Download Applications of Quantile Regression

漢珍2008商學研究與數位資源
應用研討會
分量迴歸的介紹與應用
降息刺激經濟成長？
如何增加公司利潤？
漲時看勢，跌時看質？
How Many Years for One SSCI
Publication?
How Many Years for One SSCI
Publication?
2004
2005
2006
2007
2008
SSCI 發表總篇數
1
1
0
2
7+1
IF>0.5 之 SSCI 發表總篇數
國科會評定之優良國際期刊
0
0
0
0
0
0
1
1
5
5
0.327
0.327
0
0.849
3.518
IF 總合
計量模型與方法的應用
• 分析並呈現資料的特性
• 解釋過去的經濟現象
• 預測未來
資料
• 橫斷面 (cross-section) 資料:
• 時間序列 (time series) 資料:
• 追蹤資料 (panel) 資料:
不同實證結果的爭論?
• 計量模型失靈?
• 計量學家失靈?
• 實證資料不對?
• 瞎子摸象？
不同實證結果的爭論?
• Certain puzzles of the relations between
firm profitability and its determinants:
– R&D expense
– Size effect on the profitability
– Debt ratio puzzle
不同實證結果的爭論?
• R&D expense
– Branch (1974); Grabowski and Mueller (1978);
Reinhard (1985); Guerard, et al. (1987);
Brown (1988); Kraft (1989): Chan, et al.
(1990); Morbey and Reithner (1990);
Sougiannis (1994); Deng, et al. (1999) and
Schoenecker and Swanson (2002)
不同實證結果的爭論?
• The effect of size on the profitability
– Ferri and Jones (1979), Smith and Watts
(1992), Panzar and Willig (1979), Eckard
(1990) and Paul (2001)
– Williamson (1967), Holmes, et al. (1991);
Lever (1996); Chuang (1999); Pull (2003)
不同實證結果的爭論?
• Capital structure (Debt ratio):
– Kim (1978), Schneller (1980) and Bradley, et
al. (1984)
– Titman and Wessels (1988) and Baskin (1989)
計量方法的演變
Yi =β1+β2 X2i+…+ βk Xki+ ei ,
i =1,…,N
• Specification
linear model  nonlinear model  nonparametrics
• Method
least squares (least absolute deviation), QMLE,
GMM, computationally intensive methods, etc.
• Structure
single equation  multiple equations
(simultaneous-equation model, VAR)
Does the era of linearity and leastsquares come to an end?
• Legendre:
– Least squares:
– Minimizing sum of squared errors
• Boscovich:
– Least absolute deviation
– Minimizing sum of absolute errors
• Key: “averaging” the errors
Legendre
Boscovich
An Example: Simple Regression
An Example: Multiple Regression
Regression Line
OLS and LAD
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平均數具有代表性嗎？
• 應用和計算平均數的前提條件是什麼？
– 同質性的分配
– 因為只有是同質性的分配，計算平均數才有意
義
The Perspective of Quantile
Regression (QR)
The Perspective of Quantile
Regression (QR)
How to Enhance Firm Profit?
Motivations
• Limitations of OLS and LAD methods
– Central behaviors only
– Conditional mean
• Qunantitle Regression (QR) Model
– Whole distribution
– Conditional distribution
Key Question
• The impacts of the identified
determinants of profitability
performance on firms are consistent
with different levels of firm’s
profitability quantiles?
Motivations
• Certain puzzles of the relations between
firm profitability and its determinants:
– R&D expense
– Size effect on the profitability
– Debt ratio puzzle
Motivations
• Firm life cycle
• Adizes (1988):
– Business strategies and organizational
structures of firms vary according to the
problems faced at different life cycle stages of
the organization
Prior Studies on Life-cycle
Theory
• The concept of corporate life-cycle stage has
generated considerable applied interest
– Dodge et al. (1994) on the relationship between operation
strategies and life cycles
– Beldona et al. (1997) and Robinson (1998) on effects of
operation strategies on performance at various firm life cycle
stages
– Kimberley and Miles (1980) and Dodge and Robins (1992)
positing that organization structure reflects current life cycle
stage
– Adizes (1979); Miller and Friesen (1984); Alexander et al.
