11
estimating relationships between variables. Several papers
highlight the benefits of OLS for econometric analysis.
Inder (1993) finds that OLS provides consistent estimates
of long-run equilibrium relationships between cointegrated
economic variables. Zaman, Rousseeuw, &Orhan (2000)
demonstrates the usefulness of OLS-based robust regres-
sion techniques for re-analyzing three regressions from the
economic literature. The author argues that these tech-
niques should be more widely used in applied economet-
rics. Perron &Yamamoto (2016) makes the case that OLS
should be the preferred method for estimating and testing
for structural breaks in models with endogenous regressors,
which are common in economics. Pavelescu (2004) exam-
ines several properties of OLS in depth, including how the
sizes of estimated parameters, coefficients of determination
and test statistics are determined. The author proposes a
methodology for adding new explanatory variables to a
linear regression model based on these properties. These
papers make a strong case for the advantages of OLS regres-
sion for econometric analysis due to its efficiency, consis-
tency, and applicability to a wide range of models.
Several papers note limitations of OLS regression and
propose alternative estimation methods. OLS relies on
assumptions that are often violated in economic data, lead-
ing to inconsistent estimates. The situations of dynamic
variations (Inder, 1993), data with lags and leads (Kejriwal
&Perron, 2008), data exhibiting long memory (Krämer,
Sibbertsen, &Kleiber, 2001), sensitivity to outliers (Zaman
&Bulut, 2020), exogeneity of regressors (Walstad, 1987),
and skewness (Sinha, 2010) are often observed to have
biased OLS estimations. However, a careful consideration
of the research study we have, it is our understanding that
the study does not have complexities that may make use of
OLS regression inappropriate for this study. Hence, for the
Base Model, we consider OLS regression appropriate.
We implement the OLS regression for Base Model
using “regress” command in Stata. “regress” command per-
forms OLS linear regression with ability to compute robust
and cluster standard errors. The results of the OLS regres-
sion for Base Model are presented in the results section of
our paper.
OLS regression with an additional interaction term,
that is a multiplication of two regressors of value variable
and competitive intensity variable, is used for implementa-
tion of the Moderation Model. Kolasinski &Siegel (2010)
argue that the interaction term coefficient alone can be
used to draw inferences about interactive effects, modera-
tion effect in this study. The coefficient of is interpreted as
the marginal effect of one variable on the dependent vari-
able when the change in other independent variable is held
at unity (Kolasinski &Siegel, 2010). Thus, for moderation
effect in coal block auctions, the coefficient of the interac-
tion term is of our interest and we examine if that is statis-
tically significant. The results of the OLS regression with
interaction term for Moderator Model are presented in the
results section of our paper.
Mediation Test for Mediation Model
For the mediation model, the estimation requires two stage
OLS regression. In the first stage, competitive intensity is
the dependent variable that is regressed on value variable.
The estimated values competitive intensity from the regres-
sion in first stage is then used in the second stage as a regres-
sor along with value variable when the bid amount or excess
bid is the dependent variable.
This is implemented through “paramed” command in
Stata. “paramed” is one of the Stata commands to be devel-
oped for conducting causal mediation analysis that allows
for testing statistical significance of mediator (VanderWeele,
2016). Using this command, the causal effects are automat-
ically computed by the Stata program as a function of the
regression parameters as estimated from the above specified
two stage regressions.
RESULTS
In this section, we report the results of various analyses that
we conducted using implementation methods described in
the section above. We first report the results of construc-
tion of value variable, which is latent and unobserved, by
using 8 observed characteristics. This is then followed by
the presentation of results of hypotheses testing using the
three models described in the paper. These tests results are
presented for both, bid amount and Excess Bid being the
dependent variables.
Result of Construction of Value Variable
We conducted the analyses of 8 drivers of value, namely,
Surface area, Distance from nearest Railway Siding, Project
Affected People, Proportion of Forest Land in Mining
Lease, Stripping Ratio, GCV of coal, Mine Capacity, and
Geological Reserves. The following table, Table 2, presents
the correlation matrix of these items. The notable observa-
tion from the correlation matrix is that all the values are
less than 0.7, indicating that they are not highly correlated
and thus, none of these items can be rejected as redundant.
In economics literature, the cut-off level of 0.7 has been
indicative of low level of relationships between the variables
(Kandel, 1987). Having these items then in the scale serves
a purpose and does not lead to argument of redundancy.
