10
won the block. This scheme was implemented with the
stated aim of ensuring that power generation consumers get
the benefit of lower coal prices (Mohammad, 2018). The
outcome of these auctions were negative bids that meant
these power generation units offered to pay to the govern-
ment and waive off the cost of mining to win in the auc-
tion the right to own coal blocks (Down to Earth, 2015).
The bid amounts for these coal blocks have been calculated
based on offered payment to government plus the waived
cost of coal mining (PwC, 2015).
METHODOLOGY AND
IMPLEMENTATION
In this section, we discuss the methodology for testing the
hypotheses proposed and use of Stata tools to implement
them. However, even before the test of hypotheses, our
concern for empirical study was to establish a variable for
value of coal blocks in common value auctions. The follow-
ing sub-section of the paper describes the approach taken
for that. Then, in the subsequent subsections, we describe
the methodology for testing the hypotheses.
Construction of Value Variable
Construct of value in a common value auction is depen-
dent on public and private information and as such dif-
ficult to compute for empirical studies (Kremer, 2002).
However, for coal block auctions in India, public informa-
tion that can reflect the value of a coal block are available
from the details of coal blocks provided by the government
of India, which include – Surface area, Distance from near-
est Railway Siding, Project Affected People, Proportion of
Forest Land in Mining Lease, Stripping Ratio, GCV of
coal, Mine Capacity, and Geological Reserves. These are the
observed items that reflect the value variable that cannot be
observed directly since bidders submit their bids, not their
values. Literature in economics and finance, as also other
fields of studies such as management, provide methods to
construct measurement of a latent variable such as value in
common value auctions using items that are observed such
as the attributes of coal blocks. Monica (2008) applies item
response theory (IRT) models to develop a scale measuring
financial precariousness. Fabbris (2012) discusses five tech-
niques for collecting data on interrelated items: ranking,
picking best/worst, allocating total, rating, and paired com-
parison. The paper suggests these techniques for surveys on
values, utilities, satisfaction, and preferences. Antle (2010)
develops a test to determine if economic variables follow
scale or location-scale distributions.
Cronbach’s alpha is the most widely used measure of
internal consistency or reliability of a scale with multiple
Likert items (Peterson, 1994). An instrument with a high
Cronbach’s alpha, typically 0.7 or higher, is said to have
a strong internal consistency, meaning that its items are
closely related and measure the same underlying construct
(Croasmun &Ostrom, 2011 Gliem &Gliem, 2003).
Researchers should not rely on single Likert items to mea-
sure a construct, as they are not reliable (Gliem &Gliem,
2003). Instead, researchers should develop multi-item
scales and test their internal consistency using Cronbach’s
alpha. Cronbach’s alpha provides a lower bound estimate of
a scale’s reliability, and this estimate can be further biased
downward for scales with dichotomous items (Sun et al,
2007). Sun et al (2007) developed SAS and SPSS macros to
calculate a standardized Cronbach’s alpha for dichotomous
scales using the upper bound of the phi coefficient, which
provides a better estimate of reliability.
The statistical power of a study depends in part on
the Cronbach’s alpha of the instrument used, with higher
alphas leading to greater power (Heo, Kim &Faith, 2015).
Heo, Kim &Faith (2015) derived power functions relat-
ing Cronbach’s alpha to power for various study designs.
Regardless of design, higher Cronbach’s alphas and lower
measurement error lead to increased power.
However, Cronbach’s alpha has some important limita-
tions. It always has a value, even when a scale has no inter-
nal consistency, and it does not actually measure a scale’s
internal structure (Sijtsma, 2009). Cronbach’s alpha also
provides limited information about individuals’ scores,
since it relies on a single test administration (Sijtsma,
2009). In general, a sample size of at least 30 is needed to
detect a Cronbach’s alpha of 0.7 or higher (Bujang, Omar
&Baharum, 2018).
Based on these considerations, we used the 8-items
observed, converted each into a Likert-scale observation
from 0 to 10, and then used the Cronbach’s alpha to deter-
mine if they can be used for value variable. We implement
this by using “alpha” command in Stata that provides the
levels of Cronbach’s alpha with each item included in the
scale. We present the results of our analysis in the results
section of the paper.
The regressor variables for our study, thus, are value
variables as constructed from 8 observed items and com-
petitive intensity variable taken as number of bidders for
each coalmine. The outcome variables are bid amounts as
observed and Excess Bid as computed.
