Firm Market Value and Investment: The Role of Firms Market Power - - PowerPoint PPT Presentation

Firm Market Value and Investment: The Role of Firm’s Market Power and Different Types of Adjustment Costs August 2005

Nihal Bayraktar Penn State – Harrisburg and World Bank Plutarchos Sakellaris Athens University of Economics and Business, and IMOP

• Introduction
• Models
• Data
• Indirect inference

Introduction

• Empirical specifications are based on two simplifying assumptions

– Profit function: Homogenous of degree one in capital – Capital adjustment cost function: Homogenous of degree one in capital and investment

• As a result

– Expected marginal Q (not observable) = Average Q (observable) – Coefficients of investment regressions give information about the parameters of the convex adjustment cost

• Initially disappointing empirical results

– Fundamentals (Tobin’s Q) cannot explain investment – Unreasonably high adjustment costs

Neoclassical investment models with convex adjustment costs …

One response: Introduction of nonlinearities in the investment process

Example: Barnett and Sakellaris (1999)

• Tobin’s Q and investment are nonlinearly related

when a higher order, linearly homogenous, convex capital adjustment cost is used

• Lessons:

1. Fundamentals (Tobin's Q) are informative for investment

• nce nonlinearities are allowed.

2. Lower adjustment capital cost

• Possible misspecification problem?

– Their empirical specification is based on the simplifying assumptions

Recent studies question the validity of simplifying assumptions …

1) Constant returns to scale profit function or perfectly competitive product market may not be correct. Monopoly power or decreasing returns to scale:

• Cooper and Haltiwanger (2003) at the plant level
• Bayraktar (2002), and Cooper and Ejarque (2003a and

2003b) in COMPUSTAT data at the firm level

• Bayraktar, Sakellaris, and Vermeulen (2004) with German

firm-level data.

Recent studies question the validity of simplifying assumptions …

2) Linearly homogenous convex adjustment costs may not be sufficient to capture different types of investment costs. Non-convex adjustment costs:

• Cooper and Haltiwanger (2003)
• Bayraktar (2002)
• Bayraktar, Sakellaris, and Vermeulen (2004)

Our paper …

• Can a dynamic investment model with more

realistic assumptions replicate the nonlinear relationship between investment and Tobin's Q?

– Non-convex adjustment cost function (fixed cost) – Profit function with decreasing returns to scale

• Focus is on Barnett and Sakellaris (1999)

MODELS

Model used in Barnett and Sakellaris (1999)

Value maximization subject to Π(·): homogenous degree one in K

VAit,Kit  max

Iit

Ait,Kit − CKit,Iit  EAit1∣AitVAit1,Kit1,

Iit  Kit1 − 1 − Kit

Higher order, linearly homogenous, convex cost function

CKit,Iit  pIit  1Iit  2

2 Iit Kit 2Kit

 3

3 Iit Kit 3Kit  4 4 Iit Kit 4Kit  tIit  iIit

Barnett and Sakellaris (1999)’s empirical specification

• First order condition produces …

Qit1  1  2iit  3iit

2  4iit 3  p  t  i − it1

Alternative model

Profit function where θ is the profitability parameter. If θ < 1, decreasing returns to scale.

Ait,Kit  AitKit



Adjustment Costs

• Convex costs
• Fixed costs

 2 Iit Kit 2Kit.

FKit.

Value maximization

Investment cost in case of capital adjustment Investment cost in case of no capital adjustment

V∗Ait,Kit  max VaAit,Kit,VnaAit,Kit

VjAit,Kit  max

Kit1 Ait,Kit − CjKit,Iit  EAit1∣AitV∗Ait1,Kit1

CaKit,Iit  pIit  

2 Iit Kit 2Kit  FKit

CnaKit,Iit  0

• Set of structural parameters
• Transition matrix

{,r,,,,F}

PAit1|Ait

Data

Data Set

• Unbalanced panel: 1561 U.S. manufacturing

firms

• Period: 1960-1987
• 23,207 observations.
• COMPUSTAT database (Hall, 1990).

