18_ADAS-1.ipynb

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   "source": [
    "(chap:18-adas-1)=\n",
    "# 定量的マクロ経済分析：Part 1"
   ]
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    "<div name=\"html-admonition\" style=\"font-size: 0.8em\">\n",
    "<input type=\"button\" onclick=\"location.href='https://translate.google.com/translate?hl=&sl=ja&tl=en&u='+window.location;\" value=\"Google translation\" style=\"color:#ffffff;background-color:#008080; height:25px\" onmouseover=\"this.style.background='#99ccff'\" onmouseout=\"this.style.background='#008080'\"/> in English or the language of your choice.\n",
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   "source": [
    "import japanize_matplotlib\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import py4macro\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# numpy v1の表示を使用\n",
    "np.set_printoptions(legacy='1.21')\n",
    "# 警告メッセージを非表示\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
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   "source": [
    "## はじめに"
   ]
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   "source": [
    "本章と次章の目的は，回帰分析，差分方程式，ランダム変数を駆使し，定量（数量）的マクロ経済分析をおこなうことである。使うモデルは，中級レベルのマクロ経済学ではお馴染みの総需要・総供給モデル（ADASモデル）である。より具体的には，次の２ステップに分けて定量分析をおこなう。\n",
    "1. 景気循環に関するデータに基づきADASモデルのパラメーターの値を設定するカリブレーションと呼ばれる作業をおこなう。\n",
    "1. ADASモデルの数量的な特徴を確認し，次の問いを検討する。\n",
    "\n",
    "    > GDPと価格水準の長期トレンドからの乖離（％）の変動は，何パーセントが需要ショックにより引き起こされ，何パーセントが供給ショックに起因するのか？\n",
    "\n",
    "本章では１について解説をおこない，次章で２について議論を展開する。\n",
    "\n",
    "通常の教科書でのADASモデルを使う分析では，パラメータの符号（正か負）のみを仮定し，比較静学に基づきモデルの定性的な特徴や予測を考察する。例えば，政府支出の増加を考えてみよう。利子率は上昇し，短期的にはGDPも増加することになるが，「GDPの増加」は定性的な結果（予測）である。このような分析は経済を理解する上で有用な方法であるが，例えば，「GDPがどれだけ増加するのか」について答えることはできない。GDPの増分がどの程になるのかは，定量的な問題（予測）であり，総需要曲線と総供給曲線の傾き等の値を設定してこそ答えることができる問いである。\n",
    "\n",
    "一方で，パラメータにランダムな値を使っても意味がある分析にはならない。そこで有用な手法がカリブレーションと呼ばれる分析方法である。詳細は以下で説明するが，簡単に言うと，カリブレーションではマクロ・データの特徴と整合的にパラメータの値を決定することになる。本章では，カリブレーションの考え方と中級＋レベルで使えるツールを利用した方法を解説する。一旦，パラメータの値が決まるとより興味深い定量分析が可能となるが，次章で扱うことにする。"
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   "source": [
    "```{note}\n",
    "ADASモデルの総需要曲線はISLMモデル（もしくは開放経済版であるマンデル＝フレミング・モデル）から導出できる。即ち，ADASモデルの裏ではISLMモデルが動いているため，ADAS-ISLMと表現することもできる。一方で，殆どの大学院のマクロ経済学の授業ではADAS-ISLMモデルは学ばないのではないだろうか。その大きな理由は，合理的期待に基づく消費者・企業の最適化行動が明示的に反映されていないことである。その反動かもしれないが，ADAS-ISLMモデルは「初学者用」と思われる傾向がある。しかし実際には，政策を検討する際にADAS-ISLMモデルは参考にされている。内閣府は「経済環境の変化や財政金融政策が経済に与える影響を定量的に評価するため」に[短期日本経済マクロ計量モデル](https://www.esri.cao.go.jp/jp/esri/prj/current_research/short_macro/index.html)を研究テーマとして挙げており，そこで展開されるのはADAS-ISLMモデルの開放経済版（マンデル＝フレミング・モデル）である。もちろん，変数や式の数は比べものにならない程大掛かりなモデルとなっているが，基本的にはADAS-ISLMモデルである。\n",
    "```"
   ]
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   "source": [
    "```{hint}\n",
    "論文[『経済マクロモデルについて ~その概要、歴史、シミュレーション等~』](https://www.sangiin.go.jp/japanese/annai/chousa/keizai_prism/backnumber/r03pdf/202120003.pdf)は，マクロ経済学において影響力があるモデルの歴史的な発展と現状について端的にわかり易く解説している。論文が掲載された[「経済のプリズム」](https://www.sangiin.go.jp/japanese/annai/chousa/keizai_prism/backnumber/index.html)という雑誌は参議院事務局が編集・発行しており，政治家を主な読者としているためか，難しい数式は一切ない。興味がある人は是非読んでみよう。\n",
    "```"
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   "source": [
    "## ADASモデル"
   ]
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   "source": [
    "ここでは総需要・総供給モデル（ADASモデル，Aggregate Demand and Aggregate Supply Model）の記号を整理し，景気循環データと整合性が保たれるように内生変数を解釈し直すことにより，定量分析の準備をおこなう。"
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   "source": [
    "### モデルの構造"
   ]
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   "source": [
    "#### 短期総供給曲線（AS曲線）"
   ]
  },
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   "source": [
    "$$\n",
    "P_t=P_{t}^e+a(Y_t-Y_{*})+v_t,\\qquad a>0\n",
    "$$(eq:18-as)"
   ]
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   "source": [
    "* $Y_t=$ 産出量の対数\n",
    "* $Y_{*}=$ 自然産出量の対数\n",
    "    * 長期的なトレンドに対応する。\n",
    "* $P_t=$ 物価水準の対数\n",
    "* $P_t^e=$ $P_t$に対する予測値\n",
    "* $v_t=$ **一過性の**供給ショック"
   ]
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   "source": [
    "式[](eq:18-as)自体はAS曲線の典型的な式となっている。一方で，定量分析のために次の点に関して解釈し直している。\n",
    "* 対数の役割：\n",
    "    * 内生変数である$Y_t$と$P_t$及び定数の$Y_{*}$は産出量と物価水準の対数としている。対数として解釈することにより，ADASモデルを使ってデータを捉えやすくする利点がある。また，より複雑な非線形のADASモデルを均衡周辺でテイラー近似した結果と解釈しても良いだろう。テイラー近似の手法は，研究で広く用いられる方法である。\n",
    "* 供給ショックの種類：\n",
    "    * 一過性の総供給ショック$v_t$は長期的なトレンドから**一時的な**乖離を引き起こす要因となるものである。後に導入する物価水準の長期的トレンド$P_{*}$には影響を及ぼさないと仮定する。もちろん，供給ショックとなるため$Y_{*}$にも影響しない。"
   ]
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   "source": [
    "#### 短期総需要曲線（AD曲線）"
   ]
  },
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   "source": [
    "$$\n",
    "Y_t=b-c P_t + u_t, \\qquad b,c>0\n",
    "$$(eq:18-ad)\n",
    "\n",
    "* $u_t=$ **一過性の**需要ショック"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "AD曲線はIS-LMモデルから導出することができるが，その場合，政府支出やマネーストックなど様々な変数に依存した複雑な式となる。式[](eq:18-ad)は対数線形の簡単な式となっているが，その裏にあるのが次の考え方である。\n",
    "* 政府支出や租税，マネーストック，更には，消費や投資水準は$b$及び$u_t$に含まれていると考える。また，それらの変化は全て需要ショックである$u_t$が捉えていると仮定する。\n",
    "* 需要ショックには次の２つがあると仮定する。\n",
    "    * 需要ショック$u_t$は自然産出量水準$Y_t^{*}$には影響は与えないと仮定を置くとともに，ショック自体も永続的に維持されるのではなく，時間とともにフェードアウトする**一過性の**ショックと仮定する。\n",
    "\n",
    "このように簡略化することにより，景気循環データをADASモデルの枠組みの中で扱いやすくなる利点がある。"
   ]
  },
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   "source": [
    "#### 適応的期待"
   ]
  },
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   "source": [
    "$$\n",
    "P_t^e= P_{t-1}\n",
    "$$(eq:18-pe)\n",
    "\n",
    "適応的期待は「後ろ向き」の期待形成を仮定することになり，批判の的にもなり易い。しかし，最前線の研究でも取り上げられ，データの特徴を捉えた仮定と言えるだろう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 総需要・総供給ショック"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "既に触れたが，一過性のショック項$u_t$と$v_t$は次の2点を満たすと仮定する。\n",
    "* 物価水準トレンド$P_{*}$と自然産出量$Y_{*}$に影響を及ぼさない。\n",
    "* 短期的・一時的なショックであり，永続的に正または負の一定の値を取り続けない。\n",
    "\n",
    "一方で，確率的シミュレーションを行う際は，毎期毎期において一過性の総需要ショックと総供給ショックが発生する状況を考える。その場合，次のホワイト・ノイズの仮定を採用することになる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "u_t&\\sim\\text{N}(0,\\sigma_u^2)\\\\\n",
    "v_t&\\sim\\text{N}(0,\\sigma_v^2)\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
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   "source": [
    "```{note}\n",
    "マクロ計量経済学の分野にベクトル自己回帰モデル（VAR, Vector Autoregression）と呼ばれる手法がある。その文献における「構造ショック」と$u_t$及び$v_t$がどう異なるかを考えてみよう。\n",
    "\n",
    "VARモデルには構造型VARモデルと誘導型VARモデルの２つがあるが，ここで考えるのは前者である。その考え方を簡単に説明するために，例としてGDPと失業率の２変数のVARモデルを考えてみよう。構造型VARでは，$t$期のGDPは（i）$t$期の失業率，（ii）２変数の過去の値，（iii）$t$期のGDPショックの３つに依存すると考える。同様に，$t$期の失業率は同期のGDP，２変数の過去の値，そして失業率ショックに依存する。ここで重要になるのが次の点である。（ii）で使用する変数が十分に過去を遡った値（例えば，四半期データで$t-1$期から$t-3$期もしくは更に遡った値）であれば，（iii）のショックが次の３つの特徴を満たすということである。\n",
    "1. 均一分散\n",
    "1. 自己相関はない\n",
    "1. GDPショックと失業率ショックは無相関\n",
    "\n",
    "このようなショックを「構造ショック」と呼ぶ。なぜそう呼ばれるかを直感的に考えてみよう。経済メカニズムにより発生する変数の動きは，時間的なラグが存在したり（例えば，雇用の調整にはコストが掛かるが，それが非常に高い失業率の持続性の一つの要因と考えられる），他の変数の過去の値から影響を受けたりする（例えば，失業している間に労働者のスキルは失われ，それが将来のGDPに負の影響を及ぼす可能性がある）。このような経済メカニズムに起因する効果を捉えたのが（ii）の過去の変数である。２変数の時間的なラグが十分に長くなれば，殆どの経済メカニズムの効果は捉えることができるため，残っているのは（iii）にある経済メカニズムと無関係な純粋にランダムはショックということになる。それを「構造ショック」としてGDPショック，失業率ショックと呼んでいる。\n",
    "\n",
    "ADASモデルの$u_t$と$v_t$はどうかというと，ADASモデルには十分な変数のラグが無いため上の「構造ショック」の３つの特徴を必ずしも満たすとは言えない。むしろ，$u_t$には$p_t$で捉えられていない政府，中央銀行，企業や消費者の$y_t$（$Y_t$のトレンドからの乖離）に対する影響を全て反映しており，ここではそれを総需要ショックと呼んでいる。同様に，$v_t$は適応的期待と$y_t$で捉えられていない，企業などの$p_t$（$P_t$のトレンドからの乖離）に対する影響を総需要ショックと呼んでいる。即ち，$u_t$と$v_t$には経済メカニズムにより発生するショックを含んでいると考えることができる。従って，$u_t$と$v_t$は，VARモデルでいう構造ショックとは異なることになる。\n",
    "```"
   ]
  },
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   "source": [
    "#### 長期均衡とトレンドの決定"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "長期均衡または定常状態（steady state）では次の条件が満たされることになる。\n",
    "* $u_{t}=v_t=0$\n",
    "* $P_t=P_{t-1}=P_{*}$\n",
    "* $Y_t=Y_{*}$\n",
    "\n",
    "この場合AD曲線[](eq:18-ad)は次の様になる。\n",
    "\n",
    "$$\n",
    "Y_{*}=b-c P_{*}\n",
    "$$(eq:18-lrad)\n",
    "\n",
    "この式は自然産出量と物価水準の長期的な関係を表している。\n",
    "もちろん，トレンドのデータはある程度の変動を示しながら持続的に増加しており，式[](eq:18-lrad)は満たされない。\n",
    "ここでは，数式を簡単にしつつデータと整合性がある様にするための単なる仮定であり，これにより以下で説明する式[](eq:18-as_small)と式[](eq:18-ad_small)を簡単に導出することが可能となる。\n",
    "\n",
    "一方で，自然産出量$Y_{t*}$と物価水準のトレンド$P_{t*}$が増加する改良バージョンを付録Ａで展開している。\n",
    "こちらの方がよりデータと整合的ではあるが，結局は，式[](eq:18-as_small)と式[](eq:18-ad_small)が導出されることになる。\n",
    "わざわざモデルを複雑にしなくても同じ均衡式が導出できるのであれば，簡単なバージョンで十分である。Simplicity is the best approach!"
   ]
  },
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    "jp-MarkdownHeadingCollapsed": true
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   "source": [
    "#### 図示"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ADASモデルを図示すると{numref}`fig:18-adas0`のようになる。長期均衡においてAD曲線とAS曲線は$P_*$と$Y_*$で交差することになる。短期均衡を考えるために，供給ショック$v_t$が`1`期間だけ正の値を取り，その後は`0`になるとしよう。ショックが発生するとAS曲線は上方シフトし，産出量は減少し物価水準は上昇する。適応的期待により，ショックがなくなってもAS曲線は直ぐには長期均衡に戻らず，徐々に下方シフトすることになり，最終的には長期均衡に経済は戻ることになる。\n",
    "\n",
    "このような分析は，教科書で解説される典型的な例である。長期均衡は安定的であり，産出量と物価水準は少しずつ動くという結果は直観的であり分かり易い。しかし，このような定性的な分析からは，ショック発生後に経済はどれだけの時間をかけて長期均衡に戻るかについては何もわからない。また，長期均衡に戻るスピードが何に依存しているのかも分からない。AD曲線とAS曲線の傾きが影響を及ぼしそうだと想像できるが，傾きが急だと戻るスピードが早いのだろうか，遅いのだろうか。このような問は，定量分析をおこなうことにより簡単に確認することが可能となる。"
   ]
  },
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   "source": [
    "```{figure} /images/adas0.jpg\n",
    "---\n",
    "scale: 10%\n",
    "name: fig:18-adas0\n",
    "---\n",
    "産出量と物価水準で表したADASモデル\n",
    "```"
   ]
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   "source": [
    "### 均衡式"
   ]
  },
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   "source": [
    "ADASモデルとデータの親和正を高めるために次の変数を定義しよう。\n",
    "* $p_t=P_t-P_{*}$：価格水準のトレンドからの乖離率\n",
    "* $y_t=Y_t-Y_{*}$：産出量のトレンドからの乖離率\n",
    "\n",
    "$p_t$と$y_t$を使ってAS曲線とAD曲線を書き換えることにする。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### AS曲線"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "式[](eq:18-as)に式[](eq:18-pe)を使い次の１行目となる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "P_{t}&=P_{t-1}+a(Y_{t}-Y_{*})+v_t \\\\\n",
    "&\\Downarrow\\quad\\text{両辺から$P_{*}$を引く}\\\\\n",
    "P_{t}-P_{*}&=(P_{t-1}-P_{*})+a(Y_{t}-Y_{*})+v_t\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\\Downarrow\\quad\\text{上の定義を使う}\\\\\n",
    "\\\\\n",
    "p_t &= p_{t-1}+ay_t +v_t\n",
    "\\end{aligned}\n",
    "$$ (eq:18-as_small)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この式はAS曲線を産出量と物価水準のトレンドからの乖離率で表している。また，この式から供給ショック$v_t$について次のことが言える。\n",
    "\n",
    "* 直接効果：$p_{t-1}$と$y_t$を所与とすると，$v_t$の１単位上昇は物価水準のトレンドからの乖離を１％発生させる。\n",
    "* 間接効果：$p_{t}$と$y_t$は均衡で決定されるため，$v_t$が変化すると$y_t$も変化し，その効果を通して$p_{t}$が変化する。\n",
    "\n",
    "直接効果と間接効果の相互作用により供給ショック$v_t$は$p_t$に影響を及ぼすことになる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### AD曲線"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "式[](eq:18-ad)の両辺から式[](eq:18-lrad)を引くと次の１行目となる。\n",
    "\n",
    "$$\n",
    "Y_t-Y_{*}=(b-b)-c(P_t-P_{*})+ u_t\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\\Downarrow\\quad\\text{上の定義を使う}\\\\\n",
    "\\\\\n",
    "y_t &= -cp_{t} +v_t\n",
    "\\end{aligned}\n",
    "$$ (eq:18-ad_small)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この式はAS曲線を産出量と物価水準のトレンドからの乖離率で表している。また，この式から供給ショック$v_t$について次のことが言える。\n",
    "\n",
    "この式はAD曲線を産出量と物価水準のトレンドからの乖離率で表している。また，この式から需要ショック$u_t$について次のことが言える。\n",
    "* 直接効果：$p_{t}$を所与とすると，$u_t$の１単位上昇は産出量のトレンドからの乖離を１％発生させる。\n",
    "* 間接効果：$p_{t}$と$y_t$は均衡で決定されるため，$u_t$が変化すると$p_t$も変化し，その効果を通して$y_{t}$が変化する。\n",
    "\n",
    "直接効果と間接効果の相互作用により供給ショック$u_t$は$y_t$に影響を及ぼすことになる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### 長期均衡"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "長期均衡または定常状態（steady state）では次の条件が満たされることになる。\n",
    "* $u_{t}=v_t=0$：ショックはない\n",
    "* $p_* =0$：トレンドからの乖離率はゼロ\n",
    "* $y_* =0$：トレンドからの乖離率はゼロ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### 図示"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ADASモデルを乖離率の変数$p_t$と$y_t$で表した図が{numref}`fig:18-adas1`である。原点が長期均衡となる。{numref}`fig:18-adas0`と同じように，総供給ショック$v_t$が１期間だけ正の値を取り，その後は`0`になる場合を考えてみよう。ショックが発生するとAS曲線は上方シフトし，産出量の乖離率は負の値となるが，物価水準の乖離率は正の値を取ることになる。ショックが`0`に戻った後，AS曲線は徐々に下方シフトし，最終的には長期均衡（原点）に経済は戻ることになる。以下の分析では，乖離率の変数である$p_t$と$y_t$を使うが，{numref}`fig:18-adas1`を念頭に置き結果を解釈するとわかり易いだろう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{figure} /images/adas1.jpg\n",
    "---\n",
    "scale: 10%\n",
    "name: fig:18-adas1\n",
    "---\n",
    "産出量と物価水準のトレンドからの乖離率で表したADASモデル\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## 景気循環のデータ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### トレンドからの乖離率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ここでは式[](eq:18-as_small)と式[](eq:18-ad_small)を使い定量分析をおこなうが，まず，それらの式と整合性があるデータの特徴を考える。$y_t$と$p_t$はトレンドからの乖離率となるため，`py4macro`の`trend()`関数を使い，対応する変数を作成することにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "df = py4macro.data('jpn-q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['gdp', 'consumption', 'investment', 'government', 'exports', 'imports',\n",
       "       'capital', 'employed', 'unemployed', 'unemployment_rate', 'hours',\n",
       "       'total_hours', 'inflation', 'price', 'deflator'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "$Y_t$には`gdp`を使い，$P_t$には`deflator`を使うことにする。\n",
    "\n",
    "次のコードで作成する`gdp_cycle`と`deflator_cycle`は，`0`を中心に上下する系列となる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gdp</th>\n",
       "      <th>consumption</th>\n",
       "      <th>investment</th>\n",
       "      <th>government</th>\n",
       "      <th>exports</th>\n",
       "      <th>imports</th>\n",
       "      <th>capital</th>\n",
       "      <th>employed</th>\n",
       "      <th>unemployed</th>\n",
       "      <th>unemployment_rate</th>\n",
       "      <th>hours</th>\n",
       "      <th>total_hours</th>\n",
       "      <th>inflation</th>\n",
       "      <th>price</th>\n",
       "      <th>deflator</th>\n",
       "      <th>gdp_cycle</th>\n",
       "      <th>deflator_cycle</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1980-01-01</th>\n",
