├── .DS_Store ├── LICENSE ├── README.md ├── ch1 ├── FqReport1.xlsx ├── Solow.R ├── Solowemp.R └── figures1.R ├── ch2 ├── .Rapp.history ├── Ramsey.R ├── figures2.R └── figures2appendix.R ├── ch3 └── Ramsey_tax.R ├── ch4 ├── FqReport4.csv ├── FqReport4.xlsx ├── RBC.R ├── bcycle.R └── figures4.R ├── ch5 ├── CIA.R ├── NK.R ├── NK_linear.R ├── cia_mss.csv ├── cia_techs.csv ├── figures5.R ├── nkm_mps.csv └── nkm_techs.csv ├── ch6 ├── RBC_BK.R ├── RBC_PolIter_Chebyshev.R ├── Ramsey_PolIter_Chebyshev.R └── figures6.R ├── ch7 ├── NK_commit.R ├── NK_discretion.R ├── figures7.R ├── nkm_commit.csv └── nkm_discretion.csv ├── ch8 ├── dataplot.R ├── dset_fig.csv └── figures8.R ├── ch8_dynare ├── FqReport8.csv ├── FqReport8.xlsx ├── NK_Linear_EST.mod ├── coda.R ├── main.m ├── script_dataset.m └── util_csvwrite.m ├── dynare ├── NK_det.mod ├── NK_linear_det.mod ├── NK_linear_stoch.mod ├── RBC_det.mod ├── RBC_linear_det.mod ├── RBC_linear_stoch.mod ├── RBC_stoch.mod ├── Ramsey_tax1.mod └── Ramsey_tax2.mod └── use_dynare.pdf /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rhasumi/dynamicmodels/6f4698e0d39f6495827b5fe1448991e6a3c0921b/.DS_Store -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2020 Ryo Hasumi 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 『動学マクロ経済学へのいざない』（日本評論社、2020年）プログラム 2 | 3 | 作成者：蓮見 亮 4 | 5 | サポートページは[こちら](https://rhasumi.github.io/pages/dynamicmodels/)（https://rhasumi.github.io/pages/dynamicmodels/) 6 | -------------------------------------------------------------------------------- /ch1/FqReport1.xlsx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rhasumi/dynamicmodels/6f4698e0d39f6495827b5fe1448991e6a3c0921b/ch1/FqReport1.xlsx -------------------------------------------------------------------------------- /ch1/Solow.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 1, Solow model 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | #-------------------- 11 | # ソローモデル 12 | #-------------------- 13 | 14 | alpha <- 0.30 15 | delta <- 0.1 16 | s <- 0.2 17 | g <- 0.02 18 | n <- -0.01 19 | 20 | fz1 <- function(k) s*k^alpha 21 | fz2 <- function(k) (g + n + delta)*k 22 | dk <- function(k) (s*k^alpha-(g + n + delta)*k)/(1+g)/(1+n) 23 | 24 | ks <- (s/(g+n+delta))^(1/(1-alpha)) 25 | 26 | kk <- seq(0,10,length = 201) 27 | 28 | par(ps = 15) 29 | par(mai = c(0.85, 0.85, 0.35, 0.35)) 30 | plot(cbind(kk, fz1(kk)), typ = "l", xlim = c(0, 5.7), ylim = c(0,0.6), 31 | xlab = expression(k[t]), ylab = expression(z)) 32 | lines(cbind(kk, fz2(kk))) 33 | abline(v = ks, lty = 2) 34 | abline(h = 0) 35 | 36 | text(1, 0.26, labels = expression(paste("z = s ",k[t]^alpha))) 37 | text(4.8, 0.42 , labels = expression(paste("z = ",(g+n+delta)," ", k[t]))) 38 | text(2.9, 0.5, labels = expression(paste(k[t]," = ","k*"))) 39 | 40 | axis(side=1, labels = expression(k[1]), at = ks*.5) 41 | 42 | k1 <- ks*.5 43 | segments(k1, 0, ks*.5, fz2(k1), lty = 2) 44 | arrows(k1, fz2(k1),k1, fz1(k1),length = 0.1,col=4,lwd = 2) 45 | arrows(k1, fz1(k1),k1+(fz1(k1)-fz2(k1))*6 ,fz1(k1),length = 0.1,col=4,lty=2,lwd = 2) 46 | 47 | dev.copy2eps(file= figpath %+% "solow1.eps") 48 | 49 | #----------------------------- 50 | 51 | ka <- ks*.5 52 | dka <- NA 53 | for(i in 2:110) { 54 | dka[i] <- dk(ka[i-1]) 55 | ka[i] <- ka[i-1] + dka[i] 56 | } 57 | 58 | par(ps = 17.5) 59 | par(mfrow = c(2, 1)) 60 | par(mai = c(0.85*0.5, 0.68*0.75, 0.68*0.75, 0.5)*1.1) 61 | plot(ka, xlim = c(0, 100), xlab = "", main = expression(k[t]), ylab = "", typ = "l") 62 | abline(h = k1, lty = 2, col = 2) 63 | axis(side=4, labels = expression(k[1]), at = k1, las = 2) 64 | axis(side=4, labels = expression("k*"), at = ks, las = 2) 65 | 66 | plot(dka, xlim = c(0, 100), xlab = "", main = expression(paste(Delta, k[t])), ylab = "", typ = "l") 67 | 68 | dev.copy2eps(file= figpath %+% "solow1a.eps") 69 | 70 | #----------------------------- 71 | 72 | k2 <- ks*2 73 | kb <- k2 74 | dkb <- NA 75 | for(i in 2:110) { 76 | dkb[i] <- dk(kb[i-1]) 77 | kb[i] <- kb[i-1] + dkb[i] 78 | } 79 | 80 | plot(kb, xlim = c(0, 100), xlab = "", main = expression(k[t]), ylab = "", typ = "l") 81 | abline(h = k2, lty = 2, col = 2) 82 | axis(side=4, labels = expression(k[1]), at = k2, las = 2) 83 | axis(side=4, labels = expression("k*"), at = ks, las = 2) 84 | 85 | plot(dkb, xlim = c(0, 100), xlab = "", main = expression(paste(Delta, k[t])), ylab = "", typ = "l") 86 | 87 | dev.copy2eps(file= figpath %+% "solow1b.eps") 88 | 89 | #----------------------------- 90 | 91 | 92 | fs <- function(s) (s^(alpha/(1-alpha))-s^(1/(1-alpha)))/(g+n+delta)^(alpha/(1-alpha)) 93 | 94 | par(ps = 15) 95 | par(mai = c(0.85, 0.85, 0.35, 0.35)) 96 | par(mfrow = c(1, 1)) 97 | curve(fs,0,1,ylim=c(0, 1.5), xlab = "s", ylab = expression("c*")) 98 | abline(h = 0, v = 0) 99 | 100 | cg <- fs(alpha) 101 | lines(cbind(c(0,1),c(cg,cg)),lty = 2) 102 | 103 | points(alpha,cg, pch=19) 104 | text(alpha+0.075,cg+0.075, labels = expression(paste("(",s[g],", ",c[g],")"))) 105 | 106 | text(0.8, 0.65, labels = expression("c* = f(s)")) 107 | text(0.85, 1.0, labels = expression(paste("c* = f(",s[g],")"))) 108 | 109 | dev.copy2eps(file= figpath %+% "solow2.eps") 110 | 111 | #----------------------------- 112 | 113 | fct <- function(k, s) (1-s)*k^alpha/(1+g)/(1+n) 114 | fks <- function(s) (s/(g+n+delta))^(1/(1-alpha)) 115 | dks <- function(k, s) (s*k^alpha-(g + n + delta)*k)/(1+g)/(1+n) 116 | 117 | sA0 <- 0.2 118 | sA1 <- alpha 119 | 120 | ktA <- fks(sA0) 121 | ctA <- fct(ktA[1], sA0) 122 | 123 | for(i in 2:120) 124 | ktA[i] <- ktA[i-1] + dks(ktA[i-1], sA1) 125 | 126 | ctA[2:120] <- fct(ktA[-1], sA1) 127 | 128 | 129 | par(ps = 17.5) 130 | par(mfrow = c(2, 1)) 131 | par(mai = c(0.85*0.5, 0.68*0.75, 0.68*0.75, 0.5)*1.1) 132 | plot(ctA, xlim = c(0, 100), xlab = "", main = expression(c[t]), ylab = "", typ = "l") 133 | axis(side=4, labels = expression(c[0]), at = ctA[1], las = 2) 134 | 135 | plot(ktA, xlim = c(0, 100), xlab = "", main = expression(k[t]), ylab = "", typ = "l") 136 | axis(side=4, labels = expression(k[0]), at = ktA[1], las = 2) 137 | 138 | dev.copy2eps(file= figpath %+% "solcaseA.eps") 139 | 140 | #----------------------------- 141 | 142 | sB0 <- alpha 143 | sB1 <- 0.4 144 | 145 | ktB <- fks(sB0) 146 | ctB <- fct(ktB[1], sB0) 147 | 148 | for(i in 2:120) 149 | ktB[i] <- ktB[i-1] + dks(ktB[i-1], sB1) 150 | 151 | ctB[2:120] <- fct(ktB[-1], sB1) 152 | 153 | plot(ctB, xlim = c(0, 100), xlab = "", main = expression(c[t]), ylab = "", typ = "l") 154 | axis(side=4, labels = expression(c[0]), at = ctB[1], las = 2) 155 | 156 | plot(ktB, xlim = c(0, 100), xlab = "", main = expression(k[t]), ylab = "", typ = "l") 157 | axis(side=4, labels = expression(k[0]), at = ktB[1], las = 2) 158 | 159 | dev.copy2eps(file= figpath %+% "solcaseB.eps") 160 | 161 | #----------------------------- 162 | 163 | sC0 <- 0.4 164 | sC1 <- alpha 165 | 166 | ktC <- fks(sC0) 167 | ctC <- fct(ktC[1], sC0) 168 | 169 | for(i in 2:120) 170 | ktC[i] <- ktC[i-1] + dks(ktC[i-1], sC1) 171 | 172 | ctC[2:120] <- fct(ktC[-1], sC1) 173 | 174 | plot(ctC, xlim = c(0, 100), xlab = "", main = expression(c[t]), ylab = "", typ = "l") 175 | axis(side=4, labels = expression(c[0]), at = ctC[1], las = 2) 176 | 177 | plot(ktC, xlim = c(0, 100), xlab = "", main = expression(k[t]), ylab = "", typ = "l") 178 | axis(side=4, labels = expression(k[0]), at = ktC[1], las = 2) 179 | 180 | 181 | dev.copy2eps(file= figpath %+% "solcaseC.eps") 182 | 183 | -------------------------------------------------------------------------------- /ch1/Solowemp.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 1, Empirical analysis 3 | # modified on 2019/10/23 4 | #======================================= 5 | 6 | library(xlsx) 7 | 8 | dset <- read.xlsx("FqReport1.xlsx", 1) 9 | 10 | "%+%" <- function(x, y) paste(x, y, sep = "") 11 | # figpath <- "../../figs/" 12 | figpath <- "./" 13 | 14 | library(xtable) 15 | 16 | #--------------------------------------- 17 | 18 | alpha <- 1-mean(c((dset$YWH/dset$GDP11NCY)[5:14],(dset$YWH11N/dset$GDP11NCY)[15:39])) 19 | 20 | #yset <- seq(7,32,5) 21 | yset <- seq(9,39,5) 22 | 23 | lndy <- log(dset$GDP11CY[yset]/dset$GDP11CY[yset-5])/5*100 24 | lndk <- log(dset$KITFA11[yset-1]/dset$KITFA11[yset-1-5])/5*100 25 | lndl <- log(dset$L[yset]/dset$L[yset-5])/5*100 26 | 27 | contk <- alpha*lndk 28 | contl <- (1-alpha)*lndl 29 | conta <- lndy-contk-contl 30 | 31 | rslt1 <- cbind(lndy, contk, conta, contl) 32 | colnames(rslt1) <- c("GDP成長率", "資本の寄与度", "生産性の寄与度","労働の寄与度") 33 | rownames(rslt1) <- c("1984-1988","1989-1993","1994-1998","1999-2003","2004-2008","2009-2013","2014-2018") 34 | 35 | xtable(rslt1) 36 | 37 | #print(rslt1) 38 | 39 | #--------------------------------------- 40 | 41 | s0 <- (dset$I11NCY/dset$GDP11NCY) 42 | s <- mean(s0[30:39]) 43 | 44 | delta0 <- c() 45 | for(i in 10:39) 46 | delta0[i] <- (dset$I11CY[i] - (dset$KITFA11[i]-dset$KITFA11[i-1]))/dset$KITFA11[i-1] 47 | 48 | delta <- mean(delta0[10:39]) 49 | 50 | nexo <- log(dset$L[39]/dset$L[29])/10 51 | gexo <- mean(conta[6:7])/(1-alpha)*0.01 52 | 53 | c(alpha, delta, gexo, nexo, s) 54 | 55 | kstar <- (s/(gexo+nexo+delta))^(1/(1-alpha)) 56 | 57 | tmax <- 150 58 | 59 | Y0 <- dset$GDP11CY[39] 60 | K0 <- dset$KITFA11[38] 61 | L0 <- dset$L[39] 62 | A0 <- (Y0/K0^alpha)^(1/(1-alpha))/L0 63 | 64 | A <- c(1, cumprod(rep(1+gexo, tmax-1)))*A0 65 | L <- c(1, cumprod(rep(1+nexo, tmax-1)))*L0 66 | 67 | Yest <- K0^alpha*(A[1]*L[1])^(1-alpha) 68 | Kest <- dset$KITFA11[39] 69 | 70 | for( i in 2:tmax) { 71 | Yest[i] <- Kest[i-1]^alpha*(A[i]*L[i])^(1-alpha) 72 | Kest[i] <- (1-delta)*Kest[i-1] + s*Yest[i] 73 | } 74 | 75 | yplot <- 2018:2167 76 | yplot1 <- yplot-2017 77 | 78 | Ystar <- kstar^alpha*A*L 79 | kest <- c(K0, Kest[-tmax])/A/L 80 | 81 | 82 | if (.Platform$OS.type == "windows") windows(10, 5) 83 | par(mfrow = c(1,2)) 84 | par(ps = 15) 85 | par(mai = c(0.85, 0.68*0.75, 0.68*0.75, 0.35*1.5)*1) 86 | plot(cbind(yplot,Yest[yplot1]/10^3), typ ="l", xlab = "Year", main = expression(Y[t]), xlim = range(yplot), ylim = range(Ystar/1000), log="y") 87 | lines(cbind(yplot,Ystar[yplot1]/10^3), lty = 2) 88 | axis(side=1, labels = 2018, at = 2018,las = 1) 89 | 90 | 91 | plot(cbind(yplot,kest[yplot1]), typ ="l", ylim = range(kest), xlab = "Year", main = expression(k[t]), xlim = range(yplot)) 92 | lines(cbind(yplot,kstar), lty = 2) 93 | axis(side=1, labels = 2018, at = 2018,las = 1) 94 | axis(side=4, labels = expression("k*"), at = kstar,las = 2) 95 | 96 | dev.copy2eps(file= figpath %+% "solforecast1.eps") 97 | dev.off() 98 | 99 | -------------------------------------------------------------------------------- /ch1/figures1.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 1, Other figures 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | #-------------------- 11 | # 指数関数、対数関数 12 | #-------------------- 13 | 14 | par(ps = 20) 15 | par(mai = c(0.85, 0.88, 0.35, 0.35)) 16 | curve(exp, -3, 3) 17 | dev.copy2eps(file= figpath %+% "exp.eps") 18 | 19 | curve(log, -0, 6, ylab = "ln(x)") 20 | dev.copy2eps(file= figpath %+% "log.eps") 21 | 22 | #-------------------- 23 | # 自然対数の意味 24 | #-------------------- 25 | yt <- cumprod(c(1, rep(1.05, 100)))*100 26 | plot(cbind(0:40, yt[1:41]), typ = "l", xlab = "t", ylab = expression(Y[t])) 27 | dev.copy2eps(file= figpath %+% "exln1.eps") 28 | 29 | plot(cbind(0:40, log(yt[1:41])), typ = "l", xlab = "t", ylab = expression(paste(paste("ln(", Y[t]), ")"))) 30 | dev.copy2eps(file= figpath %+% "exln2.eps") 31 | 32 | #-------------------- 33 | # 生産関数 34 | #-------------------- 35 | par(ps = 20) 36 | fk <- function(K) K^0.3 37 | curve(fk, 0, 3, xlab = "K", ylab = "f(K)") 38 | dev.copy2eps(file= figpath %+% "fk1.eps") 39 | dev.copy2pdf(file= figpath %+% "fk1.pdf") 40 | 41 | curve(fk, 0, 3, xlab = "K", ylab = "f(K)") 42 | points(cbind(c(1,1.5,2),fk(c(1,1.5,2))), pch=19) 43 | 44 | #-------------------- 45 | # 微分の意味 46 | #-------------------- 47 | b1 <- fk(2)-1 48 | b2 <- (fk(1.5)-1)/0.5 49 | # b3 <- (fk(1.1)-1)/0.1 50 | b4 <- 0.3 51 | 52 | abline(1-b1, b1, lty = 2, col = 4) 53 | abline(1-b2, b2, lty = 3, col = 4) 54 | abline(1-b4, b4, col = 4) 55 | 56 | legend(1.7, 0.3, legend = c("傾き = 0.23 ","傾き = 0.26" ,"傾き = 0.3 "), lty = c(2,3,1), col = c(4,4,4)) 57 | dev.copy2eps(file= figpath %+% "fk2.eps", family="Japan1GothicBBB") 58 | dev.copy2pdf(file= figpath %+% "fk2.pdf", family="Japan1GothicBBB") 59 | 60 | 61 | par(ps = 15) 62 | fr <- function(r) log(1+r) 63 | curve(fr, -1, 2, xlab = "r", ylab = "y") 64 | abline(0, 1, lty = 1, col = 4) 65 | 66 | text(-0.5, -2.5, "y = ln(1+r)") 67 | text(-0.75, -0.5, "y = r") 68 | 69 | dev.copy2eps(file= figpath %+% "ln1r.eps") 70 | 71 | -------------------------------------------------------------------------------- /ch2/Ramsey.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 2, Ramsey model 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | library(nleqslv) 11 | 12 | #---------------------------------------- 13 | 14 | alpha <- 0.3 15 | beta <- 0.99 16 | delta <- 0.25 17 | At <- 1.0 18 | 19 | #---------------------------------------- 20 | 21 | Kt <- ((1/beta+delta-1)/alpha/At)^(1/(alpha-1)) 22 | FCt <- function(K) At*K^alpha - delta*K 23 | Kmax <- (delta/At)^(1/(alpha-1)) 24 | 25 | if (.Platform$OS.type == "windows") windows(7, 7) 26 | par(ps = 15) 27 | par(mai = c(0.85, 0.85, 0.35, 0.35)) 28 | curve(FCt, 0, Kmax, ylim = c(0, 1), xlab = expression(K), ylab = expression(C)) 29 | abline(h = 0) 30 | 31 | lines(cbind(c(Kt, Kt),c(0, 100))) 32 | points(Kt,FCt(Kt), pch=19) 33 | 34 | text(4, 0.4, expression(paste(Delta,K[t]," = 0",sep=""))) 35 | text(2, 0.95, expression(paste(Delta,C[t]," = 0",sep=""))) 36 | 37 | axis(1, labels = c(expression(K[max])), at = Kmax) 38 | segments(Kmax, -1, Kmax, 0, lty = 2) 39 | 40 | dev.copy2eps(file= figpath %+% "dcdk.eps") 41 | 42 | #---------------------------------------- 43 | 44 | Kss <- ((1/beta+delta-1)/alpha/At)^(1/(alpha-1)) 45 | Css <- At*Kss^alpha - delta*Kss 46 | 47 | objfun0 <- function(X, maxT, X0, Xss = Css) { 48 | 49 | XX <- matrix(X, maxT, 2) 50 | C <- c(XX[, 1], Xss) 51 | K <- c(X0, XX[, 2]) 52 | 53 | ret <- matrix(NA, maxT, 2) 54 | for(t in 1:maxT) { 55 | ret[t, 1] <- C[t+1]/C[t]-beta*(alpha*At*K[t+1]^(alpha-1)-delta+1) 56 | ret[t, 2] <- K[t+1]-At*K[t]^alpha-(1-delta)*K[t]+C[t] 57 | } 58 | return(c(ret)) 59 | } 60 | 61 | maxT <- 30 62 | Xinit <- c(rep(Css,maxT), rep(Kss,maxT)) 63 | 64 | #-------------------- 65 | # シミュレーション１ 66 | #-------------------- 67 | 68 | K01 <- Kss*0.5 69 | objfun1 <- function(X) objfun0(X, maxT, K01) 70 | rslt1 <- nleqslv(Xinit, objfun1) 71 | 72 | rslt1x <- matrix(rslt1$x, maxT, 2) 73 | 74 | Ct1 <- c(rslt1x[, 1], Css) 75 | Kt1 <- c(K01, rslt1x[, 2]) 76 | 77 | #-------------------- 78 | # シミュレーション２ 79 | #-------------------- 80 | 81 | K02 <- Kss*2 82 | objfun2 <- function(X) objfun0(X, maxT, K02) 83 | rslt2 <- nleqslv(Xinit, objfun2) 84 | 85 | rslt2x <- matrix(rslt2$x, maxT, 2) 86 | 87 | Ct2 <- c(rslt2x[, 1], Css) 88 | Kt2 <- c(K02, rslt2x[, 2]) 89 | 90 | #-------------------- 91 | # 作図 92 | #-------------------- 93 | 94 | par(ps = 15) 95 | par(mai = c(0.85*0.75, 0.68*0.75, 0.68*0.75, 0.35*0.75)) 96 | par(mfrow = c(2,1)) 97 | plot(cbind(1:(maxT+1), Ct1), typ = "l", main = expression(C[t]), xlab = "", ylab = "") 98 | plot(cbind(1:(maxT+1), Kt1), typ = "l", main = expression(K[t]), xlab = "", ylab = "") 99 | 100 | dev.copy2eps(file= figpath %+% "ramck.eps") 101 | 102 | par(ps = 15) 103 | par(mai = c(0.85, 0.85, 0.35, 0.35)) 104 | par(mfrow = c(1,1)) 105 | curve(FCt, 0, 3, ylim = c(0.5, 1.1), xlab = expression(K[t]), ylab = expression(C[t])) 106 | abline(h = 0) 107 | lines(cbind(c(Kt, Kt),c(0, 100))) 108 | points(Kt,FCt(Kt), pch=19) 109 | 110 | for(i in 1:12){ 111 | arrows(Kt1[i], Ct1[i], Kt1[i+1], Ct1[i+1], length = 0.1) 112 | arrows(Kt2[i], Ct2[i], Kt2[i+1], Ct2[i+1], length = 0.1) 113 | } 114 | for(i in 13:(maxT-1)){ 115 | segments(Kt1[i], Ct1[i], Kt1[i+1], Ct1[i+1]) 116 | segments(Kt2[i], Ct2[i], Kt2[i+1], Ct2[i+1]) 117 | } 118 | 119 | dev.copy2eps(file= figpath %+% "dcdk2.eps") 120 | 121 | -------------------------------------------------------------------------------- /ch2/figures2.