Personnel and Organizational Economics

summary of some recent papers in this topic that I read in the course

1. The specificity of general human capital: Evidence from college major choice J Kinsler, R Pavan – Journal of Labor Economics, 2015

Wage gaps across majors:
college graduates in science or business often earn 25% more → 1) general ability bias; 2) heterogeneous returns to specific human capital accumulated in college → choice on job decide returns

Potential Implication:
1)  student making decision; 2) policy that encourage technical majors → perceived benefits: a) positive externality in broader economy, b) better paying off student debt
<= inefficiency if specific skill + less opportunity (e.g. competition/capacity) 

Data:
11192 gradating seniors in 1993 student aid study → surveyed in 1994, 1997, 2003 for schooling and labor market outcomes (self-report on if related job)
identify the specificity of human capital within major ← by looking at wage variation across job types

general conclusion:
Students who work in job related to major earn 15% higher + 30% for science majors
(robust to standard ability measures i.e. SAT, GPA) 
→ wage gaps across related/non-related → consistent with different type of job reward skills differently => accumulated human capital is not universally applicable  + specific one accumulated through major choice
(most researches’ focus: work experience, amount of schooling)

Missing Factors → Structural model:
unobserved productivity → gaps: e.g. math human capital + verbal human capital ← a result from schooling + accumulation varies across major
→ classic Roy(1951) structural model: workers first select into a major and then select a job type
=> wages = f(individual human capital, major, job type)individual hc = f(major, job type)
(benefits of structural model: 1) GPA are endogenous to major choice; 2) able to calculate returns to major or related for any selected subgroup; 3) decompose within-major variation in wages)

→ model also investigate: human capital specificity + skill uncertainty → affects college major choice
(face 2 uncertainty when choosing: 1] whether find a related job in future; 2] the possibility of finding a related job and wages associated  due to imperfect information about their human capitals/underlying skill)  → skill uncertainty affect major choices
# other factors in choosing majors: parents, environment, interest, fashion → all not related to the consideration of related job and wage

Detailed conclusion:
1] parameter estimates uncertain about underlying human capital when choosing major: high expected math hc → science-related, high verbal hc → away from business and science
return to mhc are large for business majors (either related job or not) + for science (only related job)
2] non-perfect information assumption is examined → human capital uncertainty
3] average returns to business or science are 0.15, 0.18/0.19, 0.23(OLS); to related for average are 0.27 (both) for science degree
4] specificity of human capital explains 19% of wage variability in science field, 4% for business and others → science related majors may be riskier human capital investment
5] students would choose to science major more if they knew their human capital better

Data details – student & labor market
1] 2476 final sample: male + age<30 + with parental information and SAT + graduating major + major-specific GPA
2] major classification → science, business, other
3] construct variables exogenous to model: fraction of college students in 3 major classification in 1993 + information of legal state of residence of student’s parents in 1993 → exogenous shifter in choosing major
4] separated GPA to construct individual-specific GPA measures for each 3 classification
→ GPA is always highest on student’s own major → selection + accumulation of human capital for chosen field (# incentive)
5] primary employment in 1994, 1997 + current job in 2003 + work hours + wages + related
→ annual salaries are significantly different according to related or not(30% for science, 3% for business, 11% for residual)) → reflect a) sorting: the higher abilities are more likely to work in related, b) varying returns to skills/hc across job types

Descriptive Evidence of the Specificity of Schooling Human Capital
sorting or aggregation bias on wage difference
0] conditional on year effects and graduate degree + control on ability (SAT & major-specific GPA→endogenous problem)
=> business and science majors earn higher incomes
1] control for this difference
=> related wages are significantly larger for science major
2] control for major dummy
=> related wages are significantly larger for both science and business major
3] inclusion of worker fixed effects → ensure the returns to related are identified by workers who switch job types
=> relatedness effect decreases significantly → indicating sorting across majors on unobserved dimensions can help to explain
4] control for detailed occupation effects
=> returns to related decline considerably → wage difference associated with training on major or job tasks is smaller than wage variation across job conditional on major → related jobs tend to cluster in highly paid occupations
5] => occupation and relatedness are tightly linked → relateness partly capturing occupation-major match

=>> human capital developed through collage is specific to particular types of jobs
← no definitive conclusions can be drawn → observable measures of ability are noisy + GPA are endogenous to major choice → descriptive analysis may be affected by sorting on unobservables and differential skill accumulation across major
=> structural model incorporates these features → + examine skill specificity and uncertainty combine to influence major choice

Model
…….

Appendix on 1

根据PayScale Inc. 对美国各专业毕业生起薪、职业稳定期薪水,以及各专业毕业生人群中高中低收入水平的统计。

1. 理工科专业学生起薪高。
比如:电子工程(Electrical Engineering) 专业毕业的学生,毕业后第一年平均收入6万美元,而国际关系(International Relations)专业毕业的学生,毕业后第一年平均收入只有4万美元。从这个角度来看,题主的观察有一定的合理性。

2. 文科专业学生收入增长潜力大。
比较表中第二列(职业稳定期薪水)和第一列(起薪),我们发现文科专业的平均增幅比理工科高。而增幅最高的是基础性的学科(如:数学、哲学)和需要积累大量工作经验、在实践中学习的学科(如:销售、经济、政治、国际关系)。那些最精、专、特殊化的专业收入增长幅度最小(如:心理咨询、室内设计、营养学)。

3. 理工科专业毕业学生收入分布更密集。文科专业毕业生收入分布更分散。而在高端(各专业前10%)人群中,二者差异不大。
表中最后四列列举了各专业毕业生职业稳定期收入水平的分布(10%,25%,75%,90%)。各行业高端人群收入相对差异明显小于低端人群和起薪收入差异。如:物理学专业和哲学专业毕业的学生,起薪差额明显(前者年薪5万美元,后者只有不到4万美元,前者比后者高25%),但职业稳定期高收入人群差异明显缩小(前者年薪17.8万美元,后者16.8万美元,前者只比后者高5%)。

以上现象,从经济学的角度一般做如下解释:
(1)理工科学生的知识专业性更强。在那些不需要工作经验和实战能力的入门级、技术性岗位上,他们凭借自身的职业技能和专业背景,比文科生占优。
(2)文科生的成长速度更快。他们更善于从工作中学习、积累经验,能适应不同类型工作的挑战。因而当在职业稳定期,面临的任务更加多样、复杂的时候,他们的优势得以充分发挥。

 

2. 

 

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Labor Economics: some Empirical papers with econometric topics

1. Practical issues on randomized controlled trials (RCT)
– Bertrand, M. and S. Mullainathan (2004). Are Emily and Greg More Employable Than
Lakisha and Jamal? A Field Experiment on Labor Market Discrimination.; American Economic Review 94(4): 991-1013.
– Kling, J. R., et al. (2007). ;Experimental Analysis of Neighborhood Effects.; Econometrica 75(1): 83-119.

