CHAPTER 5: ANALYSIS AND RESULTS
5.2 Estimation Results
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represents the impact of order diversification and 𝛽𝛽4 represent the moderation effect of it on inventory and sales. We have fifteen time dummies representing months of each observation, so we have 14 dummies in our models. 𝜍𝜍𝑝𝑝indicates plant-level random intercept; 𝜍𝜍𝑖𝑖𝑝𝑝 is the item-level random intercept, and 𝜀𝜀𝑝𝑝𝑖𝑖𝑝𝑝 is the level-1 error term.
5-2 Estimation Results
Table 5-2.1 shows the analysis of forecast sharing, forecast fluctuation (STD) and order diversification on inventory. Model(1) includes forecast sharing, forecast fluctuations and the interaction term. Model(2) and Model(3) additionally include order diversification and the interaction term. Model(4) is the full model with time dummies included. We measure forecast fluctuation not only by standard deviation, but also by median absolute of deviation (MAD) in Model(5) and quartile coefficient of dispersion (QCOD) in Model(6). The sample size of models is 7821 except for the sample size of model(6), which is 6950. It is resulted from null values of quartile coefficient of dispersion (QCOD) discussed in data section. We mainly look at our full model of Model (4). The results of likelihood ratio test show that our full model not only fits significantly better than null model but better than models form Model(1) to Model(3).
Also, the pseudo R-squared is 0.726, indicating the high correlation between the model’s predicted values and the actual values. We also compare the fitted mixed model to standard regression with no group-level random effects, and the results show that the variances of random intercepts: plant, item and month are significantly different from zero (chi2(3) = 741.87, Prob > chi2 = 0.0000). Therefore, our three-level full model fits the data better than standard regression with no group-level random effects.
The results show that forecast fluctuation, assessed by standard deviation, has a significant and negative moderating effect on the relationship between forecast and
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inventory in Model(4) (β3 = -0.0000078, p < 0.01). H2a is therefore supported. To better asses forecast fluctuation, we not only measure it with standard deviation (STD), but with median absolute of deviation (MAD) and quartile coefficient of dispersion (QCOD). Although forecast fluctuation (QCOD) moderator does not have significant moderating effect in Model(6), forecast fluctuation (MAD) moderator has significant and negative coefficient in Model(5) (β3 = -0.0000079, p < 0.01). Forecast fluctuation moderates the impact of forecast on inventory negatively. With greater forecast fluctuation, the impact of forecast on inventory decreases. The distributor discounts the forecasts when the variance of the forecast is higher, and prepares less inventory than in the condition with lower forecast fluctuation.
In addition to forecast fluctuation, we examine the other factor, order diversification, that might also impact forecast signal on inventories. In Model(4), the results show that order diversification ,how the orders are distributed among items in the plant, negatively moderates the relationship between forecast and inventory (β5 = -1.0005771, p < 0.01). H3a is supported. Because we use entropy measure to assess order diversification, higher value means less concentrated total orders. Higher value of order diversification in our models means that the total orders are distributed among various items with low volume. The estimation shows that plants with high mix low volume orders tend to discount forecast signal than plants with low mix high volume orders. Because of orders with higher product variety and demand fluctuation, it is more difficult for the distributor to analyze and understand the actual demands. Therefore, to avoid overstock, the distributor discounts forecast signal and prepare less inventory when a plant shows higher order diversification (high mix low volume).
To better realize the effect of moderators forecast fluctuation (STD) and order diversification on the forecast signal to inventories, we have Figure 5-2.1 shown.
Figure 5-2.1 shows the integral effect of forecasts on inventory including the
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moderation effects of forecast fluctuation and order diversification. Y-axis indicates the integral effect: β1+ β3× forecast fluctuations + β5× order diversification . X-axis shows the low, medium, and high levels of forecast fluctuations. Order diversification is indicated by the three lines: blue line for high level, red for medium level, and black line for low level of order diversification. We note that low and high level of forecast fluctuation and order diversification are their mean minus and add their standard deviation. From the figure, it shows that forecast fluctuation has considerably decreasing effect on forecast signal to inventories form low to high level of forecast fluctuation. The graph also shows that from low to median level of order diversification the two lines overlaps, which indicates that there is barely no different of moderation effects from low to median order diversification. However, from median to high level of order diversification, the moderation effect is significant. Therefore, it is shown that the decreasing moderation effect of order diversification is mainly significant when it is at high level.