       "      <td>269747.5</td>\n",
       "      <td>153290.7</td>\n",
       "      <td>65029.2</td>\n",
       "      <td>73039.5</td>\n",
       "      <td>18383.8</td>\n",
       "      <td>24278.8</td>\n",
       "      <td>833041.425949</td>\n",
       "      <td>5506.000000</td>\n",
       "      <td>107.666667</td>\n",
       "      <td>1.900000</td>\n",
       "      <td>124.7</td>\n",
       "      <td>686598.200000</td>\n",
       "      <td>5.766667</td>\n",
       "      <td>71.011939</td>\n",
       "      <td>91.2</td>\n",
       "      <td>0.003269</td>\n",
       "      <td>-0.025798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-04-01</th>\n",
       "      <td>268521.8</td>\n",
       "      <td>153551.9</td>\n",
       "      <td>65316.6</td>\n",
       "      <td>72164.5</td>\n",
       "      <td>18631.4</td>\n",
       "      <td>25454.5</td>\n",
       "      <td>843748.581006</td>\n",
       "      <td>5525.666667</td>\n",
       "      <td>110.000000</td>\n",
       "      <td>1.966667</td>\n",
       "      <td>124.8</td>\n",
       "      <td>689603.200000</td>\n",
       "      <td>8.166667</td>\n",
       "      <td>72.917251</td>\n",
       "      <td>93.4</td>\n",
       "      <td>-0.010845</td>\n",
       "      <td>-0.006555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-07-01</th>\n",
       "      <td>274183.1</td>\n",
       "      <td>155580.0</td>\n",
       "      <td>65765.9</td>\n",
       "      <td>72663.8</td>\n",
       "      <td>18449.3</td>\n",
       "      <td>23885.7</td>\n",
       "      <td>855449.381902</td>\n",
       "      <td>5561.333333</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>2.033333</td>\n",
       "      <td>124.0</td>\n",
       "      <td>689605.333333</td>\n",
       "      <td>8.200000</td>\n",
       "      <td>73.897654</td>\n",
       "      <td>94.4</td>\n",
       "      <td>0.000457</td>\n",
       "      <td>-0.000482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-10-01</th>\n",
       "      <td>279601.8</td>\n",
       "      <td>156162.4</td>\n",
       "      <td>66017.5</td>\n",
       "      <td>74761.1</td>\n",
       "      <td>19705.4</td>\n",
       "      <td>23716.5</td>\n",
       "      <td>867991.306098</td>\n",
       "      <td>5551.333333</td>\n",
       "      <td>123.333333</td>\n",
       "      <td>2.166667</td>\n",
       "      <td>124.0</td>\n",
       "      <td>688365.333333</td>\n",
       "      <td>8.100000</td>\n",
       "      <td>74.767147</td>\n",
       "      <td>95.4</td>\n",
       "      <td>0.010468</td>\n",
       "      <td>0.005515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1981-01-01</th>\n",
       "      <td>281995.7</td>\n",
       "      <td>156757.7</td>\n",
       "      <td>66259.0</td>\n",
       "      <td>76127.6</td>\n",
       "      <td>20289.5</td>\n",
       "      <td>24174.1</td>\n",
       "      <td>878387.487376</td>\n",
       "      <td>5568.666667</td>\n",
       "      <td>124.333333</td>\n",
       "      <td>2.200000</td>\n",
       "      <td>123.6</td>\n",
       "      <td>688287.200000</td>\n",
       "      <td>6.833333</td>\n",
       "      <td>75.690241</td>\n",
       "      <td>95.6</td>\n",
       "      <td>0.009441</td>\n",
       "      <td>0.003126</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 gdp  consumption  investment  government  exports  imports  \\\n",
       "                                                                              \n",
       "1980-01-01  269747.5     153290.7     65029.2     73039.5  18383.8  24278.8   \n",
       "1980-04-01  268521.8     153551.9     65316.6     72164.5  18631.4  25454.5   \n",
       "1980-07-01  274183.1     155580.0     65765.9     72663.8  18449.3  23885.7   \n",
       "1980-10-01  279601.8     156162.4     66017.5     74761.1  19705.4  23716.5   \n",
       "1981-01-01  281995.7     156757.7     66259.0     76127.6  20289.5  24174.1   \n",
       "\n",
       "                  capital     employed  unemployed  unemployment_rate  hours  \\\n",
       "                                                                               \n",
       "1980-01-01  833041.425949  5506.000000  107.666667           1.900000  124.7   \n",
       "1980-04-01  843748.581006  5525.666667  110.000000           1.966667  124.8   \n",
       "1980-07-01  855449.381902  5561.333333  116.000000           2.033333  124.0   \n",
       "1980-10-01  867991.306098  5551.333333  123.333333           2.166667  124.0   \n",
       "1981-01-01  878387.487376  5568.666667  124.333333           2.200000  123.6   \n",
       "\n",
       "              total_hours  inflation      price  deflator  gdp_cycle  \\\n",
       "                                                                       \n",
       "1980-01-01  686598.200000   5.766667  71.011939      91.2   0.003269   \n",
       "1980-04-01  689603.200000   8.166667  72.917251      93.4  -0.010845   \n",
       "1980-07-01  689605.333333   8.200000  73.897654      94.4   0.000457   \n",
       "1980-10-01  688365.333333   8.100000  74.767147      95.4   0.010468   \n",
       "1981-01-01  688287.200000   6.833333  75.690241      95.6   0.009441   \n",
       "\n",
       "            deflator_cycle  \n",
       "                            \n",
       "1980-01-01       -0.025798  \n",
       "1980-04-01       -0.006555  \n",
       "1980-07-01       -0.000482  \n",
       "1980-10-01        0.005515  \n",
       "1981-01-01        0.003126  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for c in ['gdp','deflator']:\n",
    "    \n",
    "    df[c+'_cycle'] = np.log(df[c]) - py4macro.trend( np.log(df[c]) )\n",
    "    \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`gdp_cycle`と`deflator_cycle`をプロットし，データのイメージを掴んでおこう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax_ = df.plot(y=['gdp_cycle','deflator_cycle'])\n",
    "ax_.axhline(0, color='red')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "以下では，`gdp_cycle`と`deflator_cycle`の３つの特徴に焦点を当て議論を進めることにする。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### データの特徴１"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GDPのトレンドからの乖離率の標準偏差：0.014833\n",
      "デフレータのトレンドからの乖離率の標準偏差：0.007490\n"
     ]
    }
   ],
   "source": [
    "y_std = df.loc[:,'gdp_cycle'].std()\n",
    "p_std = df.loc[:,'deflator_cycle'].std()\n",
    "print(f'GDPのトレンドからの乖離率の標準偏差：{y_std:.6f}')\n",
    "print(f'デフレータのトレンドからの乖離率の標準偏差：{p_std:.6f}')\n",
    "\n",
    "# 不偏分散の平方根"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "２つの数値を比べると，GDPの乖離率の標準偏差はデフレーターの約2倍あることが分かる。これは上のプロットで`gdp_cycle`の変動幅が大きいことを反映している。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "heading_collapsed": true,
    "hidden": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "### データの特徴２"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GDPのトレンドからの乖離率の自己相関係数：0.697\n",
      "デフレータのトレンドからの乖離率の自己相関係数：0.830\n"
     ]
    }
   ],
   "source": [
    "y_autocorr = df.loc[:,'gdp_cycle'].autocorr()\n",
    "p_autocorr = df.loc[:,'deflator_cycle'].autocorr()\n",
    "print(f'GDPのトレンドからの乖離率の自己相関係数：{y_autocorr:.3f}')\n",
    "print(f'デフレータのトレンドからの乖離率の自己相関係数：{p_autocorr:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "失業やインフレ率などのマクロの変数は、前期の値が高ければ（低ければ）今期も高い（低い）傾向にあるが、この特徴を持続性（persistence; 慣性とも訳される）と呼ぶ。自己相関係数は持続性をとらえており、上の数値はデフレータの方がより高い持続性があることを意味する。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "heading_collapsed": true,
    "hidden": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "### データの特徴３"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "editable": true,
    "hidden": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GDPとデフレータの乖離率の相関係数：-0.153\n"
     ]
    }
   ],
   "source": [
    "yp_corr = df.loc[:,['gdp_cycle', 'deflator_cycle']].corr().iloc[0,1]\n",
    "print(f'GDPとデフレータの乖離率の相関係数：{yp_corr:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/papermill.record/text/plain": "6"
     },
     "metadata": {
      "scrapbook": {
       "mime_prefix": "application/papermill.record/",
       "name": "t_shift"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/papermill.record/text/plain": "0.433"
     },
     "metadata": {
      "scrapbook": {
       "mime_prefix": "application/papermill.record/",
       "name": "yp_corr_shift"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from myst_nb import glue\n",
    "t_shift = 6\n",
    "tmp = df.copy()\n",
    "tmp['deflator_cycle_shift'] = tmp['deflator_cycle'].shift(-t_shift)\n",
    "ax_ = tmp[['gdp_cycle', 'deflator_cycle_shift']].plot()\n",
    "ax_.axhline(0, color='red')\n",
    "yp_corr_shift = tmp[['gdp_cycle', 'deflator_cycle_shift']].corr().iloc[0,1]\n",
    "\n",
    "glue(\"t_shift\", t_shift, display=False)\n",
    "glue(\"yp_corr_shift\", round(yp_corr_shift.item(),3), display=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "hidden": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "この値は同じ期の相関係数であり，絶対値は小さく弱い関係にある。しかし，直感的には`gdp_cycle`と`deflator_cycle`の正の相関をイメージするのではないだろうか。正のGDPの乖離率は景気が良いことを示しているため，物価水準であるデフレーターもトレンドから正の方向に乖離するのではないか，という考えである。そのような考え方は基本的には正しいと言えるだろう。ただ，データを見る限り時間のズレがあるようだ。プロットを見ると，正の方向にGDPの乖離率が発生した後にデフレーターの正の乖離が発生しているように見える。次のプロットは，$t$期の`gdp_cycle`と$t+${glue:}`t_shift`期の`deflator_cycle`を重ねて図示している。同じ方向に動いていることを示しているとともに，相関係数も約{glue:}`yp_corr_shift`となっており，正の相関を数値でも確認できる。一つの可能性として次の解釈が成り立つ。デフレーターの変化には時間がかかり，それは価格の粘着性の反映かもしれない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "editable": true,
    "hidden": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GDPと6期先のデフレータの乖離率の相関係数：0.433\n"
     ]
    },
    {
     "data": {
      "image/png": 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iBsrCNDPMei0SDFrMG5vl8xilAZ8FLRY77nprJz7cU4u1eyI3pQ1VvHvUcGRfDZV1xwSyn8ashyZQHxqXA/jgLmDLP4I+l1YjyGpPs4X+/rHE4fouj1YMh+s7g+6/s7INAOs2bdJrYeTpp4FSauRS7vlAiD7YylYlUOvL57Pf0k8E0Z/wD316gkE+2Seb9Hj9h6dBr9Ug2eRbKcLLuk80WfDn9UfkCd+9rXpikVrJKFyQ5hnU5HKlhiqgYgLuLUhPDJJ6OrQG2PoioDMBM24MasrMTDSgxWKnXjUxBldpOAfrOnHhlPyA+++uagMAnFKUBgADr9SckEzCIaaeAKCyRRlG3BclkZQaYlB5+tPDuOnl7+B0hffP5t14jzO9JB2TC/0P9StOT4BGYKMUXtlcLm+vGIZBTZ0fTw2gKDXUqyY24Omn9CDjD7BXmoHntAItx4I+H41KiE2+kHrNFEm9ig7VBa+A2lXJqodOKU4DgIFVarpbgJqd7PsR80J+GDcJA8wc74qwQpOCGmJQeemrE9h4qBGHepFTvWnx6lETCgadBsUZrFW3W2QVUgBwsmV4GYetDpd80fLx1KSQUhNL9FrObesEDn+s/FwXvDImk0YlxBxWhwvfHmelzrecNQIAcKgu8PnS6XJjTzULaqYVswXegCo15V8CEIHs8UBKYDXJG3X6yS0CHT2RqTUU1BCDht3pllNAVkd4K4imLs/Kp1DhvhpBAB66hM0cO9ncPfDtw/uRBin3btRp5MCNE2tdhZu6bNhXE3nPilin13Lug2uYQsPpLaihUQkxx5byFticbuSlmLBkKgsSTrZ0o8fu/5x5pKELPQ4Xkow6jMxiozUGVKlR+2nCQJ1+AhBx2wkKaohBo031oe0O8A8aiBaLZ+O9UJlUwCa7XzmjCBdMZBVSnVanLPMPB2pVM5+8m1XGWlfhW/61FUuf+Qon42gQqZoWqQokLVA3YZ56Si1mt/V7gz6frNSQUThm4GMO5o7JQnaSERmJBogicKTBv1qzSzIJTy1Klf2GxoFUaiINalo9bQCRdn6noIYYNNSReKBVh83pwttbKmWPiPxYr8Z7ofLj+aPw9DWn4OFLJ8Ok1yJX8pjE+vTuj/bW4voXv8XJZkvAyidAUWoau4Z+V+Eeuwt7qtogisBRaahjvBFUqeluAY6tZ9/P/xW77UWpySClZshidbiws7INh+s7Udveg/oOK442dGLjwQYAwNyx2RAEAeNykwEws7A/dnGTsOSnAVRKTZiKeNi0VQAtxwFBC5TOCflhTpdbPm8VSOetSHvVUPUTMWioP7Q9Af7Z1uypxYp3duPyGYX4w9XT5O08/eThqXG7gbW/BPQJwAUP+32+FJMel00vkn8uzUhEfYcNFS3dmF6S3offZnB5+etyfHuiBcve2in36ClI9R2AyAfFOVwiWrvtcpfZocjh+k7wuCtW0mXRhgf+fhvvHXgfcDuBvCnAxEuB1XcAXfVAVwOQlOP3+bJoVMKQ5c43d+DjffV+7xME4KzRrE3FuLxkbD7ejMMBgpqd3CQsVT4BKk+Ns5+VGj4aoXAmYEoJ+WG17Va43CIMOg3G5iWjpt0acVdhUmqIQUPdYClQ+qmu3Sbdeio1bf5O9vV7Wa+OTX8GOv2fHLwpyWTG4ZMxXgHFL/o7Ktrwjy+PA/Cv1PCuwurHDFXUM24ah/ix9he8tNXbGwVAST1NvgIwJgEZI9nPQdQaGpUwdNl2sg0AkGzSQacRoBGAVLMeRelm/PjsUbJ/cHweU2r8FVd0251yD5tpfpWa/g5qPmO3YaaeKqTKp6J0sypFSkoNEWOEkn7qlLr9enf97ehhBuNUs+pkz/+hAKBuN5B8fq/HUJoxPIIa9UWfXwi9K5842clGNFvsqO+wYkJ+6KupgUYtrzfEaQdkOf3k7R1zOYHyr9j3Ey5mt3lTWEl3/V5g9Ll+ny+DlJohSY/dJU9P/3LFAvm85m+A87i8wOmnfTUdcLlF5KYYPRY1ilLTj+knUYyoPw2glHMXpyfI0+jJU0PEHK0hpJ+6pOooHsRweJCTYlbF5fwfCmBj70OAKzUVMVzW3W13yu/TmaMy5e15ftJPgMosPMTVj/2k1AQu6bZ1AKK06k4rYbd5rJovmFLDR4p0Wp0DO7F5CNDe48Dznx+TjfQeDHL1Y5Vkkk026pBq1kMQBL8BDQCMkTw1jZ02H9+JYhJO89g+IEpNw37A0sjS/0Wzw3ooNwkXZ5jlRpMtEY5KoKCGGDQ8PDUBlRopqPFRatjPslLjtAMnNyk71O4O6RhKpRLvWFZqeAl3gkGLP14zTU5VjM5J8ru/XNY9hCugRFHEQVVQM9QDsP7A4VLmm/koNTbpvdGZAa30P5A3ld3WBa6ASjHpoZMqYvoyNDAWeXVzOR5fexAvfH5c2SiKwH9/AvxhAtBWOWjHxi/qRRkJAYMZTpJRh+IM3oTPU63h4xHUqSdggJQarpSXngnowqtK5eXcxekJsik+Uk8NpZ+IQaM1hJJuflLvtDohiiIEQYDD5ZYnF/O5T6jeCjhUgUntrpCOgaefGjpt6LG7YDZow/01Bh1+wc9JNiInxYT3bp+D6rYejJAGeHrDlZqdle34ZF8dtBoBc8dkw6AbOmuc2nYrOqyKOhePSg1vMyAIXmlWgDXdAzzNmLmSUtN0GHBYAb1v+lGjEZCRaEBDpw3NXXbkB1Dzhg2iCOx7F6jdjTN3bsdr+mYcqLsGwCR2/9d/Ana9zr7f8Sqw4NeDcpjKRT20v8e43BRUtvTgUF0HzpDUWavDJZd/z/AqehgQpYafc0vOCPuhilKTAG0fg+6hcxYj4o5Qqp+4p8blFuXAp1N1sZMnF3PX/ahz2G3bSaCnrddjSEvQy89R0RKbag2/4PPKprKsRMwZ7TvQk8PL2NcdqMePXt2GW/61Ffe/F7y/yUDDTcL8b9PYaRtWDRJDgftpUkx6+UQvY5WUGqMqqEkpAMwZgOgCGg8EfF6u5LVH2LE1FnC5RdZm/9Ba4D83A1//ETMsX2COdh9urXmABTPlXwHrH1QetPvtQUtDyZ4SaZHVG9wsvKW8Vd728b46tPc4UJBqwqkjMjz2N0kLln5VaiwsoEJy6F2EOWqlhhcyUPUTEXO0ehiFnX734V4RQElBdfQ4YIQdEwyN0GmljzCXPideCqRKHoNeenYAzIhXKldAxaavhptoc5L9G4O9uWBSHs4clYnJhSmYVpwGQQDe2lqJzw419OdhhgU3Qc4ZxYIzm9PtodzEA0ovJj9SPk8/GZOVbYIQkq/GrOeN2Ianp6bT6sCZj6/HDS99Cxz4HwDAXXwGHnJej9eckoH60weAVy9nvqRJlzEfSOsJoHr7oBwzVypKQgxqFk3OAwCs3Vsrn7fe3srSZ1fOKvYJgo3S37xflZqeFnabkBl8P++HqUzSnp4aCmqIGENd0h1YqVEFNT2Kv+Z3+n9greZOYPNzgK2LpZ8AYOTZQL7kLQg5BcXSNLGq1DR4KTW9kZtiwus/PB0f/Gwu3vvpHNx4ZhkA4N539/h4lwYLbhKeXpLmodbEE0HLuf2ln4CQfDUm6QIX6H+uL2yvaB30AbF7qztQ32HD5qONcEtzsU5OXYaXnIvxG+ct+EfijwAIgMsG5EwELnkOGL+EPXjP24NyzLJSkRFa+mlyYSrmj8uGWwT++tkxVDR34+ujzRAE4KqZRT77mwZiTEI3m08VblDjbZLmnppOqxP2CPrqUFBDDBrqSDyQp8avUtNtx7maHWzjx78GPr6XNSFLKwXSy4D8U9h9daGZhWO9Vw03CvMJ3OGyYuF4lGYmoLbdikc+2B/NQ4sYbhIen58iB2vxVtYdtJuwVZqHZfQKarivpn5fwOflvrFA5vxIaeiw4sq/bsKNL38X1ecNF94dfLpwBJqeZsCUiu0YJ9+/SncRcN1bwCnXAt97HTAkAFOuYnfufZeVyw8goih6lDSHyh0LRgMA3tlehT9vOAKANejzl8LiYxL6Vanp5kpNRvD9vFD7aQRBQIpZDy40tUWQgqKghhgUeuwuj5WivxOsKIqypwZQKp5c9QeQJvBUkQhsf4V9O/JsdpsXrlIjBTUxqtQ0StJtdoTdgc0GLVZeeQoEAXh7axW2V7T2/qB+xOpw4UQT+/tOyE9WRjvEuFLz6f56PPS//fLv1hu8j5PfCd02P54aAMgey26bDgd83v5KP9W0W+EWgeNNFjhcAzBjKADl0vt7nlZKJY25AIcalYDYYncCYxcClz0PZLCp1xh1DvMjWRo8W0MMAO09Dnmwb1EYQc2ssgycNiIDDpeI/2yrAgBcM7vY775cqek3T43TBtilUSbhBjVeKpVWI8if+UiGWlJQY2lilQLEgOJtAvMnhducbjhcinGPKzUJdVsAAAdNpwDjlyoPGCEFNVypaToM2HsPVOReNbHqqZFKs3NSQvPU+OPUERlYMI611t9X09HL3v0LH4+QmWhAdpIR2ZJXKNaDmoc/2I+Xvj6B8/7wOe5etavXNA2vfsrwN8wyUPopcwy7tTQoao4X5n5KP3WpUsVNg9ixmCs152mkoGbsIo9GdX4VKq2eeWsAYM+q/j5ED/hFPSvJGHb15R3njJa/T0/Q43xpSK83/a7UcJVG0ALG1LAeWiedv9SVeOlSyjUSX018BzWNh4A/TARW/xQA4q66YjDx/rD6O9F0ehlDuacmrYn5Z04mTQeu+Acw6lwgfQQw+jy2Y3IekJjNTIBBZHgO71VT1doD5yCuMCOlUVXS3Re40tMeYdVBtOCVTxPyUyAIwrBQapwuN6rb2MXL5WYr6wVPfYZ7/rNbTj14E7DxHuC/+glgQU4SM5Gi6ajf5zXJ6afofta7bIqqylOikVDZ0h1xN1kAKG/qRolQjzGaajhELZwjz/WYk2QJUJSAqVez2wP/Axx+GvT1E+rGc+Fy1ugseXDlpdML5eDFm35XamQ/TQagCS+s4J8VtSeQm+NbI2jAF99BzaE1zCx2bAN2VLRi5iPr8Md1gWVbInqEotSo/TSAkn7KadsJAKhPmw7ozcD/vQP8fAdgTmM7CoLKMNl7CiovxQSDVgOnW4y5FJTD5ZZb3vc1qEkdIqW+B2rZBYiXrSqemtgNauSBfVoN3r39TJw9Nhsut4i3tlZiwZOf4dZ/bcGf1h3B+gP1spnT73wzjr/qJ06WpNYESEH1l1KjXoRE+rdqsdhx7h8+x7V//yaix7vdIsqbLbJK8517PLbUuWU1AACsDrf/CfXFpwHJBSyNUhHZ60dCJH4ajiAI+OM10/CT+aOw7LyxAffrf6VGCmrM4aWeAHX1pnL+Sqf0U4RUfMtue1rw3b6jaLHY8cd1R/DC58cG97jigBavC7E/o3CndxdhqwNor0KqrRZOUYP2TCnNJAjsSw1PQYXQWVirETCzlDWrenXzyXB+jUGnWZpWrtMI/i9+YcAbvA12UHO0geXmx/KgJin2lZqqVrbyL0w3Y0ZJOv5186l45ydn4KzRWXC6Raw70ICn1x3GLf/ail+uYp9ZpaQ7jPQToAQ1zUf8Hkt/eWrUi5BITd3lzRbYnW4caejyH3j0Ql2HFTanG+drtwEA1rtn4K0tFQAg9z8BAgR0gqDMLBpAX01flBoAGJGViHsWjfdt0Kii35WaCMu5AZXSrEqfK0oNBTWhI4pA5bfyj0LTIfn7x9YexNtbBq9ldn/x7fFmPPLB/qhXPUQC/7AWSh00/So1/tJP0gpqv1gKc1KQ3C0v6678LqSGWj+VKgne+K5iSI8P8IZfPLKSjNB4N2gLE35S5F6OwYKf5LmBm1d1xXL1Ey9bLVJ1jJ1ZmoF/33oa/nfHWbh/6UQsmcqaln26vx5Wh0v+O4SVfgIUX01TgKCmn6qf1P+vkaafWqQg3eUWI2ovUN5kQTK6MVvDzufr3DOwZm8dAGBqUaq89gmYguLFBurhuP0M99SE2qMmEgZMqQnTJAx4dkTnZPShV038BjVNR5ToEoCpnakzI6XW8r96dzeWvbkD6w/UR1QrP6CIItByAjj8CdAVuIHaQx/sxz++OoGNQ6DJWot0wi5IYyd5u9PNOoCq8G621mF1yEHNVvc4pARZmaBsLqAzsc6qxzf2ejxzRmdiZmk6bE43/hpDSl1fy7nVDAWlxuUWUSN5T4qkk3z2MPDUcKXGX3XLlKJU3HLWCPzl2unITzWhx+HC5uPNcoo25OZ7nCxeAeU/qOmvPjWeSk2EQY0q3RDJJPHy5m6MFyqggwvWhAJUiLny+XtcXoqSegsU0PFig5qdivm1n5GVmgjST6FiVCk1/eIdjbCc2+50+6j2AAU1kVHpmTNNtZwAAKxYNA7XnloMtwi8t7MGt/xrK858fENAM9+g4nYD794GPF4C/Hka8PpVrCW4Hyw2p2zAHApKBFdqitKUlav3SdbHU6MKara4xwWVW5GYBcy8kX3/xVO9Ho8gCLjzXLbCff3b2FFr/K1yImUoBDX1HVY4XCJ0GgF5khzNOyW3djuG/gIjAEpQEzjFIAgCzhnPKtA+3V+Ptp5gzfekoMbkR63MkipiWo4Bbt+Ld795atRBTYT/P+qLWCQXtPJmC0ZqagEA2pxxHveNy0tCgoE1crTYAvzuKflA1jgAIhuj0M+43aL82Qh1REIkcKVGFOFRURo1uiNLP/EqOe/0eXofhlrGb1DDjWCJ7CSSbWN51+xkE3532RS885MzcdOcMqQl6NHUZRtSLeRlqrYAu99kJziNTtnm50S2q6oNXAiJZAUUbfiKLC/VJEvC3V6SMPfUJEhyudPSDtSzTqlb3WOVYZaBOPPngEYPnPzKc4J3AOaOycKMkjTYnG688MXxXvcfCnjPfeoLQyGo4Sf4gjSz3Oo9zaxMlh7MUuG+4C/95I9zJ7Dz0Ye7a+WsaZo5zPRTajFTKV12NgPNC7NBWrX3Y0l3pEpNax+DmhNNFowUagAA+txxHkNdx+WmyOeSHkeQBnvcVzMAKaiGThvsTje0GgH5qZG3ZOgN7qkB+slXE2E3YXU3dHX6nJSaSOBBzbRrAQDFLuahyUk2QhCYcfT/XTQJ159eCoC13h5yHFrDbidcDNxbzU5kTivQWu6z646KNvn7pq7BD2paVXNtZOOiV4kpP0kWSmpOSfdeACIqkYdGpCPF3MuQ+dRCYPr32fdfPNnrMQmCgDulCoJ/birHS1+dGPJl/txnkh3i3KdgDIVBh8pgP+Xir9EIMV8BFSz9pObMUVkw6TXy3yDZqPOdni6KilHYX/pJowUyRrHv/ZR195qCiZBoGIX7rNQ0WTBSYEoNMkdjulTurNUIGJmdKAc1gTqYAxhQszBPPeWnmpQ5dv2AQauRF4/94quJNKjp8K18AiDPfyKjcKh0NTJpFgCm/R8AoBCNMMLus+KdVMDk3T3V/htZDSqH1rLbiZcAepNS9dB40GfXHaousS2Wwb8wqIf1yScar9VTp80JAW5cYvgOf9T/Bb+x/QEAsMXNAo9elRoAmLOMNYQ6th7Y+Bjw8W+AD+4C2qv97j5vTBaumVUMl1vEQx/sx92rdg/pwX8RpZ8szcDbNwBH13ls5kpNt901aGke+eKf5nnxj2VfjdOllBQX96LUmPRaeYgnAKT5q3xydLNJ3ID/6idASUH5qYAyDkjzPbuPRy4U+hLUuKWWDHJQkzUG00vSAABlmQkw6bXyuSZg+gkAyuYAggZoPgq09W/BSF/KucNBEAQYdf2j0AGIuKRbUWo8F2UZVNIdJrzqKXs8kDUGLmMaNIKIyaZG2UTHmVLEgprD9Z39OwwsXJqPAU2HWNqJN53LnsBuGw547CqKIrarlJrmoaDUqHpw8Pfce/XUaXXiUs3XuKPpEVyq3YQ0dEE0Z+ANx3wASl+VoGSMUJpqff44sPkvwNYXga//5Hd3QRDw+BVTcP/SidAIbK7Kve/2Pu17sIgoqNn2ErB/NfDJAx6bk1VB4mCpNYHKW2O5AZ/co0anQVYIoyzOkVJQQKC5T5JqLGjZdGl/yGZh3141A+GpcbnFiJQW9UUs3MfXdljhdtpRIkhWgcwxuPiUQpwzPgc/O4ct+LinJmj6yZQKFM5k3/ezWhPuIMu+IFdA9ceCJcKSbn7+yk3xVmrYucjqcIetKMZpUCOlnkpOBwQB3SkjAQBTTb6+mYJUE9IT9HC6RRxSdaUcdA5/xG5L5yhN53LGs1svpeZkc7fHCWKwPTWiKPpVaqw+QY0D87Wsed4613RcZXsAFTfvxBZxPAQBSDL0kn7inHM/MO5CpmiNk6bxBvHYCIKAW84agWeunQEA+PJIUzi/3oDSFImn5sQX7LZhH9BWIW/WagSkSBOxByuoUbwn/pWaWCzr5oFaUZo5pLJ7bhYGepv7lOzbn4kjl3UHTj95/7/1FXVHYSCyv1VfPDXlTRaUCA3QCy4W7KUUIDVBj5dunI1LpxcCQGhKDaDy1fRvUHOkgV1T+qTUiGJIbSvkXjX9otREVv3UKDfe81Rqkow66LXssx2uWhOfQQ330xSfDgBoSSgDAEzQ1fnsKggCJhcytWZI+Wp46mnchco2rtR4BTU7Klnqic/TGGyzZZfNKTvw0xMUT423UtNldeAMDZsa/bJ7KbaI41HZpngNQu7LkloIXPsGcPUrwFKWwkL9XqCnLejDZpexhnwtFltEUnp/I4qi38ZVQXFYWe8ezuGPPe4e7K7CgVausTz/Sd14LxTyU82YmM/SSn7LublSEyj1BARNP/E+NdYor9h5+ol7gCLxPzX3Iag54eGnGeU34EsItUcPL+0++mmv54lIsdic2HCQLaTPGBV+0zqZLf8AHsoAyr8Oulu/KTV9GGYZqCWFICjVUOH6auIvqHFYWQ8CACg5DQBQpy8BAIwU/PsseFAzZHw13S2K0jBukbKdKzVNRzwqoLafbAMAnDOeDTvrtDoHNZXG53mY9VqYDVqlGZjXCiLFUo4coQ0ujQHHjCxg4yv5oD1qgpGcB2SMBCB6Xtz9kJFogCAAbjGy0sL+pq3bAbs0qyrkCd1VW5iZnMMVPwnuq+kYhKBG7T0JrNTEblATzgTmi04pAACMzknyvVNWaoI0n+RKTVe9z2DL/jAKi6IoG4VHSLPUwi3rdrjcHqMWIlFqeOWT/Pt7kWBkSmRQozDAVPyssUBPK7Dut2EdR6h8vK8O3XYXyjIT5I7mEbHlRTbn7sD/gu7GlRpbtJWaPgyzrPczIoHDA3r+/xMq8RfUNB4A3A6W+0tnY+crNEyaLHT6N4VNlszC+2qGSFBzdB0zCuZMBNLLlO1pZYDO7FMBtV0yCc8fly2XxkYyKCxatHg1FQt0kh1j2QEA6MyeAZOZXRD4Bzxoj5reKDmT3VYEL/PWaTWyp2EoKgT8Ap+eoPetkAlE+Zfsls/GOvEFYOuS75a7CvcMfBCn9p54B2mx7KkJtZxbzY/mjcTrt56GW84a4XtnsMZ7nCCDLdXN96JV3WdzumX1dWQ2D2rC+1t5r8jDDmqaLRghSGp7VoCgRlaFg3hqADa1e+kf2ffbXu6XWVDvbmeL6MtnFEEIlEbsjfZqdk0DgIb9QXftN6UmCsMsvdNPADC7jKk+f/38WFgjM+IvqKmX/vB5U2V58oiLrYqybJWsoZ0XUySl5mBt59Bo/sVLucct9tyu0QDZkkFQMgt32504KHmBZpamy4HEYKag+MmLm8EU855nUDPRzvw0PYVnysqMrNSEUvkUiNIz2O3Jzb3uyo2dg52y80evPWqqtwF/PQt4cSGTiAHFTzP7FhYQu+weZkjeE6V9EEYlBPOexHL1UyiN97zRagScOTrLp3ABQGjpJyDgDCiujALRu8Cpy7l5b5hwVTVv70T4QU233Hivz0oNwKqgpl/Pvv/fnYAzeoF+bXsPvj7GvHqXSX6fiDi2Xvneq0DEm37z1ERYzu1yi/J51V9H9J+dOxqJBi12VbZh7d7akJ83/oKahn3sNm+yvOmQLQM2UQe92wp0VPk8pDjDjBSTDnaXWzZ2DRqiCByT2v6PXeR7v+yrYR/w3VXtcLlF5KWYUJBmRqZ0kR5MszA/WfGcqdlf7whRxDQ3a7TnLp0rBzGV0gWi1x41wSiRgpqa7SwdqaazHnhhHvCviwG3G1nJQ1mp8W+yg9sNfP1n4MULgPo9zBi/5UXAbgGqtrJ9RpytfH64PwtKWq+9p5eVbD8gX/z9dFZVD7Uc6r2DvKmOIP0UFLlHTYhBjZfHzqRS9aKVguJ+miSjDnlSE7lwjcL8vMA7Sfc4XCEfn8stoqK5W0k/cU+RF7JRuDelhnP+Q0BCFnsPNz8T2mNC4L0dNRBF4NQRGX3rJHxUFdRYGgBL4KKGfldqwiznbrbY4BaZtpDpxzuWk2zCT+azfktPf+p/4rw/4i+oqZeiWS6/A6jvcqJc5FKt75vnaRYe5BSUpRGwtgEQPH4HGe6raWAnMp56mlGaBkD58DQPplITKP2kWkG46/cjEx3oFo3Ql86Sg5ioKDUZI4GkXKZSVG9Ttve0Av++HKjdxdSLmh3yxbSpywa4BnfQozd+y7lrdgKvXAx8ej/gdrIUJQB8+SRw5FOWek0tZioND2qOfCIrlIOZfqpqCZym4UqN3eVmg01jBIfLjdr2KJfthpJ+AoCC6ez2xJcem3UNe3G17isAYtTKurlSk2TUyZ/HsJUaKagpzjDDIDWiC7XypbKlGyZXJ7IF6b3JDB7UhBzMJWQAFzzMvt/6z5CqjHpDFEW8u50tnq+Y0QeVxuVU5trxjvJB1Jp+U2p6Iqt84qmnzERjwMaDt84diYJUE+rCSGXGX1DD8455U+RNjZ02HBNZCgpbX2bzk16+EGhUApwhUwHFg670UtZwz5tsz7Lub46zD9yMEmZEy0yKvP10X9ha3oJr//YNPtlX56PUKCca5WLlOMZSIlvdY5GSmCgHMfXShztiozDAlgZcreGGa7sFeP0aeQwDAODQh3L6yVTzLfC7AuDzJyJ/3SjDBz/mpJjYINN3bgX+djbzzehMwNKngdu+ZFJ8dzPw4V3sgSPmsfegdA5gSGJm0tqdAAa3q3BNS+DyVpNeKwe/gxFwRUpduxVuETD68QlFTKjpp9Hns9vqbcoK3u0G3rwOT+iew0LNlqgFNdzgm2TSyZVqkXpqMhINSpv8EHtqHWvsUiqfkvMDBnw81R1K+snudMPhcrNWEFoD0F7BGvL1kT3V7TjS0AWjToPFU/Ijf6LqbcwEbkoDRp3DtgUJavpPqYmsR01jCD22THotViwaH9bzxl9Q47AAWqOcc3W43GjptitBzcEPgL3vACe/ZgYxiSFTAcWDGt5cyxse1DQdgdVmw3cnmDQ4d0w2ABYVAwM/KuH1byuw+XgzfvTqNqzaxlYp/MTlr/meKK0uvxMnwqjT+AQxfTIKA+yCDjCzsKWJBTSV37LGW3OWsfsOrpEVghlVrzJlZ89/+va6UeRgLQsCxuUlsUB8zyp2x5SrgZ9+B8y6GdDqgHPvZ9u5TDxiHrvVGZST4ZYXAQxs9VN7twO/XLULXx9tAva9hycPnoulms0BvSc84GobBL9PpHCfUGG6OXIzqDehpp9S8qXFm6h0j67YDLSzgojrtBuil37yo9SEmypsloMao9wmvznE7udHG7pUlU/+VRoAqjEJwdU+i82JOb/fgMuf24QemJRFkDrdo6bhALDjtZCUnI0HGwEA503I7ZvizP00oxYAuZKdIohZ2NjvnppwuwlL6XM/fho1F59SgMkFvXzWVcRfUAMAORPYyR5MsRBF4H33HIg5E1nTpfFL2X689BuQ39QDtR1wuqIU6VZ8A2z6C7DhEeDDXwBvXMuMnX+YFPji2SSZ/gIFNWmlrPGUy4Z9+3bD6nAjJ9mIsbmsNJQrNQOdfjreZJG/5xE6P3EleJd0u93QVzIFZbd+KgRBaQrH8f45bLhZuOIb4Pm5TN3QJwLf/w8w505Wnth4AKVCPbLRigldUvVD0yGWphpk3G4R+6Wp6zO0J9jxa3TArRuAK/7OlDzOhIuVDqkAUDZX+f602wAIwM5/A3v+o6SfBiBwePGr41i1rQp3vrkTzp1vAADO1W4P6DHgjejaBnE2Vbj4LecWReDTB4CP7o0snWGTFla9KTUAMGYhu+X9iHjgC2CuZg/cLb4DLyOBN95LNuk8UoXhKH6KUqOX0+ShtlI42tClmIQDVD4BCG32E1jPm8ZOG/ZUt+PxtQeA0eeyO475CWpsXcArlwCrb/dpkeCPY42s2pB3q48YHqiOOldJM8eQUqNUPgUPajQaAU9edUrIzxufQY1X6gkA2hNHQrh9M3DDamDBb9iddbtlr0FZZiKSjDrYnG4cbezyecqwaa8G/rkE+OQ3wBcrWQOlQ2uYsbOjCtj6kv/HyUpNgH9cjUYOeMoPMFPo3DHZ8ipR9tQMcPrphBTULD9vLJKkCoQS6eJl9s5zV2+D1taGLtGECpM058lLmelT+glgJwFjKpuj01nDlLsfrgeKT2UrjlJW9j2m7Utcqf0SWqhOBGofziBR2dqNLpsTBp0GxQeZyoLJVwJFM313FgRmeOQ+rFRVHr/sLGDeL9n3/7sTuQ6movV3+sntFvGOVNLa1GWF/QQbXVIq1AdWauSAK3bST359QvveZWM6vnlOqUYLh2ATur0ZKwU1x9YDjh42HgNAi8BGw6QdejP81/eD2ihs0mvl4Lg+jBRUixRIpycYFKXGn6LcfIydM62KFcAj/RSg8gkIPf2kDur/tfkktupYd3GUf6VUEnK+/hNL4QJKZWoQ+LlwpGqCeNh0twDV29n3o89lC3WABTUBAuWhVv2keAJ7bxzqr3ggEBTU+CuLzRrL+r3Yu+QcqkYjYKKk1qh9NTanC/e9twcf7fXtRhyUgx8wI2dqCTD7VmDu3cCSp5gPAgBqd/stL+81/QTIH3BLFfOHzB2jDMiTq58GUKlptdjli+SP5o3Ex8vn4YXrZ2LuaHZcPkbhL1YCAD5xz0KCiV0MvGXaPsm2AJtkzFdfky4HfrRROTEAwHg2TiGvdj2u1kpmPFMau+UVRINFdwv2S2nQuVnd0BxgFyqceUfgx5SdBdz2BfD9Vb73zf8VU2/sXZj41c9ghD06QU1recBxFN+eaEF1Ww+zNwkNSHAy9atMqPdbCQEMjSni4eJTzm3rAj6+T9lh64vhP2mo6SeAKXQJmcx78dnjzNSZmIOXk38EAMg5uooZTvtIpyr9BEBlFg69AooP2s1MMgRXar54kqnbH90LgBlvWfopHKUm+O/s/bq3f2qFOzGHLYLUPWvaq4FNqqqoI58GVd9EUcRxaVHM+/mEja0T2PgoAJEtzlIK2O8saJmK11Hj92H936fGf1DT3u1AvZ9GjKGmn8Il7oMa/sZ6BDVanbJP7S558xQ/FVAf7a3Dv7+pwG/+uyesBkFy98fTbmPBzLn3s+Bm+g1SQNWpTBLn2LuVqbHBghrJV5PexQKyOaPVQU3/KjVWhwu/emc3Vu9UujPz1FNBqglmgxaFaWYsnJQn9yLxKOmu/A448jHcghbPOC9DkpRm8i7hDmmYZW9c/GfghxuBK1/yNRZK4ycSa7/FCE09OkUzXNxr00sn4n7l5GbgiZGY9smVKBbqcZN2LesmOnK+x+faL/lTWUdlbzRa4Ip/AInZMLccwMXaTdFJ8bx+DTPc1/vm+d+Rqj+umlmEpelKG4UMoROC1b9vjQc1g9k4MlwO1bMARF6Vf7GSKYOJzOOGgx8CnWEuiGwhGoUBKXiXBt7yi++ky7AzaR6axBSYrA2s+q2PdKmMwoByoQrHLNxiUZQa2Sjs7zzVLZmed74G1OxEU5cdebYTGCWXc/c9/cTVwLPHZmNUdiIauuz4TjuN3alOQW18FHD2AEWzWdq/sxaoCzwAt6HTBovdBa1GQElGmEGNKALb/gn8eTpT9gFg2vfZrc6oeIkCpKD6T6mR0k8BSrqv/fs3OP8Pn/v0+opoGG8IxGdQkztJ/lZWarwrE/KlHJ5UFQIAkwu5UqOcdLefZCvMZosdu6raQnt99ZiDCUs979PqlB46qoDK6nCh7sQ+ACJgTg8u9UkXt0lCOSbmp3gEbFmJXKnpn6BmzZ5avLmlEg9/cEA2CXK5dUSAlYk80NLhYiswAOWFF+OEmC97Z6Ku1AAskCmc4X8oYHqpYr4D8D/X6WjPl8zF1Vv9q2gDQc0OACLyu/ZhjeHXOK1NCo7P/Fnfnjc5D5h5E3sqzT7Yne6+nfzaq6QKPJEZsFV0251Yu4etqq+aVYzrCr0u6q0n/D5lqpl7amIj/WR3unFYCmomFaQyP9zmZ9mdFz/DZs+5ncD2V4I/0eGPgX9fAXRISoScfuqlpJsz5gJ2K0p/zylXwmAw4T8uyTC+7Z+hPU8QuFE4WVJqcnkFVBhl3dxTk6k2Cvs7T9m5P08EPv41jlfX4zn9n9ggy9HnM19hANTpp2Am5lYp/ZSfasLT10yDViPg9SYpWDq6gd3W7AR2vg4AsJ73KHqKJa/akY8RCO6nKU43h94FnFP+JWsCaGlkbSmufhU446fK/XIKyr9ZuN+UmiAl3TanC/trO9BhdeLLI40e9/GANzuE9FM4xF1QY0sqZBUuEgG7shZMY7fcLCyKOH/Xcqw3/AK1NZXygMNtFYppdP0B3ynffjm0lp1gcqd4jjng5PPX3iFvuv+9vXj01ffZD5ljAk/nVT1+pKYO54709CdwpabH4eq9VXgE8AFtTV02OZ9eLgU1ZZn+gxqznp1oxnTvYP1hNHp8W3wrAEXO9vXU9NEoHAqqYaFvuRag1jSSqWjW9qiUdkaEJPU6oEOy0AO9y8ok6FHn9v25y84CAJyuOQBA7FuaRy3R1+32uOujvXWw2F0ozUzArNJ0FHay+92i9JluOe73KflA1sHodhwJh+s74XCJSDXrUeQ4Aay6ifUJGnMB6xE0+xa247Z/Bk4BdbcA/72NmUJ3vsa2hZN+AliFmyCd6tNKgKLZMBm0eMu1gG07+qmy2o4Qb6UmOyW89JMoikqrh96Mwnx4IgCc/BpjPrwSozU1aNVmApc9H/TcmGBkF3aXW5TnpvmDv25aggFTi9Jw27yR+MotKaH1e5jq9a+LAIjA5Cux7EsdHj1czO4/HFj5kv002X5mevVG4yF2WzYXuP1bYOLFnr9rL2bhflFqHFbVMEvfhba6yvarI83y9+phvLmUfuobXanjPH5u7AoggfHAonYXW5XX7EBS+ScYpanFCvwTJ5q60G134kCt0mF4/cEQgxqeevJWaTg8oFIpNTsq2zBC5PJqkNQTADEhA7VgKafz0+s97kswaGGUVgjRVmscLjc+P6xE47z8XVZqAhjjePrpBz3/Zhtm3ohaTQ4AIFlSZPpFqemNyZcDGj0OaMdhlzgKTd2i0tCsapBSUFJQ87xzKf7ovBzutDLggkeCB7mhUjQb0BqQL7SgVKiPYlDjKcfz1NPl04sg2C0Q6lmX7+PJkhkzQFAjl3QPgqfmH18ex63/2gKLLfSFwP6aDujhxP2JqyG8cDa7GJrSgEWPs7/XhIuZZN9RHXh1//kTSrVdw37WANIpDfgLJf0EsBV0MRvei8lXAIIAs16LE2I+2swlLH3JTacRonhq2N8oJwSl5pXN5bjhpe/QaXXAYnfJQUZGokHuYeU3Tc6VGqmKL6PzEFyigA/GPgokZvnuryJBNXai2xb44t4um5bZ7/Pzc8cgI6cAe9xlbIdP7mNpwKLZcF/wO3x5pBHrnJK6X7UFsEgXcFunx3iF4419MAm3VbDbvCmsHYM3XKlp9B/UcKXG6oiiUsNVGkHrIRZw1J3Yvz7aJKtj7T2qYbyUfuobLYmePQwUpcZLAssezxqY2TvZSZavkgBcot2Ehu3/w65KNoIgPUEPjcDKvXlDtIDYuoBjknw54SL/+3gHVNJxjtL0njMGgCMNXdjlYoPwJsDzAiEIQr/NM9pa3uoxZZcHNcfl1Ung9FMOWjFVPMj+Oeb+Ap1WdlLx56nRaQQ5ZdWv5EwA7vgOf8x7DIDAPivFs9l9VVv6//X9IZ1EmsRUrE77ATTLdimG575iSAAKZwFgak2fyrrVQU39PnlqfEOHFZuOsRP+5TMK2agK0Q2kFGH0bGmWWUu536fk6aeBnpjudLnx9KeHse5AAz7Z75kqO97YFfD/aF9NO36lewNXdv2bKTTjLgRu3wxkstbv0JuA6f/Hvl/3W2DXmx7DRdF4GNjyd+Xnur0eFT8whJh+AlggdeqPWLsCKOb82iRpdV/Tt6DGx1PDe9UE8dT8a1M5vjjciE/21ctN9kx6DRIMOllR9h5yCUAJahb8Rh7a+ZTzahhGzun1OHVajdytuDuIYqEoNXrpuLR44sqp+Nw9DQDg1uiB8x4Ebv4YVY5kWOwu1CET5bqRkPsC7X8feGo88I9zZfMwNwkHSsUHpU0qv08r8X+/rNQc9Jsel6d0O6Oo1HSrUk9+FlbqoKauw4pjUlDHg920BL0cbEWLuAtq6s2jPH5uCJR+0uoUT0XlN3J/h4pENppg0rbfYs9xtuI8c3SW3LG3V7Xm6DrAZWMTwvmH0JvscaxBoK0DaD0Bm9OF9h6HbIRrNAXOGQOssmSvtKLQ1+/2ub+/ugpvPMR+d64E7a1uhyiKIaSftCgRJEUptQhIyZdPksnSSdKs18oTxlPM+ug1MuuNjJFITGGyalOXjakZwOBVQEknkVYxGRPzQ29IFTJyCmp/5EpNT5vSmVmjZxUjzcz0Xt7cDVEEyjITWD8abroung1kSBOpe1Fqop5+ajoCrBwDfPmU37sP1HbCIhlLPz+kKJHHGruw6E9f4saX/at2e6vbsVQrDU298Enge6+zShU1s29hrQWaDrM005NjWGfoI5+ydg9upxxoovkI81MArKeSNowUbME04MKVzI8H5QJXZZZW931Uarw9NTx9FGzMATfrbj7eLO+XISk03Cjc1uOQU/0yPKhJygF+8D4e0N2Fv7ouwuic0FI6PAXVEyT9zj01vDcSwLqyd834MZ5wXI2HC58HzloGaLQ4UKcEmmvt0uia9Q8Bb1/PUjN1u+WUkLzAy4og/cSVmkBBTcYIdt1w9gBt5T53y56aaCo1vVQ+ec/M+/ooM3kfqWfBXbRNwkAcBjWV+hEePweddMzTQF+sZD6K1GJsn/cPVLizkeqox4jdrPx6Zkk6zpnA0iUbDtT7Po+agx+w2wlLA6cMtHrFLFyzA42dNghwyyWLmzuCd24sb7Jgryj9nqoUFiczmAmvD6yXfvfvn8aCrj3V7ajvsKHHwdz+gZqqmQ1alAgsIBIlkx9XfPhJUhAE2VfT58Z7YZKlnhDNg5qG/Uxadjk8V9f9jRTUtCBZbjEQVVS+mvZIFZGqLQBEZmbk/0OSr4Z3Kk7lFwuueBWd2mtQk95fzfd2v82GAW56xu98ry3lit/kyyNNcpXj/3bVwO50Y291h0+g5XKLsNcdQK7QBrfWyKY9+zWklwE/+QqY/2v2fjm62QLqtStZVZJGB1z2AktTiW4l7Rlq6ikAXKkpN0rp+OptfZprJHcUlv43M0JYOMlBzbFmWZHhBmHek0gUvZQ5UVQ8HIYkWFJG4ZWuWRChwagQfSo8BWUJkn7i1U/pCZ5pnvnTxuI516X4qCFd3nZQZUFY55BSUHwwMm8Dcfgj2JwuVEp9i0ZFpNTwoCbAolajVVJQJzf73N0/Sk1oQY1WWpB+JaWg/vYFW+QsGJ8TvWOR6Leg5p///CcmT56MoqIizJ49G1999VXAfaurq3HNNdegrKwMhYWFWL58OWw2zwjvm2++wdy5c1FSUoIxY8bgb3/7W0THVSMqAYHF5pT/sfwGNTwN1FrObqddh/Gl+fi1k5lY53e+jyR0Y2ZpOs4dnwsA+PpYc2ADbneLMhF5fIDUk/dr1+5EY6cN+WhBgmCDXdRibVXw6LaypRt73dIFoumwz0U3g49KCLEFeSicbLbgWKMFOo2AH589EhqBfaC/Oc4+9CUZCdAHGFpm1mtRLLAVqCuVrULklZ/KOyNXQvW18V6YeAy1TM5jvYVEN/DW9cDK0cDjJR7dp/uDjQcbcKiuUz6JtIpJ/RPUFM2GQ9AjX2iBu/lY7/v7o0I6oZacoQxdlYLrDimtmGLSsQsUD2qKT2UXdQDoqlNVuCgoYxLs4bVP6I2TX7PbnlZmVPdCHdQ0W+xyJ+e1e5RUFN/GKW+2YJZrJwBAKJ3jf04bJ60EmH8P8LPtrCP0qbexydAAcMYdbOI0r9jkF6tQK58CYJLSt8d1o1jK19LAvD0R0qlqvgcoiktbt91XaZHgzTar23rkylGu0Oi0GlUJvyqocVrZ/x4AGBLlaqKsJIOHqhKMBGPvDfhavTw1nCmFqdAIQG27Ve69clBSarQaATvEMWg35jOF8uJnlBElhz9GZUs33CJ7j8L2kdi6lAAirTjwflJ/Lez17UjPx9FE1VMjT+hO93t3Yxd7j+ZJvdK+OdaM9QcasKuqHWa9