Financial Econometric and Statistics
Methods and Applications
By Cheng-Few Lee
The 23rd Annual Conference on
Pacific Basin Finance, Economics,
Accounting, and Management 16-17 July 2015
Distinguished Professor of Finance, Rutgers University and Visiting Chair
Professor of Finance, National Chiao Tung University
Editors of RQFA and RPBFMP
Table of Contents
A. Applications of Statistics for teaching
Investment Analysis, Security Analysis and
Portfolio Management and Futures and Options
B. Handbook of Financial Econometrics and
Statistics
C. Textbook of Financial Econometrics and
Statistics
D. Alternative Errors-in-Variable Models and Their
Applications in Finance Research
E. Application of simultaneous Equation in
Finance Research
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
1.
2.
3.
Introduction
Experience, Information Asymmetry, and Rational Forecast Bias
An Overview Of Modeling Dimensions For Performance Appraisal Of Global
Mutual Funds
4. Simulation as a Research Tool for Market Architects
5. The Motivations for Issuing Putable Debt: An Empirical Analysis
6. Multi Risk-Premia Model of US Bank Returns: An Integration of CAPM and
APT
7. Non-Parametric Bounds for European Option Prices
8. Can Time-Varying Copulas Improve Mean-Variance Portfolio?
9. Determinations of Corporate Earnings Forecast Accuracy: Taiwan Market
Experience
10. Market-Based Accounting Research (MBAR) Models: A Test of ARIMAX
Modeling
3
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
11. An Assessment of Copula Functions Approach in Conjunction with Factor
Model in Portfolio Credit Risk Management
12. Assessing Importance of Time-Series versus Cross-Sectional Changes in Panel
Data: A Study of International Variations in Ex-Ante Equity Premia and
Financial Architecture
13. Does Banking Capital Reduce Risk? An Application of Stochastic Frontier
Analysis and GMM Approach
14. Evaluating Long-Horizon Event Study Methodology
15.The Effect of Unexpected Volatility Shocks on Intertemporal Risk-Return
Relation
16. Combinatorial Methods for Constructing Credit Risk Ratings
17. Dynamic Interactions between Institutional Investors and the Taiwan Stock
Exchange Corporation: One-regime and Threshold VAR Models
18. Methods of Denoising Financial Data
19. Analysis of Financial Time-Series using Fourier and Wavelet Methods
4
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
20. Composite Goodness-of-Fit Tests for Left Truncated Loss Sample
21. Effect of Merger on the Credit Rating and Performance of Taiwan Security
Firms
22. On-/off-the-Run Yield Spread Puzzle: Evidence from Chinese Treasury
Markets
23. Factor Copula for Defaultable Basket Credit Derivatives
24. Panel Data Analysis and Bootstrapping: Application to China Mutual Funds
25.Market Segmentation and Pricing of Closed-end Country Funds: An Empirical
Analysis
26. A comparison of portfolios using different risk measurements
27.Using Alternative Models and a Combining Technique in Credit Rating
Forecasting — An Empirical Study
28. Can we use the CAPM as an investment strategy? An intuitive CAPM and
efficiency test.
29. Group Decision Making Tools for Managerial Accounting and Finance
5
Applications
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
30. Statistics Methods Applied in Employee Stock Options
31.Structural Change and Monitoring Tests
32.Consequences of Option Pricing of a Long Memory in Volatility
33.Seasonal aspects of Australian electricity market
34. Pricing commercial timberland returns in the United States
35. Optimal Orthogonal Portfolios with Conditioning Information
36. Multi-factor, Multi-indicator approach to asset pricing : method and
empirical evidence
37. Binomial OPM, Black-Scholes OPM and Their Relationship: Decision Tree and
Microsoft Excel Approach
38. Dividend payments and share repurchases of U.S. firms: An econometric
approach
39.Term Structure Modeling and Forecasting Using the Nelson-Siegel Model
40.The intertemporal relation between expected return and risk on currency
6
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
41. Quantile Regression and Value-at-Risk
42. Earnings Quality and Board Structure: Evidence from South East Asia
43. The Rationality and Heterogeneity of Survey Forecasts of the Yen-Dollar
Exchange Rate: A Reexamination
44. Stochastic Volatility Structures and Intra-Day Asset Price Dynamics
45. Optimal Asset Allocation under VaR Criterion: Taiwan Stock Market
46. Applications of Switching Model in Finance and Accounting
47. Matched Sample Comparison Group Analysis
48. A Quasi-Maximum Likelihood Estimation Strategy for Value-at-Risk
Forecasting: Application to Equity Index Futures Markets
49. Computer Technology for Financial Service
50. Long-Run Stock Return and the Statistical Inference
51. Value-at-Risk Estimation via a Semi-Parametric Approach: Evidence from the
Stock Markets
7
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
52. Modeling Multiple Asset Returns by a Time-Varying t Copula Model
53. Internet Bubble Examination with Mean-Variance Ratio
54. Quantile Regression in Risk Calibration
55. Strike Prices of Options for Overconfident Executives
56. Density and Conditional Distribution Based Specification Analysis
57. Assessing the Performance of Estimators Dealing with Measurement Errors
58. Realized Distributions of Dynamic Conditional Correlation and Volatility
Thresholds in the Crude Oil, Gold and Dollar/Pound Currency Markets
59. Pre-IT policy, Post IT policy and the Real Sphere in Turkey?
60. The Determination of Capital Structure: A LISREL Model Approach
61. Evidence on Earning Management by Integrated Oil and Gas Companies
62. A comparative study of two models SV with MCMC algorithm
63. Internal Control Material Weakness, Analysts’ Accuracy and Bias, and
