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Econometric Analysis An Applied Approach To Business And Economics 1st Edition Sharif Hossain - Solutions
Discuss different measures for the goodness of fit of limited dependent-variable models.
A researcher has obtained a random sample of the names of persons who have been arrested for a crime for the Justice Department of Bangladesh and have collected the information o the following variables:Y = The indicator variable which takes the value 1 if the person is convicted and 0 for
Data on investment (INVT in Lac TK), level of income of investors (INC in Lac TK), years of education(YEDU), and whether an investor is concerned (CON) about risk before investment in a particular stock are given below.(i) Describe how you would formulate a probit model for the given data.(ii)
Suppose you have a sample of women for which you have data on the following variables: Y is the indicator variable which takes the value of 1 if a woman works as a wage earner and 0 if a woman does not work as a wage earner; AGE indicates the age of the women; M is the dummy variable which takes 1
Describe the likelihood ratio test for testing the null hypothesis 0 1 2 k H : ???? =???? =.....=???? =0 against an appropriate alternative hypothesis in the case of a probit model.
How do you find the relative effects of two independent variables in the response probability of a probit model? Discuss.
Define an odds-ratio of the probit model.
Discuss the technique to find the marginal effect of the probit model. What does it mean? Explain.
Discuss the ML method to estimate a probit model.
Distinguish between the logit and probit models with an example of each.
Distinguish between the LPM and probit model with an example of each.
Explain the meaning of the probit model with an example.
Distinguish between the LPM and logit model with an example of each.
The data on the yearly salary ( 1 X ) in thousand USD, the total number of employees ( N ) having salary 1 X , the number of employees (n) between 55 and 65 years of age who have recently retired, and the median number of years employed ( 2 X ) are given below.(i) Describe how you would formulate a
Suppose that you have a sample of countries for which you have data on the following variables: i P indicates the ratio of recovered patients to total affected due to COVID-19 of the ith country, i AGE indicates the median age of patients of the ith country, i BSL indicates the median blood sugar
Describe the likelihood ratio test for testing the null hypothesis 0 1 2 k H : ???? =???? =.....=???? =0 against an appropriate alternative hypothesis in case of the logit model.
How do you find the relative effects of two independent variables in the response probability of a logit model?Discuss.
Define an odds-ratio of the logit model. Discuss the technique to find the changes in the probability for a unit increase in x from the odds-ratio.
Discuss the technique to find the marginal effects of the logit model. What does it mean? Explain.
Discuss the ML method to estimate a logit model.
Discuss the WLS method to estimate a logit model with an example.
What problems can happen to estimate a logit model using the OLS method? Explain. How would you solve these problems? Discuss.
Explain the meaning of the logit model with an example.
A research institute did a survey of the students who had either enrolled in an educational institution or dropped out due to the COVID-19 pandemic. Let P be the probability of enrolment of a student, INC be the monthly family income of the students, YEDU be the years of education of the family
A research institute did a survey of the students who had either enrolled or were eligible but could not enrol at the public university. Let P be the probability of enrolment of a student at a public university, INC be the monthly family income of the students, YEDU be the years of education of the
A researcher did a survey of the number of deaths due to the coronavirus pandemic. Let P be the probability of a patient dying due to the coronavirus pandemic, AGE be the age of the patients, GEN be the gender of the patients which takes 1 for male and 0 for female, BLS be the blood sugar level of
Discuss the WLS method to estimate a linear probability model (LPM).
Describe different problems that can happen if we apply the OLS method to estimate a linear probability model(LPM).
Define a linear probability model (LPM) with an example.
Define a dummy dependent variable and dummy dependent variable model with an example of each.
A researcher wants to test the causal relationships between two variables say per capita GDP (Y) and the domestic investment (X) of Bangladesh. It is found that Y is I(2) and X is I(1). Which method would be appropriate for detecting the causal relationships between Y and X? Briefly outline the
Briefly outline the Toda-Yamamoto approach for testing the causality relationship between integrated variables of different orders.
Suppose, a researcher has a set of two economic variables Y and X which are I(1) but not cointegrated. The model for the Granger causality test takes the formFrom a sample of 39 observations, it is found that the value of p is 1. The unrestricted and restricted residual sum of squares for the first
Discuss the Granger causality test to investigate the causal directions between two nonstationary variables that have no cointegration relationship.
Discuss the Granger causality test to investigate the causal directions between two nonstationary and cointegrated variables.
Briefly outline the Bounds test approach for cointegration.
