Financial Econometrics and Statistics Handbook: Applications and Research Insights

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 Simulation as a Research Tool for Market Architects 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 4. 5. 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 Applications 5

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 9

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 10

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 R ( ) = R E R R i f i m f ( ) = + + R R e 0 1 i f i i 17

Different Estimation Methods When Variables are Subject to Error (1) Classical Method (2) Grouping Method (3) Instrumental Variable Method (4) Mathematical Programming Method (5) Maxima Likelihood Method (6) LISREL and MIMIC Methods 18

Classical Method + 2 1 = plim (5) 2 U 2 1 2 1 ( ) E X = plim + 2 U 2 1 + + + + + + (( + ) ) 2 2 2 V 2 U 2 V 2 VW 2 U 2 2 2 V 2 2 2 2 = plim (12) 1 1 VW VW VW UV ( ) 2 U 2 V 2 VW 2 U 2 2 2 V 2 2 2 2 1 1 + + + + + + (( + ) ) 2 2 V 2 U 2 V 2 UV 2 U 2 2 2 V 2 2 2 2 = plim (13) 1 1 1 WV WV WV UV ( ) 2 U 2 V 2 UV 2 U 2 2 2 V 2 2 2 2 1 1 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. ( )( k ) R R , , p t t p t t = 1 = p , where ( ) 1, t n 2 , p t t = 1 i pn k pn k n n R R , , j t p t , , j t j t n k n k 1 ( = + 1 ( = + 1) n k 1) n k j p j p = = 1 1 = = = = j j , , , and R R , , p t i p t t t n 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 second- pass => 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. ( 1, t ) 1 0, t = Z ZR , where i 1 1 1 1 1 1 1 2 = i R 1 3 1 N i = = Z , , 1, i t 2, 3, i t , i t iN t and R R R R R R R R , , , , , , , , iN t f t iN t f t iN t f t iN t f t 1 1 1 1 1 = If , then instrumental variable method will 1 1 1 1 1 Z 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 ( ) 2 = Min S Min Y Y i i i 23

Mathematical Programming Method- continued Deming (1943), York (1966) and Clutton-Brock (1967) )( Min S Min w X U X ) ( )( w Y ) 2 2 ( = + (53) V Y i i i i i i i ( ) , i U = + = 1, , V i n i 24

Mathematical Programming Method- continued )( i U ) ( )( ) ) 2 2 ( = + Min S w X U X w Y V Y i i i i i i i ( = + = , 1, , where V i n i We can obtain a least-square cubic 2 i 2 i 2 i 2 i 2 i k x w X k x y w X k y w X + = 2 0 (66) 3 2 2 i k x k x y i i ( ) ( ) ( ) i i i i i i i i i i i i ( ( ) w Y ) ( ) w X + w X w Y = i i where . k ( ) i 2 i i 25

Mathematical Programming Method- continued 2 i 2 i 2 i 2 i 2 i k x w X k x y w X k y w X + = 2 0 (66) 3 2 2 i k x k x y i i ( ) ( ) ( ) i i i i i i i i i i i i ( ( ) w Y ) ( ) w X + w X w Y = i i where . k ( ) i 2 i i ( ) If no error in ; subject to errors=> ( )( ( )( i i i w Y X = w X i X iY i )( ) w Y X X Y Y => weighted regression of Y on X. ) X i i i = i 2 ( ) w Y = If no error in ; subject to errors=> )( ( )( i i i w X X X iY i X i ) ( 2 w X Y Y => weighted regression of X on Y. )( i Y Y i i = i ) 26

Maxima likelihood Method Kim (1995, 1997, 2010) The second-pass regression and the measurement error can be jointly presented as = = R V ( ) 0 1 2 1 t t t t t t t O , (87) N t 1 t 1 t t where = s is a linear function of past idiosyncratic error terms prior to the cross- sectional regression at time . ( ) 1 s t 1 t a = t 1 Additional information = (90) 1 it is is s t T ( ) ( ) 2 1 t = where a h R R h R R is is ms m is ms m s t T = ( ) 1 1 t t = = 1 ; h Var R h R h 27 is is m is ms is s t T = s t T =

Maxima likelihood Method - continued Conditional on the market return, the ratio of the idiosyncratic error variance matrix to the measurement error variance matrix is , ( it ms m it s t T = ( ) = 1 1, t , diag Nt 2 1 t ) ( ) ( ) ( ) = and (91) R R Var Var is The closed form solution ( ) 1/2 ( ) 2 + + 2 2 4 1 M M m t RV V R R = ( ) ( ) 1 t 2 1 m RV R V R ( ) = (94) m m m 2 1 t RV t VV V = R V 0 1 1 2 1 t t t t t t ( ) ( ) = 2 RV 2 1 1 where M m m RR t V ( )( ) ( ) ( = ) ( )( ) N N N N = 1 x 1 y 1 1 1 m N x y N w x x y y w xy ij i i ij = = = = 1 1 1 1 i j i j N N N N = 1 ; is the (i, j)-th element of x w x w w ij i ij ij = = = = 1 1 1 1 i j i j 28 ( ) 1/2 2 = m m m xy xy xx yy