Brokerage Reputation
8
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
64. What Increases Banks’ Vulnerability to Financial Crisis: Short-Term Financing
or Illiquid Assets?
65. Accurate Formulae for Evaluating Barrier Options with Dividends Payout and
the Application in Credit Risk Valuation
66. Pension Funds: financial econometrics on the herding phenomenon in Spain
and the United Kingdom
67. Estimating the Correlation of Asset Returns: A Quantile Dependence
Perspective
68. Multi-Criteria Decision Making for Evaluating Mutual Funds Investment
Strategies
69. Econometric Analysis of Currency Carry Trade
70. Evaluating the Effectiveness of Futures Hedging
71. Analytical bounds for Treasury bond futures prices
72. The Rating Dynamics of Fallen Angels and Their Speculative Grade-Rated
Peers: Static vs. Dynamic Approach
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HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
73. The roles of compensation scheme of portfolio managers, wealth and supply
constraints, and the relative risk aversion of traders in the creation and
control of speculative bubbles
74. Range Volatility: A Review of Models and Empirical Studies
75. Business Models: Applications to Capital Budgeting, Equity Value, and
Return Attribution
76. VAR Models: Estimation, Inferences, and Applications
77. Model Selection for High-Dimensional Problems
78. Hedonic Regression Models
79. Optimal Payout Ratio under Uncertainty and the Flexibility Hypothesis:
Theory and Empirical Evidence
80. Modeling Asset Returns with Skewness, Kurtosis, and Outliers
81. Alternative Models for Estimating the Cost of Equity Capital for
Property/Casualty Insurers: Combined Estimator Approach
82. A VG-NGARCH Model for Impacts of Extreme Events on Stock Returns
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HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
83. Risk-Averse Portfolio Optimization via Stochastic Dominance Constraints
84. Implementation Problems and Solutions in Stochastic Volatility Models of
the Heston Type
85. Stochastic Change-Point Models of Asset Returns and Their Volatilities
86. Unspanned Stochastic Volatilities and Interest Rate Derivatives Pricing
87. Alternative Equity Valuation Models
88. Time Series Models to Predict the Net Asset Value (NAV) of an Asset
Allocation Mutual Fund VWELX
89. Discriminant Analysis and Factor Analysis: Theory And Method
90. Implied Volatility: Theory and Empirical Method
91. Measuring Credit Risk in a Factor Copula Model
92. Instantaneous Volatility Estimation by Nonparametric Fourier Transform
Methods
93. A Dynamic CAPM with Supply Effect Theory and Empirical Results
11
HANDBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
94. A Generalized Model for Optimum Futures Hedge Ratio
95. Instrument Variable Approach to Correct for Endogeneity in Finance
96. Application of Poisson Mixtures in the Estimation of Probability of Informed
Trading
97. CEO stock options and analysts’ forecast accuracy and bias
98. Option Pricing and Hedging Performance under Stochastic Volatility and
Stochastic Interest Rates
12
TEXTBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
Chapter 1: Introduction
Chapter 2: Multiple Linear Regression
Chapter 3: Other Topics in Applied Regression Analysis
Chapter 4: Simultaneous Equation Models (I)
Chapter 5: Simultaneous Equation Models (2) (SUR&3SLS)
Chapter 6: General Moment Method
Chpater 7: Panel Data Analysis
Chapter 8: Alternative Methods to Deal with Measurement Error
Chapter 9: Time Series Analysis (I) (Hedge Ratio)
Chapter 10: Time Series Analysis (2)
Chapter 11: The Binomial and Multi-nomial Distributions
Chapter 12: The Relationship between Binomial Distribution and Option Pricing
Chapter 13: The Normal and Lognormal Distributions
Chapter 14: The Chi-Square and Non-Central Chi-Square Distributions
13
TEXTBOOK OF FINANCIAL ECONOMETRICS AND STATISTICS
TABLE OF CONTENTS
Chapter 15: Copula, Correlated Defaults, and Credit VaR
Chapter 16: Spurious Regression and Data Mining in Conditional Asset Pricing
Models
Chapter 17: Multivariate Analysis: Factor Analysis
Chapter 18: Stochastic Volatility Option Pricing Models
Chapter: 19:Alternative Method to Estimate Implied Variance
Chapter 20: Numerical Valuation of Asian Options with High Moments in the
Underlying Distribution
Chapter 21: ITO’s Calculus: Derivation of the Black-Scholes Option Pricing Model
Chapter 22: Constant Elasticity of Variance Option Pricing Model: Integration
and Detailed Derivation
Chapter 23: Option Pricing and Hedging Performance under Stochastic Volatility
and Stochastic Interest Rates
14
Alternative Errors-in-Variable Models and
Their Applications in Finance Research
Cheng-Few Lee
Rutgers University , USA
Alice C. Lee
Center for PBBEF Research, USA
Hong-Yi Chen
National Chengchi University , Taiwan
Introduction
1. How do EIV problems affect estimators in the regression model.
2. Alternative estimation methods dealing with EIV problem.
(1) Classical method
(2) grouping method
(3) instrumental variable method
(4) mathematical programming method
(5) maximum likelihood method
(6) LISREL method
3. Discuss how these estimation methods have been used in finance
research
(1) Cost of capital
(2) Capital structure
(3) Investment equation
(4) Capital asset pricing model test
16
Effects of Errors-in-Variables
E  Ri   R f  i  E  R m   R f 
R  R   
i
f
0
  1i  ei
17
Different Estimation Methods When Variables
are Subject to Error
(1)
(2)
(3)
(4)
(5)
(6)
Classical Method
Grouping Method
Instrumental Variable Method
Mathematical Programming Method
Maxima Likelihood Method
LISREL and MIMIC Methods
18
Classical Method
  12
ˆ
plim    2
 U   12
(5)
 12
plimˆ    2
EX 
 U   12
2
2
2
2
2
2
2
2 2
2 2