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 2, Other figures 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | #-------------------- 11 | # 効用関数 12 | #-------------------- 13 | U <- function(a, b) sqrt(a*b) 14 | Ub <- function(a, U) U^2/a 15 | 16 | feasible <- c() 17 | amax <- 6 18 | bmax <- 12 19 | budgit <- 600 20 | pa <- 100 21 | pb <- 50 22 | for (a in 0:amax) 23 | for(b in 0:bmax) 24 | if (a*pa + b*pb <= budgit) 25 | feasible <- rbind(feasible, c(a,b)) 26 | 27 | par(ps = 15) 28 | plot(feasible, xlab = "a", ylab = "b", xlim = c(0,bmax), ylim = c(0,bmax), pch = 20) 29 | 30 | dev.copy2eps(file= figpath %+% "feasible1.eps") 31 | 32 | Ub1 <- function(a) Ub(a, U(4, 4)) 33 | curve(Ub1,0,10, xlab = "a", ylab = "b", xlim = c(0,bmax), ylim = c(0,bmax)) 34 | points(feasible, pch = 20) 35 | 36 | text(4.3, 4.3, labels = "C") 37 | text(2.3, 8.3, labels = "D") 38 | text(3.3, 6.3, labels = "E") 39 | 40 | dev.copy2eps(file= figpath %+% "feasible2.eps") 41 | 42 | par(ps = 20) 43 | par(mai = c(0.85, 0.88, 0.35, 0.35)) 44 | funsqx <- function(x) sqrt(x) 45 | par(ps = 20, mai = c(0.85, 0.9, 0.68, 0.35)) 46 | curve(funsqx, 0, 6, main = "", ylab = expression(sqrt(x))) 47 | dev.copy2eps(file= figpath %+% "sqrtx.eps") 48 | 49 | funx2 <- function(x) x^2 50 | par(ps = 20, mai = c(0.85, 1.0, 0.68, 0.35)) 51 | curve(funx2, -3, 3, main = "", ylab = expression(x^2)) 52 | dev.copy2eps(file= figpath %+% "x2.eps") 53 | 54 | #-------------------- 55 | # 効用最大化 56 | #-------------------- 57 | 58 | U1 <- function(a, b, U) exp(U-log(a)) 59 | U2 <- function(a, b) U1(a, b, log(125/4)) 60 | 61 | par(ps = 15) 62 | par(mai = c(0.85, 0.85, 0.2, 0.2)) 63 | curve(U2, 0, 15, xlim=c(0,13),ylim=c(0,13),xlab = "a", ylab = "b") 64 | lines(cbind(c(0, 0),c(0,100))) 65 | lines(cbind(c(0, 100),c(0,0))) 66 | lines(cbind(c(10, 0),c(0,12.5))) 67 | 68 | points(5,6.25, pch=19) 69 | text(7.5,6.25, "(a = 5, b = 6.25)") 70 | 71 | text(5, 12, "ln(a) + ln(b) = U*") 72 | #text(10, 4, "U* = ln(a) + ln(b)") 73 | text(11, 1.9, "100a + 80b = 1000") 74 | 75 | dev.copy2eps(file= figpath %+% "util1.eps") 76 | 77 | -------------------------------------------------------------------------------- /ch2/figures2appendix.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 2, Figures of appendix 3 | # modified on 2020/7/28 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | beta <- 0.99 11 | alpha <- 0.3 12 | delta <- 0.25 13 | 14 | Kss <- ((1/beta+delta-1)/alpha)^(1/(alpha-1)) 15 | Css <- Kss^alpha - delta*Kss 16 | 17 | U <- function (C) log(C) 18 | g <- function (K, C) K^alpha + (1-delta)*K - C 19 | 20 | y <- 0 21 | for(i in 0:200) 22 | y <- y + beta^i * U(Css) 23 | 24 | #--------------------------------------- 25 | # チェビシェフ近似補間（1次） 26 | #--------------------------------------- 27 | 28 | library(nleqslv) # nleqslv 29 | 30 | xj <- function(n = 10){ 31 | -cos(0.5*(2*(1:n)-1)*pi/n) 32 | } 33 | 34 | trans0 <- function(x, a = -1, b = 1) { 35 | y <- (x-a)/(b-a)*2-1 36 | y 37 | } 38 | 39 | trans <- function(x, a = -1, b = 1) { 40 | y <- (x-a)/(b-a)*2-1 41 | y[which(y < -1)] <- -1 42 | y[which(y > 1)] <- 1 43 | y 44 | } 45 | 46 | rev <- function(y, a = -1, b = 1) (y+1)*(b-a)*0.5+a 47 | 48 | fn <- function(x, cc, nt){ 49 | size <- length(x) 50 | Tk <- matrix(1, size[1], 1) 51 | Tk <- cbind(Tk, x) 52 | for (k in 2:(nt-1)) 53 | Tk <- cbind(Tk, 2*x*Tk[, k]-Tk[, k-1]) 54 | Tk %*% cc 55 | } 56 | 57 | cheb <- function(x, coef, a, b, n) { 58 | fn(trans(matrix(x, 1), a, b), coef, n) 59 | } 60 | 61 | #--------------------------------------- 62 | # Policy Iteration 63 | #--------------------------------------- 64 | 65 | nt <- 40 66 | at <- 0.05 67 | bt <- 4.0 68 | 69 | node <- rev(xj(nt), at[1], bt[1]) 70 | apxfun <- function(x, coef) fn(trans(x, at, bt), coef, nt) 71 | 72 | niter <- 1000 73 | eps <- 0.0001 74 | 75 | # initialization 76 | f <- function (x) -45 + sqrt(x) 77 | cc <- rep(0, nt) 78 | v <- rep(0, nt) 79 | coef <- rep(0, nt) 80 | coef2 <- rep(0, nt) 81 | 82 | for(iter in 1:niter) { 83 | print(iter) 84 | v1 <- c(v) 85 | c1 <- c(cc) 86 | coef1 <- coef 87 | 88 | for(i in 1:nt) { 89 | obj <- function(ct) { 90 | st <- node[i] 91 | sa <- matrix(g(st,ct), 1) 92 | return(-U(ct)-beta*f(sa)) 93 | } 94 | opt <- optimize(obj, c(0.001, min((1 - delta) *node[i]+node[i]^alpha,bt*0.99))) 95 | cc[i] <- opt$minimum 96 | } 97 | fobj1 <- function(coef) cc - apxfun(node, coef) 98 | coef1 <- nleqslv(coef1, fobj1)$x 99 | hc <- function(x) cheb(x, coef1, at, bt, nt) 100 | 101 | for(i in 1:nt) { 102 | st <- node[i] 103 | ct <- max(min(hc(st), st), 0.001) 104 | y <- U(ct) 105 | for(k in 1:1000) { 106 | st <- g(st, ct) 107 | ct <- max(min(hc(st), st), 0.001) 108 | y <- y + beta^k * U(ct) 109 | } 110 | v[i] <- y 111 | } 112 | if (identical(abs(c(cc) - c1) < eps ,rep(T, nt))) break 113 | 114 | fobj2 <- function(coef) v - apxfun(node, coef) 115 | coef2 <- nleqslv(coef2, fobj2)$x 116 | f <- function(x) cheb(x, coef2, at, bt, nt) 117 | 118 | plot(cbind(node, v), typ = "l") 119 | print(abs(c(cc) - c1)) 120 | } 121 | 122 | #-------------------- 123 | # シミュレーション 124 | #-------------------- 125 | 126 | K01 <- Kss*0.5 127 | Kt1 <- K01 128 | Ct1 <- c() 129 | 130 | for(i in 1:31) { 131 | Ct1[i] <- hc(Kt1[i]) 132 | Kt1[i+1] <- g(Kt1[i], Ct1[i]) 133 | } 134 | 135 | K02 <- Kss*2 136 | Kt2 <- K02 137 | Ct2 <- c() 138 | for(i in 1:31) { 139 | Ct2[i] <- hc(Kt2[i]) 140 | Kt2[i+1] <- g(Kt2[i], Ct2[i]) 141 | } 142 | 143 | #-------------------- 144 | # 位相図の作図 145 | #-------------------- 146 | 147 | At <- 1 148 | Kss <- ((1/beta+delta-1)/alpha/At)^(1/(alpha-1)) 149 | FKt <- function(K) At*K^alpha + (1-delta)*K - Kss 150 | FCt <- function(K) At*K^alpha - delta*K 151 | 152 | maxT <- 31 153 | 154 | if (.Platform$OS.type == "windows") windows(7, 7) 155 | par(ps = 15) 156 | par(mai = c(0.85, 0.88, 0.35, 0.35)) 157 | par(mfrow = c(1,1)) 158 | #curve(FCt, 0, 3, ylim = c(0.3, 1.7), xlim = c(0.05, 2.5), xlab = expression(K[t]), ylab = expression(C[t]), main = "Phase Diagram",axes = F) 159 | curve(FCt, 0, 3, ylim = c(0.3, 1.225), xlim = c(0.05, 2.5), xlab = expression(K[t]), ylab = expression(C[t]), main = "",axes = F) 160 | abline(h = 0) 161 | #lines(cbind(c(Kss, Kss),c(0, 100))) 162 | 163 | lines(cbind(seq(0,3, 0.01),FKt(seq(0,3, 0.01)))) 164 | points(Kss,FCt(Kss), pch=19) 165 | 166 | axis(2) 167 | axis(1, labels = c(0:3), at = 0:3) 168 | abline(v = c(K01,K02), lty = 2) 169 | box() 170 | 171 | axis(1, labels = c(expression(K[1]^A)), at = K01) 172 | axis(1, labels = c(expression(K[1]^B)), at = K02) 173 | axis(1, labels = c(expression("K*")), at = Kss) 174 | 175 | for(i in 1:12){ 176 | arrows(Kt1[i], Ct1[i], Kt1[i+1], Ct1[i+1], length = 0.05) 177 | arrows(Kt2[i], Ct2[i], Kt2[i+1], Ct2[i+1], length = 0.05) 178 | } 179 | for(i in 13:(maxT-1)){ 180 | segments(Kt1[i], Ct1[i], Kt1[i+1], Ct1[i+1]) 181 | segments(Kt2[i], Ct2[i], Kt2[i+1], Ct2[i+1]) 182 | } 183 | 184 | 185 | FCa <- function(K, C) beta*(alpha*g(K,C)^(alpha-1)-delta+1)*C 186 | const <- 1.06 187 | 188 | Kt1a <- K01 189 | Ct1a <- hc(K01)*const 190 | for(i in 1:31) { 191 | Kt1a[i+1] <- g(Kt1a[i], Ct1a[i]) 192 | Ct1a[i+1] <- FCa(Kt1a[i], Ct1a[i]) 193 | } 194 | 195 | Kt1b <- K01 196 | Ct1b <- hc(K01)/const 197 | for(i in 1:31) { 198 | Kt1b[i+1] <- g(Kt1b[i], Ct1b[i]) 199 | Ct1b[i+1] <- FCa(Kt1b[i], Ct1b[i]) 200 | } 201 | 202 | Kt2a <- K02 203 | Ct2a <- hc(K02)*const 204 | for(i in 1:31) { 205 | Kt2a[i+1] <- g(Kt2a[i], Ct2a[i]) 206 | Ct2a[i+1] <- FCa(Kt2a[i], Ct2a[i]) 207 | } 208 | 209 | Kt2b <- K02 210 | Ct2b <- hc(K02)/const 211 | for(i in 1:31) { 212 | Kt2b[i+1] <- g(Kt2b[i], Ct2b[i]) 213 | Ct2b[i+1] <- FCa(Kt2b[i], Ct2b[i]) 214 | } 215 | 216 | for(i in 1:maxT){ 217 | if (!is.nan(Kt1a[i])) 218 | arrows(Kt1a[i], Ct1a[i], Kt1a[i+1], Ct1a[i+1], length = 0.05, col = 2, lty = 1) 219 | if (!is.nan(Kt1b[i])) 220 | arrows(Kt1b[i], Ct1b[i], Kt1b[i+1], Ct1b[i+1], length = 0.05, col = 4, lty = 1) 221 | if (!is.nan(Kt2a[i])) 222 | arrows(Kt2a[i], Ct2a[i], Kt2a[i+1], Ct2a[i+1], length = 0.05, col = 2, lty = 1) 223 | if (!is.nan(Kt2b[i])) 224 | arrows(Kt2b[i], Ct2b[i], Kt2b[i+1], Ct2b[i+1], length = 0.05, col = 4, lty = 1) 225 | } 226 | 227 | points(cbind(Kt1a[1], Ct1a[1]), pch = 15, col = 2) 228 | points(cbind(Kt1[1], Ct1[1]), pch = 4) 229 | points(cbind(Kt1b[1], Ct1b[1]), pch = 17, col = 4) 230 | 231 | points(cbind(Kt2a[1], Ct2a[1]), pch = 15, col = 2) 232 | points(cbind(Kt2[1], Ct2[1]), pch = 4) 233 | points(cbind(Kt2b[1], Ct2b[1]), pch = 17, col = 4) 234 | 235 | 236 | maxT2 <- 100 237 | 238 | Kt3a <- Kss-0.01 239 | Ct3a <- Css+0.01 240 | for(i in 1:maxT2) { 241 | Kt3a[i+1] <- g(Kt3a[i], Ct3a[i]) 242 | Ct3a[i+1] <- FCa(Kt3a[i], Ct3a[i]) 243 | } 244 | end <- min(which(is.nan(Ct3a))) 245 | #Kt3a[end] <- Kt1a[8]+0.04 246 | #Ct3a[end] <- 1.6 247 | 248 | Kt3b <- Kss+0.01 249 | Ct3b <- Css-0.01 250 | for(i in 1:maxT2) { 251 | Kt3b[i+1] <- g(Kt3b[i], Ct3b[i]) 252 | Ct3b[i+1] <- FCa(Kt3b[i], Ct3b[i]) 253 | } 254 | 255 | for(i in 1:maxT2){ 256 | if (!is.nan(Kt3a[i])) 257 | arrows(Kt3a[i], Ct3a[i], Kt3a[i+1], Ct3a[i+1], length = 0.05, col = 1, lty = 1) 258 | if (!is.nan(Kt3b[i])) 259 | arrows(Kt3b[i], Ct3b[i], Kt3b[i+1], Ct3b[i+1], length = 0.05, col = 1, lty = 1) 260 | } 261 | 262 | text(Kss, Css+0.05, "F") 263 | 264 | dev.copy2eps(file= figpath %+% "phase_ram_ck.eps") 265 | -------------------------------------------------------------------------------- /ch3/Ramsey_tax.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 3, Ramsey model with tax 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | library(nleqslv) 11 | 12 | #---------------------------------------- 13 | 14 | alpha <- 0.3 15 | beta <- 0.99 16 | delta <- 0.25 17 | At <- 1.0 18 | 19 | #---------------------------------------- 20 | 21 | #Kt <- function(tauk) ((1/beta+delta-1)/((1-tauk)*alpha*At))^(1/(alpha-1)) 22 | #FCt <- function(K, g) (1-g)*At*K^alpha - delta*K 23 | 24 | Kt <- function(tauk) ((1/beta+delta-1)/((1-tauk)*alpha*At))^(1/(alpha-1)) 25 | FCt <- function(K, g) At*K^alpha - delta*K - g 26 | 27 | #---------------------------------------- 28 | 29 | objfun0 <- function(X, Z, maxT, X0, Xss = Css) { 30 | 31 | XX <- matrix(X, maxT, 2) 32 | C <- c(XX[, 1], Xss) 33 | K <- c(X0, XX[, 2]) 34 | tauc <- Z[[1]] 35 | tauk <- Z[[2]] 36 | g <- Z[[3]] 37 | 38 | ret <- matrix(NA, maxT, 2) 39 | for(t in 1:maxT) { 40 | ret[t, 1] <- (1+tauc[t+1])*C[t+1]/(1+tauc[t])/C[t]-beta*((1-tauk[t+1])*alpha*At*K[t+1]^(alpha-1)-delta+1) 41 | ret[t, 2] <- K[t+1]-At*K[t]^alpha-(1-delta)*K[t]+C[t]+g[t] 42 | } 43 | return(c(ret)) 44 | } 45 | 46 | Kt0 <- Kt(0) 47 | FCt0 <- FCt(Kt0, 0.1) 48 | 49 | #---------------------------------------- 50 | 51 | #-------------------- 52 | # シミュレーション１ 53 | #-------------------- 54 | 55 | maxT <- 30 56 | 57 | tauc1 <- rep(0, maxT+1) 58 | tauk1 <- rep(0, maxT+1) 59 | 60 | for(t in 10:(maxT+1)) 61 | tauc1[t] <- 0.1 62 | 63 | g <- rep(0.1, maxT+1) 64 | 65 | Z1 <- list(tauc1, tauk1, g) 66 | 67 | Kss0 <- Kt(tauk = tauk1[1]) 68 | Css0 <- FCt(Kss0, g = g[1]) 69 | Xinit1 <- c(rep(Css0,maxT), rep(Kss0,maxT)) 70 | 71 | Kss1 <- Kt(tauk = tauk1[maxT+1]) 72 | Css1 <- FCt(Kss1, g = g[maxT+1]) 73 | 74 | objfun1 <- function(X) objfun0(X, Z1, maxT, Kss0, Css1) 75 | rslt1 <- nleqslv(Xinit1, objfun1) 76 | rslt1x <- matrix(rslt1$x, maxT, 2) 77 | 78 | Ct1 <- c(Css0, rslt1x[, 1], Css1) 79 | Kt1 <- c(Kss0, Kss0, rslt1x[, 2]) 80 | 81 | par(ps = 15) 82 | par(mai = c(0.85*0.75, 0.68*0.75, 0.68*0.75, 0.35*0.75)) 83 | par(mfrow = c(2,1)) 84 | plot(cbind(0:(maxT+1), Ct1), typ = "l", main = expression(C[t]), xlab = "", ylab = "") 85 | segments(0, Css0, maxT+1, Css0, lty = 2, col = "blue") 86 | 87 | plot(cbind(0:(maxT+1), Kt1), typ = "l", main = expression(K[t]), xlab = "", ylab = "") 88 | segments(0, Kss0, maxT+1, Kss0, lty = 2, col = "blue") 89 | 90 | dev.copy2eps(file= figpath %+% "pubck1.eps") 91 | 92 | #-------------------- 93 | # シミュレーション２ 94 | #-------------------- 95 | 96 | tauc2 <- rep(0, maxT+1) 97 | tauk2 <- rep(0, maxT+1) 98 | 99 | for(t in 10:(maxT+1)) 100 | tauk2[t] <- 0.1 101 | 102 | Z2 <- list(tauc2, tauk2, g) 103 | Xinit2 <- c(rep(Css0,maxT), rep(Kss0,maxT)) 104 | 105 | Kss2 <- Kt(tauk = tauk2[maxT+1]) 106 | Css2 <- FCt(Kss2, g = g[maxT+1]) 107 | 108 | objfun2 <- function(X) objfun0(X, Z2, maxT, Kss0, Css2) 109 | rslt2 <- nleqslv(Xinit2, objfun2) 110 | rslt2x <- matrix(rslt2$x, maxT, 2) 111 | 112 | Ct2 <- c(Css0, rslt2x[, 1], Css2) 113 | Kt2 <- c(Kss0, Kss0, rslt2x[, 2]) 114 | 115 | par(ps = 15) 116 | par(mai = c(0.85*0.75, 0.68*0.75, 0.68*0.75, 0.35*0.75)) 117 | par(mfrow = c(2,1)) 118 | plot(cbind(0:(maxT+1), Ct2), typ = "l", main = expression(C[t]), xlab = "", ylab = "") 119 | segments(0, Css0, maxT+1, Css0, lty = 2, col = "blue") 120 | 121 | plot(cbind(0:(maxT+1), Kt2), typ = "l", main = expression(K[t]), xlab = "", ylab = "") 122 | segments(0, Kss0, maxT+1, Kss0, lty = 2, col = "blue") 123 | 124 | dev.copy2eps(file= figpath %+% "pubck2.eps") 125 | 126 | -------------------------------------------------------------------------------- /ch4/FqReport4.csv: -------------------------------------------------------------------------------- 1 | ,GDPGAP,ROH 2 | 1980:1,-0.5,122.4 3 | 1980:2,-2.1,121.5 4 | 1980:3,-1,117.1 5 | 1980:4,0.1,115.3 6 | 1981:1,-0.1,114.2 7 | 1981:2,-0.1,113.1 8 | 1981:3,-0.6,113.5 9 | 1981:4,-1,114 10 | 1982:1,-0.6,112.6 11 | 1982:2,-0.8,110 12 | 1982:3,-1.4,110.1 13 | 1982:4,-0.9,108.3 14 | 1983:1,-1.3,109.1 15 | 1983:2,-1.4,110 16 | 1983:3,-1.1,112.5 17 | 1983:4,-1.3,115.3 18 | 1984:1,-1.2,117.4 19 | 1984:2,-0.3,118.3 20 | 1984:3,-0.6,117.8 21 | 1984:4,-1.2,119.4 22 | 1985:1,-1,118.5 23 | 1985:2,-0.1,118.8 24 | 1985:3,0.3,118.7 25 | 1985:4,0.8,117.6 26 | 1986:1,-0.4,116.2 27 | 1986:2,-1.1,113.9 28 | 1986:3,-1.6,112 29 | 1986:4,-1.5,110.2 30 | 1987:1,-2.4,111.7 31 | 1987:2,-1.7,110.6 32 | 1987:3,-1.1,113.2 33 | 1987:4,0.4,116.7 34 | 1988:1,0.9,118.7 35 | 1988:2,0.3,118.9 36 | 1988:3,1,120 37 | 1988:4,1.1,120.7 38 | 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2000:2,-1.3,108.1 84 | 2000:3,-1.4,108.1 85 | 2000:4,-0.7,108 86 | 2001:1,-0.4,104.7 87 | 2001:2,-1.2,101.8 88 | 2001:3,-2.4,97.8 89 | 2001:4,-2.9,95.1 90 | 2002:1,-3,97.1 91 | 2002:2,-2.6,100.6 92 | 2002:3,-2.5,102.9 93 | 2002:4,-2.5,103.3 94 | 2003:1,-2.7,104 95 | 2003:2,-2.4,103.9 96 | 2003:3,-2.3,105.3 97 | 2003:4,-1.5,108.3 98 | 2004:1,-1,109.4 99 | 2004:2,-1.3,110.4 100 | 2004:3,-1,111 101 | 2004:4,-1.5,109.8 102 | 2005:1,-1.2,111.2 103 | 2005:2,-0.8,112.5 104 | 2005:3,-0.1,111.1 105 | 2005:4,-0.1,112.1 106 | 2006:1,-0.1,113.1 107 | 2006:2,0,114.5 108 | 2006:3,-0.3,115 109 | 2006:4,0.9,115.6 110 | 2007:1,1.5,114.5 111 | 2007:2,1.6,114.3 112 | 2007:3,1.1,116.2 113 | 2007:4,1.6,117.7 114 | 2008:1,1.9,117.8 115 | 2008:2,1.4,115 116 | 2008:3,0.2,110.3 117 | 2008:4,-2.2,97.8 118 | 2009:1,-6.9,71.8 119 | 2009:2,-5,79.7 120 | 2009:3,-4.9,86.4 121 | 2009:4,-3.6,93.4 122 | 2010:1,-2.9,98.3 123 | 2010:2,-1.7,98.7 124 | 2010:3,0,99.3 125 | 2010:4,-0.9,100.3 126 | 2011:1,-2.4,94.8 127 | 2011:2,-3.2,87.9 128 | 2011:3,-0.9,98 129 | 2011:4,-1.2,99.3 130 | 2012:1,-0.2,101.6 131 | 2012:2,-1.1,98.6 132 | 2012:3,-1.7,94.2 133 | 2012:4,-1.6,92.2 134 | 2013:1,-0.7,94.2 135 | 2013:2,-0.1,97.7 136 | 2013:3,0.6,100.4 137 | 2013:4,0.3,102 138 | 2014:1,1,105 139 | 2014:2,-1,103.1 140 | 2014:3,-1.2,101.4 141 | 2014:4,-0.9,101.6 142 | 2015:1,0.2,101.3 143 | 2015:2,0.2,99.8 144 | 2015:3,-0.1,99.4 145 | 2015:4,-0.8,99.2 146 | 2016:1,-0.3,98 147 | 2016:2,-0.5,96.9 148 | 2016:3,-0.5,98.6 149 | 2016:4,-0.6,100.4 150 | 2017:1,0,100.7 151 | 2017:2,0.3,102.8 152 | 2017:3,0.6,102.5 153 | 2017:4,0.7,103.8 154 | 2018:1,0.3,102.2 155 | 2018:2,0.6,103.3 156 | 2018:3,-0.3,101.9 157 | 2018:4,-0.1,104.7 158 | 2019:1,0.2,100.5 159 | ,, 160 | -------------------------------------------------------------------------------- /ch4/FqReport4.xlsx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rhasumi/dynamicmodels/6f4698e0d39f6495827b5fe1448991e6a3c0921b/ch4/FqReport4.xlsx -------------------------------------------------------------------------------- /ch4/RBC.