Principles Of Econometrics 4th Edition R Hill - Solutions

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Define the coefficient of determination and interpret its meaning. Show that the coefficient of determination lies between 0 and 1.
Show that the total sum of squares can be partitioned into components’ sum of squares.
Define the (1???????? )100 percent confidence interval for a population parameter. Discuss the technique to obtain a 95% confidence interval for the regression parameters.
Discuss the t-test for testing the significance of the relationship between Y and X.
Find the sampling distribution of the OLS estimators.
Discuss the asymptotic properties of the OLS estimators.
Show that the OLS estimators are unbiased of the true population parameters.2.7: Show that the OLS estimators are the best linear unbiased estimators (BLUE).2.8: Discuss the importance of the BLUE property.
Write the important properties of OLS estimators of a simple linear regression equation.
Discuss the method of moments, OLS, and ML methods to estimate a simple linear regression equation.
Explain all the terms of a simple linear regression equation. Also, represent this equation graphically.
Define a simple linear regression equation with an example.
Define a population and sample regression functions with an example of each.
Distinguish between categorical and binary variables with an example of each.1.29: Identify the following functions: (1): q=a+p; (ii): q=a+p: (i): GDP, = GDP, (1+r)'; (iv): GDP = e; (v): q = Ay; (vi): q = Aye"; (vii): GDP =ALK; (ix): Quick Ratio = Current Assets - Inventories Current Liabilities
Distinguish between categorical and dichotomous variables with an example of each.
Distinguish between control and independent variables with an example of each.
Distinguish between dependent and independent variables with an example of each.
Distinguish between discrete and continuous variables with an example of each.
Distinguish between quantitative and qualitative variables with an example of each.
Define a variable with an example. Discuss different types of variables with an example of each.
Distinguish between time-series and panel data with an example of each.
Distinguish between cross-sectional and time-series data with an example of each.
Define data with an example. Discuss different types of data with an example of each.
Define a random error term with an example. Discuss the reasons to include the random error term in a model.
Distinguish between micro and macro relationships with an example of each.
Distinguish between static and stochastic relationships with an example of each.
Distinguish between static and dynamic relationships with an example of each.
Define different types of relationships with an example of each.
Distinguish between economic theory and econometrics.1-13. Distinguish between mathematical economics and econometrics.
Write different steps that are involved in an econometric analysis of economic models.1-11. Why do we prefer an econometric model rather than an economic model? Discuss.
What are the limitations of econometrics?
Discuss the advantages of econometrics.
Distinguish between theoretical and applied econometrics.
Distinguish between economic and econometric models with an example of each.
Distinguish between economic theory, mathematical economics and econometrics with an example of each.
Explain the ideas behind econometric modeling of economic relationships with an example.
Discuss different types of theoretical models with an example of each.
Define a theoretical model with an example.
Explain the meaning of econometrics with an example.
This exercise deals with the loan data described in Exercise 6.12. The ‘‘Chow’’ test was introduced in Chapter 7.2.3 for testing the equality of coefficients in two regressions on subsets of observations. Here we ask a similar question concerning the parameters of the probit model for
