《计量经济学导论及习题答案等教辅资源 Chapter 15.docx》由会员分享，可在线阅读，更多相关《计量经济学导论及习题答案等教辅资源 Chapter 15.docx（27页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、Introduction to Econometrics, 3e (Stock)Chapter 15 Estimation of Dynamic Causal Effects15.1 Multiple Choice1) A distributed lag regressionA) is also called AR(p).B) can also be used with cross-sectional data.C) gives estimates of dynamic causal effects.D) is sometimes referred to as ADL.Answer: C2)
2、Heteroskedasticity- and autocorrelation-consistent standard errorsA) result in the OLS estimator being BLUE.B) should be used when errors are autocorrelated.C) are calculated when using the Cochrane-Orcutt iterative procedure.D) have the same formula as the heteroskedasticity robust standard errors
3、in cross-sections.Answer: B3) Sensitivity analysis of the results may include the following with the exception ofA) stability over time analysis of the estimated multipliers.B) using homoskedasticity only rather than HAC standard errors.C) investigation of omitted variable bias.D) looking at differe
4、nt computations of the HAC standard errors.Answer: B4) A seasonal binary (or indicator or dummy) variable, in the case of monthly data, A) is a binary variable that take on the value of 1 for a given month and is 0 otherwise.B) is a variable that has values of 1 to 12 in a given year.C) is a variabl
5、e that contains Is during a given year and is 0 otherwise.D) does not exist, since a month is not a season.Answer: A5) Ascertaining whether or not a regressor is strictly exogenous or exogenous ultimately requires all of the following with the exception ofA) economic theory.B) institutional knowledg
6、e.C) expert judgment.D) use of HAC standard errors.Answer: D6) In time series, the definition of causal effectsA) says that one variable helps predict another variable.B) does not make much sense since there are not multiple subjects.C) assumes that the same subject is being given different treatmen
7、ts at different points in time.D) requires panel data.15.3 Mathematical and Graphical Problems1) One of the central predictions of neo-classical macroeconomic growth theory is that an increase in the growth rate of the population causes at first a decline the growth rate of real output per capita, b
8、ut that subsequently the growth rate returns to its natural level, itself determined by the rate of technological innovation. The intuition is that, if the growth rate of the workforce increases, then more has to be saved to provide the new workers with physical capital. However, accumulating capita
9、l takes time, so that output per capita falls in the short run.Under the assumption that population growth is exogenous, a number of regressions of the growth rate of output per capita on current and lagged population growth were performed, as reported below. (A constant was included in the regressi
10、ons but is not reported. HAC standard errors are in brackets. BIC is listed at the bottom of the table).Regression of Growth Rate of Real Per-Capita GDP on Lags of Population Growth, United States, 1825-2000(1)(2)(3)(4)(5)Lag numberDynamic multipliersDynamic multipliersDynamic multipliersDynamic mul
11、tipliersDynamic multipliers0-0.9(1.3)-1.1(1.3)-1.3(1.7)-0.2(1.7)-2.0(1.5)13.5(1.6)3.2 (1.6)1.8 (L6)0.8 (1.5)-2-1.3(1.7)-3.0 (L6)-2.2(L4)-30.2(1.7)1.5(1.2)-4-2.0(1.5)-BIC-234.4-236.1-238.5-240.0-241.8(a) Which of these models is favored by the information criterion?(b) How consistent are these estima
12、tes with the theory? Is this a fair test of the theory? Why or why not? (c) Can you think of any improved data to test the theory?Answer:(a) BIC has a minimum for no lag and this criterium therefore favors a static specification.(b) The estimates tell us that there is no dynamic multipliers other th
13、an the contemporaneous or impact effect. Even the impact effect is not statistically significant. It is unlikely that population growth is exogenous and therefore this does not represent a fair test of the theory。In addition, there is omitted variable bias with other relevant variables, such as the
14、savings rate, education, etc. missing as regressors, (c) Per capita output or income is likely to be a determinant of fertility. As a result, population growth is not likely to be exogenous. Perhaps the working age population would be a better choice here, but data for early periods are almost impos
15、sible to obtain.2) The Gallup Poll frequently surveys the electorate to quantify the publics opinion of the president. Since 1945, Gallup settled on the following wording of its presidential poll: Do you approve or disapprove of the way (name) is handling his job as president? Gallup has not changed
16、 its presidential question since then, and respondents can answer approve, disapprove, or no opinion.You want to see how this approval rating is related to the Michigan index of consumer sentiment (ICS). The monthly survey, conducted with a minimum sample of 500, asks people if they feel better/wors
17、e off with regard to current and future conditions.(a) To estimate dynamic causal effects, you collect quarterly data from 1962:1 -1998:11 for the United States. You allow a binary variable for each presidency to capture the intrinsic popularity of the President. Furthermore, you eliminate observati
18、ons that include a change in party for the presidency by using a binary variable, which takes on the value of one during the first quarter of the year after the election. Finally, a friendly political scientist provides you with (i) an events variable, (ii) a Vietnam binary variable, and (iii) a hon