2. Observation units and clustering standard errors / matching estimation
HME C7, 3.3.
– Marianne Bertrand &amp; Esther Duflo, Sendhil Mullainathan, 2004. How Much Should We Trust Differences-in- Differences Estimates? The Quarterly Journal of Economics, vol. 119(1), pages 249-275

(Clustered Standard Errors / Robust and Clustered Standard Errors /  Introduction to Robust and Clustered Standard Errors /  A practitioner’s guide to cluster-robust inference AC Cameron, DL Miller – Journal of Human Resources, 2015 / Analysis of a cluster-randomised trial in education)
(Matching Estimators / A Practical Guide to Implementing Matching Estimators 1999/ Matching Estimators Petra E. Todd 2006/ Matching methods for causal inference: A review and a look forward EA Stuart – Statistical science, 2010)

3. Instrumental variables method
HME C4.
– Autor, D. H., et al. (2013). ;The China Syndrome: Local Labor Market Effects of Import
Competition in the United States. American Economic Review 103(6): 2121-2168. ***
– Kling, J. R., et al. (2007). ;Experimental Analysis of Neighborhood Effects.; Econometrica 75(1): 83-119.
– Kondo, A. (2007). Does the first job really matter? State dependency in employment
status in Japan. Journal of the Japanese and International Economies 21(3): 379-402
3. IV&Fixed effects
– von Wachter, T. and S. Bender (2006). In the Right Place at the Wrong Time: The Role of Firms and Luck in Young Workers’ Careers. American Economic Review 96 (5): 1679- 1705. ***

(Instrumental Variables and Selection Bias / Nonparametric IV Estimation of Local Average Treatment Effects with Covariates / Treatment Effects – MIT Economics )

4. Differences in differences and applications
Method:  Petra Todd (1999) “A practical guide to implementing matching estimators”
HME C5.
– Eissa, N. and J. B. Liebman (1996). Labor Supply Response to the Earned Income Tax Credit. The Quarterly Journal of Economics 111(2): 605-637.
– Duflo, E. (2001). Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment. American Economic Review
91(4): 795-813.
– García-Gómez, P., et al. (2013). Long-Term and Spillover Effects of Health Shocks on Employment and Income.Journal of Human Resources 48(4): 873-909.

5. Regression Discontinuity Design
Method: Lee, D. S. and T. Lemieux (2010). Regression Discontinuity Designs in Economics.Journal of Economic Literature 48(2): 281-355.
HME C6.
– McCrary, J. and H. Royer (2011).The Effect of Female Education on Fertility and Infant Health: Evidence from School Entry Policies Using Exact Date of Birth. Am Econ Rev 101(1): 158-195.
– Dahl, G. B., et al. (2014). Peer Effects in Program Participation.; American Economic Review 104(7): 2049-2074. ***

6. Sample selection bias and its corrections
Method:  Cameron, A. Colin and Pravin K. Trivedi, 2005. Microeconometrics, Cambridge
University Press. Ch. 16.5.
– Lee, D. S. (2009). Training, Wages, and Sample Selection: Estimating Sharp Bounds on
Treatment Effects. The Review of Economic Studies 76(3): 1071-1102.

 

 

Continue reading “Labor Economics: some Empirical papers with econometric topics”

経済史 core-text

岡崎先生のコアテキスト経済史をメモします

理論枠組み:経済組織をcoordinationとmotivationの2つ視点から捉える
(Economics, organization and management – J Roberts, P Milgrom – 1992)

coordination: 共同生産消費、資源配分 (division of labour/cooperation mechanism)
motivation: ↑共同生産消費のために人々を動機づける

=> 制度と組織の経済史 + 他の視点 => 経済成長と経済発展

1。経済史を研究する意味

The Journal of Economic History, Explorations in Economic History, The Economic History Review

A) Toynbee, A.J.: 歴史の教訓:未来の予測ではない、「もし現代の事態とよく似ている過去の事態についての時知識があれば、未来において起こりうる諸々の」可能性について、少なくとも一つの可能性を教えてくれる」

e.g. 先進国の経済発展の経験から発展途上国が教訓を得る → 東アジアの奇跡:オーソドックスな開発政策+産業政策(産業間や企業間の資源配分に政府が介入するミクロ的な政策、援助されるべき産業の選択→国際競争)=> market friendly government → 1990年代成長率の低下と金融危機→奇跡の再検討

B) 過去と現在の共通性ではない、相違

経済関係、行動様式を与件として前提することは現在あまりに一般的としても、歴史には一般的ではなかった => 考え方を改める

e.g. Marx:資本主義は古代以来、進んできた生産仕様の発展の一段階→雇用関係を軸に経済活動が営まれるという現在の経済の基本的な仕組みが、歴史のある時期に生まれた→そこから資本主義は変革し得るものという見方

e.g. 終身雇用は日本の文化ないし国民性の差ではない→戦前の日本の離職率は高い、大企業も不況期には活発に解雇を通じた雇用調整を実施→機能や存在理由

C) 実験室としての歴史

e.g. Friedman, Schwartz: A Monetary History of the US, 1867-1960 → 貨幣残高の変動と背景 → 長期の歴史データによって相互関係を定量的に分析+歴史文書によって、変化の独立性を論証=>長期時系列データを発生させる実験室

e.g. ミクロは多数のデータを得る→歴史中政府の規制介入が行われなかった時期を見出す、理論を立つ/テスト→例えば金融恐慌のメカニズムを研究する、WWII以降は預金保険制度がある

e.g. 歴史上における規制の変更や大きな事件→自然実験→randomized trial→仮説検証→比較優位原理は貿易が存在しない状態を想定する→日本江戸時代の鎖国→実証的にテスト→しかし一国で直接は無理→アウタルキーの各財価額と貿易開始後の輸出財輸入財の価額を評価して貿易収支を計算

D) 経路依存性

Bloch, M.: 多くの社会的創造物に特有な惰力→現在の視点や諸条件から見ると非効率なことが広く長く存在している理由

e.g. David, P.: Clio and QWERTY → どうのようにしてそうなった→ 結果が時間的に離れた出来ことから重要な影響を受ける→現時点でQWERTYの特性をいくら調べても、非効率的から、広く普及している理由は説明できない→歴史を調べる→当時の技術の制約による合理的な設計→広く使われ続けている:1)user/maker補完性;2)network外部性 => 経路依存性:いったん選択されて支配的な状態が、なぜ維持され、なぜその状態に到達

path dependance in game theory: → 2 or more Nash equilibrium → no incentive to leave the less efficient one → stable status

2。経済成長

A)経済成長と測定

経済成長:経済活動が長期的に拡大 → GDP/GNP
Kuznets, S.S. → Maddison, A. → 1)16世紀から成長が続け;2)時期によって大きく異なり → 1500-1820: 0.04% (一生でも所得水準上昇の実感ない); 1820-:1.21%

地域間所得格差:
1)1820時点ですでに格差がり、west europe最高
2)1990年代まで拡大

B)新古典派成長理論

Solow, R.M.: Y =F(K,L)  → Y/L = F(K/L) 資本/労働比率→労働生産性

……

kt’ = syt/kt – δ – n  資本/労働比率毎期増加 → 投資 – 資本減耗と労働力増加

……

技術進歩の導入 → Y= F(K, AL)

……

C)理論と現実

Mankiw, N.G., Romer, D., Weil, D.N. → 国別のcross section data1人あたり産出を実証 → 人的資本の導入 H

……

3。経済の歴史的発展に関する様々な見方

A)経済発展段階論

Solow → 経済が同じmechanismで連続的に拡大
経済発展段階論 → 経済の構造、作用するmechanismが、時間とともに、非連続的に段階的に変化  → Marx: 生産仕様:アジア、古典古代、封建、資本主義 → 経済発展は [生産力の上昇 ← 技術 → 生産関係 → 生産力を支えるか妨げるか → 現在の生産関係を破壊次のに移行] / 下部構造=経済関係→上部構造=政治宗教文化