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 4, RBC model 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | library(nleqslv) 11 | 12 | #---------------------------------------- 13 | 14 | alpha <- 0.3 15 | beta <- 0.99 16 | delta <- 0.025 17 | mu <- 1.0 18 | gamma <- 1.0 19 | rho <- 0.9 20 | 21 | para <- list(alpha = alpha, beta = beta, delta = delta, mu = mu, gamma = gamma, rho = rho) 22 | 23 | #---------------------------------------- 24 | 25 | findss <- function(p, Astar = 1) { 26 | 27 | rstar <- 1/p$beta + p$delta - 1 28 | K_L <- (rstar/p$alpha/Astar)^(1/(p$alpha-1)) 29 | Y_L <- Astar*K_L^p$alpha 30 | C_L <- Y_L-p$delta*K_L 31 | 32 | wstar <- (1-p$alpha)*Astar*K_L^p$alpha 33 | Lstar <- (wstar/(p$gamma+1)/p$mu)^(1/(p$gamma+1))*C_L^(-1/(p$gamma+1)) 34 | Kstar <- K_L*Lstar 35 | Ystar <- Y_L*Lstar 36 | Cstar <- C_L*Lstar 37 | 38 | list(C = Cstar, L = Lstar, K = Kstar, Y = Ystar, w = wstar, r = rstar, A = Astar) 39 | } 40 | 41 | 42 | 43 | objfun0 <- function(X, maxT, X0, Xss, p = para) { 44 | 45 | nvar <- 7 46 | XX <- matrix(X, maxT, nvar) 47 | C <- c(XX[, 1], Xss$C) 48 | L <- c(XX[, 2], Xss$L) 49 | K <- c(X0$K , XX[, 3]) 50 | Y <- c(XX[, 4], Xss$Y) 51 | w <- c(XX[, 5], Xss$w) 52 | r <- c(XX[, 6], Xss$r) 53 | A <- c(X0$A , XX[, 7]) 54 | 55 | ret <- matrix(NA, maxT, nvar) 56 | for(t in 1:maxT) { 57 | ret[t, 1] <- -w[t]/C[t]+(p$gamma+1)*p$mu*L[t]^p$gamma 58 | ret[t, 2] <- -C[t+1]/C[t]+p$beta*(r[t+1]-p$delta+1) 59 | ret[t, 3] <- -Y[t] + A[t]*K[t]^p$alpha*L[t]^(1-p$alpha) 60 | ret[t, 4] <- -w[t] + (1-p$alpha)*A[t]*K[t]^p$alpha*L[t]^(-p$alpha) 61 | ret[t, 5] <- -r[t]+p$alpha*A[t]*K[t]^(p$alpha-1)*L[t]^(1-p$alpha) 62 | ret[t, 6] <- -K[t+1]+Y[t]+(1-p$delta)*K[t]-C[t] 63 | ret[t, 7] <- -log(A[t+1])+p$rho*log(A[t]) 64 | } 65 | return(c(ret)) 66 | } 67 | 68 | #---------------------------------------- 69 | 70 | ss <- findss(para) 71 | 72 | maxT <- 150 73 | Xinit <- c(rep(ss$C,maxT), rep(ss$L,maxT), rep(ss$K,maxT), rep(ss$Y,maxT), rep(ss$w,maxT), rep(ss$r,maxT), rep(ss$A,maxT)) 74 | 75 | K0 <- ss$K 76 | A0 <- 1.01 77 | X0 <- list(K = K0, A = A0) 78 | 79 | objfun1 <- function(X) objfun0(X, maxT, X0, Xss = ss) 80 | rslt1 <- nleqslv(Xinit, objfun1) 81 | 82 | rsltfun <- function(rslt, maxT, X0, Xss, p = para) { 83 | XX <- matrix(rslt$x, maxT, 7) 84 | C0 <- c(Xss$C, XX[, 1]) 85 | # K0 <- c(Xss$K, X0$K, XX[1:(maxT-1), 3]) 86 | Y0 <- c(Xss$Y, XX[, 4]) 87 | I0 <- Y0 - C0 88 | Iss <- Xss$Y - Xss$C 89 | 90 | sss <- 1-Xss$C/Xss$Y 91 | s <- I0/Y0 92 | 93 | C <- (c(Xss$C, XX[, 1])/Xss$C-1)*100 94 | L <- (c(Xss$L, XX[, 2])/Xss$L-1)*100 95 | K <- (c(Xss$K, X0$K, XX[1:(maxT-1), 3])/Xss$K-1)*100 96 | Y <- (c(Xss$Y, XX[, 4])/Xss$Y-1)*100 97 | w <- (c(Xss$w, XX[, 5])/Xss$w-1)*100 98 | r <- (c(Xss$r, XX[, 6])-Xss$r)*100 99 | A <- (c(Xss$A, X0$A, XX[1:(maxT-1), 7])/Xss$A-1)*100 100 | 101 | I <- (I0/Iss-1)*100 102 | list(C = C, L = L, K = K, Y = Y, w = w, r = r, A = A, I = I, s = s) 103 | } 104 | 105 | X1 <- rsltfun(rslt1, maxT, X0, ss) 106 | 107 | if (.Platform$OS.type == "windows") windows(7, 10) 108 | par(ps = 14) 109 | par(mfrow = c(4, 2)) 110 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 111 | 112 | plot(cbind(0:maxT, X1$A), xlim = c(0,50), typ = "l", main = expression(A[t]), xlab = "", ylab = "") 113 | abline(h = 0, lty = 2, col = grey(0.5)) 114 | 115 | plot(cbind(0:maxT, X1$Y), xlim = c(0,50), typ = "l", main = expression(Y[t]), xlab = "", ylab = "") 116 | abline(h = 0, lty = 2, col = grey(0.5)) 117 | 118 | plot(cbind(0:maxT, X1$C), xlim = c(0,50), typ = "l", main = expression(C[t]), xlab = "", ylab = "") 119 | abline(h = 0, lty = 2, col = grey(0.5)) 120 | 121 | plot(cbind(0:maxT, X1$K), xlim = c(0,50), typ = "l", main = expression(K[t]), xlab = "", ylab = "") 122 | abline(h = 0, lty = 2, col = grey(0.5)) 123 | 124 | plot(cbind(0:maxT, X1$L), xlim = c(0,50), typ = "l", main = expression(L[t]), xlab = "", ylab = "") 125 | abline(h = 0, lty = 2, col = grey(0.5)) 126 | 127 | plot(cbind(0:maxT, X1$I), xlim = c(0,50), typ = "l", main = expression(I[t]), xlab = "", ylab = "") 128 | abline(h = 0, lty = 2, col = grey(0.5)) 129 | 130 | plot(cbind(0:maxT, X1$w), xlim = c(0,50), typ = "l", main = expression(w[t]), xlab = "", ylab = "") 131 | abline(h = 0, lty = 2, col = grey(0.5)) 132 | 133 | plot(cbind(0:maxT, X1$r), xlim = c(0,50), typ = "l", main = expression(r[t]), xlab = "", ylab = "") 134 | abline(h = 0, lty = 2, col = grey(0.5)) 135 | 136 | dev.copy2eps(file= figpath %+% "rbc1.eps") 137 | 138 | if (.Platform$OS.type == "windows") windows(5*0.6, 3.55*0.6) 139 | par(ps = 10*15/14) 140 | par(mai = c(0.85, 0.8, 0.68, 0.35)*0.5) 141 | plot(cbind(0:maxT, X1$s), xlim = c(0,50), typ = "l", main = expression(s[t]), xlab = "", ylab = "") 142 | abline(h = 1-ss$C/ss$Y, lty = 2, col = grey(0.5)) 143 | 144 | dev.copy2eps(file= figpath %+% "rbc2s.eps") 145 | 146 | -------------------------------------------------------------------------------- /ch4/bcycle.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 4, Drawing data 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | dat <- read.csv("FqReport4.csv") 11 | 12 | # peak bottom 13 | # 1980Q1 1983Q1 14 | # 1985Q2 1986Q4 15 | # 1991Q1 1993Q4 16 | # 1997Q2 1999Q1 17 | # 2000Q4 2002Q3 18 | # 2008Q1 2009Q1 19 | # 2012Q1 2002Q4 20 | 21 | peak <- c(1980, 1985.25, 1991, 1997.25, 2000.75, 2008, 2012) 22 | bottom <- c(1983, 1986.75, 1993.75, 1999, 2002, 2009, 2012.75) 23 | 24 | cpeak0 <- c("1980Q1", "1985Q2", "1991Q1", "1997Q2", "2000Q4", "2008Q1", "2012Q1") 25 | cbottom0 <- c("1983Q1", "1986Q4", "1993Q4", "1999Q1", "2002Q1", "2009Q1", "2012Q4") 26 | 27 | cpeak <- c("80Q1", "85Q2", "91Q1", "97Q2", "2000Q4", "08Q1", "12Q1") 28 | cbottom <- c("83Q1", "86Q4", "93Q4", "99Q1", "02Q1", "09Q1", "12Q4") 29 | 30 | gap.ts <- ts(dat$GDPGAP, start = 1980, frequency = 4) 31 | roh.ts <- ts(dat$ROH, start = 1980, frequency = 4) 32 | 33 | #--------- 34 | 35 | if (.Platform$OS.type == "windows") windows(7, 4) 36 | par(ps = 13) 37 | par(mai = c(0.6, 0.85, 0.6, 0.35)) 38 | plot(gap.ts, main = "", ylab = "%", xlab = "") 39 | abline(v = bottom, lty = 2, col = grey(0.5)) 40 | abline(v = peak, col = grey(0.5)) 41 | 42 | par(ps = 13) 43 | axis(side=3, labels = cpeak, at = peak) 44 | 45 | dev.copy2eps(file= figpath %+% "gap.eps") 46 | 47 | #--------- 48 | 49 | par(ps = 13) 50 | plot(roh.ts, main = "", ylab = "2015 = 100", xlab = "") 51 | abline(v = bottom, lty = 2, col = grey(0.5)) 52 | abline(v = peak, col = grey(0.5)) 53 | 54 | par(ps = 13) 55 | axis(side=3, labels = cpeak, at = peak) 56 | 57 | dev.copy2eps(file= figpath %+% "roh.eps") 58 | 59 | -------------------------------------------------------------------------------- /ch4/figures4.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 4, Other figures 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | A0 <- 1.0 11 | A1 <- 1.01 12 | rhos <- c(0, 0.5, 0.9, 1.0) 13 | Len <- 100 14 | 15 | ar1 <- function(rho, A1, len) { 16 | a <- log(A1) 17 | for(i in 2:len) 18 | a[i] <- rho*a[i-1] 19 | exp(a) 20 | } 21 | 22 | ans1 <- c(A0, ar1(rhos[1], A1, Len)) 23 | ans2 <- c(A0, ar1(rhos[2], A1, Len)) 24 | ans3 <- c(A0, ar1(rhos[3], A1, Len)) 25 | ans4 <- c(A0, ar1(rhos[4], A1, Len)) 26 | 27 | if (.Platform$OS.type == "windows") windows(7, 7) 28 | par(mfrow = c(2,2)) 29 | par(ps = 15) 30 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 31 | 32 | plot(cbind(0:Len, ans1), xlim = c(-5, 50), typ = "l", xlab = "t", ylab = expression(A[t]), main = expression(paste(rho, " = 0"))) 33 | plot(cbind(0:Len, ans2), xlim = c(-5, 50), typ = "l", xlab = "t", ylab = expression(A[t]), main = expression(paste(rho, " = 0.5"))) 34 | plot(cbind(0:Len, ans3), xlim = c(-5, 50), typ = "l", xlab = "t", ylab = expression(A[t]), main = expression(paste(rho, " = 0.9"))) 35 | plot(cbind(0:Len, ans4), xlim = c(-5, 50), typ = "l", xlab = "t", ylab = expression(A[t]), main = expression(paste(rho, " = 1.0"))) 36 | 37 | dev.copy2eps(file= figpath %+% "rbcar.eps") 38 | 39 | -------------------------------------------------------------------------------- /ch5/CIA.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 5, CIA model 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | 8 | library(nleqslv) 9 | 10 | #---------------------------------------- 11 | 12 | beta <- 0.99 13 | mu <- 1.0 14 | gamma <- 5 #1.0 15 | rho_A <- 0.9 16 | #rho_zeta <- 0.9 17 | rho_zeta <- 0.7 18 | zeta_ss <- 0 19 | para <- list(beta = beta, mu = mu, gamma = gamma, rho_A = rho_A, rho_zeta = rho_zeta, zeta_ss = zeta_ss) 20 | 21 | #---------------------------------------- 22 | 23 | findss <- function(p, Astar = 1) { 24 | pistar <- p$zeta_ss 25 | istar <- (1-p$beta+p$zeta_ss)/p$beta 26 | Cstar <- (p$beta/p$mu/(p$gamma+1)/(1+p$zeta_ss))^(1/(p$gamma+1)) 27 | mstar <- (1+p$zeta_ss)*Cstar 28 | lamstar <- p$beta/(1+p$zeta_ss)/Cstar 29 | xistar <- (1+p$zeta_ss-p$beta)/(1+p$zeta_ss)/Cstar 30 | list(C = Cstar, ii = istar, A = Astar, pi = pistar, m = mstar, zeta = p$zeta_ss, lam = lamstar, xi = xistar) 31 | } 32 | 33 | objfun0 <- function(X, maxT, X0, Xss, p = para) { 34 | 35 | nvar <- 8 36 | XX <- matrix(X, maxT, nvar) 37 | C <- c(XX[, 1], Xss$C) 38 | ii <- c(XX[, 2], Xss$ii) 39 | A <- c(X0$A , XX[, 3]) 40 | pi <- c(XX[, 4], Xss$pi) 41 | m <- c(XX[, 5], Xss$m) 42 | zeta <- c(X0$zeta , XX[, 6]) 43 | lam <- c(XX[, 7], Xss$lam) 44 | xi <- c(XX[, 8], Xss$xi) 45 | 46 | ret <- matrix(NA, maxT, nvar) 47 | for(t in 1:maxT) { 48 | ret[t, 1] <- 1/C[t]- lam[t] - xi[t] 49 | ret[t, 2] <- A[t]*lam[t] - p$mu*(C[t]/A[t])^p$gamma*(p$gamma+1) 50 | if (t > 1) { 51 | ret[t, 3] <- -C[t] + m[t-1]/(1+pi[t]) 52 | ret[t, 4] <- -(1+pi[t])*m[t] + (1+zeta[t])*m[t-1] 53 | } else { 54 | ret[t, 3] <- -C[t] + X0$m/(1+pi[t]) 55 | ret[t, 4] <- -(1+pi[t])*m[t] + (1+zeta[t])*X0$m 56 | } 57 | ret[t, 5] <- p$beta*lam[t+1] + p$beta*xi[t+1] - (1+pi[t+1])*lam[t] 58 | ret[t, 6] <- p$beta*(ii[t]+1)*lam[t+1] - (1+pi[t+1])*lam[t] 59 | ret[t, 7] <- -log(A[t+1]) + p$rho_A*log(A[t]) 60 | ret[t, 8] <- -(zeta[t+1]-p$zeta_ss) + p$rho_zeta*(zeta[t]-p$zeta_ss) 61 | } 62 | return(c(ret)) 63 | } 64 | 65 | #---------------------------------------- 66 | 67 | ss <- findss(para) 68 | 69 | maxT <- 150 70 | Xinit <- c(rep(ss$C,maxT), rep(ss$ii,maxT), rep(ss$A,maxT), 71 | rep(ss$pi,maxT), rep(ss$m,maxT), rep(ss$zeta,maxT), rep(ss$lam,maxT), rep(ss$xi,maxT)) 72 | 73 | Ainit1 <- 1.01 74 | zetainit1 <- zeta_ss 75 | X0set1 <- list(A = Ainit1, zeta = zetainit1, m = ss$m) 76 | 77 | objfun1 <- function(X) objfun0(X, maxT, X0set1, Xss = ss) 78 | rslt1 <- nleqslv(Xinit, objfun1) 79 | 80 | rsltfun <- function(rslt, maxT, X0, Xss, p = para) { 81 | XX <- matrix(rslt$x, maxT, 6) 82 | 83 | C <- (c(Xss$C, XX[, 1])/Xss$C -1)*100 84 | ii <- (c(Xss$ii, XX[, 2])-Xss$ii)*100 85 | A <- (c(Xss$A, X0$A, XX[1:(maxT-1), 3])/Xss$A-1)*100 86 | pi <- (c(Xss$pi, XX[, 4])-Xss$pi)*100 87 | m <- (c(Xss$m, XX[, 5])/Xss$m -1)*100 88 | zeta <- (c(Xss$zeta, X0$zeta, XX[1:(maxT-1), 6])-Xss$zeta)*100 89 | r <- c(Xss$ii-Xss$pi,ii[-length(ii)]-pi[-1]) 90 | 91 | list(C = C, ii = ii, A = A, pi = pi, m = m, zeta = zeta, r = r) 92 | } 93 | 94 | X1 <- rsltfun(rslt1, maxT, X0set1, ss) 95 | 96 | par(ps = 15) 97 | par(mfrow = c(3, 2)) 98 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 99 | 100 | plot(cbind(0:50, X1$C[1:51]), main = "C", xlab = "", ylab = "", typ = "l") 101 | plot(cbind(0:50, X1$ii[1:51]), main = "i", xlab = "", ylab = "", typ = "l") 102 | plot(cbind(0:50, X1$m[1:51]), main = "m", xlab = "", ylab = "", typ = "l") 103 | plot(cbind(0:50, X1$pi[1:51]), main = "pi", xlab = "", ylab = "", typ = "l") 104 | plot(cbind(0:50, X1$A[1:51]), main = "A", xlab = "", ylab = "", typ = "l") 105 | plot(cbind(0:50, X1$r[1:51]), main = "r", xlab = "", ylab = "", typ = "l") 106 | 107 | write.csv(X1, "cia_techs.csv") 108 | 109 | Ainit2 <- 1.0 110 | zetainit2 <- -0.01 111 | X0set2 <- list(A = Ainit2, zeta = zetainit2, m = ss$m) 112 | 113 | objfun2 <- function(X) objfun0(X, maxT, X0set2, Xss = ss) 114 | rslt2 <- nleqslv(Xinit, objfun2) 115 | 116 | X2 <- rsltfun(rslt2, maxT, X0set2, ss) 117 | 118 | par(ps = 15) 119 | par(mfrow = c(3, 2)) 120 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 121 | 122 | plot(cbind(0:50, X2$C[1:51]), main = "C", xlab = "", ylab = "", typ = "l") 123 | plot(cbind(0:50, X2$ii[1:51]), main = "i", xlab = "", ylab = "", typ = "l") 124 | plot(cbind(0:50, X2$m[1:51]), main = "m", xlab = "", ylab = "", typ = "l") 125 | plot(cbind(0:50, X2$pi[1:51]), main = "pi", xlab = "", ylab = "", typ = "l") 126 | plot(cbind(0:50, X2$zeta[1:51]), main = "zeta", xlab = "", ylab = "", typ = "l") 127 | plot(cbind(0:50, X2$r[1:51]), main = "r", xlab = "", ylab = "", typ = "l") 128 | 129 | write.csv(X2, "cia_mss.csv") 130 | 131 | -------------------------------------------------------------------------------- /ch5/NK.