19、eymoon variable, which measures the effect of a higher popularity of a president immediately following the election. (The coefficients of these variables will not be reported here.)Assuming that consumer sentiment is exogenous, you estimate the following two specifications (numbers in parenthesis ar
20、e heteroskedasticity- and autocorrelation-consistent standard errors):AppmvoJt = 26.08 + 0.178 x lCSt + 0.232 x /CSm； R2= 0.667, SER = 7.00(8.83)(0.120)(0.135)Appivvalt = 26.08 + 0.178 x MCSt + 0.411 + ICSt-V K2 = 0.667, SER = 7.00(8.(17) (0.120 )(0.089)What is the difference between the two specifi
21、cations? What is the advantage of estimating the second equation, if any?(b) Assuming that the errors follow an AR(1) process, you also estimate the following alternative:Appivvalt = -4.61 + 0.300 x ICSt - 0.070 x ICSt-i- 0.054 x /CSf.2； + 0.776 x Approval(5.84)(0.083)(0.099)(0.083)(0.057)r2 = 0.868
22、, SER = 4.45How is this specification related to the previous ones? What implicit assumptions did you have to make to allow for desirable properties of the OLS estimator?(c) You finally estimate the approval equation using the quasi-difference specification and the GLS estimator.Approval产-4.61 + 0.3
23、00 x ICS/ - 0.070 x ZCSf-i；(5.84) (0.083)(0.099)R2 = 0.868, SER = 4.45人Awhere Z/= Z/-and91 = 0.896 (0.040).How is this equation related to the ones in (a) and (b)? What are the properties of the GLS estimator here, under the assumption that ICS is strictly exogenous?(d) Is it likely that the ICS is
24、exogenous here? Strictly exogenous?Answer:(a) If the regressor is exogenous, then the estimates in the first regression measure the impact effect and the one-period dynamic multiplier of a change in consumer sentiment on approval ratings. The coefficients in the second equation are cumulative dynami
25、c multipliers, where the coefficient on ICSt-l represents the long-run cumulative multiplier. The advantage of the second equation is that it allows for testing cumulative dynamic multipliers.(b) This is the ADL representation of the distributed lag model with first order autocorrelation. The assump
26、tion is that ICS is a strictly exogenous regressor. If this is the case, then the dynamic multipliers can be calculated from these estimates.(c) This is the quasi-difference representation of the distributed lag model with autoregressive errors. Given the restrictions on the parameters of the ADL mo
27、del, it simply reorganizes the regressors. If ICS were strictly exogenous, then GLS produces asymptotically efficient (BLUE) estimators.(d) If approval ratings depend on economic variables, such as the inflation rate, the unemployment rate, and income growth, then there is omitted variable bias, sin
28、ce these variables will be correlated with consumer sentiment. Furthermore, if lower approval ratings (popularity deficit) result in stimulating the economy, which in return will have an effect on consumer sentiment, then there is simultaneous causality in addition. If a variable is not exogenous, t
29、hen it is also not strictly exogenous.3) Consider the following distributed lag model Y/ = 5q + 0凶 + 必 wtiere 劭=今i“f-i + u& 也 isserially uncorrelated, and X is strictly exogenous.(a) How many parameters are there to be estimated between the two equations?(b) Using the two equations of the model abov
30、e, derive the ADL form of the model.(c) There are five regressors in the ADL model, namely Yf_1，Xf, Xfj, Xf，2 and the constant. Estimating the ADL model linearly will give you five coefficients. Can you derive the parameters of the original two equation model from these five estimates? Why or why no
31、t?(d) What alternative method do you have to retrieve the parameters of the two equation model?Answer:(a) There are four parameters to be estimated, 0o, Pl，02 and di.(b) The ADL form of the model is derived by multiplying the first equation by(j)i and lagging itz then subtracting the resulting equat
32、ion from the first equation, and using the AR(1) equation of the error term for simplification of the resulting specification.X = ft) +肉Xf+ /2Xf-l +-的 二的优 + 啊肉 Xf/ +01 仪+which, after collecting terms, results inYf = P0 (1叩1) +肉Xf +隼2 -1) X/1如师匕2 + (“广如小1) orYt =+ QI + &()Xt + 5的_1 + &2xt-2 + ut-(c)
33、The original four parameters cannot be derived without restrictions since in essence you have five equation in four unknowns.(d) The above model can be specified in quasi-differences, i.e.,(丫厂 Ql)I-l)=户OQ- 91) + 户l(Xf-) +/9iXf_2)+ utor丫 二。0+户通+ 户 2X-1 + ”The parameters now can be estimated using non
34、linear least squares, or specifically, the Cochrane-Orcutt, or the iterated Cochrane-Orcutt estimator.4) A model that attracted quite a bit of interest in macroeconomics in the 1970s was the St. Louis model. The underlying idea was to calculate fiscal and monetary impact and long run cumulative dyna
35、mic multipliers, by relating output (growth) to government expenditure (growth) and money supply (growth). The assumption was that both government expenditures and the money supply were exogenous. Estimation of a St. Louis type model using quarterly data from 1960:1-1995:IV results in the following
36、output (HAC standard errors in parenthesis):丽=0.018 + 0.006 x dmgroivtht + 0.235 x dmroiuthf. + 0.344 x dnigrowthf.2(0.004) (0.079)(0.091)(0.087)+ 0.385 x dmgrothf.2 + 0.425 x nigroiutht. + 0.170 x dggrowtht - 0.044dggrowff.i(0.097)(0.069)(0.049)(0.068)-0.003 x dggrowthf-2 - 0.079 x dggrowtht.2 + 0.
