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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