Financial Analysis, Planning and Forecasting Theory and ...

Financial Analysis, Planning and Forecasting

Theory and Application

ByAlice C. Lee

San Francisco State UniversityJohn C. Lee

J.P. Morgan ChaseCheng F. Lee

Rutgers University

Chapter 2 Accounting Information, Regression Analysis,

and Financial Management

Outline 2.1 Introduction 2.2 Financial statement: A brief review 2.3 Critique of accounting information 2.4 Static ratio analysis and its extension 2.5 Cost-volume-profit analysis and its

applications 2.6 Accounting income vs. economic income 2.7 Summary Appendix 2A. Simple regression and multiple

regression Appendix 2B. Instrumental variables and two-stage

least squares

2.1Introduction

Table 2.1 Consolidated

Balance Sheets of Johnson & Johnson Corporation and Consolidated Subsidiaries (dollars in millions)

Assets 2000 2001 2002 2003 2004 2005 2006Current AssetsCash and Cash Equivalent $4,278 $3,758 $2,894 5377 $9,203 $16,055Marketable Securities 2,479 4,214 4,581 4146 3681 83Account Receivable 4,601 4,630 5,399 6574 6831 7010Inventory 2,905 2,992 3,303 3588 3744 3959Deferred Taxes on Income 1,174 1,192 1,419 1526 1737 1845Prepaid Expenses and Other Receivable 1,254 1,687 1,670 1784 2124 2442Total Current Assets 16,691 18,473 19,266 22995 27320 31394

Marketable Securities – Non0current 657 969 121 84 46 20Property, Plant and Equipment, net 7,409 7,719 8,710 9846 10436 10830Intangible Assets, net 7,535 9,077 9,246 11539 5979 6185Deferred Taxes on Income 240 288 236 692 551 385Other Assets 1,713 1,962 2,977 3107 3122 3221Total Assets $34,245 $38,488 40,556 48263 53317 58025

Liabilities and Shareholder’s EquityCurrent LiabilitiesLoans and Notes Payable $1,489 $565 $2,117 1139 280 668Account Payable 2,122 2,838 3,621 4966 5227 4315Accrued Liabilities 2,793 3,135 3,820 2639 3523 3529Accrued Salaries, Wages and Commissions 529 969 1,181 1452 1094 1166Taxes on Income 322 537 710 944 1506 940Total Current Liabilities 7,255 8,044 11,449 13448 13927 12635

Long-term Debt 3,120 2,217 2,022 2955 2565 2017Deferred Tax liability 255 493 643 780 403 211Employee Related Obligations 1,804 1,870 1,967 2262 2631 3065Other Liabilities 1,373 1,631 1,778 1949 1978 2226

Shareowners’ EquityPreferred stock-without Par Value - - - - - -Common Stock – Par Value $1.00 3,120 3,120 3,120 3120 3120 3120Net Receivable from Employee Stock Plan -35 -30 -25 -18 -11 -Accumulated Other Comprehensive Income -461 -530 -842 -590 -515 -755Retained Earnings 18,113 23,066 26,571 30503 35223 41471Less: Common Stock Held in Treasury 342 1,393 6,127 6146 6004 5965Total Shareowners’ Equity 20,395 24,233 28,824 33015 31813 37871

Total Liabilities and Shareholders’ Equity $34,245 $38,488 440,556 48263 53317 58025

2.2 Financial statement: A Brief Review

Balance Sheet Income Statement Retained Earnings Statement Statement of changes in financial

position Annual vs. Quarterly Financial Data

Income Statement

Table 2.2: Consolidated Income Statements of Johnson & Johnson Corporation and Subsidiaries (dollars in millions)

(Dollars in Millions Except Per Share Figures) (Note 1) 2000 2001 2002 2003 2004 2005 2006Sales to customers 29,846 32,317 36,298 $41,862 47,348 $50,514

Cost of products sold 8,908 9,581 10,447 12,176 13,422 13,954Gross profit 20,938 22,736 25,851 29,686 33,926 36,560Selling, marketing and administrative expenses 11,218 11,260 12,216 14,131 15,860 16,877Research expense 3,105 3,591 3,957 4,684 5,203 6,312Purchased in-process research and development (Note 17) 66 105 189 918 18 362Interest income -429 -456 -256 -177 -195 -487Interest expense, net of portion capitalized (Note 3) 204 153 160 207 187 54Other (income) expense, net -94 185 294 -385 15 -214