Fj+cOzJ6xyLRL0HNq6++invvvRerVq1CVVUVVqxYgSVLluD4cd8VmN1ux/nnn4+ioiIcPXoU+/btw7Zt27B8+XJ5n4MHD+KCCy7AsmXLUFFRgdWrV+OBBx7A22+/HfaxqSf88igywaCV/xk94KtMzrTrMDo7CVs0p+CEOxd6uDBPfxATC1IwNjcJRelm2J1ufH1U+kN7r3y+fZ6tMnIns5N4MFTVV2o/zUkxD18ea2eD1gJQ2dqDJqTCas4FIHoOaQQ7AQDRVWp41dPssgzkpJhkKfj9Xey4yzIDd4Q067Uo1rCgxp7M/mFlT43q76IoNQMb1GQls/dL9k4USemA4xvZxHTRFVJ79Eg5XN+Jm/65BRf++Qu4pMGErWIyJvVH+smQgOoElhZNa/iWfYb3/VfuRBsS3E9TcjrrjQPIZmGu1KSY9UyR6W5mknneVHZi5CfHFt+ybt6l1i0qxtQ+47B6phL3vedxtyiK2FLOjLq8SuPzw4042tAl96ABfIOavdXtOEvD/u+EUfNDOxZBYB2hL3wC+MVBVuFy3m/ZfTwVXiG1ggi18ikAXKnpdOmAXCkN3ocUFB+TwP9feYDhFv03S3S63B7VR2ukEv8MVePFDH9mYXWwq0+Qg5pQVRqg9wZ8LrcoB9/egVKiUYexuSyg3FHRBgA4WMc+B4sm5cENDX6R+jTw8x3AjBuUMRVV36GiivUYG5mdGH76XJrXBVOaX0OuzJQr2e3xz4BOz6wBtwVEVanhnZST/Csu/Bp79thspJr16LQ58at32bng/04vkf2d0aRfdPwHH3wQd999NyZMYFLYVVddhVdeeQV/+ctf8Ic//MFj37fffhv19fV47LHHoNPpkJaWhqeffhpnnnkmHnroIWRlZeHJJ5/E2WefjSuuuAIAMHHiRPzyl7/E448/jquvvjqsY+tp6wQs7B+juaEFZrsVxclmeZsHCcWAy8A8MKVnAoZs6Kw9mJahx9d1kzBCV4crEvZAb2Xm4EVlSXitvhVf7yrH+e0fAp/+P2DhY8Dky1j66ovnALsIzLoD6O4OfqCpY9m+J3eipbQF4x0nAYioRh5c1i7sPFCF2SN8JT9RFNFU1wKz3Qln2iSgvQ449i2QqTRmy9U6YbZb0dnU5v/3joCvd52E2W7FBaVJgMWCGZkGVFZasWVvJcxuEWOTNAFfSwOgzFkHuET0aLKRYLHA0dEJs92KVLdNfly2wI47W3BG7bhDIVfj8ny/TrkFaK5hq2enDdjxKnB8CzC7f47pRHkDzHYrEtEDLdjJNkGfgGxN/7wP9eZTUNa6E4U1XwH/OQnskKrSTv8JcM79wSutnDbgxFbAKQKZp7Ag3i4CFTuBri50t3bAbLciEw7gu9fYfUVTAJuDfSWWAu0tQPUBINkzVWwCkC7aYXW40dHYhtQggXLInNwM9FhZybPoBna/Dyx4hKWAAZxsssDS0o5UnQY/mVWK3390CN/sqYC22wKzXSlXPnq8HpiunNiPHa3Cbc59gEsE8k6L7O+UWKycJ1JHs/eqXgr2hIQ+/e2TnDaY7Va4u7qAjClAxW7g6GagNHzTucPlhmDphhlAsssGWEQYAORonOi0OtHa0IoML79Lt9Xh8f5VVlphBjs38d8rX+dCrd2KjsY2IFdSulob2PugTwB6enCygv1vjE8JfH7xJl20w2y3wtbeCVh8g6EOix0mGzu2NNEOWDyDn1NzDDhZYcW+IzWYV2hGfW0zzCJw8/RsbNh2AltOaGBFKkwWC6DPANImsHT17g9hto/EuKT08P921YfY751eGPyxxlwgazozfm99Azj1h/JdZoeVvecWMXrnjbrj7LgMOVi/5TieXncYj18xVR4A3dHUBrPdikK9G/MLE/DJ/npYWqxI02nwo5l5oR9HOMcrRpmTJ0+KAMRDhw55bH/hhRfE8ePH++x/0003iddee63P9vz8fPHNN98URVEUR4wYIb7wwgse9x86dEgEINbV1fk9DqvVKra3t8tflZWVIgCxna096Yu+6Iu+6Iu+6CsGvtoBEYDY3t7eawwS9fRTTQ1LNxQUeLr8CwsLUV3tm7Otqanx2dd7f3/7FBayoXz+nhMAHnvsMaSmpspfxcVB8pAEQRAEQcQ8UU8/6fVMttVoPOOlQDlEvV7vs6/3/v726S0nee+99+Kuu+6Sf+7o6EBxcTEu/vXb+OzXrFPssxuO4i8bj+KqWYV46JJe5uao2F/bjiue24yX9b/H6dqDwAWPArNvht3pxsyHP8UPhffwc/17QNkc1leCNx9LLwNu+zL0Usz1DwHf/BUA0CMa0Jo1HfrLn8e8Z3YCAL66Z4E8oJKzdk8t7np7F6aXpOH1a8qAZ6Yzaf3uI6wPCVi+/6rnNyMnxYDPf3lOyL93IPZUt+Hq579BXqoRG+9mXUq77U7MfmQduEdw/S/ORkGa/+nLaD4OPD8H3aIRe6/biumlGZj6W9aVc9OvzpErIjYcqMfDH+7H45dPxWkjw5sI2xfcbhFTH/wELreIz345H7kpXqbPF85mhuyrXgHGnh/111/+5k58tK8Oz5zaivN23wXkTAJ+uC7qr8P5dF89Tv7nXpxjOoSRN76g+DkOfQy8eysrM772TWDk2Wy7vRvY/i/mR+Hdg899gKWrAGD1z5hxcd4K/LxqPnIOvYb79K8BhiTgR595Tg3f/TZrBV82B/i+l9nR0oQ7Xt+O9RVuPHn1KVgyJb9vv6jLwfqIOLqBW9ezmUKvX8N8PXfuArR6LP7TFyhv6sbz/zcDZ4/LwcMf7MPr3zJ/w5zRmfj7DbNwxmMb0N7jwDu3n4GJ+amoaetB/TPnY7rmGByLn4R+xvf7dpyc5+cqnaxPu03x20TAV0ca8cNXtmFcXjLe+/FpwJNjWSnwj74AsoP3wfLmYF0HLnt2EzKTDPjqHuV88pN/b8Nnhxrx4CWTcPUsz0UlP4dmJRtQlpGIrdK4mT9dMw0XTGa9Z57+9BD+9sUJ/N/pJfjNEsn3c2wj8OZ18v/AWb9fj+YuB969/UxMCNFj9pv/7sG726ux7LwxuO3sUT73bzxYj9tf24FJBSn4z0/O9Lnf5RZx6qPr0G134bQRGfj2RAtumlOKFYsmYNXWSjyweh+mFKbgtnmjcKypCyMyTDjv04UQupvxA/s9uOfHN2FifmpIxyrzn1uBQx+yRpu8E3Uw3riW+Wrm3g3M+wUA1iPq7JWfQSMAex9c2Pe2GC4n8PsyQHQBP9uBi/55BEcbLZhYkIx3fjIHnVYHTn2Uzcnadv95SDDo8OWRRiSbdJhW7N9YHJCODsCP+OGPqAc1RUVFAJi6Mnq00uiutrZWVle89+fqjhr1/v72qa1lxjJ/zwkARqMRRqOvCanBrQUSE+XvewwmJGemydtCYfzIBFw2dywcrecBFYeA6i+B+T+DAUBuQSYWtm0DNAJw6g3AyLNh+cs8JNob0XLmcmSkhPFhXng/MOYsLP+kFe/XpuHZhadi0Yg8ZOdVoKKlG0ctIjJzPY+73Cqgx2BCTl4GkD8KyMhjZq6ucrlxXEaOBj0GE6rtAsSEhD5/uFvQjR6DCcbUZPl9TEgECgqzcKShC0adBnn5mew98UdtA2AQUOnOgUVvhkVnRI+BBQ5JmamAVDV1zqyROGdW9N3yvaEBkJCegoZOGxrdOuR6f1bKZgIdR4D2g0DipVF//XIb0GMwITvZBRgEID07rM9ruCRnpeIRzQ14PSURG0aeptwx43Kg/ltmeP/yYWCiNFPo3euVIX9GHWsGePqNyjGWzQAOvwM078JpHa24LOEd5stZ8hBQ4NUdu3Ai+x0tlZ6/Y0ct8M8F+J3NjdMMT6FZ1PX9PajaCgg9QGoG+xuKbiAti5mXG7ejIedMHOhwQzCaMG1CEWDW44wppXhxBzO1nzNzJISkJIwozcHm483Y1+bCxNGJOHikBvOM5YAgQD9lcfT+ViWnAJ1SRVpqZp+e15hmQ4/BhHaNAUhJBUqnsX5c7QeBsmlhPVenlj2XPiXR45iSMlLRY+hEo9v3b9WjZ4/RJCVg+sRCfFnLfIkp2WnyvsmZaegxmFDvUj1e52afj+QUuM0JqHFo4TZokZmTDiSGNkNIn5KMHoMJHVqD3/ewGQb0GEwwp6f4vV8LYPSIXHx7ogWfVXcDBhNGleUBiYk4dXIxetYew3eNdnz3jtLZ98XU6TjXsB5zNPtQVpIDGIJceu3dbFCmoxu48ClAowGs1ez3zh8T2t999nVA1efA0dXAIuaDM2oM8nnVYUoIf/aUN60nAb2bGf1zR6DaeRw9BhOOdIlAYiIau7vQYzAhyahDQjq77s2dFuFn1hW6uTnq6afc3FxMmzYNa9as8dj+6aefYvHixT77L1q0CJ988gmcTsWMdfDgQTQ0NODcc8+V9/H3fNOmTUNubm5Yx9dldcklhk2Sq56XOIeKRiPgd5dNwdwLr2Ubyr9kBkkAZ6c1YpymCi5BD4xbDDE5H9eKD+PH9mX4R8fpYb0OjEnAhIuwxVoEF7Ty5NsSqd9LRYuv2biytdtjH3+DOXmFgdMtelSDRUqgng58qnlZZqI8kdv/E7BOmZViNnocLrk81KTXBCwDH2i4S7+xy4YOqwP/3VEll537zAmLMrVtzLSYpZHMcn4Gx0UTXmXkt/ne2fcwJaNhP1NnPrmPBTT6BNZg7u7DwPdXebar5xVQRz7B9zv+gQTBhua8ucDMm32fn5d1t1fJ/1MAgLW/BLqbkeJqxRzNvr51O+bwUu6SM9mFQ6tTunxvfxXbpKqncbnJ8ntyxqhMJBt1MOu1uGASO/fw0npeAdWyay10ghsNhuLg5bfhohrEG63qJ15WjUJpRMWRT1lfrr/NBz5fyRwNvdDlVc7NCTZpm5dTm/VanKFSXTPV1U/+Hs+rnwyJaOtxyEpweqLnuScYvU3qDnQ+UzOtJM3j5/H5rCKqJCMBc8dkwaDVYEJ+Ci6ckocEgxb/6WRq50L9Dnmopl8aDgJ/XwBs/guw9SWl5UFvjfe8Gb+E/U82H2UNX6FUPwFRqoDiFVmpRXCKSj+hDqsTbd324D3g+pF+uWKsWLECTzzxBA4fPgwAWL16NdauXYvbb7/dZ98lS5YgJycH999/P1wuF9rb23HHHXfgpptuQlYWOzH+9Kc/xfr16/H++2yg4+HDh/HII4/gnnvuiej4eFkpb83NS5zDJncykJTLImqpjPU8kd0eSpoNmNNQ027F7s4UfOQ+FR/sqYMYwklCjSiKStdj6cJanMHSOJWtviMZeHOnIjmomcZuVUGNSa+Vm9o1RmFUQpvcfdOz1HpmGZMYJ+T30lOjlQc1Oei2K0FN8gCXbgeDN+CraunG9S9+h+Vv7cKrm6W25X7e42jhdLnloYBpglQ2HGxCexRQBzU+n9eEDNYoDoDro18D37L0KC57nlVa+Ju9kzdFHqhYL2TibsdtKF/4TxZIeJOYJbX/F+XPBQ78T5mXBuAczXYlqLF1Ah/9mlVoBRoKGYhyKagpVaUYZknS/v73cPQg661z6ggliEw06vDO7Wfi3dvPRFaCHvjmr7i4+78oFupxsLoV1g0rccnx3wIArKV9T+16oJoa39fme7xnSQ8fFVAgBTV7/wNseIQN0934CPDe7X4bEqpR5j6FH9QkGLSYXpKGZJMOBq0GuamK2pInfV/Vqlq8yY33EtEsnbtSzfqwFj88qOkJGNT471GjZnpxmvy9ViPILSwEQcCrt5yGgw8vwto75+K578/ExrvnI23KQjhELUrFGqApwDDcQx+xgKbxoLLt6KfMwsDnf4Ua1BiTlTTV+gcBt9sjqIlKr5o2HtQUo6Xb7hH/VrR0y9eW7H4o2w5GvwQ11157Le6//34sXboUBQUFePTRR/HBBx9g9OjRqKqqQlFREVatYmMHdDodPvroI+zfvx/FxcWYNGkSpkyZgj/96U/y840ePRoffPABHn74YRQWFmLJkiV44IEH8L3vfS+i4+Mr0Gap+VxGGFG+B4LAJuACrI+Hy4nJbWyu0yc4AwCwXcoVA+wPzechhUqH1Qm703PwF+/MW+lPqZG2Fad7KTU1np2FuerT0BHaFN1gtPlpKQ4A18wqxu+vmIJ7L5wQ/Amk5oZVYjZ67E454h/ozsHB4P+YT3x0CLsq2wAoqph80e6s9ekN0VcaOm1wi4BeKyDBOTBBDQ9OnW7R/2p21k3oSh4FrUv67Cz4DTDxksBPaE4HLvsbcOGTuEj8E/7jOhupgdRRQQAyytj33/6V+dHW/JL9XML+p87R7kRbtxSMb3oG+OZZYPVPgb+eCRz8MCR1AW6X0k+nTDUzKH8qm6ItujHpxMsAgFOK0jweOjY3mfk3dr8JfPQrnLL/CXxpXI5n674H0xePQC+4sFl3KooufbD34wgHD6Wmb833+BBZOagpm8Mm0ANA6VnAmT9nTfl2vc58RkG6ZnvPfeKkBwlqeuSgRgeTXos3fng6XvvhaR49qPgogcrWHqUvl6zUJMn9azLDXJSaJaXEEiCo4eef1GBKjcoTMio70Wd+kVqZzk0x4bFr50DkwXOg4aWf3McWyCPnA+c/JO37qaKImDPC+7ufdRdT9Or2APv/C0EQoturRqUeefc8O9ncjabhpNQAwG233YbDhw+jpqYG3333HebOZRNVi4qKUFVVhauuukret6ioCKtXr0ZNTQ2qqqrw9NNP+/hh5s6diy1btqC6uhpHjhzBj370o4iPjQc1/J8tM8z0kwejz2O3W18EnhiJ5M5jsIk6vNkxBaIoYntFq8fuH+yuDevpuYSXbNLJq6tA6SeXW0S1NFCzhPfw4KmRxgOs0ZhEfio7gdW29z2o8R7+xtFpNbhmdomvsdYbKf1UIeagx+HC/hp28R6T07cTdzThDfjUTd/kTqfGJGVyepTVmtp29vfMTTFBkLt39m/6yazXQq9lJ2W/Iwm0eqwpuQt2UYvPTOcB837Z+5NOvQruWbeiycZOOUEbKPJRFFtfAp4/iwWLGSOBa9+EU2tGntCKlLYDTJnZ/op0TEag6RAzkW7/V+/HU/ENYGtnqlCuV5HA3LvZTfc65KEZpf764dgtzMgPQMwcC6eoQQY60SEm4C77j1G96CVoEsM0Q/ZGapHSeC1K6Se7083S8SkFwE+/Ae7cDdz0IXDBw8C1b7AUxrH1wFdPB3wu3ngv2Uup4akkfwNI5fSTFFxNLkzF7DLPz3VuihFmvRYut6gs4FTpJ34hzQxzUZooKzX+lb1QlJq8VJPcjHF8Xmh/C8MEVqDit1GntZ3N9gKAK14CTpGsDbU7lRRUqCoNJyEDOPNn7PsNjwIuR3S7CrcHDmo8lJrhEtQMZdp7HHC7RSWoiTT9BADjl7K5LuZ0dpIE8Lk4DXU2A2rbrbJSs1hy9H+4u9ZvCsrqcPltJ+4vL8lVGG+lpr7DCodLhF4rII8HEimFbGXvdgIN++R9ubRbFwWlhgeJwU4CQfFKP+2tYe/jlKIwKwT6EbWEeo40r8RjBcpTUFH21dRIfpqCVLM8obu/lRpBEOQUVFuA+U+fOyZiiu1FPG78efBmfCosdqfsgQg66mLR75myM3I+AIGpYBf9CTCnoTmXrXbHdmxiK97OWvZ+LN8HTJMmXu98o/eD2fQMu518uW81YslpEEvnQA8nfqhbg6J0P0HNpmfYa6eVQvjxl/h++mu4wX4PzrE9hc3JF+Diaf4LGPqEIACzb2WDcLkHJkJ4UAOwcw8AVp2ZXqrsNHYhsPB37Hv11HUvelNq/HUu59181cfhjSAIKMtixtLyZimYUQc1ktIe7qKUB1KBZj+1huCpAYBZpSwIm1wYYoA5VuoufHITC2LU1EpVg6nFQGIm69DLVfatL7HbcIMagFUgJmQBLceAna9FWalR0k/NXiN3Kpq7h5enZqjT3uPwNJmFODPEL3oTcMlfgF8eA275FFj8BF5K+SkANtBxn6Q6/OKCsUg0aFHd1oPtUnttTnmTBTMf/hR3r/IdPukvL8mVmoZOm3JCgqLcFKSZ5QFiEASV50N5/nwpqOFKQF+QlRpziO9j01Fg68tspW3tkC/W3CjMU3ST+mO2UYTMH5eNwjQzfrlwHG6ewzrdeqxAZbPwjqi+bp2kpOWnmeRhlkiIsgLgB67k+UtxAuwza4MBHdbQfSx8X4NW45Hf90FnAE65BrhhNXDXfuCnW4AR8wAAlhJWPDCt51v2GQKAad8HkrKBs1ewn6u2+F401DQcAA6vBSCwNIsfGqfdAQC4TrseOZpOzzs7aoCvpfT4+Q8CehNKCgvxhfsUNCEVt5w1ou+VJYE49wHg9s3BW+WHgPr973EEucDx4Kl+T8C0XiBPTTClpkflqQnGiCx2rjveyIMaZZilrNSEuShNlNJP3QF+79YAHkFv7r1wPH65cByuP70stBfOHAVkjmELzGMbPO/jCi8PZABgtNQegp+31QFnqBiTgbmspBvrH8I4Lasi5kpNoLlcIaFKP/EARiddd062WJSgZjh4aoY6bT0OtEiRZYpJF50TkEbL5jmddhsy88sAAO9ur4LTLSI72YhR2Uk4byKrlvhgt2d5+v921cBid+F/u2rkmSMcf9FuWoJelnrVJjofPw1H9tXslDfJSk0U0k+BjMJ+cTmB168GPljGPBNS6qlHlwoLzGjqtONEEzuB8VbbQ4HROcn4+lfn4KcLRiM9kf2eLRbV36qfzMI1UtCZl2rqdSJuNOHGx6MNvl4KURTlv1FYQY0890kXehuBlAI20FHCLaV7x7uPyFUdmHkju00vBTJHs74Zx30HU8pwlWbCUo/nVnM0eTZ2uUfCLNihee9HillWFIF1v2Xeh+LTgImXAlAqoFJMOnzv1AhW1AOMRiPIU5sDGWYBANnj2aRwa3vAgZe9KTXddpfH4gtQAgpzr0FNAKXGmKRSasILahJ6ST+1h6jUFKUn4KcLRvf6O3jA1ZrDXr4afm5Wzxscc4HnPoGmc/fGrJvZbLXuZvzZdh9GC1WwOV3YdLQJk/7fR3jzu4rwn9PtVj4PacWyv4kvRCuaKf00oHT0ONAkVz5F/w0fk8suCOsPsCGPM0rSIAgClk5lzYPW7Kn1mDK84RDbz+kW8dWRJo/n8hfUCIIgVzepfTW8GoobiWX4P4pfpSYaQQ331IRwctn1BpNCAbbabWBO/04zk+u3nWyBKLLj64+/TTTIUK1A5VRi3hQAAktJdATwTdXsBF5azAZEhggv5y5IUSs1gxvUNHTaZE9El80Z8mpPDmr6UNWWlF2KPe4yaFjXdJaiylQ1UBslzS7ifXO8aa9mDf4AYM6ygK9T1WrFrx23wiqY2Kr6w18wT9p7twO732I7LfydnHq7+JQCzBmdiYcvnex/OO4QxCz7K4IENTqj4her2+t3F97awNtTk2zUyd4sb7NwqEpNWSYLangQ7ddTE+Z5ovf0E0+n90HBD8TYRez2yCfMrM7hi6GC6cq2ollsgCUnkvQTwLIJN6wG8qYgXWzHm4ZHoG06hI/31cHqcOO7Ey29P4c3XfWAy87M5MkFciXa9BKmItd2WFEtXY8oqBkA2nsc8j9ZxJVPQeBTXJ3SyX6G9IeeNzYLKSYd6jts+PoYC16au2zYKVXTAMq0a06gvGSJVNZd0exHqcnw6tzLlZqG/YCT/d55KWyfqCg1oXpqnDbg89+z7wUtYGkEPmM5e0sCa9pYLv0+Q0ml8Yaf7Ng0X2m1Z0xSpHqeA1fTdAT49+VsyvJXfwz5tXh6sCjJzQarAv1uFAaUqcdHG32DGjkVINEVolrD36vkYH6aXkhL0GODW3Xin3mT5w6jpaDm6AbfdInbBXz9R8DtYBU+fNq6Hypbu7FPLMNbZQ8yT8/2fwHPzGDVQIIWWLzS4/GZSUa8duvpuKQ/vDT9hDlU0ygvJa/f4/duHtR4KzWCIMj/K95BDffUBO3ZApVS08SNwqqS7gg9kYlS8OUv7WZ1uOTtqZF6BINRcjpgTGWqa/U26UU7lE7R+arPtkarVNcCkQc1ADMN3/A+jutGIUvowJgtD+CANF3cFWabEQBK6imlENDqZJFgXF4yEgxaiKISHFJQMwC0dzvkf4j+CWo8J7/OKGVBjVGnlU96b37HTFafH26EKConmM8ONXioOLxHiXdekvtq1L1qAqaf0kpZxO+ysyooKEpNs8UefKXWCy63KBuFez0JbH+FlScm5QGLpeCm5TgAwJpU5LHr5IKhG9SY9Fp5hdmqPlnPuZPdfvuCp6ejvRp49TIlfVS3R1lx9gJX0oqMUvCpNQKG/usmzOFKzbEGi8fnEVCtmiW8U6aBUJSayJUMk16Lz4RTAQDOxDzWZExN2VmA1sAqM/iF4vDHwCuXAI+XAN/9jW07a1nQ16mS/q+6S88HFj0u/QLVrCDg+neB0yKvvhwqmLzLugORJwU1AZSaTrn5nu//f6BeNerme8HgQU11Ww87T6lLursia8nBX9Ni8w3GeSpdqxH6p6WEVg+MkSpmD37Ibuu8TMJqxqjGrvQlqAGAhAz8Jet+9lTNO3GilnXGjshXw8vMpeaS/G+RlWRUGr9C6tDQD9fYYMRnUNPjkP8I4UqXoVCamSjLrnqtIHfWBYDvnco+BJ/sr0Nzl01WZm44sxRJRhbxqnvZBFJqiv2mn7o97pMRBB9fTVqCXjYLNnRE3oCv0+qQF8RBjcL2btapFADm3c18EKocsT3Z8x825IqCQYKvQD1MkOMvArInsCq4b6WLZ2c9C2jaK5nfIzGHeT74Ki0Idqdbzkvn6FTdhPs6syUESjMToNMI6HG4ZF8PR/Y3SPjtPOwHHvwErXwKgVrzOFxn/zWOXfgmu0ioMSSy1TAAHF0PVH7HyryPf8ZW+YZk4LSfKK0YAuChep52G3Deg6zS8Ycbpaqs2Mfs3YAvELJSEzz95C/tlhHALBxq+ikj0YBkKbg42dztkX7igVK4aWqu1Nh4ObsKpehB3/fZSIGYcDG73fkaU6+5n0ZtEuaMWciqlwpmRGUx024sRJ2YDo3oxEgba47r7otSk8quZ02qRrbqoCYjwTDgXeHjNqhRetREP4rUazXyCmNiQarcGwAAJhWkYmpRKhwuEW9trcQXh1m0fMHEPMwdw7qxqlNQTQHMVt4N+KwOF+ql4KTEO6gBfHw1giBEpQKKS4yJBm1ww/Vnj7E8bFoJMOMH7GKk6m/iTPEMaqYM4fQTEOBkrdGwgA1gDeHq9gIvLWT9U5ILgOv/qzR6q/i219eo77BCFAGDToM0cWAa73HUn2FvX413+qkz1PSTNJKjL54agAXkm9yTUa8v8r8D99XsexdYdSOrNhm3BPjxV8CvTgKLH+81MOQLBLmc+6xlwPdeAzJG9OnYhxIm71EJgciT+vg0H/OrMHbJHcB9g5pAZd3efWoCIQgCRmapfDXS6zt1CfK5J1wlQB1IeQd0gXpuRZXxS9j5wNLI/HWyn2aa776JmcDPtgI3fhiVlzYZdNjqZh6pmZpDACJUalSVT6IoyqbtrCSjR1+ngU49AXEa1LT1OCIuBwwV7quZ4TUjBAC+N5tdwP+y4Sg6rE5kJBowrTgNC6T+Jxu5cdjlltNkvp4aJagRRVGWyxMNWv/eFj8zoKLRqyYkk/AXTwKb/sy+P/f/sZJdADjle0zZ0CfClaN0S81ONiKnt4Z9g4zSLdVLpZh0GSvb7GkF/nY20HqCKVI3fcgCumJJRagM3PeDw1NP+akmCLxNej/PfVITyCx8oon9zOOCkNNPslLTN1lf7qETSCHivprKb1nKKHMMcPkL7OKs6b1SRb1AKE4PMFl+GBCSURhgPVMScwCIrBzei2BKTaCybl791JunBoDcq4YFNeyz1+5izysI4Rt6jTqNPFu32ysF1d6fJmGOVq+MMPjmryqlZrr//c3pgMHPQjUCjDoNtklBzSwNU2pcvViq/KJKP1nsLtmXleml1FBQM0B09Dj6PiKhF3589igsmpSHW87yXdldPK0ACQatvFo5e2w2tBoB88dlAwB2V7WjodOKFgubp6ERfBtMFaaxk63F7kKLxY6t5czBXpaV6F825SXHdXvl8tRodBWWu28mBljZbHoG2PAw+/78h4ApVyr3afXALZ8AP98BXYoymHSoqzQAkCEFjq3eLeA1WqUvhNvJGqXd/LEyqLFEmnpduYWVRQaBK2j56nLuATAJc2Rfjcos7HS55ZTnaMlM3BFq+ikK1U+AsopuD9AYUJ7JBrCOuFe/ElZ7+RqpK3eCQTvgfoCBxGf+UzBkX42nWdjlFgMahQElOGj2qX7iRuHeg0zFLKwoNa0O9hnISDAoPblCRBAEOZjyHgPSGmDkS9SZeSPzx9XuVDoJ+1NqooxRr8VW9zh2CJrDEOCOMP2karwnZRMSDFokGHQoyVTSZAPdowaI06BGnX7qr7LhyYWpeP76mX67kSYZdbhIKu8GICs0OckmTJW66H52qFEeZJmZZPT5xzXptXLX4MrWHrwh9Rq46JQC+CVjJHPdu2zA/5YBX/8JswS26upLBVRbT5DGe9tfYfNMADYfiBtpPX6RFCA518MwOHkINd0LBD/ptfi7sE65Cph0OZuHdOOHQEq+cl/uFECfyHw3jb6rXjWKUjNw3YTV+FNqatpY12qjToOxeSxQCDn9FCVPDb9QBpzULQjA1GtYldJFfwZyJ4b1/HJrhPSE/vNVDAHMvQx29CCAr0atwKQ5m4EXzgb+p/yfcyXcO/gPNf0EKEFNRWMbq1wD0GRnzxtp0CmXdXv1qhmQ9BPABrdOUUYFMZOwn2GwUcao0+CAWIJu0YhUoRujhZrw00+i6JF+avLKepSSUjPwdNmcsrw8WCsxbhjWagScPSZb3r5gHAtwnv/smHwxCRTtcplv7d5a7Kpqh14r4MqZAXwGgqCoBDv/DXz6AK7dfzuKhfq+eWosARrvHV3HgieADVbj3V4DoF6xDeVybo7sqfEzrA9aHXDVy0wh8E4XaXVA0Uz2fZDW8wBQ2+ZHqRnA9JNc1q0Kao5LqaeyzEQ5DRR69RP31PQx/ZTQS/oJYKrgiuPA1KsC7xMAedL9ME49AYCZN98LSamRfDVeFVDy4tAM6N65iSkP2/7FypQRTKkJzSgMKEFNQ3OzvK3Rxh4XqX0gMUBA1yY33uvnoAbwrKDzZxLuB0x6LZzQYaeb9XaapTkUtlJTW1sFOKVrRmqRUnQjZRMK0sxyeo+CmgGEV2z0l6emN6aXpOOxy6fgmWune5RCX39GKQpSTTjeZMF977ETSKAPRpHUj+afX5cDABZOyguuPF3yLLDkKeCs5UBqCTRw43TNgT4qNX6Cmro9wNs/YFU+U7/HWrv3godSEwNBTbAJxL0i+2qCm4Vr5BEJ5gFtvMcZlZ0EQWCSPD9x8XLuEVmJchqJByu9ES2lhquC/trvywgCYE6L6PkDVhEOM0L21AAqpWafR9qUexN/o3tN5RMTgZrtAFSemgBKTYI+dE+NtUuqCtWZ0NTNHh9p9ap5sNNPAAtkpMnzKJzZ/68HZTzGFpGloGZpDoWt1Hy3kxWbNCAdbo3Bo/IJYIUNBZI9goKaASDR6Lky6FdDWC9ce2oJLpyS77EtK8mIF2+cjSSjTs5VB/pgcKXG5mQnmet6a8+elMMG4p33WzbID8BM4XAfPTVeLcW7W4DXrmaGvrK5wMXPhFSCnJVkxOkjM3D+xFy5Kmsok+GvpDtUuGLWi1LDg82CAR6RwDEbtLJ3i6s1clCTnSgbfjvDNQpHzVMT2uuGCzfdD3elxhRO+ilrDOv/Y++UR5sALKi/XPMFLnNI1TkZUnfnSjZZ2l/w73aLsjoUSvopxaRHZqIBCYLUeqIPE7o5XKnp9ko/+ZzP+ptL/8qmwp/6wwF5Oe6jks3CwuGwg5raStZbrMadgeNNFo8eNZzzJuQi0aDF9OL+n1PnTdwFNeoTalqCfsBr6ENhQn4Knv3+DNlHE0h9UbvMyzITcMaoMC54Ui+PWZrDaOyywRGRBV7xNfBUBLa8CHTWsJPbNa8qlU69oNEIePNHZ+DvN8yKCR8DN0a3RnJhLZoNQGAXh+ptwKf/D3jtKlYJ0dUo71brMfdJUmoG0CgMqHw1jV5BTVYikk2RpZ9S+1j9lB5K+qkPVMnpp/hQakJKP2n1bA4U4DG01d50HI/qpQ7aZ/9KuThXsaBGXf3EmzhaVROiQ0k/Aezzlghp8aXuJhzmhG6OWQ5qvNNPIXZHjxYZI4Bz7w/LyN4XuFKzwz0Gbggo1TQgxdncy6MURFFEYwMbA9MiJmN7Ravfzs6/vXgSdjxwAUoyB/5/aOhd0fsZtfQ9lCsbzh6bjSevmorxecm4cEqe333U8vi1p5aEFwwUsa6sozU1SBU7ZVMyTm5mHXBDpFW9snHagS3/kH6Be1gp4jAlqKemN0ypQK5Uwv73c1jr/iOfAB/9CnhqHPD2DbB2tcmyboGHUXiAgxovXw0PakZmJcremFDST263KCs6fVVqUs3cKBzBex8Cygy14a3UhBXUAKxbMwCsfwiwdQKiiBm7H4RZsONY4nT2Py+dV1C1BRBFOY3jFpXgVx1I9NZRWH7prEQkCDyoUXUTjtA+kCDPfwpkFB6614a+wJWaTiSg2sAqc8fY9oX8+KrWHmitrL1EK5Kwo6JV7qXmHWD226T6Xoi/oEZlUuyPxnvR5LLpRfho2TxMLUrze//IrEToNAIMOk1gg3AgEjNZ/w4AMzRHUNfeA5z4Anh5EfBu6FJou9pTs3810FXHymknXRbe8cQY6vST9xiBkOAXCICl6c65HyicxXxI+1fD+fZN0MKFZJOOvbeDYBQGPCugrA4XqiXzcllWorxA6LT1rphY7E7wt6mvnprsZPbe17VblYGiUcJic8qpkmHvqTGE4akBWNCSWsx6L639FbD7LZS2fQubqMeGMb9mzSfzprBS5Z4WoOU4DDqNPOiSr+h5usuk10ATYjn26JwkD6VGNihHeA7nKvfH++o9tvfaoiLGMaoCjdZMNqtunGN/yI/fdrIV6YLUK0hMwraTqqBmkPyp3sRfUGNWBzVDcwp0qGQmGfHSjbPx+q2nRWaYK2bejpmaw6hrtwFbX2bba3f7DgMMgMfK5tu/so2zbgk57RSr+FuBhsX8XwELHwNu+wK48QPWifiH64GbPgJ0ZiRVbMD9ulcxMjsJgqMHcEon9AH01ABKULPtZCvOefIziCLrHJuZaAhLqeHDLA1ajceJNRKKMxKg1Qiw2JUmedGC+2lSzfo+K0pDnZA7CnPMacBlL7ABnzv/DXywHADwJ+fl0GSxBRJ0BqXfSuV3ABQ1hauaskk4hMZ7nNNHZiJBCmpEQ5Iq5RHZOfyGM8qg0wj46mgTtlcw5WFXZZvS7HQQ+qsMBPxvrtMI8vl/fBhBzdaTLUgDC2paxSQcaeiSh40Olfcs/oIa1YkqUulyKDFvbDZmlUW4epcMq7M0h9HSVAcc/IBtt3eyjrghwFc2uR27mT9EawBm3dTLo2If9Qo0ogooczpwxu2+pZylZ7DutwBu1H2CZe5XWLt/gL23hiQMJGNykqHVCOi2u1DTboVeK+CGM0ohCIJS/RRCUCc33jPr+uyZMuq08kr7uJ8p4uHSbXfit+/vw3OfHcU3x5kiNtxNwkAE6SeAjfk46y72vaMbFfoR+JtriafqXTSb3VaxoMa7rJubc0NNPQGsIWemgX2G2l0GWR2I1EJQnJGAy6az4cLPrD8Ch8uNX73LGgteMq2gX2YCDgX4KIsxucnozmN/p1HOY2w2XwhsLVeUGiRkQBSVjvRD5T3rhzGkQ5tUVa40Uuly2CBF6qcIx9Bx/F02xZvTWt5rqsPpcsuN17L3SSrPlKtYlVUckJaoR6fNGVkFVDAmXoL/5dyGixpewILmN4HVb7Lt5oEZZqkmNUGPp6+ZhqP1nTh1RCZmlKbJK2w5/WR1QhTFoMFKtLoJc0ZlJ+JEkwXHGrtw5ujgTcvaexzosbvksSDevPldJf65qdxjm8+k+2GIEtSEWSQw/1fAyU1AzXY8abwDzk6dXOUEACg+FdgMX7OwV/opVJMwwPp5TcjQAC1ATbdWPu9k9WFhevuC0XhnexU2HmrEPf/ZjQO1HUhL0OP+peE1a4wlTh+ZiZ+fMxpzx2bDZnehTkxHntDKSvDVKXE/dFgdOFTfiXR9JwAgMzsP6FTuHyrpp7gLatSemqFsFB4QMsfAqk+FydGOOTUved7XdhIonBH04dxPk4xuGA7/j2087cf9caRDkowEAypbenznP0WBf7gvxrcOO35WchK5aGHD72bcEPXXCYWLA3Sp5gGKyy2i2+6Spx/7g6efkvvop+GMzE4CDjTgmNdwTU6P3YX3dlZj7d46bDraBKdbxGkjMnDDGWW4YFKuR9XjF0dYxVlRuhk1bT1wi8CUoqHfK6mvcE+NLRylBmCVUDesBhwWfPOHbQBs/pWa+n2ArUsZaumTfgo9qAGAMeksqDnSxlLjOo3QpyB5RFYiLjqlAKt31uDdHaw44tcXTui3LvNDAYNOg7suYD1qNh1rwlb3WCzVfsvaS/CgpvkYq3CbfIXHImpHRRtEEcjWdgMiUJBfCLDqbmgimMHVX8RfUKM6qQ4VuWzQ0GjQkTkdprrPkODuYumNEfNYN+DWk70+nJczn2Kqg+B2Asn5QP7U/j7qIUN6XyqggiCKIo43WrDLdT5uuHQecnMHptwzXEx6DXQaAU63iA6rI3hQIys10TnljMpmDdmOBUg/PbB6L1Ztq5J/FgTg2xMt+PZEC04pSsWqH58Jg04Dm9Mlp5z+8YNZyEoy4lBdJ2aWDt/KPU5Ys5+80RkgavWySumxQEwpAFKKgI4qoGYHMqX2/zxNG06PGjWlySyYqe1hj0tPNIRsNA7EHQtG4/1dNRBF4PSRGbgq3IKLGEYrCNjGgxreCFQUgTeuBZoOMQ/V6PPk/bdJ8wUztRbACYwoLgbQBoD9/cOdwdVfxLWnZqhXPw0EzsLZyg/jlyiDL/lsjyC0S3OfJhrYVHFkjo7y0Q1t+tSALwiNnTZ02pzQCEDpIPR5CBVBEDxSUMGIVjdhDh/hcDyAUrP1JPOE3TSnDBt+cTY2/eoc/Oyc0Ug0aLGrqh2fH2bqzNbyVlgdbmQnGzEuNxlZSUbMGZ0lX/CHM+ZwjcJedFidcLhYoOGjehcrvhqelmjxST+FF+CmaSWlR2RpxGicv8fkJuOmM0egJCMBj10+NSZ6ZEULrUbAFmm4JSq/ZZ2iq7aygAZg7T1UsP8pEUkuNgKjrKQIJmnUxlAquom/oIaUGg+MI+fI3zumfh9IL2U/tIWg1EhplzHaOraBV0DECXK31CgHNTylUpyRAKNuaF9clQqo4Ck4Ze5TdIOa6rYen66wFpsT5c3sPfzpgtEYmZ2E/FQzfnHBOFx3Guu6/Y6k4vDU09wxWXF1QQNUAy0jUWqgKJQJBq1vEMj71RzdgGwpqGnstAHdLcip+BBauMJWagQH+5tawM7b0fJwPHDRRHyxYoE8Yype0GgEHBBL0Q0TYG0HGg8Cu15XdqjeJn/rdLmxs7INCbBBK7L/dX1iptxuZKj4aYB4DGrIU+NBxtjTcQyF2OEejUMJM4E0KagJIf3EO7qWoYZtyIyvoKZPDfiCwFMq/MI9lAm1q7Ci1EQn/ZSeaJC7vvKGgJyDdZ0s959s9PFHXCGlF9YfrEdbtx1fHm4CwJpdxhthzX7yA/fI+D2PjlsEaPTAya8wvvUzAEBbRyfwysWYv+ceXKvdgIRw1TA7+zt3gys1tCjtC1pBgAta7NdI5+0TXwB731F2qNkuz/n6+lgzuu0ulJql1hJaA2BIlNO0gzHjKRBxF9Twdv6CMICtsIcwgt6MB4pewuX232JvbZdKqanwGFznD97RtcgleReyxvbnoQ45uDEu2kZhnlIZGQMrR2X+U/D0U3uUq58AJejzNgsfqGXy+MT8FJ/HjM9LwcT8FDhcIl7+uhz7pX3n9FJBNRzhQY3DJUY0JqVFHlXgJ6jJGAnMZaXfo7c9hGR044bOv7FhtwAWaraEbRSGnQX7Fp5+GkLqQCzCPTC7IKWgvvoDU2ySCwCdpN60MCfwG98yO8Kl46RWB1Il5v+dXoolU/PxgzPLBvrwAxJ3QU1xegLOHZ+D/zutFLohOPdpMJhckAoRGuytaQdSCllzLZcN6KoP+ri2bgc0cCPLISk1WXHmqZHnP/WTUpMz9JUaZVK3b2BX32HF3up2j/uj5akBVEFNg6dZmAc1E/wENYCi1jz32VEAwKSClGFd8RIIo145/0Wi1rRYeukVc9ZdQMYo6Lsb8KrhMVwtfizfdZrmAFK1YTZOlJSa1NQ0AOSJ7Cs8qNkBaaYXP9+fco3SP6t6Gxo6rFh3gN134WipLYLU7qMwzYxnr5uBGSVDx1gfd1d1jUbAizfOxsOXTh7sQxkyTC5k5at7qjtYuWaKVAHQi6+mtduOQqERetHOWqOnFvf3oQ4puFLTX+mnWFBqeDOvDj9KzY0vb8HSZ77C54cbVRO6o1dwOSqHvT/HvdJP++Wgxn/V2MWnFECrEWST69wx8Zd6Ajxb5lvD7VUDJf2UHii40JuApU8DAKZpjgEAumb/DE2GIhgEF8Zatvl/XCCkoObMCaXQawWcFad/t2jBg5rdGANA5Sc75TqgcCb7vnobVm2rgtMtYmZpOopNrOP2QA/WDYe4C2oIX3hQc6C2g8nQ6hRUENp6HBglsImtyBwFaIa2qTXaZPSDUVg9XymWlZrKlm5ZMbnvvT3ywNRoKjUjs3yVGrdbxKE61hFsUoF/pSY72Yj5Kg/NvLHxl3oCWPWaTrqwOXtJNfujNVj6iTPybOCUawEAW9xjUT51OfYlsqafY9q+Cu8FpfTTohmjcOjhxZhWnBb2MRMKGskY3y4mKAN2C2cC2WPloEas2oo3t7DrwPdmFwPdfLDu0FFmvKGghkBpRgKSjTrYnW42jTlEs3Bbtx0j5aAmvlJPgDL/qb3HAVckQy39cKLJAlFkikYsyOs8SPFWajYda5K/r2zpkX1CUfXUSEHf8aYueajoyZZudNtdMOo0KMsMrHRdPoOpkWa9Ni560gRCp5WCGlf4n1/FKNxL6m7p03g6cRlusd+NRosL242sMqqk5etefXse2FhQIxiS+tyfhlCUGrdbBCZcxDby5qk8qKnbg/qWDiSbdFg6tUAZn0NKDTGU0WgETJRWtXur21VKTXnQx7V1OzBK4H6a+Kp8AqTJ5GD9qtp7KWkOFX7xH5WTFBMlxkr6yfP3//ooa2jnvZpOjaJSU5xuhl4rwOpwo1aaP8PVoXF5yUE9cwsn5eK2eSPx2OVThnzZfH+i17D3KOpGYY8XMWN31hJ0IAmNnTbs1k1Cl2iC2dYE1O0K/QWl9BMMQz8tGwtopfOLSxSBuXcDd+4Cpl7N7kwvA8wZ0LjtGC9U4LLphawEX1ZqKKghhjg8BbW3uj0MpcahUmriL6jRazWyRyTYUMttJ1tQ124N6TkVP83QTz0B/tNPoijKSs29i8fj/Im5yv5RKukGAJ1WUWN4Cmp/jeSnyfOfelI/9t4LJ+BSaahhvCIrNREojS3BSrq94CW/jV02dDi0+Mo9hd1x+OMgj1LhcrDiBYCCmighxbNMZdbqWCDDEQRZrTlFcwxX8k7LPVJQYx666iYFNQQANgUXAPbWdABprEFZMKOww+VGQ6cVIzXxq9QAql41AXw1Rxu6cMVfN+PH/w7NFHlcrnyKjRO3v47Ch+o70dRlh1mvxfSSdDx48SSkmHTISjJGfT7MSK9xCXI5dwA/DeEJV7MiUWqau3oxCquQg5pOG7rtLmxwT2N3hBrU2FVm8AGeVD9ckdNPov+A1lXAZv9N0xxDSYbU2TwG0k9xN/uJ8M/kQnYR2F/TAVfqFGgBoL0acDlZFO/FyeZuGF0W5Orb2IY49NQA7IRe3twtn+C9OVzfKd/2NskaUHquxI5S45t++uoIU2lOHZEBg06DgjQz1t11NiDAY5BkNGBl3fU+QU2gcm7CE70mck8ND+RD8X5lJylBTY/diY2uaYAerMHbvveYp0OjBWydwLGNgKWB+W0EARi7iLWZAFjTN93Q95rFAnL6KYBK1519CpIBnCIcQxKf6xYD6ScKaggAwIisJCQYtOi2u3DcmoQxWiOTezuqmfS763Vg5k1AGivbPtrQhRGCNB4hMZsNP4tDeH+Txi7/PTdqpEqmbrsLnTannK757FAD7ntvL35/xVSPxm+8vT9XIIY6ckfhHkWp2XSM+WnmjM6Ut+WkmPrl9XnwsmprFWaUpKNGSvOND1DOTXjClZpwq5+sDpc8bTsjhCZ4WV5KTSPS0VUwB0k1XwOrfsCa9WWMAk58Dri8Fgg7Xwcue4F9T6mnqKGRlRr4XXB1pE9BMoDRmhrA0QloU1Xpp6Eb1FD6iQDApEjegXVPTaccvKDyO+CVi4EvnwL+tRToZE2YjjV2YSQ3Ccehn4ZTmMY6bPLgxZuaNsVLU6/y1azZU4uq1h6s2VMrb2vvcchpnKJ0c38cbtRROgozpcbhcuPb4zyo6f9S6YWT8nDu+BzYnG7c9TYznRZnmKNaZTWc4Z4aR5hKDa980msFJAeZzs7hSk1Tl00eaNm0+AVmUDWlsc61Rz9lAU3GSKbcTLyUKTM124HyL9gTUeopamhVQYw/saZdk4ZqUVqY1O9ntzGg1FBQQ8goZuEOxSz8/h1MrQGA1nLg35cDPW042tCFkRrpghxnnYTV5KcyBSJwUKNsr+uwqraz7ytauuVtVa3s+8xEQ9gTjAcL7qmxOd2wOlzYVdkGi92FjERDr2bdaGDQafD89TNx6bQCedtAvO5wgVc/hZt+auF+mgRDSFV63FPT0GlDt9S92JSSDZx7P7B8H7D0j8B5DwK3fwP8bDtwzb+Bq/8FTLqMPcHmZ9ktKTVRQ10W7y8F1WVz4ohbMgg3HgDcLjY6ASClhogNeFDz3s5q7O1m38NpZR/g6/8LJOUC9XuB165CQvVXGC9Usn3iWKkpkJSa2jb/1U217T2q79VBDdteqQpqKlvYtlhRaQAgyaADv6Z1Wp346ijz05wxKnPAeonotRr84eppuFGaP3PuhJwBed3hgKzUhJl+au5tRIIXPKjpsjnlC6g8pduYBMy6CThrGZAzAVAHSbNuZrfSDCIKaqKHVqNWanyDmk6rA4dEKahpOAj0tAGQ9hvC1U+xsRwkBoS5Y7KQmWhAs8WO/1UYMVkPuDR6aL/3OlB6BvB/7wL/vBCo+g6P4juAt/eIs0GWanhQUx1Aqan2k34SRVHev7qtBy63CK1GkJWaovSE/jzkqKLRCEgy6tBpdaLD6pDTaWcN8IBIjUbAby+ehF9cMFb2+RC9I3tqwlRqZJNwiEMlk4w6mPQaj3EMIQ20LD4NyJkINEjpDwpqooY6/RRQqZGDmv2Kn8aY4rd4ZKhASg0hk5tiwlf3nIMnrzoFB7MX4lPXDDyTcR8LaAAgbzJw01pYJlyNBjENACBqjcrwsziEe2rqOqw+Jwab04UmlYGYp59aLHbYnOzk7nCJ8vaqVkmpyYgdpQZQetV8tLcOh+u7kGDQ4sIp+YNyLBTQhIdS/RSmUtMVYjdhCUEQZLUGYF6ckCrhBEFRawDy1EQRjertd/lVapw4LKefDqrKuYeuSgNQUEN4YTZoceXMItxy4Vn4oeNurHXM8NwhdxK2THsUp9qexY8S/wThJ5uAlMG5gA0FspON0GkEuNwiGjs9K6Dq2z1/5g34arxSVTwFJQc1MaTUAEpX4b9/yVIEV80simrnYKL/UNJPYXpqQu0mrCJbNQndrA+ji/PUawC9pNCQUhM1PIzCAZSao6LUnNLSCDQdYd8PYZMwQEENEQDZANvum1Y52tAFQIA2f0pcm4QBlpfOlcqVvVNQ3j9zRcZ7e4Uc1PD0U4wpNVIA09bNKqB+IHlbiKGPXk4/hafU8KAmnGaKaqUmLCO8KQWYcqX0wPgcPtofaHsxCndaHeiGCa0GadF6chO7HcImYYCCGiIA+VJapdPqRJfNc1ghb3Q2OgamSA8Egcq6uUmYmynrAwQ1VS3dzGcjKTXFsRbUqFI+C8ZlY2Q2fS5iBV2EzffkYZYhemoA76AmzHlb5z8EzP81cMZPw3scERBBEGRPtr/0U5fUXqIlcRTbcPJrdktKDRGLJBl1cv8J77lFRxsoqFGTn+a/rJv/PF0a6tjUZYfN6ZK36yXpv6KlGx09TnRKwWNhWmyln3hXYQC4+awRg3gkRLjIYxLCrH5qjSj9pDRgNIcb1JjTgPn3KP2ziKjAU1D+/vz8fNSRLKnxrSfYLSk1RKySJ6WgKKgJjlzW7fU+8e62kwpSYNCxf7WGDpsc1PAJ1pWtPaiUUk9ZScbwT/iDDE8/jclJGvCqJ6Jv8MA6YqUmjKAmK1nZN2ylhugXeNuFYEpNT5pXyw5SaohYhQc16l4rzV02tHY7IAh87g4RqKy7Vvq5IM2M3BQmvdd3WOWg5vSRrFtnRUt3zPppAOD8ibnITzXh3gvHh9SIjRg66DSRDbRskkzx6pRSb3gYhWOkueRwR1Fq/BuFAcCeMc7zDlJqiFgl349Sc0RSaYrSzTCFU8EwjCkI0FWYVzkVpJmRn6KoObx3DQ9qGjttOFKvvK+xxpzRWdh877k4Z3zuYB8KESa8+skZRvWT1eGSUxNZSWEENWpPDZ07hgTcLOzfKCx5KbPGAFAtVqikm4hV8lKlC7Gqvb+ceiKVRiZw+okrNSbkSoFPRUu33LtmQn6K7Fv65gSblxRr5dxEbKOMSQhdqeGtCww6jYefqjf6ZBQm+gVNMKOwFLgmJqUAGSqvXAIFNUSM4k+pIT+NLzyoabHY5WF9nVZlOGV+qhl5UvppR0UbANanIz1Bj+IMFsRsLWeNrWJRqSFil0gGWvKJ9NlJxrDSjVke6ScKaoYCXKnxl37i568kow7InqDcEY/ppwMHDmDx4sUoLS1FaWkpHn30UYh+IkGOKIpYuXIlxo0bh8LCQsyfPx/79+/32KetrQ0/+tGPUFJSgsLCQpx77rnYvXt3fxw+IaF4apSghsq5fUkx6dg/PhR1hr9nqWY9Eo06WfXaUcGCl4I0EwRBQLHUPZh3GOZBDkEMBHKfmjCqn7hSkxWGnwYATHqtrOyQUjM00AYzCttY36kkow7IGa/cEW9G4aamJixYsAALFy5EeXk5Nm3ahNdeew0rV64M+JhHHnkEL7/8MjZs2ICqqipccsklOO+889DW1ibvc8UVV6CnpwcHDhxAdXU1LrnkEpx//vlobW2N9q9ASChKDbtQi6KI/TUdAIDxNAlZRhAE+b3igy25aZhvz5Ma9PGqEa7ulHgFMaTUEANJJH1qmlRKTbjwFBQZhYcGGsH/39/hcstzupJNca7UPP/888jOzsayZcsgCAIKCwvx8MMP46mnnoLD4fDZv6enBytXrsTDDz+MwsJCCIKA5cuXIysrC6+88goAoL6+Hu3t7XjhhReQmMjaZP/85z+H0+nEl19+Ge1fgZDg5tbWbgesDhcaO21ottihEYBxecmDfHRDiwKvBnw8uOGN+bjqxeHbvZUZvp0gBgK5T0046acIKp84/DGk1AwNeFDrPaWbl3MDXKmRghqNHjAO7XN/1IOaDRs24KKLLvLYtnTpUjQ2NmL79u0++2/ZsgVdXV1YsmSJz2PWrl0LAMjNzcXWrVuRkKBcACoqKtDe3o6UFP+Kgc1mQ0dHh8cXER4pZp08o6Wu3Yr9tew9HJmdRJVPXniXdfMyeN6YzzuoKfAT1GQnG+l9JQYUuU9NBOmnSIKaEVlsUcpbHBCDiyZA9RM3CZv1Whb45kwEZvwAmP8rYIi3bYh6UFNTU4OCggKPbUajEZmZmaiurva7f0ZGBkwmr5VsYaHf/QHg2LFjWLx4MebNm4ezzz7b7z6PPfYYUlNT5a/iYupEGS4eaRVVUDMxn1JP3niXdSvpJxa85CQbPc4F/tJPlHoiBhrepyackm4l/RR64z3O3ReMwzPXTh+0Ke6EJ9oASo1sEubVbRoNcPGfgXl3D+jxRUJYQU1jYyOKiooCfq1cuRJ6vR4aje/TBnLJh7v/22+/jRkzZuCMM87Ahx9+GHC/e++9F+3t7fJXZWVlGL8pwZG7Cnf0yH6aiQUU1HjjXdbtnX7SazUe1R8FkoKjTjcVUzk3McDIfWoiKOmORKnJTDLiolMKYNSRIjkU4M33vP/8XKnhLSdiibCOODs7G1VVVUH32bBhA2pqajy22Ww2tLa2orCw0Gf/oqIiNDU1wW63w2BQIv/a2lqf/X/729/ihRdewBtvvIELL7ww6HEYjUYYjSRx9hV1BdQBSamZQEqND96eGl4Fla9KO+WlmOQLAg9mTHot8lJMqOuwklJDDDiRjEmQS7ojCGqIoUWg9FOnVap8CqMP0VAh6umnRYsWYc2aNR7bNm7ciIyMDMyYMcNn/xkzZiA7OxsfffSRx/Z169Zh8eLF8s/PPPMM3nrrLWzbtq3XgIaIHvyifLzRguNNFgCUfvJHocpTs7e6XVZsClRKTG6KKsBRBTs8BUWN94iBRh6TEGL6SRRFNHWyCr5wugkTQxN5TIK3UZgrNRTUADfccANqa2vx3HPPAWCKy4oVK7B8+XLo9Xqf/fV6PZYtW4b77rsPdXV1AIBnn30W5eXluP766wEwU/BvfvMbvP/++z5+HaJ/4f1VvjjcCFFkqzNaofmSm8reE5vTjaXPfAW7041Eg9YjeOEBYnay0UN+v33BKCyZmo/Fk/MG9qCJuEcfZvrJYnehx8EaTFJQE/sEVmpUjfdijKgfcXp6OtatW4c77rgDjzzyCAwGA2699VasWLFC3ueqq64CAKxatQoAcM8998DlcuH000+H3W7HuHHjsG7dOqSns3bMGzduhNVqxYIFC3xe7+qrr8Yf/vCHaP8ahES+pC40dCqt/QlfjDotSjISUNHSDb1WwIVT8vHDuSPl5maAos4UeJVtzx+Xg/njcgb0eAkCCL+km6dPEw1aJMbgBY/whJ+evJvvcaUmyegrRAx1+uVTOWnSJGzcuDHg/TyY4Wg0Gtx333247777/O7/gx/8AD/4wQ+ieoxEaHiXIlPqKTB/uW469lS344KJeX7VLG6wnlJI7yExNJCb74VY0s0rn8LtJkwMTQJN6eaemlhMP8XeERMDSr53UEOVTwGZWpSGqUVpAe+fPzYbHy+bh7Is8s4QQwN5TEKYSk0k3YSJoUfAPjXW2PXUxN4REwNKRqIBBp0Gdmk2ESk1kSMIAnViJoYUykDL0JSavpRzE0OPQEbhTlvsempoSjcRFHUDPpNeI3cEJQgi9gm3+V4TlXMPKxSlxnN7l3fzvRiCghqiV/gwxnF5KXIHSoIgYp9wq5/kCd2UfhoWyM33AhqFKaghhiFcqaHUE0EMLyKtfiKlZnggj0kIUNIdi54aCmqIXlk4iVXzXDSV5rUQxHBCH2H1ExmFhwe9DbRMNlFJNzEMWTwlH4tpAB1BDDt0EVY/UUn38EDKPvqkn2K5+R4pNQRBEHGKXP0UglIjiiKautiIBEo/DQ8CpZ+6bNLsJwpqCIIgiFhBrwldqenoccIuGYqzkgy97E3EAho/RmGHyw2rg/2dyVNDEARBxAxKn5reg5rGLjakNcWk85hdRsQu/pQaXs4NkFJDEARBxBBySXcI6acGqnwadvgzCnOTsFmvlT1XsUTsHTFBEAQRFXRhpJ/ITzP8UPrUKNs6Y7jxHkBBDUEQRNwSzpgEpUeNqZc9iVjBb/qJl3PHYOoJoKCGIAgibpEHWoYwJkHpJkwm4eGCP6Mwn9BNSg1BEAQRU+hUngpRDB7Y0Nyn4Qe3zPjz1MRi5RNAQQ1BEETcojaC9lYB1SwFNVmJFNQMF7R+jMKx3HgPoKCGIAgibuHVT0DvFVAt3SwtkZFI6afhgr+gRhlmGXsjEgAKagiCIOIWXv0E9K7UtFiYUpNOQc2wgVc/uf14aij9RBAEQcQUHkpNLxVQrRZSaoYbfvvUxPCEboCCGoIgiLhFEAQ5BRGsAsrmdMlpiYwECmqGC1p/1U828tQQBEEQMQqvgArWq6ZN8tNoNULMruAJX4KNSaCSboIgCCLmkHvVBPHUtFhYN+H0BL2csiBiHyX9pGzrIqWGIAiCiFV0Icx/4kEN+WmGF/6MwhYKagiCIIhYhVdABat+UpQaCmqGE/6Mwnbpc6CPwWGWAAU1BEEQcY08qTtIUNPaTUrNcMSfUdglKXa6GE0zUlBDEAQRx8hDLUNIP1GPmuEFF2PURmEe3OpIqSEIgiBiDb2md6NwK/fUUPppWOEv/cRL+7Wk1BAEQRCxhmwUDlLS3UxG4WGJv/QT/xyoGzPGEhTUEARBxDGyUThI8z3y1AxP/PWp4Z8D9QiNWCI2j5ogCIKICvoQlJoWaUQCeWqGFxpZqVG28VSUjpQagiAIItbghtBgJd3kqRme+FVqXFT9RBAEQcQoOk3w5nuiKKKlm1c/6QfsuIj+x59R2EXpJ4IgCCJW6W1MgsXugt3JAh7y1Awv/BuFKf1EEARBxChyn5oAnhqeejLpNUgwxGbrfMI/fvvUUPM9giAIIlbhaQZngOqnFvLTDFs0XkqN2y2Cfwyo+R5BEAQRc/RW/aT4aSioGW5ovTw16sCW0k8EQRBEzNFb9VNLF/WoGa7I1U8iD2qUwJbSTwRBEETMoe+l+ok33qMJ3cMPOf0kKTTqwJaqnwiCIIiYQzEK9+KpIaVm2KH0qWE/q0u7SakhCIIgYg5dLyXdNCJh+MKVGq7ScV+VRlB62MQaFNQQBEHEMb2ln7hSQ0bh4YdsFJbiWWeMN94DKKghCIKIa3o1ClNJ97DFu09NrDfeAyioIQiCiGt0vZV0W2hEwnBFKykySkl3bDfeAyioIQiCiGv0vTTfa+1mE7rJUzP84GMSlJJurtTEbmgQu0dOEARB9JlgYxJcbhFtZBQetnDrjFLSTUoNQRAEEcMEG2jZ0eOQ2+ZTn5rhh/dAS2VCNwU1BEEQRAzCL2AOP9VPzZKfJtmkk4MfYvig9KnxbL5H6SeCIAgiJgnWp4Z61AxvNBpSagiCIIhhhDzQ0o9SI1c+UeppWCIbhaU/Pa+Ao5JuLw4cOIDFixejtLQUpaWlePTRRyGK/p31ACCKIlauXIlx48ahsLAQ8+fPx/79+wPu/8c//hGCIOCzzz7rh6MnCIKIH3ijNX99alqloCaTlJphSaAp3dR8T0VTUxMWLFiAhQsXory8HJs2bcJrr72GlStXBnzMI488gpdffhkbNmxAVVUVLrnkEpx33nloa2vz2XfPnj3485//jKysrGgfOkEQRNzhr0/N/poOPPnxITz32TEA1E14uKLxMgrLfWpIqVF4/vnnkZ2djWXLlkEQBBQWFuLhhx/GU089BYfD4bN/T08PVq5ciYcffhiFhYUQBAHLly9HVlYWXnnlFY99rVYrrrvuOjzxxBNITEyM9qETBEHEHUr6iV3YdlS04sI/f4m/bDyKipZu6DQCFozLGcxDJPqJgEZh8tQobNiwARdddJHHtqVLl6KxsRHbt2/32X/Lli3o6urCkiVLfB6zdu1aj22//OUvMWbMGFx55ZW9HofNZkNHR4fHF0EQBOGJkn5iq/TjjRYAQFG6GU9fcwq23ncelkzNH7TjI/oPXuTkaxSm9JNMTU0NCgoKPLYZjUZkZmaiurra7/4ZGRkwmUwe2wsLCz32X7NmDd555x387W9/C+k4HnvsMaSmpspfxcXFEfw2BEEQwxtZqZFW6d12JwBgSmEqLptehDQyCQ9b5PSTd/O9GE4/6cLZubGxEdOnTw94/5133gm9Xg+NnyhPEPy/SaHs39DQgJtvvhkvv/xyyF6ae++9F3fddZf8c0dHBwU2BEEQXshKjXRhs9hdAIAEQ1iXByIG8U4/8eBGG8Ppp7A+tdnZ2aiqqgq6z4YNG1BTU+OxzWazobW1FYWFhT77FxUVoampCXa7HQaDsiKora2V97/ppptwxRVXYPHixSEfq9FohNFoDHl/giCIeMTbKNxtY0pNolE7aMdEDAw+RmFJrYvlRotRP/JFixZhzZo1Hts2btyIjIwMzJgxw2f/GTNmIDs7Gx999JHH9nXr1slBzJo1a/Dcc89BEAT56+TJk1iwYAGKioqi/SsQBEHEDd5jEkipiR8UpYb97BwGSk3Ug5obbrgBtbW1eO655wAwxWXFihVYvnw59Hrf0fV6vR7Lli3Dfffdh7q6OgDAs88+i/Lyclx//fUAWB8b76/S0lJs3LixV+WIIAiCCIz3mATuqUk0kFIz3NFq/Jd06+PFUxMK6enpWLduHe644w488sgjMBgMuPXWW7FixQp5n6uuugoAsGrVKgDAPffcA5fLhdNPPx12ux3jxo3DunXrkJ6eHu3DIwiCIFR4j0mw2CSlxkhKzXDH1ygc+9VP/fKpnTRpEjZu3Bjwfh7McDQaDe677z7cd999Ib9GeXl5pIdHEARBSOi9PTWk1MQN6jST2y3CxZvvUfqJIAiCiEV8qp9IqYkbtKoqY5coqqZ0U1BDEARBxCCk1MQv6iyTyy2qSrpjNzSI3SMnCIIg+oyPp4aqn+IGj/STKMqBbSwbhSmoIQiCiGN8qp+oT03coFGln5xukUq6CYIgiNiG+tTEL95GYR7UUPM9giAIIibRqaZ0i6KoeGpIqRn2eBiF3aIc2FL1E0EQBBGT6FWm0B6HS66AIaVm+KPReFY/OamkmyAIgohl1OW77T0O+fsEqn6KC3SqUQlKSXfshgaxe+QEQRBEn/EX1Bh0mpj2VRCho1GNSuDN98goTBAEQcQk6vRTezcLaqhHTfzAfTVulaeGSroJgiCImESjEcAX5lypIT9N/CAPtfQo6Y7d0CB2j5wgCIKICtxDwYMaqnyKH3hAqzYKk1JDEARBxCx66cpGSk38odX4pp9ieUp37B45QRAEERW4UtNBSk3coVUZhXn6iUq6CYIgiJiFpxtIqYk/+KgEl1uEQ5r9RFO6CYIgiJhF65V+ouqn+EGr6lPjotlPBEEQRKzDPRSyUmMkpSZekJUaUV3SHbuhQeweOUEQBBEVvNNPpNTED54l3dR8jyAIgohxvEu6yVMTP8jpJ1E9pZuCGoIgCCJG0cmeGjahm+Y+xQ9ynxpVSTc13yMIgiBiFr1XSTd5auIHjz41vPkepZ8IgiCIWIWX8Nqlkl7y1MQP/ozCNKWbIAiCiFn0XukG8tTED/5nP5FSQxAEQcQo3s3WqKNw/OBhFHbR7CeCIAgixvFON5BSEz8oHYVBSg1BEAQR+3gbQ0mpiR/8pZ+o+R5BEAQRs/ikn0ipiRu0gm/6iZQagiAIImbxTT+RUhMvcI+4h1JDfWoIgiCIWMU3/URKTbzgL/1EU7oJgiCImEWt1GgEwKijS0O8oBiFlfSTjtJPBEEQRKyiLuFNNOggCLF7USPCgys1TrcbklBDzfcIgiCI2EWn8lAkUOVTXMGNwnanW9lGSg1BEAQRq+i8lBoifuABjE0V1FDzPYIgCCJmUfclIaUmvvAX1JBSQxAEQcQsamModROOLzQa3/QTlXQTBEEQMYvaGEoTuuML7qnhSo1GUAKdWISCGoIgiDhH3acmgXrUxBVaL6VGF8MqDUBBDUEQRNxDSk38opGVGheA2G68B1BQQxAEEfeoq13IUxNf8HiWp59i2SQMUFBDEAQR96iNwjShO77wTj/F8oRugIIagiCIuEedfiKlJr7wTj+RUkMQBEHENJ5jEkipiSd8lBoKagiCIIhYxnNMAik18YTGq6Q7luc+ARTUEARBxD00JiF+8S3pJqWGIAiCiGFoTEL84j0mgUq6CYIgiJjGo/qJlJq4wtcoHNthQWwfPUEQBNFnPJQaMgrHFfxPr5R0k1JDEARBxDAenhoyCscV3rOfqKTbDwcOHMDixYtRWlqK0tJSPProoxBFMeD+oihi5cqVGDduHAoLCzF//nzs37/fZ7+33noLkydPRmFhIUaPHo0nnniiPw6fIAgirlBXP1FJd3zhPaU7lid0A/0Q1DQ1NWHBggVYuHAhysvLsWnTJrz22mtYuXJlwMc88sgjePnll7FhwwZUVVXhkksuwXnnnYe2tjZ5n7fffhvLli3Dv//9b1RXV2Pt2rV48cUXsX379mj/CgRBEHGFx5gEUmriClJqeuH5559HdnY2li1bBkEQUFhYiIcffhhPPfUUHA6Hz/49PT1YuXIlHn74YRQWFkIQBCxfvhxZWVl45ZVXAAButxsrVqzA7373O0ybNg0AMGbMGOzfvx8zZsyI9q9AEAQRV6h7k5j1pNTEE95KDVU/ebFhwwZcdNFFHtuWLl2KxsZGv6rKli1b0NXVhSVLlvg8Zu3atQCA3bt34+TJk7j00ks99tFq6Z+PIAiir/DqJ7NeG/MrdSI85D41Lpr95JeamhoUFBR4bDMajcjMzER1dbXf/TMyMmAymTy2FxYWyvsfPXoU+fn52LVrF8466yyUlpZiwYIF+PzzzwMeh81mQ0dHh8cXQRAE4Ut6ogEAkJ1sHOQjIQYann6Sf47xoDas5GljYyOmT58e8P4777wTer0eGj9GI0Hw/0aFsr/L5UJXVxeefPJJrFq1Cjk5OXj77bdxwQUXYPPmzX5TUI899hgefPDBUH4tgiCIuKYwzYzn/28mCtPMg30oxACj8QpiYr2kO6ygJjs7G1VVVUH32bBhA2pqajy22Ww2tLa2orCw0Gf/oqIiNDU1wW63w2AwyNtra2vl/UtKStDZ2YkXXngB+fn5AIBrr70Wr7zyCt544w2/Qc29996Lu+66S/65o6MDxcXFof+yBEEQccSiyXmDfQjEIOAdw1DzPS8WLVqENWvWeGzbuHEjMjIy/AYfM2bMQHZ2Nj766COP7evWrcPixYsBAFOmTEFaWhrsdrvP441G/3Kp0WhESkqKxxdBEARBEAre6Saa0u3FDTfcgNraWjz33HMAmOKyYsUKLF++HHq93md/vV6PZcuW4b777kNdXR0A4Nlnn0V5eTmuv/56AEBSUhJ+8Ytf4Oabb0ZDQwNEUcR//vMffPHFF7juuuui/SsQBEEQRFzgnX6KK09NKKSnp2PdunW444478Mgjj8BgMODWW2/FihUr5H2uuuoqAMCqVasAAPfccw9cLhdOP/102O12jBs3DuvWrUN6err8mF//+tdwu92YNWsW7HY7ysrKsGbNGkycODHavwJBEARBxAXeU7l1MV79JIjBWv0OIzo6OpCamor29nZKRREEQRAEgFVbK/HL/+yWf77hjFI8dMnkQTwiX8K5fsd2SEYQBEEQRMR4p5tiPf1EQQ1BEARBxCk+RuEYTz/F9tETBEEQBBExmmHWfI+CGoIgCIKIU6ikmyAIgiCIYYGvUhPbYUFsHz1BEARBEBHjrdTQlG6CIAiCIGISb19wrM9+oqCGIAiCIOIUSj8RBEEQBDEs8C3pJqWGIAiCIIgYREsl3QRBEARBDAe8B1rqKf1EEARBEEQsQmMSCIIgCIIYFngbhamkmyAIgiCImMSnTw2lnwiCIAiCiEW8jcKk1BAEQRAEEZN4CzNU0k0QBEEQREziaxSO7bAgto+eIAiCIIiI8U4/0ZRugiAIgiBiEu8+NVTSTRAEQRBETOJrFI7tsCC2j54gCIIgiIjxLekmpYYgCIIgiBjEO/1EJd0EQRAEQcQkPkZhSj8RBEEQBBGL0OwngiAIgiCGBd5BDE3pJgiCIAgiJvFOP2nJU0MQBEEQRCziMyYhxtNPusE+gKGGy+WCw+EY7MMgiJDQ6/XQarWDfRgEQcQow81TQ0GNhCiKqKurQ1tb22AfCkGERVpaGvLy8iAIsX0yIghi4NEMs+Z7FNRI8IAmJycHCQkJdIEghjyiKKK7uxsNDQ0AgPz8/EE+IoIgYg0fo3CMe2ooqAFLOfGAJjMzc7APhyBCxmw2AwAaGhqQk5NDqSiCIMLCxygc4+mn2NaZogT30CQkJAzykRBE+PDPLXnBCIIIF++OwlTSPYyglBMRi9DnliCIvsDVGUHwDXJiDQpqCIIgCCKO4SmoWFdpAApq4orPPvssJlb1giDgs88+G+zDIAiCiAt4LBPrfhqAghqCIAiCiGu4UhPrE7oBCmoIgiAIIq7hPppYn9ANUFATEFEU0W13DviXKIphHWd1dTUuuugiFBUVYfLkybjsssswadIk2Gw2rF69GpMnT0ZBQQHmz5+P3bt3ezz2t7/9La688kr8/ve/x8iRI5GXl4c777wTVqs1pNc+efIkrrjiChQVFaGoqAi33HILOjo68PbbbyM5ORkWi0Xe991330VWVhZsNhucTid+97vfYfTo0SgsLMQZZ5yBzZs3B3yd1atXY9q0aSgoKMDs2bPxxRdfhPUeEQRBEIHhaafhkH6iPjUB6HG4MPGBjwf8dfc/tBAJhtD/LDfccANmzpyJ999/H+Xl5TjzzDOxevVq7N+/H9dccw3ee+89LFq0CCdOnMCll17q8/iPPvoII0aMwKFDh9DS0oJFixbhN7/5DZ566qmgr2uxWDBv3jwsXboUJ06cgMvlwq233orHH38cDz30EP5/e/ceF3O+/wH8NTEzSLVS0cxURlHkltJyXNYqSyiXZZEol3DclnRcfiy55mhZOqfjtptaFudodSzWtVzqKCusu7RUdEGlJGqaxuf3R6fvMabLRNM04/18PHrs9p339/v9vOc903x85vP9fgICAhAVFQVfX18AwL59+zBp0iQIhUIsXLgQR44cwenTpyGVSnH48GH4+Pjgzp07EAqFSuc5evQovL298csvv8DNzQ3Hjh2Dp6cnbt68CWtra7WfJ0IIIZX730Rh3e/U0EiNjktISICvry94PB6kUin69OmDuLg47Nq1C56enhg8eDAAQCqVYs2aNSr7W1paYuPGjeDz+WjVqhWCgoKwc+fOGkeMoqOjUVRUhO+++w58Ph9NmjRBeHg41q9fj8aNG2PmzJmIjIwEABQWFuLYsWOYPn06SktLsW3bNgQHB0MqlQIAhg8fjrt376p0aABgy5Yt8PPzg5ubGwBg6NChGDBgAMLDwz/oeSOEEFKu4usnXV+hG6CRmio15TfCndWDtHLe2nB2dkZkZCSCg4Px8OFDnDt3DjNmzMDp06fRtWtXpVhjY2OV/cVisdIVUe3bt0dRURFyc3Nhbm5e5XnT09Nha2sLgUDAbXv7/6dPn45169YhPT0dsbGxcHV1hYODAzIzM1FcXIwOHTooHe/tfd+WkZGB33//HceOHeO2lZSU0J2fCSGkjujTJd3UqakCj8er1ddA2rJo0SL4+/sjKioKTZo0wcqVK+Hu7o6ffvoJ9+/fV4p98uSJyv55eXlKv6empsLQ0BBmZmbVntfGxgapqamQy+Xg8/nc9rKyMjRu3BgWFhYYPXo09u7diwsXLmDGjBkAAHNzczRt2hTJycno2LEjt9+7x6lgZ2cHb29vrFixouYngxBCSK3p05wa3e+WfeT8/Pywd+9ePHz4EHfu3MGcOXMAAP7+/jh27BiOHDkCALh27RqCgoJU9r99+zY2bdqEN2/eIC8vDytWrMC0adNqvJ/NyJEjYWhoiK+//hoymQwKhQKrVq2Cj48PFzN37lz88MMPuH79Or788ksA5SMys2fPxpIlS/DHH38AAJKSktC+fXtuYca3zZ8/H1u3bsX58+cBlI/SLF26FHv27Kn9k0UIIURFxQCNrq/QDdBIjc5bv349RowYgebNm0MoFMLS0hJz587FhAkTEB0djSVLlmDq1KlwdHTExo0bMXz4cKX9+/Tpg/z8fNjZ2aGkpASjRo1CcHBwjec1NDREXFwcFi5ciLZt28LAwAB9+vRBaGgoF+Pq6gpjY2OMHDlSab7Mhg0bYG5uDg8PDxQXF6N169bYvn07LCwsVM7j7u6OiIgIBAYGIjMzE02aNMGIESO4ThIhhJAPw92nRg9GanisttcQ66jCwkKYmJjgxYsXKnNLSkpKkJqaCqlUiiZNmmiphbVXUFAAFxcXBAcHw8vLC6WlpTh69Ch8fHxQUFAAIyOjavcPCgrCuXPnNHb33pKSElhaWiIxMRH29vYaOQfR3dcvIaRhGLDpHB7mvIKT9SeIntVb281RUd3n97topEaHZWdn48GDBxCJRBAKhRAKhWCMwczMDE2bNv2gY2dkZKBnz56VPubg4IAzZ85Uu39+fj5Wr14NV1dX6tAQQkgDRhOFSYPQoUMH7NixAzNnzkRBQQF4PB66dOmCM2fOoHHjDyutRCJBRkbGe+/v7e2N58+f48CBAx/UDkIIIZqlTxOFqVOj46ZPn47p06e/176VTRyuK8ePH9fYsQkhhNQdA1r7iRBCCCH6oGKERh8mCmukU3P37l14eHjAxsYGNjY2WLduXbV3qGWMISQkBPb29hCLxejfvz/u3LmjFHP16lUMHToUVlZWsLKygoeHB65du6aJ5hNCCCEfDa5ToweXdNd5Brm5ufj8888xaNAgpKWl4eLFi/jpp58QEhJS5T5r167F7t27ERsbi4yMDAwfPhzu7u4oKCgAUL5o42effYZBgwYhPT0daWlpcHd3R//+/ZGZmVnXKRBCCCEfDRqpqcb27dthbm6O+fPng8fjQSwWY82aNdi0aRPkcrlKfHFxMUJCQrBmzRrulv0LFiyAmZkZfvzxRwBAfHw8+Hw+5s2bBwMDAzRq1AgLFy6EgYEBLl26VNcpEEIIIR8N7j41NFKjKjY2Fp6enkrbhg0bhpycHFy9elUl/vLlyygqKsLQoUNV9qmYbNqtWze8fPkSFy5c4B7/z3/+A5lMBmdn57pOgRBCCPloVFzJrQ+rdNf51U9ZWVkQiURK24RCIVq2bFnpV0VZWVkwNTVVuWmYWCzG0aNHAQD29vb4+eef4e/vDycnJzDGkJ+fj3PnzsHGxqbSdshkMshkMu73wsLCD02NEEII0Tv6dEl3rUZqcnJyIJFIqvwJCQkBn8+HQSU38KlqLSF14x89egRjY2O4urrCxcUFaWlpOHXqVJUTkIODg2FiYsL9WFlZ1SZVndamTRtERESoFRsdHY127dpBIpFgwYIF4PF4GrvDcEMSERGBNm3aaP0cEokEBw8e5H6Pi4tD586dIZFIMHr0aI22jxBCgLcv6db9r59qNVJjbm5e4w3ZYmNjkZWVpbRNJpMhPz8fYrFYJV4ikSA3NxelpaUQCATc9uzsbC5+3759CAkJwY0bN2BiYgIAmDZtGrp27QorKyv4+vqqHHfp0qUICAjgfi8sLPyoOjbqKC0thY+PDyIjIzF69GgUFBRgy5Ytau9/+PBhnD9/Hps3b9ZcI/Xcu++nyZMnY+bMmQgMDERBQQFWrFgBe3t7TJgwQUstJIToO5ooXI3Bgwfj119/Vdp29uxZmJqaonv37irx3bt3h7m5OU6cOKG0/cyZM/Dw8ABQPlHYycmJ69AAQIsWLeDi4lLlRGGhUAhjY2OlH6IsOzsbr1+/houLCwDgk08+qdX+165dw/PnzzXQso/XgwcPlOpx4cKFSifYE0JIXWlEN9+r2qRJk5CdnY1//OMfAMo/OBctWoQFCxaAz+erxPP5fMyfPx/Lly/HkydPAABhYWFIS0vDxIkTAQCff/45YmJiuI4PYwy//PILjh8/jkGDBtV1CvjvSYDSV/X/U8v1RTMyMjBixAi0bt0aDg4OCAsLU3o8Li4Of/rTnyASidCpUyccOnQIAJCQkMCt7dSrVy9IJBIoFAqV40dERMDBwQGWlpbo3bs3bt26BQD44YcfsHnzZhw8eBASiQRr164FADx9+hQTJ06EjY0N2rRpg0mTJuHp06fc8YKCgjBu3Djs378fbdu2RUJCQo05RkdHw8nJCWKxGB06dEB4eDgAYMiQIZg8ebJSrJeXF+bMmQMASE9Px5dffsl9PTp16tQq51a9fv0agYGBkEqlsLKywsSJE5GXl1dj2yqeI1tbW7Rq1QoDBw7E3bt3lR6PjIyEo6MjzM3NMWbMGLx+/Zp7rOLrvoyMDEgkEgDAmDFjIJFI4O7ujoSEBAQEBEAikSAmJkat9hBCSG0Y6NFITZ1PFG7RogXOnDmDOXPmYO3atRAIBJg2bRoWLVrExYwZMwYAuLkEixcvhkKhQM+ePVFaWgp7e3ucOXMGLVq04OJlMhlWrlyJqVOnQqFQwNbWFnv27MHw4cPrOoVy8tfAelHNcXXt/7IAgaFaoQqFAqNGjUKnTp3w6NEjMMawbNkyPHr0CED5SMrAgQMRHh4Ob29vJCUlwd3dHVZWVujVqxcSEhIglUqRkJBQ6dyPe/fuYfny5Th58iQcHR0REBCAyZMn4/Lly5g6dSoeP36MtLQ0bv5OcXEx+vTpAzc3N6SkpAAA5s2bhz59+uDGjRvcIpuPHz/GpUuXkJKSgkaNGlWb45EjR+Dt7Y1jx45hwIABSE5OxhdffAFXV1fMnTsXX331Ff7+97/D0NAQz58/x8mTJ3H58mW8evUK/fr1w7Bhw5CamgqFQoFp06Zhw4YNWL9+vcp5fH19kZmZiaSkJBgZGcHf3x9+fn44cuRIte17+fIl/P39kZycDKlUisjISBQXF3OPZ2ZmIj4+HlevXkVxcTG6du2K8PBwruNVoWKtLR6Ph4MHD6J///4AgP79+8PPzw9+fn7VtoMQQt6XPl3SrZG1nxwdHXH27NkqH397YiQAGBgYYPny5Vi+fHmV+/j4+MDHx6fO2qgPrly5gitXriAmJoabjxQSEsJ1MsLCwuDm5gZvb28AgIuLCyZPnoywsDC1JhI7ODggNTWVG2Hz9fXF3/72tyrjDx06hPz8fISGhnLtCQ0NhaWlJaKjo7l23L59GydPnqyxQwMAW7duxbRp0zBgwAAA5VfCpaSkQCAQwNHREZaWlvj5558xadIkHDx4EN27d0eXLl2wd+9eFBUV4bvvvgOfzwefz0d4eLjSvK0KGRkZiIqKwm+//YaWLVsCALZs2QIzMzOkpaVVO9lXIBDAzMwMkZGRCAgIUOl8NGvWDFu3buVWUX97tIsQQhqCijk1dEm3PuM3Kx810cZ51fTw4UOYmZnByMiI28bj8dC8eXMA5R/WiYmJSh/KpaWl6NSpk1rHf/XqFVatWoVTp04hPz8fCoUCZWVlVcanpaWhbdu2Sh0HgUCAtm3bIi0tjdvWuXNnro01SU9Px6hRo5S2VRyfx+Nh1qxZiIiIwKRJk7Bv3z5ucc/09HTY2tqqtKUyFZN1K0YQK5iYmODhw4fVdmqEQiEuXryI1atXw9bWFp6entiyZQs3/6tFixZo1ux/NRUIBCgpKVErd0IIqQ8G3CXdNFKjv3g8tb8G0hZLS0vk5uYiPz+f+6pOJpNxy0vY2dlBJBJxc1BqKzAwEFeuXEFUVBTs7Oxw9+5ddOzYscp4a2trpKamoqysDI0bl7+05HI5UlNTYW1tzcWpM0JTwcbGBsnJyUrb5HI5N3o0efJkrFixAgkJCbh58ybGjh3L7ZeamqoUC0CpbRXs7OwAABcuXFBqp7qkUil2796NwsJCjBs3DkuWLMG2bdtqfRxCCNGGivnBNFGYaFWfPn3QsWNHzJs3DzKZDEVFRfD19eVGU2bNmoWoqChERUWBMYaysjJs3boVwcHBah2/sLAQ1tbWkEqlKCoqwl//+lcA4Ca6NmvWDM+ePQNjDAUFBRg1ahSaN2+OgIAAyOVyyOVyBAQEwMjICCNHjnyvHOfPn49du3bh1KlTAMonIvfu3Zu727SJiQl8fHzg6+sLb29vblRk5MiRMDQ0xNdffw2ZTAaFQoFVq1ZV+hWmmZkZfHx8MGPGDG5S84MHD7g7YVcnOzsbCxYsQE5ODoyNjeHk5IQXL168V66VqXiOX716hdLS0jo7LiGEVDBpylf6ry6jTo0Oa9SoEU6ePIlXr17B2toaTk5OGDx4MPf1UseOHXH8+HGEhoZCJBLB1tYW169f576iqcn69euRl5cHsViMTz/9FGPGjEG7du1w8+ZNAMCoUaO4CbKHDh2CoaEh4uPjkZOTAzs7O9ja2iI3Nxfx8fEwNHy/Ua9hw4bhwIEDWLp0KUQiEfr27Yvx48dzl/sDwPTp05GSkqKUl6GhIeLi4pCbm4u2bduiTZs2uHfvHkJDQys9z44dO9C1a1f06tULVlZWGD16NCZPngxzc/Nq22dqago+n49u3bpBIpEgLi6u0onI78vf3x8hISFwdXXF7du36+y4hBBSYdbndlg93BEjnVTvJadreKyqW/LqmcLCQpiYmODFixcq96wpKSlBamoqpFKpynINpOHbv38/QkND1bo8XB/R65cQos+q+/x+F82pIVq1efPmKu9I/M0332DGjBlV7vvmzRukpKRgzZo1+OabbzTVRO7+Me8yNDRUme9DCCFEe6hTQ7QqICBAaTmL2sjOzoazszOmTZuGcePG1XHL/qempUEIIYQ0DNSpITpLLBajqKhI280ghBDSQNBEYUIIIYToBerUEEIIIUQvUKfmLW/evNF2EwipNXrdEkJIOZpTg/Jb1xsYGCArKwvm5uYQCATg8XT/zopEvzHGUFpaipycHBgYGFS5DAQhhHwsqFOD8gU1pVIpsrOzkZWlhfWeCPkAzZo1g7W1NQz0YN0WQgj5ENSp+S+BQABra2uUlZVBoVBouzmEqKVRo0Zo3LgxjSwSQgioU6OEx+OBz+crLYBICCGEEN1A49WEEEII0QvUqSGEEEKIXqBODSGEEEL0wkczp6ZiMfLCwkItt4QQQggh6qr43K74HK/OR9OpycvLAwBYWVlpuSWEEEIIqa2XL1/CxMSk2piPplNjamoKAHj06FGNTwoA9OjRA5cvX1b7+LWJ11RsYWEhrKys8PjxYxgbG2utHZo6dm3z01Q7ahtbm3hN1rC28ZTj+8fSe7F+2lHb2NrE0+u0/tpRUzxjDC9fvoRIJKrxOB9Np6bixmQmJiZqFa9Ro0Zqv1lrG6+p2ArGxsZ1nmNDeT4A9fPTZDs0+XwAmqlhbeMpxw9rB0DvxfpoB71OP6wdgG68TtUZjABoonCVZs+erbF4TcXWlibboe85avL50ORxKcf6ia2thlIXXcyRXqcf1o7a0IW68Jg6M2/0QGFhIUxMTPDixYta92J1hb7nqO/5AZSjvtD3HPU9P4By1FUfzUiNUCjEypUrIRQKtd0UjdH3HPU9P4By1Bf6nqO+5wdQjrrqoxmpIYQQQoh++2hGagghhBCi36hTQwghhBC9QJ0aQgghhOgFnerUvHnzBomJiQgICICpqSkiIiKUHv/9998xYMAAiEQiiMViBAQEoKSkRCkmJiYGn332GSQSCWxsbPDVV1/hwYMHSjGJiYno27cvrK2t0a5dO+zcuVPTqXHqK0djY2OIRCJIJBLuZ9GiRZpOr07yO3jwILp06QJLS0u0b98e27dvVzmPrtdQnRy1VUMACA8PR6dOnSAWi+Hg4IBt27YpPS6TybBkyRLY2dlBJBLBy8sLmZmZSjGZmZkYO3Ys2rRpA7FYjAULFkAmkynFaLOO9ZWjrtcxJycHkZGR6NevH6RSaaXn0VYd6ys/Xa9hRkYGxo4dCysrK0gkEowYMQJpaWlKMdp8L9YK0yHff/8969GjB1u2bBkzMzNju3fv5h57+vQpa9myJQsLC2Nv3rxhBQUFzMvLi/n5+XExV65cYUKhkP3rX/9ijDFWUlLC5s+fzyQSCXv9+jVjjLG7d+8yIyMjFhUVxRhj7Pbt26xVq1bsn//8p97kWFBQwHg8HispKamXnN72ofmdPn2aGRsbs4sXLzLGGLt37x5r3749i4iI4GJ0vYbq5KjNGv74449MIpGwW7duMcbKn29LS0u2d+9eLmbKlCmsX79+LD8/n8nlcrZgwQLWuXNnVlZWxhhjTCaTsQ4dOrCAgAAml8tZfn4+69u3L/vzn//MHUObdayvHHW9jowx1rVrVzZu3Dg2YcIEZmNjo3IebdWxvvLT9RqWlpYye3t7tmjRIlZaWsrKyspYYGAg69ChA5PL5dxxtfk3tTZ0qlPzNhsbG6UPi127djEHBwelmLy8PMbn89mTJ08YY4xt2LCBOTk5KcUUFBQwAOzKlSuMMcamTp3Khg0bphTz7bffquxXHzSV461bt5iFhYVmG6+G98lvwoQJbObMmUox0dHRrFOnTtzvul5DdXLUZg1nzZrF9u3bp7QtICCAjRw5kjHGWHp6OjMwMGBJSUnc4zKZjLVs2ZIdPnyYMcbYnj17mKmpKZPJZFxMUlISEwgELCcnhzGm3TrWV466Xse37d69u9IPfW3Vsb7y0/Ua3rhxg/Xv35+9efOGiyksLGQA2PXr1xljDetvak106uun6rx48YJbCqGCUCgEYwwJCQkAAGdnZ9y/fx/37t3jYo4dOwYLCwu0b98eABAbGwtPT0+l43h6euLatWt4+vSphrOoXl3lmJGRAYlEUn8NV5M6+VUW07RpU9y6dQsFBQUAdL+G6uSozRqGhYVh/PjxSttu3rzJ3bzr3LlzaNWqFZydnbnHBQIBvvjiCxw/fhxAeY0GDRoEgUDAxTg7O6Nly5aIiYnhYrRVx/rKUdfrqA5t1bG+8tP1Gnbu3Blnz54Fj8dTOgYAGBkZAWjYf1PfpTedmhEjRuDhw4fYsmUL5HI5nj9/Dn9/fzRr1gxPnjwBALi7u2Pr1q0YMmQIpkyZgmHDhiEqKgpxcXFo3rw5ACArK0tl0SyxWAwAKt9D1re6yjEjIwNCoRCzZ8+Gg4MDOnbsiKVLl+L169faTE+t/MaPH489e/YgNjYWjDEkJydj3bp1AMDF6HoN1cmxodRQLpdj7ty5SEhIQGBgIIDKn3+gvAYVz//7xmijjprMUdfrqI6GUEdN5qdvNbxy5QrGjBkDPz8/bg5RQ6ihuvSmU2Nra4vz58/jxIkTsLW1xcCBAzFq1CjY2NigcePydTsVCgUePXqE1q1bo0ePHujevTtu3LiB8+fPc8fh8/kq/0p+uwerTXWVo0wmw8uXL+Hj44Pbt2/j1KlTSEhIwNSpU7WVGgD18vP29sb27duxePFi2NjYYO7cuVi9ejUAcDG6XkN1cmwINUxPT0ffvn0RExOD+Ph4dOrUCUDlzz+gXIP3janvOmo6R12vozq0XUdN56dPNQwNDUXfvn3h5+eH77//ntuu7RrWija/+/oQ785VqIxcLmdNmzZlsbGxjDHG1q1bx1xcXFhpaSkXk5qayoyMjNi5c+cYY4w5ODiwXbt2KR3njz/+YAC4OQ/1RVM5ViYxMZEZGBiwoqKiOmm7Ot4nv8rEx8czPp/PTdTT9RpW5t0cK1OfNUxKSmLm5uZs4cKFKm06cOAAE4vFKvv4+Phwc4VmzpzJJkyYoBIjkUjYgQMHGGPar2N95FgZXarj26qac6LNOtZHfpXRtRoqFAo2ZcoU1q5dO5aYmKgSr+33Ym3ozUgNAJXhvpMnT0IoFKJXr14AgPj4ePTu3Rt8Pp+LadOmDezs7HDp0iUAwODBg/Hrr78qHef06dPo1q0bWrVqpeEMalYXOQLllx2/TaFQANB+77um/CqL+fe//w03Nzdu/RJdr2FlMe/mCGivhunp6RgyZAjCwsLw7bffqqwbM2DAADx79gw3btxQatvZs2fh4eEBoLxGp06dQllZGRdz7949PHv2DG5ublyMtupYXzkCul1HdWirjvWVH6D7NfzLX/6C+/fvIykpCZ9++qnKeRr631Ql2u5Vva93/wV88+ZNZmFhwX777TfGWHkvsl27diwsLIyL2bhxI2vdujUXU1ZWxnbu3Mn4fD43OzwlJYUZGxtzM8OTk5OZWCxm+/fvr6fM/kdTOW7YsIENHDiQZWZmMsYYy8rKYr1792YTJ06sp8zKvU9+O3fuZN27d+f+dXDixAn2ySefcFd2Mab7NVQnR23W0MPDgwUFBVUbM336dObm5sZevHjBysrK2OLFi5mjoyN3iahcLmeOjo5syZIlrKysjBUUFDA3Nzc2Y8YM7hjarGN95ajrdXxbVSMZ2qpjfeWn6zVMTExkZmZmLDc3t8pjNKS/qTXRm04NY+Uvug4dOjCRSMTs7e3Zzp07lR5XKBRsy5YtrHPnzkwkErFWrVoxd3d3FhMToxR34cIF5uLiwkQiEbOzs2M7duzQdDqV0lSOxcXFbNmyZczW1pZZWloykUjE5s2bx93Hpr68T34ymYwtXryYWVtbM5FIxHr27Mni4uJUjq3LNVQnR23WEACzsLBgYrFY5adCxf2RxGIxa926NfPy8mKPHz9WOs7jx4+Zl5cXs7S0ZGKxmM2fP19l+FxbdayvHPWhjhWq+3pGG3Wsr/x0vYZBQUGsSZMmlR5j06ZNXFxD+ZtaE1qlmxBCCCF6Qa/m1BBCCCHk40WdGkIIIYToBerUEEIIIUQvUKeGEEIIIXqBOjWEEEII0QvUqSGEEEKIXqBODSGEEEL0AnVqCCGEEKIXqFNDCCGEEL1AnRpCCCGE6AXq1BBCCCFEL1CnhhBCCCF64f8B9dbfC5YkJvgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_shift = 6\n",
