ECN6540 ECONOMETRIC METHODS – COURSEWORK 2022
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The answers to the questions must be type-written. The preference is that
symbols and equations should be inserted into the document using the
equation editor in Word. Alternatively, they can be scanned and inserted as an
image (providing it is clear and readable). Maximum words 1,500 excluding any
Stata output and commands.
The coursework comprises two questions where the second is a short Stata
assignment. Both questions 1 and 2 carry equal weight and the marks shown
within each question indicate the weighting given to component sections. Any
calculations must show all workings otherwise full marks will not be awarded.
YOU MUST USE A TURNITIN SUBMISSION TEMPLATE – SEE INFORMATION ON
BLACKBOARD UNDER ASSESSMENT INFORMATION/TURNITIN SUBMISSION.
PLEASE WRITE YOUR STUDENT REGISTRATION NUMBER IN THE
SUBMISSION TITLE BOX.
ANSWER ALL QUESTIONS SET.
In the following regression model 𝑌𝑖 = 𝛽0 + 𝛽1𝑋1𝑖 + 𝛽2𝑋2𝑖 + 𝑖
(where 𝑖 denotes the unit of observation) under the scenario that
the two independent variables 𝑋1 and 𝑋2 are highly collinear:
i) provide an algebraic expression for the correlation coefficient
between the two independent variables;
ii) explain, using the appropriate formula, the effect of high
collinearity on the standard errors of the parameter estimates
and on the t-statistics.
The following sums were obtained from a sample of 240 time series
observations (i.e. 𝑡=1,2,…,240) on the variables 𝑌 and 𝑋.
∑ 𝑌𝑡 = 144, ∑ 𝑋𝑡 = 216, ∑ 𝑌𝑡
2 = 888, ∑ 𝑋𝑡
2 = 2160, ∑ 𝑋𝑡𝑌𝑡 = 1080
i) Calculate the least squares estimates of the intercept and
slope parameters in the regression model: 𝑌𝑡 = 𝛽0 + 𝛽1𝑋𝑡 + 𝑡
ii) Briefly explain the assumption of no autocorrelation in the
context of the error term 𝑡.
iii) Explain the consequences of corr(𝑋𝑡, 𝑡) ≠ 0.
Using Chinese data over the period 2006 quarter 1 to 2012 quarter
4 sales are modelled as a function of lagged sales, disposable
income, consumer confidence, and seasonal effects:
𝑠𝑎𝑙𝑒𝑠𝑡 = 𝛽0 + 𝛽1𝑠𝑎𝑙𝑒𝑠𝑡−1 + 𝛽2log(𝑌)𝑡 + 𝛽3 (
Variable Definitions
sales = nominal sales (in ¥ million)
log(Y) = Natural logarithm of nominal income
recip_cc = 1 [consumer confidence, cc] (%)
d2 = 1 if second quarter of year; 0 otherwise
d3 = 1 if third quarter of year; 0 otherwise
d4 = 1 if fourth quarter of year; 0 otherwise
After undertaking auxiliary regressions the following ANOVA
results were obtained in Stata. ‘L’ denotes the lag operator.
regress L.sales logY recip_cc d2 d3 d4
Source | SS df MS
————-+———————————-
Model | 10605.7128 5 2121.14256
Residual | 1884.14964 21 89.7214112
————-+———————————-
Total | 12489.8624 26 480.379324
[15 marks]
regress logY L.sales recip_cc d2 d3 d4
Source | SS df MS
————-+———————————-
Model | .05355609 5 .010711218
Residual | .048758535 21 .002321835
————-+———————————-
Total | .102314625 26 .003935178
regress recip_cc L.sales logY d2 d3 d4
Source | SS df MS
————-+———————————-
Model | .000022717 5 4.5435e-06
Residual | .000022837 21 1.0875e-06
————-+———————————-
Total | .000045554 26 1.7521e-06
Calculate the R-squared and the variance inflation factor (VIF)
associated with each auxiliary regression. Discuss the implications
of the value of the VIFs for OLS analysis and potential solutions.
