4. Empirical Results
4.1. Ordinary Least Square Regressions
4.1.3. CEPs Model 3—GDP, Interest Rates, and Industrial Production
4.1.3. CEPs Model 3—GDP, Interest Rates, and Industrial Production
The next VAR model used CEPs differenced by one year in conjunction with one-month differenced variables including GDP, the effective federal funds rate, and industrial production of business equipment. One-month differenced GDP, effective federal funds rate, and industrial production of business equipment had not been tested for a unit root. Because of this, Dickey Fuller unit root tests were conducted before the VAR was executed in order to ensure validity.
Table 4-12 Lag Selection Order Criteria Statistics for One-Month Differenced GDP, One-Month Differenced Effective Federal Funds Rates, and One-Month Differenced Industrial Production of Business Equipment VAR
The lag order selection criteria tests were more mixed than the previous lag order selection tests. With the prior VARs, lag order selection tests tended to all choose the same lag order selection. However, with this VAR model it was not the case with HQIC and SBIC statistics chose 3 lags while AIC and FPE chose 6 lags and the LR statistic favored 8 lags. However in spite of this, this VAR will continue to trust the usefulness of the AIC statistic since the literature suggests it fails to under-parameterize and over-parameterize VAR models. Therefore, 6 lags were used for this particular VAR model. The results of the VAR equation are below in Table 4-13.
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Table 4-13 VAR Equation Results for Month Differenced GDP, One-Month Differenced Effective Federal Funds Rates, and One-One-Month
Differenced Industrial Production of Business Equipment
As can be seen by the results, all variables are statistically significant in the VAR equations.
However, not all variables enjoyed the same share of variance in accordance with the variance of the population as can be seen by the R-squared statistics. While ti can be said that construction equipment prices and GDP enjoyed a high R-squared statistic, the effective federal funds rate only enjoyed a statistic of .51 while industrial production of business equipment suffered from an R-squared statistic of .32 signifying on 32 percent of its variance can explain the variance of its population. Nonetheless, the OIRFs that followed these VAR equations provides additional insight on the relationship between these variables. Moreover, the R-square statistics tend to somewhat reflect the efficacy of the OIRFs in determining the relationship between them and CEPs.
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Figure 4-12 OIRF of One-Month Differenced GDP Impulse and CEPs Response
The first OIRF used tests the impulse variable of one-month differenced GDP against CEPs. The above chart suggests that an impulse of one-month differenced GDP negatively shocks CEPs differenced by one year for at least 10 steps. Moreover, the 90 percent confidence bands are negative for the entirety of all ten steps asserting that there is at least a 90 percent chance that the impact on CEPs from GDP is negative for these ten steps. As mentioned, the R-square statistic of one-month differenced GDP was extremely high and also the 90 percent confidence bands are entirely negative suggesting that GDP differenced by one month is a very good predictor of CEPs.
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Figure 4-13 OIRF of One-Month Differenced Effective Federal Funds Rates Impulse and CEPs Response
The next OIRF tested the impulse variable of one-month differenced effective federal funds rate against the response variable of CEPs differenced by a year. The OIRF suggests that it is impossible to tell if the impact of the impulse variable on the response variable is positive or negative. Because of this, it can be surmised the relationship, to use the parlance of other methodologies, is not substantively significant. Therefore, it is difficult to suggest that one-month differenced interest rates are a good indicator of CEPs. As mentioned previously, the R-squared statistic for this variable was relatively low which appears to be a strong indicator of whether or not the variables in the VAR models are good predictor variables of the explanatory variables used.
However, it could be the case that this is not an efficacious variable to use in testing against CEPs
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due to the nature of the data. That is to say, the variable of the effective federal funds rate suffers from a lack of variance, leptokurtosis, and does not change often enough on a month-to-month basis for it to be useful as a VAR variable. Perhaps though, a better method to analyze this relationship is the OLS method which was expounded upon previously in this chapter.
Figure 4-14 OIRF of One-Month Differenced Industrial Production of Business Equipment Impulse and CEPs Response
The final OIRF used in this particular VAR model was one-month differenced industrial production of business equipment against one-year differenced equipment prices. The OIRF shows that a shock from industrial production produces a positive increase in CEPs. However, the 90 percent confidence band does not entirely surpass the zero-baseline point suggesting that for some
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of the steps it is impossible to determine if the impact is entirely positive or entirely negative.
However, this is not the case for all steps. Even so, it should be noted that the R-square statistic on this variable was the lowest of all variables in the model. Therefore, it is not surprising that this variable is not a consistently efficacious variable in predicting the movement of CEPs. Moreover, it should be taken into consideration that one-month differenced variables in macroeconomic terms are highly volatile. Therefore, the differenc between months is much less smoothed than between years. It appears that because of this, using the relationships between one-month differenced variables against one-year differenced CEPs is much less sagacious than using one-year differenced variables in analyzing construction equipment price movements.
Table 4-14 Lagrange-Multiplier Test for CEPs VAR Model 3
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After the OIRFs were executed, a Lagrange-multiplier test was conducted to determine if there was autocorrelation at any of the lag orders. While the fourth and fifth lags suffered from autocorrelation, the first, second, third, and sixth did not. Again, since the highest order lag did not suffer from autocorrelation, this model is apparently a good enough fit for the specifications.
Table 4-15 Granger Causality Test Results for One-Month Differenced GDP, One-Month Differenced Effective Federal Funds Rates, and One-Month Differenced Industrial Production of Business Equipment
The second last test used in this model was the Granger causality equation extrapolated upon in the method section. Using an alpha level of 0.10, it can be surmised that GDP differenced by one month is the only variable that Granger causes CEPs differenced by one year. Moreover, CEPs do not Granger cause any other variables in the model reinforcing the précis that CEPs are
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a legitimate response variable, but also that CEPs operationalize as a response variable and not as an explanatory variable. Figure 4-15 demonstrates the Granger causality relationships between these variables.
Figure 4-15 Granger Causality Map for Month Differenced GDP, One-Month Differenced Effective Federal Funds Rates, and One-One-Month Differenced Industrial Production of Business Equipment
While CEPs do not entirely act as a response variable throughout the Granger causality results, it appears to be the case that it is more a response variable than an explanatory variable.
This is evident through the results which assert that CEPs Granger cause only one variable, industrial production, while both industrial production and GDP Granger cause CEPs.
Nonetheless, the relationship between these one-month differenced variables and long-term CEPs is more complicated than simply between one-year differenced variables tested and one-year differenced CEPs.
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Figure 4-16 Dynamic Forecasts for One-Month Differenced GDP, One-Month Differenced Effective Federal Funds Rates, and One-Month Differenced Industrial Production of Business Equipment
Finally, the forecasts of this model assert a very similar trend as prior forecasts with additional insight on the efficacy of forecasting in the long-term with short-term variables. To address the former point, this model also shows that equipment prices are likely to decrease in 2020. Moreover, the accuracy of this model asserts that this downturn will occur throughout the year whereas other models were less certain or confident about the duration of the directionality.
As to the latter point, it appears to be the case that with the exception for GDP in very short-term forecasts, short-term variables are difficult to use for long-term forecasts. This is evident with the horizontal nature of the forecasts’ moving averages in conjunction with the 9 percent confidence
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intervals suffering from high variance dramatically above and below the horizontal zero reference line.
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4.1.4. CEPs Model 4—One-Month Differenced NASDAQ, Interest Rates, and Steel