After knowing that external and internal complexity, specified as forecast fluctuation and order diversification, decrease the forecast signal to distributor’s inventories, we discuss how the overall forecast sharing impacts inventories. The results from Table 5-2.1 show that forecast sharing significantly impacts inventory (β1=6.98, p<0.01). However, the integral effect of forecast sharing on inventories should include the moderation effect of forecast fluctuation and order diversification 𝐹𝐹𝐼𝐼𝐼𝐼𝑚𝑚𝐹𝐹𝑚𝑚𝐹𝐹𝐼𝐼𝐹𝐹ℎ𝑚𝑚𝐼𝐼𝑚𝑚𝑚𝑚𝑎𝑎(𝛽𝛽1+ 𝛽𝛽3× 𝑒𝑒𝐼𝐼𝐼𝐼𝑚𝑚𝐹𝐹𝑚𝑚𝐹𝐹𝐼𝐼 𝑒𝑒𝑜𝑜𝑜𝑜𝐹𝐹𝐼𝐼𝑜𝑜𝑚𝑚𝐼𝐼𝑚𝑚𝐼𝐼𝑚𝑚𝐹𝐹 + 𝛽𝛽5× 𝐼𝐼𝐼𝐼𝑚𝑚𝑚𝑚𝐼𝐼 𝑚𝑚𝑚𝑚𝐼𝐼𝑚𝑚𝐼𝐼𝐹𝐹𝑚𝑚𝑒𝑒𝑚𝑚𝐹𝐹𝑚𝑚𝐼𝐼𝑚𝑚𝐼𝐼𝑚𝑚).
Figure 5-2.1 shows that both forecast fluctuation and order diversification decrease the effect of forecast sharing on inventories. When both the levels of forecast fluctuation and order diversification are high, the negative moderation effect is the highest. The total effect of forecast sharing on inventories is still positive. Also, the 95% confidence intervals are significantly different from zero at all ranges, indicating significant effect
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of forecast sharing. Therefore, H1a is supported. It indicates that greater forecast of an item contributes to higher inventory of the item. The distributor does prepare stock according to the forecast, and the forecast signal is essential to its replenishment.
Fig 5-2.1 The total effect of forecasts on inventory
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Table 5-2.1 Estimated results for forecast in models of Inventory.
Model(1) β1: ForecastSharing 4.1808589***
(0.1078030)
β4: OrderDiversification -1.558e+04 (1.847e+04)
TimeDum Not included in models Included in models but not shown
N 7821 7821 7821 7821 7821 6950
Pseudo 𝑅𝑅2 0.6924 0.6925 0.6918 0.726 0.7184 0.67
Wald chi2 2462.74 2458.45 2375.77 3338.09 3028.9 1839.13
Log likelihood -112675.04 -112674.69 -112658.5 -112212.6 -112272.54 -100309.77 Standard errors are reported in parentheses. Chi-Square test statistic indicates the rejection of the null hypothesis that all model coefficients are zero. + Indicates statistical significance at 15% level.* Indicates statistical significance at 10%
level.** Indicates statistical significance at 5% level.***Indicates statistical significance at 1% level.
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國立 政 治 大 學
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Table 5-2.2 shows the analysis of forecast sharing, forecast fluctuation (STD) and order diversification on sales. Model(1) includes forecast sharing, forecast fluctuations and the interaction term. Model(2) and Model(3) additionally include order diversification and the interaction term. Model(4) is the full model with time dummies included. Like models for inventory, we also measure forecast fluctuation by median absolute of deviation (MAD) in Model(5) and by quartile coefficient of dispersion (QCOD) in Model(6). The sample size of models is 7821 except for the sample size of model(6), which is 6950. It is resulted from null values of quartile coefficient of dispersion (QCOD) discussed in data section. The results of likelihood ratio test show that our full model not only fits significantly better than null model but better than models form Model(1) to Model(3). Also, the pseudo R-squared is 0.7599, indicating the high correlation between the model’s predicted values and the actual values. We also compare the fitted mixed model to standard regression with no group-level random effects, and the results show that the variances of random intercepts: plant, item and month are significantly different from zero (chi2(3) = 1973.54, Prob > chi2 = 0.0000).
Therefore, our three-level full model fits the data better than standard regression with no group-level random effects.
