Über die Autorin bzw. den Autor

G.S.Maddala was one of the leading figures in field of econometrics for more than 30 years until he passed away in 1999. At the time of his death, he held the University Eminent Scholar Professorship in the Department of Economics at Ohio State University. His previous affiliations include Stanford University, University of Rochester and University of Florida.

Kajal Lahiri is Distinguished Professor of Economics, and Health Policy, and Management and Behaviour at the State University of New York, Albany where he is also Director of the Econometric Research Institute. Professor Lahiri is an Honorary Fellow of the International Institute of Forecasters.

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Maintaining G.S. Maddala’s brilliant expository style of cutting through the technical superstructure to reveal only essential details, while retaining the nerve centre of the subject matter, Professor Kajal Lahiri has brought forward this new edition of one of the most important textbooks in its field.

The new edition continues to provide a large number of worked examples, and some shorter data sets. Further data sets and additional supplementary material to assist both the student and lecturer are available on the companion website www.wileyeurope.com/college/maddala

New features for the fourth edition:

• Chapters 5 and 6, on Heteroscedasticity and Autocorrelation, now reflect the latest professional practice in dealing with these common variations of the basic regression model.
• Chapter 10 includes extensive discussion on diagnostic checking in linear models, various nested and non-nested model selection procedures, specification testing, data transformations, and tests for non-normality.
• The first three chapters of Part III cover an introduction to time-series analysis, including the Box–Jenkins approach, forecasting and seasonality, models of expectations and distributed lag models, and vector auto-regressions, unit roots, and cointegration.
• Chapters 15 and 16 cover, respectively, the latest developments in panel data analysis and various re-sampling methods for use in small sample inference.

Aus dem Klappentext

Maintaining G.S. Maddala’s brilliant expository style of cutting through the technical superstructure to reveal only essential details, while retaining the nerve centre of the subject matter, Professor Kajal Lahiri has brought forward this new edition of one of the most important textbooks in its field.

The new edition continues to provide a large number of worked examples, and some shorter data sets.  Further data sets and additional supplementary material to assist both the student and lecturer are available on the companion website www.wileyeurope.com/college/maddala

New features for the fourth edition:

• Chapters 5 and 6, on Heteroscedasticity and Autocorrelation, now reflect the latest professional practice in dealing with these common variations of the basic regression model.
• Chapter 10 includes extensive discussion on diagnostic checking in linear models, various nested and non-nested model selection procedures, specification testing, data transformations, and tests for non-normality.
• The first three chapters of Part III cover an introduction to time-series analysis, including the Box–Jenkins approach, forecasting and seasonality, models of expectations and distributed lag models, and vector auto-regressions, unit roots, and cointegration.
• Chapters 15 and 16 cover, respectively, the latest developments in panel data analysis and various re-sampling methods for use in small sample inference.

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Introduction to Econometrics

John Wiley & Sons

Chapter One

What is in this Chapter?

This chapter explains the scope and methodology of econometrics. Econometrics deals with the application of statistical tools to economic data. The first task an econometrician faces is that of formulating an economic relationship, which is necessarily a simplified model of the real-world process. Estimation and testing of these models with observed data and the use of the estimated models for prediction and policy analysis are the other two major goals of econometrics.

This chapter also contains a schematic depiction of the various methodological steps involved in an econometric analysis.

1.1 What is Econometrics?

Literally speaking, the word "econometrics" means "measurement in economics." This is too broad a definition to be of any use, because most of economics is concerned with measurement. We measure our gross national product, employment, money supply, exports, imports, price indexes, and so on. What we mean by econometrics is:

The application of statistical and mathematical methods to the analysis of economic data, with the purpose of giving empirical content to economic theories and verifying them or refuting them.

In this respect, econometrics is distinguished from mathematical economics, which consists of the application of mathematics only, and the theories derived need not necessarily have an empirical content.

The application of statistical tools to economic data has a very long history. Stigler (1954) notes that the first "empirical" demand schedule was published in 1699 by Charles Davenant, and that the first modern statistical demand studies were made by Rodulfo Enini, an Italian statistician, in 1907. The main impetus to the development of econometrics, however, came with the establishment of the Econometric Society in 1930 and the publication of the journal Econometrica in January 1933.