In Chapter 7.5.3 we examined the Tennessee’s Project STAR.19 In the experiment, children were randomly assigned within schools into three types of classes: small classes with 13–17 students, regular-sized classes with 22–25 students, and regularsized classes with a full-time teacher aide to
Using the data set from Exercise 15.18, consider the model lnð Þ¼ PRODit b1t þ b2t lnð Þþ AREAit b3t lnð Þþ LABORit b4t lnð Þþ FERTit eit(a) Estimate three seemingly unrelated regressions for the years 1995, 1996, and 1997 and report the results.(b) What assumptions are you making when
The file rice.dat contains 352 observations on 44 rice farmers in the Tarlac region of the Phillipines for the eight years 1990 to 1997. Variables in the dataset are tonnes of freshly threshed rice (PROD), hectares planted (AREA), person-days of hired and family labor (LABOR), and kilograms of
Consider the production function Q ¼ f Kð Þ ; L where Q is output, K is capital, and L is labor. Suppose that the function fðÞis a CES or constant elasticity of substitution production function. The elasticity of substitution, which we denote by v, measures the degree to which capital and
The U.S. Secretary of Agriculture asks a staff economist to provide a basis for determining cattle inventories in the Midwest, Southwest, and West. Let i ¼ 1,2,3 denote the three regions. The economist hypothesizes that in each region cattle numbers at the end of the year ð Þ Cit depend on
In the model ln GAS CAR ¼ b1 þ b2 ln Y POP þ b3 ln PMG PGDP þ b4 ln CAR POP þ e GAS=CAR is motor gasoline consumption per car, Y=POP is per capita real income, PMG=PGDP is real motor gasoline price, and CAR=POP is the stock of cars per capita. The data file gascar.dat contains 19
Consider the three demand equations lnð Þ¼ Q1t b11 þ b12 lnð Þþ P1t b13 lnð Þþ Yt e1t lnð Þ Q2t ¼ b21 þ b22 lnð Þ P2t þ b23 lnð Þ Yt þ e2t lnð Þ¼ Q3t b31 þ b32 lnð Þþ P3t b33 lnð Þþ Yt e3t where Qit is the quantity consumed of the ith commodity, i = 1,2,3, in the tth
This exercise illustrates the transformation that is necessary to produce generalized least squares estimates for the random effects model. It utilizes the data on investment(INV), value (V), and capital (K) in the file grunfeld11.dat. The model is INVit ¼ b1 þ b2Vit þ b3Kit þ ui þ eit We
This exercise uses the data file nls_ panel.dat that was introduced in Section 15.1 and carried through as an example in Sections 15.2 to 15.6.We are interested in estimating the equation LWAGEit ¼ b1i þ b2EDUCi þ b3EXPERit þ b4EXPER2 it þ b5HOURSitþ b6BLACKi þ eit Our primary focus is on
Macroeconomists are interested in factors that explain economic growth. An aggregate production function specification was studied by Duffy and Papageorgiou.22 The data are in the file ces.dat. They consist of cross sectional data on 82 countries for 28 years, 1960 to 1987.(a) Estimate a
What is the relationship between crime and punishment? This important question has been examined by Cornwell and Trumbull21 using a panel of data from North Carolina. The cross sections are 90 counties, and the data are annual for the years 1981–1987. The data are in the file crime.dat. In these
Consider the NLS panel data on young women discussed in Section 15.4.3. However, let us consider only years 1987 and 1988. These data are contained in the file nls_panel2.dat. We are interested in the wage equation that relates the logarithm of WAGE to EDUC, EXPER, its square EXPER2, BLACK, SOUTH,
Consider the NLS panel data on young women discussed in Section 15.4.3. However, let us consider only years 1987 and 1988. These data are contained in the file nls_panel2.dat. We are interested in the wage equation that relates the logarithm of WAGE to EXPER, its square EXPER2, SOUTH, and UNION.(a)
This exercise uses data from the STAR experiment introduced in Chapter 7, Sections 7.5.3 and 7.5.4. In the STAR experiment children were randomly assigned within schools into three types of classes: small classes with 13–17 students, regular-sized classes with 22–25 students, and regular-sized
