1.1 What is Econometrics?
Econometrics is based upon the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy. ex) we will consider the effect of school spending on student performance in the field of education.
1.2 Steps in empirical economic analysis
An empirical analysis uses data to test a theory or to estimate a relationship.
How does one go about structuring an empirical economic analysis? It is worth emphasizing that the first step in any empirical analysis is the careful formation of the question of interest. ex) the question might deal with testing a certain aspect of an economic theory, or it might pertain to testing the effects of a government policy.
In some cases, especially those that involve the testing of economic theories, a formal economic model is constructed. An economic model consists of mathematical equations that describe various relationships. Economists are well-known for their building of models to describe a vast array of behaviors.
(...) We can never eliminate error term entirely. In fact, dealing with this error term or disturbance term is perhaps the most important component of any econometric analysis.
Cross-Sectional Data
A cross-sectional data set 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 (We would ignore any minor time differences in collecting the data).
An important feature of cross-sectional data is that we can often assume that they have been obtained by random sampling from the underlying population.
* Random sampling: Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.
* unbiased: what is an unbiased estimator? If the estimator(the sample mean) equals the parameter(the population mean), then it's an unbiased estimator.
Time Series Data
A time series data set consists of observations on a variable or several variables over time.
Past events can influence future events and lags in behavior are prevalent in the social sciences. Time is an important dimension in a time series data set. Unlike the arrangement of cross-sectional data, the chronological ordering of observations in a time series conveys potentially important information.
A key feature of time series data that makes them more difficult to analyze than cross-sectional data is the fact that economic observations can rarely, if ever, be assumed to independent across time. Another feature of times series data that can require special attention is the data frequency at which the data are collected. In economics, the most common frequencies are daily, weekly, monthly, quarterly, and annually.
Pooled Cross Sections
Some data sets have both cross-sectional and time series features. In order to increase our sample size, we can form a pooled cross section by combing the two years.
Pooling cross sections from different years is often an effective way of analyzing the effects of a new government policy. The idea is to collect data from the years before and after a key policy change.
Panel or Longitudinal Data
A panel data (or longitudinal data) set consists of a time series for each cross-sectional member in the data set.
The key feature of panel data that distinguishes them from a pooled cross section is the fact that the same cross-sectional units are followed over a given time period. Observing the same units over time leads to several advantages over cross-sectional data or even pooled cross-sectional data. The benefit is that having multiple observations on the same units allows us to control certain unobserved characteristics of individuals, firms, and so on. A second advantage of panel data s that they often allow us to study the importance of lags in behavior or the result of decision making.
1.4 Causality and the notion of ceteris paribus in econometric analysis
In most tests of economic theory, and certainly for evaluating public policy, the economist's goal is to infer that one variable (such as education) has a causal effect on another variable (such as worker productivity).
The notion of ceteris paribus - which means "other (relevant) factors being equal" plays an important role in causal analysis.
You probably remember from introductory economics that most economic questions are ceteris paribus by nature. For example, in analyzing consumer demand, we are interested in knowing the effect of changing the price of a good on it's quantity demanded, while holding all other factors - such as income, prices, of other goods, and individual tastes - fixed. If other factors are not held fixed, then we cannot know the causal effect of a price change on quantity demanded.
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