11 - Correlation and Regression

Sample Covariance Cov(x,y) = [SUM(Xi-X)(Yi-Y)]/(n-1)

Sample Correlation r(x,y) = Cov(x,y)/[(StdDevX)(StdDevY)]

StdDevX^2 = [(Xi-X)^2]/(n-1)

Correlation -> Linearidade

Limitations to correlation analysis
- Outliers (dados extremos que podem levar a falsas conclusões e/ou prejudicar o sample)
- Spurious Correlation (correlação ao azar, sem razão, simples coincidência)
- Nonlinear Relationships (correlaçao é uma funçao de 1o grau, caso haja uma correlaçao mais complexa (ex. y=x^2) não linear acarretará em um r aprox. 0)

Variavéis
- Dependent: Explained, Endegenous, Predicted
- Independent: Explanatory, Exogenous, Predicting

Assumptions
- Linear Relationship (independent -> dependent)
- ñ existe correlaçao (independent -> resíduo)
- Expected Value (resíduo) = 0
- Var(resíduo) = constante
- Resíduo is normally distributed and independent r(residuo,residuo)= 0

Simple Linear Regression Model
- Yi = b0 + b1*Xi
- Beta = Slope Coeficient -> b1 = Cov(x,y)/StdDev^2(x)

Interpretation of Regression Coefficient
Beta -> Sistematic Risc & Alpha -> Risk Adjust



Hypothesis test

15 - Regulation & Antitrust policy

Two main category of Gov.Regulation is:
- Economic (control the prices that regulated firms are permited to charge in order to prevent excessive monopoly profits and predatory competitive practices)
- Cost-of-service Regulation (prices based on Avg.Cost of producing)
- Rate-of-return Regulation (prices that doesn't earn positive economic profit)
- Social (set product quality, safety, and safety of employees on workplace)

Effects of Regulation

- Creative Response (adequate but not intent). One example is the "Feedback Effect".
- Capture Hypothesis (firms will influence Reg.Agency)
- Share-the-gains, Share-the-pains (Reg.Agency will try to satisfy Gov.,Customer & Firms)

Conclusion
- Regulation
- More regulation -> higher cost of production -> higher prices for consumer
- Not easy to measure the cost impact of regulation
- Deregulation
- Negative effects on short-term (lower quality, higher prices)
- Positive effects on long-run (better quality, variety and lower cost)
- Contestable Markets - Number of firm is not determinant on the price (the market adjust automaticaly, excessive profit incentive more firms, lower profit you have bankrupts)

14 - Economic Growth

Rule of 70 - Utilizada para descobrir em quantos anos, dado uma certa taxa de crescimento constante, o GDP dobre (aumente em 100%)
Yrs = 70 / Tx.de.crescimento

Sources de um Economic Growth
- Land
- Labor
- Capital gods
- Entrepreneurial ability (how to combine the 3 keys above)

Precondition for Economic Growth
3 social institutions that incentives people to produce on sectors which they have some advantage.
- Market
- Properties Right
- Exchange rate

Productivity Curve (Labor Productivity X Capital labor/hour)
2 factors that contribute to the growth of Labor Productivity
- Physical Capital per labor/hour
- Technology

One-Third Rule states that at certain Technology level, an increase of 1% on the Capital increases the Labor Productivity on 1%/3.

Persistent Economic Growth
- Savings and Investing in new capital
- Investing in Human Capital (knowledge)
- Discovery of New technology (making physical capital and human capital more productive)

Growth Theory
Classical - Growth is temporary. Population Explosion. Subsistence Level.
Neoclassical - Population growth independent of Economic growth. You only have economic growth with technology. Change technology lead more savings and investment which increase capital per labor/hour. Growth stops at Target rate of Return (Derivada da curva)
New Theory - Growth increase with technology without barriers. People always search for profit.