((




)








2 )
VW V
VW UV
U V
VW
U 2
V 1
1
plim ˆ    VW 2
2
(U2V2  VW
)  U2 22  V212  12 22
(12)
2
WV 12  WV V2  WV UV   ((U2V2  UV
)  U2 22  V2 12   12 22 )
plim ˆ   
2
(U2V2  UV
)  U2 22  V212  12 22
(13)
19
Grouping Method
• Wald’s (1940) grouping method (2 groups) in deal with errors-in-variable
problem
- using groups instead of individual securities can minimize measurement error.
• CAPM test: (k-groups)
Black et al. (1972), Blume and Friend (1973), Fame and MacBath (1973),
Lizenberger and Ramaswamy (1979), etc.
  ˆ
k
ˆ1,t 
p 1
 ˆt
p ,t

n
i 1
pn
k

ˆ p ,t 
j 1 ( p 1)
n
k
p ,t
ˆ p ,t  ˆt

 Rt 
, where
2
pn
k

ˆ j ,t
n
k
 R
, R ip ,t
j 1 ( p 1)
n
k
n
R p ,t
n
k
, ˆt 
 ˆ j ,t
j 1
n
n
, and Rt 
R
j 1
j ,t
n
20
Grouping Method - continued
• Advantages
-
is intuitive and easy to implement with real data.
is convenient to incorporate other estimation methods or examine model
misspecification (multi-factor models).
• Limitations:
-
-
-
shrinks number or observations and the range of beta risk in the secondpass => the variance of the estimator becomes larger and reduce statistic
power.
The formation of portfolios for the second-pass estimation might cause a
loss of valuable information about cross-sectional behavior among
individual securities, since the cross-sectional variations would be
smoothed out.
may get different results by using different portfolio grouping methods.
(e.g., Ahn et al., 2009)
21
Instrumental Variable Method
Durbin (1953) proposes an instrumental variable method to deal with
the errors-in-variables problem in a regression model.
ˆ0,t 
ˆ
 ˆ   Zβ
 1,t 
 
1
ZR i , where
1 1 1
Z  
1 2 3
and Ri   RiN ,t  R f ,t
If
1 1 1
Z  
 1 1 1
1 1
1 1
1
 1
, βi  
N 
 i1,t
RiN ,t  R f ,t
1
1
i 2,t
i 3,t
RiN ,t  R f ,t
1 
,
iN ,t 
RiN ,t  R f ,t 
, then instrumental variable method will
reduce to Wald’s 2-group method.
 Grouping method is a special case of instrumental method.
 Instrumental variable method is more generalized.
22
Mathematical Programming Method
Min S  Min i

Yˆi  Yi

2
23
Mathematical Programming Method- continued
• Deming (1943), York (1966) and Clutton-Brock (1967)

Min S  Min i w  X i 

Uˆ i  X i

2

 w Yi  Vˆi  Yi

2
(53)
Vˆi    Uˆ i ,
 i  1,
, n
24
Mathematical Programming Method- continued



where Vˆi    Uˆ i ,
 i  1,
Min S   i w  X i 
Uˆ i  X i
2

 w Yi  Vˆi  Yi
, n

2
We can obtain a “least-square cubic”

ki2 xi2
ki2 xi yi
ki2 yi2 


2
2
 i
 2  i
   i ki xi   i
   i ki xi yi  0
w Xi 
w Xi 
w Xi  



3
where ki 
w  X i  w Yi 
 w Yi   w  X i 
2
(66)
.
25
Mathematical Programming Method- continued

ki2 xi2
ki2 xi yi
ki2 yi2 


2
2
 i
 2  i
   i ki xi   i
   i ki xi yi  0
w Xi 
w Xi 
w Xi  



3
where ki 
w  X i  w Yi 
 2 w Yi   w  X i 
(66)
.
• If no error in X i ; Yi subject to errors=> w  X i   
w Y   X  X Y  Y 