37、018 x ggrowthf-4；(0.040)(0.051)(0.027)R2 = 0.346, SER=0.03where ygrowth is quarterly growth of real GDP, mgrozuth is quarterly growth of real money supply (M2), and ggrowth is quarterly growth of real government expenditures, d in front of growth and mgroivth indicates a change in the variable.(a) A
38、ssuming that money and government expenditures are exogenous, what do the coefficients represent? Calculate the /-period cumulative dynamic multipliers from these. How can you test for the statistical significance of the cumulative dynamic multipliers and the long-run cumulative dynamic multiplier?(
39、b) Sketch the estimated dynamic and cumulative dynamic fiscal and monetary multipliers.(c) For these coefficients to represent dynamic multipliers, the money supply and government expenditures must be exogenous variables. Explain why this is unlikely to be the case. As a result, what importance shou
40、ld you attach to the above results?Answer:(a) In that case the coefficients represent dynamic multipliers.Lag numberMonetary Dynamic MultiplierMonetary CumulativeMultiplierFiscal Dynamic MultiplierFiscal Cumulative Multiplier00.0060.0060.1700.17010.2350.241-0.0440.12620.3440.585-0.0030.12330.3850.97
41、0-0.0790.04440.4251.3950.0180.062To test for the significance of the cumulative dynamic multipliers and the long-run cumulative dynamic multiplier, the equation must be reestimated with all regressors appearing in differences with the exception of the longest lag. The coefficients of these regressor
42、s then represent cumulative dynamic multipliers and t-statistics can be used to test for their statistical significance.(b) See the accompanying figures. o 11二0123Lag (in Quarters)6 4 2 1 3 6 4111 o o o0.2-Cumulative Monetary Dynamic Multiplier - -CumulatixeFiscal Dynamic Multiplier(c) There is litt
43、le reason to believe that these government instruments are exogenous. Even if the monetary base and those components of government expenditures which do not respond to business cycle fluctuations had been chosen rather than the above regressors, then these instruments respond to changes in the growt
44、h rate of GDP. As a matter of fact, government reaction functions were also estimated at the time to capture how government instruments respond to changes in target variables. As a result, the regressors will be correlated with the error term, OLS estimation is inconsistent, and inference not depend
45、able. It is hard to imagine how useable information can be retrieved from these numbers.5) Your textbook used a distributed lag model with only current and past values of Xj coupled with an AR(1) error model to derive a quasi-difference mode, where the error term was uncorrelated.(a) Instead use a s
46、tatic model Yf = pQ + ut here, where the error term follows an AR(1). Derive thequasi difference form. Explain why in the case of the infeasible GLS estimators you could easily estimate the ps by OLS.(b) Since cj” (the autocorrelation parameter for iif) is unknown, describe the Cochrane-Orcutt estim
47、ation procedure.(c) Explain how the iterated Cochrane-Orcutt estimator works in this situation. Iterations stop when there is convergence in the estimates. What do you think is meant by that?(d) Your textbook has pointed out that the iterated Cochrane-Orcutt GLS estimator is in fact the nonlinear le
48、ast squares estimator of the model. Given that -1 1, suggest a grid search or some strategy toAnail down the value of which minimizes the sum of squared residuals. This is the so-called Hildreth-Lu method.Answer:(a) The quasi-difference model is derived by multiplying the equation by 包 and lagging it, then subtracting the resulting equation from the first