Queen Mary University: BUSM112 Applied Empirical Methods Examination

This document presents a comprehensive solution to an applied empirical methods assignment, addressing key econometric concepts. The solution begins with an analysis of statistical significance in a regression model, identifying significant variables based on p-values. It then explores regression coefficients, including the interpretation of income and female coefficients. The assignment delves into heteroscedasticity and its correction methods. Furthermore, the solution covers the difference-in-difference method, outlining its equation, assumptions, and the role of the regression coefficient. Propensity score matching is discussed as an alternative to OLS, with logistic regression as a suitable approach. The assignment also explores multicollinearity, its impact on OLS coefficients, detection methods (correlation matrix, incorrect signs, instability, VIF), and correction strategies. Finally, the document addresses endogeneity, explaining the instrumental variables method, the characteristics of a good instrument, and tests for instrument validity (2SLS, GMM, F-statistic, J-Test). This assignment provides a thorough understanding of empirical methods used in economics.

Economics
Applied empirical methods
Ans 1)
a)
The variables which show low p – values are statistically significant at the 10 % significance
level. Here, income and _cons terms are significant.
b)
The regression coefficient of income has a value of 0.1010786
c)
The coefficient of female in this regression is 0.0234885
d)
Heteroscedasticity refers to a situation where a variable’s variability is not equal for a given
range of values for another variable which is used for its prediction. Variance can be used to
measure it.
The estimated values of variance and covariance for the OLS model can be corrected to make
them consistent. If this OLS regression suffered from Heteroscedasticity, then it can be
corrected by using any other estimator than the OLS estimator for the parameter estimation
for the model.
Ans 2)
a)
The equation is given by :
Y = b0 + b1 [t] + b2 [i] + b3 [t*i] + b4 [cv] + e

Here, t = time, i = intervention, cv = covariate
The regression coefficient measures the difference-in-difference impact is ‘b3’ which shows
the difference between any changes which time.
b) The assumptions to be met for the difference-in-difference method to yield unbiased
estimates of the impact of a policy on a treated group, when a policy has not been randomized
are : positivity, exchangeability and SUTVA ( Stable Unit Treatment Value Assumption ) or
absence of any spill over effect and parallel trend in the outcome. The difference between the
groups ( treating and controlling ) must not change w.r.t. time.
Ans 3)
The propensity score matching is used to estimate the probability of participating into a
policy. OLS is not most suitable regression because if random experiment is done, then for
every covariate it is assumed that the participating group will be balanced but it is not true
practically.
The regression which must be used is the logistic regression as it consists of 2 outcomes – 0
( for not participating ) and 1( for participating ) \.
Ans 4)
a) Multicolinearity in the OLS concept is seen amongst the various regressors. It follows
the assumptions of OLS. It shows big values of standard error, R – square value,
correlation for the coefficients estimated and variables which are independent.
It affects the validity of OLS coefficients. If a minor change is done in the model, the
coefficients show large sensitivity. The precision for the coefficients estimated
decreases. This makes the strength of the regression model in statistical terms very
small. The p – values of the statistically significant variables which are independent
cannot be relied upon.
Since, the design matrix becomes degenerated. Also, the there will be no possible outcome
with a unique solution for any linear algebra problem in the OLS. There are a lot of good
solutions.
.
b) Detection and correction for multicollinearity

Multicollinearity becomes a big problem since it increases the regression coefficients
variance and also make them difficult and at the same time unstable. The significance of one
variable that is independent on any of the dependent variable because there is a lot of
collinearity with other independent variable.
The various steps to detect and correct the multilinearity are :
First step would be to review the correlational matrix which is having a lot of scattered points
as a scatter plot. Since a scatter plot may show the type of relation between different
variables. This can be very easily detected. Next step would be to detect the incorrect signs
in the coefficients. If the signs go up or down then that indicate multicollinearity. Next
indication may be to check the instability of the different coefficients. And this can be
checked by running regression on different variables. Another step that is very commonly
used is to review the variance inflation factor. This measures the variance of regression
estimated as compared to predicted variable .
There a few steps that you may take to remove the multicolinearity. If you check the VIF is
high for more than two or more factors then the step should be to remove one of the factor.
The steps that you may take to remove these are best subset regression. Next step could be to
cut the predictors to smaller set use pls method.
Ans 5)
a) The instrumental variables method can be used to correct for endogeneity. If a regressor is
endogenous, it mean that it shows some correlation to the error term. To rectify this problem,
the instruments are found which show a correlation to the endogenous regressors and do not
show a correlation to the error term. Inorder to assess an instrument’s validity, the methods
used are : 2SLS (two-stage least square) and GMM ( generalized method of moments ).
b) Characteristics a good instrument to deal with endogeneity :
The instrument must easily separate variation in an independent variable that may be
endogeneous. That may also have some way to test on what endogeneity is in the data and the
solution must be a genuine one.
The tool must be easily able to find the appropriate instrument.

That should be rigour and transparent.
It should be able to test exogeneity and excludability.
c) Tests needed to empirically assess the validity of the instruments used :
An instrument is considered to be weak if it shows very less variance for the endogenous
regressor. The coefficients estimated using a weak instrument are not accurate. The
estimator’s distribution is not similar to the normal distribution for large samples also.
If there are n instruments and single endogenous regressor is employed, then if all the
coefficients for all instruments for TSLS estimate are equal to zero, then instrument is not
capable of explaining the variation in regressor. The methods used are : F- statistic
calculation and J – Test.