=> weighted regression of Y on X.

 w Y   X  X 
i
i
i
i
2
i
i
i
• If no error in Yi ; X i subject to errors=> w Yi   

 i w  X i  Yi  Y 
2
 i w  X i   X i  X Yi  Y 
=> weighted regression of X on Y.
26
Maxima likelihood Method
• Kim (1995, 1997, 2010)
The second-pass regression and the measurement error can be jointly presented
as
 εt   R t   0t   1t βt   2t Vt 1 
ηt  
  
 ξ t 1  
where
 
Ω
 


βˆ t 1  βt
N  O, Ω 
(87)
 

 
ξ t1 is a linear function of past idiosyncratic error terms ε s prior to the crosssectional regression at time  s  t  1 .
Additional information
it 1 

where ais  his Rms  Rm
 
t 1
s t T
t 1
a
s t T

his Rms  Rm
his  1 Var  is  ; Rm   s t T his Rms
t 1
(90)
is is


2
t 1
s t T
his
27
Maxima likelihood Method - continued
Conditional on the market return, the ratio of the idiosyncratic error variance
matrix to the measurement error variance matrix is  1  diag 1t , ,  Nt  ,
and  it 
2
t 1
 R
ms
s t T
 Rm
 Var   Var  
it
(91)
is
The closed form solution
 

M   M 2  4 t m 2 ˆ 1  ˆ RV ˆ ˆV ˆ Rˆ
R

ˆ
 1t 
2mRˆ 1  ˆ RV ˆ ˆV ˆ Rˆ
 

ˆ2t  mRV  ˆ1t mˆV



2 1/2


mVV
(94)
ˆ0t  Rt  ˆ1t ˆt 1  ˆ2tVt 1

2
where M  mRR 1  ˆ RV
   t mˆ ˆ 1  ˆ 2ˆV

N
N
mxy  1 N  x  1x  ˆ 1  y  1 y   1 N   i 1  j 1 wij  xi  x  yi  y 
x   i 1  j 1 wij xi
N
ˆ  mxy
2
xy
 
