From f98f4dd7f28c71a569721454bdb36ee487e28851 Mon Sep 17 00:00:00 2001 From: spring-haru Date: Fri, 3 Jan 2025 01:30:58 +0000 Subject: [PATCH] deploy: 7be45e9d85b0af412b25afa8890b5c8e5f5c0188 --- 11a_Okun_Phillips.html | 2 +- 11b_Money_Inflation.html | 78 ++++----- 13a_Random_Variables.html | 162 ++++++++--------- 13b_Stochastic_Solow.html | 164 +++++++++--------- 18_ADAS-1.html | 8 +- 18_ADAS-2.html | 48 ++--- 6_Regression.html | 2 +- ...98d8b196ffe7fcac4cd02882096ce75003f2cd.png | Bin 0 -> 42497 bytes ...033bb79a7b2556d8c6b948fd2d88907d119694.png | Bin 48914 -> 0 bytes ...b450f4c969b985532d73071c143506feca301c.png | Bin 0 -> 10708 bytes ...7819532cf5a329146c16276f3c9bf0b578c6af.png | Bin 31267 -> 0 bytes ...e705c8bb67a06dc34a3f452aaddee5cbc46572.png | Bin 0 -> 63667 bytes ...07a9d774651eda2a840bd78341e105b7ff4a50.png | Bin 0 -> 40035 bytes ...d1bbdfe26879c56def140827d11178f34df266.png | Bin 7681 -> 0 bytes ...75b5b88bcfc066048d832130b361ea97908c0a.png | Bin 0 -> 11716 bytes ...55cc94069e60bc541361bfca749c8888642787.png | Bin 0 -> 7097 bytes ...f4e82e65496fd8802afb62551b965d37350703.png | Bin 50691 -> 0 bytes ...f9ad545ac53c9215f9fe4e3e122c9cda75c9c6.png | Bin 10931 -> 0 bytes ...e0138e9d25e50b98d1c30183f318f8a5952f86.png | Bin 0 -> 34230 bytes ...5344f30db23ed5dfb49d77e8de59cab651ebe2.png | Bin 45241 -> 0 bytes ...5600284c6a8ff50c54389e42d3487aaa3e97ee.png | Bin 0 -> 44564 bytes ...78eb80fa112c2783f2c20012d2739d3f7dc7b4.png | Bin 38962 -> 0 bytes ...7922967c113f84e5f41192e82b8f3b80fa07d5.png | Bin 0 -> 76935 bytes ...96a6c55c1d706e9fe6d07921bf0482ecf893e5.png | Bin 11745 -> 0 bytes ...3dcc1c06c58d78e8a7abbadd1e67ed6a0bb56e.png | Bin 32787 -> 0 bytes ...df5ad5f1ba761a733d35771f373c5985f9d5e0.png | Bin 41069 -> 0 bytes ...57b79b642010ad1fd4ac6f2a77ec60e8d9b081.png | Bin 0 -> 40459 bytes ...687a0b53770cd6f38a3c1400c9d3b082e19ea1.png | Bin 0 -> 45053 bytes ...e359335ed540ee903236ac61e7105d39c4777c.png | Bin 76789 -> 0 bytes ...9b42a43efdd45dcd11760a2c34e82a46f786f9.png | Bin 59715 -> 0 bytes ...fe47aeb643db32d911a7fb1feaf926ad9a087a.png | Bin 0 -> 48981 bytes _sources/18_ADAS-1.ipynb | 8 +- _sources/index.ipynb | 10 +- searchindex.js | 2 +- 34 files changed, 243 insertions(+), 241 deletions(-) create mode 100644 _images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png delete mode 100644 _images/0ccc371866a21987df211f7faf033bb79a7b2556d8c6b948fd2d88907d119694.png create mode 100644 _images/1060e595f76c5b0611c3ed484eb450f4c969b985532d73071c143506feca301c.png delete mode 100644 _images/1fd4ed086eb2f122776e7a077c7819532cf5a329146c16276f3c9bf0b578c6af.png create mode 100644 _images/39be1bdfba89c425b86879c9b6e705c8bb67a06dc34a3f452aaddee5cbc46572.png create mode 100644 _images/3b51f61252c671e49b945e439507a9d774651eda2a840bd78341e105b7ff4a50.png delete mode 100644 _images/3e861834efdb7a49f614713195d1bbdfe26879c56def140827d11178f34df266.png create mode 100644 _images/453bb7eed15269c9257b75f79075b5b88bcfc066048d832130b361ea97908c0a.png create mode 100644 _images/48a6596ed520d1771b23a1a02155cc94069e60bc541361bfca749c8888642787.png delete mode 100644 _images/5183e8799a5de10cda15034d5cf4e82e65496fd8802afb62551b965d37350703.png delete mode 100644 _images/5f9e5a782f241d5dfd07e89165f9ad545ac53c9215f9fe4e3e122c9cda75c9c6.png create mode 100644 _images/8833571bac3c8e59ccaec2675ce0138e9d25e50b98d1c30183f318f8a5952f86.png delete mode 100644 _images/8ad4051082caff7b62c965a4565344f30db23ed5dfb49d77e8de59cab651ebe2.png create mode 100644 _images/8f29efe00569168d5ff4b9ee085600284c6a8ff50c54389e42d3487aaa3e97ee.png delete mode 100644 _images/aa77d668f0bc4f08e4f1f60f7878eb80fa112c2783f2c20012d2739d3f7dc7b4.png create mode 100644 _images/afcc1f5acbca950514c0269f037922967c113f84e5f41192e82b8f3b80fa07d5.png delete mode 100644 _images/aff93ba8ca0807c48213648c4496a6c55c1d706e9fe6d07921bf0482ecf893e5.png delete mode 100644 _images/c0da3bcfc3afe5f377a47ab5473dcc1c06c58d78e8a7abbadd1e67ed6a0bb56e.png delete mode 100644 _images/c69aff5a769726b55773075cc2df5ad5f1ba761a733d35771f373c5985f9d5e0.png create mode 100644 _images/ca191948269b7124da4be711eb57b79b642010ad1fd4ac6f2a77ec60e8d9b081.png create mode 100644 _images/cefc63931e1da6d11040316320687a0b53770cd6f38a3c1400c9d3b082e19ea1.png delete mode 100644 _images/dd26fadedfae37bc7bcd5a2125e359335ed540ee903236ac61e7105d39c4777c.png delete mode 100644 _images/ebe1fd1db8278d9e821af856199b42a43efdd45dcd11760a2c34e82a46f786f9.png create mode 100644 _images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png diff --git a/11a_Okun_Phillips.html b/11a_Okun_Phillips.html index d351b54c..7514f68f 100644 --- a/11a_Okun_Phillips.html +++ b/11a_Okun_Phillips.html @@ -707,7 +707,7 @@

