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Leeds University
Business School
Assessed Coursework Coversheet
For use with individual assessed work
Student Identification Number:
Module Code: LUBS5108M01
Module Title: Applied Econometrics
Module Leader: Kausik Chaudhuri
Declared Word Count: 1497
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Applied Econometrics: Project 5
Introduction
Using data from the last two waves of the British Household Panel Survey: this project analyses
results from a produced panel data-set consisting of a cross-sectional unit with added regional
dummies. The aim is thus to determine the influence certain factors have on individuals’ job
satisfaction where total pay represents our dependent variable, jbsat2x.
A Random Effects (RE) and Fixed Effects (FE) model were initially performed, holding the
assumption of uncorrelated and correlated individual-specific effects on the independent
variables respectively, with a subsequent Hausman test to compare the previously stored results.
The null hypothesis for such a test is that the Re and Fe are asymptotically equivalent given
exogenous unobserved effects:
𝐻0 ∶ β̂ 𝑅𝐸 = β̂ 𝐹𝐸
Note the standardized coefficient vectors represent the time-varying explanatory variables,
excluding the time variables (McManus, 2011, p.36).
The test results (see Appendix 1) elucidate a significant difference between the results: with a
chi2 of 40.90 and a Prob>chi2 value significant at the 0.05 level (0.0006), thus we reject the null
hypothesis. It can therefore be inferred that the RE model is inconsistent, and hence the FE
model is preferred.
Despite FE being preferred there are some noteworthy drawbacks to the model which need to be
discussed before advancing, as clarified by McManus (2011, p.19); firstly, time-varying
unobserved effects and time-varying measurement error can still exist, and therefore the method
is not a solution for all sources of endogeneity bias. Secondly, as all time-constant effects are
omitted there can be no estimation of effects for gender and race, along with vague estimates
given minor variations in the dataset such as an individual’s education in adulthood. Lastly, the
model ignores between-unit variation and opts to use only within-unit change, whilst allowing for
greater standard errors and an incorrect estimation of the 𝑅2
statistic.
In response to some of these drawbacks; the data used in this project consists of two waves,
(Wave 17 and Wave 18) with many entities, as opposed to numerous waves and limited entities,
thus it can assumed that although not controlling completely of endogeneity bias, time-varying
causes are restricted to a high degree. To attain the correct estimation for the 𝑅2
statistic in the
FE model, an areg function was computed into STATA, resulting in a value of 0.8201 (see
Appendix 2). Thus we can say that 82% of the variance in jbsat2x can be explained by the
independent variables, a relatively high percentage for a model of this type.
Microeconometric datasets used in panels are likely to display cross-sectional correlation and
sequential patterns: thus overlooking, or failing to control for heteroscedasticity could lead to
biased statistical implications. Justifiably the need for a robust estimation of the standard errors
in our FE model is needed, which is attainable in STATA with the command addition of variance-
covariance matrix of estimators - (vce)robust.
The ordering of the explanatory variables in the model allows for control over a base category in
which we can compare the other variable coefficients in that division to. For the purpose of this
project, the controlled variables dropped are: neduc, mastatd6, fisitcd3, fisitxd3, and reg1x, with
the last variable representing London from our regional dummy variables included. Additionally,
male, reg6, reg11x, and reg12x were all omitted due to collinearity.