N
m
xx
myy 
1/2
N
N
i 1
j 1
wij ; wij is the (i, j)-th element of ˆ 1
 
N
N
i 1
j 1
wij
28
Structural Model
•
•
Jöreskog and Goldberger (1975) develop a structure equation model with multiple
indicators and multiple causes of a single latent variable, MIMIC mode, and obtain
maximum likelihood estimates of parameters.
Variables in a rectangular box denote observable variables, while variables in an
oval box are latent constructs. In this diagram, observable variables X1, X2, and X3
are causes of the latent variable η, while Y1, Y2, and Y3 are indicators of η. In
studies on determinants of capital structure, X’s are determinants of capital
structure (η), which are then measured by Y’s.
29
Structural Model- continued
• A structural equation model is composed of two sub-models-structural sub-model and measurement sub-model. The structural
model can be defined as
 =  X + ,
(93)
Y = y   ,
(94)
where Y is a vector of indicators of the latent variable , and X is a
vector of causes of .
• The latent variable  is linearly determined by a set of observable
exogenous causes, X = (x1, x2, …, xq)’, and a disturbance . The
latent variable , in turn, linearly determines a set of observable
endogenous indicators, Y = (y1, y2, …, yp)’ and a corresponding set
of disturbance,  = (1, 2, …, p)’.
30
Applications of Errors-in-Variables Models in
Finance Research
(1) Cost of Capital
(2) Capital Asset Pricing Model
(3) Capital Structure
(4) Investment Equation
31
32
ˆ0
33
34
35
Cost of Capital
The true relation between value and anticipated earnings, when replaced
by the observable estimates, implies a simultaneous system of
relationships:
X i  X i*  vi
Vi *   X i*    j Z ij  ui
j
X    j Z ij  wi
*
i
j
where
Vi * 
Vi   c Di
;
Ai
X (1   c )
Ai
ui and wi are
X i* 
= (the true anticipated earnings);
regression residuals;
vi = Measurement errors associated with current earnings;
Xi = Observable estimate of earnings derived from the accounting
statements;
Zij = Other relevant variables determining earnings.
36
Capital Asset Pricing Model (CAPM)
R t   0,t   1,t βt  εt
Ri ,t  i ,t  ˆi ,t Rm,t  i ,t
Rt   0,t   1,t ˆt 1   t
 1,t
ˆ
37
Capital Asset Pricing Model (CAPM) - continued
Why beta fails?
Model misspecification
Fama & French (1992), Carhart (1996), Chordia & Shivakumar (2006) suggest
new risk factors can explain cross-sectional average returns. (size, B/M, price
momentum factor, and earnings momentum factor.)
Errors-in-variables problem
Roll (1969 and 1977), Lee (1984)
The errors-in-variables problem underestimates the market beta which is suffered
measurement error and overestimates other risk factors with no measurement
error.
Correction:
Lee (1973), Gibbons (1985), Shanken (1992), Kim (1995, 1997, 2011), etc.
38
Study
Testing Period
Method
Results
Black et al. (1972)
1931-1965
Grouping (10 groups)
- Reject both the CAPM and the zero-beta CAPM.
Blume and Friend (1973)
1955-1968
Grouping (12 groups)
- Linear model is better than quadratic model in explaining expected return.
- Reject both the CAPM and the zero-beta CAPM.
Fama and MaBeth (1973)
1955-1968
Grouping (20 groups),
period by period
Lee (1977)
1967-1972
Wald’s Grouping /
Instrumental Variable
Litzenberger and
Ramaswamy (1979)
1936-1977
MLE, OLS, GLS
(individual stock)
Cheng and Grauer (1980)
1935-1977
Gibbons (1982)
1926-1975
MacKinlay and Richardson
(1991)
Shanken (1992)
1926-1988
Grouping (20groups),
Price-level testing
(Invariance Law)
One-step GuassNorman Procedure (40
groups)
GMM
- Find a linear relationship between the expected return and beta risk, beta is the only
risk measure in explaining expected return, and risk premium is greater than zero.
- CAMP and efficient capital market hold.
- Adjust for measurement error of market return (first-step).
- Estimated risk premium is larger than realized risk premium.
- Reject CAPM.
- Before-tax expected rates of return are linearly related to systematic risk and
dividend yield.
- MLE can obtain consistent estimators without losing efficiency.
- CAPM is rejected because of nonzero .
- Neither framework of Invariance Law or security market line can accommodate the
possibility that the CAPM may hold for each
ˆ0period.
- Reject CAPM.
- Guass-Norman procedure can increase the precision of estimated risk premium.
- Reject CAPM.
Fama and French (1992)
1963-1990
1935-1968
- Conclusions of mean-variance efficiency vary by settings.
MLE (individual stock) - To deal with small-sample bias in the second-step cross-sectional regression
estimates due to measurement error in the betas.
- The adjustment doesn’t have much effect on Fama and MacBeth’s (1973)
conclusion.
- Support CAPM.
2-way grouping
- The market capitalization and the book-to-market ratio can replace beta altogether.
(10x10)
- Reject CAPM.
Jagannathan and Wang(1993) 1962-1990
Multifactor Asset
Pricing Model
Kim (1995, 2010)
1936-1991
MLE (individual stock
– 20x20 groups)
Kim (1997)
1963-1993
Multifactor, MLE
- Including human capital and business cycle can increase explanatory power of
expected return.
- Support CAPM
- MLE method can effectively adjust the errors-in-variables bias and CAPM holds.
- Support CAPM.