Suppose a researcher has a set of five economic variables. t Y (t =1 , 2,……,T) denotes a (5×1) vector of variables and he wishes to test the existence of cointegrating relationships using the Johansen test procedure. What is the implication of finding that the rank of the long-run matrix ????
Compare the Johansen maximum eigenvalue test with the trace test. Set up the null and alternative hypotheses in each case.
Briefly outline the Johansen test procedure for testing the cointegration relationships between a set of variables in the context of a VAR model. Give one or more examples from the economic growth literature where the Johansen test has been employed. What conclusion can be drawn from the results of
Let us consider a first-order Gaussian VAR model of the type ???? t 1 t-1 t Y =???? Y ???? where t Y is a (2×1) vector of endogenous variables and each of y’s is I(1); t ???? is a (2×1) vector of disturbance terms that are assumed to be independently, identically distributed errors with the
Define a cointegrated VAR model with an example. Derive a cointegrated VAR model from a pth-order Gaussian VAR model and then interpret all the terms of a cointegrated VAR model.
Define a vector error correction model and derive a VEC model from a pth-order Gaussian VAR model .
Define an error correction model (ECM) with an example. Obtain the error correction model from an ARDL model and interpret all the terms of an error correction model.
Discuss the techniques to obtain the feasible GLS estimators of SURE model.
Show that the GLS estimator is more efficient than the OLS estimator for a SURE model.
Obtain the OLS and GLS estimators of the seemingly unrelated regression model.
Derive a seeming unrelated regression equations (SURE) model from m multiple linear regression equations.
Define a seemingly unrelated regression model with an example.
What are the advantages and disadvantages of the VAR model?
To examine empirically the supply-leading or demand-following hypotheses in case of the USA, three timeseries variables, say economic growth, money supply, and domestic credit are used. Estimate the VAR model and obtain the forecast error variance decomposition for each variable. Show your results
Define the forecast error variance decomposition. Discuss the technique to obtain it.
Illustrate the impulse response functions for the bivariate VAR model. To illustrate how impulse response functions operate, we consider the simulated sequences model without the intercept of the type t t-1 t Z = ???? Z + w , where t tt yZ =x???? ???????? ???????? ????, and 1t t2t w ????????????
Discuss the technique to forecast a VAR model.
Let a bivariate VAR model be estimated with four lags. Assume that the original sample contains 50 observations on each variable (denoted -3 -2 50 y ,y ,.....,y ) and the sample observations 1 through 46 are used to estimate the VAR(4) model. Under the null hypothesis, the VAR(3) model is estimated
Discuss the likelihood ratio test for testing a joint null hypothesis in case of a VAR model.
Discuss the OLS and ML methods to estimate a VAR model.
Discuss the AIC, SBIC, and HQIC criteria to detect the optimum lag length of a VAR model.
Discuss the likelihood ratio test to detect the optimal lag length of a VAR model.
Express a VAR(1) model into a VMA(????) .
Define a vector moving-average process. Find the mean vector and variance-covariance matrix of the VMA process.
Define a structural VAR model with an example. Write a structural VAR model in a standard form.
Find the mean vector and the autocovariance matrix of a VAR(p) model.
Write a VAR(p) model of k endogenous variables and rewrite it as a VAR(1) model.
Define a stationary VAR model with an example. A researcher estimated a VAR model of two variables. The estimated results are given below:t t-1 t 1.2 -0.4 Y = Y + 0.6 0.3 ???????? ???????? ???????? ????Do you think that the VAR model is stationary and stable? Why?
Define a vector autoregressive model with an example. Write a VAR(p) model of three variables.
Discuss the Phillips-Ouliaris-Hansen test for cointegration. Find the cointegration relationship between government revenue collection and government expenditure using the Phillips-Ouliaris-Hansen test based on numerical data of a developing country.
Discuss the Augmented Engle-Granger test for cointegration. Find the cointegration relationship between financial and economic development of the USA using the Augmented Engle-Granger test based on numerical data.
Discuss the Engle and Granger test for cointegration. Test the existence of the long-run Purchasing Power Parity theorem between Bangladesh and the USA using the Engle-Granger test based on numerical data.
Define cointegration with an example. Write the names of different tests for cointegration.
Define spurious regression. Explain it with an example.
Discuss the estimation technique of a distributed lag model.
Define a distributed lag model of order p. Find the long-run effect of X on Y. Find the proportion of the long-run effect felt by the ith period of time. Explain it with an example.
Define an autoregressive distributed lag model of order p. Find the long-run effect of X on Y.
Define a dynamic model with an example.