    "tmp = df.copy()\n",
    "tmp['deflator_cycle_shift'] = tmp['deflator_cycle'].shift(-t_shift)\n",
    "ax_ = tmp.plot(y=['gdp_cycle', 'deflator_cycle_shift'])\n",
    "ax_.axhline(0, color='red')\n",
    "yp_corr_shift = tmp[['gdp_cycle', 'deflator_cycle_shift']].corr().iloc[0,1]\n",
    "print(f'GDPと{t_shift}期先のデフレータの乖離率の相関係数：{yp_corr_shift:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "hidden": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "> これらのデータの特徴１〜３をどこまで**再現**できるかに基づいてADASモデルを評価することになる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "## カリブレーション"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### はじめに"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "定量分析を進めるためには，ADASモデルのパラメータに値を設定する必要がある。\n",
    "ここでは景気循環のデータに基づき，次の4つのパラメーターの値を決めていく\n",
    "* $a$ （AS曲線の傾き）\n",
    "* $c$ （AD曲線の傾き）\n",
    "* $\\sigma_v$ （供給ショックの標準偏差）\n",
    "* $\\sigma_u$ （需要ショックの標準偏差）\n",
    "\n",
    "パラメーターの値の決め方には主に次の２つある。\n",
    "1. データに基づいて計量経済学的な手法などを用いて推定した結果を使う。\n",
    "1. 既存の実証研究で報告され推定値を使う。\n",
    "\n",
    "多くの研究の場合，これらの方法を駆使して値を決めることになる。\n",
    "また，必ずしも対象の経済モデルに基づいた推定結果でなくとも構わない。\n",
    "以下では１番目の方法を使い議論を進めることにする。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### カリブレーションとは"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "２つの体重計があるとしよう。\n",
    "一つは，市販の正確な体重計で誤差はない。\n",
    "もう一つは自作の体重計で，作ったばかりなので精度に欠ける。\n",
    "自作体重計にはスイッチが取り付けられており，それを調整することにより誤差を小さくし精度を高めることができる。\n",
    "そのスイッチの使い方は次のようになる。\n",
    "まず市販の体重計で自分の体重を測る。\n",
    "次に自作体重計で測り同じ数値が出るようにスイッチを調整する。\n",
    "このように，基準となる機器に基づいて測定器の誤差をなくすための調整をおこなうことを**カリブレーション**と呼ぶ。\n",
    "自分の体重を使ってカリブレーションをおこない，親族や友達が使っても体重を正確に測れる場合は，手作り体重計の成功ということである。\n",
    "一方で，自分以外の体重を測ると誤差が残る場合は，手作り体重計は100％成功とは言えないだろう。\n",
    "60kg以上の体重は誤差が大きいが，60kg未満であればある程度の精度が確保できている場合はどうだろうか。\n",
    "「60kg未満の体重を測る」が目的である場合，手作り体重計の成功と考えることもできるだろう。\n",
    "\n",
    "このカリブレーションという手法は，最近のマクロ経済学の研究で広く使われており，その分野を定量的（数量的）マクロ経済学と呼ぶ。\n",
    "ここではAD-ASモデルに応用しようというのが目的である。\n",
    "体重計の例を使うと，AD-ASモデルと実際経済の関係は次のようになる。\n",
    "* 市販の正確な体重計　→　日本経済\n",
    "* 手作り体重計　→　ADASモデル\n",
    "* 手作り体重計のスイッチ　→　ADASモデルのパラメーター（外生変数）\n",
    "* スイッチの調整　→　パラメーターの値の設定\n",
    "* カリブレーションで使うデータ\n",
    "    * 自分の体重　→　景気循環に関する特徴\n",
    "* 評価方法\n",
    "    * 他の人の体重を測り手作り体重計の誤差を確認　→　ADASモデルのパラメーターの設定に使われていないデータをどれだけ説明できるかの確認"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 均衡式の整理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "式[](eq:18-as_small)と[](eq:18-ad_small)を再掲する。\n",
    "\n",
    "$$\n",
    "p_{t}=p_{t-1}+ay_{t}+v_{t}\n",
    "$$ (eq:18-as_small2)\n",
    "\n",
    "$$\n",
    "y_t=-c p_t + u_t\n",
    "$$ (eq:18-ad_small2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "カリブレーションでは，パラメータ`a`と`c`を推定する必要があるが，上の式を回帰式として使うには同時性の問題がある。\n",
    "式[](eq:18-as_small2)を$\\Delta p_{t}=ay_{t}+v_{t}$，$\\Delta p_{t}\\equiv p_{t}-p_{t-1}$に変形して回帰式として解釈し，$a$を推定することが考えられる。しかし，供給ショック$v_t$は$p_t$に影響を与え，式[](eq:18-ad_small2)を通して$y_t$にも影響を及ぼすことが考えられる。即ち，$v_t$と$y_t$が相関し，このままでは$a$の推定値は不偏性も一致性も失うことになる。また，式[](eq:18-ad_small2)をそのまま回帰式として解釈し，$c$を推定しても類似の問題が考えられる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この点を回避するために，式[](eq:18-ad_small)を式[](eq:18-as_small)に代入し次のように整理する。\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p_{t}\n",
    "&=p_{t-1}+a(-c p_{t} + u_{t})+v_{t} \\\\\n",
    "(1+a c)p_{t}&=p_{t-1} +a u_{t}+v_{t} \\\\\n",
    "p_{t}&=h p_{t-1}+h\\left(a u_{t}+v_{t}\\right)\n",
    "\\end{aligned}$$ (eq:18-eq-ppp)\n",
    "\n",
    "ここで\n",
    "\n",
    "$$\n",
    "h\\equiv\\frac{1}{1+a c}<1\n",
    "$$ (eq:18-h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "また，式[](eq:18-eq-ppp)を[](eq:18-ad_small2)に代入し，`h`の定義を利用し整理すると次式となる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "y_t\n",
    "&=-c\\left[hp_{t-1}+h\\left(a u_{t}+v_{t}\\right)\\right]+u_t\\\\\n",
    "&=-ch p_{t-1}-ch\\left(a u_{t}+v_{t}\\right)+u_t\\\\\n",
    "&=-ch p_{t-1}+(1-ach)u_t-ckv_t\\\\\n",
    "&=-ch p_{t-1}+\\left(1-\\dfrac{ac}{1+ac}\\right)u_t-ckv_t\\\\\n",
    "&=-ch p_{t-1}+\\dfrac{1}{1+ac}u_t-ckv_t\\\\\n",
    "&=-ch p_{t-1}+hu_t-ckv_t\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この結果を利用すると，ADASモデルを次の２つの式で表すことができる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "$$\n",
    "p_{t}=hp_{t-1}+e_{pt},\n",
    "\\qquad\\quad\n",
    "e_{pt}\\equiv h\\left(a u_{t}+v_{t}\\right)\n",
    "$$ (eq:18-eq-p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "$$\n",
    "y_t = -chp_{t-1} + e_{yt}\n",
    "\\qquad\\quad\n",
    "e_{yt}\\equiv h(u_t-cv_t)\n",
    "$$ (eq:18-eq-y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 準備：$h$の推定値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "式[](eq:18-eq-p)を回帰式と捉えて，まずは$h$の推定値を計算する。\n",
    "まず，`df`のメソッド`.shift()`を使って`deflator_cycle`を１期ずらした列を`deflator_cycle_lag`として`df`に追加しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>deflator</th>\n",
       "      <th>gdp_cycle</th>\n",
       "      <th>deflator_cycle</th>\n",
       "      <th>deflator_cycle_lag</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1980-01-01</th>\n",
       "      <td>91.2</td>\n",
       "      <td>0.003269</td>\n",
       "      <td>-0.025798</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-04-01</th>\n",
       "      <td>93.4</td>\n",
       "      <td>-0.010845</td>\n",
       "      <td>-0.006555</td>\n",
       "      <td>-0.025798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-07-01</th>\n",
       "      <td>94.4</td>\n",
       "      <td>0.000457</td>\n",
       "      <td>-0.000482</td>\n",
       "      <td>-0.006555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-10-01</th>\n",
       "      <td>95.4</td>\n",
       "      <td>0.010468</td>\n",
       "      <td>0.005515</td>\n",
       "      <td>-0.000482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1981-01-01</th>\n",
       "      <td>95.6</td>\n",
       "      <td>0.009441</td>\n",
       "      <td>0.003126</td>\n",
       "      <td>0.005515</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            deflator  gdp_cycle  deflator_cycle  deflator_cycle_lag\n",
       "                                                                   \n",
       "1980-01-01      91.2   0.003269       -0.025798                 NaN\n",
       "1980-04-01      93.4  -0.010845       -0.006555           -0.025798\n",
       "1980-07-01      94.4   0.000457       -0.000482           -0.006555\n",
       "1980-10-01      95.4   0.010468        0.005515           -0.000482\n",
       "1981-01-01      95.6   0.009441        0.003126            0.005515"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['deflator_cycle_lag'] = df['deflator_cycle'].shift()\n",
    "df.iloc[:5,-4:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`deflator_cycle_lag`には１期前の`deflator_cycle`の値が，`d_deflator_cycle`には前期との差分が並んでいるのが確認できる。\n",
    "\n",
    "まず回帰分析をおこない，その結果を表示する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         deflator_cycle   R-squared:                       0.689\n",
      "Model:                            OLS   Adj. R-squared:                  0.688\n",
      "Method:                 Least Squares   F-statistic:                     384.1\n",
      "Date:                Sun, 12 Jan 2025   Prob (F-statistic):           8.56e-46\n",
      "Time:                        22:22:40   Log-Likelihood:                 716.66\n",
      "No. Observations:                 175   AIC:                            -1429.\n",
      "Df Residuals:                     173   BIC:                            -1423.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              0.0002      0.000      0.795      0.428      -0.000       0.001\n",
      "deflator_cycle_lag     0.8194      0.042     19.597      0.000       0.737       0.902\n",
      "==============================================================================\n",
      "Omnibus:                       48.339   Durbin-Watson:                   1.616\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              109.483\n",
      "Skew:                           1.218   Prob(JB):                     1.68e-24\n",
      "Kurtosis:                       6.014   Cond. No.                         136.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res_h = smf.ols('deflator_cycle ~ deflator_cycle_lag', data=df).fit()\n",
    "print(res_h.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**＜推定結果について＞**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/papermill.record/text/plain": "1.616"
     },
     "metadata": {
      "scrapbook": {
       "mime_prefix": "application/papermill.record/",
       "name": "durbin_watson_h"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.stats import stattools\n",
    "res_hg = smf.ols('deflator_cycle ~ deflator_cycle_lag', data=df).fit()\n",
    "dw_h = stattools.durbin_watson(res_hg.resid)\n",
    "glue(\"durbin_watson_h\", round(dw_h.item(),3), display=False)\n",
    "# print(dw_h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "残差の自己相関を考えてみよう。ダービン・ワトソン検定統計量は{glue:}`durbin_watson_h`であり，「不明」の領域にある。しかし，[付録Ｂ](sec:18-1-appendix_B)ではBreusch-Godfrey検定とLjung-Box検定をおこなっているが，帰無仮説である「残差の自己相関なし」は棄却されてしまう。この結果により，説明変数`deflator_cycle_lag`と誤差項の相関の疑いがあり，`h`の推定値は不偏性も一致性も満たさないことになってしまう。この問題を解決するために，一般化最小二乗法の一つであるコクラン＝オーカット推定法（Cochrane-Orcutt推定方）を使い推定をおこなうことにする。残差はAR(1)と置いて推定を進める。\n",
    "\n",
    "$$\n",
    "e_{pt}=\\rho_pe_{pt-1}+\\eta_t\n",
    "$$ (eq:18-ar1-p)\n",
    "\n",
    "* $1<\\rho_p<1$\n",
    "* $\\eta_t$はホワイト・ノイズ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "コードは簡単で，`statsmodels`の`.ols()`関数の代わりに`.glsar()`関数を使う（`glsar`は**G**eneralized **L**inear **S**quares with **A**utoreg**r**essive Errorsの略）。ただ，次の点が異なる。\n",
    "* 引数は`.ols()`関数と似ている。\n",
    "    * 第一引数：文字列の推定式（`.ols()`と同じ）\n",
    "    * 第二引数（`data`）：データの指定（`.ols()`と同じ）\n",
    "    * 第三引数（`rho=1`）：`n`次自己回帰過程の`n`を指定（デフォルトは`1`）\n",
    "* 未知の自己相関係数を計算する反復推定をおこなうために，`.fit()`の代わりに次の引数を使い`iterative_fit()`を使用する。\n",
    "    * `itermax=3`：反復計算を最大回数（デフォルトは`3`）。\n",
    "    * `cov_type='HC1'`（オプショナル）：不均一分散頑健推定を指定（不均一分散頑健推定については[Pythonで学ぶ入門計量経済学ー不均一分散](https://py4etrics.github.io/14_Hetero.html)を参照しよう）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           GLSAR Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:         deflator_cycle   R-squared:                       0.641\n",
      "Model:                          GLSAR   Adj. R-squared:                  0.639\n",
      "Method:                 Least Squares   F-statistic:                     175.0\n",
      "Date:                Sun, 12 Jan 2025   Prob (F-statistic):           5.17e-28\n",
      "Time:                        22:25:48   Log-Likelihood:                 720.75\n",
      "No. Observations:                 174   AIC:                            -1438.\n",
      "Df Residuals:                     172   BIC:                            -1431.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HC1                                         \n",
      "======================================================================================\n",
      "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              0.0002      0.000      0.448      0.654      -0.001       0.001\n",
      "deflator_cycle_lag     0.8188      0.062     13.230      0.000       0.697       0.940\n",
      "==============================================================================\n",
      "Omnibus:                       53.697   Durbin-Watson:                   2.037\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.719\n",
      "Skew:                           1.257   Prob(JB):                     1.13e-33\n",
      "Kurtosis:                       6.822   Cond. No.                         137.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity robust (HC1)\n"
     ]
    }
   ],
   "source": [
    "res_h_glsar = smf.glsar('deflator_cycle ~ deflator_cycle_lag',  # 推定式\n",
    "                        data=df,      # データの指定\n",
    "                        rho=1         # AR(1)を指定\n",
    "                       ).iterative_fit(itermax=10,      # 最大反復計算回数\n",
    "                                       cov_type='HC1'   # 不均一分散頑健推定\n",
    "                                      )\n",
    "print(res_h_glsar.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`h`の推定値は大きく変わらないが，残差の系列相関はそれ程大きくないためだ。統計的優位性も高く，コクラン＝オーカット推定法による式の変形後の残差の系列相関も排除できる。またこの計算では，不均一分散の可能性も排除できないため，不均一分散頑健推定も使っており，$t$検定は有効と考えることができる。ここで計算した値を`h`の推定値として採用し変数`hhat`に割り当てることにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "hhat = res_h_glsar.params['deflator_cycle_lag']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "また以下の分析では残差も必要になるが，コクラン＝オーカット推定法で計算した$\\hat{e}_{pt}$を変数`ep`に割り当てることにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "ep = res_h_glsar.resid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "````{note}\n",
    "反復計算をする度に係数の推定値と$\\hat{\\rho}_p$の値は変化するが\n",
    "```\n",
    "res_h_glsar.history\n",
    "```\n",
    "を使うと確認することができる。式[](eq:18-ar1-p)の自己相関係数$\\hat{\\rho}_p$の推定値にアクセスするには次のコードを使うと良いだろう。\n",
    "```\n",
    "res_h_glsar.model.rho\n",
    "```\n",
    "また，残差$e_{pt}$は\n",
    "```\n",
    "res_h_glsar.resid\n",
    "```\n",
    "で，また$\\eta_t$は\n",
    "```\n",
    "res_h_glsar.wresid\n",
    "```\n",
    "で抽出できる。\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 最初のスイッチ：$c$の値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここでは`hhat`を利用して`c`の推定値を計算するために，式[](eq:18-eq-y)を回帰式として使う。\n",
    "式[](eq:18-eq-y)を再掲しよう。\n",
    "\n",
    "$$\n",
    "y_t = dp_{t-1} + e_{yt}\n",
    "$$ (eq:18-regression-d)\n",
    "\n",
    "* $d\\equiv -ch$\n",
    "* $e_{yt}\\equiv hu_t-chv_t$\n",
    "\n",
    "説明変数である$p_{t-1}$は誤差項$e_{yt}$とは期間がズレているため，残差に系列相関がなければ推定値は一致性を満たすことになる（不偏性は満たさない）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              gdp_cycle   R-squared:                       0.041\n",
