Please enable JavaScript.
Coggle requires JavaScript to display documents.
APPLIED ECONOMETRICS (The Linear Regression Model (Functional forms…
APPLIED ECONOMETRICS
The Linear Regression Model
Model: Y = beta0 + beta1*Xi + ui
Economic data structure
Time series data
Cross sectional data
Panel data
Assumptions of the Classical LRM
Hypothesis testing
Testing individual coefficient: t test
Testing multiple coefficients: F test
Functional forms
Linear model
"Beta" change in Y when X increases by 1 unit.
Log-linear
The slope coefficients can be interpreted as elasticities
Lin-Log
If X increases by 100%, predicted Y increases by "beta" units
Reciprocal
The slope is negative
Polynomial
The slope is nonlinear
Critical Evaluation of the LRM
Multicollinearity
Definition
There is no exact linear relationship among the regressors
Perfect or Imperfect multicollinearity
Sources
Data collection method used
Model specification
Economic function
Variables sharing a common time trend
Consequences
The R square value may be very high
OLS estimators are still BLUE
Making the t ratios small
Detection
VIF
High pair-wise correlations
Significant F test for auxiliary regressions
Wrong expected sign but high R square
Solution
Do nothing
Restructuring of the model
Dropping one independent variable
Heteroskedasticity
Definition
The error term is constant or homoskedastic
Reasons
The presence of outliers
Incorrect functional form
Mixing observations with different measures of scale
Consequences
The estimators are less efficient
Making statistical inference less reliable
Detection
Graph squared residuals (or residuals) against predicted Y
Breusch-Pagan (BP) test
White’s test
Solutions
Weighted Least Squares (WLS)
Robust standard errors
Specification errors
Sources
Incorrect choice of variables
Omission of Relevant Variables
Regression coefficients will be biased
Inclusion of Irrelevant Variables
Unbiased and Consistent
Tests of hypotheses are invalid
Incorrect functional forms
Models of Limited Dependent Variables
Logit and Probit model
Binary dependent variable
OLS with binary dep var
The Linear Probability Model
Disadvantages
Linearly correlate
May be out of [0,1]
Non-normally distribution
Unequal variance
Logit model
Logistic distribution with the Logit model
Assumes the logit linearly correlates with Xi
"beta" is the change in log-odd ratio when xj increase by 1 unit
The marginal effect of Xi changes
Normal distribution with the Probit model
Estimation method: Maximum likelihood
Multinominal logit model
Nominal dependent variable
Logistic distribution
Estimation method: Maximum likelihood
Ordered Probit model
Ordinal dependent variable
Normal distribution
Estimation method: Maximum likelihood
Tobit model
Y is Censored & Truncated data
Applying OLS => Biased
Estimation method: Maximum likelihood
Three types of marginal effects
Count model
The dep var is a non-negative integer
OLS may result in negative values
Poisson distribution
Assumption: mean = variance
mean > variance: UNDERDISPERSION
mean < variance: OVERDISPERSION
Estimation method: Maximum likelihood
If assumption is violated => negative binomial model
Basic models with Panel data
Panel data
Combine time series and cross sectional data
Pooled OLS regression
No distinction between subjects and times
Fixed effect model
The Fixed effect Least-Squared Dummy variables model
The Fixed effect Within-Group estimator
The Fixed effect First difference estimator
FE vs Pooled OLS: F test
Random effects model
Assumed not to correlate with regressors
RE vs Pooled OLS: BP test
FE vs RE: Hausman test
Endogeneity
The fourth assumption of OLS is violated
Sources
Omitted variables
Simultaneity or reverse causality
Measurement error
Consenquences
Biased and Inconsistent
Solutions
IV estimation
Panel data: fixed effects, random effects
GMM
Regression discontinuity
Natural experiments
DID or PSM
Do Huu Luat
2019
luat.do@luatdo.com