introductory econometrics exam memo

UNIVERSITY OF JOHANNESBURG

DEPARTMENT OF ECONOMICS AND ECONOMETRICS

JULY SUPPLEMENTARY EXAMINATION 2008

Course : Methods of Economic Investigation A (EKN03X7)Examiners : Mrs M Pretorius

Mrs AM Pretorius (Monash University)Time : 3 hours Marks : 125

Instructions:

1. Answer all the questions.2. This paper consists of 4 pages.3. An Excel sheet is provided with 4 sheets. The number of the question will

correspond with the Excel sheet name.

SECTION A [35]

1. Define the following econometric concepts:

a. Panel data (2)Data have both a time series and cross-sectional component.

b. Distributed lag model (2)When the value of the dependent variable at a given point in time should depend not only on the value of the explanatory variable at that time period, but also on values of the explanatory variable in the past.

c. Univariate time series analysis (2)Models that concentrate on only one series (dependent variable).

d. Stationarity (2)Stationary time series do not have a long memory but can exhibit trend behaviour through the incorporation of a deterministic trend.

e. Null hypothesis (2)A statement about the value of a parameter that is being tested.

Course: EKN03X7June examination 2008

f. Cointegration (2)If Y and X have unit roots but some linear combination of them is stationary then we can say the Y and X are cointegrated.

g. Spurious regression (2)If Y and X have unit roots then all the usual regression results might be misleading and incorrect.

h. Autoregressive Distributed lag model (2)The dependent variable in this model depends on p lags of itself, the current value of the explanatory variable, X, and q lags of X.

i. Multicollinearity (2)Problem that arises if some or all of the explanatory variables are highly correlated with each other.

j. Heteroskedasticity (2)When the error term in a model does not have a constant variance (which cause the t-stats to be misleading), is known as heteroskedasticity.

2. Give three reasons why dummy variables are usually utilised in econometric models. (3)To turn qualitative data into quantitative dataTo accommodate for structural breaksTo deseasonalize data

3. Give three reasons why it is necessary to include an error in an econometric model. (3)Measurement errorsTrue relationship probably more complicated so the straight line might just be an approximation.Important variable that might influence Y may be omitted.

4. Give a complete description of the steps used to select the optimal lag length in a distributed lag model. (4)Step 1: Choose the maximum possible lag length, , that seems reasonable to you.Step 2: Estimate the distributed lag model

If the p-value for testing = 0 is less than the significance level you

choose then go no further. Use as lag length. Otherwise go on to the next step.Step 3: Estimate the distributed lag model

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If the p-value for testing =0 is less than the significance level you

choose then go no further. Use as lag length. Otherwise go on to the next step.Step 4: Estimate the distributed lag model

If the p-value for testing = 0 is less than the significance level you

choose then go no further. Use as lag length. Otherwise go on to the next step, etc.

5. Name three factors that will influence the accuracy of the coefficients in a model. (3)Large number of data points.Less scattering / less variability in errorsMore variability in X

6. Give the conditions when the following models are stationary and when they are nonstationary:

a. (2)Stationary if and nonstationary if

Section B [12]

Data on the real effective exchange rate (REER) of South Africa is given. Use the data provided and answer the following questions.

1. What exactly is the real effective exchange rate? (2)The effective exchange rate is a weighted average rate which is derived by weighing the exchange rates between the rand and the main currencies, using the different countries’ shares in South Africa’s foreign trade as weights. Real means it has been adjusted for inflation.

2. Calculate and interpret the two measures of central tendency for the REER in South Africa. (4)

Mean = 110.21 - The average REER in the sample period was 110.21Median = 111.72 – The middle value if the values have been ordered from the smallest to the largest is 111.72Mode = N/A – There is no value that occurred the most in the sample period.

3. Calculate and interpret three measures of dispersion for the REER in South Africa. (6)

Variance = 151.39 – shows how dispersed the data is around the mean.Standard deviation = 12.30 – the square root of the variance.Range = 50.14 – the difference between the biggest and the smallest values.

SECTION C [25]

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Credit extended to the private sector is influenced by the Consumer Price Index (CPI), M3 money supply, the Prime lending rate as well as Vehicle sales (Veh_sales). Use the data provided in sheet “Section C” and answer the following questions:Dependent Variable: CREDITMethod: Least SquaresDate: 03/28/07 Time: 12:22Sample: 1995M01 2003M06Included observations: 102

Variable Coefficient Std. Error t-Statistic Prob.

