Chapter 3. Methodology
3.4 Empirical models and Variable Description
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3.4 Empirical Models and Variable Description
This study examines the hypotheses with regression models which combined inventory expectations models and sales, earnings and profit margin prediction models. Section 3.4.1 and 3.4.2 first identify the sales, earnings and profit margin prediction models and the inventory expectations models based on previous literature.
Then Section 3.4.3 discusses the models which combines the two models to determine the inventory predict ability of sales, earnings, and profit margin, and how this study tests the hypotheses.
3.4.1 Predicting Sales and Earnings
The sales, earnings and margin prediction equations are the first order autoregressive models in seasonal differences. According to Foster (1977), each quarterly sales and earnings appears to have both (a) a seasonal component and (b) an adjacent quarter-to-quarter component. This is apparent from both inspection of the cross sectional autocorrelation function and from one-step ahead forecasting results.
Foster concludes that there is strong evidence of seasonality in the quarterly sales and earnings, and a strong association between seasonal component and adjacent
component of sales and earnings. Accordingly, the models in this section utilize seasonal differences of adjacent quarters to predict sales and earnings. The economic intuition of the models is that when the seasonal difference of sales and earnings between quarter t-1 and quarter t-5 increase, the seasonal difference of sales and earnings between quarter t and quarter t-4 would also increase.
The prediction equations are:
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: Income before extraordinary items in quarter t
However, according to Bernard (1991), a potential problem for sales and
earnings prediction equations is that the seasonal difference may be affected by major changes in the scales of operations, such as major expansion, merger and acquisition, or discontinued operation. Under these circumstances, the seasonal difference for one quarter may not be an appropriate prediction for the adjacent quarter. For example, if a company acquired a subsidiary and sales doubled in quarter t-1, the regressor in the model (
) will reflect the scale change, and the model will predict another sales increase for the adjacent quarter. This result is incorrect.
In order to adjust for this problem, Bernard scales every variable by a
contemporaneous variable and develops another prediction equation, profit margins prediction model. Profit margins are defined as earnings divided by contemporaneous sales. Because profit margins follow a stationary process, the effect of the changes in the scales of operations in this model can be mitigated.
The profit margin prediction model is as follow:
Basic Sales and Earnings Prediction Models
Basic Profit Margins Prediction Model
(1)
(2)
(3)
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3.4.2 Predicting Total Inventory
In this section, the inventory expectations model is developed to estimate the unexpected inventory measure, which will be added to the prediction models to examine the predictability of inventory for sales and earnings. From production smoothing and stockout models, we know that inventory can convey information such as inventory decisions and the characteristics of the decision rules. The purpose of the inventory expectations model is to isolate this information, which is contained in unexpected inventory, for use in predicting sales and earnings.
The unexpected inventory is the difference between actual inventory and expected inventory. Expected inventory is identified by the regressor in the inventory
expectations model, while unexpected inventory is the residual in the model.
According to Bernard (1991), the estimated unexpected inventory will consist of two components: (1) the unexpected inventory that would be calculated if the actual decision rules were known, and (2) the difference between expected inventory given the actual decision rules and expected inventory given the simplified decision rules.
Any stockout or smoothing effect will remain in the estimate of unexpected inventory, as part of the first component.
The inventory expectations model is presented as follow:
: Sales in quarter t
: Income before extraordinary items in quarter t : Total inventory in quarter t
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To control for size, all the variables are divided by sales. Without such an
adjustment, it would be hard to compare the inventory number in the model because of the changes in scale of operations. Because of the use of the inventory to sales ratio, even if the company expands operation and doubled its size, the inventory-to-sales ratios would most possibly stay constant. As a result, the object of the model is to predict the inventory-to-sales ratio.
To control for seasonality, the seasonal lag of the inventory-to-sales ratio was inserted in the model. Besides seasonality in sales, there are still some seasonal patterns in production. For example, inventory production usually decreases in fourth quarter to reduce inventory taxes at year end. Thus, inserting seasonal lag could help mitigate the seasonality of production.
In this model, the inventory can be LIFO inventory or IFRS inventory:
: Sales in quarter t
: Income before extraordinary items in quarter t : Total inventory under LIFO method in quarter t
: Total inventory under IFRS method in quarter t Inventory Expectations Model -- Inventory Reported under LIFO method
Inventory Expectations Model -- Inventory Reported under IFRS method
(5)
(6)
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According to Bernard (1991), when is the inventory reported under LIFO method, the residual in the inventory expectations model is the proxy for LIFO inventory, and when is the inventory reported under IFRS method, the residual in the inventory expectations model is the proxy for IFRS inventory.
In the next section, the residual and will be added as regressor in the sales, earnings and margin prediction equations. These regression models will be used to determine the inventories’ predictability of future sales and earnings.
