Applied Econometrics 4th Edition Dimitrios Asteriou, Stephen G. Hall - Solutions

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Show how to detect possible multicollinearity in a regression model?
Explain what the VIF is and its use.
From Chapter 4 we know that βˆ = (XX)−1(XY). What happens to βˆ when there is perfect collinearity among the Xs? How would you know if perfect collinearity exists?
In the following model:Y = β1 + β2X2 + β3X3 + β4X4 + ut assume that X4 is a perfect linear combination of X2. Show that in this case it is impossible to obtain OLS estimates.
Define multicollinearity and explain its consequences in simple OLS estimates.
The file Cobb_Douglas_us.wf1 contains data for output (Y), labour (L) and stock of capital (K) for the United States. Estimate a Cobb–Douglas type regression equation and check for constant returns to scale using the Wald test.
Use the data in the file money_uk.wf1 to estimate the parameters α, β and γ in the equation below:ln(M/P)t = a + β ln Yt + γ ln Rt + ut(a) Briefly outline the theory behind the aggregate demand for money. Relate your discussion to the specification of the equation given above. In particular,
Use the data from the file wage.wf1 and estimate an equation that includes as determinants of the logarithm of the wage rate the variables, educ, exper and tenure.(a) Comment on your results.(b) Conduct a test of whether another year of general workforce experience (captured by exper) has the same
The file health.xls contains data for the following variables: birth_weight = the weight of infants after birth; when low this can put an infant at risk of illness; cig = number of cigarettes the mother was smoking during pregnancy; and fam_inc = the income of the family; the higher the family
Write down a regression equation and show how you can test whether one of the explanatory variables is redundant.
Describe the steps involved in performing the Wald test for linear restrictions.
Show how one can test for constant returns to scale for the following Cobb–Douglas type production function:Q = ALaKβwhere Q is output, L denotes labour units, K is capital and A is an exogenous technology parameter.
Prove that the OLS estimates for the k explanatory variables case are BLU estimators.
Derive the OLS solutions for βˆ for the k explanatory variables case using matrix algebra.
The file salaries_01.wf1 contains data for senior officers from a number of UK firms. The variable salary is the salary that each officer gets, measured in thousands of pounds.The variable years_senior measures the number of years they have been senior officers, and the variable years_comp measures
Obtain time series data on real business fixed investment (I) and an appropriate rate of interest (r). Consider the following population regression function:It = α0 + α1rt + et(a) What are the expected signs of the coefficients in this equation?(b) Explain your reasoning in each case.(c) How can
The following equation has been estimated by OLS:Rˆt = 0.567 + 1.045Rmt n = 250(0.33) (0.066)where Rt and Rmt denote the excess return of a stock and the excess return of the market index for the London Stock Exchange.(a) Derive a 95% confidence interval for each coefficient.(b) Are these
Obtain annual data for the inflation rate and the unemployment rate of a country.(a) Estimate the following regression, which is known as the Phillips curve:πt = a0 + a1UNEMPt + ut where πt is inflation and UNEMPt is unemployment. Present the results in the usual way.(b) Estimate the alternative
In the Keynesian consumption function:Ct = a + δYd tthe estimated marginal propensity to consume is δˆ, and the average propensity to consume is C/Yd = aˆ/Yd + δˆ. Using data on annual income and consumption (both of which were measured in £ sterling) from 200 UK households we found the
The table below shows the average growth rates of GDP and employment for 25 OECD countries for the period 1988–97.
The following data refer to the quantity sold of good Y (measured in kg), and the price of that good X (measured in pence per kg), for 10 different market locations:Y: 198 181 170 179 163 145 167 203 251 147 X: 23 24.5 24 27.2 27 24.4 24.7 22.1 21 25(a) Assuming a linear relationship between the
State the assumptions of the simple linear regression model and explain why they are necessary.
Prove that the OLS coefficient for the slope parameter in the simple linear regression model is a BLU estimator.
Prove that the OLS coefficient for the slope parameter in the simple linear regression model is unbiased.
Regression equations are sometimes estimated using an explanatory variable that is a deviation from some value of interest. An example is a capacity utilization rate–unemployment rate equation, such as:ut = a0 + a1(CAPt − CAPf t ) + et where CAP f t is a single value representing the capacity
An outlier is an observation that is very far from the sample regression function. Suppose the equation is initially estimated using all observations and then re-estimated omitting outliers. How will the estimated slope coefficient change? How will R2 change? Explain.