C -193641.3 42855.69 -4.518450 0.0000CPI 6722.709 759.3509 8.853232 0.0000M3 0.268431 0.081776 3.282525 0.0014

PRIME -2145.710 578.3961 -3.709759 0.0003VEH_SALES -0.792994 0.387891 -2.044375 0.0436

R-squared 0.990744 Mean dependent var 499498.0Adjusted R-squared 0.990362 S.D. dependent var 142775.7S.E. of regression 14016.45 Akaike info criterion 21.98163Sum squared resid 1.91E+10 Schwarz criterion 22.11030Log likelihood -1116.063 F-statistic 2595.704Durbin-Watson stat 0.438932 Prob(F-statistic) 0.000000

1. Estimate the model and write down your regression. (2)Credit = -193641.3 + 6722.709CPI + 0.268431M3 – 2145.71Prime – 0.792994Veh_Sales

2. Interpret the coefficients of the model. (8)If CPI increases with 1 unit, Credit will increase with 6722.71 units, ceteris paribus.If M3 increases with 1 unit, Credit will increase with 0.27 units, ceteris paribus.If Prime increases with 1 unit, Credit will decrease with 2145.71 units, ceteris paribus.If Vehicle sales increase with 1 unit, Credit will decrease with 0.79 units, ceteris paribus.

3. Are the independent variables statistically significant? Explain by using an appropriate test for each. (4)H0: β = 0t-stats – Reject if t >2:CPI t = 8.85, Reject because t > 2, CPI is statistically significantM3 t = 3.28, Reject because t > 2, M3 is statistically significantPrime t = -3.71, Reject because absolute t > 2, Prime is statistically significantVehicle Sales t = -2.04, Reject because absolute t > 2, Vehicle sales is statistically significant

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p-values – Reject if p < 0.05:CPI p = 0, Reject because p < 0.05, CPI is statistically significantM3 p = 0.0014, Reject because p < 0.05, M3 is statistically significantPrime p = 0.0003, Reject because p < 0.05, Prime is statistically significantVehicle sales p = 0.0436, Reject because p < 0.05, Vehicle sales is statistically significant

4. Is this a good model? Explain and interpret by using a relevant measure.(3)

Adjusted R2 = 0.990362, this is a very good model seeing that the adjusted R2 is very close to 1. 99% of the variation in Credit is explained by CPI, M3, Prime and Vehicle Sales

5. Is this model overall significant? Explain and interpret by using the correct measure. (3)H0: β1 = β2 = β3 = β4 = 0Reject if p-value of F-stat < 0.05p = 0Therefore reject and conclude that the model is overall significant.

6. By looking at the regression do you suspect multicollinearity? Why or why not? (2)Multicollinearity is not suspected seeing that although we have a very high R2 value all the independent variables are statistically significant.

7. Use another method to determine whether multicollinearity is present in the model. State and interpret your results. (3)

CPI M3 PRIME VEH_SALESCPI 1.000000 0.992088 -0.493706 -0.223533M3 0.992088 1.000000 -0.506209 -0.197002

PRIME -0.493706 -0.506209 1.000000 -0.119157VEH_SALES -0.223533 -0.197002 -0.119157 1.000000

Multicollinearity is now expected seeing that there is a very high correlation between CPI and M3 money supply of 0.99.

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SECTION D [35]

The festive season (a dummy variable was created to represent this), personal disposable income (PDI) and the production price index (PPI) all influence retail trade in South Africa. Use the data in sheet “Section D” and answer the following questions:Dependent Variable: RETAILMethod: Least SquaresDate: 03/28/07 Time: 12:43Sample: 1998Q2 2006Q3Included observations: 34


C 52023.77 3755.385 13.85311 0.0000DUMMY 11154.45 853.5553 13.06823 0.0000

PDI 0.286604 0.026213 10.93373 0.0000PPI -412.6818 69.71964 -5.919161 0.0000

R-squared 0.940255 Mean dependent var 59870.38Adjusted R-squared 0.934281 S.D. dependent var 8199.612S.E. of regression 2102.033 Akaike info criterion 18.24933Sum squared resid 1.33E+08 Schwarz criterion 18.42890Log likelihood -306.2386 F-statistic 157.3787Durbin-Watson stat 0.897953 Prob(F-statistic) 0.000000

1. State the regression model. (2)Retail = 52023.77 + 11154.45Dummy + 0.286604PDI - 412.6818PPI

2. Interpret the coefficients of the model. (6)During the festive season, retail trade increases with 11154.45 units, ceteris paribus.If PDI increases with 1 unit, retail trade increases with 0.29 units, ceteris paribus.If PPI increases with 1 unit, retail trade decreases with 412.68 units, ceteris paribus.

