Introductory Econometrics Using Monte Carlo Simulation With Microsoft Excel 1st Edition Humberto Barreto, Frank Howland - Solutions

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Here are 12 observations on a variable y.43, 62, 26, 46, 48, 3, 52,−10, 37, 5, 42, 4(a) Compute the mean.(b) Compute the standard deviation.(c) Compute the correlation coefficient of y with x in Question 2.(d) Include the following data points in the set and compute the correlation coefficient
Here are 12 observations on a variable x:86, 109, 81, 53, 86,−14, 65,−39, 65, 34, 79,−27(a) Compute the mean.(b) Compute the sequence of mean deviations.(c) Compute the standard deviation.(d) How many of these data points lie more than (i) one, (ii) two, or (iii) three standard deviations
Are the following statements true or false?(a) The correlation of a variable with itself is always 1.(b) Chebyshev’s rule says that at least a proportion 1∕m2 of any sample lies beyond m standard deviations from the mean.(c) The least absolute values fitting method is more influenced by
The files Norway.wfl, Sweden.wfl and Finland.wfl contain data for gross domestic product 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 the variables applying both the EG and
Use the file in exercise 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.wfl contains data on three variables (x, y and z). Test the variables for their order of integration and then apply the EG approach for the three different pairs of variables. In -,..·hich of the pairs do you find cointegration?
The file korea_phillips.wfl contains data for wages and unemploymt>nt for ti1e Korean economy. Test for cointegration among those two variables with the EG approach and comment on the validity of the Phillips curve theory for the Korean economy.
Is it possible to have two l(l) variables and two 1(2) variables, in a Johansen test for cointegration, and find that the 1(2) variables are cointegrated with the 1(1)?Explain analytically.
State the drawbacks of the Engle-Granger (EG) approach, and discuss these drawbacks in face of its alternative (i.e. the Johansen approach).
Explain step by step how can one test for cointegration using the EG approach.
What are the good 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 serjes that are integrated of the same order in order to possibly have cointegration? Give examples.
Explain the meaning of cointegration. Why is it so important for economic analysis?
The file Nelson_Pioser. wfl contains data from various macroeconomic indicators of the US economy. Check for the order of integration of all the vanables using both the ADF and PP tests. Summarize your results in a table and comment on them.
The file Korea.wfl 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.
Explain the term spurious regression and provide an example from economic timeseries data.1===+EXercise 16.1 The file gdp_uk.wfl contains data for the UK GDP in quarterly frequency from 1955 until 1998. Check for the possible order of integration of the GDP variable using both the ADF and the PP
Describe how someone can test for stationarity.
Explain why it is important to test for stationarity.
You are working in a financial institution and your boss proposes to upgrade the financial risk-management methodology that the company uses. In particular, in order 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
The file arch. wfl contains daily data for the logarithmic returns FTSE-1 00 (named r Jtse)and three more stocks of the UK stockmarket (name r stock I, r stock2 and r stock3 respectively). For each of the stock series do the following:(a) Estimate an AR(l) up to AR(lS) model and test the individual
Explain the effect of the dummy variable in the TARCH 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 we be very careful of in estimating ARCH/GARCH models?
Explain the meaning of symmetries in news, and provide appropriate specifications for GARCH models that can capture those effects.
What is meant by the comment that 'GARCH(l,l) is an alternative parsimonious process for an infinite ARCH(q) process'. Prove this mathematically. •
Explain how we may estimate models with ARCH and GARCH effects.
Explain how we can test for the presence of ARCH(q) effects in a simple OLS estimation framework.
Explain what is the meaning of ARCH and GARCH models showing how each of the two is a form of heteroskedasticity. ---
The file ARIMA. wfl 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(l) process can be expressed as an infinite AR process.
Discuss analytically the three stages that are 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 stationarity and invertibility and state which are the conditions for stationarity in the AR models and invertibility for the MA models.
Explain what is the implication behind the AR and MA models by giving examples of each.
The file cons_us.wfl contains data of consumption expenditure (CE) and personal disposable income (PDI) (measured in constant prices) for the US economy.(a) Estimate the partial adjustment model forCE by OLS.(b) Provide an interpretation of the estimated coefficients.(c) Calculate the implied
The model:Coefficient-7.692041 0.521338 0.442484 0.958482 0.588722 0.032454 0.148036 161.6191 0.869852 Std. Error t-Statistic 3.124125 0.234703 0.045323-2.46214e 2.221233 9.762089 Mean dependent var S.D.dependentvar Akaike info criterion Schwarz criterion· F -statistic Prob (F-statistic)Ct = fh +
Assume we have the following distributed lag model:Yt = 0.847 + 0.236Xt + 0.366Xt-t + 0.581Xt-2+0.324Xt-3 +0.145Xt-4 ( 11.40)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 to 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 p;oceed with the estimation of this model.
