家計消費とプランク分布
(イタリア 2020)

不動産宇宙と固定為替相場(解説1)
住宅家賃とマクスウェル分布(解説2)
家計消費とプランク分布
国 2020 | 都市 2020

 消費品目分布の理論値(青線)は、プランク分布を変数(大人1人あたりの年間消費金額) E で割ったもの(プランク度数分布) E 2 e E k T - 1 に比例する。ただし、 E の単位は ukT である。(消費品目分布のピークを1単位目と2単位目のあいだに置くため、 u は0.8から1.59の範囲にある。また、消費品目分布のフィッティングは1単位目から3単位目までに着目する。)為替指数(物価指数にある定数 aをかけたもの)は、1単位目から3単位目までの消費品目数の総和とフィッティングで得た kT の積を観測データ(これは u の自由度だけ存在する)とする反復最小二乗法(為替指数との比が最小になる観測データを選んでから最小二乗法により新たな aを求める手続きの反復)から求まる。 kT を普遍的な値とすると、現地通貨建ての kT が小さいほどその現地通貨が高くなる。ただし、現地通貨建ての kT は消費品目数の影響を受けるので、その影響を排除したもの(為替指数)を考える必要がある。したがって、為替指数の比が固定為替相場である。なお、物価指数と為替指数の比 aの値は生活レベル(1人あたりの米ドル建て消費支出)を測定する年ごとに決まる。(未来への投資は今の生活レベルを下げるので、物価指数と為替指数の比 aが更新されるとき、投資の過不足分が過去の生活レベルに加算される。)また、消費品目分布の観測値(赤線)と物価指数は以下のページにもとづく。
https://www.istat.it/
https://www.imf.org/
イタリアの生活レベル
2020年

※左=物価指数と為替指数の比aの初期値
※中央=反復最小二乗法から求まるaの不動点
※右=生活レベル(米ドル建て1人あたり(NPISHs控除前)家計最終消費支出)の候補
※太字は住宅家賃分布(マクスウェル分布)にもとづく確定値

100,120,91632
200,200,54979
300,220,49981
400,220,49981
500,220,49981
600,1480,7429
700,1480,7429
800,1480,7429
900,1480,7429
1000,1480,7429
1100,1480,7429
1200,1480,7429
1300,1480,7429
1400,1480,7429
1500,1480,7429
1600,1480,7429
1700,1480,7429
1800,1480,7429
1900,1480,7429
2000,1480,7429
2100,1480,7429
2200,1480,7429
2300,1480,7429
2400,1480,7429
2500,1480,7429
2600,1480,7429
2700,1480,7429
2800,1480,7429
2900,1480,7429
3000,1480,7429
3100,1480,7429
3200,1480,7429
3300,1480,7429
3400,1480,7429
3500,1480,7429
3600,1480,7429
3700,1480,7429
3800,1480,7429
3900,1480,7429
4000,1480,7429
4100,1480,7429
4200,1480,7429
4300,1480,7429
4400,1480,7429
4500,1480,7429
4600,1480,7429
4700,1480,7429
4800,1480,7429
4900,1480,7429
5000,1480,7429

イタリアの消費品目分布
2019年
u=1.59, kT=5415

イタリアの消費品目
2019年

※左=大人1人あたりの年間消費金額(0.01ユーロ)
※右=消費品目

000000159,post-secondary non-tertiary education (ISCED 4)
000000313,financial services n.e.c.
000000565,hospital services
000000645,postal services
000001032,education not definable by level
000001271,other major durables for recreation and culture
000001585,secondary education
000001652,pre-primary and primary education
000001769,glassware tableware and household utensils
000002334,household textiles
000003354,telephone and telefax equipment
000003926,social protection
000004454,audio-visual photographic and information processing equipment
000004982,tools and equipment for house and garden
000005302,tertiary education
000007053,maintenance and repair of the dwelling
000007833,personal effects n.e.c.
000009388,household appliances
000009455,accommodation services
000012410,package holidays
000012681,newspapers books and stationery
000013664,alcoholic beverages
000014653,tobacco
000014899,transport services
000016121,other services n.e.c.
000017024,footwear
000017209,furniture and furnishings carpets and other floor coverings
000022996,other recreational items and equipment gardens and pets
000023015,non-alcoholic beverages
000024225,recreational and cultural services
000031881,goods and services for routine household maintenance
000032096,out-patient service
000032440,telephone and telefax services
000040040,medical products appliances and equipment
000042504,insurance
000046012,personal care
000049151,water supply and miscellaneous services relating to the dwelling
000050798,actual rentals for housing
000051111,purchase of vehicles
000053409,clothing
000070403,catering services
000072198,electricity gas and other fuels
000111181,operation of personal transport equipment
000262237,food
000355055,imputed rentals for housing