The EViews file ‘Spreadss and GDP’ gives data on the following variables for France, over the period 1997m01 to 2013m12: catogdp_fr: the ratio of the current account balance to GDP. dgdp_fr: the monthly percentage change in GDP. oilp: the world oil price. sp_fr: the spread between French and
Discuss how you would split the coefficient driver set into two parts to derive the bias-free coefficient.
Explain the concept of a coefficient driver.
Use the two EViews workfiles with models labelled ‘forward model’ and ‘backward model’ to do the following:a Examine the model equations by going to ‘view’ and ‘view equations’.b Follow the steps outlined in the last section of the chapter and replicate the simulations presented
The files Norway.wf1, Sweden.wf1 and Finland.wf1 contain data for GDP and various financial proxies as in the computer example for the UK case presented in this chapter.For each of these countries, test for cointegration among the pairs of variables by applying both the EG and the Johansen approach
Use the file in Exercise 17.2 and verify your results by using the Johansen approach.Include all three variables in a multivariate Johansen cointegration test. What is your result? Can you identify the cointegrating vector(s)?
The file cointegration.wf1 contains data on three variables (x, y and z). Test the variables for their order of integration and then apply the EG approach to the three different pairs of variables. In which of the pairs do you find cointegration?
The file korea_phillips.wf1 contains data for wages and unemployment for the Korean economy. Test for cointegration between the two variables using the EG approach and comment on the validity of the Phillips curve theory for the Korean economy.
Is it possible to have two I(1) variables and two I(2) variables in a Johansen test for cointegration, and to find that the I(2) variables are cointegrated with the I(1)?Explain analytically
State the drawbacks of the EG approach, and discuss these with reference to its alternative (that is the Johansen approach).
Explain step by step how can one test for cointegration using the Engle–Granger(EG) approach.
What are the features of the ECM that make it so popular in modern econometric analysis?
What is the error-correction model? Prove that the ECM is a reparametrization of the ARDL model.
Why is it necessary to have series that are integrated of the same order to make cointegration possible? Give examples.
Explain the meaning of cointegration. Why is it so important for economic analysis?
The file VAR_US_DATA.xlsx contains data for various macroeconomic variables for the US, 1960–2019. Create a new file on EViews, with yearly data frequency during this period. Copy and paste the data in EViews.The variables are:debt: government debt as percent of GDP gov: government expenditures
The file Nelson_Ploser.wf1 contains data from various macroeconomic indicators of the US economy. Check for the order of integration of all the variables using both the ADF and PP tests. Summarize your results in a table and comment on them.
The file Korea.wf1 contains data from various macroeconomic indicators of the Korean economy. Check for the order of integration of all the variables using both the ADF and PP tests. Summarize your results in a table and comment on them.
The file gdp_uk.wf1 contains data for the UK GDP in quarterly frequency from 1955 to 1998. Check for the possible order of integration of the gdp variable using both the ADF and the PP tests and following the steps described in Figure 16.5.
Explain the term spurious regression and provide an example from economic timeseries data.
Describe how a researcher can test for stationarity.
Explain why it is important to test for stationarity.
The file VAR_US_DATA.xlsx contains data for various macroeconomic variables for the US for a time span of 1960–2019. Create a new file on EViews, with yearly data frequency for 1960–2019. Copy and paste the data in EViews.The variables are:debt: government debt as percent of GDP gov: government
The file Data_GDP_CO2.xlsx contains data for real GDP per capita and CO2 emmisions for 1990–2018 for all countries (data are taken from the World Bank, World Development Indicators database; for more see: https://databank.worldbank.org/source/worlddevelopment-indicators). Create a new file in
The file Data_GDPpc_UNEMP.xlsx contains data for real GDP per capita and unemployment rates for 1960–2018 for all countries (data are taken from the World Bank, World Development Indicators database; for more see:https://databank.worldbank.org/source/world-development-indicators). Create a new
The file Exchange_Rates.xlsx contains the following daily observations for exchange rates against the US dollar. The time span is from 2 January 1980 to 21 May 1987.There are some missing dates due to non-availability of the data and the final sample contains 1,867 observations. The series are
The file Exchange_Rates.xlsx contains the following daily observations for exchange rates against the US dollar. The time span is from 2 January 1980 to 21 May 1987.Some dates are missing due to non-availability of the data, and the final sample contains 1,867 observations. The series are defined
You are working in a financial institution and your boss proposes to upgrade the financial risk-management methodology the company uses. In particular, to model the FTSE-100 index your boss suggests estimation using an ARCH(1) process. You disagree and wish to convince your boss that a GARCH(1,1)
The file arch.wf1 contains daily data for the logarithmic returns FTSE-100 (named r_ftse) and three more stocks of the UK stock market (named r_stock1, r_stock2 and r_stock3, respectively). For each of the stock series do the following:(a) Estimate an AR(1) up to AR(15) model and test the
Explain the effect of the dummy variable in the TGARCH model. Why does it enter the variance equation in a multiplicative form, and what is the rationale behind this?