The following Stata output shows the results of estimating the
model from part (c) and sample means of continuous variables.
i) Calculate the slope and elasticity associated with income and
consumer confidence, based at the sample mean.
ii) Explain why a reciprocal functional form is used.
iii) What does the estimate on the lagged dependent variable
iv) Test for autocorrelation at the 5% level.
v) Interpret the seasonal (quarterly) effects. Rewrite the model
in part (c) to allow for a concurrent regression and explain in
detail how this could be tested.
regress sales L.sales logY recip_cc d2 d3 d4
Source | SS df MS
————-+———————————-
Model | 11816.1851 6 1969.36419
Residual | 1195.78871 20 59.7894355
————-+———————————-
Total | 13011.9738 26 500.460532
——————————————————
sales | Coefficient Std. err. t P>|t|
————-+—————————————-
L1. | .220576 .1781372 1.24
logY | 98.99456 35.01764 2.83 0.010
recip_cc | -4616.62 1618.058 -2.85 0.010
d2 | 23.94257 10.42623 2.30 0.033
d3 | 32.59669 8.305721 3.92 0.001
d4 | 63.50859 6.105048 10.40 0.000
_cons | -371.7605 144.322 -2.58 0.018
——————————————————
Durbin–Watson d-statistic( 7, 27) = 1.929705
[10 marks]
[10 marks]
[20 marks]
[15 marks]
sum sales L.sales logY cc recip_cc
Variable | Obs Mean Std. dev.
————-+————————————
–. | 28 98.12636 23.61535
L1. | 27 96.28344 21.91756
logY | 28 4.532284 .0645629
cc | 28 160.7179 26.71612
recip_cc | 28 .0064294 .0013157
STATA ASSIGNMENT
2. The following data set “wages.dta” is cross sectional based upon
2,220 individuals in 2020 from the U.S. The variables in the data are:
wage = hourly wage rate in cents
educ = years of schooling of the individual
fatheduc = father’s years of schooling
motheduc = mother’s years of schooling
black = dummy variable (0 white, 1 black)
IQ = Intelligence score
married = dummy variable (0 unmarried, 1 married)
exper = years of labour market experience
Load the data into Stata. Then type the following commands:
set seed 200212232
replace wage=wage*abs(rnormal(0,1))
where the number after “set seed” is your student registration number e.g.
200212232 (this ensures that each student has unique data). Next save your data
as “ECN6540_Assignment_mydata.dta”. It is important that you work with this
file if you close and reopen Stata at a later date.
a. Load your unique data from the file “ECN6540_Assignment_mydata.dta”.
Using a semi log wage specification estimate a wage equation where YOU
choose the independent variables BUT THESE MUST include, “black”,
“married”, “educ”, “fatheduc” and “motheduc” at a minimum. [5 marks]
b. Interpret the estimated parameters of your model. [10 marks]
c. Test whether the individual parameters estimated are individually statistically
significant and jointly statistically significant BY HAND and then compare with
the Stata output. [15 marks]
d. Test your estimated model for heteroscedasticity using the WHITE test BY
HAND (without using any inbuilt Stata test commands). [20 marks]
e. Use tsset id in order to set “id” as the time series identifier (although note
that the data is cross sectional). Test whether the model estimated in part (a)
exhibits auto correlation at the 5% level. What does this result imply? [5 marks]
f. Test whether the parameters associated with “fatheduc” and “motheduc” in
part (a) are equal to unity at the 5% level BY HAND (without using any inbuilt
Stata test commands). Use Stata to construct the appropriate RSS. [15 marks]
g. Using your initial model from part (a) test whether “black” and “married”
individuals exhibit different returns to education (“educ”) at the 1% level BY
HAND (without using any inbuilt Stata test commands). Use Stata to construct
the appropriate RSS. [20 marks]
h. At the end of your document provide the text from your Stata *.do file.
[10 marks]
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