Show how we might obtain an estimate of the marginal propensity to consume out of expected income, although we do not have data for expected income, using the adaptive expectations autoregressive model.
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 of 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 dummies together but need to exclude one dummy that will be the reference dummy. What is the meaning of a reference dummy
Show what is the combined effect of the use of a dichotomous dummy variable on the constant and the slope coefficient (both graphically and mathematically) of the simple regression model.
Explain how we can use dummy variables to quantify qualitative informatidn in a regression model. Use appropriate examples from the economic theory.
The file wages_Ol.wfl contains data for monthly wage rates (measured in UK pounds)and IQ scores of a large number of City University graduates, after five years of employment:(a) Find summary statistics for the above mentioned variables and discuss them.(b) Estimate a functional form that will show
The file product.wfl contains data for the following variables, q =quantity of a good produced during various years, p = price of the good, f = amount of fertilizer used in the production of this good and r = amount of rainfall during each production year.Estimate a regression equation that
The file investment. wfl contains data for the following variables, I= investment, Y =income and R = interest rate. Estimate a regression equation that .has as dependent variable the investment, and as expl
Describe the steps of the DW test for autocorrelation. What are its disadvantages and which alternative tests can you suggest?
Explain how autocorrelation can be resolved when p is unknown.
Explain what are the consequences of autocorrelation and how can it be resolved when p is known.
What is autocorrelation? Which assumption of the CLRM is violated and why?
Use the data in the file houseprice.xls to estimate the following equation:price= bo + b1lotsize + bzsqrft + b3bdrms + u (7.43)(a) Check whether there is evidence of heteroskedasticity.(b) Reestimate the equation but this time instead of price use log(price) as the dependent variable. Check for
The file sleep.xls contains data for 706 individuals concerning sleeping habits and possible determinants of sleeping time. Estimate the following regression equation:sleep = bo + b1 totwrk + bzeduc + b3age + b4yngkid + bsmale + u (7 .42)(a) Check whether there is evidence of heteroskedasticity.(b)
Use the data in police.wfl to estimate the equation that relates the actual v~Jue of the current budget (Y) with the expected value of the budget (X). Check for heteroskedasticity in this regression equation with all the known tests described in this chapter.
Use the data in Greek_SME.wfl to estimate the effect of size (proxied by number of employees) to the profit/sales ratio. Check whether the residuals in this equation are heteroskedastic by applying all the tests we have described (both formal and informal) for detection of heteroskedacity. If there
Use the data in the file houseprice.wfl to estimate a model of:price; = {J1 + {J2sqfeet; + u;Check for heteroskedasticity using the White and the Goldfeld-Quandt tests. Obtain the generalized least squares estimates for the following assumptions: (a) Var(u;) =a2sqfeet; and (b) Var(u;) = a2sqfeetf.
Define heteroskedasticity and provide examples of econometric models where heteroskedasticity is likely to exist.
Consider the following model:Y; = fJ1 + /hXz; + fJ3X3; + u;where Var(u;) = a 2Xz;. Find the generalized least squares estimates.
Discuss and show mathematically what is the problem in terms of interpretation of the estimated coefficients, when applying WLS and the weight is an' explanatory'variable of the original model.
Show how one can apply the method of weighted least squares in order to resolve heteroskedasticity.
Describe the Goldfeld-Quandt test for detection of heteroskedasticity.
State briefly what are the consequences of heteroskedasticity in simple OLS.
Use the data in the file money_uk02.wfl to estimate the parametersa, {3 andy, in the equation below:ln(M/Plt =a+ {Jln Yt + y lnRlt + Ut where Rlt is the 3-months treasury bill rate. For ·the rest of the variables the usual notation applies.(a) Use as an additional variable in the above equation
The file cars.wfl contains data on new cars sold in the United States as a function of various variables. Develop a suitable model for estimating a demand function for cars in the United States. If you include all variables as regressors, do you expect to find multicollinearity and why? Provide
The file imports_us.wfl contains data for imports ([}, gross national product (Y) and the consumer price index (P) for the USA. Use these data to estimate the following model: •!nit= fh + {Jzln Yt + f33lnPt +lit Check whether there is multicollinearity in the data. Calculate the correlation
The file imports_uk_y.wfl contains yearly observations of the variables mentioned in Exercise 6.1. Repeat Exercise 6.1 using the yearly data. Do your results change?
