Econometrics

V SemesterIIM Tiruchirappalli

Course structure

Course DescriptionIntroduction to econometric models and techniques, simultaneous equations, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable and time series models.

Course evaluationQuizzes, Home Assignments 10%Mid-term 25%End-term 25%Project reports (2) & presentations (2) 30%Class attendance, Attitude 10%

Text BooksEconometric Methods by Jack Johnston and John DiNardo 4th Edition. Econometric models and economic forecasts by Robert S. Pindyck and Daniel L.

Rubinfeld 4th EditionAn introduction to applied econometrics – a time series approach by Kerry Patterson

Wine talk and other examplesBordeaux & Burgundies wine – 18 -24 months in oak casks & then put for aging in bottles

Wine tasting done after 4 months during fermentation;-Influences the wine futures market

Low rainfall – concentrated grapesHigh temperature – grapes ripe faster with lower acidity

Wine quality = 12.145 + .00117 winter rainfall + .0614 average growing season temperature - .00386 harvest rainfall

Robert Parker publishes Wine Spectator and The Wine Advocate

Ashenfelter published results in Liquid Assets http://www.liquidasset.com/ Journal of Wine Economics

Refer to: http://www.nytimes.com/1990/03/04/us/wine-equation-puts-some-noses-out-of-joint.html?

Baseball & LoJack

Bill James published results in Baseball Abstracts (refer to Michael Lewis’s Moneyball) Runs created = (Hits + Walks) Total Bases / (At Bats + Walks)Later, Boston Red Sox, under Theo Epstein won the world championship.SABR – Society for American Baseball Research;Sabermetrics – Research in baseball

Studies use regression and randomization to promote better public policy

LoJack – small radio transmitter hidden in car that can be remotely activated when the car is stolen. Are there any positive externalities in installing LoJack?Results – As percentage of cars with LoJack increased, the level of auto theft fell. Insurance companies did not give enough discounts to pass on the reduction in payouts of unprotected cars.

The impact of LoJack: Ian Ayres and Steven D. Levitt, “Measuring the positive externalities from unobservable victim precaution: An empirical analysis of LoJack,” 113 Q.J.Econ.43(1998) http://pricetheory.uchicago.edu/levitt/Papers/LevittAyres1998.pdf

Framing the right question to solve the problem If drug dealers are floating in money, why do they still stay with their mothers? Why are street prostitutes like a department store Santa? Why do terrorists tend to be drawn from educated, middle class or high income backgrounds? Why should suicide bombers buy life insurance? How do prostitutes and their customers, or “johns,” find one another? How much do prostitutes charge for a service, or “trick,” and how is that price negotiated? If a

john prefers not to use a condom, how much more does he have to pay? How does a prostitute’s wage compare to what she earns for doing other jobs? What happens when there’s a sudden surge in demand for prostitutes, and how do prostitutes

meet this demand?

STEVEN D. LEVITT AND SUDHIR ALLADI VENKATESH “AN ECONOMIC ANALYSIS OF A DRUG-SELLING GANG’S FINANCES” Q.J.Econ. (2000). http://pricetheory.uchicago.edu/levitt/Papers/LevittVenkateshAnEconomicAnalysis2000.pdf

STEVEN D. LEVITT AND SUDHIR ALLADI VENKATESH An Empirical Analysis of Street-Level Prostitution. 2007.

Freakonomics Steven D. Levitt & Stephen J. Dubner

Super Freakonomics

Steven D. Levitt & Stephen J. Dubner

Super Crunchers Ian Ayres

Data – newer & faster sourcesWeb data mining Crowd-sourced tracking system (Google trends, Google Flu, Flu near you, GrippeNet.fr, Twitter)

Sources: Google Flu Trends (www.google.org/flutrends); CDC; Flu Near You

DataData sourcesData definitionCross section data; time series dataPanel data - , where (i,t) individual I at time t.Implication of . Or, Data transformation & aggregation (example, is it better to forecast all component inflation series and then aggregate the forecasts, or is it better to aggregate right away?

PreliminariesData cleaning

Non random attritionSample selection bias (non random sample)Influential observations – robust estimation methods

find parameters which minimize

Appropriate econometric modelNormal distribution of dependent variable Binary dependent variable Replace π by probit model.Time series data: or

Parameter estimation

Ordinary least squares all have common variance Generalized least squares have variances Non linear least squares non linear in parameters,

Preliminaries continued

Alternative estimation methods Maximum likelihood method – find such that are most likely values Bayesian method – estimate posterior distribution of the parameters using data,

model and priors

Diagnostics Portmanteau test or model specification test Tests on the error terms Comparing two models – Likelihood Ratio (LR) test or Lagrange Multiplier (LM)

principle or Wald method

Specification

Examples

Convergence between rich and poor countriesDo countries converge in per capita GDP? Or in living standards? Or, instead,

are they caught in a poverty trap?

