【正文】 = e。 r=eigrs(x39。x)。 print r39。 invx=invpd(x39。x)。 print invx。 e=e/10。 endo。 GAUSS Programming Example 2 ? Write a singleline GAUSS function to convert a quarterly time series into the annual series by taking the average of every four data points. How you extend the singleline version of time series conversion function to a multiline procedure so that it can handle the conversion of more than one time series? fn qtoa1(x) = meanc(reshape(x,rows(x)/4,4)39。)。 proc qtoa(x)。 local r,c,y,i。 r = rows(x)。 c = cols(x)。 y = qtoa1(x[.,1])。 i = 2。 do until i c。 y = y~qtoa1(x[.,i])。 i = i+1。 endo。 retp(y)。 endp。 GPE2 for GAUSS ? GPE2 is a package of econometric procedures written in GAUSS. There are four main functions, driven by a set of global control variables: ? Reset Set up global control (input and output) variables. ? Estimate Estimation of a linear or generalized linear model. ? Forecast Forecasting based on a linear or generalized linear model. ? Optimize Estimation of a nonlinear model. ? Gpehelp Online help of using GPE2. GPE2 for GAUSS Selected Global Control Variables ? Input Control Variables _names, _begin, _end, _rstat, _rtest, _rplot, _rlist,_const, _restr, _vcov, _hacv, _weight, _ivar, _dlags, _pdl, _eq, _id, _ar, _ma, _arma, _garch, _acf, _acf2, _nlopt, _method, _iter, _tol, _step, _conv, _fbrgin, _fend, _fstat, _fplot, _splag, _spw, _spwd ? Output Control Variables __y, __x, __e, __b, __vb, __v, __rss, __r2, __f, __vf, __t, __a, __va GPE2 for GAUSS A Typical Program Using GPE2 ? /* ? ** Comments on program title, purposes, and the usage of the program ? */ ? use gpe2。 @ using GPE package (version 2) @ ? // this must be the first executable statement ? /* ? ** Writing output to file or sending it to printer: ? ** specify file name for output ? */ ? // Loading data: read data series from data files. ? /* ? ** Generating or transforming data series: ? ** create and generate variables with data scaling or transformation ? ** (. y and x are generated here and will be used below) ? */ ? call reset。 @ initialize global variables @ ? /* ? ** Set input control variables for model estimation ? ** (. _names for variable names, see Appendix A) ? */ ? call estimate(y,x)。 @ do model estimation @ ? // variables y, x are generated earlier ? /* ? ** Retrieve output control variables for model evaluation and analysis ? */ ? /* ? ** Set more input control variables if needed, for model prediction ? ** (. _b for estimated parameters) ? */ ? call forecast(y,x)。 @ do model prediction @ ? end。 @ important: don’t fet this @ GPE2 for GAUSS Examples ? More than 70 examples covering linear and nonlinear least squares, instrumental variables, system of simultaneous linear equations, time series analysis, panel data, limited dependent variables, maximum likelihood, generalized methods of moments, and … ? The latest extensions include spatial lag model estimation, hypothesis testing, and robust inference. ? Updates for spatial econometric analysis (, ). Software Demonstration ? Installation ? GAUSS Light ? GPE2 for GAUSS ? Example: China GDP Output ? CobbDouglas Production Function ln(GDP) = a + b ln(L) + g ln(K) + e ? Generalized CobbDouglas Production Function ln(GDP) + q GDP = a + b ln(L) + g ln(K) + e China GDP Output Production Using GPE2 for GAUSS: A Review ? CobbDouglas Production Function () ? OLS Estimator ? Hypothesis Testing ? Constant Returns to Scale? ? Homoscedasticity? ? Generalized Production Function (Zellner and Revanka, 1970) () ? Output Effects? ? Instrumental Variables References ? . Lin, Computational Econometrics: GAUSS Programming for Econometricians and Financial Analysts, ETEXT Publishing, Los Angeles, 2020. ? . Chung, Learning Econometrics with GAUSS, Institute of Economics, Academia Sinica, 2020. ? A. Zellner and N. Revankar, Generalized Production Functions, Review of Economic Studies, 1970, 241250. Spatial Econometric Analysis Using GAUSS 3 KuanPin Lin Portland State University Spatial Weights Matrix ? Anselin (1988) [] ? China 30 Provinces [, ] ? Ertur and Kosh (2020) [] ? Homework ? . 48 Lower States [] ? . 3109 Counties [] [] Spatial Contiguity Weights Matrix Anselin (1988): W1, W2, W3 use gpe2。 n=49。 load wd[n,n]=c:\course09\WISE\data\anselin\