封建制→資本主義 => 資本の本源的蓄積 → 生産手段(土地、機械)を持つ資本家とない労働者……

Marxの限界:1)技術進歩が外生、市場mechanism機能は説明しない;2)普遍的な法則として、特定地域で特定時期に特定の生産仕様が支配的になる理由

B)宗教

Weber, M.: 特定地域で特定時期に顕著な経済発展 → 近代のwest europeが資本主義経済発展を先駆け → 他ならぬ西洋の文化的諸現象 → protestismの宗教経済論理 → 近代資本主義の精神 (他の宗教の経済論理は資本主義をできない)

検証の難点:1)逆の因果関係;2)内生性 → Becker, S.O. & Woessmann, L.: IV → significant → channel: protestismの宗教経済論理により職業態度 → 代替仮説:識字能力で検証 = 教育で人的資本の形成 → IV → 識字significant → not 職業態度

C)経済的後進性仮説

WeberはMarxの非経済的条件 → 発展段階を否定するではない

Gerschenkron, A.: 後進国の経済発展過程は先進国とは同じ段階ではなく、本質的に異なる → 先進国の技術を借用、短時間で経済発展を達成 → 技術gapが大きいほど → 速くなる + しかし技術導入際に克服しなければならない障害も大きくなる:
1)工業化ための労働力不足 ← 労働生産のための土地を持たず、工場で規律労働に従事する能力を持つ労働力 → 逆に資本集約度の高い技術を導入
2)産業相互の補完性 ← 工業化を成功するために、補完性をもつ産業を同時に発展させる必要
e.g. ドイツ:銀行system → 産業と密接な関係、産業企業金融に大きな役割 → 資本集約度の高い産業を同時に発展 / ロシア:国家主導の産業発展
→ 障害の難易度が相違、対応して克服ための組織制度も異なる

4。制度と経済発展

A) The rise of the west

North & Thomas: それまで考えられてきた「様々な要因(技術革新、規模の経済、教育、資本蓄積など)」は成長の要因ではない、成長そのもの→Weberのような始動させた独自の要因をprotestismの経済論理に求めるもなく→効率的な経済組織→取引コストを削減して個人的なbenefitを社会的なbenefitに近づける諸制度(TC:調査、交渉、実施コスト)→ 16-18世紀のwest europeの国家によるproperty right保護制度(中世の小規模な分散的統治から集権的国家)→ 契約の実行と国家の恣意を担保、取引を促す → e.g. 1688 glorious revolution: 制度変化、三権分立(単に政府がproperty right保護宣言だけではなく、人や組織が宣言や約束を守ることのincentiveを与えて、信頼を作る)→ 債務残高増加、利子低下+民間金融市場拡大

B) 制度と経済発展 

regressionの内生性問題→IV→Acemoglu: 植民当時のヨーロッパ人の死亡リスク→植民地政策のtypeは資源収奪か本国移植か→独立後も持続的な影響(死亡リスクは直接に現代の経済performanceと相関は小さい)

The colonial origins of comparative development: An empirical investigation D Acemoglu, S Johnson, JA Robinson – 2000

C) 比較歴史制度分析

TC経済学の経済史への応用:経済主体のincentiveが制度から影響を受ける
(Marx主義はincentiveを無視、neoclassicalはincentiveを理論に組み込んて、制度の影響を考慮しない)
TCの問題点:TCを節約するような管理制度が採用され→その管理制度がなぜ有効に機能する、当事者たちがなぜそれに従う→Northの研究の限界:制度は「社会におけるゲームのルール」、「人々によって考案された制約であり、人々の相互作用を形作る」→ なぜ制約は相互作用を形つくる、なぜ人々は制約を遵守する→制約が外部から実行されという想定、国家による保護に対象が限定され (内部incentive)

→ Grief, A.: 比較歴史制度分析 / Aoki: 比較制度分析 → 制度を「技術以外の要因によって決定される行動に対する自己拘束(self-enforcing)的な制約」← 人々がその制約に従うincentiveを持っている → game theory nash equilibrium → 様々な制度を分析

Micro theory and recent developments in the study of economic institutions through economic history A Greif – 1997

5。市場経済の発展

A) 市場経済の歴史

Greece: 農業より、外国貿易に比較優位があった ← 貨幣の使用
Rome: ローマ帝国の安定した長期支配 → 治安の安定、所有権と契約執行を規制するローマ法
Medieval: イスラム教の侵入→ 地中海を支配+アジアから切り離された → 西europeが孤立、非商業的、自給自足的な性格で独特の経済社会systemが発達 → 社会分業縮小、発達した都市衰退、人口は農村に集中、領主が支配する荘園に所属(耕作地を保有、貢租を納める、離れる自由がない)→ 商業ないし市場経済は著しく衰退
Vines: 当初から海上商業を活発に行い、東方との貿易を従事 → イスラムの支配を受けなかった東地中海で、europeの東側の窓として、商業活動を発達、イスラム勢力を排除
Scandinavian:古代から羊毛工業、優れた航海技術でBaltic Seaで海上商業に専念
=> 二つの貿易圏の結合から→商業の復活→中世都市が発達

中世日本:13世紀中国からの銅銭流入が市場経済の発達を強く促進 / 年貢の財を販売するため、畿内周辺の港町が年貢の保管輸送販売業務によって商業機能に純化した近世の問屋が成長
中世日本:戦国は中世の分散荘園と異なる中央領主の分権制を弱め、統一し、城下町を建設、通行税を廃止、商業を振興、分業関係を形成、最後徳川の政策下で、市場経済を発達 → 兵農分離と石高制 → 地域間分業/藩領域間の分業
近世日本:人口と実質貨幣残高の増加により市場経済が持続的に成長

B)中世地中海商業の比較歴史制度分析

Greif: 11世紀地中海商業の復活を可能にした制度 → 統一的な国家でもない、各地域外国商人の契約を保護する仕組みを備えてない → Maghribi Traders’ Coalitionの私的制度による契約執行保護のメカニズムで遠隔地貿易、agency/commitment problemを解決 → 1)不正のない限り長期取引;2)不正の場合取引しない、不正の情報を共有、共同で取引拒否、すなわち名誉を作る(Multilateral Punishment Strategy)

← このStrategyを参加する個々の商人のincentive:multilateral punishment → 高い賃金じゃないでも不正の機会費用↑ → 不正経歴のあるagentを排除、低い賃金で誠実な行動を引き出す → 商人がstrategyをとるincentiveをもつ、予測の予測を共有(ゲームの均衡)→ information network

(#game theory内informationの効率と非効率)

(#→日本社会の再就職困難の理由?)