イタリアの消費品目分布
2016年
u=1.59, kT=5030

イタリアの消費品目
2016年

※左=大人1人あたりの年間消費金額(0.01ユーロ)
※右=消費品目

000000097,post-secondary non-tertiary education (ISCED 4)
000000260,financial services n.e.c.
000000764,postal services
000000921,other major durables for recreation and culture
000000976,hospital services
000001012,education not definable by level
000001564,secondary education
000001758,pre-primary and primary education
000002747,glassware tableware and household utensils
000002965,household textiles
000003159,telephone and telefax equipment
000003371,social protection
000004524,tertiary education
000005791,audio-visual photographic and information processing equipment
000006028,tools and equipment for house and garden
000007956,personal effects n.e.c.
000008684,accommodation services
000009824,maintenance and repair of the dwelling
000009897,household appliances
000011061,package holidays
000012559,furniture and furnishings carpets and other floor coverings
000013614,tobacco
000013657,alcoholic beverages
000013669,other services n.e.c.
000014172,newspapers books and stationery
000015252,transport services
000016865,footwear
000020583,non-alcoholic beverages
000022930,other recreational items and equipment gardens and pets
000023991,recreational and cultural services
000030504,out-patient service
000030698,goods and services for routine household maintenance
000033761,telephone and telefax services
000037442,medical products appliances and equipment
000041596,purchase of vehicles
000042494,insurance
000043410,personal care
000045902,actual rentals for housing
000047224,water supply and miscellaneous services relating to the dwelling
000054854,clothing
000067171,electricity gas and other fuels
000069087,catering services
000107664,operation of personal transport equipment
000251085,food
000357379,imputed rentals for housing

イタリアの消費品目分布
2015年
u=1.59, kT=4608

イタリアの消費品目
2015年

※左=大人1人あたりの年間消費金額(0.01ユーロ)
※右=消費品目

000000102,post-secondary non-tertiary education (ISCED 4)
000000416,financial services n.e.c.
000000530,hospital services
000000778,postal services
000000820,other major durables for recreation and culture
000000832,education not definable by level
000001870,pre-primary and primary education
000001936,secondary education
000002630,social protection
000002648,glassware tableware and household utensils
000002866,telephone and telefax equipment
000002998,household textiles
000004181,tertiary education
000005249,tools and equipment for house and garden
000005334,audio-visual photographic and information processing equipment
000007753,personal effects n.e.c.
000007795,accommodation services
000008749,maintenance and repair of the dwelling
000009093,household appliances
000011012,package holidays
000012043,furniture and furnishings carpets and other floor coverings
000012707,alcoholic beverages
000013184,newspapers books and stationery
000013697,transport services
000013896,tobacco
000015127,other services n.e.c.
000016346,footwear
000019731,non-alcoholic beverages
000021975,other recreational items and equipment gardens and pets
000023948,recreational and cultural services
000030924,goods and services for routine household maintenance
000032263,out-patient service
000034297,telephone and telefax services
000034514,purchase of vehicles
000035220,medical products appliances and equipment
000042461,insurance
000044029,personal care
000044947,water supply and miscellaneous services relating to the dwelling
000050456,actual rentals for housing
000053533,clothing
000066053,catering services
000069306,electricity gas and other fuels
000112038,operation of personal transport equipment
000246669,food
000355419,imputed rentals for housing



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