Economic Terms

The OLS fitted values and residuals have some important properties that are immediate extensions from the single variable case:

1. The sample average of the residuals is zero and so ybar = yhatbar. 2. The sample covariance between each independent variable and the OLS residuals is zero. Consequently, the sample covariance between the OLS fitted values and the OLS residuals is zero. The point 3. (xbar_1, xbar_2, ..., xbar_k, ybar) is always on the OLS regression line: ybar = βhat_0 + βhat_1⁢ xbar_1 + βhat_2⁢ xbar_2 + ⋯ + βhat_k⁢ xbar_k.

Causal Effect

A ceteris paribus change in one variable that has an effect on another variable

Pooled Cross Section

A data configuration where independent cross sections, usually collected at different points in time, are combined to produce a single data set.

Panel Data (Longitudinal Data)

A data set constructed from repeated cross sections over time. With a balanced panel, the same units appear in each time period. With an unbalanced panel, some units do not appear in each time period, often due to attrition. set consists of a time series for each cross-sectional member in the data set.

Counterfactual Reasoning

A method of policy evaluation in which we imagine an identical observation (individual, firm, country, etc.) under two different states of the world (e.g. with a policy and without a policy).

Multiple Linear Regression

A model linear in its parameters, where the dependent variable is a function of independent variables plus an error term Statistical method that can be used to project future demand; several variables are utilized.

Random Sampling

A sampling scheme whereby each observation is drawn at random from the population. In particular, no unit is more likely to be selected than any other unit, and each draw is independent of all other draws

OLS slope estimate

A slope in an OLS regression line. known as βhat_1, ... , βhat_k

OLS intercept estimate

The intercept in an OLS regression line. known as βhat_0

Data Frequency

The interval at which time series data are collected. Yearly, quarterly, and monthly are the most common data frequencies.

First order conditions

The set of linear equations used to solve for the OLS estimates.

exogeneous variable

Variables that are outside of a decision-maker's control

Partial Equilibrium Model

a model in which some key macroeconomic variables, such as the nominal interest rate, are exogenous; a model in which individuals or firms make a choice that affects the supply or demand in a market whose price is exogenous looking at only one market at a time

Multiple Regression Analysis

A type of analysis that is used to describe estimation of and inference in the multiple linear regression model. useful for generalizing functional relationships between variables. The power of multiple regression analysis is that it provides this ceteris paribus interpretation even though the data have not been collected in a ceteris paribus fashion. The power of multiple regression analysis is that it allows us to do in nonexperimental environments what natural scientists are able to do in a controlled laboratory setting: keep other factors fixed.

(1) the ceteris paribus (other things the same) assumption (2) the supposition that economic decision-makers seek to optimize something (3) a careful distinction between "positive" and "normative" questions

All economic models incorporate three common elements:

Ceteris Paribus

All other relevant factors are held fixed. other (relevant) factors being equal

Econometric Model

An equation relating the dependent variable to a set of explanatory variable and unobserved disturbances, where unknown population parameters determine the ceteris paribus effect of each explanatory variable.

Experimental data

Are often collected in laboratory environments in the natural sciences, but they are more difficult to obtain in the social sciences

Retrospective Data

Data collected over time on one or more variables.

Key assumption for general multiple regression model is easy to state in terms of a conditional expectation

E(u|x_1, x_2, ..., x_k) = 0

Expectation Hypothesis

Given all information available to investors at the time of investing, the expected return on any two investments is the same.

Econometrics

Has evolved as a separate discipline from mathematical statistics because the former focuses on the problems inherent in collecting and analyzing non experimental economic data.

How u is related to X_1 and X_2

It means that, for any values of x_1 and x_2 in the population, the average of the unobserved factors is equal to zero. the important part of the assumption is that the expected value of u is the same for all combinations of x_1 and x_2; that this common value is zero is no assumption at all as long as the intercept β_ is included in the model

Observational Data

See non experimental data

Utility Maximization

The assumption that individual make choices to maximize their well-being, subject to resource constraints, gives us a very powerful framework for creating tractable economic models and making clear predictions.

Counterfactual Outcomes (Potential Outcomes)

The different outcomes that results from a counterfactual reasoning process.

Partial effect

The effect of an explanatory variable on the dependent variable, holding other factors in the regression model fixed.

Marginal Propensity to Consume (MPC)

The fraction of any change in disposable income spent for consumer goods; equal to the change in consumption divided by the change in income The change in consumption with respect to the change in income

Non-experimental data

are not accumulated through controlled experiments of individual, firms, or segments of the economy. (Non experimental data are sometimes called observational data, or retrospective data, to emphasize the fact that the researcher is a passive collector of the data. Data that have not been obtained through a controlled experiment.

rhat_i_1

are the OLS residuals from a simple regression of x_1 on x_2, using the sample at hand

Ordinary Least Squares

chooses the estimates to minimize the sum of squared residuals. That is, given n observations on y, x_1, and x_2, {(x_i_1, x_i_2, y_i): I = 1, 2, ..., n}, the estimates βhat_0, βhat_1, and βhat_2 are chosen simultaneously to make: equation OLS minimizes the average squared prediction error, which says nothing about the prediction error for any particular observation

Cross -Sectional Data

consists of a sample of individuals, households, firms, cities, states, countries, or a variety of other units, taken at a given point in time. Sometimes, the data on all units do not correspond to precisely the same time period.

Economic Model

consists of mathematical equations that describe various relationships. A relationship derived from economic theory or less formal economic reasoning.

The OLS estimates, k + 1 of them, are chosen to minimize the sum of squared residuals

equation

The case with more than two independent variables is similar. The OLS regression line is

equation

The estimates βhat_1 and βhat_2 have partial effect , or ceteris paribus , interpretations. From equation (3.14), we have

equation

This minimization problem can be solved using multivariable calculus (see Appendix 3A). This leads to k + 1 linear equations in k + 1 unknowns βhat_0, βhat_1, ..., βhat_k:

equation

general case with k independent variables, we seek estimates, βhat_0, βhat_1, ..., βhat_k in the equation (ordinary least squares regression line) or (sample regression function (SRF))

equation

The residual for observation i is defined just as in the simple regression case

equation There is a residual for each observation. If uhat_i >0, then yhat_i is below y_i, which means that, for this observation, y_i is underpredicted. If uhat_i < 0, then y_i < yhat_i, and y_i is overpredicted.

After obtaining the OLS regression line, we can obtain a fitted or predicted value for each observation. For observation i, the fitted value is simply

equation We should not forget about the intercept in obtaining the fitted values; otherwise, the answer can be very misleading.

variable u

error term or disturbance, contains factors other than x_1, x_2, ...,x_k that affect y

E(u|x_1, x_2, ..., x_k) = 0

implies that Ordinary Least Squares (OLS) is unbiased and will derive the bias that arises when a key variable has been omitted from the equation.

innate

inborn; natural

β_0

is the intercept

β_1

measures the change in y with respect to x_1, holding other factors fixed parameter associated with x_1

β_2

measures the change in y with respect to x_2, holding other factors fixed is the parameter associated with x_2

Geographical Units

nations, states, regions, counties, cities, or neighborhoods

Unfeasible

not capable of being carried out or put into practice

Slope parameters

parameters other than intercept

Time Series Data

set consists of observations on a variable or several variables over time. Data collected over time on one or more variables.

Econometrics

the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy.

βhat_0

the estimate of β_0

βhat_1

the estimate of β_1

βhat_2

the estimate of β_2

Empirical analysis

uses data to test a theory or to estimate a relationship

Estimated OLS equation

y-hat = βhat_0 + βhat_1x_1 + βhat_2x_2