C) 近世日本における株仲間の役割

市場経済の枠組みとしての国家の役割が大きとしても、十全ではない → 金公事の紛争の国家による契約執行が行われない → 株仲間という組織の私的な制度 → 不正を行った仲買人と一切商売をしない、他の仲間メンバーと一緒 → 様々な問屋仲間などが、商取引における不正に対して多角的罰

(#均衡に至る経緯は必ずしも明確ではない)→ 株仲間が特定地域における特定事業の同業者集団 + 大きなものではない + 不正をメンバーに周知する公式の手続きを持っていました(行司の役)

18世紀普及、19世紀全面禁止 → strategy機能の実証テスト機会
→ 1)価格裁定機能、同じ財の地域間の価格差から市場経済の発達度を測る → 大阪、江戸、など13地域の米価データを用い、2地域ずつ時系列について相関係数を求める → 1833-41 / 42-50 機能低下
→ 2)経済成長とそれに影響する変数についてデータを見出して、禁止の変数を加えて回帰分析

注意点:この制度のままで、より長期に渡る経済発展を続けることは難しい → 情報共有ため、取引相手の数が比較的に限定され → 近代国家の司法制度が近いメカニズムを拡大

6。生産組織I:工場と企業

A)産業革命

工場制:賃金を対価として雇用された労働者が、工場で経営者が課す規律に服して集団的に働く生産組織
Ashton, T.S.: 18世紀末モスリン需要 → 綿織り物工業が活況 → 新しい紡績機を発明 → 綿糸の供給不足を解決 → 力織り機の普及 → 機械化によって多数労働者が工場で集め、経営者の管理下で → 工場生産 → 産業革命 ← 固有の障害が取り除かれ、systematic change: 1)労働者を確保、管理 → 支配人、職長など監視管理職を設置+incentiveを刺激する賃金体系、罰金制度 → 賃金労働者、全国労働市場の形成
2)銀行、金融システムが工場からの資金需要を供給

Crafts, N.: 定量的な研究を通じて劇的な変化という産業革命観を修正
1)経済成長率は産業革命期に上昇したが、変化は連続、成長率は高くない + 技術進歩の寄与度が急激に上昇ではない、むしろ18世紀末低下
2)綿工業生産の経済全体に占めるweightが小さかった(鉱工業、建築業)

Pomerantz, K.: 再び産業革命の画期性を強調 → 産業革命の中心を変わる + 長期持続すれば指数関数の上昇
18世紀末まで、西europeと中国、Englandと長江デルタ地域を所得水準が同、その後格差が拡大 ← 成長を阻害する共通の制約の顕在化:土地、燃料、食料等環境制約 → England: 1)燃料の木材から石炭への転換;2)アメリカ大陸からの土地集約的財の輸入

経済史分野における経済成長理論の研究:Allen, R.C., 2009, Clark, G., Joel Mokyr, 2009.  + 歴史の出来ことを組み込む:Kremer, M. 2009, Galor, O. 2011

B)Order/Hierarchy

産業革命 → macro的画期じゃなく、micro level技術変化、働き方変化、生産組織変化

Adam Smith: 工場制→分業生産
Marx: 工場制→資本家による労働者を搾取
→ 1970年代radical economics: Marglin, S.: What do bosses do? → Marx主義の立場から工場制の本質を論じ → 問題:技術が社会経済組織を形作るのか、あるいは逆/工場制という生産組織は技術の必然? → 工場制の本質は位階制的構造「hierarchy」(すなわち工場経営者が労働者の生産活動を管理する)→現存する技術はherarchy的な生産組織に適合する (個々の労働者が自分生産管理でも高い効率性を実現できるような技術を設計できる?→しかし諸制度全体に合う仕組みから、経済全体変革が必要)
=> 技術と制度、組織の補完性 → 経路依存的な経済システムの進化

→ なぜ工場制とhierarchyが形成 → 問屋制(生産物管理権の集中)と工場制(生産過程管理権の集中)の二段階により労働者管理権の喪失 → 技術変化に先行して生産組織が変化という歴史的な証拠(自立労働と同じ技術のままで、問屋制さらに工場制への移行という事例:機械化が実用化される前に、手織工は仕事場に集められ → 収益源は優れた技術訳ではない)→ 規律と監督によって生産性を高める
→ Coaseを言及、しかし、企業を市場と代替的な資源配分の仕組みを評価が、TCの節約する手段より労働者を服従されるための手段を強調

# it makes sense if we only see firm as a cooperating function for economics of scale/division of labor, but firm also works as an information processing function (in nature or in further sense a kind of lowering transaction costs or efficient risk taking) and an incentive function. → so yes, technology may come from organizational change with some interactions, but there is no way of a technological route for non-hierarchy structure.

→ Landes, D.S.: What do bosses really do?  → 生産性上げるには規律と監督だけではない → marketingにおける時間や能力 + 技術も重要 → 集中作業場が機械化によって競争優位を確立

→ O.E., Williamson: Economic institutions of Capitalism: Firm, Markets and Relational contracts: 規律と監督を労働者の搾取という所得配分の視点ではなく → 規律を監督の役割をTCの節約を捉え(怠業、原材料詐取、粗悪品を生産) → hierarchy (価値判断)

C)The visible hand

Chandler A.D.: 新しい企業組織の革新:19世紀後半以降、産業革命の成果である工場制や鉄道が広大な国土をもつアメリカに移植され、大企業が形成され、経済の仕組みを変えた ← 企業内部資料調査

鉄道は原動力:1)企業規模増大→組織革新を先導;2)広大な国土を一つ市場に統合→大量流通、大量生産の条件を形成 (1870年鉄道網完成)
→ 幹線鉄道会社はそれまでのない企業特徴:1)格段に規模、事業が大きく(資本金、従業員);2)複雑的な管理能力が必要

=> 新しい組織構造を発達させ:line and staff: line→社長、総支配人、管区支配人という現業部門の縦のorder system; staff→本社の運送、動力、財務など職能部門の管理者は現場と分離、社長を補佐する位置づけ
←機能するために、上の階層から下に命令指示、下から上に報告+管区支配人の業績を評価 (incentive仕組み)+原価計算を含む会計systemを整備

=> 巨大市場→ 専門化から大量生産機能と大量流通機能を一つの組織の中に統合 → 3つのパターン:1)低価格の商品の生産に連続工程の大量生産技術を導入;2)使用とメンテナンスに特別なサービスを必要とする製品を生産する;3)腐敗しやすいため流通過程で特別な取り扱いを必要とする商品 => 複数の地域の事業と複数の職能を担う→ 職能別複数のlineをもつline and staff → 本社機能を拡充:社長、取締役、職能部長が構成する経営委員会がtop mangement機能を担う(評価、調整、企画)

* 経済systemが機能するため ← coordination function + incentive function → not only by market but also by organizational hierarchy (visible hand)

D)生産、流通組織の選択

TC: TCは取引の属性と統治構造によって異なる → 属性に応じてTC最小の構造が選ばれる
属性: e.g. asset specificity → high TC (# according to Demsetz not tc but risk and hurdle to transaction) → TCを節約する統治構造:長期契約/将来事態想定難い場合→取引を企業内部化(vertical integration)

TC→Chandlerの市場と企業の関係の変化を説明 + 不可逆的な歴史的傾向ではなく、特定条件の下で生じる可逆的な現象 (“Beyond Markets and Hierarchies: Toward a new Synthesis of American Business History”, AHR, 2003)
(背景:1980年代以前、統合された大企業がアメリカ経済で主要な地位をしめ、最大規模企業のrankingがほとんど変化しない(Edwards, R.) → 1912年にUS大規模企業top100の54社は1995年に17社残り、かつ26社だけ実質資本金を増加(Marshall’s” Trees” and the Global” Forest”: Were” Giant Redwoods” Different? L Hannah – Learning by doing in markets, firms, and countries, 1999)→1980年代以降に、大規模企業が大幅に後退←当時conglomerate企業の株価市場評価が低下し、買収対象とされ解体され )

TC → 19世紀末の垂直統合 → 大量生産体制を支える製品原材料流通機構が存在しない + asset specificityにより高いTC → 内部化
TC → 20世紀末の統合解体 → 現代多くの流通企業が設備と専門的なnowhowを蓄積、需要に応えることができる + 需要が多いによりasset specificityが低下により低いTC → 市場を利用する(組織内取引の方が高い→incentiveの低下、incentive仕組みが必要 /market competition→incentive)