The file mexican.dat contains data collected in 2001 from the transactions of 754 Mexican sex workers. There is information on four transactions per worker.20 The labels ID and TRANS are used to describe a particular woman and a particular transaction. There are three categories of variables.1. Sex
The file liquor.dat contains observations on annual expenditure on liquor (L) and annual income (X), (both in thousands of dollars) for 40 randomly selected households for three consecutive years. Consider the model Lit ¼ b1i þ b2Xit þ eit
Consider the model yit ¼ b1i þ b2xit þ eit(a) Show that the fixed effects estimator for b2 can be written as b^2; FE ¼N i¼1T t¼1ð Þ xit xi ð Þ yit yiN i¼1T t¼1ð Þ xit xi 2(b) Show that the random effects estimator for b2 can be written as b^2; RE ¼N i¼1T t¼1 xit a^ xi x x
Another way to estimate the model in Exercise 15.2 is to pool all the observations and use dummy variables for each of the years 1960, 1970, and 1980.(a) If you estimate the model this way, what different assumptions are you making about the error terms, relative to the assumptions made for
The system of equations in Exercise 15.1 is estimated with some restrictions imposed on the parameters. The restricted estimations are G60 ¼ 0:0352 0:4286 POP60 þ 0:1361 INV60 0:0000011 IGDP60 þ 0:0150 SEC60ðseÞ ð0:0153Þ ð0:1889Þ ð0:0206Þ ð0:0000010Þ ð0:0100ÞG70 ¼ 0:0251 0:4286
This exercise uses data from the paper: Zhenjuan Liu and Thanasis Stengos, ‘‘Nonlinearities in Cross Country Growth Regressions: A Semiparametric Approach,’’Journal of Applied Econometrics, Vol. 14, No. 5, 1999, pp. 527–538. There are observations on 86 countries, in three time periods,
Consider the quarterly rates of growth contained in gfc.dat used in Exercise 13.13. A researcher in the Euro area (this is the group of countries in Europe where the Euro currency is the legal tender) is interested in testing the proposition that growth in the Euro region is affected by its own
The data file warner.dat contains daily returns to holding shares in Time Warner Inc.The sample period is from January 3, 2008 to December 31, 2008 (260 observations)and a graph of the returns appears in Figure 14.12.(a) Estimate a GARCH(1,1) model and an ARCH(5) model. Which model would you
The seminal paper about ARCH by Robert Engle was concerned with the variance of UK inflation. The data file uk.dat contains seasonally adjusted data on the UK consumer price index (UKCPI) for the sample period 1957:06 to 2006:06.(a) Compute the monthly rate of inflation (y) for the sample period
The data file gold.dat contains 200 daily observations on the returns to shares in a company specializing in gold bullion for the period December 13, 2005 to September 19, 2006.(a) Plot the returns data. What do you notice about the volatility of returns? Identify the periods of big changes and the
Figure 14.11 shows the daily term premiums between a 180-day bank bill rate and a 90-day bank rate for the period July 1996 to December 1998 (data file term.dat). Preliminary unit root tests confirm that the series may be treated as a stationary series, although the value of r, the autocorrelation
Figure 14.10 shows the weekly returns to the US S&P 500 for the sample period January 1990 to December 2004 (data file sp.dat).(a) Estimate an ARCH(1) model and check that you obtain the following results:r^t ¼ 0:197 ^ht ¼ 3:442 þ 0:253e^2 t1ðtÞ ð2:899Þ ð22:436Þ ð5:850Þ
Figure 14.9 (see page 532) shows the time series for monthly changes to the $US/$A exchange rate and its histogram for the period 1985:07 to 2010:06 (data file exrate.dat). (a) Comment on the unconditional distribution of the series. Is it normal?(b) Estimate a GARCH(1,1) model and check that you
The data file euro.dat contains 204 monthly observations on the returns to the Euro share price index for the period 1988:01 to 2004:12. A plot of the returns data is shown in Figure 14.8(a), together with its histogram in Figure 14.8(b).(a) What do you notice about the volatility of returns?