3. State the regression model when South Africa is in the festive season. (2)Retail = 52023.77 + 11154.45(1) + 0.286604PDI – 412.6818PPI

= 63178.22 + 0.29 PDI – 412.68PPI

4. State the regression model when South Africa is not in the festive season.(2)

Retail = 52023.77 + 11154.45(0) + 0.286604PDI – 412.6818PPI= 52023.77 + 0.286604PDI – 412.6818PPI

5. Is there a significant difference between retail trade in the festive season and other seasons? Explain. (3)Yes there is seeing that the dummy variable is statistically significant (t = 13.07 which is > 2, therefore reject H0)

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6. Does the model make economic sense? Explain. (6)The dummy variable makes economic sense, during the festive season people usually spend more compared to other periods, increased spending will be reflected in increased retail trading.PDI also makes economic sense, if consumers’ income increases (and everything else stays constant) they will usually decide to spend more seeing that they have more money available. Increases spending will cause retail trade to increase as well.PPI also makes economic sense, if producer price inflation increases it means that it is more expensive to produce goods and the selling price of goods will therefore increase as well. Increased prices will cause people to buy less (seeing that goods are more expensive) and therefore retail trade will decrease.

7. Is there heteroscedasticity present in the model? Explain. (3)H0: No heteroskedasticityReject if p < 0.05

White Heteroskedasticity Test:

F-statistic 4.992238 Prob. F(5,28) 0.002155Obs*R-squared 16.02457 Prob. Chi-Square(5) 0.006774

Therefore we reject the H0 and conclude that there is heteroskedasticity present in the model.

8. Is there autocorrelation present in the model? Explain. (3)H0: No autocorrelationReject if p < 0.05

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 3.976553 Prob. F(2,28) 0.030193Obs*R-squared 7.521064 Prob. Chi-Square(2) 0.023271

Therefore we reject the H0 and conclude that there is autocorrelation present in the model.

9. What can you do in order to rectify the problems (if any) in 7 and 8? Apply it to the given model and give the new t-statistics for the variables. (4)Seeing that we have autocorrelation AND heteroskedasticity we have to apply the Newey-West method to the model. New t-stats:C - 9.419901Dummy - 18.05371PDI - 14.85578PPI - -5.914482

10.Use the model exactly as it is and add one lag of PDI to the regression. Report your results.

(2)

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Dependent Variable: RETAILMethod: Least SquaresDate: 03/28/07 Time: 13:02Sample (adjusted): 1998Q3 2006Q3Included observations: 33 after adjustmentsNewey-West HAC Standard Errors & Covariance (lag truncation=3)


C 50726.94 4548.255 11.15305 0.0000DUMMY 11338.30 710.5452 15.95718 0.0000

PDI 0.179246 0.024941 7.186651 0.0000PPI -412.1552 69.50072 -5.930229 0.0000

PDI(-1) 0.115716 0.037096 3.119349 0.0042

R-squared 0.962163 Mean dependent var 60000.76Adjusted R-squared 0.956758 S.D. dependent var 8290.881S.E. of regression 1724.064 Akaike info criterion 17.88148Sum squared resid 83227069 Schwarz criterion 18.10823Log likelihood -290.0445 F-statistic 178.0056Durbin-Watson stat 0.978364 Prob(F-statistic) 0.000000

Retail = 50726.94 + 11338.3Dummy + 0.179246PDI – 412.1552PPI + 0.115716PDI(-1)

11.Are you going to keep the lag in the regression model? Why or why not?(2)

Yes, seeing that it is statistically significant (t = 3.12 which is > 2)

SECTION E [8]

1. Use the data provided in “Section E” to determine whether there is a long term relationship between investment and the interest rate of South Africa. Show all your steps. (8)First we need to determine whether the variables contain unit roots:Investment:

Null Hypothesis: INV has a unit rootExogenous: ConstantLag Length: 1 (Automatic based on SIC, MAXLAG=11)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -1.689654 0.4332Test critical values: 1% level -3.502238

5% level -2.89287910% level -2.583553

*MacKinnon (1996) one-sided p-values.

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It seems that investment contains a unit root on the level. Next we test the first difference:

Null Hypothesis: D(INV) has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=11)

t-Statistic Prob.*


5% level -2.89287910% level -2.583553


Investment is integrated to the first order [I(1)]

Prime:

Null Hypothesis: PRIME has a unit rootExogenous: ConstantLag Length: 1 (Automatic based on SIC, MAXLAG=11)

t-Statistic Prob.*


5% level -2.89287910% level -2.583553


Prime is stationary on the level [I(0)].

Because the two variables are not integrated to the same order we can not go further and use the Engle-Granger test in order to test for cointegration.

There is therefore NOT a long term relationship between investment and prime.

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introductory econometrics exam memo

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