7。生産組織II:奴隷制、地主制、問屋制

8。金融取引と制度

Market Dynamism

This topic is related to The Rise of Market Power and the Implications and Firm Turnover and Competition

papers that argue High market dynamism

The changing nature of competition in the US manufacturing sector, 1950—2002
LG Thomas, R D’Aveni – Strategic Organization, 2009

The age of temporary advantage RA D’Aveni, GB Dagnino… – Strategic management …, 2010

The rise in firm-level volatility: Causes and consequences D Comin, T Philippon – NBER macroeconomics annual, 2005

Survival and size mobility among the world’s largest 100 industrial corporations, 1912-1995 L Hannah – The American Economic Review, 1998

Marshall’s” Trees” and the Global” Forest”- Were” Giant Redwoods” Different? L Hannah – Learning by doing in markets, firms, and countries, 1999

 

papers that argue lowing market dynamism

*Changes in Persistence of Performance Over Time VM Bennett, CM Gartenberg – 2016

The Other Aging of America: The Increasing Dominance of Older Firms I Hathaway, R Litan – Brookings Institution, 2014

Declining business dynamism in the United States: A look at states and metros I Hathaway, RE Litan – Brookings Institution, 2014

The secular decline in business dynamism in the US R Decker, J Haltiwanger, R Jarmin… – … draft, University of …, 2014

Declining business dynamism: Implications for productivity
RA Decker, J Haltiwanger, RS Jarmin… – … Center Working Paper …, 2016

Declining Entrepreneurship, Labor Mobility, and Business Dynamism: A Demand-Side Approach
M Konczal, M Steinbaum – New York, NY: The Roosevelt …, 2016

Low formation and start-up

What’s Driving the Decline in the Firm Formation Rate? A Partial Explanation
I Hathaway, RE Litan – The Brookings Institution, 2014

A Start-Up Slump Is a Drag on the Economy. Big Business May Be to Blame. nonacademic summing-up

 

Good DID papers

Introduction:

Applied Microeconomics Lecture 3: Difference-in-Difference Estimation

The recommends on paper illustrating DiD methods are gathered according to a tweet talk:

Entitled to work: Urban property rights and labor supply in Peru E Field – The Quarterly Journal of Economics, 2007

Individual vessel quotas and increased fishing pressure on unregulated species
F Asche, DV Gordon, CL Jensen, SU Rashid… – Land economics 2007

Water for life: The impact of the privatization of water services on child mortality
S Galiani, P Gertler… – Journal of political …, 2005

Effective Policy for Reducing Poverty and Inequality? The Earned Income Tax Credit and the Distribution of Income Hoynes and Patel 2017

Cycling to School: Increasing Secondary School Enrollment for Girls in India Karthik Muralidharan & Nishith Prakash AMERICAN ECONOMIC JOURNAL: APPLIED ECONOMICS VOL. 9, NO. 3, JULY 2017

The incidence of mandated maternity benefits J Gruber – The American economic review, 1994

Decriminalizing indoor prostitution: Implications for sexual violence and public health NBER working paper S Cunningham, M Shah – 2014

Did unilateral divorce laws raise divorce rates? A reconciliation and new results
F Gregg – The American Economic Review, 2006

How much should we trust differences-in-differences estimates? M Bertrand, E Duflo… – The Quarterly journal of …, 2004

Consumers as Tax Auditors (Revise and Resubmit, American Economic Review)

Schooling and labor market consequences of school construction in Indonesia: Evidence from an unusual policy experiment E Duflo – 2000 – nber.org

Outsourcing at will: The contribution of unjust dismissal doctrine to the growth of employment outsourcing DH Autor – Journal of labor economics, 2003

The Effect of Health Risk on Housing Values: Evidence from a Cancer Cluster Lucas W. Davis AMERICAN ECONOMIC REVIEW VOL. 94, NO. 5, DECEMBER 2004

Others:

Causal Friday: Some Real Effects of the Flint Water Crisis…

 

 

 

The cooperation evolution 2

(See last post “Cooperation under institutions, norms and culture evolution” for articles introducing the theory of culture evolution, evolutionary biology, evolutionary anthropology, and even a math modeling which explain the evolution of cooperation, norm, and institution in human society.)

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The coevolution of kinship systems, cooperation, and culture Benjamin Enke 2017

 

How cooperation evolves: History, expectations, and leadership Daron Acemoğlu, Matthew Jackson  2011

 

Search Theory

From wiki

search theory: studies buyers or sellers who cannot instantly find a trading partner, and must therefore search
In labor economics → analyze frictional unemployment from job hunting by workers
In consumer theory → analyze purchasing decisions
→ a given job or product is acceptable → depends on the searcher’s beliefs about the alternatives available in the market
=> an individual’s optimal strategy → choosing from a series of potential opportunities of random quality ← under the assumption that delaying choice is costly
=>> search models: how best to balance the cost of delay against the value of the option to try again (optimal stopping problems in math)

Search from a known distribution

George J. Stigler proposed thinking of searching for bargains or jobs as an economically important problem
– Stigler, George J. (1961). “The economics of information”. Journal of Political Economy69 (3): 213–225
– Stigler, George J. (1962). “Information in the labor market”. Journal of Political Economy70 (5): 94–105.

John J. McCall proposed a dynamic model of job search, based on the mathematical method of optimal stopping (base of later work)
– McCall, John J. (1970). “Economics of information and job search”. Quarterly Journal of Economics. 84 (1): 113–126. 
→ which job offers an unemployed worker should accept, and which reject ← when the distribution of alternatives is known and constantvalue of money is constant
=> optimal strategy → reservation wage  (reservation price in consumers searching for low price)
<= reservation wage may change over time if some of the conditions assumed are not met
a) a worker who fails to find a job might lose skills or face stigma, in which case the distribution of potential offers that worker might receive will get worse, the longer he or she is unemployed → optimal reservation wage will decline over time
b) if the worker is risk averse, the reservation wage will decline over time if the worker gradually runs out of money while searching.
Danforth, John P. (1979). “On the role of consumption and decreasing absolute risk aversion in the theory of job search”. In Lippman, S. A.; McCall, J. J. Studies in the Economics of Search. New York: North-Holland.
c) reservation wage would also differ for two jobs of different characteristics (compensating differential)
=>>  greater variance of offers → may make the searcher better off + prolong optimal search, even if risk averse → wait longer(set a higher reservation wage) in hopes of receiving an exceptionally high wage offer

Search from an unknown distribution
→ an additional motive for search: by searching longer, more is learned about the range of offers available (multi-armed bandit problem)
optimal search strategies for an unknown distribution have been analyzed using allocation indices such as the Gittins index.

A violation of the law of one price
when buyers do not have perfect information about where to find the lowest price (whenever search is necessary) → sellers may wish to offer different price
=> a trade-off between the frequency and the profitability of their sales (target on consumers with the highest/low reservation prices)
– Butters, G. R. (1977). “Equilibrium distributions of sales and advertising prices”. Review of Economic Studies. 44: 465–491. doi:10.2307/2296902.
– Jump up ^ Burdett, Kenneth; Judd, Kenneth (1983). “Equilibrium price dispersion”. Econometrica. 51 (4): 955–969.

## it is reasonable to argue that the seller is able to change or affect reservation prices if buyer needs to learn the distribution of price from past searching. However, knowledge or other reserved information may also work in the process of searching and learning of distribution.