OLS Regression for Base Model and with Interaction
Term for Moderation Model
Ordinary least squares (OLS) regression is one of the most
commonly used statistical techniques in economics for
won the block. This scheme was implemented with the
stated aim of ensuring that power generation consumers get
the benefit of lower coal prices (Mohammad, 2018). The
outcome of these auctions were negative bids that meant
these power generation units offered to pay to the govern-
ment and waive off the cost of mining to win in the auc-
tion the right to own coal blocks (Down to Earth, 2015).
The bid amounts for these coal blocks have been calculated
based on offered payment to government plus the waived
cost of coal mining (PwC, 2015).
METHODOLOGY AND
IMPLEMENTATION
In this section, we discuss the methodology for testing the
hypotheses proposed and use of Stata tools to implement
them. However, even before the test of hypotheses, our
concern for empirical study was to establish a variable for
value of coal blocks in common value auctions. The follow-
ing sub-section of the paper describes the approach taken
for that. Then, in the subsequent subsections, we describe
the methodology for testing the hypotheses.
Construction of Value Variable
Construct of value in a common value auction is depen-
dent on public and private information and as such dif-
ficult to compute for empirical studies (Kremer, 2002).
However, for coal block auctions in India, public informa-
tion that can reflect the value of a coal block are available
from the details of coal blocks provided by the government
of India, which include – Surface area, Distance from near-
est Railway Siding, Project Affected People, Proportion of
Forest Land in Mining Lease, Stripping Ratio, GCV of
coal, Mine Capacity, and Geological Reserves. These are the
observed items that reflect the value variable that cannot be
observed directly since bidders submit their bids, not their
values. Literature in economics and finance, as also other
fields of studies such as management, provide methods to
construct measurement of a latent variable such as value in
common value auctions using items that are observed such
as the attributes of coal blocks. Monica (2008) applies item
response theory (IRT) models to develop a scale measuring
financial precariousness. Fabbris (2012) discusses five tech-
niques for collecting data on interrelated items: ranking,
picking best/worst, allocating total, rating, and paired com-
parison. The paper suggests these techniques for surveys on
values, utilities, satisfaction, and preferences. Antle (2010)
develops a test to determine if economic variables follow
scale or location-scale distributions.
Cronbach’s alpha is the most widely used measure of
internal consistency or reliability of a scale with multiple
Likert items (Peterson, 1994). An instrument with a high
Cronbach’s alpha, typically 0.7 or higher, is said to have
a strong internal consistency, meaning that its items are
closely related and measure the same underlying construct
(Croasmun &Ostrom, 2011 Gliem &Gliem, 2003).
Researchers should not rely on single Likert items to mea-
sure a construct, as they are not reliable (Gliem &Gliem,
2003). Instead, researchers should develop multi-item
scales and test their internal consistency using Cronbach’s
alpha. Cronbach’s alpha provides a lower bound estimate of
a scale’s reliability, and this estimate can be further biased
downward for scales with dichotomous items (Sun et al,
2007). Sun et al (2007) developed SAS and SPSS macros to
calculate a standardized Cronbach’s alpha for dichotomous
scales using the upper bound of the phi coefficient, which
provides a better estimate of reliability.
The statistical power of a study depends in part on
the Cronbach’s alpha of the instrument used, with higher
alphas leading to greater power (Heo, Kim &Faith, 2015).
Heo, Kim &Faith (2015) derived power functions relat-
ing Cronbach’s alpha to power for various study designs.
Regardless of design, higher Cronbach’s alphas and lower
measurement error lead to increased power.
However, Cronbach’s alpha has some important limita-
tions. It always has a value, even when a scale has no inter-
nal consistency, and it does not actually measure a scale’s
internal structure (Sijtsma, 2009). Cronbach’s alpha also
provides limited information about individuals’ scores,
since it relies on a single test administration (Sijtsma,
2009). In general, a sample size of at least 30 is needed to
detect a Cronbach’s alpha of 0.7 or higher (Bujang, Omar
&Baharum, 2018).
Based on these considerations, we used the 8-items
observed, converted each into a Likert-scale observation
from 0 to 10, and then used the Cronbach’s alpha to deter-
mine if they can be used for value variable. We implement
this by using “alpha” command in Stata that provides the
levels of Cronbach’s alpha with each item included in the
scale. We present the results of our analysis in the results
section of the paper.
The regressor variables for our study, thus, are value
variables as constructed from 8 observed items and com-
petitive intensity variable taken as number of bidders for
each coalmine. The outcome variables are bid amounts as
observed and Excess Bid as computed.
OLS Regression for Base Model and with Interaction
Term for Moderation Model
Ordinary least squares (OLS) regression is one of the most
commonly used statistical techniques in economics for