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 5, New Keynesian model 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | 8 | library(nleqslv) 9 | 10 | #---------------------------------------- 11 | 12 | beta <- 0.99 13 | mu <- 1.0 14 | gamma <- 5 15 | eta <- 10 16 | varrho <- 0.9 17 | phi_pi <- 1.5 18 | phi_y <- 0.5 19 | rho_A <- 0.9 20 | rho_v <- 0.7 21 | 22 | para <- list(beta = beta, mu = mu, gamma = gamma, varrho = varrho, eta = eta, phi_pi = phi_pi, phi_y = phi_y, rho_A = rho_A, rho_v = rho_v) 23 | 24 | #---------------------------------------- 25 | 26 | findss <- function(p) { 27 | pistar <- 0 28 | pitilstar <- 0 29 | vstar <- 0 30 | istar <- (1-p$beta)/p$beta 31 | Dstar <- 1/(1-p$varrho*p$beta) 32 | Fstar <- (p$eta-1)/p$eta/(1-p$varrho*p$beta) 33 | phistar <- (p$eta-1)/p$eta 34 | Astar <- 1 35 | Cstar <- ((p$eta-1)/p$eta/p$mu/(p$gamma+1))^(1/(p$gamma+1)) 36 | 37 | list(C = Cstar, phi = phistar, ppi = pistar, ppitil = pitilstar, 38 | F = Fstar, D = Dstar, A = Astar, ii = istar, v = vstar) 39 | } 40 | 41 | objfun0 <- function(X, maxT, X0, Xss, p = para) { 42 | 43 | nvar <- 4 44 | XX <- matrix(X, maxT, nvar) 45 | C <- c(XX[, 1], Xss$C) 46 | ppi <- c(XX[, 2], Xss$ppi) 47 | F <- c(XX[, 3], Xss$F) 48 | D <- c(XX[, 4], Xss$D) 49 | 50 | A <- c(X0$A) 51 | v <- c(X0$v) 52 | for(t in 1:maxT) { 53 | A[t+1] <- exp(p$rho_A*log(A[t])) 54 | v[t+1] <- p$rho_v*v[t] 55 | } 56 | phi <- p$mu*(C/A)^(p$gamma+1)*(p$gamma+1) 57 | ppitil <- p$eta/(p$eta-1)*F/D*(1+ppi)-1 58 | ii <- Xss$ii + p$phi_pi*ppi + p$phi_y*log(C/Xss$C/A) + v 59 | 60 | ret <- matrix(NA, maxT, nvar) 61 | for(t in 1:maxT) { 62 | ret[t, 1] <- -(1+ppi[t+1])*C[t+1]/C[t] + p$beta*(1+ii[t]) 63 | ret[t, 2] <- -F[t] + phi[t] + p$varrho*p$beta*(1+ppi[t+1])^p$eta*F[t+1] 64 | ret[t, 3] <- -D[t] + 1 + p$varrho*p$beta*(1+ppi[t+1])^(p$eta-1)*D[t+1] 65 | ret[t, 4] <- -(1+ppi[t])^(1-p$eta) + (1-p$varrho)*(1+ppitil[t])^(1-p$eta)+p$varrho 66 | } 67 | return(c(ret)) 68 | } 69 | 70 | rsltfun <- function(rslt, maxT, X0, Xss, p = para) { 71 | 72 | nvar <- 4 73 | XX <- matrix(rslt, maxT, nvar) 74 | C <- c(XX[, 1], Xss$C) 75 | ppi <- c(XX[, 2], Xss$ppi) 76 | F <- c(XX[, 3], Xss$F) 77 | D <- c(XX[, 4], Xss$D) 78 | 79 | A <- c(X0$A) 80 | v <- c(X0$v) 81 | for(t in 1:maxT) { 82 | A[t+1] <- exp(p$rho_A*log(A[t])) 83 | v[t+1] <- p$rho_v*v[t] 84 | } 85 | phi <- p$mu*(C/A)^p$gamma*(p$gamma+1)/A*C 86 | ppitil <- p$eta/(p$eta-1)*F/D*(1+ppi)-1 87 | ii <- Xss$ii + p$phi_pi*ppi + p$phi_y*log(C/Xss$C/A) + v 88 | 89 | ans0 <- list(C = C, phi = phi, ppi = ppi, ppitil = ppitil, 90 | F = F, D = D, A = A, ii = ii, v = v) 91 | 92 | C1 <- (c(Xss$C, C)/Xss$C-1)*100 93 | phi1 <- (c(Xss$phi, phi)/Xss$phi-1)*100 94 | ppi1 <- (c(Xss$ppi, ppi)-Xss$ppi)*100 95 | ppitil1 <- (c(Xss$ppitil, ppitil)-Xss$ppitil)*100 96 | F1 <- (c(Xss$F, F)/Xss$F-1)*100 97 | D1 <- (c(Xss$D, D)/Xss$D-1)*100 98 | A1 <- (c(Xss$A, A)/Xss$A-1)*100 99 | ii1 <- (c(Xss$ii, ii)-Xss$ii)*100 100 | v1 <- (c(Xss$v, v) - Xss$v)*100 101 | r1 <- c(Xss$ii-Xss$ppi,ii1[-length(ii1)]-ppi1[-1]) 102 | 103 | ans1 <- list(C = C1, phi = phi1, ppi = ppi1, ppitil = ppitil1, 104 | F = F1, D = D1, A = A1, ii = ii1, v = v1, r = r1) 105 | 106 | return(list(lev = ans0, dev = ans1)) 107 | } 108 | 109 | #---------------------------------------- 110 | 111 | ss <- findss(para) 112 | 113 | maxT <- 150 114 | Xinit <- c(rep(ss$C,maxT), rep(ss$ppi,maxT), rep(ss$F,maxT), rep(ss$D,maxT)) 115 | 116 | A0a <- 1.01 117 | v0a <- 0 118 | X0a <- list(A = A0a, v = v0a) 119 | 120 | objfun1 <- function(X) objfun0(X, maxT, X0a, Xss = ss) 121 | rslt1 <- nleqslv(Xinit, objfun1, control=list(maxit=10^4)) 122 | print(rslt1) 123 | 124 | X1 <- rsltfun(rslt1$x, maxT, X0a, ss) 125 | X1[[1]] 126 | X1[[2]] 127 | 128 | par(ps = 15) 129 | par(mfrow = c(3, 2)) 130 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 131 | 132 | plot(cbind(0:50, X1[[2]]$C[1:51]), main = "C", xlab = "", ylab = "", typ = "l") 133 | plot(cbind(0:50, X1[[2]]$ii[1:51]), main = "i", xlab = "", ylab = "", typ = "l") 134 | plot(cbind(0:50, X1[[2]]$ppi[1:51]), main = "pi", xlab = "", ylab = "", typ = "l") 135 | plot(cbind(0:50, X1[[2]]$r[1:51]), main = "r", xlab = "", ylab = "", typ = "l") 136 | plot(cbind(0:50, X1[[2]]$A[1:51]), main = "A", xlab = "", ylab = "", typ = "l") 137 | plot(cbind(0:50, X1[[2]]$v[1:51]), main = "v", xlab = "", ylab = "", typ = "l") 138 | 139 | write.csv(X1$dev, "nkm_techs.csv") 140 | 141 | 142 | #---------------------------------------- 143 | 144 | A0b <- 1 145 | v0b <- 0.01 146 | X0b <- list(A = A0b, v = v0b) 147 | 148 | objfun2 <- function(X) objfun0(X, maxT, X0b, Xss = ss) 149 | rslt2 <- nleqslv(Xinit, objfun2, control=list(maxit=10^4)) 150 | print(rslt2) 151 | 152 | X2 <- rsltfun(rslt2$x, maxT, X0b, ss) 153 | X2[[1]] 154 | X2[[2]] 155 | 156 | par(ps = 15) 157 | par(mfrow = c(3, 2)) 158 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 159 | 160 | plot(cbind(0:50, X2[[2]]$C[1:51]), main = "C", xlab = "", ylab = "", typ = "l") 161 | plot(cbind(0:50, X2[[2]]$ii[1:51]), main = "i", xlab = "", ylab = "", typ = "l") 162 | plot(cbind(0:50, X2[[2]]$ppi[1:51]), main = "pi", xlab = "", ylab = "", typ = "l") 163 | plot(cbind(0:50, X2[[2]]$r[1:51]), main = "r", xlab = "", ylab = "", typ = "l") 164 | plot(cbind(0:50, X2[[2]]$A[1:51]), main = "A", xlab = "", ylab = "", typ = "l") 165 | plot(cbind(0:50, X2[[2]]$v[1:51]), main = "v", xlab = "", ylab = "", typ = "l") 166 | 167 | write.csv(X2$dev, "nkm_mps.csv") 168 | 169 | -------------------------------------------------------------------------------- /ch5/NK_linear.R: -------------------------------------------------------------------------------- 1 | #====================================================== 2 | # Chapter 5, New Keynesian model (linear approximation) 3 | # modified on 2019/10/19 4 | #====================================================== 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | 8 | library(nleqslv) 9 | 10 | #---------------------------------------- 11 | 12 | beta <- 0.99 13 | mu <- 1.0 14 | gamma <- 5 15 | varrho <- 0.9 16 | phi_pi <- 1.5 17 | phi_y <- 0.5 18 | rho_A <- 0.9 19 | rho_v <- 0.7 20 | 21 | kappa <- (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho 22 | 23 | para <- list(beta = beta, phi_pi = phi_pi, phi_y = phi_y, rho_A = rho_A, rho_v = rho_v, kappa = kappa) 24 | 25 | #---------------------------------------- 26 | 27 | objfun0 <- function(X, maxT, X0,p = para) { 28 | 29 | nvar <- 2 30 | XX <- matrix(X, maxT, nvar) 31 | x <- c(XX[, 1], 0) 32 | ppi <- c(XX[, 2], 0) 33 | 34 | a <- c(X0$a) 35 | v <- c(X0$v) 36 | for(t in 1:maxT) { 37 | a[t+1] <- p$rho_A*a[t] 38 | v[t+1] <- p$rho_v*v[t] 39 | } 40 | ii <- p$phi_pi*ppi + p$phi_y*x + v 41 | 42 | ret <- matrix(NA, maxT, nvar) 43 | for(t in 1:maxT) { 44 | ret[t, 1] <- -x[t] + x[t+1]-(ii[t]-ppi[t+1])+(p$rho_A-1)*a[t] 45 | ret[t, 2] <- -ppi[t] + p$beta*ppi[t+1]+kappa*x[t] 46 | } 47 | return(c(ret)) 48 | } 49 | 50 | rsltfun <- function(rslt, maxT, X0, Xss, p = para) { 51 | 52 | nvar <- 2 53 | XX <- matrix(rslt, maxT, nvar) 54 | x <- c(XX[, 1], 0) 55 | ppi <- c(XX[, 2], 0) 56 | 57 | a <- c(X0$a) 58 | v <- c(X0$v) 59 | 60 | for(t in 1:maxT) { 61 | a[t+1] <- p$rho_A*a[t] 62 | v[t+1] <- p$rho_v*v[t] 63 | } 64 | ii <- p$phi_pi*ppi + p$phi_y*x + v 65 | r <- ii-c(ppi[-1],0) 66 | 67 | dev <- list(x = x, ppi = ppi, a = a, ii = ii, v = v, r = r) 68 | 69 | return(dev) 70 | } 71 | 72 | #---------------------------------------- 73 | 74 | 75 | maxT <- 150 76 | Xinit <- c(rep(0, maxT), rep(0, maxT)) 77 | 78 | a0a <- 0.01 79 | v0a <- 0 80 | X0a <- list(a = a0a, v = v0a) 81 | 82 | objfun1 <- function(X) objfun0(X, maxT, X0a) 83 | rslt1 <- nleqslv(Xinit, objfun1, control=list(maxit=10^4)) 84 | print(rslt1) 85 | 86 | X1 <- rsltfun(rslt1$x, maxT, X0a) 87 | X1[[1]] 88 | X1[[2]] 89 | 90 | par(ps = 15) 91 | par(mfrow = c(3, 2)) 92 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 93 | 94 | maxT2 <- 50 95 | plot(cbind(0:maxT2, c(0, X1$x[1:maxT2])), main = "x", xlab = "", ylab = "", typ = "l") 96 | plot(cbind(0:maxT2, c(0, X1$ii[1:maxT2])), main = "i", xlab = "", ylab = "", typ = "l") 97 | plot(cbind(0:maxT2, c(0, X1$ppi[1:maxT2])), main = "pi", xlab = "", ylab = "", typ = "l") 98 | plot(cbind(0:maxT2, c(0, X1$r[1:maxT2])), main = "r", xlab = "", ylab = "", typ = "l") 99 | plot(cbind(0:maxT2, c(0, X1$a[1:maxT2])), main = "a", xlab = "", ylab = "", typ = "l") 100 | plot(cbind(0:maxT2, c(0, X1$v[1:maxT2])), main = "v", xlab = "", ylab = "", typ = "l") 101 | 102 | #---------------------------------------- 103 | 104 | a0b <- 0 105 | v0b <- 0.01 106 | X0b <- list(a = a0b, v = v0b) 107 | 108 | objfun2 <- function(X) objfun0(X, maxT, X0b) 109 | rslt2 <- nleqslv(Xinit, objfun2, control=list(maxit=10^4)) 110 | print(rslt2) 111 | 112 | X2 <- rsltfun(rslt2$x, maxT, X0b, ss) 113 | X2[[1]] 114 | X2[[2]] 115 | 116 | par(ps = 15) 117 | par(mfrow = c(3, 2)) 118 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 119 | 120 | maxT2 <- 50 121 | plot(cbind(0:maxT2, c(0, X2$x[1:maxT2])), main = "x", xlab = "", ylab = "", typ = "l") 122 | plot(cbind(0:maxT2, c(0, X2$ii[1:maxT2])), main = "i", xlab = "", ylab = "", typ = "l") 123 | plot(cbind(0:maxT2, c(0, X2$ppi[1:maxT2])), main = "pi", xlab = "", ylab = "", typ = "l") 124 | plot(cbind(0:maxT2, c(0, X2$r[1:maxT2])), main = "r", xlab = "", ylab = "", typ = "l") 125 | plot(cbind(0:maxT2, c(0, X2$a[1:maxT2])), main = "a", xlab = "", ylab = "", typ = "l") 126 | plot(cbind(0:maxT2, c(0, X2$v[1:maxT2])), main = "v", xlab = "", ylab = "", typ = "l") 127 | 128 | -------------------------------------------------------------------------------- /ch5/cia_mss.csv: -------------------------------------------------------------------------------- 1 | "","C","ii","A","pi","m","zeta","r" 2 | "1",0,0,0,0,0,0,0.0101010101010101 3 | "2",0.167645962691876,-0.707070616687453,0,-0.167365385844722,-0.83403048956634,-1,0.167365385844722 4 | "3",0.117145475270264,-0.494949466836888,0,-0.950063149329648,-0.583674432194425,-0.7,0.242992532642195 5 | 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"151",1.81615389394096e-07,0,1.51346157828414e-07,-1.34529846968035e-08,1.81615389394096e-07,-4.49918494755954e-23,-1.69996903396076e-07 153 | -------------------------------------------------------------------------------- /ch5/figures5.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 5, Other figures 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | fx <- function(x) sin(x)+1.5 11 | 12 | if (.Platform$OS.type == "windows") windows(7, 7) 13 | par(ps = 18) 14 | par(mai = c(0.85, 0.85, 0.35, 0.35)) 15 | curve(fx, -0.5, 4, ylim = c(0, 3), ylab = "y") 16 | abline(h = 0) 17 | lines(c(0.5, 0.5), c(0, fx(0.5))) 18 | lines(c(3.0, 3.0), c(0, fx(3.0))) 19 | text(0.0, 0.75, "x = a") 20 | text(3.5, 0.75, "x = b") 21 | text(2.0, 2.7, "y = f(x)") 22 | grids <- seq(0.5, 3.0, length =100) 23 | dots <- rbind(c(0.5,0),cbind(grids, fx(grids)),c(3.0,0)) 24 | polygon(dots,col="gray") 25 | 26 | dev.copy2eps(file= figpath %+% "integ.eps") 27 | 28 | #--------------------------------------- 29 | 30 | nkm_techs <- read.csv("nkm_techs.csv") 31 | cia_techs <- read.csv("cia_techs.csv") 32 | 33 | par(ps = 15) 34 | par(mfrow = c(3, 2)) 35 | par(mai = c(0.85, 0.68, 0.68, 0.35*2)*0.5) 36 | 37 | plot(cbind(0:50, nkm_techs$C[1:51]), col = 4, main = expression(C[t]), xlab = "", ylab = "", typ = "l", ylim = c(0,1)) 38 | lines(cbind(0:50, cia_techs$C[1:51]), col = 2, lty = 2) 39 | 40 | plot(cbind(0:50, nkm_techs$ii[1:51]), col = 4, main = expression(i[t]), xlab = "", ylab = "", typ = "l") 41 | lines(cbind(0:50, cia_techs$ii[1:51]), col = 2, lty = 2) 42 | 43 | plot(cbind(0:50, nkm_techs$ppi[1:51]), col = 4, main = expression(pi[t]), xlab = "", ylab = "", typ = "l", ylim = c(-0.5, 0.1)/5) 44 | axis(4, at = seq(-1, 1, 0.02), labels = seq(-1, 1, 0.02)*10) 45 | lines(cbind(0:50, cia_techs$pi[1:51]/10), col = 2, lty = 2) 46 | 47 | plot(cbind(0:50, nkm_techs$r[1:51]), col = 4, main = expression(r[t]), xlab = "", ylab = "", typ = "l", ylim = c(-0.5, 0.5)/5) 48 | axis(4, at = seq(-1, 1, 0.05), labels = seq(-1, 1, 0.05)*10) 49 | lines(cbind(0:50, cia_techs$r[1:51]/10), col = 2, lty = 2) 50 | 51 | plot(cbind(0:50, cia_techs$m[1:51]), col = 2, lty = 2, main = expression(m[t]), xlab = "", ylab = "", typ = "l") 52 | 53 | plot(cbind(0:50, nkm_techs$A[1:51]), col = 4, main = expression(A[t]), xlab = "", ylab = "", typ = "l") 54 | lines(cbind(0:50, cia_techs$A[1:51]), col = 2, lty = 2) 55 | 56 | dev.copy2eps(file= figpath %+% "nkm_cia_techs.eps") 57 | 58 | #--------------------------------------- 59 | 60 | nkm_mps <- read.csv("nkm_mps.csv") 61 | cia_mss <- read.csv("cia_mss.csv") 62 | 63 | plot(cbind(0:50, nkm_mps$C[1:51]), col = 4, main = expression(C[t]), xlab = "", ylab = "", typ = "l", ylim = c(-1, 0.25)) 64 | lines(cbind(0:50, cia_mss$C[1:51]), col = 2, lty = 2) 65 | 66 | plot(cbind(0:50, nkm_mps$ii[1:51]), col = 4, main = expression(i[t]), xlab = "", ylab = "", typ = "l", ylim = c(-4, 1)/5) 67 | lines(cbind(0:50, cia_mss$ii[1:51]), col = 2, lty = 2) 68 | 69 | plot(cbind(0:50, nkm_mps$ppi[1:51]), col = 4, main = expression(pi[t]), xlab = "", ylab = "", typ = "l", ylim = c(-5, 0)/5) 70 | lines(cbind(0:50, cia_mss$pi[1:51]), col = 2, lty = 2) 71 | 72 | plot(cbind(0:50, nkm_mps$r[1:51]), col = 4, main = expression(r[t]), xlab = "", ylab = "", typ = "l", ylim = c(0, 0.3)) 73 | lines(cbind(0:50, cia_mss$r[1:51]), col = 2, lty = 2) 74 | 75 | plot(cbind(0:50, cia_mss$m[1:51]), col = 2, lty = 2, main = expression(m[t]), xlab = "", ylab = "", typ = "l") 76 | 77 | plot(cbind(0:50, nkm_mps$v[1:51]), col = 4, main = expression(paste(v[t], ", ", zeta[t])), xlab = "", ylab = "", typ = "l", ylim = c(-5, 5)/5) 78 | lines(cbind(0:50, cia_mss$zeta[1:51]), col = 2, lty = 2) 79 | 80 | dev.copy2eps(file= figpath %+% "nkm_cia_ms.eps") 81 | 82 | 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"150",0,2.22044604925031e-14,7.67091036387902e-23,0,0,0,0,0,1.18716182322945e-23,-7.67091036387902e-23 152 | "151",0,2.22044604925031e-14,4.16109553643811e-23,0,0,0,0,0,8.31013276260613e-24,-4.16109553643811e-23 153 | "152",0,2.22044604925031e-14,0,0,0,0,0,0,5.81709293382429e-24,0 154 | -------------------------------------------------------------------------------- /ch6/RBC_BK.R: -------------------------------------------------------------------------------- 1 | #================================================== 2 | # Chapter 6, RBC model (linear approximation) 3 | # modified on 2019/10/19 4 | #================================================== 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | alpha <- 0.3 11 | beta <- 0.99 12 | delta <- 0.025 13 | mu <- 1.0 14 | gamma <- 1.0 15 | rho <- 0.9 16 | 17 | Astar <- 1 18 | rstar <- 1/beta + delta - 1 19 | K_L <- (rstar/alpha/Astar)^(1/(alpha-1)) 20 | Y_L <- Astar*K_L^alpha 21 | C_L <- Y_L-delta*K_L 22 | wstar <- (1-alpha)*Astar*K_L^alpha 23 | Lstar <- (wstar/(gamma+1)/mu)^(1/(gamma+1))*C_L^(-1/(gamma+1)) 24 | Kstar <- K_L*Lstar 25 | Ystar <- Y_L*Lstar 26 | Cstar <- C_L*Lstar 27 | Rstar <- rstar+1 28 | 29 | nvar <- 7 30 | Bmat <- matrix(0, nvar, nvar) 31 | Cmat <- matrix(0, nvar, nvar) 32 | 33 | Bmat[2,1] <- 1.0 34 | Bmat[2,5] <- -Rstar*beta 35 | Bmat[6,6] <- Kstar 36 | Bmat[7,7] <- 1.0 37 | 38 | Cmat[1,1] <- 1.0 39 | Cmat[1,2] <- gamma 40 | Cmat[1,4] <- -1.0 41 | Cmat[2,1] <- 1.0 42 | Cmat[3,2] <- -alpha+1.0 43 | Cmat[3,3] <- -1.0 44 | Cmat[3,6] <- alpha 45 | Cmat[3,7] <- 1.0 46 | Cmat[4,2] <- -alpha 47 | Cmat[4,4] <- -1.0 48 | Cmat[4,6] <- alpha 49 | Cmat[4,7] <- 1.0 50 | Cmat[5,2] <- -alpha+1.0 51 | Cmat[5,5] <- -Rstar/(Rstar-1.0) 52 | Cmat[5,6] <- alpha-1.0 53 | Cmat[5,7] <- 1.0 54 | Cmat[6,1] <- -Cstar 55 | Cmat[6,3] <- Ystar 56 | Cmat[6,6] <- -Kstar*(delta-1.0) 57 | Cmat[7,7] <- rho 58 | 59 | A <- solve(Cmat) %*% Bmat 60 | 61 | # Policy/Transition Function を求める関数 62 | # 加藤涼[2007]も参照 63 | 64 | W <- eigen(A)[[2]] 65 | theta <- eigen(A)[[1]] 66 | Q <- solve(W) 67 | 68 | ntheta <- length(theta) 69 | 70 | ## Extract unstable vectors 71 | sjjw <- which(theta - 1.0 < 0) 72 | n <- length(sjjw) 73 | UQ <- Q[sjjw,] 74 | 75 | ## Extract stable vectors 76 | sjw <- setdiff(c(1:ntheta),sjjw) 77 | k <- length(sjw) 78 | SQ <- Q[sjw,] 79 | 80 | ## Extract stable roots 81 | VLL <- theta[sjw] 82 | VL <- diag(1.0/VLL) 83 | 84 | # Elements in Q 85 | PA <- UQ[1:n,1:n] 86 | PB <- UQ[1:n,(n+1):(n+k)] 87 | PC <- SQ[1:k,1:n] 88 | PD <- SQ[1:k,(n+1):(n+k)] 89 | P <- -solve(PA) %*% PB 90 | PE <- PC %*% P + PD 91 | 92 | # Solution 93 | AA <- solve(PE) %*% VL %*% PE 94 | 95 | # funcition for simulation 96 | rbc_sim <- function(AA, P, len_t, S_0){ 97 | Ss <- S_0 98 | S <- matrix(0, nrow=len_t-1, ncol=ncol(AA)) 99 | for (i in 1:(len_t-1)){ 100 | q <- AA %*% Ss 101 | S[i,] <- t(q) 102 | Ss <- S[i,] 103 | } 104 | SY <- rbind(t(S1), S) 105 | X <- t(P %*% t(SY)) 106 | return(list(X, SY)) 107 | } 108 | 109 | # Time span 110 | nsim <- 100 111 | 112 | # Initial Values 113 | S1 <- matrix(c(0, 1), ncol=1) 114 | 115 | # SIMULATION 116 | simrslt <- rbc_sim(AA, P, nsim, S1) 117 | X <- simrslt[[1]] 118 | SY <- simrslt[[2]] 119 | 120 | # C,L,Y,w,R,K,A 121 | par(mfrow=c(2,2), ps = 15, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 122 | plot(cbind(0:nsim, c(0, X[, 1])), typ = "l", col = 4, lwd = 1, xlab = "", ylab = "", main = expression(C[t])) 123 | plot(cbind(0:nsim, c(0, SY[, 1])), typ = "l", col = 4, lwd = 1, xlab = "", ylab = "", main = expression(K[t])) 124 | plot(cbind(0:nsim, c(0, X[, 2])), typ = "l", col = 4, lwd = 1, xlab = "", ylab = "", main = expression(L[t])) 125 | plot(cbind(0:nsim, c(0, SY[, 2])), typ = "l", col = 4, lwd = 1, xlab = "", ylab = "", main = expression(A[t])) 126 | dev.copy2eps(file= figpath %+% "bk_rbc_ckla.eps") 127 | 128 | -------------------------------------------------------------------------------- /ch6/RBC_PolIter_Chebyshev.R: -------------------------------------------------------------------------------- 1 | #================================================== 2 | # Chapter 6, RBC model (Chebyshev approximation) 3 | # modified on 2019/10/19 4 | #================================================== 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | beta <- 0.99 11 | alpha <- 0.3 12 | gamma <- 1.0 13 | delta <- 0.025 14 | rho <- 0.9 15 | mu <- 1.0 16 | 17 | r_ss <- 1/beta-1+delta 18 | k_l <- (r_ss/alpha)^(1/(alpha-1)) 19 | w_ss <- (1-alpha)*(k_l)^alpha 20 | c_l <- k_l^alpha-delta*k_l 21 | l_ss <- ((w_ss/mu/(1+gamma)) * c_l^(-1))^(1/(gamma+1)) 22 | k_ss <- k_l*l_ss 23 | c_ss <- c_l*l_ss 24 | 25 | U <- function (x) log(x[1]) - mu * x[2]^(gamma+1) 26 | 27 | g <- function (s, x, epsilon) { 28 | wt <- (1-alpha) * s[1]^alpha / x[2]^alpha * s[2] 29 | rt <- alpha * x[2]^(1-alpha) / s[1]^(1-alpha) * s[2] 30 | s1 <- x[2] * wt + s[1] * rt + (1 - delta) * s[1] - x[1] 31 | s2 <- exp(rho * log(s[2]) + epsilon) 32 | c(s1, s2) 33 | } 34 | 35 | y <- 0 36 | for(i in 0:500) 37 | y <- y + beta^i * U(c(c_ss,l_ss)) 38 | 39 | #--------------------------------------- 40 | # チェビシェフ近似補間（２次） 41 | #--------------------------------------- 42 | 43 | library(nleqslv) # nleqslv 44 | 45 | xj <- function(n = 10){ 46 | -cos(0.5*(2*(1:n)-1)*pi/n) 47 | } 48 | 49 | trans0 <- function(x, a = -1, b = 1) { 50 | y <- (x-a)/(b-a)*2-1 51 | y 52 | } 53 | 54 | trans <- function(x, a = -1, b = 1) { 55 | y <- (x-a)/(b-a)*2-1 56 | y[which(y < -1)] <- -1 57 | y[which(y > 1)] <- 1 58 | y 59 | } 60 | 61 | rev <- function(y, a = -1, b = 1) (y+1)*(b-a)*0.5+a 62 | 63 | fn2 <- function(x, cc, nt){ 64 | size <- dim(x) 65 | lTk <- vector("list", size[2]) 66 | for (i in 1:size[2]){ 67 | Tk <- matrix(1, size[1], 1) 68 | Tk <- cbind(Tk, x[, i]) 69 | for (k in 2:(nt-1)) 70 | Tk <- cbind(Tk, 2*x[, i]*Tk[, k]-Tk[, k-1]) 71 | lTk[[i]] <- Tk 72 | } 73 | Tkk <- c() 74 | for (i in 1:size[1]) { 75 | rTk <- lTk[[1]][i,] 76 | for (k in 2:size[2]) 77 | rTk <- lTk[[k]][i,] %x% rTk 78 | Tkk <- rbind(Tkk, rTk) 79 | } 80 | rownames(Tkk) <- NULL 81 | Tkk %*% cc 82 | } 83 | 84 | xj2 <- function(n = 10){ 85 | as.matrix(expand.grid(xj(n),xj(n))) 86 | } 87 | 88 | trans2 <- function(x, a, b) cbind(trans(x[, 1], a[1], b[1]), trans(x[, 2], a[2], b[2])) 89 | rev2 <- function(y, a, b) cbind(rev(y[, 1], a[1], b[1]), rev(y[, 2], a[2], b[2])) 90 | 91 | cheb2x <- function(x, coef, a, b, n, vc, z) { 92 | ans <- fn2(trans2(matrix(x, 1), a, b), coef, n) 93 | ans 94 | } 95 | 96 | #--------------------------------------- 97 | # Policy Iteration 98 | #--------------------------------------- 99 | 100 | getcoef <- function(nt, f) { 101 | ngrid <- nt*nt 102 | at <- c(1.0, 0.90) 103 | bt <- c(30.0, 1.10) 104 | 105 | node <- cbind(rev(xj(nt), at[1], bt[1]), rev(xj(nt), at[2], bt[2])) 106 | xjgrid <- rev2(xj2(nt), at, bt) 107 | apxfun <- function(x, coef) fn2(trans2(x, at, bt), coef, nt) 108 | 109 | niter <- 1000 110 | eps <- 0.001 111 | 112 | # initialization 113 | cc <- rep(0, ngrid) 114 | v <- rep(0, ngrid) 115 | coef1 <- rep(0, ngrid) 116 | coef2 <- rep(0, ngrid) 117 | 118 | hl <- function(ct, s) 119 | ((1-alpha)*s[1]^alpha*s[2]/(gamma+1)/mu/ct)^(1/(alpha+gamma)) 120 | 121 | for(iter in 1:niter) { 122 | print(iter) 123 | v1 <- c(v) 124 | c1 <- c(cc) 125 | 126 | for(i in 1:ngrid) { 127 | obj <- function(ct) { 128 | st <- c(xjgrid[i, ]) 129 | lt <- hl(ct, st) 130 | xt <- c(ct, lt) 131 | sa <- matrix(g(st,xt , 0), 1) 132 | - U(xt) - beta*f(sa) 133 | } 134 | opt <- optimize(obj, c(0.001, (1 - delta)*xjgrid[i, 1])) 135 | cc[i] <- opt$minimum 136 | } 137 | fobj1 <- function(coef) cc - apxfun(xjgrid, coef) 138 | coef1 <- nleqslv(coef1, fobj1)$x 139 | hc <- function(x) cheb2x(x, coef1, at, bt, nt, node, cc) 140 | 141 | for(i in 1:ngrid) { 142 | st <- c(xjgrid[i, ]) 143 | ct <- max(min(hc(st), (1 - delta) * st[1]), 0.1) 144 | xt <- c(ct, hl(ct, st)) 145 | y <- U(xt) 146 | for(k in 1:500) { 147 | st <- g(st, xt, 0) 148 | ct <- max(min(hc(st), (1 - delta) * st[1]), 0.1) 149 | xt <- c(ct, hl(ct, st)) 150 | y <- y + beta^k * U(xt) 151 | } 152 | v[i] <- y 153 | } 154 | if (identical(abs(c(cc) - c1) < eps ,rep(T, nt*nt))) break 155 | 156 | fobj2 <- function(coef) v - apxfun(xjgrid, coef) 157 | coef2 <- nleqslv(coef2, fobj2)$x 158 | f <- function(x) cheb2x(x, coef2, at, bt, nt, node, v) 159 | 160 | persp(node[, 1], node[, 2], matrix(v, nt, nt)) 161 | print(abs(c(cc) - c1)) 162 | } 163 | return(list(coef1, coef2, cc)) 164 | } 165 | 166 | f <- function (x) -45 + sqrt(x[1]) + sqrt(x[2]) 167 | at <- c(1.0, 0.90) 168 | bt <- c(30.0, 1.10) 169 | nt1 <- 10 170 | coefset1 <- getcoef(10, f) 171 | 172 | f2 <- function(x) cheb2x(x, coefset1[[2]], at, bt, nt1) 173 | nt2 <- 15 174 | 175 | coefset2 <- getcoef(nt2, f2) 176 | hc <- function(x) cheb2x(x, coefset2[[1]], at, bt, nt2) 177 | hl <- function(ct, s) 178 | ((1-alpha)*s[1]^alpha*s[2]/(gamma+1)/mu/ct)^(1/(alpha+gamma)) 179 | cc <- coefset2[[3]] 180 | 181 | #--------------------------------------- 182 | # Plot 183 | #--------------------------------------- 184 | 185 | nt <- nt2 186 | node <- cbind(rev(xj(nt), at[1], bt[1]), rev(xj(nt), at[2], bt[2])) 187 | 188 | st <- c(k_ss, 1.0) 189 | kt <- c(k_ss) 190 | for (t in 1:10000) { 191 | ct <- hc(st) 192 | lt <- hl(ct, st) 193 | st <- g(st, c(ct, lt), 0) 194 | kt[t+1] <- st[1] 195 | } 196 | k_sn <- kt[t+1] 197 | 198 | nsim <- 101 199 | X <- matrix(NA, nsim, 4) 200 | X[1, 3:4] <- c(k_sn, 1.0) 201 | X[1, 1] <- hc(X[1, 3:4]) 202 | X[1, 2] <- hl(X[1, 1], X[1, 3:4]) 203 | X[2, 3:4] <- g(X[1, 3:4], X[1, 1:2], 0.01) 204 | 205 | for (i in 2:nsim) { 206 | X[i, 1] <- hc(X[i, 3:4]) 207 | X[i, 2] <- hl(X[i, 1], X[i, 3:4]) 208 | if (i < nsim) 209 | X[i+1, 3:4] <- g(X[i, 3:4], X[i, 1:2], 0) 210 | } 211 | 212 | if (.Platform$OS.type == "windows") windows(7, 7) 213 | par(ps = 12, mai = c(0.85, 0.68, 0.68, 0.35)*0.3) 214 | persp(node[, 1], node[, 2], matrix(cc, nt, nt), 215 | theta = -30, phi = 30, expand = 0.5, ticktype = "detailed", 216 | col = "lightgray", border = "red", xlab = "K", ylab = "A", zlab = "C") 217 | 218 | dev.copy2eps(file= figpath %+% "polit_rbc_pol.eps") 219 | 220 | par(mfrow=c(2,2), ps = 15, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 221 | plot(cbind(0:(nsim-1), (log(X[, 1])-log(c_ss))*100), typ = "l", col = 2, lwd = 1, xlab = "", ylab = "", main = expression(C[t])) 222 | plot(cbind(0:(nsim-1), (log(X[, 3])-log(k_ss))*100), typ = "l", col = 2, lwd = 1, xlab = "", ylab = "", main = expression(K[t])) 223 | plot(cbind(0:(nsim-1), (log(X[, 2])-log(l_ss))*100), typ = "l", col = 2, lwd = 1, xlab = "", ylab = "", main = expression(L[t])) 224 | plot(cbind(0:(nsim-1), log(X[, 4])*100), typ = "l", col = 2, lwd = 1, xlab = "", ylab = "", main = expression(A[t])) 225 | dev.copy2eps(file= figpath %+% "polit_rbc_ckla.eps") 226 | 227 | -------------------------------------------------------------------------------- /ch6/Ramsey_PolIter_Chebyshev.R: -------------------------------------------------------------------------------- 1 | #================================================== 2 | # Chapter 6, Ramsey model (Chebyshev approximation) 3 | # modified on 2019/10/19 4 | #================================================== 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | beta <- 0.99 11 | alpha <- 0.3 12 | delta <- 0.25 13 | 14 | Kss <- ((1/beta+delta-1)/alpha)^(1/(alpha-1)) 15 | Css <- Kss^alpha - delta*Kss 16 | 17 | U <- function (C) log(C) 18 | g <- function (K, C) K^alpha + (1-delta)*K - C 19 | 20 | y <- 0 21 | for(i in 0:200) 22 | y <- y + beta^i * U(Css) 23 | 24 | #--------------------------------------- 25 | # チェビシェフ近似補間（1次） 26 | #--------------------------------------- 27 | 28 | library(nleqslv) # nleqslv 29 | 30 | xj <- function(n = 10){ 31 | -cos(0.5*(2*(1:n)-1)*pi/n) 32 | } 33 | 34 | trans0 <- function(x, a = -1, b = 1) { 35 | y <- (x-a)/(b-a)*2-1 36 | y 37 | } 38 | 39 | trans <- function(x, a = -1, b = 1) { 40 | y <- (x-a)/(b-a)*2-1 41 | y[which(y < -1)] <- -1 42 | y[which(y > 1)] <- 1 43 | y 44 | } 45 | 46 | rev <- function(y, a = -1, b = 1) (y+1)*(b-a)*0.5+a 47 | 48 | fn <- function(x, cc, nt){ 49 | size <- length(x) 50 | Tk <- matrix(1, size[1], 1) 51 | Tk <- cbind(Tk, x) 52 | for (k in 2:(nt-1)) 53 | Tk <- cbind(Tk, 2*x*Tk[, k]-Tk[, k-1]) 54 | Tk %*% cc 55 | } 56 | 57 | cheb <- function(x, coef, a, b, n) { 58 | fn(trans(matrix(x, 1), a, b), coef, n) 59 | } 60 | 61 | #--------------------------------------- 62 | # Policy Iteration 63 | #--------------------------------------- 64 | 65 | nt <- 20 66 | at <- 0.5 67 | bt <- 3.0 68 | 69 | node <- rev(xj(nt), at[1], bt[1]) 70 | apxfun <- function(x, coef) fn(trans(x, at, bt), coef, nt) 71 | 72 | niter <- 1000 73 | eps <- 0.0001 74 | 75 | # initialization 76 | f <- function (x) -45 + sqrt(x) 77 | cc <- rep(0, nt) 78 | v <- rep(0, nt) 79 | coef <- rep(0, nt) 80 | coef2 <- rep(0, nt) 81 | 82 | for(iter in 1:niter) { 83 | print(iter) 84 | v1 <- c(v) 85 | c1 <- c(cc) 86 | coef1 <- coef 87 | 88 | for(i in 1:nt) { 89 | obj <- function(ct) { 90 | st <- node[i] 91 | sa <- matrix(g(st,ct), 1) 92 | return(-U(ct)-beta*f(sa)) 93 | } 94 | opt <- optimize(obj, c(0.001, min((1 - delta) *node[i]+node[i]^alpha,bt*0.99))) 95 | cc[i] <- opt$minimum 96 | } 97 | fobj1 <- function(coef) cc - apxfun(node, coef) 98 | coef1 <- nleqslv(coef1, fobj1)$x 99 | hc <- function(x) cheb(x, coef1, at, bt, nt) 100 | 101 | for(i in 1:nt) { 102 | st <- node[i] 103 | ct <- max(min(hc(st), st), 0.001) 104 | y <- U(ct) 105 | for(k in 1:1000) { 106 | st <- g(st, ct) 107 | ct <- max(min(hc(st), st), 0.001) 108 | y <- y + beta^k * U(ct) 109 | } 110 | v[i] <- y 111 | } 112 | if (identical(abs(c(cc) - c1) < eps ,rep(T, nt))) break 113 | 114 | fobj2 <- function(coef) v - apxfun(node, coef) 115 | coef2 <- nleqslv(coef2, fobj2)$x 116 | f <- function(x) cheb(x, coef2, at, bt, nt) 117 | 118 | plot(cbind(node, v), typ = "l") 119 | print(abs(c(cc) - c1)) 120 | } 121 | 122 | #--------------------------------------- 123 | # Plot 124 | #--------------------------------------- 125 | 126 | if (.Platform$OS.type == "windows") windows(7, 7) 127 | par(ps = 20) 128 | par(mai = c(0.85, 1, 0.25, 0.1)) 129 | plot(cbind(node, cc), typ = "l", xlab = expression(K[t]), ylab = expression(C[t])) 130 | dev.copy2eps(file= figpath %+% "polit_ram_ct.eps") 131 | 132 | plot(cbind(node, v), typ = "l", xlab = expression(K[t]), ylab = expression(V(K[t]))) 133 | dev.copy2eps(file= figpath %+% "polit_ram_v.eps") 134 | 135 | #-------------------- 136 | # シミュレーション 137 | #-------------------- 138 | 139 | K01 <- Kss*0.5 140 | KK <- K01 141 | CC <- c() 142 | 143 | for(i in 1:31) { 144 | CC[i] <- hc(KK[i]) 145 | KK[i+1] <- g(KK[i], CC[i]) 146 | } 147 | 148 | par(ps = 15) 149 | par(mai = c(0.85*0.75, 0.68*0.75, 0.68*0.75, 0.5)) 150 | par(mfrow = c(2,1)) 151 | plot(cbind(1:31, CC[1:31]), typ = "l", main = expression(C[t]), xlab = "", ylab = "") 152 | axis(side=4, labels = c(expression(C[1]),expression("C*")), at = c(CC[1],Css), las = 2) 153 | 154 | plot(cbind(1:31, KK[1:31]), typ = "l", main = expression(K[t]), xlab = "", ylab = "") 155 | axis(side=4, labels = c(expression(K[1]),expression("K*")), at = c(KK[1],Kss), las = 2) 156 | 157 | dev.copy2eps(file= figpath %+% "polit_ram_ck.eps") 158 | 159 | -------------------------------------------------------------------------------- /ch6/figures6.