ANSWER ALL QUESTIONS ON THE EXAM PAPER AND SHOW FULL WORKING Question 1 Heteroskedasticity[10 marks] A researcher on the economics of innovation is interested in the country-level factors that...

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Answer To: ANSWER ALL QUESTIONS ON THE EXAM PAPER AND SHOW FULL WORKING Question 1 Heteroskedasticity[10...

Mohd answered on Jul 28 2021
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3305AFE APPLIED ECONOMETRICS FINAL EXAM
TRIMESTER 1 2021         WEIGHT 50%
ANSWER ALL QUESTIONS ON THE EXAM PAPER AND SHOW FULL WORKING
Question 1    Heteroskedasticity    [10 marks]
A researcher on the economics of innovation is interested in the country-level factors that predict R&D (Research and Development) investment. To study this, they take data on 27 OECD countries and regress R&D investment (as a percentage of GDP) against economic output (measured as the log of GDP), and educational attainments (the fraction of young people that have some tertiary education).
The following regression equation is used to model the relationship. Here y denotes the fraction of expenditure on R&D and and are the GDP and educational variables respectively.
The economist is worried that the error term from this model might be ‘heteroskedastic’. Give a brief definition/des
cription of heteroskedasticity and explain why it is a problem for regression models such as this.
A. Heteroskedastic refer to the condition in which standard deviation of error term of regression model is not constant. Its negatively impact performance of our regression model. We can explain his variability by one or more explanatory variable.
(2 marks)
A plot of the residual terms against the log of real GDP is given below in Figure 1. On the basis of this graph, what would you conclude about the error variance in your model? What problems would it raise for your estimation? Discuss.
Figure 1. Residuals Log GDP per Capita – R&D Model
(2 marks)
Suppose you feel that the error term of the stated model is heteroskedastic and has the structure
Perform a GLS transformation of the model such that the errors will be homoskedastic. State the transformed model.
(3 marks)
Prove theoretically that the errors from the transformed model will have a constant variance.
(3 marks)
Question 2    Autocorrelation    [8 marks]
A researcher studying energy markets is trying to produce a model for daily electricity prices () based upon daily temperatures (). A data set containing 201 observations is analyzed where prices are measured in cents per kilowatt-hour while temperatures are in degrees Celsius. The model below is estimated
where both variables are stationary.
The output from Eviews is given in Table 1.
Table 1. Eviews Output for Electricity Model
    Dependent Variable: PRICE
    
    
    Method: Least Squares
    
    
    
    
    
    Sample: 1 201
    
    
    
    Included observations: 201
    
    
    
    
    
    
    
    
    
    
    
    
    Variable
    Coefficient
    Std. Error
    t-Statistic
    Prob.
    
    
    
    
    
    
    
    
    
    
    C
    10.67810
    1.115281
    9.574360
    0.0000
    TEMP
    0.571329
    0.055512
    10.29205
    0.0000
    
    
    
    
    
    
    
    
    
    
    R-squared
    0.347383
        Mean dependent var
    22.05066
    Adjusted R-squared
    0.344104
        S.D. dependent var
    2.646967
    S.E. of regression
    2.143710
        Akaike info criterion
    4.372854
    Sum squared resid
    914.5033
        Schwarz criterion
    4.405722
    Log likelihood
    -437.4718
        Hannan-Quinn criter.
    4.386154
    F-statistic
    105.9263
        Durbin-Watson stat
    0.386975
    Prob(F-statistic)
    0.000000
    
    
    
    
    
    
    
    
    
    
    
    
    
To visualise the model the researcher also produces the following plot:
Figure 2. Residual, Actual and Fitted Series for Electricity Price Model
Note: Observation numbers ordered by time are given on the horizontal axis. The right vertical axis gives price and the left vertical axis gives the residual.
Based on Figure 2 comment briefly on the performance of the model. Are the standard errors reported in Table 1 likely to be correct? Why or why not?
We have different measure scale for both explanatory variable and response variable that could be significant cause behind autocorrelation. Yes, the standard errors are likely to be correct | P-value << 0.05.
(2 marks)
A Lagrange Multiplier (LM) test may be used to check for autocorrelation in the residuals of the model given in Table 1. The output of the test is given below in Table 2.
Table 2. Lagrange Multiplier Test for Autocorrelation – Electricity Price Model
    Breusch-Godfrey Serial Correlation LM Test:
    
    
    
    
    
    
    
    
    
    
    
    F-statistic
    167.8504
        Prob. F(2,197)
    0.0000
    Obs*R-squared
    126.6675
        Prob. Chi-Square(2)
    0.0000
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Test Equation:
    
    
    
    Dependent Variable: RESID
    
    
    Method: Least Squares
    
    
    
    
    
    Sample: 1 201
    
    
    
    Included observations: 201
    
    
    Presample missing value lagged residuals set to zero.
    