3.4.3 Predicting Sales and Earnings with Inventory
In this section, the residual and from inventory expectations models are added as regressor in the sales, earnings and margin prediction equations and develop a new model. The purpose of the new models is to predict sales, earnings, and profit margin with total inventory reported under LIFO and IFRS inventory valuation
method, and determine which inventory valuation method can come up with inventory levels which can be stronger indicators of future sales and earnings.
The prediction equations are as follows:
: Sales in quarter t
: Income before extraordinary items in quarter t
: The unexpected inventory reported under LIFO method in quarter t : The unexpected total inventory reported under IFRS method in quarter t Final Sales, Earnings and Profit Margins Prediction Models
(7) (8)
(9)
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If both and are positive, both IFRS and LIFO inventory are positively related to future sales. The result is consistent with production smoothing model. If
is significant and is insignificant, IFRS inventory is the stronger indicator of future sales, and hypothesis 1 is true. If is significant and is insignificant, LIFO inventory is the stronger indicator of future sales, and hypothesis 1 is rejected.
If both and are significant, and is larger than , IFRS inventory is the stronger indicator of future sales and hypothesis 1 is true. If both and are significant, and is larger than , LIFO inventory is the stronger indicator of future sales and hypothesis 1 is rejected. The result is the same for and
If both and are negative, both IFRS and LIFO inventory are negatively related to future sales. The result is consistent with stockout model. If is
significant and is insignificant, IFRS inventory is the stronger indicator of future sales, and hypothesis 2 is true. If is significant and is insignificant, LIFO inventory is the stronger indicator of future sales, and hypothesis 2 is rejected. If both
and are significant, and is smaller than , IFRS inventory is the stronger indicator of future sales and hypothesis 2 is true. If both and are significant, and is smaller than , LIFO inventory is the stronger indicator of future sales and hypothesis 2 is rejected. The result is the same for and
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4. EMPIRICAL RESULTS AND ANALYSIS
4.1 Descriptive Statistic
Table 4-1 Descriptive Statistics of Final Prediction Models Descriptive Statistics of Final Sales Prediction Model
N Min. Max. 1Q Mean Median 3Q S.E.
Y 1779 -0.883 3.230 -0.036 0.063 0.062 0.150 0.006 X 1779 -0.883 3.230 -0.038 0.062 0.062 0.150 0.006 1779 -1.751 4.320 -0.044 0.000 -0.006 0.040 0.004 1779 -2.058 4.230 -0.052 0.000 -0.007 0.042 0.004 X:
Y:
: Sales in quarter t
: The unexpected inventory reported under LIFO method in quarter t : The unexpected inventory reported under IFRS method in quarter t
Descriptive Statistics of Final Earnings Prediction Model
N Min. Max. 1Q Mean Median 3Q S.E.
Y 1779 -9.350 11.460 -0.021 0.011 0.006 0.031 0.009 X 1779 -9.350 11.460 -0.020 0.011 0.006 0.030 0.009 1779 -1.750 4.320 -0.044 0.000 -0.006 0.040 0.004 1779 -2.060 4.230 -0.052 0.000 -0.007 0.042 0.004
X:
Y:
: Sales in quarter t
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: Income before extraordinary items in quarter t
: The unexpected inventory reported under LIFO method in quarter t : The unexpected inventory reported under IFRS method in quarter t
Descriptive Statistics of Final Profit Margin Prediction Model
N Min. Max. 1Q Mean Median 3Q S.E.
: Income before extraordinary items in quarter t
: The unexpected inventory reported under LIFO method in quarter t : The unexpected inventory reported under IFRS method in quarter t
The descriptive statistic results show that there is no extreme observation in the variables that reflects data distortion. The medians, means, first quartile and third quartile for independent variables and dependant variables are close, indicating that the distributions of the variables are quite normal.
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4.2 Empirical Results
4.2.1 Basic Prediction Model
Table 4-2 Basic Sales Prediction Model
Coefficients: Std. Error t value p value
0.022051 0.004594 4.80 1.71e-06 ***
X 0.658251 0.018111 36.35 < 2e-16 ***
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level;
Adjusted R-squared: 0.4183
F-statistic: 1321 on 1 and 1835 DF, p-value: < 2.2e-16 X:
: Sales in quarter t
Table 4-2 reports the estimates of the Basic Sales Prediction Model. X is equal to the first lag seasonal difference in sales scaled by the base quarter. The model shows that the first lag seasonal difference in sales explains much of the current seasonal difference in sales, with the R-squared equals 0.4183. The coefficient on the first lag seasonal difference in sales is positive and significant at 0.001 level, indicating that the variable is positively and highly related to current seasonal difference in sales, and the variable is a necessary control variable in forming sales prediction.