Let t JPN CPI is the consumer price index in Japan at time t (in Yen per good), tUSA CPI is the consumer price index in the United States at time t (in USD per good), t ER is the exchange rate between two currencies (Yen per USD) and is defined as t JPN ttUSA ER = CPI .CPI The logarithmic form of
Let tUK CPI be the consumer price index in the United Kingdom at time t (in GBB per good), tUSA CPI is the consumer price index in the United States at time t (in USD per good), where t ER is the exchange rate between the UK and the USA at time t (GBP per USD) which is defined as tUK ttUSA ER = CPI
Let us consider a regression equation for the real GDP of a developing country of the type????GDPt = ????+????GDPt-1+????t , where 2????t ~i.i.d(0, ???? ) , ????GDPt = GDPt ????GDPt-1 and ???? = ????-1 . The OLS estimates for this equation are given below:Do you think the time-series data GDP is
Discuss the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) tests for stationarity.
Using the same type of regression equation of (9-8) but different data, the researcher obtains the OLS estimates 1 ????ˆ = ???? 0.325 and 1 SE(????ˆ ) ???? 0.225 .(i) Set up the null hypothesis against an appropriate alternative hypothesis.(ii) Perform the test at a 5% level of significance.(iii)
Derive the Augmented Dickey-Fuller tests for detecting the presence of the unit root problem in a data for case 2.
Derive the Phillips-Perron tests for detecting the presence of a unit root problem in time series data for case 2.
A researcher wants to test the order of integration of a time series variable Y. He decided to use a DF test. That is why, he estimates a regression equation of the type : ????yt = ????0 +????yt-1+????t . The OLS estimate of ????1 is 1 ????ˆ = ???? 0.025 and 1 SE(????ˆ ) ???? 0.325 .(i) Set up
Derive the Dickey-Fuller tests for an AR(1) model without serial correlation for different cases:
What is meant by the functional central limit theorem (FCLT)? Let us consider the random walk model of the type, t t-1 t y = y +???? , where, 0 y = 0, and ????t ~i.i.d(0, 1) , then show that (i): T3Ly =1 I L ' W(r)dr, (ii): Te, > oW(1), (ii): Tt > oW(1)of Wd, === =1 (iv): T[W(r)]dr, (v): T y, o
What is meant by a Brownian motion? Explain the meaning of the Brownian motion by considering the random walk model of the type, yt = yt-1+????t , where, y0 = 0, and ????t ~i.i.d(0, 1).
Explain why we can't apply the usual t-test for testing the null hypothesis 0 H : ???? = 1of the Gaussian AR(1)process t t-1 t y = ????y +???? .
Why is it important to test for non-stationary in time-series data before doing empirical analysis?
Define a unit root with an example. Why are we interested in it?
Explain the meaning of the unit root with an example. What are the implications of the presence of a unit root?
Estimate an appropriate ARCH, GARCH, and GARCH-M models for the variable stock return considering the Standard & Poor's 500 Index (S&P500) over a period of time.
Estimate, AR, MA, ARMA, ARCH and GARCH models using the consumer price index (CPI) data of the UK and then compare them with those of the USA.
Using the data set given in problem 8-31, the researcher obtains both AR(1) and AR(2) models with the following results ( standard errors in parentheses):t t-1 t y = 2.75 + 0.78y + e SE: (3.562) (0.09)???? ???? ????t t-1 t-2 t y = 2.5 + 0.75y + 0.18 y + e SE: (3.562) (0.10) (0.07)???? ???? ????(i)
Suppose you obtain the following sample autocorrelations and partial autocorrelations for a sample of 65 observations from actual data of the inflation rate.(i) Does the above pattern indicate that an AR or MA process is more appropriate? Why?(ii) Use the Box-Pierce (1970) Q-test and Ljung-Box
Using the same data given in 8-32, the researcher calculates the partial autocorrelation functions that given below:(i) What do you mean by the sample partial autocorrelation function? Why is the first partial autocorrelation equal to the first autocorrelation coefficient (0.78)?(ii) Does the above
A researcher uses a sample of 60 observations on Y , the unemployment rate, to model the time-series behaviour of the series and to generate predictions. First, he computes the sample autocorrelation functions with the following results:(i) What do you mean by the sample autocorrelation function?
Define a GARCH-M(p, q) model. Discuss the estimation technique of GARCH-M(p, q) models.
Discuss the technique to estimate a GARCH model.
Define a GARCH(p, q) model. Show that the GARCH(1, 1) model can be converted into an ARCH(????).
Define the autoregressive conditional heteroscedastic (ARCH) model. Discuss the technique to estimate an ARCH model.
Discuss the Box-Jenkins approach to estimate ARMA(p, q) models.
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