variables. The coherence statistic (which applies to any two waves of equal cycles) can take a value between zero and one and is analogous to the R-squared of re gression. Coherence measures the proportion of variance in one frequency as explained by the other. The second statistic is the phase value. The phase statistic is used to estimate lead/lag relationships by wavelength pairs, and measures the time difference for comparable frequencies.

It is important to note a distinct feature of the phase statistic. The interpretation of the phase spectrum is highly dependent on the values of the coherence spectrum (Warner, 1998). The phase can only be estimated reliably if the coherence is reasonably high. This is because the statistical sampling error of the phase is inversely related to the squared coherence. As coherence falls, the error in estimating the phase gets larger. This implies we need relatively high coherence values between pairs of frequencies in order to obtain reliable estimates of lead/lag relationships.

There is, however, no uniform approach to identifying lead-lag relationships in economic data with spectral methods, and some researchers do not think this is feasible at all. With these caveats in mind, our approach to lag estimation follows. Our choice as to the criteria used in selecting cut-off points is to ascertain confidence bands around coherence values. This can be combined with a selection process that relies on selecting frequencies that have relatively high densities. This will help rule out some of the phase estimates on statistical grounds, and the most likely phase leads will then be those with highest coherence. The figures for the T-bill rates, sales, and inventories (Figures 4, 5 and 6) give a visual flavor of this selection process. First, they show waves with coherence above .70 and individual frequency densities for each variable higher than two percent. More rigorous criteria are then used to narrow down this first set. Using the confidence bands around the coherence to help rule out so me of these frequencies, we end up with coherence values above .80 and individual density requirements of five percent and higher. This narrower selection in turn leaves us with the most likely phase leads as determined by the highest coherence values. All coherence values show ninety percent confidence bands, as derived from tables developed by Amos and Koopmans (1963).

Cross Spectral Analysis of the T-bill Interest Rate and Sales

We now turn our attention to the cross spectral relationship of the T-bill interest rate and sales. The statistics for real sales and T-bill interest rate are shown in Table 2 and Figure 4. Once again, for graphical convenience Figure 4 shows only the first twenty of 186 frequencies. There are two sets of data shown in this figure. One set has coherence values above .70 and density values higher than two percent (thick and dotted lines). As Table 2 shows, the lead of the T-bill interest rate on sales ranges from twenty-five months for frequency four, to ten months for frequency fourteen. The second set has more stringent requirements, with coherence values above .80, and frequencies for the T-bill interest rate and sales with density values explaining five percent or more of their respective variation. These correspond to frequencies four through eight (thick lines only). The leads of the T-bill interest rate frequencies on the respective sales frequencies are now narrower, and range from twenty-five months for frequency four, to eighteen months for frequency eight. Our selection rule indicates that out of all these possible leads, the most likely lead is that of the frequency with the highest coherence. This occurs at frequency six with a coherence value at .90, and a corresponding lead of nineteen months on the T-bill interest rate. Frequency six happens to be the sixty-two month cycle, which we previously saw explained the most variance for all variables in Table 1. These spectral statistics support the hypothesis that interest rates operate on sales with a long lag. Their role is apparently that of a cost factor that slows or increases real sales over time, as rates rise or fall.

We have applied this last cross spectral result of a nineteen-month lead to the actual time domain data on the T-bill rate and sales. Both variables are shown in Figure 7. This figure plots the twelve-month change in the T-bill interest rate against the twelve-month change in sales, with the T-bill rate "shifted forward" in time by nineteen-months, suggesting a relatively consistent lead.

Cross-Spectral Analysis: Sales and Inventories

Figure 5 also shows two areas with relevant statistics for sales and inventories, separated by a gap marked with thin lines. The heavier bands show coherence above .80 and individual densities for sales and inventories above five percent. The lighter bands show coherence above .70 and density values two percent and higher. Unlike the T-bill rate and sales figure, the higher set of coherence values is itself separated into two areas or peaks. A further difference is that the sales-inventory relationship has the first two frequencies outside the three-to-fifteen month range used previously to define the length of business cycles.