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Table 4-3 Basic Earnings Prediction Model
Coefficients: Std. Error t value p value
0.008923 0.008563 1.042 0.298
X 0.200658 0.022920 8.755 <2e-16 ***
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level;
Adjusted R-squared: 0.03957
F-statistic: 76.65 on 1 and 1835 DF, p-value: < 2.2e-16 X:
: Sales in quarter t
: Income before extraordinary items in quarter t
Table 4-3 reports the estimates of the Basic Earnings Prediction Model. X is equal to the first lag seasonal difference in earnings scaled by the base quarter. The R-squared is equal to 0.03957. This shows that the first lag seasonal difference in earnings doesn’t explain the current seasonal difference in earnings well. However, the coefficient on the first lag seasonal difference in earnings is positive and
significant at 0.001 level, implying that there is still a strong association between the first lag seasonal difference in earnings and current seasonal difference in earnings, and the variable is a necessary control variable in forming earnings prediction.
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Table 4-4 Basic Profit Margins Prediction Model
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level;
Adjusted R-squared: 0.009495;
F-statistic: 6.867 on 3 and 1833 DF, p-value: 0.0001342 X1:
: Income before extraordinary items in quarter t
Table 4-4 reports the estimates of the Basic Profit Margins Prediction Model. X1 is the first lag profit margins, X2 is the fourth lag profit margins, and X3 is the first lag seasonal difference in profit margins. The R-squared is equal to 0.009495. This shows that the Independent variables in profit margins cannot explain much of the current profit margins. However, the coefficients on all the independent variables are positive and significant at 0.001 levels, indicating that there is still a strong
association between these variables and current profit margins. The estimates of are significant, suggesting that the model used for sales and earnings would have been inadequate for profit margins. The estimates of are significant, suggesting the
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presence of seasonality in margins. The estimates of are not significant, conforming the stationarity in the series.
4.2.2 Inventory Expectations Models
Table 4-5 Inventory Expectations Model—LIFO method
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level Adjusted R-squared: 0.8049
: Total inventory under LIFO method in quarter t
Table 4-5 reports the estimates of the LIFO Inventory Expectations Model. The
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model explains much of the variance in inventories, with the R-squared equals 0.8049.
The coefficients on the fourth lag of inventory-to-sales ratio and the first lag in seasonal difference are both positive and significant at 0.001 levels, indicating that these variables are necessary control variables in forming inventory expectations.
The coefficients in the LIFO inventory expectations model show that the LIFO inventory-to-sales ratios are negatively and significantly related to current sales, indicating that production cannot adjust instantaneously to demand changes, and that inventory-to-sales ratios decline as sales increase. According to Bernard (1991), if inventory is a buffer for sales, there should also be a positive relationship between current inventory-to-sales and past sales, as production is adjusted for inventory excesses or shortfalls in the previous quarter. This is the case, with current
inventory-to-sales ratios positively related to sales changes lagged on quarter, and the coefficient roughly equal in magnitude to the coefficient on current sales changes. The buffering behavior is consistent with the stockout model of inventory, while it is inconsistent with production smoothing model, for which inventory-to-sales ratios would be a leading indicator of sales.
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Table 4-6 Inventory Expectations Models—IFRS method
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level Adjusted R-squared: 0.8076
: Total inventory under IFRS method in quarter t
Table 4-6 reports the estimates of the IFRS Inventory Expectations Model. The model explains the variance in inventories well, with the R-squared equals 0.8076.
The coefficient on the fourth lag of inventory-to-sales ratio and the first lag in seasonal difference are both positive and significant at 0.001 levels, indicating that
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these variables are essential control variables in forming inventory expectations. The IFRS inventory are also negatively related to current sales changes and positively related to first lag sales changes, indicating the buffer effect of first lag sales change.
4.3 Final Prediction Models
Table 4-7 Final Sales Prediction Model
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level;
Adjusted R-squared: 0.4124
F-statistic: 417 on 3 and 1775 DF, p-value: < 2.2e-16 X:
: Sales in quarter t
: The unexpected inventory reported under LIFO method in quarter t : The unexpected inventory reported under IFRS method in quarter t
In the final prediction models, the residuals from the inventory expectations model are added as a regressor in prediction models for sales, earnings, and margins to evaluate the predictive ability of inventory. Table 4-7 reports the estimates of the Final Sales Prediction Model. The model shows that the first lag seasonal difference
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in sales explains the current seasonal difference in sales quite well, with the R-squared equals 0.4183. The coefficient on the first lag seasonal difference in sales is positive and significant at 0.001 level, indicating that the variable is strongly related to current seasonal difference in sales.