- Linear relationship between beta and expected return.
- Book-to-market ratio has significant explanatory power for expected return,
39but
size has not.
Capital Structure
• Titman and Wessel (1998) use LISREL method to
investigate determinates of capital structure.
• Chang et al. (2009) apply a MIMIC model with refined
indicators to reexamine Titman and Wessel’s (1998) work
on determinants of capital structure. Under a
simultaneous cause-effect frame work, 7 determinants of
capital structure have significant effects on capital
structure decision.
• Yang et al. (2009) apply a LISREL model to find
determinants of capital structure and stock return, and
estimate the impact of unobservable attributes on capital
structure decision and stock returns.
• Lee and Tai (2014) find that SEM with CFA approach
outperform MIMIC model and 2SLS method in terms of
the joint determinants of capita l structure and stock
return.
40
Investment Equation
• Modern q theory developed by Lucas and Prescott (1971) and
Mussa (1977)
- marginal q should summarize the effects of all factors relevant
to the investment decision.
- Empirical work in testing association between the investment
decision and cash flow is inconsistent to the q theory (e.g.
Fazzari et al., 1988).
I it K it  i   qit*   CFit K it  uit
where Iit represents the investments of firm i at time t, K it is
capital stock of firm i at time t, q is the marginal , CF is cash
flow of firm i at time t, i is the firm-specific effect, and uit is
the innovation term.
*
it
it
41
Investment Equation - continued
• Most empirical studies therefore use Tobin’s q as a proxy for
marginal q to test the q theory of investment.
- Erickson and Whited (2000) use generalized method of
moments (GMM) and show that cash flow does not affect
firms’ financial decision, even for financially constrained firms,
and the q theory is held if measurement error is taken into
account.
- Almeida et al. (2010) conclude that estimators from GMM are
unstable across different specifications and not economically
meaningful, while estimators from a simple instrumental
method are robust and conform to q theory.
42
Conclusion
• We show how EIV problems affect estimators in the regression model. - --In a multivariate regression, we show that the EIV leads an underestimation
of the independent variable with measurement error and an overestimation
of the independent variable without measurement error.
• We provide six alternative estimation methods dealing with EIV problem.
- Classical method, grouping method, instrumental variable method,
mathematical programming method, maxima likelihood method, and
LISREL method are discussed in detailed.
• We investigate how EIV problem can affect empirical results in issues of
cost of capital, asset pricing models, capital structure, and investment
decision and how alternative EIV methods have been used to correct
estimation bias in those issues.
• We suggest future studies should pay more efforts on dealing with EIV and
obtain robust empirical results from EIV models.
43
Appendix A. The Impact of
measurement errors on R-square
estimates.
• Hence, the estimate R-square measured with errors
can be defined as
𝑘
𝑘
𝛿𝑖2 𝑔𝑖
𝑅′2 = 𝑅2 𝑔𝑦
𝑖=1
𝛿𝑖2 = 𝑅2 𝑔𝑦 𝑔𝑤 ,
𝑖=1
• Where 𝑔𝑤 is a weighted mean of the coefficients of
reliability of the 𝑥𝑖 . In our case, we have only one
independent variable, therefore 𝑔𝑤 = 𝑔1 .
• 𝑅 2 represents multiple coefficient estimation without
measurement errors and R′2 represents multiple
coefficient with errors. In our case, 𝑅𝑝𝑡 can be
measured with errors if the mutual fund’s returns are 44
Appendix A1. The Impact of
measurement errors on R-square
estimates.
• From our empirical work, we find 17 out of 67 ethical
mutual funds with significant 𝛾 estimates and 20 out of
67 traditional mutual funds with significant 𝛾 estimates
(see Table C1). This implied 𝑅𝑝𝑡 has measurement
errors. Investigating investment function, Peters and
Taylor (2014) found that measurement errors of
dependent variable can substantially affect the Rsquare estimates.
• Bramante, Petrella and Zappa (2013) use a delay
information model to show that R-square is a direct
measure of market efficiency. Their model is a special
case of our equation (C1). If R-square is a direct
measure of price efficiency, therefore it is questionable
45
that R-square can also be used to measure the
Table A1. Alpha, Gamma, and R-Square estimates for both
ethical mutual funds and traditional mutual funds for lag
dependent model. (*significant at 0.05)
Ethical Funds
ADJEX
AHRAX
ARGFX
CAAAX
CAACX
CAAPX
CALCX
CCACX
CCAFX
CCLAX
CCVAX
CEGIX
CEYIX
CIEYX
CISIX
CMAAX
CMACX
CMICX
CMIFX
CSCCX
CSECX
CSIEX
CSVIX
CSXAX
CSXCX
CVALX
DIEQX
DSEFX
DSEPX
DSFRX
GCEQX
MGNDX
MMDEX
MMSCX
MMSIX
MVIAX
MVIIX
MYPVX
NBSLX
NBSRX
NBSTX
NRAAX
NRACX
Gamma
-0.04045
0.04825*
-0.05376
0.02246
0.000949
-0.05369
0.46893*
-0.00616
-0.00644
0.46683*
-0.03682
-0.00845
0.03255
0.00463
0.00606
0.16125*
0.16198*
0.03956*
0.03969*
-0.03527
0.03311
0.03269
-0.0343
0.00665
0.00778
0.02754*
0.01495
0.01455
0.01082
0.01518
0.03227*
0.04265*
0.04163*
0.01963
0.01934
0.00802
0.00528
0.02277*
0.04346*
0.04938*
0.04974*
0.07163