回帰分析# Model: OLS Adj. R-squared: 0.387 Method: Least Squares F-statistic: 111.5 Date: Fri, 03 Jan 2025 Prob (F-statistic): 1.84e-20 -Time: 01:09:27 Log-Likelihood: -275.03 +Time: 01:29:46 Log-Likelihood: -275.03 No. Observations: 176 AIC: 554.1 Df Residuals: 174 BIC: 560.4 Df Model: 1 diff --git a/11b_Money_Inflation.html b/11b_Money_Inflation.html index 1ba211bc..6c903009 100644 --- a/11b_Money_Inflation.html +++ b/11b_Money_Inflation.html @@ -623,122 +623,122 @@

resample() 2019-01-01 10 - 7.068212 + 5.277740 2019-02-01 20 - 5.507801 + 5.179652 2019-03-01 30 - 4.659180 + 6.903653 2019-04-01 40 - 6.750383 + 5.135640 2019-05-01 50 - 5.770613 + 5.288257 2019-06-01 60 - 5.057649 + 5.916110 2019-07-01 70 - 5.291954 + 3.649450 2019-08-01 80 - 5.090206 + 5.648054 2019-09-01 90 - 5.229165 + 5.053249 2019-10-01 100 - 4.371847 + 3.050738 2019-11-01 110 - 5.835155 + 5.287720 2019-12-01 120 - 6.839144 + 4.231305 2020-01-01 10 - 3.745913 + 4.562625 2020-02-01 20 - 4.395061 + 5.890086 2020-03-01 30 - 6.024376 + 3.438143 2020-04-01 40 - 6.345998 + 4.802732 2020-05-01 50 - 3.855593 + 4.888795 2020-06-01 60 - 3.339227 + 4.790555 2020-07-01 70 - 5.439351 + 4.667200 2020-08-01 80 - 5.569649 + 5.209155 2020-09-01 90 - 6.225637 + 5.379132 2020-10-01 100 - 5.086193 + 5.970429 2020-11-01 110 - 3.244917 + 4.291284 2020-12-01 120 - 4.087981 + 5.559605 @@ -766,7 +766,7 @@

resample()
-
<pandas.core.resample.DatetimeIndexResampler object at 0x107bf6b40>
+
<pandas.core.resample.DatetimeIndexResampler object at 0x10f1fe6f0>
 
@@ -807,42 +807,42 @@

resample() 2019-01-01 20.0 - 5.745064 + 5.787015 2019-04-01 50.0 - 5.859548 + 5.446669 2019-07-01 80.0 - 5.203775 + 4.783584 2019-10-01 110.0 - 5.682049 + 4.189921 2020-01-01 20.0 - 4.721784 + 4.630285 2020-04-01 50.0 - 4.513606 + 4.827361 2020-07-01 80.0 - 5.744879 + 5.085162 2020-10-01 110.0 - 4.139697 + 5.273773 @@ -883,12 +883,12 @@

resample() 2019-01-01 65.0 - 5.622609 + 5.051797 2020-01-01 65.0 - 4.779991 + 4.954145 @@ -973,12 +973,12 @@

resample() 2019-01-01 0.5547 - 0.154317 + 0.201180 2020-01-01 0.5547 - 0.237913 + 0.143355 @@ -1638,7 +1638,7 @@

変化率の計算 -
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
 
@@ -1653,7 +1653,7 @@

変化率の計算 -
<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+
<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
 
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html index af71e3cd..8cefe07a 100644 --- a/13a_Random_Variables.html +++ b/13a_Random_Variables.html @@ -659,53 +659,53 @@

.cov 0 - 9.226527 - 59.884129 + 9.986898 + 65.226378 1 - 8.447087 - 10.864864 + 10.950868 + 25.126103 2 - 9.089684 - 98.844441 + 8.616695 + 91.922990 3 - 9.307079 - 30.984169 + 9.438771 + 2.279898 4 - 10.704744 - 79.099151 + 10.677754 + 19.288365 5 - 9.598606 - 55.097851 + 10.055099 + 23.828399 6 - 9.372898 - 8.376976 + 9.469716 + 89.078437 7 - 8.954774 - 73.010548 + 9.359286 + 24.031391 8 - 10.789657 - 65.658884 + 9.010822 + 31.161343 9 - 9.109282 - 35.203200 + 11.323700 + 29.797652 @@ -746,13 +746,13 @@

.cov X - 0.551495 - 8.565577 + 0.766032 + -11.157834 Y - 8.565577 - 882.945539 + -11.157834 + 945.832728 @@ -795,11 +795,11 @@

.cov X 1.000000 - 0.388167 + -0.414524 Y - 0.388167 + -0.414524 1.000000 @@ -816,7 +816,7 @@