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 6, Dynamic programming 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | xj <- function(n = 9){ 11 | -cos(0.5*(2*(1:n)-1)*pi/n) 12 | } 13 | 14 | phi <- function(x, j) { 15 | if (j == 0) { 16 | y <- rep(1, length(x)) 17 | } else if (j == 1) { 18 | y <- x 19 | } else { 20 | y <- 2*x*phi(x, j-1) - phi(x, j-2) 21 | } 22 | return(y) 23 | } 24 | nodes <- seq(-1,1,length = 100) 25 | 26 | if (.Platform$OS.type == "windows") windows(7,2.5) 27 | par(ps = 10, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 28 | plot(cbind(xj(),rep(0,9)),main = expression(z["i"]), xlab = "", ylab = "",axes = F) 29 | axis(1) 30 | axis(2, labels = "", at = 0) 31 | box() 32 | dev.copy2eps(file= figpath %+% "chebnode.eps") 33 | 34 | if (.Platform$OS.type == "windows") windows(7,7) 35 | par(mfrow = c(3,3), ps = 15, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 36 | 37 | ff <- function(x) phi(x, j=0) 38 | curve(ff, -1, 1, main = expression(paste(phi[0],"(z)"))) 39 | 40 | ff <- function(x) phi(x, j=1) 41 | curve(ff, -1, 1, main = expression(paste(phi[1],"(z)"))) 42 | 43 | ff <- function(x) phi(x, j=2) 44 | curve(ff, -1, 1, main = expression(paste(phi[2],"(z)"))) 45 | 46 | ff <- function(x) phi(x, j=3) 47 | curve(ff, -1, 1, main = expression(paste(phi[3],"(z)"))) 48 | 49 | ff <- function(x) phi(x, j=4) 50 | curve(ff, -1, 1, main = expression(paste(phi[4],"(z)"))) 51 | 52 | ff <- function(x) phi(x, j=5) 53 | curve(ff, -1, 1, main = expression(paste(phi[5],"(z)"))) 54 | 55 | ff <- function(x) phi(x, j=6) 56 | curve(ff, -1, 1, main = expression(paste(phi[6],"(z)"))) 57 | 58 | ff <- function(x) phi(x, j=7) 59 | curve(ff, -1, 1, main = expression(paste(phi[7],"(z)"))) 60 | 61 | ff <- function(x) phi(x, j=8) 62 | curve(ff, -1, 1, main = expression(paste(phi[8],"(z)"))) 63 | 64 | dev.copy2eps(file= figpath %+% "chebfun.eps") 65 | 66 | -------------------------------------------------------------------------------- /ch7/NK_commit.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 7, Optimal MP (commitment) 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | library(nleqslv) 11 | 12 | #---------------------------------------- 13 | 14 | beta <- 0.99 15 | gamma <- 5 16 | eta <- 10 17 | varrho <- 0.9 18 | phi_pi <- 1.5 19 | phi_y <- 0.5 20 | 21 | kappa <- (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho 22 | lambda <- (1-varrho)*(1-varrho*beta)/eta/varrho*(1+gamma) 23 | 24 | para <- list(beta = beta, kappa = kappa, lambda = lambda) 25 | 26 | #---------------------------------------- 27 | 28 | objfun0 <- function(X, maxT, X0,p = para) { 29 | 30 | nvar <- 4 31 | XX <- matrix(X, maxT, nvar) 32 | x <- c(XX[, 1], 0) 33 | ppi <- c(XX[, 2], 0) 34 | ii <- c(XX[, 3], 0) 35 | psi <- c(XX[, 4], 0) 36 | 37 | e <- c(X0$e, rep(0, maxT)) 38 | 39 | ret <- matrix(NA, maxT, nvar) 40 | for(t in 1:maxT) { 41 | ret[t, 1] <- -ppi[t] + p$beta*ppi[t+1]+kappa*x[t]+e[t] 42 | ret[t, 2] <- -x[t] + x[t+1]-(ii[t]-ppi[t+1]) 43 | if (t == 1) { 44 | ret[t, 3] <- ppi[t]+psi[t] 45 | } else { 46 | ret[t, 3] <- ppi[t]+psi[t]-psi[t-1] 47 | } 48 | ret[t, 4] <- p$lambda*x[t]-p$kappa*psi[t] 49 | } 50 | return(c(ret)) 51 | } 52 | 53 | rsltfun <- function(rslt, maxT, X0, p = para) { 54 | 55 | nvar <- 4 56 | XX <- matrix(rslt, maxT, nvar) 57 | x <- c(XX[, 1], 0) 58 | ppi <- c(XX[, 2], 0) 59 | ii <- c(XX[, 3], 0) 60 | psi <- c(XX[, 4], 0) 61 | 62 | e <- c(X0$e, rep(0, maxT)) 63 | r <- ii-c(ppi[-1],0) 64 | 65 | dev <- list(x = x, ppi = ppi, psi = psi, ii = ii, e = e, r = r) 66 | 67 | cumbeta <- c(1, cumprod(rep(p$beta, maxT))) 68 | W <- -0.5*sum(cumbeta*ppi^2+p$lambda*cumbeta*x^2) 69 | 70 | 71 | return(list(dev = dev, W = W)) 72 | } 73 | 74 | #---------------------------------------- 75 | 76 | maxT <- 150 77 | Xinit <- c(rep(0, maxT), rep(0, maxT), rep(0, maxT), rep(0, maxT)) 78 | 79 | e0 <- 1 80 | X0 <- list(e = e0) 81 | 82 | objfun1 <- function(X) objfun0(X, maxT, X0) 83 | rslt1 <- nleqslv(Xinit, objfun1, control=list(maxit=10^4)) 84 | print(rslt1) 85 | 86 | X1 <- rsltfun(rslt1$x, maxT, X0) 87 | X1[[1]] 88 | X1[[2]]/10^4 89 | 90 | par(ps = 15) 91 | par(mfrow = c(3, 2)) 92 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 93 | 94 | maxT2 <- 10 95 | plot(cbind(0:maxT2, c(0, X1[[1]]$x[1:maxT2])), main = expression(x[t]), 96 | xlab = "", ylab = "", typ = "l") 97 | plot(cbind(0:maxT2, c(0, X1[[1]]$ii[1:maxT2])), main = expression(i[t]), 98 | xlab = "", ylab = "", typ = "l") 99 | plot(cbind(0:maxT2, c(0, X1[[1]]$ppi[1:maxT2])), main = expression(pi[t]), 100 | xlab = "", ylab = "", typ = "l") 101 | plot(cbind(0:maxT2, c(0, X1[[1]]$psi[1:maxT2])), main = expression(psi[t]), 102 | xlab = "", ylab = "", typ = "l") 103 | plot(cbind(0:maxT2, c(0, X1[[1]]$e[1:maxT2])), main = expression(e[t]), 104 | xlab = "", ylab = "", typ = "l") 105 | 106 | write.csv(X1[[1]], "nkm_commit.csv", row.names = F) 107 | dev.copy2eps(file= figpath %+% "nkm_commit.eps") 108 | 109 | 110 | -------------------------------------------------------------------------------- /ch7/NK_discretion.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 7, Optimal MP (discretion) 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | library(nleqslv) 11 | 12 | #---------------------------------------- 13 | 14 | beta <- 0.99 15 | gamma <- 5 16 | eta <- 10 17 | varrho <- 0.9 18 | phi_pi <- 1.5 19 | phi_y <- 0.5 20 | 21 | kappa <- (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho 22 | lambda <- (1-varrho)*(1-varrho*beta)/eta/varrho*(1+gamma) 23 | 24 | para <- list(beta = beta, kappa = kappa, lambda = lambda) 25 | 26 | #---------------------------------------- 27 | 28 | objfun0 <- function(X, maxT, X0, p = para) { 29 | 30 | nvar <- 3 31 | XX <- matrix(X, maxT, nvar) 32 | x <- c(XX[, 1], 0) 33 | ppi <- c(XX[, 2], 0) 34 | ii <- c(XX[, 3], 0) 35 | 36 | e <- c(X0$e, rep(0, maxT)) 37 | 38 | ret <- matrix(NA, maxT, nvar) 39 | for(t in 1:maxT) { 40 | ret[t, 1] <- -ppi[t] + p$beta*ppi[t+1]+kappa*x[t]+e[t] 41 | ret[t, 2] <- -x[t] + x[t+1]-(ii[t]-ppi[t+1]) 42 | ret[t, 3] <- p$lambda*x[t]+p$kappa*ppi[t] 43 | } 44 | return(c(ret)) 45 | } 46 | 47 | rsltfun <- function(rslt, maxT, X0, p = para) { 48 | 49 | nvar <- 3 50 | XX <- matrix(rslt, maxT, nvar) 51 | x <- c(XX[, 1], 0) 52 | ppi <- c(XX[, 2], 0) 53 | ii <- c(XX[, 3], 0) 54 | 55 | e <- c(X0$e, rep(0, maxT)) 56 | r <- ii-c(ppi[-1],0) 57 | 58 | dev <- list(x = x, ppi = ppi, ii = ii, e = e, r = r) 59 | 60 | cumbeta <- c(1, cumprod(rep(p$beta, maxT))) 61 | W <- -0.5*sum(cumbeta*ppi^2+p$lambda*cumbeta*x^2) 62 | 63 | 64 | return(list(dev = dev, W = W)) 65 | } 66 | 67 | #---------------------------------------- 68 | 69 | maxT <- 150 70 | Xinit <- c(rep(0, maxT), rep(0, maxT), rep(0, maxT)) 71 | 72 | e0 <- 1 73 | X0 <- list(e = e0) 74 | 75 | objfun1 <- function(X) objfun0(X, maxT, X0) 76 | rslt1 <- nleqslv(Xinit, objfun1, control=list(maxit=10^4)) 77 | print(rslt1) 78 | 79 | X1 <- rsltfun(rslt1$x, maxT, X0) 80 | X1[[1]] 81 | X1[[2]]/10^4 82 | 83 | par(ps = 15) 84 | par(mfrow = c(3, 2)) 85 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 86 | 87 | maxT2 <- 10 88 | plot(cbind(0:maxT2, c(0, X1[[1]]$x[1:maxT2])), main = expression(x[t]), 89 | xlab = "", ylab = "", typ = "l") 90 | plot(cbind(0:maxT2, c(0, X1[[1]]$ii[1:maxT2])), main = expression(i[t]), 91 | xlab = "", ylab = "", typ = "l") 92 | plot(cbind(0:maxT2, c(0, X1[[1]]$ppi[1:maxT2])), main = expression(pi[t]), 93 | xlab = "", ylab = "", typ = "l") 94 | plot(cbind(0:maxT2, c(0, -X1[[1]]$ppi[1:maxT2])), main = expression(psi[t]), 95 | xlab = "", ylab = "", typ = "l") 96 | plot(cbind(0:maxT2, c(0, X1[[1]]$e[1:maxT2])), main = expression(e[t]), 97 | xlab = "", ylab = "", typ = "l") 98 | 99 | write.csv(X1[[1]], "nkm_discretion.csv", row.names = F) 100 | 101 | Y1 <- read.csv("nkm_commit.csv") 102 | 103 | par(ps = 15) 104 | par(mfrow = c(3, 2)) 105 | par(mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 106 | 107 | maxT2 <- 10 108 | plot(cbind(0:maxT2, c(0, X1[[1]]$x[1:maxT2])), main = expression(x[t]), 109 | xlab = "", ylab = "", typ = "l") 110 | lines(cbind(0:maxT2, c(0, Y1$x[1:maxT2])), lty = 2) 111 | plot(cbind(0:maxT2, c(0, X1[[1]]$ii[1:maxT2])), main = expression(i[t]), 112 | xlab = "", ylab = "", typ = "l") 113 | lines(cbind(0:maxT2, c(0, Y1$ii[1:maxT2])), lty = 2) 114 | plot(cbind(0:maxT2, c(0, X1[[1]]$ppi[1:maxT2])), main = expression(pi[t]), 115 | xlab = "", ylab = "", typ = "l", ylim = range(X1[[1]]$ppi[1:maxT2],Y1$ppi[1:maxT2])) 116 | lines(cbind(0:maxT2, c(0, Y1$ppi[1:maxT2])), lty = 2) 117 | plot(cbind(0:maxT2, c(0, -X1[[1]]$ppi[1:maxT2])), main = expression(psi[t]), 118 | xlab = "", ylab = "", typ = "l", ylim = range(-X1[[1]]$ppi[1:maxT2],Y1$psi[1:maxT2])) 119 | lines(cbind(0:maxT2, c(0, Y1$psi[1:maxT2])), lty = 2) 120 | plot(cbind(0:maxT2, c(0, X1[[1]]$e[1:maxT2])), main = expression(e[t]), 121 | xlab = "", ylab = "", typ = "l") 122 | 123 | dev.copy2eps(file= figpath %+% "nkm_discretion.eps") 124 | 125 | -------------------------------------------------------------------------------- /ch7/figures7.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 7, Other figures 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | beta <- 0.99 11 | gamma <- 5 12 | varrho <- 0.9 13 | 14 | kappa <- (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho 15 | 16 | phi_y1 <- -1 17 | phi_y2 <- 3 18 | 19 | phi_pi1 <- -(1-beta)*phi_y1/kappa+1 20 | phi_pi2 <- -(1-beta)*phi_y2/kappa+1 21 | 22 | if (.Platform$OS.type == "windows") windows(7, 7) 23 | par(ps = 15) 24 | par(mai = c(0.68*1.5, 0.68*1.5, 0.34, 0.34)) 25 | 26 | plot(NA, xlim = c(0, 2), ylim = c(0, 2), main = "", xlab = expression(phi[y]), ylab = expression(phi[pi])) 27 | polygon(c(phi_y1, phi_y2, phi_y2, phi_y1, phi_y1), c(phi_pi1, phi_pi2, -1, -1, phi_pi1), col = "grey", border = "grey") 28 | box() 29 | 30 | text(1, 0.4, "indeterminate") 31 | text(1, 1.5, "determinate") 32 | 33 | dev.copy2eps(file= figpath %+% "nkm_indet.eps") 34 | 35 | 36 | -------------------------------------------------------------------------------- /ch7/nkm_commit.csv: -------------------------------------------------------------------------------- 1 | "x","ppi","psi","ii","e","r" 2 | -4.38013820601573,0.438013820601573,-0.438013820601573,2.21541942207227,1,2.46157713563586 3 | -1.91856107037987,-0.246157713563586,-0.191856107037987,0.970384325296806,0,1.07820480588534 4 | -0.840356264494532,-0.107820480588534,-0.0840356264494532,0.425041745775134,0,0.472268606416816 5 | -0.368087658077716,-0.0472268606416816,-0.0368087658077716,0.186174158982129,0,0.20686017664681 6 | -0.161227481430906,-0.020686017664681,-0.0161227481430906,0.0815468546730471,0,0.0906076163033857 7 | 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2.29519158643846e-24,-1.87368817019936e-25,-2.00789075125067e-24,0,-1.76385269901235e-24 151 | 6.01638408032299e-25,-2.44038052238322e-25,-6.92913195455322e-25,0,-6.92913195455322e-25 152 | 0,0,0,0,0 153 | -------------------------------------------------------------------------------- /ch8/dataplot.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 8, Drawing data 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | dset <- read.csv("dset_fig.csv") 8 | # figpath <- "../../figs/" 9 | figpath <- "./" 10 | 11 | if (.Platform$OS.type == "windows") windows(7, 8) 12 | par(mfrow = c(3, 1), ps = 13) 13 | par(mai = c(0.7,1.2, 0.5, 0.35)*0.5) 14 | par(family="Japan1GothicBBB") 15 | plot(ts(dset$GAP, start = c(1980, 2), freq = 4), main = "ＧＤＰギャップ", xlab = "", ylab = "％") 16 | plot(ts(dset$PC_PGDP, start = c(1980, 2), freq = 4), main = "ＧＤＰデフレーター（前期比伸び率）", xlab = "", ylab = "％") 17 | plot(ts(dset$IRS, start = c(1980, 2), freq = 4), main = "短期金利", xlab = "", ylab = "％") 18 | 19 | # GAP PC_PGD IRS 20 | dev.copy2pdf(file=figpath %+% "dataplot.pdf",family="Japan1GothicBBB") 21 | # [0 0 504 575] 22 | 23 | -------------------------------------------------------------------------------- /ch8/dset_fig.csv: -------------------------------------------------------------------------------- 1 | GAP,PC_PGDP,IRS 2 | -2.100000,2.566845,12.471670 3 | -1.000000,1.147028,12.063830 4 | 0.100000,0.927835,10.008170 5 | -0.100000,0.204290,8.515300 6 | -0.100000,0.509684,7.120030 7 | -0.600000,0.405680,7.250900 8 | -1.000000,0.808081,6.850270 9 | -0.600000,0.801603,6.609230 10 | -0.800000,-0.099404,7.172230 11 | -1.400000,0.398010,7.118300 12 | -0.900000,-0.198216,6.841230 13 | -1.300000,0.794439,6.635670 14 | -1.400000,0.098522,6.190930 15 | -1.100000,0.000000,6.458770 16 | -1.300000,0.295276,6.283670 17 | -1.200000,0.588813,6.181770 18 | -0.300000,0.292683,5.844300 19 | -0.600000,0.389105,6.152770 20 | -1.200000,0.678295,6.221100 21 | -1.000000,0.384986,6.248730 22 | -0.100000,0.191755,6.068570 23 | 0.300000,-0.191388,6.254030 24 | 0.800000,0.287632,7.281830 25 | -0.400000,0.956023,6.053000 26 | -1.100000,0.568182,4.435730 27 | -1.600000,0.376648,4.562530 28 | -1.500000,-0.375235,4.120730 29 | -2.400000,-0.188324,3.998030 30 | -1.700000,-0.283019,3.281770 31 | -1.100000,0.378430,3.248930 32 | 0.400000,-0.188501,3.524970 33 | 0.900000,0.566572,3.488570 34 | 0.300000,-0.375587,3.332370 35 | 1.000000,0.565504,3.778130 36 | 1.100000,0.281162,3.888570 37 | 2.000000,0.467290,3.909160 38 | -0.100000,1.023256,4.360840 39 | 0.300000,0.644567,5.183260 40 | 2.200000,0.548948,6.035370 41 | 0.500000,0.636943,6.516260 42 | 2.200000,0.632911,7.100170 43 | 3.200000,0.269542,7.441210 44 | 2.200000,1.254480,7.909520 45 | 2.500000,0.619469,8.080540 46 | 2.600000,0.791557,8.031670 47 | 1.800000,0.523560,7.260740 48 | 1.900000,0.868056,6.454880 49 | 1.400000,0.000000,5.543340 50 | 0.800000,0.860585,4.680300 51 | 0.700000,-0.170648,4.201530 52 | -0.500000,0.085470,3.905450 53 | -0.400000,0.341588,3.389970 54 | -1.700000,-0.255319,3.134180 55 | -2.600000,0.341297,3.020260 56 | -2.700000,0.255102,2.418150 57 | -2.000000,-0.169635,2.195600 58 | -2.900000,0.424809,2.046270 59 | -2.200000,-0.423012,2.069860 60 | -2.900000,0.169924,2.202980 61 | -2.200000,-0.508906,2.154710 62 | -1.600000,-0.170503,1.320100 63 | -0.800000,0.085397,0.746670 64 | -0.900000,0.085324,0.403330 65 | -0.400000,-0.511509,0.403330 66 | 0.400000,0.085690,0.413330 67 | 0.100000,-0.085616,0.406670 68 | 1.000000,-0.171380,0.423330 69 | 1.000000,-0.085837,0.436670 70 | 0.100000,1.030928,0.436670 71 | 0.000000,-0.170068,0.436670 72 | -0.200000,0.170358,0.423330 73 | -1.600000,-0.085034,0.433330 74 | -2.200000,-0.170213,0.416670 75 | -2.200000,-0.341006,0.363330 76 | -1.700000,0.171086,0.216670 77 | -3.200000,-0.597780,0.120000 78 | -------------------------------------------------------------------------------- /ch8/figures8.