This is in line with the technical assessment of the items as
estimating relationships between variables. Several papers
highlight the benefits of OLS for econometric analysis.
Inder (1993) finds that OLS provides consistent estimates
of long-run equilibrium relationships between cointegrated
economic variables. Zaman, Rousseeuw, &Orhan (2000)
demonstrates the usefulness of OLS-based robust regres-
sion techniques for re-analyzing three regressions from the
economic literature. The author argues that these tech-
niques should be more widely used in applied economet-
rics. Perron &Yamamoto (2016) makes the case that OLS
should be the preferred method for estimating and testing
for structural breaks in models with endogenous regressors,
which are common in economics. Pavelescu (2004) exam-
ines several properties of OLS in depth, including how the
sizes of estimated parameters, coefficients of determination
and test statistics are determined. The author proposes a
methodology for adding new explanatory variables to a
linear regression model based on these properties. These
papers make a strong case for the advantages of OLS regres-
sion for econometric analysis due to its efficiency, consis-
tency, and applicability to a wide range of models.
Several papers note limitations of OLS regression and
propose alternative estimation methods. OLS relies on
assumptions that are often violated in economic data, lead-
ing to inconsistent estimates. The situations of dynamic
variations (Inder, 1993), data with lags and leads (Kejriwal
&Perron, 2008), data exhibiting long memory (Krämer,
Sibbertsen, &Kleiber, 2001), sensitivity to outliers (Zaman
&Bulut, 2020), exogeneity of regressors (Walstad, 1987),
and skewness (Sinha, 2010) are often observed to have
biased OLS estimations. However, a careful consideration
of the research study we have, it is our understanding that
the study does not have complexities that may make use of
OLS regression inappropriate for this study. Hence, for the
Base Model, we consider OLS regression appropriate.
We implement the OLS regression for Base Model
using “regress” command in Stata. “regress” command per-
forms OLS linear regression with ability to compute robust
and cluster standard errors. The results of the OLS regres-
sion for Base Model are presented in the results section of
our paper.
OLS regression with an additional interaction term,
that is a multiplication of two regressors of value variable
and competitive intensity variable, is used for implementa-
tion of the Moderation Model. Kolasinski &Siegel (2010)
argue that the interaction term coefficient alone can be
used to draw inferences about interactive effects, modera-
tion effect in this study. The coefficient of is interpreted as
the marginal effect of one variable on the dependent vari-
able when the change in other independent variable is held
at unity (Kolasinski &Siegel, 2010). Thus, for moderation
effect in coal block auctions, the coefficient of the interac-
tion term is of our interest and we examine if that is statis-
tically significant. The results of the OLS regression with
interaction term for Moderator Model are presented in the
results section of our paper.
Mediation Test for Mediation Model
For the mediation model, the estimation requires two stage
OLS regression. In the first stage, competitive intensity is
the dependent variable that is regressed on value variable.
The estimated values competitive intensity from the regres-
sion in first stage is then used in the second stage as a regres-
sor along with value variable when the bid amount or excess
bid is the dependent variable.
This is implemented through “paramed” command in
Stata. “paramed” is one of the Stata commands to be devel-
oped for conducting causal mediation analysis that allows
for testing statistical significance of mediator (VanderWeele,
2016). Using this command, the causal effects are automat-
ically computed by the Stata program as a function of the
regression parameters as estimated from the above specified
two stage regressions.
RESULTS
In this section, we report the results of various analyses that
we conducted using implementation methods described in
the section above. We first report the results of construc-
tion of value variable, which is latent and unobserved, by
using 8 observed characteristics. This is then followed by
the presentation of results of hypotheses testing using the
three models described in the paper. These tests results are
presented for both, bid amount and Excess Bid being the
dependent variables.
Result of Construction of Value Variable
We conducted the analyses of 8 drivers of value, namely,
Surface area, Distance from nearest Railway Siding, Project
Affected People, Proportion of Forest Land in Mining
Lease, Stripping Ratio, GCV of coal, Mine Capacity, and
Geological Reserves. The following table, Table 2, presents
the correlation matrix of these items. The notable observa-
tion from the correlation matrix is that all the values are
less than 0.7, indicating that they are not highly correlated
and thus, none of these items can be rejected as redundant.
In economics literature, the cut-off level of 0.7 has been
indicative of low level of relationships between the variables
(Kandel, 1987). Having these items then in the scale serves
a purpose and does not lead to argument of redundancy.
This is in line with the technical assessment of the items as