0.77

• 0.22

1.76 0.14 0.60 βQit+1- P 1.86 0.83 1.83 1.20 1.68 Qit+1 1.94 0.84 2.12 1.23 1.77 Qit 0.023 0.09 0.24 0.15 0.20 Iit/Kit-1 75th percentile 25th percentile St. dev median Mean Summary Statistics

Distribution of the Investment Rate

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 < = . 3 . 6 . 9 . 1 2 . 1 5 . 1 8 . 2 1 . 2 4 . 2 7 . 3 . 3 3 . 3 6 . 3 9 . 4 2 . 4 2 >

Profitability and Shocks

Estimation of the profit function and the profit shocks θ is estimated at 0.87, with a standard error of 0.07.

Calculation and decomposition

• f the profit shocks

Ait,Kit  c ∗ witLit

Ait/c  witLit/Kit

 

• Decompose into a fixed component, and time

varying component by regression the log of on (a constant and) fixed firm effects.

– Residuals of the regression = (total profit shocks)

• They are estimates of the time varying part of the profit

shock (in logs):

• Split to obtain estimates of the aggregate and the

idiosyncratic components at and ait by regressing

• n time dummies.

– Residuals of the regression = (idiosyncratic shocks) – Time dummies = (aggregate shocks)

Ait/c

Ait/c  ait at  ait  ait  ait  at  ait

Autocorrelation : 0.67

• Std. dev. : 0.078
• Std. dev. : 0.24

Max: 0.71 Min: -0.82 Features of the firm demeaned profit shocks (in logs): 

ait  ait  ait  at

Tobin’s Q

Numerator = market value of common stock + liquidating value of preferred stock + market value of long-term debt + book value of short-term debt Denominator = Replacement value of fixed capital + Replacement value of inventories

The relationship between investment and Tobin’s Q

Qit1  1  2iit  3iit

2  4iit 3  p  t  i − it1

= present discounted value of end-of- period average Q p = relative price of new investment

Qit1

Table 3: Auxiliary Regression Barnett and Sakellaris (1999) (Table 4 on page 257) iit 1.44* (0.08) iit2

• 0.36* (0.04)

iit3 0.023* (0.003)

Adjusted R-sq

0.65

Note: The dependent variable is Qit1 − Pt. * significant at the 1% level.

Structural Estimation Indirect Inference

Structural Estimation

r = 0.0413, β = 1/(1+r) = 0.96, δ = 0.1, p = 0.978, θ = 0.87. Structural parameters to be estimated

Θ ≡ ,F

Indirect inference: a) Fix Θ. Solve dynamic program. Generate corresponding optimal policy functions. b) Use these policy functions and arbitrary initial conditions to generate simulated data (10 panels × 1000 firms × 27 years). c) Use simulated data to calculate the model analogues of coefficients d) where W is a weighting matrix (3x3).

min

Θ JΘ  d − sΘ′Wd − sΘ

Definition of Tobin’s Q in the model

Qit1 

EAit1∣AitV∗Ait1,Kit1 pKit1

= present discounted future value of the firm

Kit+1 = end-of-period capital stock

EAit1∣AitV∗Ait1,Kit1

0.045 F 0.020 γ Estimate Parameter Estimates of the structural parameters

(0.002) 0.008 (0.003) 0.023 (0.010)

• 0.067

(0.04)

• 0.36

(0.016) 0.312 (0.08) 1.44

• Std. error

Model

• Std. error

Data Coefficient Auxilliary Regression Coefficients Actual vs simulated data Dependent variable: Qit1 − p

iit

iit

2

iit

3

0.20 0.20 mean(iit) 0.64 0.24 stdev(iit) 0.82 1.76 stdev(βQit+1-p) 0.89 0.60 mean(βQit+1-p) 0.24 0.23 corr(βQit+1-p, iit) MODEL DATA Comparing moments

Initial Result

• Even in the absence of homogeneity

assumptions of the conventional Q-theory, the nonlinear and significant responsiveness

• f investment to changes in average Q can

be explained.

THE END

0.310 Corr(Iit/Kit-1, Iit-1/Kit-2) 0.216 Iit/Kit-1 > 0.25 0.319 Iit/Kit-1 > 0.2 0.014 Iit/Kit-1 < 0.025 0.004 Iit/Kit-1 < 0.01 Features of the distribution of the investment rate

0.045 F 0.020 γ Standard error Estimate Parameter Estimates of the structural parameters