Campus Presentation at National Taiwan University

Wesley Shu

Assistant Professor

San Diego State University

Short Biography

BA in Economics, National Taiwan University

MBA in Finance & Decision Sciences, Indiana University

Ph.D. in MIS, University of Arizona

IT Productivity and Productive Efficiency in Taiwan

What is Productivity?

The amount of output produced given an input

Output/Input What if multiple input?

A Cobb-Douglas Function

01

0

assumption: constant return to scale,

unity elasticity of substitution

marginal product

ln ln ln

ln,

ln

i

n

ii

i i

i j

j i

y x

y x

x xm

m m

Other Functional Forms

CES

translog

1

1

n

i ii

y a x

01

1

2

ln ln ln lnn n n

i i ij i ji i j

ij ji

y x x x

Productivity and Productive Efficiency

Productivity is to measure how much business value an input factor can contribute to.

Productive efficiency is to measure the gap between observed and optimal values of output and input.

Three Types of Inefficiency

Technical inefficiency Allocative inefficiency Scale inefficiency

Technical Inefficiency

The gap between the observed output and the production frontier under the current technology

01

i

n

ii

y x e

Technical Inefficiency, continued

x1

x2 Production frontier

A

B

Allocative Inefficiency

A firm chooses the input ratio when the marginal ratio = input price ratio to minimize its total cost. When they are not equal,

1 1

juj jMP we

MP w

Scale Inefficiency

A firm chooses its production level when the marginal cost = output price. If not, then

MC pe

Characteristics of Previous Studies

Measuring single deterministic production function

Not incorporating some basic business assumptions

Deterministic Approach

Deterministic approach assumes all deviations except the error terms are under management control

It in fact uses observed data to construct the production frontier (optimal output level.)

Not Imbedding the Basic Business Assumption

Firms want to either maximize their profits or minimize their costs

So, they will decide the output and input quantities based on the price information

This price information and firms’ decision behavior are not captured in a single production function approach, but in the error terms.

So, there is bias because the explanatory variables are correlated with the error terms.

Not Imbedding the Basic Business Assumptioncontinued

Hal Varian, Microeconomic Analysis, 3rd Edition“If the managers observe these effects (of price changes,) then they will certainly take that information into account when they determine their optimal choice of inputs. Thus, the right-hand variables (of a production function) will not be statistically independent from the error term.”

Our Model - formalize the business assumption

0

1

01

w, max

. .

i

i t

n

i ixi

nt

ii

p py w x

st

y x e

Profit maximization model with inefficiency measurement

Our Model, continued

0

1

1 1 1

1 1 1 11 2

2

ln ln

ln ln ln ln ln , ,

ln ln ln ln ln ln ln j

n

i i ti

j j j j

n nu

i ji j

y x t

x x w w u j n

x y p w e

Endogenous variable: xi

Exogenous variable: p, wi

Our Model, continued

Intrilligator, Bodkin, and Hsiao Estimating the complete system is generally superior to estimating only

the first equation (the production function) from both economic and econometric standpoints.

From an economic standpoint, estimating the complete system expresses the assumption that the data reflect both the behavior of the decision maker (the firm) and the technology, while the first equation (the production function) reflects only the technology.

From an econometric standpoint, the estimators of only the first equation involves simultaneous equations bias, so the estimators will be biased and inconsistent.

Data Requirement

Assets, output price, Employment Compensation are publicly available.

IT Employment Compensation IT Spending, including hardware, software,

maintenance, and training Prices (Price deflators)

Our Production Function

0

ln ln ln ln

ln lnIT IT NIT NIT

LIT LIT NLIT NLIT

y x x

x

Data Source

Year 2000 - 2002 Survey of more than 300 companies, 187 with valid data (all three years) A variety of industries

Data Requirement – IT Capital

From survey The survey is “IT Spending”. Need to

convert “flow” into “stock”. Companies may know ‘spending’ but not

‘stock’ or ‘asset’. Since we only have 3-year data, we assume

IT life cycle is 2 years.

Data Requirement – IT Capital

Rate of depreciation, ex., in a year, ½ of IT to be obsolete.

12 11 1 ,ijt i ijt i ij tK d I d K

id

Data Requirement – IT price

Rental price = very complicated formula Our research: survey

Finding, Productivity

Variable Estimate t-statistic

Constant, ln 0 16.7743 47.1859

IT Capital, IT 0.5431 26.7491

Non IT Capital, NIT 0.1569 24.2481

IT Labor, LIT 0.4985 19.1504

Non IT Labor, NLIT 0.1421 18.1548

Findings - Inefficiency

Technical: -0.1350 Allocative uNIT: -0.7989 decrease non-IT

uLIT: 0.6138

uNLIT: -0.2314

Scale: 0.2423 over produce

Findings - Overall Percentage Loss

Variable Value LT 18.32% LA 1.669% LS 0.496%

Future Direction

After March when 2003 data available – complete the research

Add ‘panel data consideration’ into the model

Analysis of Panel Data

Cross section and time series

With consideration of stochastic form or not

Y

I

Company A

Company B

Company C

Future Direction continued

Put into consideration the company size and industry difference

Relax constraints - CES Measure input substitution effect – translog

function

01

1

2

ln ln ln lnn n n

i i ij i ji i j

ij ji

y x x x