Before any statistical analysis with economic data can be done, one needs a clear mathematical formulation of the relevant economic theory. To take a very simple example, saying that the demand curve is downward sloping is not enough. We have to write the statement in mathematical form. This can be done in several ways. For instance, defining q as the quantity demanded and p as price, we can write

q = [alpha] + p < 0

or

q = [Ap.sup.] < 0

As we will see later in the book, one of the major problems we face is the fact that economic theory is rarely informative about functional forms. We have to use statistical methods to choose the functional form, as well.

1.2 Economic and Econometric Models

The first task an econometrician faces is that of formulating an econometric model. What is a model?

A model is a simplified representation of a real-world process. For instance, saying that the quantity demanded of oranges depends on the price of oranges is a simplified representation, because there are a host of other variables that one can think of that determine the demand for oranges. For instance, income of consumers, an increase in diet consciousness ("drinking coffee causes cancer, so you better switch to orange juice," etc.), an increase or decrease in the price of apples, and so on. However, there is no end to this stream of other variables. In a remote sense, even the price of gasoline can affect the demand for oranges.

Many scientists have argued in favor of simplicity, because simple models are easier to understand, communicate, and test empirically with data. This is the position of Karl Popper (1959, p. 142) and Milton Friedman (1953, p. 14). The choice of a simple model to explain complex real-world phenomena leads to two criticisms:

1. The model is oversimplified.

2. The assumptions are unrealistic.

For instance, in our example of the demand for oranges, to say that it depends only on the price of oranges is an oversimplification and also an unrealistic assumption. To the criticism of oversimplification, one can argue that it is better to start with a simplified model and progressively construct more complicated models. This is the idea expressed by Koopmans (1957, pp. 142-143). On the other hand, there are some who argue in favor of starting with a very general model and simplifying it progressively based on the data available. The famous statistician L. J. (Jimmy) Savage used to say that "a model should be as big as an elephant." Whatever the relative merits of this alternative approach are, we will start with simple models and progressively build more complicated models.

The other criticism we have mentioned is that of "unrealistic assumptions." To this criticism Friedman (1953, pp. 14-15) argues that the assumptions of a theory are never descriptively realistic. He says:

The relevant question to ask about the "assumptions" of a theory is not whether they are descriptively "realistic" for they never are, but whether they are sufficiently good approximations for the purpose at hand. And this question can be answered by only seeing whether the theory works, which means whether it yields sufficiently accurate predictions.

Returning to our example of demand for oranges, to say that it depends only on the price of oranges is a descriptively unrealistic assumption. However, the inclusion of other variables, such as income and price of apples in the model, does not render the model more descriptively realistic. Even this model can be considered to be based on unrealistic assumptions because it leaves out many other variables (such as health consciousness, etc.). But the issue is which model is more useful for predicting the demand for oranges. This issue can be decided only from the data we have and the data we can get.

In practice, we include in our model all the variables that we think are relevant for our purpose and dump the rest of the variables in a basket called "disturbance." This brings us to the distinction between an economic model and an econometric model.

An economic model is a set of assumptions that approximately describes the behavior of an economy (or a sector of an economy). An econometric model consists of the following:

1. A set of behavioral equations derived from the economic model. These equations involve some observed variables and some "disturbances" (which are a catch-all for all the variables considered as irrelevant for the purpose of this model as well as all unforeseen events).

2. A statement of whether there are errors of observation in the observed variables.

3. A specification of the probability distribution of the "disturbances" (and errors of measurement).

With these specifications we can proceed to test the empirical validity of the economic model and use it to make forecasts or use it in policy analysis.

Taking the simplest example of a demand model, the econometric model usually consists of:

1. The behavioral equation

q = [alpha] + p + u

where q is the quantity demanded and p the price. Here p and q are the observed variables and u is a disturbance term.

2. A specification of the probability distribution of u, which says that E(u|p) = 0 and that the values of u for the different observations are independently and normally distributed with mean zero and variance...