4. Empirical Results
4.1. Ordinary Least Square Regressions
4.1.1. CEPs Model 1—NASDAQ, Data Processing, and Technology CPI
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4.1.1. CEPs Model 1—NASDAQ, Data Processing, and Technology CPI
The first VAR used included as dependent variables CEPs, the NASDAQ Composite, technology hardware prices, and data processing PPI. All variables are one-year differenced.
Table 4-4 Selection-Order Criteria Test for One-Year Differenced NASDAQ, Construction Equipment, Data Processing, and Technology CPI
Several tests are included in this producing various statistics such as the final prediction error (FPE), Akaike’s information criterion (AIC), the Hannan and Quinn information criterion (HQIC), likelihood ratio (LR), and Schwarz’s Bayesian information criterion (SBIC). According to the spectrum of selection-order criteria, six lags appear to be the most statistically significant with the variables of CEPs, data processing PPI, technology CPI, and the NASDAQ Composite.
Not only do six lags enjoy the most statistically significance, but also the AIC is among those statistics which is statistically significant. As previously discussed, some econometricians prefer to use or emphasize the importance of the AIC statistic due to the fact that it quantifies the amount of information ‘lost’ on differenced variables relative to the goodness of fit. Therefore, a total of six lags were used for the first VAR model. Next, the VAR equation is conducted.
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Table 4-5 VAR Equation Results for the NASDAQ, Construction Equipment, Data Processing, and Technology CPI
In the quadra-variate VAR model, the results demonstrate that all variables are statistically significant. Moreover, all variables enjoy a high R-squared demonstrated a strong representation between the model’s variance and the variance of the population. The coefficient results were excluded since there was a total of 30 coefficients. The difficulty of interpreting so many coefficients was previously discussed. Therefore, the next step is to show the OIRFs which were generated after the VAR. Since this thesis is focused on determinants of equipment prices, the OIRFs are limited to relationships where other variables aside from CEPs act as the impulse variable while CEPs act as the response variable.
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Figure 4-1 OIRF of Data Processing Impulse and CEPs Response
The first OIRF to be run was that between data processing CPI and CEPs. As can be seen, the moving average of the OIRF is below zero for every period except for the first, third, and fifth where it seems to hug the zero line in addition to the fourth where it appears to be positive. Aside from these steps or periods, the response of CEPs from data processing CPI is entirely negative. It should also be pointed out though that the 90 percent confidence interval or the mean square error variance band never fully reaches negative, but rather just the variance-covariance matrix appears to be negative. While one may be compelled to rightly assert that the response of CEPs from an impulse of data processing CPI is more likely than not to be negative, it is not possible to confidently assert this to be the case.
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Figure 4-2 OIRF of Technology Hardware CPI Impulse and CEPs Response
The same issue which afflicted the VAR of data processing on CEPs also burdened the OIRF of a shock from technology CPI on construction equipment. The 90 percent confidence bands never fully reached below or above 0. Because of this, it is impossible to determine whether the impact on construction equipment would be positive or negative. One could potential argue that the overall trend is negative. Indeed, other VARs with different parameters using technological CPI indicates a statistically significant negative impact where the 90 percent confidence bands are entirely negative for a number of steps as can be seen with the VAR including technology CPI and ECDPs. Moreover, other VARs testing technology CPI prices against CEPs with different lag periods or including different variables not shown demonstrated a stronger relationship. However,
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with this specified model, this was not the case. At any rate, a negative relationship would be consistent with the OLS results and also the theoretical foundations which asserts that technological hardware CPI enjoys a negative relationship with prices.
Figure 4-3 OIRF of the NASDAQ Composite and CEPs Response
With the NASDAQ Composite though, there were somewhat more robust results than with technology CPI. With a shock of the NASDAQ Composite on CEPs, the moving average of the VAR was negative for all 10 steps graphed in the OIRF. For four of the periods, the 90 percent confidence band was entirely negative. While these results are not entirely as robust as other VAR results, it still points to a negative relationship between the two variables given the specific model created. Moreover, it is consistent with the OLS model results and theoretical literature which
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asserts that investment in technology increases technological advancement which in turn increases the efficiency of production and finally lowers prices.
Figure 4-4 OIRF of CEPs Impulse and CEPs Response
The final OIRF of this VAR model merely demonstrates a shock of CEPs on CEPs themselves. The results demonstrate that it must take more than 10 full steps for prices to return to normal. Because of this, it can be surmised that holding all other variables constant, CEPs impact CEPs over the long-run. Moreover, recovery from these shocks is not resolved in the short- or medium-term and in all likelihood is resolved in the long-term.
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Table 4-6 Granger Causality Tests for the NASDAQ, Construction Equipment, Data Processing, and Technology CPI
This model then used the Granger causality equation to determine the directionality of the relationship between these variables. As can be seen, if a 90 percent significance level or 10 percent alpha level is used, then it can be said that technology CPI and the NASDAQ Composite Granger causes CEPs. Conversely, CEPs also Granger cause the NASDAQ Composite in this model, but equipment prices do not Granger cause any other variables in the model. There are also a number of interactions among the other technology variables in the model. For instance, technology CPI and the NASDAQ Composite Granger cause data processing while the NASDAQ also Granger causes technology CPI. The model of causality then can be articulated as:
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Figure 4-5 Granger Causality Map for the NASDAQ, CEPs, Data Processing, and Technology CPI
A post-estimation test on autocorrelation was also conducted using the Lagrange-multiplier method. As can be seen by the below table, three of the six lags failed to reject the null hypothesis that there is no autocorrelation at that specific lag order. While not ideal, the three lags which rejected the null hypothesis are lower order lags in the model overall. Moreover, overparameterization is an issue as well that is important to avoid. Since this is the case, it appears to be that this VAR is not necessarily as valid as others, but is valid enough.
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Table 4-7 Lagrange-Multiplier Test for CEPs VAR Model 1
Finally, we can use a dynamic forecast using the predicted values from the VAR Model to infer how these variables may move in future periods. According to the results, there is a 90 percent confidence that CEPs will be increasing by 2021 after a sharp decline throughout 2020. As for the NASDAQ Composite, the forecast also asserts with 90 percent confidence that technology investment will increase throughout 2020 and into int0 2021. The model cannot assert with 90 percent confidence whether data processing will enjoy a positive increase or suffer a negative decrease throughout 2020 and into 2021. Finally, the model asserts with 90 percent confidence that technology CPI will decrease throughout 2020 and into 2021.
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Figure 4-6 Dynamic Forecasts for for NASDAQ, CEPs, Data Processing, and
Technology CPI
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