Abstract
This chapter continues our discussion of advanced statistical techniques. More specifically, this chapter introduces and demonstrates the use of advanced statistical techniques that enable higher education policy analysts to exploit the use of emerging macro panel data. These statistical techniques include heterogeneous coefficient regression (HCR) with dynamic coefficient common correlated estimation (DCCE) and mean group (MG) estimators. Using these techniques, analysts can distinguish between: (1) short-run and long-run relationships and; (2) overall average beta coefficients and unit-specific beta coefficients .
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9.5 Appendix
9.5 Appendix
*Chapter 9 Stata Syntax *create Fig. 9.1. Trends in Log of Appropriations by State, FY 1980 to FY 2018 twoway (line lny1 fy), by(State) xlabel(1980 (8) 2018, labsize(small)) /// ytitle(Logs) ytitle(Log of Appropriations) xtitle(Fiscal Year) *create Fig. 9.2. Trends in Log of GSP by State, FY 1980 to FY 2018 twoway (line lnx4 fy), by(State) xlabel(1980 (8) 2018, labsize(small)) /// ytitle(Logs) ytitle(Log of GSP) xtitle(Fiscal Year) *Use the Stata routine xtpurt, with test options proposed by Herwartz and /// Siedenburg (2008), Demetrescu and Hanck (2012), and /// Herwartz et al. (2019). In the three test options, the null /// hypothesis is that the panels (i.e., states) contain non-stationary data /// or unit roots. * xtpurt, with test options proposed by Herwartz and Siedenburg (hs) xtpurt lny1, test(hs) xtpurt lnx1, test(hs) xtpurt lnx2, test(hs) xtpurt lnx4, test(hs) * xtpurt, with test options proposed by Demetrescu and Hanck (dh) xtpurt lny1, test(dh) xtpurt lnx1, test(dh) xtpurt lnx2, test(dh) xtpurt lnx4, test(dh) * xtpurt, with test options proposed by Herwartz, Maxand, and Walle (hmw) xtpurt lny1, test(hmw) trend xtpurt lnx1, test(hmw) trend xtpurt lnx2, test(hmw) trend xtpurt lnx4, test(hmw) trend * xtpurt, with all test options with first-differences (D1) xtpurt D1lny1, test(all) xtpurt D1lnx1, test(all) xtpurt D1lx2, test(all) xtpurt D1lnx4, test(all) * xtcointtest - tests for cointegration *test for no cointegration with and without demeaning /// (first subtracting the cross-sectional averages from the series ) the data /// xtcointtest kao lny1 lnx1 lnx2 lnx4 xtcointtest kao lny1 lnx1 lnx2 lnx4, demean xtcointtest pedroni lny1 lnx1 lnx2 lnx4 xtcointtest pedroni lny1 lnx1 lnx2 lnx4, demean xtcointtest westerlund lny1 lnx1 lnx2 lnx4 xtcointtest westerlund lny1 lnx1 lnx2 lnx4, demean *ECM-based cointegration test, developed by Westerlund (2007), that is robust /// to structural breaks in the intercept and slope of the cointegrated /// regression, serial correlation, and heteroscedasticity . xtwest lny1 lnx1 lnx2 lnx4, constant lags(0 3) *Tests using Stata user-written routine xtcdf (Wursten 2017) for /// cross-sectional independence, using updated version ssc install xtcdf, replace xtcdf lny1 lnx1 lnx2 lnx4 *Test of homogeneous coefficients utilize the Stata user-written /// xthst (Ditzen and Bersvendsen 2020) routine ssc install xthst, replace xthst D1.lny1 D1.L1.lny1 D1.lnx1 D1.lnx2 D1.lnx4, hac whitening xthst lny1 L1.lny1 lnx1 lnx2 lnx4, hac whitening *HCR with DCCE and MG estimators *using the Stata-user written xtdcce2133 (Ditzen 2018b) search xtdcce2, all *click on st0536, then install or type: net install st0536.pkg, replace *run a autoregressive model with distributed lags (ARDLs) of (1 1 1) and /// cross-sectional with lags (3 3 3 3) within an ECM framework xtdcce2 D1.lny1 L1.D1.lny1 L1.D1.lnx1 L1.D1.lnx2 L1.D1.lnx4, reportc /// cr(_all) cr_lags(3 3 3 3) lr(L1.lny1 lnx1 lnx2 lnx4) lr_options(ardl) *Pesaran (2015) test for weak cross-sectional dependence xtcd2 *run xtdcce2 with the options lr(xtpmg) and exponent xtdcce2 D1.lny1 L1.D1.lny1 L1.D1.lnx1 L1.D1.lnx2 L1.D1.lnx4, reportc /// cr(_all) cr_lags(3 3 3 3) lr(L1.lny1 lnx1 lnx2 lnx4) lr_options(xtpmg) exponent *If we want to see the estimates for the individual states, then we include the /// option showindividual. xtdcce2 D1.lny1 L1.D1.lny1 L1.D1.lnx1 L1.D1.lnx2 L1.D1.lnx4, /// reportc cr(_all) cr_lags(1 3 3 3) lr(L1.lny1 lnx1 lnx2 lnx4) /// lr_options(ardl) exponent showin *end
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Titus, M. (2021). Advanced Statistical Techniques:II. In: Higher Education Policy Analysis Using Quantitative Techniques . Quantitative Methods in the Humanities and Social Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-60831-6_9
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