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Basic Econometrics Individual Assignment   This is an individual assignment where you must work alone

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Basic Econometrics

Individual Assignment

 

This is an individual assignment where you must work alone.  You must submit an electronic copy of your assignment in Canvas in pdf, doc or docx format along with your R-code.  Hard copies will not be accepted. Show your calculations (if any) as well as answering the questions in clear full sentences.  Log referrers to natural logarithm!

 

Use the dataset: WDI_2310.RData

 

Use R to run a cross sectional regression on GDP per capita for the listed countries as follows:

 

Ln(GDPpc) =  β0+β1lnConspc+ β2Trade+β3Alco+β4Popgr+u

 

 

The variables are defined as follows:

GDPpc = GDP per capita, PPP (current international $)

Conspc = Households and NPISHs final consumption expenditure per capita (constant 2015 US$) [NE.CON.PRVT.PC.KD]

Trade = Trade (% of GDP) [NE.TRD.GNFS.ZS]

Alco = Total alcohol consumption per capita (liters of pure alcohol, 15+ years of age) [SH.ALC.PCAP.LI]

Popgr = Population growth (annual %) [SP.POP.GROW]

 

You will have to take the natural log of GDPpc and Consumption per capita yourself using R!

 

 

1. Present your regression results in a table below (R output):

5 marks

 

2. Interpret the constant (2.5 marks) and its p-value (1.5 marks).                                         

4 marks

 

 

3. Interpret the coefficient on household and NPISH consumption and its p-value (1.5 marks each).

3 marks

 

 

4. Interpret the coefficient on trade and its p-value (1.5 marks each). Hint: Use a large change for trade, such as a “10% point” change for example.

3 marks

 

5. Interpret the coefficient on alcohol consumption and carry out (meaning: calculate with the official formula) a t-test to determine the significance of the coefficient (1.5 marks each).

3 marks

5. 1.  
6. Interpret the R² of the regression.

2 marks

 

 

 

7. Run the regression in Q1 with an additional independent variable, the quadratic form of  “Popgr”.

 

Ln(GDPpc) =  β0+β1lnConspc+ β2Trade+β3Alco+β4Popgr+β5Popgr2+ u

 

 

Explain if adding Popgr2

 is a good idea or not.  (1 mark)

 

 

Interpret whether the relationship between Ln(GDPpc) and Popgr it is U-shaped or inverted U-shaped in Q7. (2 marks)

 

Interpret the impact of population growth on the GDP per capita in Q7 when population growth is 3%. (3 marks)

6 marks

 

 

8. Run the following regression:

Ln(GDPpc) =  β0+β1Alco+

u

 

 

Comment on how the coefficient on “Alco” differs from that of Q1! (1 mark)

Why do you observe this difference and what does it mean for the (un)biasedness of the coefficient in Q8?  (2 mark)

3 marks

 

 

9. Describe each of the Gauss Markov Assumptions (2.5 marks) and specifically explain if they are likely to hold for the regression in Q1 or not (2.5 marks).

5 marks

 

10. Present a functioning R code reproducing the results.                                           

6 marks

 

 

 

 

Assignment Total: 40 marks

 

FORMULA SHEET

 

 

Critical values for the standard normal distribution (z)

 

Confidence level (1-α)	Level of Significance (α)	Two–Sided Critical Value cα/2	One-Sided, Upper-Tail Critical Value cα	One-Sided, Lower-Tail Critical Value -cα
90%	10%	1.645	1.28	-1.28
95%	5%	1.96	1.645	-1.645
99%	1%	2.58	2.33	-2.33

 

 

Formula for a t-statistic

 

t =estimate-hypothesised valuestandard error

 

 

 

Formula for a (1-α)% confidence interval

CI1-α=β-cα/2*seβ, β+cα/2*seβ

 

 

Logarithmic/Quadratic/Interaction specifications

 

For the model logy=β0+β1x1+β2x2

, the exact effect of a change in explanatory variable x₂ is:

 

%?y=100expβ2?x2-1

 

 

 

For a quadratic specification of the form:

y=β0+β1x+β2x2+u

 

 

 

The turning point (maximum/minimum) is given by:

x*=β1/(2β2)

 

 

The approximation of the marginal effect of x on y is given by:

?y?x≈β1+2β2x

 

 

For a interaction specification of the form:

y=β0+β1x1+β2x1*x2+u

 

 

The approximation of the marginal effect of x₁ on y is given by: ?y?x1≈β1+β2x2

 

Basic Econometrics

Individual Assignment

 

This is an individual assignment where you must work alone.  You must submit an electronic copy of your assignment in Canvas in pdf, doc or docx format along with your R-code.  Hard copies will not be accepted. Show your calculations (if any) as well as answering the questions in clear full sentences.  Log referrers to natural logarithm!