.cov

-
0.38816740703052205
+
-0.4145235186574958
 
@@ -1019,53 +1019,53 @@

.cov() 0 - 10.743490 + 8.268658 NaN 1 - 11.515666 - 10.743490 + 9.506594 + 8.268658 2 - 11.058309 - 11.515666 + 10.519143 + 9.506594 3 - 9.699965 - 11.058309 + 10.633746 + 10.519143 4 - 10.317081 - 9.699965 + 10.210946 + 10.633746 5 - 8.613991 - 10.317081 + 11.047005 + 10.210946 6 - 11.934332 - 8.613991 + 10.337397 + 11.047005 7 - 11.172057 - 11.934332 + 11.335130 + 10.337397 8 - 10.105710 - 11.172057 + 8.454739 + 11.335130 9 - 10.341831 - 10.105710 + 9.659399 + 8.454739 @@ -1114,13 +1114,13 @@

.cov() X - 0.921925 - -0.137977 + 1.050337 + 0.061156 X_lag - -0.137977 - 1.031133 + 0.061156 + 1.165773 @@ -1165,11 +1165,11 @@

.cov() X 1.000000 - -0.133756 + 0.064691 X_lag - -0.133756 + 0.064691 1.000000 @@ -1186,7 +1186,7 @@

.cov()

自己共分散がゼロであれば,ランダムに散らばっているはずであり,何らかのパターンも確認できないはずである。

@@ -1431,7 +1431,7 @@

自己共分散 -_images/aff93ba8ca0807c48213648c4496a6c55c1d706e9fe6d07921bf0482ecf893e5.png +_images/453bb7eed15269c9257b75f79075b5b88bcfc066048d832130b361ea97908c0a.png

\(\rho\)の値が高くなると、定常状態の\(0\)に戻ろうとする作用が弱くなり、持続性が強くなることがわかる。

@@ -1689,7 +1689,7 @@

3つの例:持続性の違い -_images/c0da3bcfc3afe5f377a47ab5473dcc1c06c58d78e8a7abbadd1e67ed6a0bb56e.png +_images/8833571bac3c8e59ccaec2675ce0138e9d25e50b98d1c30183f318f8a5952f86.png

\(\rho\)が非常に高いため、持続性も非常に強くなっている。即ち、今期の値は前期の値に対する依存度が大きい。

diff --git a/13b_Stochastic_Solow.html b/13b_Stochastic_Solow.html index 6990f05b..595b372d 100644 --- a/13b_Stochastic_Solow.html +++ b/13b_Stochastic_Solow.html @@ -1094,10 +1094,10 @@

TFP#

-
TFPの自己相関係数:0.663
+
TFPの自己相関係数:0.535
 
-_images/1fd4ed086eb2f122776e7a077c7819532cf5a329146c16276f3c9bf0b578c6af.png +_images/3b51f61252c671e49b945e439507a9d774651eda2a840bd78341e105b7ff4a50.png