Turning our attention to the phase values in Table 3, we note these range from a tie at ten months for frequencies three and four, to seven months for frequency thirteen. Though this range is narrow, our conherence and density selection rules indicate once again that out of all the frequencies shown in Table 3, the most likely lead is that of the frequency with the highest coherence. This can be seen in Table 3 for frequency three, which shows a coherence value at .90, as well as a corresponding lead of sales leading inventories by ten months. This lead has also been applied to the actual time domain data and is shown in Figure 8. This figure plots the twelve-month change in sales against the twelve-month change in inventories. The sales graph has been "moved forward" by nine months to show both the closeness of the co-movements of sales and inventories as well as the lead of sales. The relationship of sales to inventories discussed here is straightforward. Sales lead and are positively related to inventorie s. Both the lead and the positive association support the Metzler view of reactive inventory behavior. According to Metzler, if sales grow faster than inventories an ensuing inventory build-up follows, which seeks to restore proportionality to the sales-inventory ratio. If sales growth is lower than inventory growth, inventories are liquidated to once again restore proportionality. Our findings here are in accord with the prevailing empirical research literature, and are at variance with the negative association predicted by the production-smoothing inventory model.

Cross-Spectral Analysis: the T-Bill Rate and Inventories

The relationship of inventories to interest rates is empirically less clear cut than their relationship to sales. The production-smoothing model predicts a negative association of inventories to interest rates. Yet Blinder and Maccini's (1991) assessment of inventory research finds inventory investment to be insensitive to changes in interest rates. They consider this insensitivity to be an important, troublesome and open research question. In a somewhat similar vein, our cross-spectral statistics show ambiguity. The interest rate-inventory cycle appears to be characterized by two opposing results. On the one hand, the data indicate interest rates are positively correlated to, and lead inventories by seven to ten months. On the other hand the spectral statistics also show interest rates to be negatively related to inventories, albeit at substantially longer leads. (A parallel to this behavior is found in auto-correlations in which sign reversals are observed as leads or lags are systematically increased)

This is visible in the data presented in Table 4 which shows two sets of phase statistics. Both sets have the same coherence values, but the phase values are distinctly different in sign, magnitude and interpretation. The first set displays a negative relationship in which interest rates lag inventories. The lag ranges from fifteen months at frequency nine, to nine months at frequency two. The set also includes a sign reversal for the phase value at the statistically important frequency six, which shows interest rates leading inventories by thirty months. The second set of phase statistics displays a positive relationship in which interest rates lead inventories. The lead is tightly packed, and frequencies nine to twelve each suggest leads of six months. Frequency 6 also shows a sign reversal, but it is now only one month. The net effect is that the negative interest rate-inventory relationship is statistically less satisfactory than the positive relationship. The latter is, of course, at variance with the i nterest rate prediction of the production smoothing model.


Why are nominal interest rates apparently a leading indicator of real sales? We expect that it is because inflation imposes real costs on the economy. Nominal interest rates have a real rate and an inflationary expectations component. An increase in real interest rates is unarguably a cost for business and consumers. What is less clear is that increases in nominal interest rates due to inflation are also a cost factor.

Early theorizing assumed inflation's effects to be neutral, resulting in uniform price increases across all sectors of the economy. Such inflation neutrality, however, has seldom been achieved in practice. To the contrary, Romer (1996) concludes that inflation may have very real and substantial costs. (9) On a general level, inflation imposes real costs by reducing the purchasing power of individuals as wages lag inflation growth. Inflation also creates a signal extraction problem, because agents find it difficult to differentiate relative price changes (Benabou 1988), which contain genuine market mechanism signals, from a rise in the general price level, which does not. The result is that the transactions system becomes less efficient as the cost of information gathering increases (Cuikerman 1984). Inflation also redirects resources from productive uses toward risk hedging. All of the above affect sales.