The data file share.dat contains time-series data on the Straits Times share price index of Singapore.(a) Compute the time series of returns using the formula rt ¼ 100 lnðyt=yt1Þ, where yt is the share price index. Generate the correlogram of returns up to at least order 12, since the frequency
The GARCH(1,1) model shown below can also be re-expressed as an ARCH (q)model, where q is a large number (in fact, infinity). Derive the ARCH form of a GARCH model using the method of recursive substitution.ht ¼ d þ a1e2 t1 þ b1ht1
Consider the following T-ARCH model:ht ¼ d þ a1e2 t1 þ gdt1e2 t1 dt ¼ 1 et < 0 ðbad newsÞ0 et 0 ðgood newsÞ(a) If g is zero, what are the values of ht when et1 ¼ 1, when et1 ¼ 0, and when et1 ¼ 1?(b) If g is not zero, what are the values of ht when et1 ¼ 1, when et1 ¼ 0, and when et1
The equations of an ARCH-in-mean model are shown below:yt ¼ b0 þ uht þ et etjIt1 Nð0; htÞht ¼ d þ a1e2 t1 d > 0; 0 a1 < 1 Let yt represent the return from a financial asset and let et represent ‘‘news’’ in the financial market. Now use the third equation to substitute out ht in the
The ARCH model is sometimes presented in the following multiplicative form:yt ¼ b0 þ et et ¼ zt ffiffiffiffi ht p ; zt Nð0; 1Þht ¼ a0 þ a1e2 t1; a0 > 0; 0 a1 < 1:This form describes the distribution of the standardized residuals et= ffiffiffiffi ht p as standard normal zt. However, the
The file gfc.dat contains data about economic activity in two major economies: the United States and the Euro Area (the group of countries in Europe where the Euro currency is the legal tender). Specifically, the data are the logs of their Gross Domestic Product (GDP), standardized so that the
Financial analysts often debate the role of dividends in the determination of share prices. Figure 13.9 shows plots of the rate of change in dividends and price computed as DVt ¼ 100 lnðDNt=DNt1Þ; SPt ¼ 100 lnðPNt=PNt1Þwhere PN is the Standard and Poor Composite Price Index; DN is the nominal
Figure 13.8 shows the time series for two exchange rates—the EURO per $US and the STERLING per $US (data file sterling.dat). Both the levels and the changes in the data are shown.(a) Which set of data would you consider using to estimate a VEC model, and which set to estimate a VAR? Why?(b) Apply
Research into the Phillips curve is concerned with providing empirical evidence of a tradeoff between inflation and unemployment. Can an economy experience lower unemployment if it is prepared to accept higher inflation? Figure 13.7 plots the changes in a measure of the unemployment rate (DU) and
The quantity theory of money says that there is a direct relationship between the quantity of money in the economy and the aggregate price level. Put simply, if the quantity of money doubles, then the price level should also double. Figure 13.6 shows the percentage change in a measure of the
The data file var.dat contains 100 observations on two generated series of data, w and z. The variables are nonstationary but not cointegrated. Estimate a VAR model of changes in the variables. As a check, the results are (the intercept terms were not significant):Db wt ¼ 0:743Dwt1 þ
The data file vec.dat contains 100 observations on two generated series of data, x and y. The variables are nonstationary and cointegrated without a constant term. Save the cointegrating residuals (^e) and estimate the VEC model. As a check, the results for the case normalized on y are Dbyt ¼
The data file fred.dat contains the log of real personal disposable income (Y) and the log of real personal consumption expenditure (C) for the U.S. economy over the period 1960:1 to 2009:4.(a) Are the series stationary, or nonstationary? In particular, test whether the series are trend
The data file gdp.dat contains quarterly data on the real GDP of Australia (AUS) and real GDP of the United States (USA ) for the sample period 1970:1 to 2000:4.(a) Are the series stationary or nonstationary?(b) Test for cointegration allowing for an intercept term. You will find that the intercept
VAR and VEC models are popular forecasting models because they rely on the past history of observed outcomes to predict the expected future values.(a) Consider the following estimated VAR model:yt ¼ ^d11yt1 þ ^d12xt1 þ ^v1t xt ¼ ^d21yt1 þ ^d22xt1 þ ^v2t What are the forecasts for ytþ1 and
The VEC model is a special form of the VAR for I(1) variables that are cointegrated.Consider the following VEC model:Dyt ¼ a10 þ a11ðyt1 b0 b1xt1Þ þ v y tDxt ¼ a20 þ a21ðyt1 b0 b1xt1Þ þ v x tThe VEC model may also be rewritten as a VAR, but the two equations will contain common
Consider the following first-order VAR model of stationary variables:yt ¼ d11yt1 þ d12xt1 þ v y txt ¼ d21yt1 þ d22xt1 þ v x tUnder the assumption that there is no contemporaneous dependence, determine the impulse responses, four periods after a standard deviation shock for(a) y following a