Matching theory
→ More recently, job search, and other types of search, have been incorporated into macroeconomic models, using a framework called ‘matching theory’.
→ Peter A. Diamond, Dale Mortensen, and Christopher A. Pissarides won the 2010 Nobel prize in economics for their work on matching theory.
=> the rate at which new jobs are formed is assumed to depend both on workers’ search decisions, and on firms’ decisions to open job vacancies

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Markets with Search Frictions The Nobel Prize in Economic Sciences 2010 – Advanced Information

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Classic papers

Information and consumer behavior P Nelson – Journal of political economy, 1970

Economics of information and job search JJ McCall – The Quarterly Journal of Economics, 1970

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Job search papers

Directed Search: A Guided Tour R Wright, B Julien, P Kircher, V Guerrieri – 2017

Search theory → understanding many phenomena troublesome for classical theory
(e.g.  coexistence of unemployment and vacancies + price or wage dispersion and stickiness + bid-ask spreads + the difficulties of bilateral trade that generate a role for money and related institutions + partnership formation + long and variable durations in the time to execute trades in labor, housing and other markets)

→ a relatively recent branch of the field called directed, or competitive, search

older literature on random search:
On goods markets, see Burdett and Judd (1983), Rubinstein and Wolinsky (1987), Shi (1995) or Trejos and Wright (1995).
On labor, see Mortensen and Pissarides (1994), Burdett and Mortensen (1998) or Pissarides (2000).
On marriage, see Mortensen (1988), Burdett and Coles (1997) or Shimer and Smith (2000). 

Traditional search theory
→ typically assumes the agents meet bilaterally and at random
← a meeting results in matching (trading or forming a relationship) can be endogenous, especially when there is heterogeneity
→ assume the terms of trade are determined by bargaining, or some related mechanism, after agents meet

Directed/Competitive search
agents have information to target their search towards particular types, or sometimes particular individuals, in the market
→ the terms of trade (prices, or more generally, contracts or mechanisms) are announced or posted in advance to attract/direct agents on the other side of the market

=> posted prices have an allocative role → giving agents incentives to seek out particular counterparties → often leads to efficiency  ## can also be misleading  
=> posting entails commitment → circumvents holdup problems with bargaining  (# a claimant of welcome for bargain or no bargain improve efficiency of searching given the bargaining cost)

More realistic
In contrast to what happens in [random] search models, exchanges in actual market economies are organized by specialist traders, who mitigate search costs by providing facilities that are easy to locate.
(Thus when people wish to buy shoes they go to a shoe store; when hungry they go to a grocer; when desiring to sell their labor services they go to firms known to offer employment. Few people would think of planning their economic lives on the basis of random encounters.”)

Peter Howitt (2005) “Beyond Search: Fiat Money in Organized Exchange,” IER 46, 405-429.

“someone wishing to exchange his house goes to estate agents or advertises — he does not, like some crazed particle, wait to bump into a buyer.”
“I think the bilateral monopoly problem has been solved. There are stores that compete. I know where the drug store and the supermarket are, and I take their posted prices as given. If some supermarket offers the same quality of services and charges lower prices, I shop at that lower price supermarket.”

frictions take center stage, even when the set of agents is large
← Research often makes a concerted effort to analyze strategic aspects of markets with finite numbers of agents → in several settings as these numbers get large, strategic considerations vanish
→ a competitive search model means a limiting large economy → large markets, finite markets and limiting results (limiting results are nice because intuition that markets becoming competitive when the set of agents is large, but formalizing this can be difficult (see Gale 2000 and references therein))
=> some sellers can have few or no customers, while others have more than they can handle → leading to rationing, unsold inventories, the coexistence of vacancies and unemployment, etc.

A simple yet powerful idea:
if you post more favorable terms customers come to you with higher probability, but not necessarily probability 1, due to capacity issues
=> Agents on both sides of the market face thus a trade off between prices and probabilities →  may not be smart to go where everyone else goes
=> pricing not only quantities but also the time required to trade → delivers unique outcomes with remarkable efficiency properties (traditional search theory is typically rife with inefficiencies) → competitive search can also accommodate complications (like private information or liquidity frictions) → may lead to multiplicity or inefficiency

 

Search-theoretic models of the labor market: A survey R Rogerson, R Shimer… – Journal of …, 2005

Empirical 

Looking into the black box: A survey of the matching function B Petrongolo, CA Pissarides – Journal of Economic literature, 2001

Matching 

Sorting through search and matching models in economics H Chade, J Eeckhout, L Smith – Journal of Economic Literature, 2017

 

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Consumer search theory papers

Firm Pricing with Consumer Search Simon P Anderson § Régis Renault CEPR Discussion Paper

Search costs are often ignored by economist ← few people actually actively searched much + less visible as a friction in market + treating set of available products as effectively given and known => important for better matching and lower prices from more competition (less oligopoly pricing)
Consumer search: internet → lower search cost + low transaction costs for shipping => consumers enable to access a huge variety of options → used to be silently curtailed by sc now visible → nonetheless, significant search frictions remains

2. Price dispersion

Stigler (1961):  price dispersion may persist ← consumers are not aware of all prices + therefore cannot properly arbitrage price differences
=> costly search by buyers generates price dispersion → from the price mixed strategies used by firms

2.1 Imperfect buyer information yields price dispersion

n firms: pc=0, homogeneous production
m consumers: valuation=r, σ shoppers: sc=0 → always buy at the lowest price in the market,  (m-σ) shoppers: observe only one price for free and high sc for an additional price → buy from free price quote, γ=(m-σ)/n = captive consumer per firm → firm guarantee a profit of γr by charging the monopoly price r and selling exclusively to γ

Bertrand undercutting: no pure strategy equilibrium for a price exceeds mc → a firm at a price above mc could always profitably capture entire σ demand by slightly undercutting price
← but pricing at mc cannot be an equilibrium → no profit → can always guarantee a strictly positive profit by giving up selling to σ and extracting the entire surplus from γ
→ it is optimal for that firm to charge r and get γr

=> minimum equilibrium price:  (γ + σ)p = γr  →  p_ = γ/(γ+σ) * r
(no one does actually search again in equilibrium → prices are rationally expected to be same for all firms → no search that monopoly price sustains)

(even a small search cost radically tips the Bertrand Paradox to the Diamond Paradox which has all firms pricing at monopoly price)

(## 1) there is not reasonable to assume 0 sc if we think of unknown of unknown. 2) why cannot firm also search for the type of consumer, then price r to γ and p to σ ? 3) firm can affect the consequent searching cost by misleading when they touch with consumers. 4) why are price dispersion shown among different brands rather than different districts, while the later seems more related to sc)

Varian(1980) + followers: unique symmetric mixed strategy equilibrium
スクリーンショット 2017-10-01 14.16.11スクリーンショット 2017-10-01 14.10.15

2.2 Simultaneous search and the coordination problem

2.3 Sequential search and the Diamond paradox

2.4 Price advertising 

3. Matching products to consumers

3.1 optimal search behavior

3.2 Equilibrium and comparative statics

3.3 Mergers and cartels

3.4 Ordered search

4. Seller heterogeneity 

5. Buyer heterogeneity

6. Conclusions

 

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Business as usual: A consumer search theory of sticky prices and asymmetric price adjustment L Cabral, A Fishman – International Journal of Industrial Organization, 2012

Empirical evidence suggests that prices are sticky with respect to cost changes. Moreover, prices respond more rapidly to cost increases than to cost decreases. We develop a search theoretic model which is consistent with this evidence and allows for additional testable predictions. Our results are based on the assumption that buyers do not observe the sellers’ costs, but know that cost changes are positively correlated across sellers. In equilibrium, a change in price is likely to induce consumer search, which explains sticky prices. Moreover, the signal conveyed by a price decrease is different from the signal conveyed by a price increase, which explains asymmetry in price adjustment.