シミュレーションを行う度に図と自己相関係数は異なることになる。

@@ -1612,95 +1612,95 @@

実行#< 8.500577e+05 1.000000 0.366461 - 272210.617761 - 213095.442439 + 2.722106e+05 + 2.130954e+05 59115.175322 - 13.704888 - -5.182883 - 0.083737 - -8.373726 - 12.616727 - -10.239564 - 12.371891 - -10.239564 - 11.089639 - -10.239564 + 13.780344 + -12.728463 + 0.073138 + -7.313825 + 12.633292 + -11.896071 + 12.388456 + -11.896071 + 11.106204 + -11.896071 1 8.879214e+05 - 0.956201 + 0.521533 0.367346 - 265042.428091 - 207483.947333 - 57558.480757 - 13.760500 - -6.386177 - 0.086970 - -13.175700 - 12.642392 - -15.474724 - 12.397556 - -15.474724 - 11.115304 - -15.474724 + 1.445601e+05 + 1.131664e+05 + 31393.688704 + 13.836467 + -13.982835 + 0.080885 + -73.186687 + 12.663656 + -78.220508 + 12.418820 + -78.220508 + 11.136567 + -78.220508 2 - 9.232819e+05 - 3.177727 + 8.971171e+05 + 7.485312 0.368233 - 895439.064586 - 700979.209461 - 194459.855125 - 13.816080 - -8.039004 - 0.090150 - 106.601600 - 12.667994 - 103.707559 - 12.423158 - 103.707559 - 11.140905 - 103.707559 + 2.087540e+06 + 1.634195e+06 + 453344.817356 + 13.892510 + -18.556844 + 0.088586 + 192.435649 + 12.693945 + 185.755185 + 12.449109 + 185.755185 + 11.166856 + 185.755185 3 - 1.094660e+06 - 3.142032 + 1.328034e+06 + 1.544094 0.369123 - 943621.976175 - 738698.380549 - 204923.595627 - 13.871555 - 3.439931 - 0.093143 - 105.172659 - 12.693371 - 106.411034 - 12.448535 - 106.411034 - 11.166282 - 106.411034 + 4.971370e+05 + 3.891752e+05 + 107961.777870 + 13.948307 + 15.090339 + 0.095738 + 33.869922 + 12.723597 + 39.302444 + 12.478761 + 39.302444 + 11.196508 + 39.302444 4 - 1.272217e+06 - 1.718926 + 1.402795e+06 + 0.725768 0.370015 - 546252.979147 - 427624.834154 - 118628.144993 - 13.926802 - 12.946903 - 0.096481 - 44.521859 - 12.719010 - 49.182744 - 12.474174 - 49.182744 - 11.191922 - 49.182744 + 2.388969e+05 + 1.870163e+05 + 51880.526247 + 14.003574 + 15.040307 + 0.103041 + -42.356623 + 12.753208 + -36.942112 + 12.508372 + -36.942112 + 11.226120 + -36.942112 @@ -1716,7 +1716,7 @@

実行#<

-_images/5183e8799a5de10cda15034d5cf4e82e65496fd8802afb62551b965d37350703.png +_images/8f29efe00569168d5ff4b9ee085600284c6a8ff50c54389e42d3487aaa3e97ee.png

トレンドの傾きは成長率を表しているが,徐々に減少していることが分かる。最初は成長率に対する資本蓄積の効果が大きいが,定常状態に近づくにつれて資本蓄積の効果が減少しているためである。

@@ -1730,7 +1730,7 @@

実行#<
-_images/0ccc371866a21987df211f7faf033bb79a7b2556d8c6b948fd2d88907d119694.png +_images/cefc63931e1da6d11040316320687a0b53770cd6f38a3c1400c9d3b082e19ea1.png

絶対値で概ね2%内に収まった変動となっている。データでは,リーマンショック時はマイナス約4%程乖離したが,それ以外は絶対値で2%以内に収まっており,シミュレーションは概ねデータと同じような特徴を持っていると言える。

@@ -1754,11 +1754,11 @@

結果1:自己相関
--- シミュレーション:変動の自己相関係数 ---
 
-Yの変動: 0.395
-Cの変動: 0.395
-Iの変動: 0.395
-Kの変動: 0.828
-Aの変動: 0.394
+Yの変動: 0.538
+Cの変動: 0.538
+Iの変動: 0.538
+Kの変動: 0.901
+Aの変動: 0.532
 
@@ -1842,8 +1842,8 @@

結果2:GDPとの相関\(h\)の推定値 Model: OLS Adj. R-squared: 0.688 Method: Least Squares F-statistic: 384.1 Date: Fri, 03 Jan 2025 Prob (F-statistic): 8.56e-46 -Time: 01:09:49 Log-Likelihood: 716.66 +Time: 01:30:09 Log-Likelihood: 716.66 No. Observations: 175 AIC: -1429. Df Residuals: 173 BIC: -1423. Df Model: 1 @@ -1348,7 +1348,7 @@