Prices around the world tend to move together. The data file ukpi.dat contains information about the price indices in the United Kingdom and in the Euro Area (the United Kingdom is a member of the European Union, but not a member of the single European currency zone) for the period
The file inter2.dat contains 300 observations of a generated I(2) process shown in Figure 12.6 below. Show that the variable called inter2 is indeed an I(2) variable by conducting a number of unit root tests—first on the level of the data, then on the first difference and finally on the second
The data file mexico.dat contains real GDP for Mexico and the Unites States from the first quarter of 1980 to the third quarter of 2006. Both series have been standardized so that the average value in 2,000 is 100.(a) Perform the test for cointegration between Mexico and the Unites States for all
The data file csi.dat contains the Consumer Sentiment Index (CSI), produced by the University of Michigan for the sample period 1978:01–2006:12.(a) Perform all three Dickey–Fuller tests. Are the results consistent? If not, why not?(b) Based on a graphical inspection of the data, which test
The data file canada.dat contains monthly Canadian/U.S. exchange rates for the period 1971:01 to 2006:12. Split the observations into two sample periods—a 1971:01–1987:12 sample period and a 1988:01–2006:12 sample period.(a) Perform a unit root test on the data for each sample period. Which
The data file usa.dat contains the data shown in Figure 12.1. Consider the two time series, real GDP and the inflation rate.(a) Are the series stationary, or nonstationary? Which Dickey–Fuller test (no constant, no trend; with constant, no trend; or with constant and with trend) did you use?(b)
The data file texas.dat contains 57 quarterly observations on the real price of oil(RPO), Texas nonagricultural employment (TXNAG), and nonagricultural employment in the rest of the United States (USNAG). The data cover the period 1974Q1 through 1988Q1 and were used in a study by Fomby and
The data file oz.dat contains quarterly data on disposable income and consumption in Australia from 1985:1 to 2005:2.(a) Test each of these series for stationarity.(b) What do you conclude about the ‘‘order of integration’’ of each of these series?(c) Is consumption cointegrated with, or
The data file bond.dat contains 102 monthly observations on AA railroad bond yields for the period January 1968 to June 1976.(a) Plot the data. Do railroad bond yields appear stationary, or nonstationary?(b) Use a unit root test to demonstrate that the series is nonstationary.(c) Find the first
The data file oil.dat contains 88 annual observations on the price of oil (in 1967 constant dollars) for the period 1883–1970.(a) Plot the data. Do the data look stationary, or nonstationary?(b) Use a unit root test to demonstrate that the series is stationary.(c) What do you conclude about the
A time series process of the form yt ¼ a þ yt1 þ vt; vt Nð0; s2Þ can be rearranged as yt yt1 ¼ Dyt ¼ a þ vt. This shows that yt is integrated of order one, since its first difference is stationary. Show that a time series of the form yt ¼2yt1 yt2 þ a þ vt is integrated of order two.
Figure 12.5 (data file unit.dat) shows plots of four time series. Since Wand Y appear to be fluctuating around a nonzero mean, a Dickey–Fuller test 2 (with constant but no trend) was performed on these variables. Since X and Z appear to be fluctuating around a trend, a Dickey–Fuller test 3
(a) Consider an AR(1) model yt ¼ ryt1 þ vt; jrj < 1 Rewrite y as a function of lagged errors. (Hint: perform recursive substitution.)What is the mean and variance of y? What is the covariance between yt and yt2?
Reconsider the example used in Section 11,7 on the supply and demand for fish at the Fulton Fish Market. The data are in the file fultonfish.dat. In this exercise we explore the behavior of the market on days in which changes in fish inventories are large relative to those days on which inventory
Reconsider the example used in Section 11,7 on the supply and demand for fish at the Fulton Fish Market. The data are in the file fultonfish.dat.
This exercise examines a supply and demand model for edible chicken, which the U. S. Department of Agriculture calls ‘‘broilers.’’ The data for this exercise is in the file newbroiler.dat, which is adapted from the data provided by Epple and McCallum (2006).7(a) Consider the demand equation

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Principles Of Econometrics 4th Edition R Hill - Solutions

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