14,070 14,838 16,560 19,378 21,088 22,904Earnings before provision for taxes on income 6,868 7,898 9,291 10,308 12,838 13,656Provision for taxes on income (Note 8) 1,915 2,230 2,694 3,111 4,329 3,245Net earnings 4,953 5,668 6,597 $7,197 8,509 $10,411Basic net earnings per share (Notes 1 and 19) 1.65 1.87 2.2 $2.42 2.87 $3.50Diluted net earnings per share (Notes 1 and 19) 1.61 1.84 2.16 $2.40 2.84 $3.46

Statement of Equity

Table 2.3:

Consolidated Statements of

Equity of Johnson &

Johnson Corporation and

Subsidiaries (dollars in millions)

Statement of Equity (cont’d)

Table 2.3:

Consolidated Statements of

Equity of Johnson &


Subsidiaries (dollars in millions)

(Cont’d)

Statement of Cash Flows

Table 2.4:

Consolidated Statement of

Cash Flow of Johnson &


Consolidated Subsidiaries,

December 31, 2000,

December 31, 2001,

December 31, 2002,

December 31, 2003,

December 31, 2004,

December 31, 2005,

December 31, 2006.

(Dollars in Millions) (Note 1) 2000 2001 2002 2003 2004 2005 2006Cash flows from operating activitiesNet earnings 4,953 5,668 6,597 7,197 8,509 $10,411Adjustments to reconcile net earnings to cash flows: Depreciation and amortization of property and intangibles 1,592 1,605 1,662 1,869 2,124 2,093 Purchased in-process research and development 66 105 189 918 18 362 Deferred tax provision -128 -106 -74 -720 -498 -46 Accounts receivable allowances 41 99 -6 6 3 -31Changes in assets and liabilities, net of effects from acquisitions: Increase in accounts receivable -468 -258 -510 -691 -111 -568 (Increase)/decrease in inventories 128 -167 -109 39 11 -396 (Decrease)/increase in accounts payable and accrued liabilities 41 1,401 1,420 2,192 607 -911 Decrease/(increase) in other current and non-current assets 124 -270 -1,429 -746 -395 620 Increase in other current and non-current liabilities 554 787 436 531 863 343

Net cash flows from operating activities 6,903 8,864 8,176 10,595 11,131 11,877

Cash flows from investing activitiesAdditions to property, plant and equipment -1,689 -1,731 -2,099 -2,262 -2,175 -2,632Proceeds from the disposal of assets 166 163 156 335 237 154Acquisitions, net of cash acquired (Note 17) -151 -225 -478 -2,812 -580 -987Purchases of investments -5,676 -8,188 -6,923 -7,590 -11,617 -5,660Sales of investments 4,827 5,967 7,353 8,062 12,061 9,187Other (primarily intangibles) -142 -79 -206 -259 -273 -341

Net cash used by investing activities -2,665 -4,093 -2,197 -4,526 -2,347 -279

Cash flows from financing activitiesDividends to shareholders -1,724 -2,047 -2,381 -2,746 -3,251 -3,793Repurchase of common stock -973 -2,570 -6,538 -1,183 -1,384 -1,717Proceeds from short-term debt 814 338 2,359 3,062 514 1,215Retirement of short-term debt -1,485 -1,109 -560 -4,134 -1,291 -732Proceeds from long-term debt 591 14 22 1,023 17 6Retirement of long-term debt -35 -391 -245 -196 -395 -196Proceeds from the exercise of stock options 387 514 390 311 642 696

Net cash used by financing activities -2,425 -5,251 -6,953 -3,863 -5,148 -4,521

Effect of exchange rate changes on cash and cash equivalents -47 -40 110 277 190 -225

Increase in cash and cash equivalents 1,766 -520 -864 2,483 3,826 6,852Cash and cash equivalents, beginning of year (Note 1) 2,512 4,278 3,758 2,894 5,377 9,203

Cash and cash equivalents, end of year (Note 1) 4,278 3,758 2,894 5,377 9,203 $16,055

Supplemental cash flow dataCash paid during the year for: Interest 215 185 141 206 222 $151 Income taxes 1,651 2,090 2,006 3,146 3,880 3,429Supplemental schedule of noncash investing and financing activitiesTreasury stock issued for employee compensation and stock option plans, net of cash proceeds 754 971 946 905 802 $818Conversion of debt 504 815 131 2 105 369AcquisitionsFair value of assets acquired 241 1,925 550 3,135 595 $1,128Fair value of liabilities assumed -5 -434 -72 -323 -15 -141

