STATISTICS AND ECONOMETRICS

(Complete, Easy & Detailed Notes for UGC NET – Economics)

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1. Introduction

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data for decision-making.

Why do economists use statistics?

• To measure and summarize economic activities (GDP, inflation, unemployment, poverty)

• To test hypotheses (e.g., Does education increase income?)

• To explain relationships (e.g., demand & price, interest & investment)

• To forecast future trends (e.g., stock markets, rainfall, exchange rates)

Econometrics is the application of statistical and mathematical tools to economic data to verify theories and predict outcomes.

Econometrics = Economics + Mathematics + Statistics + Computer science

Hal Varian: Econometrics gives empirical content to economic relationships and helps estimate real-world cause-and-effect using data.

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PART A – STATISTICS

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2. Types of Data

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3. Measurement Scales

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4. Probability Concepts

Probability = Likelihood that an event occurs.

Rules of Probability

• $0\le P(A)\le 1$

• $P(S)=1$
  

• Complement: $P(A^{\mathrm{\prime }})=1-P(A)$
  

• Addition: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
  

Conditional Probability

$$P(A\mathrm{\mid }B)=\frac{P(A\cap B)}{P(B)}$$

Bayes’ Theorem

$$P(A\mathrm{\mid }B)=\frac{P(B\mathrm{\mid }A)P(A)}{P(B)}$$

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5. Probability Distributions

Discrete Distributions

Continuous Distributions

Most economic variables are normally distributed (e.g., heights, test scores, errors).

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6. Central Limit Theorem

When sample size is large, the distribution of sample mean tends toward normal, regardless of population distribution.

$$\bar{x}\sim N(\mu ,{\sigma }^2\mathrm{/}n)$$

Basis of hypothesis testing.

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7. Descriptive Statistics

Measures of Central Tendency

$$\bar{x}=\frac{\sum x_i}{n}$$

Measures of Dispersion

$${\sigma }^2=\frac{\sum (x_i-\bar{x}{)}^2}{n},\sigma =\sqrt{{\sigma }^2}$$

$$CV=\frac{\sigma }{\bar{x}}\times 100$$

Moments

Used to measure shape of distribution.

• Skewness → symmetry

• Kurtosis → peakedness

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8. Correlation

$$r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x{)}^2][n\sum y^2-(\sum y{)}^2]}}$$

 $-1\le r\le +1$

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9. Index Numbers

Types: Wholesale Price Index, CPI, Laspeyres, Paasche

$$P_L=\frac{\sum P_1{Q}_0}{\sum P_0{Q}_0}\times 100$$

PART B – ECONOMETRICS

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1. Linear Regression Model

$$Y={\beta }_0+{\beta }_{1}X+u$$

OLS Estimators

$${\beta }_1=\frac{\sum (x-\bar{x})(y-\bar{y})}{\sum (x-\bar{x}{)}^2},{\beta }_0=\bar{y}-{\beta }_1\bar{x}$$

Interpretation: Regression gives the best linear predictor of Y given X.

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2. BLUE (Gauss-Markov Theorem)

OLS is Best Linear Unbiased Estimator if:

1. Linear in parameters

2. Zero mean error

3. No autocorrelation

4. Homoscedasticity (constant variance)

5. No perfect multicollinearity

6. X is non-stochastic

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3. Hypothesis Testing

• t-test: significance of each coefficient

• F-test: significance of model

• R²: goodness of fit

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4. Model Problems

Solutions

• White test, Breusch-Pagan, Durbin-Watson

• GLS, HAC estimators, Cochrane-Orcutt

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5. Simultaneous Equation Models

• Exact, under, over-identified

• 2SLS, 3SLS, LIML estimators

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6. Discrete Choice Models

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7. Time Series

Components: Trend, Seasonal, Cyclical, Irregular

Stationarity

$$E(Y_t)=\mu ,Var(Y_t)={\sigma }^2$$

ADF Test for unit roots.

ARIMA models

$$ARIMA(p,d,q)$$

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What This Unit Helps You Achieve

• Understand data & probability

• Build and interpret econometric models

• Perform hypothesis testing

• Forecast economic variables

• Distinguish correlation vs causation