      "Model:                            OLS   Adj. R-squared:                  0.035\n",
      "Method:                 Least Squares   F-statistic:                     7.398\n",
      "Date:                Sat, 11 Jan 2025   Prob (F-statistic):            0.00719\n",
      "Time:                        15:39:21   Log-Likelihood:                 492.28\n",
      "No. Observations:                 175   AIC:                            -980.6\n",
      "Df Residuals:                     173   BIC:                            -974.2\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept          -6.676e-05      0.001     -0.060      0.952      -0.002       0.002\n",
      "deflator_cycle_lag    -0.4099      0.151     -2.720      0.007      -0.707      -0.112\n",
      "==============================================================================\n",
      "Omnibus:                       58.282   Durbin-Watson:                   0.633\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              236.393\n",
      "Skew:                          -1.212   Prob(JB):                     4.66e-52\n",
      "Kurtosis:                       8.152   Cond. No.                         136.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res_d = smf.ols('gdp_cycle ~ deflator_cycle_lag', data=df).fit()\n",
    "print(res_d.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**＜推定結果について＞**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "res_dg = smf.ols('gdp_cycle ~ deflator_cycle_lag', data=df).fit()\n",
    "dw_d = stattools.durbin_watson(res_dg.resid)\n",
    "glue(\"durbin_watson_d\", round(dw_d.item(),3), display=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$d$の推定値である$\\hat{d}$は負であり，モデルに沿った結果である。\n",
    "しかし，`Durbin-Watson`検定統計量は{glue:}`durbin_watson_d`であり残差の正の系列相関が強く疑われる。\n",
    "従って，`deflator_cycle_lag`と残差の相関の可能性があり，推定値の一致性が失われている可能性が高い。\n",
    "この問題に対処するために，`h`の推定値を計算した時と同じように，コクラン＝オーカット推定法を使い推定をおこなう。\n",
    "結果は次の通りである。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           GLSAR Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:              gdp_cycle   R-squared:                       0.007\n",
      "Model:                          GLSAR   Adj. R-squared:                  0.001\n",
      "Method:                 Least Squares   F-statistic:                    0.5500\n",
      "Date:                Sat, 11 Jan 2025   Prob (F-statistic):              0.459\n",
      "Time:                        16:33:46   Log-Likelihood:                 544.68\n",
      "No. Observations:                 174   AIC:                            -1085.\n",
      "Df Residuals:                     172   BIC:                            -1079.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HC1                                         \n",
      "======================================================================================\n",
      "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              0.0004      0.003      0.147      0.883      -0.005       0.005\n",
      "deflator_cycle_lag    -0.2202      0.297     -0.742      0.458      -0.802       0.362\n",
      "==============================================================================\n",
      "Omnibus:                      151.661   Durbin-Watson:                   2.052\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3130.415\n",
      "Skew:                          -3.044   Prob(JB):                         0.00\n",
      "Kurtosis:                      22.867   Cond. No.                         75.8\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity robust (HC1)\n"
     ]
    }
   ],
   "source": [
    "res_d_glsar = smf.glsar('gdp_cycle ~ deflator_cycle_lag', data=df).iterative_fit(10, cov_type='HC1')\n",
    "print(res_d_glsar.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`d`の推定値は絶対値で大きく減少しており，系列相関の影響が大きいことを示している。\n",
    "不均一分散の可能性も排除できないため，不均一分散頑健推定を使っているが，残念ながら統計的優位性は低い。\n",
    "この値を`d`の推定値として変数`dhat`に使うことにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "dhat = res_d_glsar.params['deflator_cycle_lag']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`d`の推定値が確定した訳だが，$-d\\equiv ch$で与えられ，$c$の推定値を次式で計算することができる。\n",
    "\n",
    "$$\n",
    "\\hat{c} = -\\frac{\\hat{d}}{\\hat{h}}\n",
    "$$\n",
    "\n",
    "この値を`chat`に割り当てよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2689802972319807"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chat = -dhat / hhat\n",
    "chat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これが「最初のスイッチの調整」である。\n",
    "また以下の分析では残差も必要になるため，コクラン＝オーカット推定法で計算した$\\hat{e}_{yt}$を変数`ep`に割り当てることにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "ey = res_d.resid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### ２つ目のスイッチ：$a$の値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "式[](eq:18-h)では，$h$は$a$と$c$の関数となっている。\n",
    "すでに$h$と$c$の推定値を計算しているため，この式を使うことにより簡単に$a$の推定値を計算することができる。\n",
    "式[](eq:18-h)を整理すると次式となる。\n",
    "\n",
    "$$\n",
    "\\hat{a} = \\left(\\dfrac{1}{\\hat{h}}-1\\right)\\frac{1}{\\hat{c}}\n",
    "$$\n",
    "\n",
    "計算結果を`ahat`に割り当てよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8227478597459131"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ahat = (1/hhat - 1) / chat\n",
    "ahat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "これが「2つ目のスイッチの調整」である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### ３つ目のスイッチ：$\\sigma_v$の値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sigma_v^2$の値も回帰式の結果を使い設定する。\n",
    "式[](eq:18-eq-p)の誤差項$e_{pt}$は$u_t$と$v_t$の線形関数となっており，同様に，式[](eq:18-eq-y)の誤差項$e_{yt}$も$u_t$と$v_t$の線形関数となっている。\n",
    "以下に再掲する。\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "e_{pt}&=h(a u_{t}+v_{t})\\\\\n",
    "e_{yt}&=h(u_t-cv_t)\n",
    "\\end{align*}\n",
    "$$ (eq:18-ept-eyp)\n",
    "\n",
    "これはAD-ASモデルを前提とした理論上の関係であり，全てが観測不可能である。\n",
    "しかし，$a$と$h$にはその推定値$\\hat{a}$と$\\hat{h}$を使い，$e_{pt}$と$e_{yt}$については残差$\\hat{e}_{pt}$と$e_{yt}$を用いることにより，$u_t$と$v_t$を求めることが可能である。\n",
    "式[](eq:18-ept-eyp)は$u_t$と$v_t$の線形連立方程式となっているため，簡単に次のように書き直すことができる。\n",
    "\n",
    "$$\n",
    "\\hat{v}_t=\\hat{e}_{pt}-\\hat{a}\\hat{e}_{yt}\n",
    "$$ (eq:18-vt)\n",
    "\n",
    "$$\n",
    "\\hat{u}_t=\\hat{c}\\hat{e}_{pt}+\\hat{e}_{yt}\n",
    "$$ (eq:18-ut)\n",
    "\n",
    "ここで$\\hat{e}_{pt}$と$\\hat{e}_{yt}$は残差を，$\\hat{a}$と$\\hat{c}$は推定値を表しており，これらを使って計算した需要・供給ショックを$\\hat{v}_t$と$\\hat{u}_t$として表している。\n",
    "まず式[](eq:18-vt)を使い，結果を`vt`に割り当てよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "vt = ep - ahat*ey"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`vt`のデータ型は`Series`であり，メソッド`.std()`を使うと簡単に`vt`の標準偏差を計算することができる。\n",
    "結果を`v_std`に割り当てよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012546750971860659"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v_std = vt.std()\n",
    "v_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この値を$\\sigma_v$に使うことにする。これが「3つ目のスイッチの調整」である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### ４つ目のスイッチ：$\\sigma_u$の値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "同様に，式[](eq:18-ut)を使うと，$\\hat{u}_t$の標準偏差を計算することができる。\n",
    "`u_std`に割り当てる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.014633934415485182"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ut = ey + chat*ep\n",
    "u_std = ut.std()\n",
    "u_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この値を$\\sigma_u$に使うが，これが「最後のスイッチの調整」となる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### パラメーターの値：再掲"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aの値：0.823\n",
      "cの値：0.269\n",
      "vの標準偏差：0.012547\n",
      "uの標準偏差：0.014634\n"
     ]
    }
   ],
   "source": [
    "print(f'aの値：{ahat:.3f}')\n",
    "print(f'cの値：{chat:.3f}')\n",
    "print(f'vの標準偏差：{v_std:.6f}')\n",
    "print(f'uの標準偏差：{u_std:.6f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`v_std`と`u_std`を比べると，後者の値が若干大きい様である。\n",
    "比率を計算してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.166352504190573"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_std / v_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ショックの直接的な影響だけを考えると，比較的にAD曲線の変動幅が大きいことを示している。\n",
    "次章では，これらの値を使い定量分析を更に進めていく。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## 付録"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "(sec:18-1-appendix_A)=\n",
    "### 付録Ａ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この付録は次の2点を示すことを目的としている。\n",
    "* 自然産出量と物価水準のトレンドは成長し変動するように本文のADASモデルを拡張する。\n",
    "* 拡張モデルの下でも式[](eq:18-as_small)と式[](eq:18-ad_small)が導出される。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### 拡張モデル"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "物価水準のトレンドの式は\n",
    "\n",
    "$$\n",
    "P_t^{*}=P_{t-1}^{*}+aY_t^{*} + A_t+V_t\n",
    "\\tag{a1}\n",
    "$$\n",
    "\n",
    "で与えられ，次式で自然産出量が決定されると仮定する。\n",
    "\n",
    "$$\n",
    "Y_t^{*}=B_{t}-cP_t^{*} + U_t\n",
    "\\tag{a2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここで\n",
    "* $A_t=$ $P_t^{*}$の変化を決定する項\n",
    "* $V_t=$ $P_t^{*}$に影響を及ぼすランダムなショック\n",
    "* $B_t=$ $Y_t^{*}$の増加を決定する項\n",
    "* $U_t=$ $Y_t^{*}$に影響を及ぼすランダムなショック"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一方で，AS曲線とAD曲線を次のように仮定する。\n",
    "\n",
    "$$\n",
    "P_t=P_{t-1}+aY_t + A_t+V_t+v_t\n",
    "\\tag{a3}\n",
    "$$\n",
    "\n",
    "$$\n",
    "Y_t=B_{t}-cP_t + U_t+u_t\n",
    "\\tag{a4}\n",
    "$$\n",
    "\n",
    "* $V_t$は$P_t^{*}$に影響を与えるという意味で，$P_t$に対する恒常的な需要ショックと解釈できる。\n",
    "* $U_t$は$Y_t^{*}$に影響を与えるという意味で，$Y_t$に対する恒常的な需要ショックと解釈できる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### 式[](eq:18-as_small)と[](eq:18-ad_small)の導出"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "式(a1)の両辺から式(a3)を引くと次式となる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "P_t-P_t^{*}&=P_{t-1}-P_{t-1}^{*}+a(Y_t-Y_t^{*}) +v_t\\\\\n",
    "p_t&=p_{t-1}+ay_t+v_t\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "2行目は式[](eq:18-as_small)と同じである。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に式(a2)の両辺から式(a4)を引くと次式となる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "Y_t-Y_t^{*}&=-c(P_t-P_t^{*}) + u_t\\\\\n",
    "y_t&=-cp_t + u_t\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "2行目は式[](eq:18-ad_small)と同じとなっている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### $Y_t^{*}$と$P_t^{*}$について"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次の仮定を置こう。\n",
    "\n",
    "$$\n",
    "A_t=-aY_{t-1}^{*}\n",
    "$$\n",
    "\n",
    "1期遅れで自然産出量は$P_t^{*}$を減少させる。\n",
    "自然産出量の増加は生産性の上昇に起因するものであり，それにより物価水準とそのトレンドは減少するというメカニズムを捉えている。\n",
    "\n",
    "この仮定を使い，式(a3)を次の様に書き換えよう。\n",
    "\n",
    "$$\n",
    "P_t^{*}-P_{t-1}^{*}=aY_t^{*} - aY_{t-1}^{*}+V_t\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Delta P_t^{*}=a\\Delta Y_t^{*} + V_t\n",
    "\\tag{a5}\n",
    "$$\n",
    "\n",
    "* $\\Delta P_t^{*}=P_t^{*}-P_{t-1}^{*}$： 物価水準のトレンドの増加率\n",
    "* $\\Delta Y_t^{*}=Y_t^{*}-Y_{t-1}^{*}$： 自然産出量の増加率\n",
    "\n",
    "この式は，物価水準トレンドの増加率$\\Delta P_t^{*}$は自然産出量の成長率と比例し，$V_t$によりランダムに変動することを示しているの。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に式(a4)の差分を次の様に計算しよう。\n",
    "\n",
    "$$\n",
    "Y_t^{*}-Y_{t-1}^{*}=B_t-B_{t-1}-c(P_t^{*}-P_{t-1}^{*}) + U_t-U_{t-1}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Delta Y_t=\\Delta B_t-c\\Delta P_t^{*} + \\Delta U_t\n",
    "\\tag{a6}\n",
    "$$\n",
    "\n",
    "* $\\Delta B_t=B_t-B_{t-1}$： 生産性の増加率と解釈する（例えば，`0.02`の様な定数にすると毎期`2`％の成長率となる）\n",
    "* $\\Delta U_t=U_t-U_{t-1}$： 恒常的な需要ショックの差分"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "式(a5)を式(a6)に代入し整理すると次式となる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\Delta Y_t&=\\Delta B_t-c[a\\Delta Y_t^{*}+V_t] + \\Delta U_t\\\\\n",
    "(1+ac)\\Delta Y_t&=\\Delta B_t-cV_t + \\Delta U_t\\\\\n",
    "&\\Downarrow\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Delta Y_t=\\frac{\\Delta B_t-cV_t + \\Delta U_t}{1+ac}\n",
    "\\tag{a7}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "式(a7)は自然産出量の成長率を表しており，ランダムなショックにより，変動しながら増加することになる。ショックがない定常状態（$V_t=U_t=U_{t=1}0$）では\n",
    "\n",
    "$$\n",
    "\\Delta Y_t=\\frac{\\Delta B_t}{1+ac}\n",
    "\\tag{a8}\n",
    "$$\n",
    "\n",
    "の率で増加することになる。また式(a8)を式(a5)に代入すると次式となる。\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\Delta P_t^{*}\n",
    "&=a\\frac{\\Delta B_t-cV_t + \\Delta U_t}{1+ac} + V_t\\\\\n",
    "&=a\\frac{\\Delta B_t+V_t + \\Delta U_t}{1+ac}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "自然産出量と同様に，変動しつつ増加することになる。ショックがない定常状態では\n",
    "\n",
    "$$\n",
    "\\Delta P_t^{*}\n",
    "=\\frac{a}{1+ac}\\Delta B_t\n",
    "$$\n",
    "\n",
    "の率で増加することになる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "(sec:18-1-appendix_B)=\n",
    "### 付録Ｂ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 残差の自己相関の検定"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Breusch-Godfrey検定を考えよう。\n",
    "\n",
    "＜帰無仮説＞\n",
    "\n",
    "$$\n",
    "e_{pt}=\\rho_{p}e_{pt-1}+e_{pt}\n",
    "$$\n",
    "\n",
    "* $H_0$：$\\rho_{p}=0$\n",
    "* $H_A$：$\\rho_{p}\\ne0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.diagnostic import acorr_breusch_godfrey\n",
    "\n",
    "acorr_breusch_godfrey(res_h, nlags=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上から次の値となる。\n",
    "* $LM$検定統計量\n",
    "* $LM$検定統計量に関する$p$値\n",
    "* $F$検定統計量\n",
    "* $F$検定統計量に関する$p$値"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5％の有意水準で帰無仮説を棄却できる。即ち，残差の自己相関があるようだ。\n",
    "\n",
    "次に，Ljung-Box検定もおこなってみよう。\n",
    "\n",
    "＜帰無仮説＞\n",
    "\n",
    "* $H_0$：残差は独立分布\n",
    "* $H_A$：残差は独立分布ではない"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.diagnostic import acorr_ljungbox\n",
    "\n",
    "acorr_ljungbox(res_h.resid, lags=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "左の値が検定統計量であり，右の値が$p$値となる。5％の有意水準で帰無仮説を棄却される。自己相関が疑われる結果である。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "from myst_nb import glue\n",
    "glue(\"ahat_glued\", ahat)\n",
    "glue(\"chat_glued\", chat)\n",
    "glue(\"u_std_glued\", u_std)\n",
    "glue(\"v_std_glued\", v_std)"
   ]
  }
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