The file imports_uk.wfl contains quarterly data for imports (imp), gross domestic product (gdp) and the consumer price index (cpi) for the USA. Use these data to estimate the following model:•In impt = fit + fiz In gdpt + fi3 In cpir + Ut Check whetner there is multicollinearity in the data.
Explain w~at the VIF is and what is its use.·1===+5 Show how we can proceed in order to detect possible multicollinearity in a regression model.
From Chapter 5 we know that p = (X'X)- 1(X'Y). What happens top when there is p~rfect collinearity among the Xs? How would you know if perfect collinearity exists.
In the following model:Y = fh + fizXz + fi3X3 + fi4X4 + ur 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.wfl contains data for output (Y), labour (L) and stock of tapital (K) for the United States. Estimate a Cobb-Douglas type regression equation and ch~ck for constant returns to scale using the Wald test.
The file living.xls contains data for a variety of economic and social measures for a sample of 20 different countries, where:Y =GNP per capita, 1984 $US;X2 =average% annual inflation rate (1973-84);X3 =% of labour force in -agriculture;X4 =life expectancy at birth, 1984 (years);XS =number enrolled
Use the data in the file money _uk. wfl to estimate the parameters a .{3 and y, in the equation below:ln(M/P)r =a+ {Jln Yt + y lnRr + 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.wfl and estimate an equation which i!lcludes 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
The file health.xls contains data for the following variables: birth_ weight= the weight of infants after birth, when low can put an infant in risk of illnesses; cig =number of cigarettes that 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 in redundant.
Describe the steps involved for performing the Wald test for linear restrictions.
Show how one can test for constant returns to scale for the following Cobb-Douglas type prodqction function:Q = ALaKf3 where. Q is output, L denotes labour units, K is capita and A is an exogenous technology parameter.
Prove that the OLS estimates for the k explanatory variables case are BLUE.
Derive the OLS solutions for j3 for the k explanatory variables case using matrix algebra.
'The file salaries_oi:wn contains data for senior officers from a large number of UK firms.The variable salary is the salary that each one of them gets, measured in thousand pounds. The variable years_senior measures the number of years for which they are senior officers, while the variable
Obtain time series data on real business fixed investment (I) and an appropriate rate of interest (r). Consider the following population regression function:It = ao + a1 't + er(a) What are the expected signs of the coefficients in this equation?(b) Explain the rationale for each of these signs.(c)
The following equation has been estimated by OLS:Rt = 0.567 + 1.045Rmt n = 250(0.33) (0.066)where R1 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:rr1 = ao + a1 UNEMP1 + u1 where rr1 is inflation and UNEMP1 is unemployment. Present the results in the usual way.(b) Estimate the alternative
In the Keynesian consumption function:Ct=a+8Ytd GDP 7.73 5.64 2.86 2.01 2.98 2.79 2.60 1.17 1.15 4.18 1.97 2.46 the estimated marginal propensity to consume is simply 8 while the average propensity to consume is c;yd = a;Yd +8. Using data from 200 UK households on annual income and consumption
The table below shows the average growth rates of GDP and employment for 25 OECD countries for the period 1988-97.Countries Empl. GDP Countries Empl.Australia 1.68 3.04 Korea 2.57 Austria 0.65 2.55 Luxembourg 3.02 Belgium 0.34 2.16 Netherlands 1.88 Canada 1.17 2.03 New Zealand 0.91 Denmark 0.02
The following data refer to the quantity sold for a 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 among 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 BLUE.
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 rateunemployment rate equation, such as:Ut = ao + a1 (CAPt -CAP[)+ er where CAP~ is a single value representing the capacity utilization
An outlier is :m observation that is very far from the sample regression function.Suppose the equation is initially estimated using all observations and t~en reestimated omitting outliers. How will the estimated slope coefficient change? How will R2 change? Explain.
Suppose we were interested in estimating δ1. Can 2SLS be used? Explain.
Run a Monte Carlo simulation to approximate the sampling distribution of 2SLS a1. Is 2SLS biased? Explain.
Use the data to find the 2SLS estimate of α1. Describe your procedure and explain your results.
Run a Monte Carlo simulation to approximate the sampling distribution of a1. Is OLS biased? Explain.
Use LINEST to regress Q on P in order to find the single-equation OLS estimate of α1. Show the results from a single sample.

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Introductory Econometrics Using Monte Carlo Simulation With Microsoft Excel 1st Edition Humberto Barreto, Frank Howland - Solutions

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