Net cash paid for acquisitions 236 1,491 478 2,812 580 $987Treasury stock issued at fair value -85 -1,266 –Net cash paid for acquisitions 151 225 478 2,812 580 $987

Annual vs. Quarterly Financial Data

2.3 Critique of accounting information

Criticism

Methods for improvement

a) Use of Alternative Information

b) Statistical Adjustments

c) Application of Finance and Economic Theories

2.4 Static ratio analysis and its extension

Static determination of financial ratios Dynamic analysis of financial ratios Statistical distribution of financial ratios

Static determination of financial ratiosTable 2.5: Company ratios period 2003-2004

sliabilitieCurrent

assetCurrent

sliabilitieCurrent

CAotherinventoryCA

assetTotal

debtTotal

equityTotal

debtTotal

equityTotal

assetTotal

ensesInterest

EBIT

exp

Ratio Classification Formula J&J Industry

2003 2004 2003 2004

Liquidity Ratio

Current Ratio 1.71 1.96 1.59 1.7

Quick Ratio 1.21 1.47 1.048 1.174

Leverage Ratio

Debt-to-Asset 0.44 0.40 0.36 0.35

Debt-to-Equity 0.80 0.58 1.3 1.45

Equity Multiplier 1.80 1.45 3.61 4.14

Times Interest Paid 12.6 14.6 23.8 27.3

Static determination of financial ratios

Table 2.5: Company ratios period 2003-2004 (Continued)

365/

Re

Sales

ceivableAccount

ceivableAcounts

Sales

Re

Inventory

SoldGoodofCost

assetsFixed

Sales

assetsTotal

Sales

Sales

incomeNet

assetsTotal

incomeNet

equityTotal

IncomeNet

shareperEarning

shareperpriceMarket

sharepervalueBook

shareperpriceMarket

Ratio Classification Formula J&J Industry

2003 2004 2003 2004

Activity Ratios

Average collection period 57.32 52.66 58.3 56.6

Accounts receivable Turnover 6.37 6.93 6.26 6.45

Inventory Turnover 3.39 3.58 3.28 3.42

Fixed Asset Turnover 2.9 2.8 4.5 4.7

Total Asset Turnover 0.95 0.92 0.79 0.78

Profitability Ratios

Profit margin 13.2% 15.3% 17.19% 17.97%

Return on assets 14.91% 15.96% 7.34% 7.06%

Return on equity 26.79% 26.75% 14% 12.44%

Market value

Price/earnings 30.15 24.2 21.35 22.1

Price-to-book-value 5.52 4.68 5.71 5.92

Dynamic Analysis of Financial Ratios

(2.1)

where

0j1, and

j = A partial adjustment coefficient;

Yj,t = Firm’s jth financial ratio period t;

Yj,t-1 = Firm’s jth financial ratio period t-1; and

Y*j,t = Firm’s jth financial ratio target in period t,

*, , 1 , , 1( ), j t j t j j t j tY Y Y Y


where

Zj,t = Yj,t - Yj,t-1;

Wj,t-1 = Xj,t-1 - Yj,t-1;

Aj and Bj = Regression parameters,

and j,t = The error term.

, , 1 , 1 , 1[ ] (2.3)j t j t j j t j tY Y X Y

, , 1 , (2.4)j t j j j t j tZ A B W

*, , 1 , (2.2)j t j t j tY CX


Z′j,t = A′j + B′jW′j,t-1 + ′j,t, (2.5)

where

Z′j,t = log (Yj,t) - log (Yj,t-1);

W′j,t-1 = log (Xj,t-1) - log (Yj,t-1);

and

′j,t = The Error term.


, , 1

, 1 , 1

j,t , 1

j,t-1 , 1

log( / )

log( / )% change in [Y / ]

(2.6)% change in [X / ]

j t j tj

j t j t

j t

j t

Y YB

X YY

Y

*j,t , 1Y (2.7)j tCX

, 1 , 1 2 , 1 ,ˆ ˆ ˆ (2.8)j t j t j t j tY A B X B Y

Dynamic Analysis of Financial RatiosTable 2.6: Dynamic adjustment ratio regression results

* Partial adjustment coefficient significant at 95% level

Variable Current Ratio Leverage Ratio

Mean Z 0.0075 -0.03083

Mean W -0.14583 0.361666667

Var(Z) 0.013039 0.006099

Cov(Z,W) 0.074 0.009

Bj` 0.810* 0.259

t-Statistics [3.53] [1.06]