 

Use the dataset: WDI_2310.RData

 

Use R to run a cross sectional regression on GDP per capita for the listed countries as follows:

 

Ln(GDPpc) =  β0+β1lnConspc+ β2Trade+β3Alco+β4Popgr+u

 

 

The variables are defined as follows:

GDPpc = GDP per capita, PPP (current international $)

Conspc = Households and NPISHs final consumption expenditure per capita (constant 2015 US$) [NE.CON.PRVT.PC.KD]

Trade = Trade (% of GDP) [NE.TRD.GNFS.ZS]

Alco = Total alcohol consumption per capita (liters of pure alcohol, 15+ years of age) [SH.ALC.PCAP.LI]

Popgr = Population growth (annual %) [SP.POP.GROW]

 

You will have to take the natural log of GDPpc and Consumption per capita yourself using R!

 

 

1. Present your regression results in a table below (R output):

5 marks

 

2. Interpret the constant (2.5 marks) and its p-value (1.5 marks).                                         

4 marks

 

 

3. Interpret the coefficient on household and NPISH consumption and its p-value (1.5 marks each).

3 marks

 

 

4. Interpret the coefficient on trade and its p-value (1.5 marks each). Hint: Use a large change for trade, such as a “10% point” change for example.

3 marks

 

5. Interpret the coefficient on alcohol consumption and carry out (meaning: calculate with the official formula) a t-test to determine the significance of the coefficient (1.5 marks each).

3 marks

5. 1.  
6. Interpret the R² of the regression.

2 marks

 

 

 

7. Run the regression in Q1 with an additional independent variable, the quadratic form of  “Popgr”.

 

Ln(GDPpc) =  β0+β1lnConspc+ β2Trade+β3Alco+β4Popgr+β5Popgr2+ u

 

 

Explain if adding Popgr2

 is a good idea or not.  (1 mark)

 

 

Interpret whether the relationship between Ln(GDPpc) and Popgr it is U-shaped or inverted U-shaped in Q7. (2 marks)

 

Interpret the impact of population growth on the GDP per capita in Q7 when population growth is 3%. (3 marks)

6 marks

 

 

8. Run the following regression:

Ln(GDPpc) =  β0+β1Alco+

u

 

 

Comment on how the coefficient on “Alco” differs from that of Q1! (1 mark)

Why do you observe this difference and what does it mean for the (un)biasedness of the coefficient in Q8?  (2 mark)

3 marks

 

 

9. Describe each of the Gauss Markov Assumptions (2.5 marks) and specifically explain if they are likely to hold for the regression in Q1 or not (2.5 marks).

5 marks

 

10. Present a functioning R code reproducing the results.                                           

6 marks

 

 

 

 

Assignment Total: 40 marks

 

FORMULA SHEET

 

 

Critical values for the standard normal distribution (z)

 

Confidence level (1-α)	Level of Significance (α)	Two–Sided Critical Value cα/2	One-Sided, Upper-Tail Critical Value cα	One-Sided, Lower-Tail Critical Value -cα
90%	10%	1.645	1.28	-1.28
95%	5%	1.96	1.645	-1.645
99%	1%	2.58	2.33	-2.33

 

 

Formula for a t-statistic

 

t =estimate-hypothesised valuestandard error

 

 

 

Formula for a (1-α)% confidence interval

CI1-α=β-cα/2*seβ, β+cα/2*seβ

 

 

Logarithmic/Quadratic/Interaction specifications

 

For the model logy=β0+β1x1+β2x2

, the exact effect of a change in explanatory variable x₂ is:

 

%?y=100expβ2?x2-1

 

 

 

For a quadratic specification of the form:

y=β0+β1x+β2x2+u

 

 

 

The turning point (maximum/minimum) is given by:

x*=β1/(2β2)

 

 

The approximation of the marginal effect of x on y is given by:

?y?x≈β1+2β2x

 

 

For a interaction specification of the form:

y=β0+β1x1+β2x1*x2+u

 

 

The approximation of the marginal effect of x₁ on y is given by: ?y?x1≈β1+β2x2