When do consumers search? MS Lewis, HP Marvel – The Journal of Industrial Economics, 2011

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Oligopolistic markets with sequential search and production cost uncertainty
M Janssen, P Pichler… – The RAND Journal of …, 2011

Search costs in concentrated markets: An experimental analysis C Moellers, T Stühmeier, T Wenzel – 2016

 

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# Questions:

What decide the searching costs which is surly subjective and endogenous?
How does the distribution of results which is also subjective change along with searching activities? (bayesian adjustment)

Moreover, there is searching strategy like inquiring someone who has better knowledge about searching cost and result distribution. (directed search) However in such case, there are also adverse selection problem born from asymmetric information.

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Appendix

Other theories about consumer searching (marketing & behavior economics)

Consumer information search revisited: Theory and empirical analysis S Moorthy, BT Ratchford… – Journal of consumer …, 1997

Toward a positive theory of consumer choice R Thaler – Journal of Economic Behavior & Organization, 1980

A model of consumer information search behavior for new automobiles GN Punj, R Staelin – Journal of consumer research, 1983

Consumer information search behavior and the Internet RA Peterson, MC Merino – Psychology & Marketing, 2003

A proposed model of external consumer information search JB Schmidt, RA Spreng – Journal of the academy of marketing science, 1996

Gary S. Becker’s Economics Imperialism

Investment in human capital- A theoretical analysis GS Becker – Journal of political economy, 1962

A Theory of the Allocation of Time GS Becker – The economic journal, 1965

A theory of marriage- Part I GS Becker – Journal of Political economy, 1973

A theory of social interactions GS Becker – Journal of political economy, 1974

De gustibus non est disputandum GJ Stigler, GS Becker – The american economic review, 1977

A theory of competition among pressure groups for political influence GS Becker – The quarterly journal of economics, 1983

A theory of rational addiction GS Becker, KM Murphy – Journal of political Economy, 1988

Barriers to the advance of organizational science- Paradigm development as a dependent variable J Pfeffer – Academy of management review, 1993

Human capital revisited GS Becker – Human Capital- A Theoretical and Empirical Analysis …, 1994

 

A history of Becker’s Economics of discrimination by JB Fleury (& how “imperialism” is just ex-post rationalization)

Continue reading “Gary S. Becker’s Economics Imperialism”

Basic Econometrics: why log?

 

1. heteroscedasticity

对数据做一些变换的目的是它能够让它符合我们所做的假设,使我们能够在已有理论上对其分析。
对数变换(log transformation)是特殊的一种数据变换方式,它可以将一类我们理论上未解决的模型问题转化为已经解决的问题。我将说两类比较有代表性的模型。

A. 理论上:随着自变量的增加,因变量的方差也增大的模型。

先给个很经典的例子,如分析美国每月电力生产数。
左边是正常数据,可以看到随着时间推进,电力生产也变得方差越来越大,即越来越不稳定。这种情况下常有的分析假设经常就不会满足(误差服从独立同分布的正态分布,时间序列要求平稳)。
这必然导致我们寻求一种方式让数据尽量满足假设,让方差恒定,即让波动相对稳定。而这种目的可以通过对数转换做到。

理论上,我们将这类问题抽象成这种模型,即分布的标准差与其均值线性相关
\sqrt{Var(Z_{t})} =\mu _{t}\times \sigma ,其中E(Z_{t}) =\mu _{t}
由定义可推:Z_{t}=\mu _{t}\left( 1+\frac{Z_{t}-\mu _{t}}{\mu _{t}}  \right) ,利用log函数的性质:log(1+x)\approx x(当x足够小)
那么log(Z_{t})\approx log(\mu _{t})+\frac{Z_{t}-\mu _{t}}{\mu _{t}} .
那么很容易就知道E(log(Z_{t})) \approx log( \mu _{t})Var(log(Z_{t})) \approx \sigma ^{2} .

所以对数变换能够很好地将随着自变量的增加,因变量的方差也增大的模型转化为我们熟知的问题。

B. 经验上:研究数据的增长率分布存在一定规律的模型。

再给个例子:实际研究中,某一研究对象自身性质难以研究,但其增长率是服从一定分布。例如说:Z_{t}=(1+X_{t}) \times Z_{t-1},其中X_{t}是每年增长率(不很大)。
我们可以考虑对数变换:log(Z_{t})-log(Z_{t-1})=log\left(  \frac{Z_{t}}{Z_{t-1}}  \right)=log\left( 1+X_{t} \right)\approx X_{t}
这样,我们又可以将研究数据的增长率分布存在一定规律的模型转化为我们熟知的问题。

在对数转换后,人们又思考了很多其他的转换方式(如Cox-Box转换)。但总而言之,每一种转换方式都是为了让数据符合我们的假设,来对其进行分析。

Caveats:

异方差的角度是从数据出发来解释为什么取对数。但是这里有两点需要注意:

  1. 做OLS回归的时候,异方差对系数估计的一致性没有影响,但是对假设检验有影响
  2. 计量经济学看中DGP,也就是数据生产过程。而取不取对数取决与研究人员对DGP的belief是怎样的,而这种belief是从理论或者直觉上来的

 

2. Distribution and Economics meaning

A. 将数据取对数有一定的经济含义

log(1+x)=x,这个关系在x比较小的时候接近成立。因此数据取对数之后再差分有增长率的含义,举个例子:log(GDP_year2)-log(GDP_year1) = log(GDP_year2/GDP_year1)=(GDP_year2/GDP_year1)-1,即GDP的增速。取对数之后可以比较方便地研究增长率的问题。

B. 将右偏的数据形态变为正态

首先什么是“右偏”?图像上看,右偏是这种形态的分布:
简而言之,分布非对称,右边的尾部偏长,表示有一些非常大的极端值,大部分样本的数据集中在偏左的部分。
而在计量经济学的应用中,通常希望分布是正态的,或者至少是对称的,既不往左也不往右偏,也就是下面这种形状:
大多数的经济数据都是呈右偏的形态如收入分布,企业的资产规模,等等,取了对数之后可以一定程度地修正数据的右偏形态,使其更接近于正态。数据的正态性对于统计量的各种小样本性质,统计量的有限样本分布,极大似然估计方法的应用都有比较重要的含义。