Sales for investment purposes are also negatively affected by inflation. The capital markets issue nominal debt instruments subject to price and value volatility as nominal interest rates vary. The increased uncertainty brought about by varying inflation on nominal interest rates, and therefore on investment value, may make creditors and debtors reticent in financing investment projects. This "investment decision uncertainty" may explain in part why statistical analysis shows inflation and investment to be negatively correlated (Fischer, 1993). Finally, real ex-post capital losses to either borrowers or lenders depend on whether ex-ante inflation expectations, which determine the inflation premium added to real rates, turn out to be different from actual ex-post inflation. These arguments lend support to our view that the inflation component of nominal interest rates can be, over time, a real cost to business and consumers. This may explain the twenty-month lagged negative relationship between nominal intere st rates and real business sales.

Why do real sales appear to lead real inventories? Again, we can only suggest a possible rationale. This is that businessmen are probably not proactive. That is, they may not forecast future sales, or if they do, they probably do not act on their forecasts. This may be because the cost of acting on the basis of a wrong forecast could be substantial. It is conceivable then, that businessmen may instead be reactive to unanticipated changes in current sales, possibly waiting several months to confirm the emergence of a new trend. When and if a new sales trend appears to be firmly in place, then and only then will inventory policy be likely to change. The cost of this reactive policy is probably acceptable, since it may only involve the far more limited expenses of a somewhat delayed adjustment in inventories to the new sales trend.

Our spectral analysis of sales and inventories appears to lend weak-to-moderate support to the accelerator model of inventory behavior. We can speculate that the data show inventories attempt to keep the same proportion to sales, albeit on an inter-temporal or lagged basis of seven-to-ten months. The lagged structure of inventories has recently been tested by Bils and Khan (2000), who find that inventories vary in proportion to anticipated sales in the long run. Additionally, they find the sales-inventory ratio to be strongly persistent and pro-cyclical, suggesting inventories are sluggish or lagged in the short run. Their data show that inventories are counter-cyclical relative to sales, and therefore fail to keep up with sales over the business cycle. Our findings show this countercyclical behavior only in the neighborhood of turning points, as shown in Figure 8, with the rest of the figure showing a positive co-movement between sales and inventories.










No. Of Length Density Cumulative No. Of Length Density
Cycles (months) (weight) Density Cycles (months) (weight)

1 372 0.021 0.021 1 372 0.055
2 186 0.035 0.056 2 186 0.056
3 124 0.061 0.117 3 124 0.061
4 93 0.083 0.200 4 93 0.075
5 74 0.090 0.290 5 74 0.108
6 62 0.105 0.395 6 62 0.135
7 53 0.073 0.468 7 53 0.090
8 47 0.057 0.525 8 47 0.052
9 41 0.050 0.574 9 41 0.027
10 37 0.035 0.609 10 37 0.014
11 34 0.037 0.646 11 34 0.030
12 31 0.041 0.687 12 31 0.052
13 29 0.031 0.718 13 29 0.041
14 27 0.017 0.734 14 27 0.019
15 25 0.012 0.747 15 25 0.006

No. Of Cumulative No. Of Length Density Cumulative
Cycles Density Cycles (months) (weight) Density

1 0.055 1 372 0.043 0.043
2 0.110 2 186 0.056 0.098
3 0.171 3 124 0.074 0.172
4 0.246 4 93 0.071 0.243
5 0.354 5 74 0.094 0.337
6 0.490 6 62 0.130 0.467
7 0.580 7 53 0.092 0.560
8 0.632 8 47 0.064 0.623
9 0.659 9 41 0.061 0.684
10 0.674 10 37 0.042 0.726
11 0.704 11 34 0.045 0.771
12 0.756 12 31 0.058 0.828
13 0.796 13 29 0.042 0.870
14 0.815 14 27 0.019 0.889
15 0.821 15 25 0.009 0.899


Frequency Length Phase Coherence Confidence Bands (90%)
 (Months) (Months) Lower Upper

4 93 24.9 0.83 0.72 0.91
5 74 21.5 0.85 0.74 0.92
6 62 19.2 0.90 0.83 0.93
7 53 18.0 0.84 0.72 0.91
8 47 18.0 0.84 0.73 0.92
9 41 17 0.85 0.72 0.91
10 37 16.1 0.71 0.49 0.82
11 34 16.3 0.76 0.55 0.84
12 31 14.5 0.83 0.72 0.91
13 29 12.1 0.81 0.71 0.94
14 27 10 0.71 0.49 0.82


