Chapter 4 Empirical Analysis
4.2 Model Construction
As discussed previously, the HB model will involve 2 stage of analysis—
the first stage will be a structural form model using macro-economic variables as
explanatory variables to represent the general factors influencing sales of each
customer. Then, the second stage will draw insight from a model that incorporates
firm specific features to allow adjustment for each account’s heterogeneity. For the
purpose of out-sample forecasting comparison, 3 periods of observation will be
reserved and 36 periods will be used for parameter estimation. Data for aggregate
level were extracted from TEJ database (Taiwan Economic Journal); for individual
level, firm attributes in Exhibit 1 are used as explanatory variables of the model.
In both the aggregate and individual stage, step-wise regression procedure
is adopted to choose variables with the maximum collective explanatory power from
the pool of relevant factors initially proposed in Exhibit3. By doing so, the number
of variables will be reduced since variables with less contribution will be screened
out. Only those with highest relevancy will be retained. As noted in later sections,
most of the sales of end product are directed toward China region. Consequently,
macro-economic situations in China would be the most relevant issue in the
aggregate level. Therefore, it makes more sense that many macro-economic indices
entertained in the model are China-based statistics instead of the world. Also,
industry specifics such as demand/supply conditions and compliments demand are
considered to relate to the characteristics of technological product forecasts, which
emphasize on industrial competitive and trend analysis. For example, BB ratio is an
indicator of demand/ supply strengths in semi-conductor industry. Dividing total
industry order quantity with number of orders filled, it measures the degree of
demand exceeds current supply capacity. A BB ratio over one signifies greater
demand than current supply, whereas a BB ratio less than one imply oversupply in
the industry.
Exhibit 3 Initial Macro-economic Variable Pool
Category Variable
Capital Market
NumStock :the numer of stock that company has issued
StockA :A Stock index in China
StockB :B Stock index in China
LoanRate :current one-year borrow rate in China
AvgRate:current one-year average rate in China
DIProj :numbers of direct investment projects in China
International Trade Exchage Rate :RMB to TWD
Price Index
CPI:consumer price index in China
CCI:consumer confidence index in China
PMI:purchase manager index in China
Infrustructure
TeleServ :Telecom Service Availability in China
TeleIm :Telecom Equipment & Services Import In China
TeleEx:Telecom Equipment & Services Export In China
Supply/ Demand/
Complements
BBRatio:Book-to-Bill ratio
NumPhone :industry sales volume of mobile phone in China
LCD:Small Size LCD shipment
Economic indices
Leading :Leading Macro-Economic Climate Index in China
Concur:Coincident Macro-Economic Climate Index in China
Warning :China Monitoring Signals of Macro-Economic Climate Index in China
Exhibit 4 Aggregate Variables
Category Code Definition
Seasonality Yt-12 sales quantity lag 12 periods
Macro-economic
LoanRate China Official Interest Rates of Loans (1 year)
Concur China Macro-Economic Climate Index Warning China Monitoring Signals of
Macro-Economic Climate Index
PMI Purchase Manager Index
Demand/Supply BBRatio Book-to-Bill ratio
Complements lnLCD Small Size LCD shipment; taking natural logarithms
The first stage aggregate model was derived in the form of multiple
regression and can be written as
Because a lagged 12 period variable is included, the original data size of 36 has been
reduced to a size of 24 effective samples. Therefore, the dependent variable, , is a
vector, representing the 24 period monthly sales quantity of account .
is a matrix, composed of the values of 7 selected economic variables
(listed in Exhibit 4, including intercept) in the 24 periods. is a vector of
regression coefficients obtained by regressing the sales quantities of account on
these 8 explanatory variables. Finally, is the normally distributed error term
vector. The prior probability density function for the variance is an Inverted
Gamma Distribution written as
In the individual level, will be treated as the dependent variable that
would be influenced by firm specific attributes. In order to compare forecast results,
the MLE method is also employed to generate parameter estimation. The MLE
estimation of would be
Exhibit 5 Correlation Matrix of Aggregate Variable and Sales
Sales LoanRate PMI BBRatio LCD Concur Warning
Sales 1.000 0.705 -0.265 -0.819 0.908 0.098 0.062
At the aggregate level, loan rate has a positive correlation with sales
quantity, suggesting that firms would rather view storing inventory as an alternative
way of funding similar to an interest rate free loan from the seller. Thus, the higher
the current interest rate is, the more then would order since it become relative cheap
to stock materials. On the other hand, BB ratio shows a negative correlation with
sales. This could be interpreted as an adjustment process of supply and demand. If
current BB ratio is high, meaning order has exceeded available capacity, sales would
decline. This is either done with a price hike from the suppliers or purchasers would
have satisfied the necessary level of stock and reduced ordering. On the other hand,
shipmentof complement goods of mobile phone chipset, small size LCD that
functions as the screen for handsets, has a strong positive correlation with sales. This
is in line with economic intuition that the more chipsets are sold to make mobile
phones, the more LCDs are needed to go with it.
The variables selected here can be categorized into 4 types of indices. A
lagged variable is included to address seasonality problem, which can be observed
clearly from the pattern of monthly sales data. Then, 4 economic factors are deemed
to be effective in influencing aggregate sales volume, namely interest rate, 2
economic indices, and 1 price index. Because these customers are manufacturing
purchasing product as inventory, PMI is in place of CPI (Consumer Price Index).
Book-to-Bill ratio is the measure in semi-conductor industry, which is the amount
booked divided by the amount billed. It reflects the relative strength in demand as
compared with supply. A Book-to-Bill ratio larger than 1 signifies the industry has a
demand stronger than capacity, a sing welcomed by the producers. Reversely, when
Book-to-Bill ratio falls below 1, the producers are essentially over-supplying and
either their price will suffer or the average cost will rise due to slack capacity.
Exhibit 6 Individual Variables
Category Code Definition
Business Model Segment Dummy variable; Brand=1, otherwise=o
Inventory Policy Inventory Days of Inventory
Sales Region
China
percentage of end-product sales allocated the area
Russia India Latin AM
The second stage model regresses the aggregate coefficients on account
attributes to adjust for individual heterogeneity for each customer. It can be
expressed as
is the vector of covariates for account and is a matrix of
regression coefficients because 6 variables representing individual account
heterogeneity are selected in this level (including intercept). here is a
vector of error terms. Note that the smaller covariance matrix of , , is, the
more variation in individual account from the predicted value of aggregate level is
explained by firm attributes. Its prior probability density function is an Inverted
Gamma Distribution
3 categories of account attributes have entered into the second stage
model, namely type of business model, inventory policy, and sales region. In order
to verify on the value-adding effect of branding generally claimed, a dummy
variable “Segment” is created. Accounts operating under its own brand were given a
value of 1 to distinguish it from other business models such as ODM or IDH, in
which cases a value of 0 were assigned. Inventory policy refers to the days of
inventory stocked before this customer sells it to its clients. In addition, different
composition of sales region mix is also a relevant issue in the individual level. The
percentage of final product sold in each region of the world, most notably the
“BRICS”, are shown to influence the quantity demanded by the key accounts. It is
the geometric average percentage across the data period.