In the model, is the estimated unexpected inventory from LIFO inventory expectations model, and is the estimated unexpected inventory from IFRS inventory expectations model. According to Bernard and Stober (1989), if the production smoothing model holds, the unexpected inventory would contain information about future demand, and positive unexpected inventory would predict sales and earnings increases. If the stockout model holds, then unexpected inventory would contain information about the difference between current sales and current demand, and positive unexpected inventory would predict sales and earnings decrease.
If neither of these models hold and the simple decision rules are adequate to describe the production decision, then unexpected inventory is noise, and would not be able to predict future sales or earnings. As a result, the coefficients of and represent either the ability of LIFO inventory and IFRS inventory to predict future sales, or the noises in the models.
Table 4-7 shows the positive relation between unexpected inventory and future sales for LIFO inventory, and negative relation between the two variables for IFRS inventory. The results show that the predictability of LIFO inventory for future sales tends to be consistent with production smoothing model, while the predictability of IFRS inventory for future sales tend to be consistent with stockout model. However, the coefficients on both LIFO and IFRS inventory are statistically insignificant. These results indicate that the effect of production smoothing model and stockout model on inventory is not significant.
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Table 4-8 Final Earnings Prediction Model
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level;
Adjusted R-squared: 0.03873
F-statistic: 24.88 on 3 and 1775 DF, p-value: 9.1e-16 X:
: Sales in quarter t
: Income before extraordinary items in quarter t
: The unexpected inventory reported under LIFO method in quarter t : The unexpected inventory reported under IFRS method in quarter t
Table 4-8 reports the estimates of the Final Earnings Prediction Model. The model shows that the independent variables do not explain the dependent variable well, with the R-squared equals 0.03873. The coefficient on the first lag seasonal difference in earnings is positive and significant at 0.001 level, indicating that there is a strong association between the two variables.
The results show a positive relation between unexpected inventory and future earnings for LIFO inventory, and a negative relation for the two variables for IFRS
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inventory, implying the smoothing effect for LIFO inventory and stockout effect for IFRS inventory. However, the coefficients on both LIFO and IFRS inventory are statistically insignificant, indicating that neither production smoothing nor stockout model holds. The unexpected inventories from LIFO inventory and IFRS inventory may be the noises in the models.
Table 4-9 Final Profit Margins Prediction Model
1.076e-01 1.181e-02 0.000 1.000000
X1 1.076e-01 3.192e-02 3.370 0.000768***
X2 7.893e-02 2.482e-02 3.180 0.001498 **
X3 -3.356e-02 3.142e-02 -1.068 0.285711
3.752e-02 5.246e-02 0.715 0.474607
-3.960e-02 5.244e-02 -0.755 0.450262
*** denotes significant at 0.001 level; ** denotes significant at 0.01 level;
*denotes significant at 0.01 level;
Adjusted R-squared: 0.03873
: Income before extraordinary items in quarter t
: The proxy of total inventory reported under LIFO method in quarter t : The proxy of total inventory reported under IFRS method in quarter t
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Table 4-9 reports the estimates of the Final Profit Margins Prediction Model. The R-squared is equal to 0.03873, suggesting that the independent variables do not explain the dependent variable well. The coefficient on the first lag seasonal difference in profit margins is positive and significant at 0.001 level, indicating a strong relation between the dependent and independent variables.
The results once again show that the unexpected inventory is a positive leading indicator of profit margins for LIFO inventory, but a negative leading indicator of profit margins for IFRS inventory. The coefficients for LIFO and IFRS inventory are statistically insignificant suggest that the production smoothing effect and stockout effect are not prevailed. The unexpected inventories from LIFO inventory and IFRS inventory are the noises in the models.
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In economic literature, production smoothing model and stockout model address the predictability of inventory disclosure on sales and earnings. Based on these models, Bernard and Noel (1991) show that inventory disclosure predicts sales and earnings. This study further investigates and compares the predictability of the sales and earnings by inventory reported under last in, last out (LIFO) and that under International Accounting Standard 2 (IAS 2). Thus this study compares the predicting ability of inventory on sales and earnings under IFRS and non-IFRS.
This study selects a group of companies adopting LIFO and disclosing LIFO reserves to be the sample companies, and the LIFO reserves are added to the inventories reported under LIFO method to generate the inventories reported under IFRS inventory valuation method. IFRS inventory valuation method is defined as the inventory valuation methods recommended under IAS 2, which may be FIFO method
This study selects a group of companies adopting LIFO and disclosing LIFO reserves to be the sample companies, and the LIFO reserves are added to the inventories reported under LIFO method to generate the inventories reported under IFRS inventory valuation method. IFRS inventory valuation method is defined as the inventory valuation methods recommended under IAS 2, which may be FIFO method