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 8, Other figures 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | "%+%" <- function(x, y) paste(x, y, sep = "") 7 | # figpath <- "../../figs/" 8 | figpath <- "./" 9 | 10 | #---------------------------- 11 | # 主な確率分布 12 | 13 | f1 <- function(x) dnorm(x, 0, 1) 14 | f2 <- function(x) dgamma(x, 1, 1) 15 | f3 <- function(x) dbeta(x, 2, 2) 16 | f4 <- function(x) dunif(x, -1, 1) 17 | 18 | par(mfrow = c(2,2), ps = 15, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 19 | curve(f1, -4, 4, main = expression(paste("N(",mu," = 0, ", sigma^2," = 1 )"))) 20 | abline(h = 0, col = 'grey') 21 | 22 | curve(f2, 0, 5, main = expression(paste("Ga(",s," = 1, ", r," = 1 )")),xlim = c(0,4)) 23 | abline(h = 0, col = 'grey') 24 | lines(cbind(c(0, 0), c(0, 1)),lty=2) 25 | 26 | curve(f3, 0, 1, main = expression(paste("Be(",a," = 2, ", b," = 2 )"))) 27 | abline(h = 0, col = 'grey') 28 | 29 | curve(f4, -1, 1, main = expression(paste("Unif(",a," = -1, ", b," = 1 )")),ylim = c(0, 1)) 30 | lines(cbind(c(-1.0, -1.0), c(0, 0.5)),lty=2) 31 | lines(cbind(c(1.0, 1.0), c(0, 0.5)),lty=2) 32 | abline(h = 0, col = 'grey') 33 | 34 | dev.copy2eps(file= figpath %+% "distribution.eps") 35 | 36 | #---------------------------- 37 | # ベイズ推定の例（ベルヌーイ過程） 38 | 39 | N <- c(5, 20, 100, 1000) 40 | theta <- 0.6 41 | set.seed(101) 42 | vec <- runif(N[4]) 43 | rslt <- rep(0, N[4]) 44 | rslt[vec < theta] <- 1 45 | 46 | a0 <- 2 47 | b0 <- 2 48 | x1 <- seq(0,1,length = 200) 49 | y1 <- dbeta(x1, a0, b0) 50 | fb1 <- function(x) dbeta(x, a0+sum(rslt[1:N[1]]), b0+N[1]-sum(rslt[1:N[1]])) 51 | fb2 <- function(x) dbeta(x, a0+sum(rslt[1:N[2]]), b0+N[2]-sum(rslt[1:N[2]])) 52 | fb3 <- function(x) dbeta(x, a0+sum(rslt[1:N[3]]), b0+N[3]-sum(rslt[1:N[3]])) 53 | fb4 <- function(x) dbeta(x, a0+sum(rslt[1:N[4]]), b0+N[4]-sum(rslt[1:N[4]])) 54 | 55 | par(mfrow = c(2,2), ps = 15, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 56 | 57 | curve(fb1, 0, 1, main = "N = 5", ylim = c(0, 5)) 58 | lines(cbind(x1, y1), lty = 2) 59 | lines(cbind(c(theta,theta),c(0, 10^4)),col=3) 60 | 61 | curve(fb2, 0, 1, main = "N = 20", ylim = c(0, 5)) 62 | lines(cbind(x1, y1), lty = 2) 63 | lines(cbind(c(theta,theta),c(0, 10^4)),col=3) 64 | 65 | curve(fb3, 0, 1, main = "N = 100", ylim = c(0, 10)) 66 | lines(cbind(x1, y1), lty = 2) 67 | lines(cbind(c(theta,theta),c(0, 10^4)),col=3) 68 | 69 | curve(fb4, 0, 1, main = "N = 1000", ylim = c(0, 30)) 70 | lines(cbind(x1, y1), lty = 2) 71 | lines(cbind(c(theta,theta),c(0, 10^4)),col=3) 72 | 73 | dev.copy2eps(file= figpath %+% "bernoulli.eps") 74 | 75 | #---------------------------- 76 | # マルコフ過程の例 77 | 78 | set.seed(101) 79 | aa <- c(0, -100, 100) 80 | rho <- 0.5 81 | 82 | vec1 <- aa[1] 83 | vec2 <- aa[2] 84 | vec3 <- aa[3] 85 | 86 | for(i in 1:999) { 87 | vec1[i+1] <- rho*vec1[i] + rnorm(1) 88 | vec2[i+1] <- rho*vec2[i] + rnorm(1) 89 | vec3[i+1] <- rho*vec3[i] + rnorm(1) 90 | } 91 | 92 | if (.Platform$OS.type == "windows") windows(10,7) 93 | par(ps = 15) 94 | plot(vec1[1:200], typ = "l", xlab = "", ylab = "", main = expression(a[t]), ylim = c(-5, 5)) 95 | lines(vec2[1:200], col = 2,lty=2) 96 | lines(vec3[1:200], col = 4,lty=4) 97 | 98 | dev.copy2eps(file= figpath %+% "markov.eps") 99 | 100 | #---------------------------- 101 | # MHアルゴリズムの例 102 | 103 | set.seed(102) 104 | 105 | ff <- function(x) log(dgamma(x, 5, 1)) 106 | x2 <- seq(0,15,length = 200) 107 | y2 <- dgamma(x2, 5, 1) 108 | 109 | niter <- 1200 110 | chain4 <- rgamma(niter, 5, 1) 111 | 112 | Metropolis <- function(init, sig2) { 113 | chain <- init[1] 114 | for(i in 2:niter) { 115 | cand <- chain[i-1] + rnorm(1, sd = sqrt(sig2)) 116 | prob <- min(exp(ff(cand)-ff(chain[i-1])), 1) 117 | if (runif(1) < prob) { 118 | chain[i] <- cand 119 | } else { 120 | chain[i] <- chain[i-1] 121 | } 122 | } 123 | return(chain) 124 | } 125 | 126 | chain1 <- Metropolis(9, 0.1) 127 | chain2 <- Metropolis(9, 20) 128 | chain3 <- Metropolis(9, 5000) 129 | 130 | rejrate1 <- sum(chain1[201:1200] == chain1[201:1200-1])/1000 131 | rejrate2 <- sum(chain2[201:1200] == chain2[201:1200-1])/1000 132 | rejrate3 <- sum(chain3[201:1200] == chain3[201:1200-1])/1000 133 | 1-c(rejrate1,rejrate2,rejrate3) 134 | 135 | if (.Platform$OS.type == "windows") windows(7,7) 136 | 137 | par(mfrow = c(2,2), ps = 15, mai = c(0.85, 0.68, 0.68, 0.35)*0.5) 138 | par(family="Japan1GothicBBB") 139 | 140 | hist(chain1[201:1200], xlab = "", main = expression(paste(sigma^2, " = 0.1")), probability = T, xlim = c(0, 15)) 141 | lines(cbind(x2, y2)) 142 | 143 | hist(chain2[201:1200], xlab = "", main = expression(paste(sigma^2, " = 20")), probability = T, xlim = c(0, 15)) 144 | lines(cbind(x2, y2)) 145 | 146 | hist(chain3[201:1200], xlab = "", main = expression(paste(sigma^2, " = 5000")), probability = T, xlim = c(0, 15)) 147 | lines(cbind(x2, y2)) 148 | 149 | hist(chain4[201:1200], xlab = "", main = "(参考)", probability = T, xlim = c(0, 15), ylim = c(0, 0.2)) 150 | lines(cbind(x2, y2)) 151 | 152 | dev.copy2pdf(file=figpath %+% "metropolis.pdf",family="Japan1GothicBBB") 153 | 154 | -------------------------------------------------------------------------------- /ch8_dynare/FqReport8.csv: -------------------------------------------------------------------------------- 1 | ,GDPGAP,PGDP11@,CMBEMTU 2 | 1980:1,-0.5,93.5,9.17557 3 | 1980:2,-2.1,95.9,12.47167 4 | 1980:3,-1,97,12.06383 5 | 1980:4,0.1,97.9,10.00817 6 | 1981:1,-0.1,98.1,8.5153 7 | 1981:2,-0.1,98.6,7.12003 8 | 1981:3,-0.6,99,7.2509 9 | 1981:4,-1,99.8,6.85027 10 | 1982:1,-0.6,100.6,6.60923 11 | 1982:2,-0.8,100.5,7.17223 12 | 1982:3,-1.4,100.9,7.1183 13 | 1982:4,-0.9,100.7,6.84123 14 | 1983:1,-1.3,101.5,6.63567 15 | 1983:2,-1.4,101.6,6.19093 16 | 1983:3,-1.1,101.6,6.45877 17 | 1983:4,-1.3,101.9,6.28367 18 | 1984:1,-1.2,102.5,6.18177 19 | 1984:2,-0.3,102.8,5.8443 20 | 1984:3,-0.6,103.2,6.15277 21 | 1984:4,-1.2,103.9,6.2211 22 | 1985:1,-1,104.3,6.24873 23 | 1985:2,-0.1,104.5,6.06857 24 | 1985:3,0.3,104.3,6.25403 25 | 1985:4,0.8,104.6,7.28183 26 | 1986:1,-0.4,105.6,6.053 27 | 1986:2,-1.1,106.2,4.43573 28 | 1986:3,-1.6,106.6,4.56253 29 | 1986:4,-1.5,106.2,4.12073 30 | 1987:1,-2.4,106,3.99803 31 | 1987:2,-1.7,105.7,3.28177 32 | 1987:3,-1.1,106.1,3.24893 33 | 1987:4,0.4,105.9,3.52497 34 | 1988:1,0.9,106.5,3.48857 35 | 1988:2,0.3,106.1,3.33237 36 | 1988:3,1,106.7,3.77813 37 | 1988:4,1.1,107,3.88857 38 | 1989:1,2,107.5,3.90916 39 | 1989:2,-0.1,108.6,4.36084 40 | 1989:3,0.3,109.3,5.18326 41 | 1989:4,2.2,109.9,6.03537 42 | 1990:1,0.5,110.6,6.51626 43 | 1990:2,2.2,111.3,7.10017 44 | 1990:3,3.2,111.6,7.44121 45 | 1990:4,2.2,113,7.90952 46 | 1991:1,2.5,113.7,8.08054 47 | 1991:2,2.6,114.6,8.03167 48 | 1991:3,1.8,115.2,7.26074 49 | 1991:4,1.9,116.2,6.45488 50 | 1992:1,1.4,116.2,5.54334 51 | 1992:2,0.8,117.2,4.6803 52 | 1992:3,0.7,117,4.20153 53 | 1992:4,-0.5,117.1,3.90545 54 | 1993:1,-0.4,117.5,3.38997 55 | 1993:2,-1.7,117.2,3.13418 56 | 1993:3,-2.6,117.6,3.02026 57 | 1993:4,-2.7,117.9,2.41815 58 | 1994:1,-2,117.7,2.1956 59 | 1994:2,-2.9,118.2,2.04627 60 | 1994:3,-2.2,117.7,2.06986 61 | 1994:4,-2.9,117.9,2.20298 62 | 1995:1,-2.2,117.3,2.15471 63 | 1995:2,-1.6,117.1,1.3201 64 | 1995:3,-0.8,117.2,0.74667 65 | 1995:4,-0.9,117.3,0.40333 66 | 1996:1,-0.4,116.7,0.40333 67 | 1996:2,0.4,116.8,0.41333 68 | 1996:3,0.1,116.7,0.40667 69 | 1996:4,1,116.5,0.42333 70 | 1997:1,1,116.4,0.43667 71 | 1997:2,0.1,117.6,0.43667 72 | 1997:3,0,117.4,0.43667 73 | 1997:4,-0.2,117.6,0.42333 74 | 1998:1,-1.6,117.5,0.43333 75 | 1998:2,-2.2,117.3,0.41667 76 | 1998:3,-2.2,116.9,0.36333 77 | 1998:4,-1.7,117.1,0.21667 78 | 1999:1,-3.2,116.4,0.12 79 | -------------------------------------------------------------------------------- /ch8_dynare/FqReport8.xlsx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rhasumi/dynamicmodels/6f4698e0d39f6495827b5fe1448991e6a3c0921b/ch8_dynare/FqReport8.xlsx -------------------------------------------------------------------------------- /ch8_dynare/NK_Linear_EST.mod: -------------------------------------------------------------------------------- 1 | //=========================================== 2 | // Chapter 8, Model definition and estimation 3 | // modified on 2019/10/19 4 | //=========================================== 5 | 6 | // 1. 内生変数、外生変数の宣言 7 | var x ppi a ii v; 8 | varexo epsilon z e; 9 | 10 | // 2. パラメータの宣言 11 | parameters beta gamma varrho phi_pi phi_y rho_A rho_v; 12 | 13 | // パラメータ値の代入 14 | beta = 0.99; 15 | gamma = 5; 16 | varrho = 0.9; 17 | phi_pi = 0.5; 18 | phi_y = 0.5; 19 | rho_A = 0.9; 20 | rho_v = 0.7; 21 | 22 | // 3. 方程式の定義 23 | model(linear); 24 | # kappa = (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho; 25 | x = x(+1)-(ii-ppi(+1))+(rho_A-1)*a; 26 | ppi = beta*ppi(+1) + kappa*x + e; 27 | ii = (1+phi_pi)*ppi + phi_y*x + v; 28 | v = rho_v*v(-1) + z; 29 | a = rho_A*a(-1) + epsilon; 30 | end; 31 | 32 | shocks; 33 | var epsilon; stderr 0.5; 34 | var z; stderr 0.5; 35 | var e; stderr 0.5; 36 | end; 37 | 38 | // 全てゼロになることを念のためチェック 39 | steady; 40 | 41 | // モデルのチェック 42 | check; 43 | 44 | estimated_params; 45 | gamma, gamma_pdf, 5, 2; 46 | varrho, beta_pdf, 0.9, 0.05; 47 | phi_pi, gamma_pdf, 0.5, 0.25; 48 | phi_y, gamma_pdf, 0.5, 0.25; 49 | rho_A, beta_pdf, 0.9, 0.05; 50 | rho_v, beta_pdf, 0.7, 0.1; 51 | stderr epsilon, inv_gamma_pdf, 5, 1; 52 | stderr z, inv_gamma_pdf, 2, 1; 53 | stderr e, inv_gamma_pdf, 1, 0.5; 54 | end; 55 | 56 | varobs x ppi ii; 57 | 58 | estimation(datafile='dset.mat', mh_replic=125000, mh_drop = 0.2, mh_nblocks=2, mh_jscale=0.6, mode_compute = 4, mode_check); 59 | 60 | chain1 = load(strcat('./NK_Linear_EST/metropolis/NK_Linear_EST_mh1_blck1.mat')); 61 | chain2 = load(strcat('./NK_Linear_EST/metropolis/NK_Linear_EST_mh1_blck2.mat')); 62 | csvwrite('chain1.csv',chain1.x2, 1, 0); 63 | csvwrite('chain2.csv',chain2.x2, 1, 0); 64 | 65 | -------------------------------------------------------------------------------- /ch8_dynare/coda.R: -------------------------------------------------------------------------------- 1 | #======================================= 2 | # Chapter 8, Post-processing 3 | # modified on 2019/10/19 4 | #======================================= 5 | 6 | library(coda) 7 | library(xtable) 8 | 9 | chain1 <- read.csv("chain1.csv") 10 | chain2 <- read.csv("chain2.csv") 11 | 12 | colnames(chain1) <- c("epsilon", "z", "e", "gamma", "varrho", "phi_pi", "phi_y", "rho_A", "rho_v") 13 | colnames(chain2) <- c("epsilon", "z", "e", "gamma", "varrho", "phi_pi", "phi_y", "rho_A", "rho_v") 14 | 15 | vorder <- c(7, 8, 9, 1, 2, 3, 4, 5) 16 | varnames <- c("$gamma$", "$varrho$", "$phi_pi$", "$phi_y$", "$rho_A$", "$rho_v$", "$sigma_varepsilon$", "$sigma_z$","$sigma_e$") 17 | 18 | rslt <- mcmc.list(mcmc(chain1[25001:125000, ]), mcmc(chain2[25001:125000, ])) 19 | sum <- summary(rslt) 20 | gew <- geweke.diag(rslt) 21 | 22 | ans0 <- as.matrix(sum$statistics[,1:2]) 23 | ans0 <- cbind(ans0, gew[[1]]$z, gew[[2]]$z) 24 | ans <- ans0[c(4:9, 1:3), ] 25 | 26 | rownames(ans) <- varnames 27 | colnames(ans) <- c("Mean","SD","Z(1)", "Z(2)") 28 | 29 | print(ans) 30 | 31 | cbind(1-rejectionRate(rslt[[1]][,1]), 1-rejectionRate(rslt[[2]][,1])) 32 | 33 | xtable(ans,digits = 3) 34 | -------------------------------------------------------------------------------- /ch8_dynare/main.m: -------------------------------------------------------------------------------- 1 | %======================================= 2 | % Chapter 8, Estimation 3 | % modified on 2020/01/02 4 | %======================================= 5 | 6 | % パスのセット 7 | cd 'C:\Users\USERNAME\ch8_dynare_test' 8 | 9 | % データセットの作成 10 | script_dataset 11 | 12 | % Dynareのパスのセット 13 | addpath C:\programs\dynare\4.5.7\matlab 14 | 15 | % パラメータ推定、出力 16 | dynare NK_Linear_EST 17 | 18 | -------------------------------------------------------------------------------- /ch8_dynare/script_dataset.m: -------------------------------------------------------------------------------- 1 | %======================================= 2 | % Chapter 8, Preparing data 3 | % modified on 2019/10/19 4 | %======================================= 5 | 6 | FqReport8 = csvread('FqReport8.csv', 1, 1); 7 | 8 | GAP0 = FqReport8(:,1); 9 | PGDP0 = FqReport8(:,2); 10 | IRS0 = FqReport8(:,3); 11 | 12 | PC_PGDP0 = [NaN; (PGDP0(2:end)./PGDP0(1:end-1)-1)*100]; 13 | 14 | tt = 2:77; 15 | MGAP = mean(GAP0(tt)); 16 | MPC_PGDP = mean(PC_PGDP0(tt)); 17 | MIRS = mean(IRS0(tt)); 18 | 19 | GAP = GAP0(tt)-MGAP; 20 | PC_PGDP = PC_PGDP0(tt)-MPC_PGDP; 21 | IRS4 = (IRS0(tt)-MIRS)*0.25; 22 | 23 | x = GAP; 24 | ppi = PC_PGDP; 25 | ii = IRS4; 26 | 27 | save dset.mat x ppi ii; 28 | 29 | out2 = [GAP0(tt) PC_PGDP0(tt) IRS0(tt)]; 30 | lab2 = {'GAP', 'PC_PGDP', 'IRS'}; 31 | util_csvwrite('dset_fig.csv', out2, lab2); 32 | -------------------------------------------------------------------------------- /ch8_dynare/util_csvwrite.m: -------------------------------------------------------------------------------- 1 | function [] = util_csvwrite(filename, x, str) 2 | 3 | fid = fopen(filename,'wt'); % 書き込み用にファイルオープン 4 | [rows,cols] = size(x); 5 | if cols > 1 6 | fprintf(fid, '%s,', str{1,1:end-1}); % 文字列の書き出し 7 | fprintf(fid, '%s\n', str{1,end}); % 行末の文字列は、改行を含めて出力 8 | for i = 1:rows 9 | fprintf(fid, '%f,', x(i,1:end-1)); 10 | fprintf(fid, '%f\n', x(i, end)); 11 | end 12 | else 13 | fprintf(fid, '%s\n', str{1}); 14 | for i = 1:rows 15 | fprintf(fid, '%f\n', x(i)); 16 | end 17 | end 18 | fclose('all'); 19 | % ファイルクローズ 20 | -------------------------------------------------------------------------------- /dynare/NK_det.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 5, New Keynesian model, 3 | // deterministic solution 4 | // modified on 2020/01/02 5 | //======================================= 6 | 7 | // 1. 内生変数、外生変数の宣言 8 | var C phi ppi ppitil F D A ii v; 9 | varexo e z; 10 | 11 | // 2. パラメータの宣言 12 | parameters beta mu gamma varrho eta phi_pi phi_y rho_A rho_v istar Cstar; 13 | 14 | // パラメータ値の代入 15 | beta = 0.99; 16 | mu = 1.0; 17 | gamma = 5; 18 | eta = 10; 19 | varrho = 0.9; 20 | phi_pi = 1.5; 21 | phi_y = 0.5; 22 | rho_A = 0.9; 23 | rho_v = 0.7; 24 | 25 | // 3. 方程式の定義 26 | model; 27 | (1+ppi(+1))*C(+1)/C = beta*(1+ii); 28 | (1+ppitil)/(1+ppi) = eta/(eta-1)*F/D; 29 | F = phi + varrho*beta*(1+ppi(+1))^eta*F(+1); 30 | D = 1 + varrho*beta*(1+ppi(+1))^(eta-1)*D(+1); 31 | (1+ppi)^(1-eta) = (1-varrho)*(1+ppitil)^(1-eta)+varrho; 32 | ii = istar + phi_pi*ppi + phi_y*log(C/Cstar/A) + v; 33 | log(A) = rho_A*log(A(-1)) + e; 34 | v = rho_v*v(-1) + z; 35 | phi - mu*(C/A)^(gamma+1)*(gamma+1) = 0; 36 | end; 37 | 38 | // 4. 定常状態の計算 39 | pistar = 0; 40 | pitilstar = 0; 41 | vstar = 0; 42 | istar = (1-beta)/beta; 43 | Dstar = 1/(1-varrho*beta); 44 | Fstar = (eta-1)/eta/(1-varrho*beta); 45 | phistar = (eta-1)/eta; 46 | Astar = 1; 47 | Cstar = ((eta-1)/eta/mu/(gamma+1))^(1/(gamma+1)); 48 | 49 | initval; 50 | C = Cstar; 51 | phi = phistar; 52 | ppi = pistar; 53 | ppitil = pitilstar; 54 | F = Fstar; 55 | D = Dstar; 56 | A = Astar; 57 | ii = istar; 58 | v = vstar; 59 | end; 60 | 61 | steady; 62 | 63 | // モデルのチェック 64 | check; 65 | 66 | // 5. シミュレーション(deterministic) 67 | // シナリオの設定 68 | shocks; 69 | var e; periods 1; values 0.01; 70 | end; 71 | 72 | // シミュレーションの実行 73 | //simul(periods=150); 74 | perfect_foresight_setup(periods=150); 75 | perfect_foresight_solver; 76 | 77 | // グラフ描写など 78 | C1 = (C./Cstar-1)*100; 79 | i1 = (ii-istar)*100; 80 | pi1 = (ppi-pistar)*100; 81 | A1 = (A./Astar-1)*100; 82 | phi1 = (phi./phistar-1)*100; 83 | v1 = (v-vstar)*100; 84 | 85 | figure(1) 86 | subplot(3,2,1) 87 | plot(0:50, C1(1:51)); title('C') 88 | subplot(3,2,2) 89 | plot(0:50, i1(1:51)); title('i') 90 | subplot(3,2,3) 91 | plot(0:50, pi1(1:51)); title('pi') 92 | subplot(3,2,4) 93 | plot(0:50, phi1(1:51)); title('phi') 94 | subplot(3,2,5) 95 | plot(0:50, A1(1:51)); title('A') 96 | subplot(3,2,6) 97 | plot(0:50, v1(1:51)); title('v') 98 | 99 | shocks; 100 | var e; periods 1; values 0; 101 | var z; periods 1; values 0.01; 102 | end; 103 | 104 | //simul(periods=150); 105 | perfect_foresight_setup(periods=150); 106 | perfect_foresight_solver; 107 | 108 | C2 = (C./Cstar-1)*100; 109 | i2 = (ii-istar)*100; 110 | pi2 = (ppi-pistar)*100; 111 | A2 = (A./Astar-1)*100; 112 | phi2 = (phi./phistar-1)*100; 113 | v2 = (v-vstar)*100; 114 | 115 | figure(2) 116 | subplot(3,2,1) 117 | plot(0:50, C2(1:51)); title('C') 118 | subplot(3,2,2) 119 | plot(0:50, i2(1:51)); title('i') 120 | subplot(3,2,3) 121 | plot(0:50, pi2(1:51)); title('pi') 122 | subplot(3,2,4) 123 | plot(0:50, phi2(1:51)); title('phi') 124 | subplot(3,2,5) 125 | plot(0:50, A2(1:51)); title('A') 126 | subplot(3,2,6) 127 | plot(0:50, v2(1:51)); title('v') 128 | -------------------------------------------------------------------------------- /dynare/NK_linear_det.