Aj` 0.032 -0.042


Table 2.7: Ratio correlation coefficient matrix

CR AT GPM LR

CR1.0

AT -0.443841 1.0

GPM 0.363273 0.381393 1.0

LR -0.51175 0.21961 -0.05028 1.0


Z1,t = A0 +A1Z2,t + A2W1 + 1,t, (2.9a)

Z2,t = B0 + B1Z1,t + B2W2 + 2,t. (2.9b)where

Ai, Bi (i = 0, 1, 2) are coefficients, 1 and 2 are error terms, and

Z1,t = Individual firm’s current ratio in period t - individual firm’s current ratio in period t-1;

Z2,t = Individual firm’s leverage ratio in period t - individual firm’s leverage ratio period t-1;

W1,t = Industry average current ratio in period t-1 - individual firm’s current ratio period t-1;

W2,t = Industry average leverage ratio in period t-1 - individual firm’s leverage ratio in period t-1.


Table 2.8: Johnson & Johnson empirical results for the simultaneous equation system

A0(B0) A1(B1) A2(B2)

(2.9a) -0.071[-1.80]

-0.378[-5.52]

0.080[1.20]

(2.9b) -0.0577[-1.59]

-0.842[-6.07]

0.074[0.91]

Statistical Distribution of Financial Ratios2 2( ) / 21

[ ] ( X ), (2.10)2

XF X e

where and 2 are the population mean and variance, respectively, and e and are given constants; that is, = 3.14159 and e = 2.71828.

Statistical Distribution of Financial Ratios

There is a direct relationship between the normal distribution and the log-normal distribution. If Y is log-normally distributed, then X = log Y is normally distributed. Following this definition, the mean and the variance of Y can be defined as:

where exp represents an exponential with base e.

2

2 2 2

1exp( ), (2.11a)

2exp(2 )(exp( ) 1), (2.11b)

Y x x

Y x x x

Statistical Distribution of Financial Ratios

2.5 COST-VOLUME-PROFIT ANALYSIS AND ITS APPLICATIONS

Deterministic analysis Stochastic analysis

2.5.1 Deterministic Analysis

Operating Profit = EBIT = Q(P－ V)－ F, (2.12)

where

Q = Quantity of goods sold;

P = Price per unit sold;

V = Variable cost per unit sold;

F = Total amount of fixed costs; and

P - V = Contribution margin.

2.5.1 Deterministic Analysis (cont’d)

* (2.13)( )

FQ

P V

% Change in profits ( ) Fixed CostsDOL =1 (2.14)

% Change in sales ( ) Profits

Q P V

Q P V F

*

1. (2.15)

[1 ( / )]DOL

Q Q

If operating profit is equal to zero, Eq. (2.12) implies that Q(P-V)-F=0 or that Q(P-V)=F, that is,

Equation (2.13) represents the break-even quantity, or that quantity of sales at which fixed costs are just covered.

The definition of the degree of operating leverage (DOL) is,

Based upon the definition of linear break-even quantity defined in Eq. (2.13), the degree of operating leverage can be rewritten as

2.5.2 Stochastic Analysis

In reality, net profit is a random variable because the quantity used in the analysis should be the quantity sold, which is unknown and random, rather than the quantity produced, which is internally determined. This is the simplest form of stochastic CVP analysis; for there is only one stochastic variable and one need not be concerned about independence among the variables. The distribution of sales is shown graphically in Fig. 2.5.

2.6 ACCOUNTING INCOME VS. ECONOMIC INCOME

Et = At + Pt, (2.17)

where

Et = Economic income,

At = Accounting earnings, and

Pt = Proxy errors.

2.7 SUMMARY

In this chapter, the usefulness of accounting information in financial analysis is conceptually and analytically evaluated. Both statistical methods and regression analysis techniques are used to show how accounting information can be used to perform active financial analysis for the pharmaceutical industry.

In these analyses, static ratio analysis is generalized to dynamic

ratio analysis. The necessity of using simultaneous-equation technique in conducting dynamic financial ratio analysis is also demonstrated in detail. In addition, both deterministic and stochastic CVP analyses are examined. The potential applications of CVP analysis in financial analysis and planning are discussed in some detail. Overall, this chapter gives readers a good understanding of basic accounting information and econometric methods, which are needed for financial analysis and planning.