0.07033
Alpha
0.00373
-0.00171
0.00858*
-0.00218*
-0.0024
0.00661*
-0.003
0.00119
0.00189
-0.0025
0.000809
-0.00085
-1.2E-05
0.00068
-6.2E-05
-0.00348*
-0.00401*
-0.00182*
-0.00111
0.000401
-0.00108
-0.00046
0.00186
-0.0005
-0.00132
-0.00085
4.22E-05
-0.00033
0.000107
-3.6E-05
-0.00137
2.28E-05
0.000388
0.00275
0.00317
-0.00145
-0.00137
-0.00086
0.000355
0.000168
3.59E-05
-0.00011
-0.00071
R-Square
0.9844
0.9951
0.9687
0.9983
0.9957
0.983
0.9846
0.9865
0.9865
0.9846
0.9857
0.9873
0.9955
0.936
0.9968
0.9944
0.9944
0.9977
0.9977
0.9862
0.9955
0.9955
0.9863
0.9968
0.9968
0.9981
0.9971
0.9971
0.9971
0.9971
0.9968
0.9928
0.9927
0.973
0.9729
0.9938
0.9932
0.9979
0.9809
0.9949
0.9949
0.9277
0.9282
Traditional
Funds
ABBIX
ACIIX
ADJPX
AGWYX
AVGIX
BIBDX
CLGYX
CLVLX
CNVBX
DSCVX
DXDDX
EMG
EVX
FCLTX
FGADX
FKASX
FMCAX
FMDBX
FMPTX
FSPCX
FXZ
GEPSX
HAABX
HFMRX
HTCSX
IDROX
IOEIX
IYEAX
JORRX
LCEVX
LPCAX
LPEIX
LTEIX
LTWKX
MMUGX
MTHIX
MTHRX
NECCX
NMGAX
NMGCX
NYVBX
OGNAX
OGNIX
Gamma
-0.0133
0.18061*
0.02531
-0.08555*
0.00662
0.07702
-0.05003
0.00295
-0.034
-0.08724*
-0.05179
-0.02211
-0.03958
-0.08703*
-0.07197
-0.0533
0.00819
-0.01653
-0.02044
-0.06454
-0.07721
-0.00709
-0.02216*
0.01637
0.04887
-0.02654
0.06494*
0.00122
-0.01972
0.06288*
0.68856*
0.1234*
0.07617*
-0.04462*
0.07436
0.1459*
0.14662*
-0.01029
-0.04462
-0.04158
0.02308
0.65515*
0.65226*
Alpha
-0.00315*
-0.00305
-0.00199
-0.00214
-0.00053
-0.00264
0.000572
-0.00284*
-0.00465
0.00994*
-0.00865
0.00494*
-0.0014
0.00683*
-0.00663
0.00479
0.00228
0.00586
0.00317
0.00117
0.00776
0.000945
-0.00152
-0.00046
-0.00184
0.00352
-0.00189
-0.00149
0.01025
-0.00095
-0.00409
0.00296
-0.00374*
-0.00279*
-0.00203
-0.0042*
-0.00456*
0.00103
0.00279
0.00211
-0.00172
-0.00427
-0.00424
R-Square
0.9979
0.9886
0.9605
0.9576
0.9724
0.932
0.9388
0.9987
0.9807
0.9685
0.904
0.9904
0.967
0.9854
0.7306
0.9788
0.9843
0.9918
0.9876
0.9787
0.9367
0.9941
0.9983
0.9394
0.99
0.927
0.9933
0.9245
0.9686
0.9931
0.9442
0.8949
0.996
0.9932
0.9801
0.9378
0.9374
0.9968
0.8781
0.8795
0.9967
0.9725
0.9723
46
Table A1. (Continued) Alpha, Gamma, and R-Square estimates
for both ethical mutual funds and traditional mutual funds for
lag dependent model. (*significant at 0.05)
NRARX
PARMX
PARSX
0.0707
0.03392
-0.05937
-0.00029
0.00191
0.00496
0.9278
0.9922
0.9725
OIBHX
OISGX
PIXDX
0.04352*
-0.03248
-0.02573
0.9924
0.9866
0.99
0.02667*
-0.00057
0.09422
0.0562
-0.01962
-0.0005
0.00244
0.00785*
0.00538*
-0.0009
0.00387*
0.000674
2.93E-05
0.00144
0.000328
PARWX
PRBLX
-0.0072 0.00446*
0.08088* -0.00021
0.9892
0.9933
PLVBX
PLVCX
0.01135
-0.0181
PWGIX
PXGRX
PXSCX
PXSIX
PXSRX
-0.01208
-0.0127
0.03963
0.04038
0.03938
0.9906
0.9905
0.9094
0.9101
0.9094
PPXJX
RDLFX
REDAX
RMOCX
RSGEX
PXWEX
PXWGX
-0.00631
-0.01685
0.9952
0.9909
PXWIX
SRIAX
SRICX
-0.01312
0.02077
0.02038
0.000711
0.00031
0.00388
0.0041
0.00368
0.00409*
0.00142
0.00394*
0.00213
0.00151
RYIYX
RYMZX
0.77294*
0.68637*
-0.00764
-0.00429
0.8055
0.8962
0.9959
0.9518
0.9516
RYSJX
SEA
SECGX
0.59974*
0.11565
-0.00939
0.824
0.7538
0.9939
0.9519
0.9516
0.9989
0.9989
0.9855
0.9989
0.9875
0.8666
0.9957
SEIAX
SFISX
SLEAX
SSCPX
STDIX
TCGCX
TWHIX
VBCVX
VSOIX
0.02623
-0.047
0.0319
-0.00333
-0.01244
0.01463
-0.0251
0.01928
-0.05054
-0.01163
0.00267
-0.00247
0.00533*
0.000529
-0.00254
0.000842
0.0046
0.00241
0.00124
0.000199
0.00339
SRIDX
SRIGX
TICRX
TISCX
TRPSX
TRSCX
WAEGX
WASOX
WSEFX
0.01938 0.00232
0.01938 0.00211
0.01467 0.000276
0.01522 0.000325
0.01646 -2.5E-05
0.01349 9.24E-05
-0.00918 -0.00066
-0.04411 0.00109
0.03899* -0.00149
0.9946
0.9971
0.9982
0.9911
0.9665
0.9751
0.9947
0.996
0.9401
0.9934
0.9881
0.9789
0.9859
0.9798
0.9899
0.9671
47
Application of Simultaneous Equation in
Finance Research: Methods and Empirical
Results
Cheng-Few Lee
Rutgers University, USA
Woan-lih Liang
National Chiao Tung University, Taiwan
Fu-Lai Lin
Da-Yeh University, Taiwan
Yating Yang
National Chiao Tung University, Taiwan
Abstract
The main purposes of this paper are: i) to review finance literature used in
simultaneous equations method, ii) to show that both two-stage least squares (2SLS)
and three-stage least squares (3SLS) are special cases of generalized method of
moments (GMM) estimator in estimating simultaneous equations and iii) to investigate
the interrelationship among investment, financing, and dividend decisions. We review
studies that apply the simultaneous equation estimation on capital structure, corporate
investment, payout decisions, ownership structure, corporate governance, stock return,
firm performance and/or other corporate issues. Detailed descriptions about the concept
of 2SLS, 3SLS, and GMM estimation are introduced. We also investigate the
interrelationship among investment, financing and dividend decisions using 2SLS,
3SLS, and GMM methods based on the U.S. listed firm annual data between 1965 and
2012. Our results are consistent with Lambrecht and Myers’s (2012) theory that
dividend and investment decisions are jointly determined. In addition, these three
corporate decisions are co-determined and the interaction among them should be taken
into account in a simultaneous equation framework.
• Introduction