Direct mail target selectionBas Donkers, Richard Paap, Jedid-Jah Jonker, Philip Hans Franses “Deriving target selection rules from endogenously selected samples”. Journal of Applied Econometrics Volume 21, Issue 5, pages 549–562, July/August 2006. DOI: 10.1002/jae.858. http://ideas.repec.org/a/jae/japmet/v21y2006i5p549-562.html

Forecasting sharp increases in unemployment Censored latent effects autoregressive model with and and is censored variable

With and an explanatory variableFranses, Ph.H.B.F and R.Paap “Censored latent effects autoregression, with an application to US unemployment” Journal of Applied Econometrics Volume 17, Issue 4, pages 347–366, July/August 2002. http://hdl.handle.net/1765/1532

Modelling brand choice dynamicsPaap, R.; Franses, P. H. A Dynamic Multinomial Probit Model for Brand Choice with Different Long-run and Short-run Effects of Marketing-Mix Variables JOURNAL OF APPLIED ECONOMETRICS; 15; 717-744.

Examples

Voting decisionsUndecided voters tend to fall as elections near. Results show that undecided voters start to make up their minds nine weeks before the national elections.

Forecasting weekly temperaturesIs the forecast uncertainty for weekly temperatures constant throughout the year?Franses, Philip Hans, Jack Neele and Dick J.C. van Dijk (2001), Modeling asymmetric volatility in weekly Dutch temperature data, Environmental Modeling and software, 16, 131-137. http://repub.eur.nl/res/pub/1533/

DistributionNormal distribution

Probability density function Cumulative distribution function

Area under pdf for a normal distribution

Log-normal distribution

Pdf:

Probability density function Cumulative distribution function

DistributionThe probability density function (pdf) of an exponential distribution is

Probability density function Cumulative distribution function

The probability density function (pdf) of an cauchy distribution is

Probability density function Cumulative distribution function

Distribution

Operations on a single random variableIf X is distributed normally with mean μ and variance σ2, then•The exponential of X is distributed log-normally: eX ~ ln(N (μ, σ2)).•The absolute value of X has folded normal distribution: |X| ~ Nf (μ, σ2). If μ = 0 this is known as the 

half-normal distribution.•The square of X/σ has the noncentral chi-squared distribution with one degree of freedom: X2/σ2 ~ χ2

1(μ2/σ2). If μ = 0, the distribution is called simply chi-squared.

•The distribution of the variable X restricted to an interval [a, b] is called the truncated normal distribution.•(X − μ)−2 has a Lévy distribution with location 0 and scale σ−2.

Combination of two independent random variables

If X1 and X2 are two independent standard normal random variables with mean 0 and variance 1, then•Their sum and difference is distributed normally with mean zero and variance two: X1 ± X2   ∼ N(0, 2).•Their product Z = X1·X2 follows the "product-normal" distribution with density function fZ(z) = π−1K0(|

z|), where K0 is the modified Bessel function of the second kind. This distribution is symmetric around

zero, unbounded at z = 0, and has the characteristic function φZ(t) = (1 + t 2)−1/2.•Their ratio follows the standard Cauchy distribution: X1 ÷ X2  Cauchy(0, 1).∼•Their Euclidean norm    has the Rayleigh distribution, also known as the chi distribution with 2 degrees of freedom.

Distribution

Combination of two or more independent random variables•If X1, X2, …, Xn are independent standard normal random variables, then the sum of their squares has

the chi-squared distribution with n degrees of freedom

•If X1, X2, …, Xn are independent normally distributed random variables with means μ and variances σ2,

then their sample mean is independent from the sample standard deviation, then the ratio of these two quantities will have the Student's t-distribution with n − 1 degrees of freedom:

•If X1, …, Xn, Y1, …, Ym are independent standard normal random variables, then the ratio of their

normalized sums of squares will have the F-distribution with (n, m) degrees of freedom:

DistributionA discrete random variable X is said to have a Poisson distribution with parameter λ>0, if for n=0,1,…The probability mass function is given as, . The real number is equal to expected value of X and also its variance.

Probability mass function Cumulative distribution functionExamples: The number of phone calls arriving at a call centre within a minute.

The number of goals in sports involving two competing teams.

Central Limit theorem

As the number of discrete events increases, the function begins to resemble a normal distribution

Comparison of probability density functions,p(k) for the sum of n fair 6-sided dice to show their convergence to a normal distribution with increasing n, in accordance to the central limit theorem.

Classical assumptions1. Regression model is linear, correctly specified with an additive error term.

2. Error term has zero population mean

3. All explanatory variables are uncorrelated with the error term

4. Observations of the error term are uncorrelated with each other (no serial correlation)

5. Error term has constant variance (no heteroskedasticity)

6. No explanatory variable is a perfect linear function of any other explanatory variables

7. Error term is normally distributed

Regression analysis1. Review the literature and develop the theoretical model2. Specify the model3. Hypothesize the expected sign of the coefficients4. Collect the data. Inspect and clean the data5. Estimate and evaluate the equation6. Document the result