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ECS4863 Assignment 1 Memo | Due 16 May 2025. All questions fully answered. Question 1: (15 marks)
1.1 Explain the concept of omitted variable bias and distinguish between positive and
negative bias ( 4)
1.2 Explain in your own words how you test serial correlation with strictly exogenous
variables (3)
1.3 Explain, in your own words, the concept of heteroscedasticity and implications for
inferences in econometrics (4)
1.4 Explain in your own words what is meant by the following: (4)
a) Covariance stationary process
b) Sequential exogeneity
Question 2: (5 marks)
In this question you need to gather and analyze time series data for a country (other than South
Africa!) (5)
1. Select any country which starts with the same letter as your surname (if you
cannot find one, use the first letter of your name)
2. Now choose any macroeconomic variable from that country (e.g. inflation, GDP,
imports/exports, etc.)
3. Data source: you can use any data source (e.g. World Bank, IMF, country specific
central banks, etc.)
Your time series must have at least 60 observations.
You may use any interval, (e.g. quarterly, monthly)
It can be nominal or real data.
Make sure to provide (at least) the following:
– Your surname (or name)
– The name of the country and time series you chose.
– A graph of the data
– A stationarity test and interpretation
Question 3: (55 marks)
In this question, you must estimate a time series model for consumer prices in South Africa
using data in the Excel file ECS4863.xls . You are provided with the following data:
Variable names and descriptions:
SA_CPI = South African headline consumer price index (all urban areas)
EXCH= South African rand per euro
Rand = South African rand per US dollar
OIL = Brent crude oil in South African rand per barrel
M3 = South African money supply in million rands
EU_CPI = Euro area Harmonised consumer price index
US_CPI = United States of America consumer price index
NB, Log transform all the variables. ‘L’ indicates the logarithmic function is used.
3.1 Use the data to calculate the annual consumer price inflation and annual South Africa
per Euro exchange rate growth. [ N.B Calculate the month-on-same-month of the
previous year (i.e. 12 months) inflation and growth rate]. Plot both series in a scatterplot
and comment on the relationship. Perform the Ganger causality test and interpret the
results. Find the correlation coefficient between the series and determine if it is
statistically significant (6)
3.2 Test the variables LOIL, LEXCH, and LEU_CPI for stationarity (transform all applicable
variables). Also comment on their respective orders of integration. Provide your results
in the table below (please add rows where necessary):
Variable Model Lags ADF test Conclusion
statistic
LOIL Trend &
Intercept
Intercept
None
LEU_CPI Trend
&Intercept
Intercept
None
LEXCH Trend &
Intercept
Intercept
None
Statistically significant at the: 10% level (*), 5% level (**), 1 % level (***)
You can assume that all other variables are non-stationary, integrated of order 1(1).
3.3 Test for possible cointegration between variables:
(i) Estimate the following long-run cointegration equation using OLS. Copy and paste your
EViews results window in your answer sheet. (1)
LSA_CPlt = Po+ P1LEXCHt + P2LOILt + P3LEU_CPlt + P4LM3t + μt ……. ( 1)
(ii) What are your apriori expectations in terms of sign? (4)
(iii) Interpret the estimated coefficients in equation (1). (4)
(iv) Determine the hypothesis of complete exchange rate and euro area consumer price
passthrough to the South African consumer price index, that is, p1 = 1 and p3 = 1 (4)
(v) Determine whether LM3 and LEU_CPI are redundant variables in equation (1). (4)
(vi) Determine whether LUS_CPI and LRAND are omitted variables in the model (4)
(vii)Generate the residual series for your long-run equation and determine if cointegration
exists between the variables in the long-run model. (3)
3.4 Construct a short-run (Error Correction) component for your model.
llLSA_CPlt = Po+ P1llLSA_CPlt-l + P2llLOILt + P3llLOILt-l + P4llLEU_CPlt + P5llLM3t-i +
P6llLEXCHt-i + P7Residualt-i + Et …………. (2)
(i) Estimate the short-run cointegration equation. Copy and paste your EViews results
window in your answer sheet. (1)
(ii) Interpret the coefficients p1 to P7 of the short-run model. (7)
(iii) Perform the required diagnostic and stability tests on the residuals of the Error Correction
Model given by equation (2). Interpret the test results and make conclusions. (8)
a) Jarque-Bera
b) Breusch Godfrey LM TEST
c) Glejser test
d) Ramsey RESET
[Total = 75 marks]
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