Econometric Methodology

• DOI: https://doi.org/10.1108/S0573-8555(2005)0000272008
• Date: 21 May 2005
• Pages: 23-28
• Published date: 21 May 2005
• Author: M. McAleer,Daniel Slottje,Pei Syn Wee

CHAPTER 4

Econometric Methodology

4.1.

INTRODUCTION

This book will rely on and utilize the model developed in the

Basmann et

al.

(1987) study, and subsequently modified in Basmann

et al. (2005) to include patent activity variables as technology

changers. As we believe the exposition in the two papers is concise

and clear, the discussion in this chapter will closely follow the two

papers that preceded this study.

4.2.

THE AGGREGATE PRODUCTION FUNCTION

Let the real-valued function

y(X;

0) describe the maximum output y

which can be produced from any given set of inputs (X\,...,

X„).

This

production function is a single-valued mapping from input space into

output space, since the maximum attainable output for any stipulated

set of inputs is

unique.

Second partial derivatives are continuous with

respect to X, where 0 designates the vector of all parameters.

Let 7?-n)(X; 0), i= 1,2, ...,w

—

1, designate the marginal rate of

technical substitution (MRTS) of Xt for Xn at the point

X,

and let ak,

k=

1,2,...,m,

be an observable magnitude different from X and its

components. Assume that the output v and all of its first and second

partial derivatives, y,- and y,y, respectively, are differentiable at all

points (X) of the cost domain at least once with respect to each of the

technology-changing variables,

ax,...,

am. It follows that each of the

MRTSsR)n\i=

l,2,...,n-

1,

is differentiable at every point (X) of