【正文】 ? Command (Input / Output) ? Batch Mode ? Writing Program ? Online Help GAUSS Basics ? Basic Operations on Matrices + ^ .* ./ % ! * / . .= .== .= . ./= = == = /= .not .and .or .xor not and or xor ~ | .*. *~ ? Special Operators [] {} : . 39。 then。 elseif。 ? For Loop for i (start,stop,step)。 ? Do Loop do while ... endo。 GAUSS Programming Write Your Own Functions ? Single Line Function fn fn_name(args) = code_for_function。 local list of local variables。 retp(ret_list)。 GAUSS Programming Example 1 ? Do you know the accuracy of your puter39。X are 4+e2, e2, e2, and e2. How small of the value of e your puter will allow so that X39。 e=。 x=one|(e.*eye(4))。 r=eigrs(x39。 print r39。x)。 e=e/10。 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)。 r = rows(x)。 y = qtoa1(x[.,1])。 do until i c。 i = i+1。 retp(y)。 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。 initialize global variables ? /* ? ** Set input control variables for model estimation ? ** (. _names for variable names, see Appendix A) ? */ ? call estimate(y,x)。 do model prediction ? end。 n=49。 w1=wd。 w3=denseSubmat(sparseOnes(spwpower(spw(w1),3),n,n),0,0)。 w5=denseSubmat(sparseOnes(spwpower(spw(w1),5),n,n),0,0)。 call spwplot(spw(w1))。 include gpe\。 local x,y,d。 convert to radian y=pi*yc/180。).*sin(y)+cos(y39。x)))。 endp。 ( 39。 ) 39。 )ij i jk Ei j nV a ree????? ? ? ? ? ? ????????XX εεβ X X X X X X1? ( 39。????yX βεβ X X X y( | ) 0( | )EV a r???εXεXSpatial HAC Estimator General Heteroscedasticity ? HuberWhite Estimator 239。? ?? ( ) ( 39。( 39。, 1 , 2 , . . . , 0ij i jijk i jki j n i jee ?? ? ?? ? ? ? ??????? ? ?XXSpatial HAC Estimator General Heteroscedasticity and Autocorrelation ? First Law of Geography ? Kelejian and Prucha (2020) 39。? ?? ( ) ( 39。( 39。139。1111? ?39。 ) 39。 )ni i iiLni i i i i iiLVareee?? ? ?? ? ???????? ? ???????????X X x xx x x xβ X X X X X XCrime Equation Anselin (1988) [] ? Basic Model (Crime Rate) = a + b (Family Ine) + g (Housing Value) + e ? Spatial HAC Estimator OLS Parameter OLS . Robust Robust b g a R2 GDP Output Production China 2020 [] ? CobbDouglass Production Function ln(GDP) = a + b ln(L) + g ln(K) + e ? Spatial HAC Estimator OLS Parameter OLS . Robust Robust b g a R2 Spatial Exogeneity Lagged Explanatory Variables ? Spatial Exogenous Model 39。)EWVa r W E e????? ???εXIε X ε ε GDP Output Production China 2020 [] ? CobbDouglass Production Function ln(GDP) = a + b ln(L) + g ln(K) + bw W ln(L) + gw W ln(K) + e OLS Parameter OLS . Robust b g bw gw a R2 Spatial Endogeneity Lagged Dependent Variable ? Spatial Lag Model W?? ? ?y y X βε11 , 2 , .. .,ni j jj wyWin??????????y2( | , ) 0( | , ) (