最初のスイッチ:\(c\)残差の自己相関の検定 -
  • \(H_0\):残差は独立分布(無相関)

  • -
  • \(H_A\)\(\rho_{p}\ne0\)

  • +
  • \(H_0\):残差は独立分布

  • +
  • \(H_A\):残差は独立分布ではない

  • -_images/ebe1fd1db8278d9e821af856199b42a43efdd45dcd11760a2c34e82a46f786f9.png +_images/39be1bdfba89c425b86879c9b6e705c8bb67a06dc34a3f452aaddee5cbc46572.png

    \(u_t\)\(v_t\)が毎期毎期変動しており,その結果として\(p_t\)\(y_t\)が変動していることになる。 @@ -1095,7 +1095,7 @@

    プロット
    -_images/dd26fadedfae37bc7bcd5a2125e359335ed540ee903236ac61e7105d39c4777c.png +_images/afcc1f5acbca950514c0269f037922967c113f84e5f41192e82b8f3b80fa07d5.png

    このプロットから次の点を確認できる。

    @@ -1149,8 +1149,8 @@

    GDPと価格水準の乖離率の標準偏差 -
    -
    -0.10826051696903893
    +
    -0.11107441089736105
     
    @@ -1278,11 +1278,11 @@

    結果のまとめと拡張-0.15298

    WNショック

    -

    0.01375

    -

    0.01415

    -

    0.04270

    -

    0.81852

    -

    -0.10826

    +

    0.01379

    +

    0.01421

    +

    0.04869

    +

    0.82093

    +

    -0.11107

    AR(1)ショック

    0.01252

    @@ -1471,8 +1471,8 @@

    \(p_t\)に対する影響

    需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために,式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。

    -
    -(145)#\[\begin{align} +
    +(145)#\[\begin{align} 1&= \frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})} +\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})} @@ -1580,8 +1580,8 @@

    \(y_t\)に対する影響
  • \(p_t\)の総変動の大きさ(水準)を決定する上で,\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合,一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち,定常状態から離れた状態が長くなる。そのような状況下で,更にショックが発生すると,定常状態から更に乖離する結果につながることになり,変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。

  • 需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために,式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。

    -
    -(151)#\[\begin{align} +
    +(151)#\[\begin{align} 1 &=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})} +\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\ @@ -1814,8 +1814,8 @@

    付録#<

    付録B:式(150)の導出#

    (144)と式(149)を式(147)に代入し整理する。

    -
    -(152)#\[\begin{align} +
    +(152)#\[\begin{align} \text{Var}(y_{t}) &=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\ &=(ch)^2\left[ @@ -1839,8 +1839,8 @@

    付録#< +\frac{(ch)^2}{1-h^2}\text{Var}(v_{t}) \end{align}\]

    ここで

    -
    -(153)#\[\begin{align} +
    +(153)#\[\begin{align} 1+(ach)^2-h^2 &=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\ &=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\ @@ -1852,8 +1852,8 @@

    付録#<

    付録C:式(u-y)と(v-y)の導出#

    式(u-y)に式(150)を代入して整理する。

    -
    -(154)#\[\begin{align} +
    +(154)#\[\begin{align} \left[ \begin{split} &y_t\text{の変動に対する}\\ @@ -1880,8 +1880,8 @@

    付録#< \tag{u-y} \end{align}\]

    同様に式(v-y)に式(150)を代入して整理する。

    -
    -(155)#\[\begin{align} +
    +(155)#\[\begin{align} \left[ \begin{split} &p_t\text{の変動に対する}\\ diff --git a/6_Regression.html b/6_Regression.html index bf5f3ada..9b05fb5c 100644 --- a/6_Regression.html +++ b/6_Regression.html @@ -611,7 +611,7 @@

    回帰分析# Model: OLS Adj. 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