    
    
    
    
    
    
    
    
    
    Variable
    Coefficient
    Std. Error
    t-Statistic
    Prob.
    
    
    
    
    
    
    
    
    
    
    C
    -0.107613
    0.681878
    -0.157818
    0.8748
    TEMP
    0.005326
    0.033939
    0.156932
    0.8755
    RESID(-1)
    0.800328
    0.071299
    11.22498
    0.0000
    RESID(-2)
    -0.008061
    0.071390
    -0.112916
    0.9102
    
    
    
    
    
    
    
    
    
    
    R-squared
    0.630186
        Mean dependent var
    3.92E-15
    Adjusted R-squared
    0.624555
        S.D. dependent var
    2.138344
    S.E. of regression
    1.310240
        Akaike info criterion
    3.397998
    Sum squared resid
    338.1957
        Schwarz criterion
    3.463735
    Log likelihood
    -337.4988
        Hannan-Quinn criter.
    3.424598
    F-statistic
    111.9003
        Durbin-Watson stat
    1.939251
    Prob(F-statistic)
    0.000000
    
    
    
    
    
    
    
    
    
    
    
    
    
Give the test equation, the hypotheses, the test statistic and the appropriate p-value. What order of autocorrelation appears to be present in the residuals? Discuss.
The test rejects the hypothesis of no serial correlation up to order two. The Q-statistic and the LM test both indicate that the residuals are serially correlated and the equation should be re-specified before using it for hypothesis tests and forecasting. “The null hypothesis of the test is that there is no serial correlation in the residuals up to the specified order. EViews reports a statistic labelled “F-statistic” and an “Obs*R-squared” (the number of observations times the R-square) statistic. The statistic has an asymptotic distribution under the null hypothesis. The distribution of the F-statistic is not known, but is often used to conduct an informal test of the null.”
(2 marks)
Another test for autocorrelation in comes from the correlogram. The output is reported in Table 3.
Table 3. Correlogram Q-Statistics of Residuals – Electricity Price Model
Are the results of the correlogram consistent with the results from the LM test? Why or why not? Explain your answer.
A. The correlogram has spikes at lags up to eight and at lag twenty-eight. The Q-statistics are significant at all lags, indicating significant serial correlation in the residuals.
(2 marks)
Given the results of the LM test and the correlogram, how could the original equation
be modified to model the autocorrelation more effectively? Give equations for two alternative regression models that could potentially account for any autocorrelation that you have observed.
A. The Q-statistic and the LM test both indicate that the residuals are serially correlated and the equation should be re-specified before using it for hypothesis tests and forecasting.
(2 marks)
Question 3    Dummy Variables    [8 marks]
A political scientist is interested in the factors that influence voter preferences. To model the effect of various characteristics of US political candidates upon polling performance, the following equation can be estimated
where is the candidate’s vote share, is the candidate’s age, is the budget of the campaign and is the number of endorsements the candidate received.
The political scientist feels that there may be structural differences in the regression equations for candidates that do and do not have advanced degrees. Let D denote a dummy variable that is equal to zero if the candidate does not have an advanced degree; and one if the candidate does have an advanced degree.
Help the political scientist by showing the procedure used to conduct the Chow test. Give the unrestricted and restricted models and the null and alternative hypotheses. What conclusion should the political scientist draw if the null hypothesis is rejected?
A. As a matter of course the Chow breakpoint test tests whether there is a primary change in the entirety of the condition boundaries. In any case if the condition is direct EViews permits you to test whether there has been a primary change in a subset of the boundaries.
B. We partition the information into at least two subsamples. Each subsample should contain a larger number of perceptions than the quantity of coefficients in the condition so the condition can be assessed. The Chow breakpoint test...
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