Appendix 2A. Simple regression and multiple regression

2. A.1 INTRODUCTION

2. A.2 SIMPLE REGRESSION

Variance of

Multiple Regression

b


(2.A.1a)

(2.A.1b)

(2.A.2a)

(2.A.2b)

1t t tY a bX

1log logt t tY a b X

1

1 1 1 2cov , 2cov , 2cov , ,

t t t

t t t t t t

Var Y Var a bX

Var a Var bX Var a bX a bX

21t t tVar Y b Var X Var


(2.A.3)

(2.A.4)

(2.A.5a)

(2.A.5b)

2

21

Variation explained by the explanatory variable

Total variation in the dependent variable

t

t

R

b Var X

Var Y

2 2

11 1

ˆˆ ˆn n

t t t tt t

ESS Y Y Y a bX

11

( ) ˆˆ2 0n

t tt

ESSY a bX

a

1 11

( ) ˆˆ2 0n

t t tt

ESSX Y a bX

b


(2.A.6a)

(2.A.6b)

11 1

ˆˆn n

t tt t

an b X Y

21 1 1

1 1 1

ˆˆn n n

t t t tt t t

a X b X X Y


(2.A.7)

(2.A.7a)

1

1 1 1 11 1 1 1 1

2 21 11

1 11

21 1

1 1

( ) ( )ˆ

( )

n

tt

n n n n n

t t t t t t tt t t t t

n nn

t ttt tt

n n

t tt t

n Y

X X Y n X Y X Yb

n X Xn X

X X

1

1

[ , ]ˆ[ ]

t t

t

Cov X Yb

Var X


(2.A.8)

(2.A.8a)

12

2 1 1 11 1 1 1 1 1

2 211 1

1 121 1

2 21 1 1 1 1 1

1 1 1 1 1 1

( )( ) ( )( )ˆ

( )

( )[ ( ) ( ) ] ( )[ ( ) ( )( )]

t n n n n

t t t t tt t t t t t t

n nt

t tt t

t t

n n n n n n

t t t t t t t tt t t t t t t

Y XY X X X YX Y X

an X n X XX X

Y n n X X X n n X Y X X

1

2 21 1

1 1( )

n

n n

t tt t

n X X

ˆa Y Xb

Variance of Equation (2.A.7a) implies that:

(2.A.7b)

Where

b

1121 111

( )ˆ n nt t

t tnt ttt

x yb W y

x

1 1

11 2

11

t t

t t

tt n

tt

x X X

y Y Y

xW

x

Variance of

(2.A.7c)

(2.A.9)

b

1 1 11 1

ˆ n n

t t t tt t

b W bx W

2

21 1 1

1 1

21 1 1

1 1

21 1 1

1 1

ˆ ˆ( ) ( )

( )

[( 1) ]

( ) , since 1.

n n

t t t tt t

n n

t t t tt t

n n

t t t tt t

Var b E b b

E W bX W b

E W x b W

E W W x

2 20 1 0 1 1 2 1 2

ˆ( ) [( ) 2( ) ( ) ]Var b E W W W W

Variance of b

2 20 1 1 2

2 2 2 20 1 1 2

ˆ( ) ( ) ( )

( ) ( )

Var b E W E W

W E W E

2 21

1

221

1

ˆ( ) ( )

n

t tt

n

tt

Var b W E

W

2112

1 2 221 1 11 1

1

( )

nntt

t n nt t tt t

xW

x x

Variance of b

(2.A.10)

(2.A.11)

(2.A.12)

2

211

ˆ( )n

tt

Var bx

2112

211

ˆ( )n

ttn

tt

xVar a

n x

22

11

ˆˆ( , )n

tt

XCov a b

x

Multiple Regression

(2.A.13a)

The error sum of squares can be defined as:

Where

1, 1 2, 1t t t tY a bX cX

2 2ˆˆ ( )t t tESS Y Y

1, 1 2, 1ˆˆ ˆ ˆt t t tY a bX cX

Multiple Regression

(2.A.14a)

(2.A.14b)

(2.A.14c)

1, 1 2, 10 or t t t

ESSY na b X c X

a

21, 1 1, 1 1, 1 1, 1 2, 10 or t t t t t t

ESSX Y a X b X c X X

b

22, 1 2, 1 1, 1 2, 1 2, 10 or t t t t t t

ESSX Y a X b X X c X

c

Multiple Regression

0 = na + b(0) + c(0), (2.A.15a)

(2.A.15b)

(2.A.15c)

21, 1 1, 1 1, 1 2, 1(0)t t t t tx y a b x c x x

22, 1 1, 1 2, 1 2, 1(0)t t t t tx x a b x x c x

Multiple Regression

(2.A.16a)