Provide a GARCH-M(q,p) model and explain the intuition behind this model.
What should researchers be very careful of in estimating ARCH/GARCH models?
Explain the meaning of asymmetries in news, and provide appropriate specifications for GARCH models that can capture these effects.
What is meant by the comment that ‘GARCH(1,1) is an alternative parsimonious process for an infinite ARCH(q) process’? Prove this mathematically.
Explain how one may estimate models with ARCH and GARCH effects.
Explain how one can test for the presence of ARCH(q) effects in a simple OLS estimation framework.
Explain the meaning of ARCH and GARCH models, showing how each is a form of heteroskedasticity.
The file Data_GDPpc_UNEMP.xlsx contains data for real GDP per capita and unemployment rates for 1960–2018 for all countries (data are taken from the World Bank, World Development Indicators database; for further information see:https://databank.worldbank.org/source/world-development-indicators).
The file ARIMA.wf1 contains quarterly data for the consumer price index (cpi) and gross domestic product (gdp) of the UK economy. Follow the steps described in the example for the Box–Jenkins approach regarding gdp for the cpi variable.
Show that an MA(1) process can be expressed as an infinite AR process.
Write an analytical report of all your analysis. This should include: (a) a short Introduction; (b) a short Literature Review; (c) a Data Set section; (d) an Empirical Results section; and (e) a Conclusions section. Discuss the choice of the best ARIMA model, including references if you refer to
Compare your findings with those of other empirical studies on this topic.
Present your results in suitable tables. Interpret and evaluate your results. Appraise the adequacy of the results and formulate appropriate diagnostic procedures. Make forecasts and discuss your findings about their accuracy.
Choose a group of 8–10 stocks of the market you wish to analyze and estimate which is the best-fitting ARIMA model, following the Box–Jenkins methodology.Write a short section (two or three pages) describing the ARIMA methodology and forecasting using ARIMA models.
Discuss analytically the three stages involved in the Box–Jenkins process for ARIMA model selection.
Define and explain the concepts of stationarity and invertibility. Why are they important in the analysis of time series data? Present examples of stationary and non-stationary, invertible and non-invertible processes.
Define the concepts of stationarity and invertibility and state the conditions for stationarity in the AR models and invertibility for the MA models.
Explain the implication behind the AR and MA models by giving examples of each.
Use the file Binary_Loan to repeat Exercise 12.1 in order to check if there is discrimination for individuals that belong to the Black and Hispanic ethnic minorities in a simple model that includes one explanatory variable only. What are your conclusions? If you add additional determinants, does
in order to check if there is discrimination between males and females or between married and non-married individuals using a simple model that includes one explanatory variable only. What are your conclusions? If you add more variables how are your results affected?