Caveats:为什么很多数据是这样的分布。

取对数的原因很简单,经济学理论大多可以得到取对数的函数形式,或者直觉告诉我们,不取对数与现实不符。

举几个例子:

a)人口

这个应该是最容易理解的,如果不考虑自然条件的限制,生物的种群总是指数增长的:\frac{dP}{dt}=rP,其中P为人口,r为人口的自然增长率。现在我们假设有两个国家D=0,1,两个国家的人口一般说来是增长率的差异,比如差\beta,所以模型可以写成:\frac{dP}{dt}=\left( r+\beta D \right) P,整理一下就可以写成d\log{P}=r+\beta D。如果你写成P=e^{rt}+\beta D是什么意思呢?每年国家1比国家2多\beta个人,这样显然不现实。

b)GDP
这个可以从生产函数Y=AK^{\alpha}L^{1-\alpha}导出\log{Y}=\log{A}+\alpha \log{K}+\left( 1-\alpha \right) \log{L}。这个生产函数形式是经济学最常用的。
也许你会说,这个生产函数是个假设,我也可以假设Y=A+\alpha K+\beta L的形式啊。但是如果你这样假设,会跟现实差距很大,比如用C-D的假设可以得出GDP的增长率跟劳动和资本的增长率大约是同阶的,但是用线性的就得不到。还有很多其他的观察,比如规模报酬、要素的替代等等。一个假设肯定是以为其对现实拟合的很好才会被保留下来的(这里的拟合不仅仅是直接的拟合,还包括理论的其他推论的拟合)。

c)国际贸易
也就是我们说的引力模型了。如果你假设了消费者的适当的效用函数形式以及以上的生产函数形式,经过一系列复杂的一般均衡的推导,可以得到两个国家之间的贸易量有如下形式:
X_{i,j}=\frac{X_i X_j}{D_{i,j}}\eta _{i,j}
其中左手边是两个国家之间的贸易量,右手边是两个国家的产出和距离。做回归的时候,自然也就得到了log的形式。

Matching Function
具体我就不介绍了,可以看Shouyong Shi 的文章<Pricing and Matching with Frictions>。这个函数的右手边是市场上工作的个数和工人的个数,左手边是匹配成功的个数。以下的函数形式也是在很简单的假设下推导出来的,当n m很大的时候,这个函数也是慢慢变成齐次的,用C-D来表示是个很好的近似:

其他例子我就不举了。其实仔细想一下这个问题,理论都是基于假设,而理论的验证则是看理论的推测是不是满足现实。所以剩下来的没有被抛弃的理论都是前人经验没有推翻的。所以,与其说是理论告诉我们要取对数,还不如说是前人的经验告诉我们,绝大多数level的变量都要取对数。

 

3. Statistics

总的说来,对数变换是数据变换的一种常用方式,数据变换的目的在于使数据的呈现方式接近我们所希望的前提假设,从而更好的进行统计推断。但需要注意的是,数据是离散变量时进行对数变换要额外小心!

当然,我们可以追问的更多:

A. (Why)为什么需要做数据变换?

  • 从直观上讲,是为了更便捷的发现数据之间的关系(可以理解为更好的数据可视化)。举个栗子,下图的左图是各国人均GDP和城市人口数量的关系,可以发现人均GDP是严重左偏的,并且可以预知在回归方程中存在明显的异方差性,但如果对GDP进行对数变换后,可以发现较明显的线性关系。为什么呢?因为我们度量相关性时使用的Pearson相关系数检验的是变量间的线性关系,只有两变量服从不相关的二元正态分布时,Pearson相关系数才会服从标准的t-分布,但如果变量间的关系是非线性的,则两个不独立的变量之间的Pearson相关系数也可以为0.
  • 所以,数据变换后可以更便捷的进行统计推断(t检验、ANOVA或者线性回归分析)。例如通常构造估计量的置信区间时是使用样本均值加减两倍标准差的方式,而这就要求样本均值的分布是渐近正态分布,如果数据呈现出明显的偏度,则此时使用上述统计推断方式就是不适用的;另外,最经典的例子就是回归分析中的异方差性,误差项的方差随着自变量的变化而变化,如果直接进行回归估计残差的方差会随着自变量的变化而变化,如果对变量进行适当变换,此时残差服从同一个正态分布。

B. (Why)为什么可以做数据变换?

    • 这个问题很难,每当做数据变换时,禁不住会想这样原始的数据信息是否经过变换后存在损失?数据变换有没有标准程序原始数据的统计推断又该怎么进行?我也没有完全理清思路,但想通过几个例子抛砖引玉。
    • 先从理论情形下去考虑,例子1,如果一个数是连续的,并且服从对数正态分布ln(X)\sim N(\mu,\sigma^{2}),可以很容易知道X的概率密度函数(PDF)f_{X}(x)=\frac{1}{x\sqrt{2\pi}\sigma} e^{-\frac{(lnx-\mu)^2}{2\sigma^{2}} } ,这样E(X)=e^{\mu+\frac{\sigma^{2}}{2}}Var(X)=\left( e^{\sigma{2}-1}  \right)e^{2\mu+\sigma^2} ,此时可以看到已知变换后的数据的统计特征可以反过来推导出原始数据的统计特征,不存在数据信息的损失(可以看到对数转换后变量的均值可以直接由样本数据的均值得到,但不进行变化却需要由样本均值方差两方面去推断得到);例子2,如果一个数是离散的,服从负二项分布,概率质量函数(PMF)可以写成f\left( k:\theta,p\right)=C_{\theta-1}^{k+\theta-1} \left( 1-p \right)^\theta p^k,如果对这个变量进行对数变换后,情形又会怎样呢?此时,E\left( k \right) =\frac{p^{\theta}}{1-p} Var\left( k \right)=\frac{p^\theta}{(1-p)^2} ,假设数据的生成过程服从负二项分布,并且在不同的\theta=0.5,1,2,5,10,100下模拟生成数据,再用不同的方式去估计\tilde{\mu}=Y ,可以设计评价指标B=\frac{1}{S}\Sigma_{\left(s\right)} \tilde{\mu} -\mu,可以看到不同的数据变换方式下的估计精度是不同的。可以看到,如果假设数据服从负二项分布,估计的误差很小,如果假设数据对数变换后服从正态分布时会出现较大误差(由于离散分布时数据可以取0,此时对数变换需要用ln\left( x+k \right) 的形式,可以发现k取值并非随意),如果假设数据根号变换后服从正态分布时的误差要小于对数变换。所以,从一个小的随机模拟实验可以看出,数据的变换方式并非随意,并且对数变换也不一定是最好的变换,尤其是离散数据情况下(详见”Do not log-transform count data”).
  • 但上述仅仅是在理论前提下数据变换的讨论,但实际应用中呢?理论前提下,即使再复杂总能找到处理的办法,但应用问题却没有标准答案。在我看来,数据变换方法的使用更是一门艺术(先验知识+经验+运气),需要结合应用领域的专门知识。例如,在宏观计量中,许多不平稳的经济数据要进行时间序列建模,就需要进行差分变换或者去除趋势,按照经济增长理论,经济数据应该存在趋势,那对数据应该进行去除趋势变换,但后来实证发现数据进行差分变换后的ACF/PACF图更符合模型的假设,这就要求建模时使用差分变换而非去除趋势变换(从理论上可以证明一个非平稳的变量如果错误进行变换仍然是非平稳的),所以这就存在困惑(貌似说的有点远……)。

至于,怎么去做数据变换(Box-Cox正态性变换还是均匀变换)?(When)什么时候需要做什么样的数据变换?(What)数据变换后的结果是什么,如何解释?当理清上述两个为什么时,我想应该基本就能回答了。

 

4. Conclusion

取对数的原因是
(1) 时间序列和面板数据, 都要做平稳的单位根检验, 取对数一般能使序列平稳(stationary), 不然就取差分进行平稳.
(2) 能使模型的残差呈现随机的特性, 而不是趋势或者截距.
(3) 减少共线性和异方差(heteroscedasticity)出现的概率
(4) 有经济学意义上, 比如增长率, 变化率和弹性.
(5) 统计学认为变量具有内在的指数增长的趋势, 取对数可以让联合分布 (对应的F-statistics)呈现正态, level形式的数据, 特别是时间序列, 最好做Lavene检验
(6) Log-linearization 取对数方便最小二乘的线性拟合, 乘积运算用对数就变成了求和