The results show that forecast fluctuation negatively moderates the impact of forecast on sales in Model(4) (γ3= -0.0000014, p< 0.01). We assess forecast fluctuation not only by standard deviation but also by median absolute of deviation (MAD) and quartile coefficient of dispersion (QCOD). In the Model (5), forecast fluctuation (MAD) also has significant and negative coefficient (γ3= -0.0000015, p<
0.01). In addition, in the Model (6) forecast fluctuation (QCOD) has significant and negative coefficient (γ3= -0.3496, p< 0.01). With greater forecast fluctuation, the effect of forecast signal on sales reduces. H2b is supported. The higher forecast fluctuation might result from customers’ forecasting behavior: forecast volatility and inflation. And
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it’s because when customers face substantial uncertainty about the market demand, they revise forecast frequently as they receive updated information. The forecast with higher forecast variance does not represent sales as well as forecast with lower forecast variance. Therefore, the effect of forecast signal on sales is discounted when forecast fluctuation is higher.
In addition to forecast fluctuation, we examine how the other factor order diversification moderates the relationship between forecast sharing and sales. In Model (4), the results show that order diversification, how the orders are distributed among items in the plant, negatively moderates the relationship between forecast and sales (γ5 = -0.9719, p< 0.01). H3b is supported. Plants with higher value of order diversification we measured indicates that the orders of the plants distributed among high variety of items with low volume, which is alike high mix low volume in manufacturing literature. The estimation shows that the impact of forecast signal on sales decreases in the plants with high mix low volume orders (higher value of order diversification) compared to in the plants with low mix high volume orders (lower value of order diversification). Because the demand of high mix low volume orders is more variable, the effect of forecast signal on sales reduces.
Furthermore, Figure 5-2.2 shows the effect of moderators forecast fluctuation (STD) and order diversification on the forecast signal to sales. Y-axis indicates the integral effect: γ1 + γ3× forecast fluctuations + γ5× order diversification. X-axis shows the low, medium, and high levels of forecast fluctuations. Order diversification is indicated by the three lines: blue line for high level, red for medium level, and black line for low level of order diversification. We note that low and high level of forecast fluctuation and order diversification are their mean minus and add their standard deviation. Figure 5-2.2 shows that forecast fluctuation has marginally decreasing effect on forecast signal. Compared to forecast fluctuation, order diversification has more
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moderation effects on forecast signal. From low to median and to high level of order diversification, the decreasing moderation effect is significant.
After knowing that external and internal complexity, specified as forecast fluctuation and order diversification, decrease the forecast signal to distributor’s sales, we discuss how forecast sharing impacts sales integrally. The results from Table 5-2.2 show that forecast sharing has significant and positive coefficient in Model (4) (γ1= 4.311, p< 0.01). However, the integral effect of forecast sharing on sales should include the moderation effect of forecast fluctuation and order diversification 𝐹𝐹𝐼𝐼𝐼𝐼𝑚𝑚𝐹𝐹𝑚𝑚𝐹𝐹𝐼𝐼𝐹𝐹ℎ𝑚𝑚𝐼𝐼𝑚𝑚𝑚𝑚𝑎𝑎(𝛾𝛾1+ 𝛾𝛾3× forecast fluctuations + 𝛾𝛾5× order diversification).
Figure 5-2.2 shows that both forecast fluctuation and order diversification decrease the effect of forecast sharing on sales. When both the levels of forecast fluctuation and order diversification are high, the negative moderation effect is the highest. The total effect of forecast sharing on sales is still positive. Also, the 95% confidence intervals are significantly different from zero at all ranges, indicating significant effect of forecast sharing on sales. Therefore, H1b is supported. The estimation confirms a positive relationship between forecast and sales. Higher forecast of an item is related to higher sales of it. The forecast signal reflects customer demands, and the sales of the distributor.
Fig 5-2.2 The total effect of forecasts on sales
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Table 5-2.2 Estimated results for forecast in models of sales.
Model(1) γ1: ForecastSharing
1.5691724*** γ2: ForecastFluctuation
(STD)
γ4: OrderDiversification
9.028e+03 γ2: ForecastFluctuation
(MAD) γ2: ForecastFluctuation
(QCOD)
-3.262e+03 (7.549e+03)
γ3:ForecastSharing X ForecastFluctuation (QCOD)
-0.3496858***
(0.1188788)
TimeDum Not included in models Included in models but not shown
N 7821 7821 7821 7821 7821 6950
Pseudo 0.7654 0.7648 0.7523 0.7599 0.7559 0.745
Wald chi2 2125.05 2124.78 2099.72 2316.69 2232.71 1886.1
Log likelihood -104501.83 -104500.88 -104384.2 -104323.34 -104334.5 -93066.747 Standard errors are reported in parentheses. Chi-Square test statistic indicates the rejection of the null hypothesis that all model coefficients are zero. + Indicates statistical significance at 15% level.* Indicates statistical significance at 10%
level.
** Indicates statistical significance at 5% level.***Indicates statistical significance at 1% level.
𝑅𝑅2
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