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 5, New Keynesian model, 3 | // linearized, deterministic solution 4 | // modified on 2020/01/02 5 | //======================================= 6 | 7 | // 1. 内生変数、外生変数の宣言 8 | var x ppi a ii v; 9 | varexo e z; 10 | 11 | // 2. パラメータの宣言 12 | parameters beta kappa phi_pi phi_y rho_A rho_v; 13 | 14 | // パラメータ値の代入 15 | beta = 0.99; 16 | gamma = 5; 17 | varrho = 0.9; 18 | kappa = (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho; 19 | phi_pi = 1.5; 20 | phi_y = 0.5; 21 | rho_A = 0.9; 22 | rho_v = 0.7; 23 | 24 | // 3. 方程式の定義 25 | model(linear); 26 | ppi = beta*ppi(+1)+kappa*x; 27 | x = x(+1)-(ii-ppi(+1))+(rho_A-1)*a; 28 | ii = phi_pi*ppi + phi_y*x + v; 29 | a = rho_A*a(-1) + e; 30 | v = rho_v*v(-1) + z; 31 | end; 32 | 33 | // 全てゼロになることを念のためチェック 34 | steady; 35 | 36 | // モデルのチェック 37 | check; 38 | 39 | // 5. シミュレーション(deterministic) 40 | shocks; 41 | var e; periods 1; values 0.01; 42 | end; 43 | 44 | //simul(periods=150); 45 | perfect_foresight_setup(periods=150); 46 | perfect_foresight_solver; 47 | 48 | figure(1) 49 | subplot(3,2,1) 50 | plot(0:50, x(1:51)*100); title('x') 51 | subplot(3,2,2) 52 | plot(0:50, ii(1:51)*100); title('i') 53 | subplot(3,2,3) 54 | plot(0:50, ppi(1:51)*100); title('pi') 55 | subplot(3,2,5) 56 | plot(0:50, a(1:51)*100); title('a') 57 | subplot(3,2,6) 58 | plot(0:50, v(1:51)*100); title('v') 59 | 60 | shocks; 61 | var e; periods 1; values 0; 62 | var z; periods 1; values 0.01; 63 | end; 64 | 65 | //simul(periods=150); 66 | perfect_foresight_setup(periods=150); 67 | perfect_foresight_solver; 68 | 69 | figure(2) 70 | subplot(3,2,1) 71 | plot(0:50, x(1:51)*100); title('x') 72 | subplot(3,2,2) 73 | plot(0:50, ii(1:51)*100); title('i') 74 | subplot(3,2,3) 75 | plot(0:50, ppi(1:51)*100); title('pi') 76 | subplot(3,2,5) 77 | plot(0:50, a(1:51)*100); title('a') 78 | subplot(3,2,6) 79 | plot(0:50, v(1:51)*100); title('v') 80 | -------------------------------------------------------------------------------- /dynare/NK_linear_stoch.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 5, New Keynesian model, 3 | // linearized, stochastic solution 4 | // modified on 2020/01/02 5 | //======================================= 6 | 7 | // 1. 内生変数、外生変数の宣言 8 | var x ppi a ii v; 9 | varexo e z; 10 | 11 | // 2. パラメータの宣言 12 | parameters beta kappa phi_pi phi_y rho_A rho_v; 13 | 14 | // パラメータ値の代入 15 | beta = 0.99; 16 | gamma = 5; 17 | varrho = 0.9; 18 | kappa = (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho; 19 | phi_pi = 1.5; 20 | phi_y = 0.5; 21 | rho_A = 0.9; 22 | rho_v = 0.7; 23 | 24 | // 3. 方程式の定義 25 | model(linear); 26 | ppi = beta*ppi(+1)+kappa*x; 27 | x = x(+1)-(ii-ppi(+1))+(rho_A-1)*a; 28 | ii = phi_pi*ppi + phi_y*x + v; 29 | a = rho_A*a(-1) + e; 30 | v = rho_v*v(-1) + z; 31 | end; 32 | 33 | // 全てゼロになることを念のためチェック 34 | steady; 35 | 36 | // モデルのチェック 37 | check; 38 | 39 | // 5. シミュレーション(stochastic) 40 | shocks; 41 | var e = 1; 42 | end; 43 | 44 | stoch_simul(order=1, irf = 100) x ii ppi a v; 45 | 46 | shocks; 47 | var e = 0; 48 | var z = 1; 49 | end; 50 | 51 | stoch_simul(order=1, irf = 100) x ii ppi a v; 52 | -------------------------------------------------------------------------------- /dynare/RBC_det.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 4, RBC model, deterministic solution 3 | // modified on 2020/01/02 4 | //======================================= 5 | 6 | // 1. 内生変数、外生変数の宣言 7 | var C L K Y w r A; 8 | varexo e; 9 | 10 | // 2. パラメータの宣言 11 | parameters alpha beta delta mu gamma rho; 12 | 13 | // パラメータ値の代入 14 | alpha = 0.3; 15 | beta = 0.99; 16 | delta = 0.025; 17 | mu = 1.0; 18 | gamma = 1.0; 19 | rho = 0.9; 20 | 21 | // 3. 方程式の定義 22 | model; 23 | w/C = (gamma+1)*mu*L^gamma; 24 | C(+1)/C = beta*(r(+1)-delta+1); 25 | Y = A*K^alpha*L^(1-alpha); 26 | w = (1-alpha)*A*K^alpha*L^(-alpha); 27 | r = alpha*A*K^(alpha-1)*L^(1-alpha); 28 | K = Y(-1)+(1-delta)*K(-1)-C(-1); 29 | log(A) = rho*log(A(-1)) + e; 30 | end; 31 | 32 | // 4. 定常状態の計算 33 | Astar = 1; 34 | rstar = 1/beta + delta - 1; 35 | K_L = (rstar/alpha/Astar)^(1/(alpha-1)); 36 | Y_L = Astar*K_L^alpha; 37 | C_L = Y_L-delta*K_L; 38 | wstar = (1-alpha)*Astar*K_L^alpha; 39 | Lstar = (wstar/(gamma+1)/mu)^(1/(gamma+1))*C_L^(-1/(gamma+1)); 40 | Kstar = K_L*Lstar; 41 | Ystar = Y_L*Lstar; 42 | Cstar = C_L*Lstar; 43 | 44 | // Dynareに定常状態を計算させる際の初期値 45 | initval; 46 | C = Cstar; 47 | L = Lstar; 48 | K = Kstar; 49 | Y = Ystar; 50 | w = wstar; 51 | r = rstar; 52 | A = Astar; 53 | end; 54 | 55 | // Dynareに定常状態を計算させる 56 | steady; 57 | 58 | // 初期値と結果が変わらないことをチェック 59 | [Cstar; Lstar; Kstar; Ystar; wstar; rstar; Astar] 60 | 61 | // モデルのチェック 62 | check; 63 | 64 | // 5. シミュレーション 65 | // シナリオの設定 66 | shocks; 67 | var e; 68 | periods 1; 69 | values 0.01; 70 | end; 71 | 72 | // シミュレーションの実行 73 | //simul(periods=150); 74 | perfect_foresight_setup(periods=150); 75 | perfect_foresight_solver; 76 | 77 | // 定常状態からの乖離率の計算 78 | C1 = (C./Cstar-1)*100; 79 | L1 = (L./Lstar-1)*100; 80 | K1 = (K./Kstar-1)*100; 81 | Y1 = (Y./Ystar-1)*100; 82 | w1 = (w./wstar-1)*100; 83 | r1 = (r-rstar)*100; 84 | A1 = (A./Astar-1)*100; 85 | I1 = ((Y-C)./(Ystar-Cstar)-1)*100; 86 | 87 | // グラフ描写 88 | figure(1) 89 | subplot(2,2,1) 90 | plot(0:50, A1(1:51)); title('A') 91 | subplot(2,2,2) 92 | plot(0:50, Y1(1:51)); title('Y') 93 | subplot(2,2,3) 94 | plot(0:50, C1(1:51)); title('C') 95 | subplot(2,2,4) 96 | plot(0:50, K1(1:51)); title('K') 97 | 98 | figure(2) 99 | subplot(2,2,1) 100 | plot(0:50, L1(1:51)); title('L') 101 | subplot(2,2,2) 102 | plot(0:50, I1(1:51)); title('I') 103 | subplot(2,2,3) 104 | plot(0:50, w1(1:51)); title('w') 105 | subplot(2,2,4) 106 | plot(0:50, r1(1:51)); title('r') 107 | -------------------------------------------------------------------------------- /dynare/RBC_linear_det.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 4, RBC model, 3 | // linearized, deterministic solution 4 | // modified on 2021/03/03 5 | //======================================= 6 | 7 | // 1. 内生変数、外生変数の宣言 8 | var C L K Y w R A; 9 | varexo e; 10 | 11 | // 2. パラメータの宣言 12 | parameters alpha beta delta mu gamma rho Rstar Kstar Ystar Cstar; 13 | 14 | // パラメータ値の代入 15 | alpha = 0.3; 16 | beta = 0.99; 17 | delta = 0.025; 18 | mu = 1.0; 19 | gamma = 1.0; 20 | rho = 0.9; 21 | 22 | model; 23 | w-C = gamma*L; 24 | C(+1)-C = beta*Rstar*R(+1); 25 | Y = A + alpha*K + (1-alpha)*L; 26 | w = A + alpha*K - alpha*L; 27 | Rstar/(Rstar-1)*R = A + (alpha-1)*K + (1-alpha)*L; 28 | Kstar*K = Ystar*Y(-1)+(1-delta)*Kstar*K(-1)-Cstar*C(-1); 29 | A = rho*A(-1) + e; 30 | end; 31 | 32 | // 4. 定常状態の計算 33 | Astar = 1; 34 | rstar = 1/beta+delta-1; 35 | K_L = (rstar/alpha/Astar)^(1/(alpha-1)); 36 | Y_L = Astar*K_L^alpha; 37 | C_L = Y_L-delta*K_L; 38 | wstar = (1-alpha)*Astar*K_L^alpha; 39 | Lstar = (wstar/(gamma+1)/mu)^(1/(gamma+1))*C_L^(-1/(gamma+1)); 40 | Kstar = K_L*Lstar; 41 | Ystar = Y_L*Lstar; 42 | Cstar = C_L*Lstar; 43 | Rstar = rstar+1; 44 | 45 | // 全てゼロになることを念のためチェック 46 | steady; 47 | 48 | // モデルのチェック 49 | check; 50 | 51 | // 5. シミュレーション 52 | // シナリオの設定 53 | shocks; 54 | var e; 55 | periods 1; 56 | values 0.01; 57 | end; 58 | 59 | // シミュレーションの実行 60 | //simul(periods=150); 61 | perfect_foresight_setup(periods=150); 62 | perfect_foresight_solver; 63 | 64 | I = (Y*Ystar-C*Cstar)./(Ystar-Cstar); 65 | 66 | // グラフ描写 67 | figure(3) 68 | subplot(2,2,1) 69 | plot(0:50, A(1:51)*100); title('A') 70 | subplot(2,2,2) 71 | plot(0:50, Y(1:51)*100); title('Y') 72 | subplot(2,2,3) 73 | plot(0:50, C(1:51)*100); title('C') 74 | subplot(2,2,4) 75 | plot(0:50, K(1:51)*100); title('K') 76 | 77 | figure(4) 78 | subplot(2,2,1) 79 | plot(0:50, L(1:51)*100); title('L') 80 | subplot(2,2,2) 81 | plot(0:50, I(1:51)*100); title('I') 82 | subplot(2,2,3) 83 | plot(0:50, w(1:51)*100); title('w') 84 | subplot(2,2,4) 85 | plot(0:50, R(1:51)*100); title('r') 86 | -------------------------------------------------------------------------------- /dynare/RBC_linear_stoch.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 4, RBC model, 3 | // linearized, stochastic solution 4 | // modified on 2020/01/02 5 | //======================================= 6 | 7 | // 1. 内生変数、外生変数の宣言 8 | var c l k y w R a; 9 | varexo e; 10 | 11 | // 2. パラメータの宣言 12 | parameters alpha beta delta mu gamma rho Rstar Kstar Ystar Cstar; 13 | 14 | // パラメータ値の代入 15 | alpha = 0.3; 16 | beta = 0.99; 17 | delta = 0.025; 18 | mu = 1.0; 19 | gamma = 1.0; 20 | rho = 0.9; 21 | 22 | model; 23 | w-c = gamma*l; 24 | c(+1)-c = beta*Rstar*R(+1); 25 | y = a + alpha*k + (1-alpha)*l; 26 | w = a + alpha*k - alpha*l; 27 | Rstar/(Rstar-1)*R = a + (alpha-1)*k + (1-alpha)*l; 28 | Kstar*k = Ystar*y(-1)+(1-delta)*Kstar*k(-1)-Cstar*c(-1); 29 | a = rho*a(-1) + e; 30 | end; 31 | 32 | // 4. 定常状態の計算 33 | Astar = 1; 34 | rstar = 1/beta+delta-1; 35 | K_L = (rstar/alpha/Astar)^(1/(alpha-1)); 36 | Y_L = Astar*K_L^alpha; 37 | C_L = Y_L-delta*K_L; 38 | wstar = (1-alpha)*Astar*K_L^alpha; 39 | Lstar = (wstar/(gamma+1)/mu)^(1/(gamma+1))*C_L^(-1/(gamma+1)); 40 | Kstar = K_L*Lstar; 41 | Ystar = Y_L*Lstar; 42 | Cstar = C_L*Lstar; 43 | Rstar = rstar+1; 44 | 45 | // 全てゼロになることを念のためチェック 46 | steady; 47 | 48 | // モデルのチェック 49 | check; 50 | 51 | // 5. シミュレーション(stochastic) 52 | // シナリオの設定 53 | shocks; 54 | var e = 1; 55 | end; 56 | 57 | // シミュレーションの実行 58 | stoch_simul(order=1, irf = 100) c l k y w R a; 59 | -------------------------------------------------------------------------------- /dynare/RBC_stoch.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 4, RBC model, stochastic solution 3 | // modified on 2020/01/02 4 | //======================================= 5 | 6 | // 1. 内生変数、外生変数の宣言 7 | var C L K Y w R A; 8 | varexo e; 9 | 10 | // 2. パラメータの宣言 11 | parameters alpha beta delta mu gamma rho; 12 | 13 | // パラメータ値の代入 14 | alpha = 0.3; 15 | beta = 0.99; 16 | delta = 0.025; 17 | mu = 1.0; 18 | gamma = 1.0; 19 | rho = 0.9; 20 | 21 | // 3. 方程式の定義 22 | model; 23 | exp(w)/exp(C) = (gamma+1)*mu*exp(L)^gamma; 24 | exp(C(+1))/exp(C) = beta*(exp(R(+1))-delta); 25 | exp(Y) = exp(A)*exp(K)^alpha*exp(L)^(1-alpha); 26 | exp(w) = (1-alpha)*exp(A)*exp(K)^alpha*exp(L)^(-alpha); 27 | exp(R)-1 = alpha*exp(A)*exp(K)^(alpha-1)*exp(L)^(1-alpha); 28 | exp(K) = exp(Y(-1))+(1-delta)*exp(K(-1))-exp(C(-1)); 29 | A = rho*A(-1) + e; 30 | end; 31 | 32 | // 4. 定常状態の計算 33 | Astar = 1; 34 | rstar = 1/beta + delta - 1; 35 | K_L = (rstar/alpha/Astar)^(1/(alpha-1)); 36 | Y_L = Astar*K_L^alpha; 37 | C_L = Y_L-delta*K_L; 38 | wstar = (1-alpha)*Astar*K_L^alpha; 39 | Lstar = (wstar/(gamma+1)/mu)^(1/(gamma+1))*C_L^(-1/(gamma+1)); 40 | Kstar = K_L*Lstar; 41 | Ystar = Y_L*Lstar; 42 | Cstar = C_L*Lstar; 43 | 44 | // Dynareに定常状態を計算させる際の初期値 45 | initval; 46 | C = log(Cstar); 47 | L = log(Lstar); 48 | K = log(Kstar); 49 | Y = log(Ystar); 50 | w = log(wstar); 51 | R = log(1+rstar); 52 | A = log(Astar); 53 | end; 54 | 55 | // Dynareに定常状態を計算させる 56 | steady; 57 | 58 | // 初期値と結果が変わらないことをチェック 59 | [log(Cstar); log(Lstar); log(Kstar); log(Ystar); log(wstar); log(rstar+1); log(Astar)] 60 | 61 | // モデルのチェック 62 | check; 63 | 64 | // 5. シミュレーション(stochastic) 65 | // シナリオの設定 66 | shocks; 67 | var e = 1; 68 | end; 69 | 70 | // シミュレーションの実行 71 | stoch_simul(order=1, irf = 100) C L K Y w R A; 72 | -------------------------------------------------------------------------------- /dynare/Ramsey_tax1.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 3, Ramsey model with tax 1 3 | // modified on 2020/01/02 4 | //======================================= 5 | 6 | // 1. 内生変数、外生変数の宣言 7 | var C K; 8 | varexo tauc tauk g; 9 | 10 | // 2. パラメータの宣言 11 | parameters alpha beta delta At; 12 | 13 | // パラメータ値の代入 14 | alpha = 0.3; 15 | beta = 0.99; 16 | delta = 0.25; 17 | At = 1.0; 18 | 19 | // 3. 方程式の定義 20 | model; 21 | (1+tauc(+1))*C(+1)/(1+tauc)/C-beta*((1-tauk(+1))*alpha*At*K^(alpha-1)-delta+1) = 0; 22 | K-At*K(-1)^alpha-(1-delta)*K(-1)+C+g = 0; 23 | end; 24 | 25 | // 4. 初期値の定義 26 | initval; 27 | C = 1; 28 | K = 1; 29 | tauc = 0; 30 | tauk = 0; 31 | g = 0.1; 32 | end; 33 | 34 | steady; 35 | 36 | // 5. 定常状態の計算と終端値の定義 37 | endval; 38 | C = 1; 39 | K = 1; 40 | tauc = 0.1; 41 | tauk = 0; 42 | g = 0.1; 43 | end; 44 | 45 | steady; 46 | 47 | // 6. モデルのチェック 48 | check; 49 | 50 | // 7. シミュレーションの実行 51 | shocks; 52 | var tauc; periods 1:9; values 0; 53 | end; 54 | 55 | //simul(periods=31); 56 | perfect_foresight_setup(periods=31); 57 | perfect_foresight_solver; 58 | 59 | // グラフ描写 60 | figure(1) 61 | subplot(2,1,1) 62 | plot(0:30, C(1:31)) 63 | subplot(2,1,2) 64 | plot(0:30, K(1:31)) 65 | 66 | -------------------------------------------------------------------------------- /dynare/Ramsey_tax2.mod: -------------------------------------------------------------------------------- 1 | //======================================= 2 | // Chapter 3, Ramsey model with tax 2 3 | // modified on 2020/01/02 4 | //======================================= 5 | 6 | // 1. 内生変数、外生変数の宣言 7 | var C K; 8 | varexo tauc tauk g; 9 | 10 | // 2. パラメータの宣言 11 | parameters alpha beta delta At; 12 | 13 | // パラメータ値の代入 14 | alpha = 0.3; 15 | beta = 0.99; 16 | delta = 0.25; 17 | At = 1.0; 18 | 19 | // 3. 方程式の定義 20 | model; 21 | (1+tauc(+1))*C(+1)/(1+tauc)/C-beta*((1-tauk(+1))*alpha*At*K^(alpha-1)-delta+1) = 0; 22 | K-At*K(-1)^alpha-(1-delta)*K(-1)+C+g = 0; 23 | end; 24 | 25 | // 4. 初期値の定義 26 | initval; 27 | C = 1; 28 | K = 1; 29 | tauc = 0; 30 | tauk = 0; 31 | g = 0.1; 32 | end; 33 | 34 | steady; 35 | 36 | // 5. 終端値（定常状態）の定義 37 | endval; 38 | C = 1; 39 | K = 1; 40 | tauc = 0; 41 | tauk = 0.1; 42 | g = 0.1; 43 | end; 44 | 45 | steady; 46 | 47 | // 6. モデルのチェック 48 | check; 49 | 50 | // 7. シミュレーションの実行 51 | shocks; 52 | var tauk; periods 1:9; values 0; 53 | end; 54 | 55 | //simul(periods=31); 56 | perfect_foresight_setup(periods=31); 57 | perfect_foresight_solver; 58 | 59 | // グラフ描写 60 | figure(2) 61 | subplot(2,1,1) 62 | plot(0:30, C(1:31)) 63 | subplot(2,1,2) 64 | plot(0:30, K(1:31)) 65 | -------------------------------------------------------------------------------- /use_dynare.pdf: -------------------------------------------------------------------------------- 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