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Analysis:
For relevant analysis purposes, only variables which have a significant influence on the
dependent variable will be considered, or more precisely, the variables in which we reject the null
hypothesis (𝐻0) that the coefficient is significantly different from 0 for the corresponding p-value
lower than 0.05. The correlation between errors u_i and the regressors in the fixed effects model
is given as -0.8552 or -85.52% (see Appendix 3 for full data page).
With or without the vce(robust) option, the estimated coefficients remained the same, however a
difference occurred with larger standard errors across the model and slightly differing p-values,
although the difference was minimal enough for the significant variables to remain significant in
both approaches. The F-test is also effected in the cluster robust model, whereby the value is
unreported due to the problematic nature in computing the statistic, it could be that the number of
clusters are too small to support the number of predictors in the model, or perhaps that one or
more of the clusters for one of the variables has no variation.
Despite running the model various times with a different base variable in regards to the
educational category, we fail to reject the 𝐻0 due to large corresponding p-values in each case.
This indicates that the estimations are of little significance to us at the 0.05 or even 0.1 level,
The rho value, or intraclass correlation, of 0.8686 is automatically calculated via the following
formula:
(𝑠𝑖𝑔𝑚𝑎_𝑢)2
(𝑠𝑖𝑔𝑚𝑎_𝑢)2 + (𝑠𝑖𝑔𝑚𝑎_𝑒)2
Where rho represents the correlation of the observations in a cluster, we can infer that 86.9% of
the variance is due to differences across panels. This is an extremely high percentage, and
therefore the less unique any additional information is for each individual in the cluster.
Mastatd1: p-value = 0.035 < 0.05
With a coefficient value of 0.63636, we can infer that a married individual is 63.6% more likely to
be satisfied with his or hers total pay compared to an individual who never married, with regards
to the other six variable categories. The rationale behind such a percentage could be due to the
income from the individuals’ partner whereby they’re jointly comfortable with their finances,
however this insinuates correlation with an unobserved absent variable. Thus the more logical
reasoning behind the percentage value could be due to personal satisfaction with their partner as
opposed to material possessions for an unmarried person. Note: these assumptions are clearly
speculative and do not represent any empirical findings.
Fisitcd1: p-value = 0.005 < 0.05
In regards to a change in an individual’s financial situation compared to the previous year, with a
coefficient value of 0.13396 we can infer that an individual who is financially better off is 13.4%
more likely to be satisfied with their total pay compared to an individual whose financial situation
is about the same as the previous year, with regards to the other six variable categories.
Although it would be easy to hypothesise this percentage to be extremely high, the variable is
unable to elaborate the measureable extent in which an individual’s financial situation is better
off, and therefore it could be any additional amount. Furthermore the source of an increase in
finances is unstipulated and could be unrelated to an individuals’ total pay from employment,
hence the relatively low percentage in regards to satisfaction for total pay.

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Fisitcd2: p-value = 0.000 < 0.05
Similarly as before, in regards to a change in an individual’s financial situation compared to the
previous year, with a coefficient value of -0.23420 we can infer that an individual is 23.4% less
likely to be satisfied with their total pay when they’re worse off compared to an individual who is
about the same in the previous year, with regards to the other six variable categories. The
absolute coefficient from this variable was expected to be higher than fisitcd1 as being financially
worse off than the previous year would directly cause a decrease in satisfaction regardless of the
circumstances for the individual, and hence more liability would be directed at an individuals’ total
pay value.
Reg7x: p-value = 0.009 < 0.05
With a coefficient value of 2.30788, we can infer that an individual residing in the North-West of
the UK is 2.3 times more likely to be satisfied with their total pay compared to an individual who
lives in London, with regards to the other six variable categories.
Reg8x: p-value = 0.000 < 0.05
With a coefficient value of 4.61463, we can infer that an individual living in Yorkshire and the
Humber is 4.6 times more likely to be satisfied with their total pay compared to an individual who
lives in London, with regards to the other six variable categories.
Reg9x: p-value = 0.002 < 0.05
With a coefficient value of 2.80599, we can infer that an individual who lives in the North-East of
the UK is 2.8 times more likely to be satisfied with their total pay compared to an individual who
lives in London, with regards to the other six variable categories.
Reg10x: p-value = 0.000 < 0.05
With a coefficient value of 4.61185, we can infer that an individual situated in Wales is 4.6 times
more likely to be satisfied with their total pay compared to an individual who lives in London, with
regards to the other six variable categories.
Collectively reporting on the significant regional dummies is simplified due to the results, whereby
individuals residing outside of London are at least more than two times likely to be satisfied with
their total pay as opposed to living in the capital. The foremost rational behind such a result can
be postulated towards the living costs which are at their highest when living in the capital of
England, and cheaper as you move further north of the country.

5. 5
Reference List
McManus, P.A. 2011. Introduction to Regression Models for Panel Data Analysis. [Online].
[Accessed 14th May 2016]. Available from:
http://www.indiana.edu/~wim/docs/10_7_2011_slides.pdf.
Appendices
Appendix 1:
Appendix 2:
Appendix 3: (on next page for easier viewing)

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