Use the file Binary_Loan to repeat
The file Binary_Loan contains data for the following variables:appinc: applicant income, $1000s married: =1 if married dep: number of dependents emp: years employed in line of work yjob: years at this job self: =1 if self employed pubrec: =1 if filed bankruptcy hrat: housing expenses % total income
Consider the following model:Ct = α0 + α1Yt + α2Ct−1 + u1t It = β0 + β1Rt + β2It−1 + u2t Rt = γ0 + γ1Yt + γ2Mt + u3t Yt = Ct + It + Gt where:Ct denotes real consumption, Yt denotes real national income, It denotes real investments, Mt denotes real money supply, Rt denotes the interest
Consider the following model that examines the relationship between cigarette sales and advertisement costs:Y1t = α1 + β1Y3t + β2Y4t + γ1X1t + γ2X2t + u1t Y2t = α2 + β3Y3t + β4Y4t + γ3X1t + γ4X2t + u2t Y3t = α3 + β5Y1t + β6Y2t + u3t Y4t = α4 + β7Y1t + β8Y2t + u4t where:Y1 denotes
Consider the following model:Ct = a0 + a1Yt + a2C(t−1) + a3Pt + u1t Yt = β0 + β0It + β2Y(t−1) + u2t It = Yγ + Yγ Yt + γ2Kt + u3t Kt = δ0 + δ1Kt−1 + δ2Rt + u4t where the real variables are defined as follows:Ct denotes real consumption, Yt denotes real national income, It denotes real
Consider the following model:Y1 = 2Y2 − 3X1 − 2X2 + u1 Y2 = −2Y3 + X3 + u2 Y3 = −Y1 − Y2 + X1 − X3 + u3 The variables Y1, Y2, Y3 are endogenous and X1, X2, X3 are exogenous. Do the following:(a) Write the model in its typical form.(b) Write the model using the matrix notation form for
The file cons_us.wf1 contains data on consumption expenditure (CE) and personal disposable income (PDI) (measured in constant prices) for the US economy.(a) Estimate the partial adjustment model for CE by OLS.(b) Provide an interpretation of the estimated coefficients.(c) Calculate the implied
The model:CEt = β1 + β2YDt + β3CEt−1 + vt (10.41)(where CE = aggregate consumer expenditure and YD = personal disposable income)was estimated by simple OLS using data for the UK economy. The results are given in Table 10.2. Is this model a satisfactory one? Explain (using the adaptive
Assume we have the following distributed lag model:Yt = 0.847 + 0.236Xt + 0.366Xt−1 + 0.581Xt−2+ 0.324Xt−3 + 0.145Xt−4 (10.40)Find (a) the impact effect, and (b) the long-run effect, of a unit change in X on Y.
Show how the Koyck transformation transforms an infinite distributed lag model into an autoregressive model. Explain the advantages of this transformation.
Explain how we can test for serial correlation in autoregressive models.
Derive the Almon polynomial transformation for p = 5 and r = 4. Explain how to proceed with the estimation of this model.
Show how we might obtain an estimate of the marginal propensity to consume out of expected income, despite not having the data for expected income, using the adaptive expectations autoregressive model.
Write an analytical report of all your analysis. This should include: (a) a short Introduction; (b) a short Literature Review; (c) a Data Set section; (d) an Empirical Results section; and (e) a Conclusions section. Discuss the stock market anomaly and its effects on the market, including
Compare your findings with those of other empirical studies on this topic.
Choose a group of eight to ten stock market indices and examine empirically whether or not they fit the anomaly.
Write a short summary (two pages) of the anomaly and the literature, suggesting how and why this anomaly works.
Choose a stock market anomaly to examine. (In the book we have analysed the January effect and the day-of-the-week effect, but there are many others.)
(a) The file SLEEP_DUM.xls contains the following variables for 1,388 US mothers:age: in years black: = 1 if Black clerical: = 1 if clerical worker construc: = 1 if construction worker educ: years of schooling earns74: total earnings, 1974 gdhlth: = 1 if in good or excellent health inlf: = 1 if in
The file BWGHT_DUM.xls contains the following variables for 1,388 US mothers:faminc: 1988 family income, $1000s cigtax: cigarette tax in home state, 1988 cigprice: cigarette price in home state, 1988 bwght: birth weight, ounces fatheduc: father’s years of education motheduc: mother’s years of
The file wage2.dum.xls contains the following cross-sectional data:wage: monthly earnings hours: average weekly hours IQ: IQ score KWW: knowledge of work score educ: years of education exper: years of work experience tenure: years with current employer age: age in years married: = 1 if married
Describe the steps involved in conducting the Chow test for structural stability. Is the Chow test preferable to the dummy variables approach? Explain why or why not.
Provide an example from economic theory where the use of seasonal dummy variables is required. Explain why, when there is a constant included in the model, we cannot use all the dummies together but must exclude one dummy, which will act as the reference dummy. What is the meaning of a reference
Show (both graphically and mathematically) the combined effect of the use of a dichotomous dummy variable on the constant and the slope coefficient of the simple regression model.

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Applied Econometrics 4th Edition Dimitrios Asteriou, Stephen G. Hall - Solutions

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