(1993); and Maturi (1999) examining the relationship
between CEO leadership styles and life cycle stages
– Anthony and Ramesh (1992), Black (1998) and Jorion and
Talmor (2001) testing the impact of life-cycle on corporate
earnings.
Key Limitation of Prior
Studies
• Segment sample companies into various
subsets
– Use criteria such as earnings and/or age
– Apply traditional optimization techniques such
as ordinary least squares (OLS) and least
absolute deviation (LAD) to fit their subsets
Key Limitation of Prior
Studies
• The analytical framework in these studies was
based on unconditional distribution of firm
samples
• This form of “truncation of samples” may yield
invalid results
• As demonstrated by Heckman (1979), such
methods often exhibit sample selection bias
Key Advantage of QR
• A valid alternative is the quantile regression
framework, which segments the sample into
subsets defined by conditioning covariates
• Moreover, in comparison with the least square
method, quantile regression offers a relatively
rich description of the conditional mean for
extreme cases in the samples
Empirical Methods
• No quantile models: OLS and LAD
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Empirical Methods
• Quantile regression model
y i  x     ui
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Quant  ( y i xi )  inf y : Fi ( y x)   x   
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Quant  (ui xi )  0
Empirical Methods
• Quantile regression model
min
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Data
• Sample S&P500 firms over the 10-year
period from 1996 to 2005 were analyzed
• Financial firms were excluded
• Firms were also excluded from the
analysis if the specified financial data were
not available for the entire 10-year period
• The final sample included 2,078 firm
observations
• All data were obtained from the Compustat
database.
Data
• Return on equity (ROE) was selected as the
proxy variable for firm profitability
• Five determinants of profitability were recorded:
–
–
–
–
–
R&D expense
Company size
Debt ratio
Total asset turnover
Current ratio
Empirical Results
Table 1 Definitions of Dependent/Independent Variables
Variables
Dependent Variable
ROE
Independent Variables
RD
SIZE
DR
TAT
CR
Definitions
Return on equity= Net income/ shareholder’s Equity
(ROE reveals how much profit a company generates with the
money shareholders have invested in the company)
Per research and development expenses=R&D expenses/employee
numbers
(Discovering new knowledge about products, processes, and
services, and then applying that knowledge to create new and
improved products, processes, and services that fill market needs)
Natural log of book value of total asset=Ln (total assets)
Debt ratio=Total liabilities/total assets
(Debt ratio shows how much the company relies on debt to finance
assets)
Total asset turnover=Net sales/total assets
(TAT is a measure of how well assets are being used to produce
revenue)
Current ratio=Current assets/current liability
(Current ratio is an indication of a company's ability to meet
short-term debt obligations; the higher the ratio, the more liquid
the company is)
Conclusions and Directions for
Future Research
• A comparative analysis: QR, OLS and
LAD estimates
• The nonlinearities derived from conditional
QR:
– size, significance and sign
• It should be noted that certain existing
puzzles of the relations between firm
profitability and its determinants could be
satisfactorily accounted for in this study
Conclusions and Directions for
Future Research
• Certain caveats
– U.S. S&P 500 firms
– Comparisons with models with other dynamic
parameter designs
– Proxy variable selection
– Other determinants of firm profitability
– Panel data
Application #2:
降息刺激經濟成長？
Table 1 Definition of Dependent/Independent Variables
Variables
Definitions
Dependent Variable
GGDP
Growth rates of real GDP
Independent Variables
GGOV
SR
Growth rates on government-consumption-expenditure/GDP
ratios
3-month short term interest rates
GIVT
GEXT
Growth rates on investment/GDP ratios
Growth rates on export/GDP ratios
GIMT
Growth rates on import/GDP ratios
Application #3
漲時看勢，跌時看質？