Frequency Length Phase Coherence Confidence Bands (90%)
 (Months) (Months) Lower Upper

1 372 9.0 0.97 0.93 0.99
2 186 9.0 0.89 0.82 0.94
3 124 10.4 0.90 0.83 0.93
4 93 10.0 0.89 0.82 0.94
5 74 9.8 0.84 0.72 0.91
6 62 9.7 0.80 0.64 0.88
12 31 7.9 0.89 0.82 0.94
13 29 7.3 0.93 0.88 0.96


Frequency Length Phase * Coherence Confidence
 (Months) (Months) Lower
 (1) (2)

6 62 29.9 (1.1) 0.81 0.71
9 41 (14.9) 5.8 0.91 0.83
10 37 (13.0) 5.6 0.92 0.88
11 34 (10.7) 6.2 0.83 0.72
12 31 (9.2) 6.3 0.79 0.64

Frequency Bands 90%

6 0.94
9 0.93
10 0.96
11 0.91
12 0.88

* Phase values for the (1) inverted T-Bill and Inventories and the (2)
negatively correlated T-Bill and inventories

(1.) A regression between twelve-month changes in real manufacturing and trade sales and twelve-month changes in monthly U.S. industrial production for the 1970 to 2000 period shows an adjusted [R.sup.2] of .998 and a regression coefficient of 1.1. For the same period changes in real sales and changes in monthly interpolated real GDP show an adjusted [R.sup.2] of .981 and a regression coefficient of .991.

(2.) It is ironic that, given its popularity, the majority of received empirical work rejects the conclusions of the production-smoothing model. Nevertheless, limited but not fully convincing support of the model's predictive power is found in Ramey (1989), who shows that in contrast to the literature, inventories respond negatively to interest rates, but with low elasticity estimates. Niemira (1990), also shows interest rates appear to be negatively correlated to inventories, but with a long enough lead to be viewed as a long-leading indicator of inventory behavior. Support for the output-inventories predictions of the model is found in Christiano (1988), and in Kydland and Prescott (1982) who do a calibration analysis showing inventories smooth production and have a negative correlation with output.

(3.) In particular Fiorito et al (1994), PP. 251, 57, King and Watson (1996), pp. 35, 39, and Boldrin et al., (2001), pp. 149, 160. Business cycle analysts working on Leading Indicators have long recognized that interest rates are associated with future output (see Zarnowitz (1988)).

(4.) This stronger association between nominal interest rates and business cycle variables may in part be due to the practice of individuals and firms to typically base their financial planning in nominal rather than in real terms (Romer, 1996).

(5.) Our work is based on nominal rates because there are several considerations that argue against real interest rates. On the one hand, there is little evidence that real interest rates have a stable relationship to the business cycle, (Mishkin, 1981). On the other, there is strong evidence that nominal rates rise in recoveries and fall in downturns. Last but not least, there are nontrivial data problems in transforming nominal interest rates into real rates. Boskin (1996), found serious overestimation in CPI inflation data over the 1974 to 1994 period. The result of this mis-reporting has been to distort the historical values of calculated real interest rates.

(6.) A result attributed to Rotenburg and Woodford (1994), in King and Watson (1995), pp. 37.

(7.) It is notably different from the typical spectral shape that Granger (1966) identifies for the level of many economic time series, in which much of the power occurs at very low frequencies, in King and Watson (1995).

(8.) King and Watson (1995) call this pattern "the typical spectral shape of growth rates."

(9.) See Benabou (1988, 1992), Benabou and Gertner (1993), Diamond (1993), Tommasi (1994), and Ball and Romer (1993).


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Maurice Larrain is an Associate Professor of Finance at Pace University and was the director of research and forecasting for International Capital Markets Corporation. He began his forecasting career in a joint venture with Columbia University's Center for International Business Cycle Research. His bachelor, masters and Ph.D are all from Columbia University.
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Author:Larrain, Maurice
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Geographic Code:1USA
Date:Apr 1, 2002
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