Structural Model J reskog 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 , while Y1, Y2, and Y3are indicators of . In studies on determinants of capital structure, X s are determinants of capital structure ( ), 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

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0 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: = + * i X X v i i = + + * * i V X Z u i j ij i j = + * i X Z w j ij i j where V D = * ; i c i V i A i (1 ) X = (the true anticipated earnings); ui and wi are 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. = * i c X A i 36

Capital Asset Pricing Model (CAPM) = + + R 0, 1, t t t t t = + + R R , , , , , i t i t i t m t i t = + + R 0, 1, 1 t t t t t 1,t 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) Blume and Friend (1973) 1931-1965 1955-1968 Grouping (10 groups) Grouping (12 groups) - Reject both the CAPM and the zero-beta CAPM. - Linear model is better than quadratic model in explaining expected return. - Reject both the CAPM and the zero-beta CAPM. - 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 period. - Reject CAPM. - Guass-Norman procedure can increase the precision of estimated risk premium. - Reject 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 Grouping (20groups), Price-level testing (Invariance Law) One-step Guass- Norman Procedure (40 groups) GMM 0 Gibbons (1982) 1926-1975 MacKinlay and Richardson (1991) Shanken (1992) 1926-1988 - Conclusions of mean-variance efficiency vary by settings. 1935-1968 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. - The market capitalization and the book-to-market ratio can replace beta altogether. - Reject CAPM. Fama and French (1992) 1963-1990 2-way grouping (10x10) Jagannathan and Wang(1993) 1962-1990 Multifactor Asset Pricing Model - 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. Kim (1995, 2010) 1936-1991 MLE (individual stock 20x20 groups) Kim (1997) 1963-1993 Multifactor, MLE - Linear relationship between beta and expected return. - Book-to-market ratio has significant explanatory power for expected return, but size has not. 39

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). = + + CF K + * it I K q u it it i it it it where represents the investments of firm i at time t, is capital stock of firm i at time t, is the marginal , is cash flow of firm i at time t, is the firm-specific effect, and is the innovation term. K itI it * it q CF it i it u 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 ? ? 2?? 2=?2?? ??, ? 2= ?2?? ?? ?? ?=1 ?=1 Where ?? is a weighted mean of the coefficients of reliability of the ??. In our case, we have only one independent variable, therefore ?? = ?1. ?2represents multiple coefficient estimation without measurement errors and R 2 represents multiple coefficient with errors. In our case, ???can be measured with errors if the mutual fund s returns are infrequently traded. Following Cartwright and Lee 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 ? estimates and 20 out of 67 traditional mutual funds with significant ? estimates (see Table C1). This implied ??? has measurement errors. Investigating investment function, Peters and Taylor (2014) found that measurement errors of dependent variable can substantially affect the R- square 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 that R-square can also be used to measure the performance of mutual funds. 45

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) 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 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 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 -0.0005 0.00244 0.00785* - 0.00538* -0.0009 - 0.00387* 0.000674 2.93E-05 0.00144 0.000328 0.9924 0.9866 0.99 PARWX PRBLX -0.0072 0.08088* 0.00446* -0.00021 0.9892 0.9933 PLVBX PLVCX 0.01135 -0.0181 0.9946 0.9971 PWGIX PXGRX PXSCX PXSIX PXSRX -0.01208 -0.0127 0.03963 0.04038 0.03938 0.000711 0.00031 0.00388 0.0041 0.00368 - 0.00409* 0.00142 - 0.00394* 0.00213 0.00151 0.9906 0.9905 0.9094 0.9101 0.9094 PPXJX RDLFX REDAX RMOCX RSGEX 0.02667* -0.00057 0.09422 0.0562 -0.01962 0.9982 0.9911 0.9665 0.9751 0.9947 PXWEX PXWGX -0.00631 -0.01685 0.9952 0.9909 RYIYX RYMZX 0.77294* 0.68637* -0.00764 -0.00429 0.8055 0.8962 PXWIX SRIAX SRICX -0.01312 0.02077 0.02038 0.9959 0.9518 0.9516 RYSJX SEA SECGX 0.59974* 0.11565 -0.00939 -0.01163 0.00267 -0.00247 - 0.00533* 0.000529 -0.00254 0.000842 0.0046 0.00241 0.00124 0.000199 0.00339 0.824 0.7538 0.9939 SRIDX SRIGX TICRX TISCX TRPSX TRSCX WAEGX WASOX WSEFX 0.01938 0.01938 0.01467 0.01522 0.01646 0.01349 -0.00918 -0.04411 0.03899* 0.00232 0.00211 0.000276 0.000325 -2.5E-05 9.24E-05 -0.00066 0.00109 -0.00149 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 0.996 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.