(2.A.16b)

(2.A.17)

21,21,1

21,2

21,1

1,21,11,22

1,21,1

)())((

)(ˆ

tttt

ttttttt

xxxx

xxyxxyxb

22, 1 1, 1 1, 1 1, 1 2, 1

2 2 21, 1 2, 1 1, 1 2, 1

( )ˆ

( )( ) ( )t t t t t t t

t t t t

x y x x y x xc

x x x x

1 2ˆˆˆ ˆa Y bX cX

Multiple Regression

(2.A.13b)

(2.A.18)

(2.A.19)

1, 1 2, 10.2837 0.7564 0.2990 (0.4323) (0.3288) (0.2240)

t t tY X X

ˆ 1.7071(0.7564)(1.8448)(0.2990)(1.6904) 0.2837a

ˆ ˆ( ) ( ) ( )t t t t t tY Y Y Y Y Y

1, 1 2, 1ˆˆ ˆ ˆt t tY a bX cX

Multiple Regression

(2.A.20)

where

TSS = Total sum of squares;

ESS = Residual sum of squares; and

RSS = Regression sum of squares.

2 2 2ˆ ˆ( ) ( ) ( ) , TSS ESS RSS

t t t t t tY Y Y Y Y Y

Multiple Regression

(2.A.21)

(2.A.22)

where

and k = the number of independent variables.

2 22

2 2

ˆ ˆ( )RSS1

TSS ( ) ( )t t t

t t t t

Y YR

Y Y Y Y

22 ˆ

1( )

t

t

RVar Y

22 ˆ

ˆ( ) ttVar

n k

2( )

( )1

tt

Y YVar Y

n

Multiple Regression

(2.A.23)

where F(k-1, n-k) represents F-statistic with

k－ 1 and n－ k degrees of freedom.

2 2 11 (1 )

nR R

n k

2

2( 1, )

1 1

R n kF k n k

R k

Appendix 2B. Instrumental Variables and Two-Stage Least Squares

2. B.1 ERRORS-IN-VARIABLE PROBLEM2. B.2 INSTRUMENTAL VARIABLES2. B.3 TWO-STAGE, LEAST-SQUARE

2. B.1 ERRORS-IN-VARIABLE PROBLEM

(2.B.1)

(2.B.2)

(2.B.3)

ttmjjtj RBAR ,,

*, ,m t m t tR R V

* 2 2, ,( ) ( )m t m t t m VVar R Var R V

2. B.1 ERRORS-IN-VARIABLE PROBLEM

(2.B.4)

(2.B.5)

ttmjjtj RBAR *,

*,

*, , ,

*, ,

,

2 2,

( , ) ( , )ˆ( ) ( ) ( )

( , , ) ( , )

( ) ( ) 1 /

m t jt m t t j j m t tj

m t m t t

j m t m t t t j

m t t V M

Cov R R Cov R V B RB

Var R Var R Var V

B Cov R R Cov V B

Var R Var V

2. B.2 INSTRUMENTAL VARIABLES

(2.B.6)

(2.B.7)

(2.B.8a)

(2.B.8b)

( , ) ( , ) ( , )j j mCov R Z B Cov R Z Cov Z

*

( , ) ( , )ˆ( , ) ( , )

j jj

m m

Cov R Z Cov R ZB

Cov R Z Cov R Z

12101 EYAAY

2121102 EZBYBBY

2. B.2 INSTRUMENTAL VARIABLES

(2.B.9a)

(2.B.9b)

(2.B.10a)

(2.B.10b)

1222101 EZAYAAY

2121102 EZBYBBY

1 0 1 2 2 2 3 3 1Y A AY A Z A Z E Y

2121102 EZBYBBY

2.B.3 TWO-STAGE LEAST-SQUARE

(2.B.11a)

(2.B.11b)

(2.B.10′a)

(2.B.10′b)

133221101 EZCZCZCCY

233221102 EZDZDZDDY

133222101ˆ EZAZAYAAY

2121102ˆ EZBYBBY

2.B.3 TWO-STAGE LEAST-SQUARE

(2.B.12a)

(2.B.12b)

21 1 10.2399 0.8198 1.9004 , 0.3449,

(0.1012) (0.2802) (1.245)Y Z Z R

22 1 20.0746 0.1133 0.7849 , 0.4240,

(0.0195) (0.0541) (0.2405)Y Z Z R

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