• Literature review
• GMM Methodology
• Application in investment, financing and dividend
policy
The investment, dividend, and debt financing are major decisions of a firm. Past studies
argue some relations among investment, dividend and debt financing. To control for the
possible endogenous problems among these three decisions, we apply 2SLS, 3SLS, and
GMM methods to estimate the simultaneous-equations model that consider the interaction of
the three policies. Higgins (1972), Fama (1974), Morgan and Saint-Pierre (1978), Smirlock
and Marshall (1983), Lee et al. (2011), and Chen et al. (2013) investigate the relationship
between investment decision and dividend decision. Fama and French (2002) and Aivazian
et al. (2006) consider the interaction between dividend and financing decisions. Dhrymes
and Kurz (1967), McDonald et al. (1975), McCabe (1979), Peterson and Benesh (1983),
Switzer (1984), and Pruitt and Gitman (1991) argue that the investment decision is related to
financing decision and dividend decision. Chava and Roberts (2008) show how financing
impacts corporate investment via debt covenants. Lambrecht and Myers (2012) develop a
combined theory of payout, debt, and investment.
There are three equations in our simultaneous-equations system; each equation contains the
remaining two endogenous variables as explanatory variables along with other exogenous
variables. The three endogenous variables are investment (Invit), dividend (Divit), and book
leverage (Leverageit of firm i in year t. Inv denotes net property, plant, and equipment. Div
denotes dividends. Following Fama (1974), both Inv and Div are measured on a per share
basis. We follow Fama and French (2002) to use book leverage, Leverage as the proxy for
leverage. Leverage is defined as the ratio of total liabilities to total assets.
We also use the following exogenous variables in the model. In addition to lag-terms of the
tree policies, we follow Fama (1974) to respectively incorporate sales plus change in
inventories (Qit), and net income minus preferred dividends (Pit) into investment and dividend
decisions. Moreover, we follow Fama and French (2002) to add natural logarithm of lagged
total assets (In Ai, t-1) and the lag of earnings before interest and taxes divided by total assets
(Ei, t-1 /Ai, t-1) as the determinants of leverage. Finally, Leary and Roberts (2014) argue that the
characteristic of peer firms is important to influence firms’ capital structure and thus we also
follow them to consider lagged industry averages book leverage (Industryi, t-1) into our
leverage decision. The structural equations are estimated as follows:
Conclusion
In this paper, we investigate the endogeneity problems related to simultaneous equations
system, and introduce how 2SLS, 3SLS, and GMM estimation methods deal with endogeneity.
We discuss these three methods and present Pagan and Hall's (1983) test of heteroskedasticity
and weak instruments test for selecting the applicable method and testing the validity of
instruments. In addition to reviewing applications of simultaneous equations on many finance
issues, we also use U.S. listed firms from 1965 to 2012 to examine the interrelationship among
corporate investment, leverage, and dividend payout policies in a simultaneous-equation
system by employing 2SLS, 3SLS, and GMM.
Our results from 2SLS, 3SLS, and GMM are similar. First, we show that dividend outlays
influence investment decisions and vice versa. The fact that dividend payout does not cut back
to finance capital investment confirms the model prediction of Lambrecht and Myers (2012).
Moreover, the investment has a positive impact on debt financing and vice versa. An increase
in debt financing enhances the funds available to outlays for investment, and the increase in
investment raises willingness of fund supply by the increase in mortgage of capital investment
or investment’s future profitability, and thus further improves firm’s debt capacity. The impact
of debt financing on dividend is significantly negative, showing that the firms may have
greater capability to pay dividend when they have lower leverage level. Accordingly, our
findings suggest that these three corporate decisions are jointly determined and the interaction
among them should be taken into account in a simultaneous equations framework.
Reference
1.
2.
3.
4.
5.
Statistics for Business and Financial Economics 3rd edition, (with John C. Lee
and Alice C. Lee), Springer Academic Publishers, 2013. (ISBN: 978-1-46145896-8)
Handbook of Financial Econometrics and Statistics (with John C. Lee), Springer
Academic Publishers, 2014.
Textbook of Financial Econometrics and Statistics (with Hong-Yi Chen, Alice C.
Lee and John Lee), Springer Academic Publishers, forthcoming.
“Alternative Errors-in-Variable Models and Their Applications in Finance
Research,” (with Alice C. Lee and Hong-Yi Chen), The Quarterly Review of
Economics and Finance, forthcoming, 2015.
“Application of Simultaneous Equation in Finance Research: Methods and
Empirical Results,” (with Woan-lih Liang, Fu-Lai Lin, and Yating Yang),
Review of Quantitative Finance and Accounting, forthcoming.