Autoregressive Conditional Heteroskedasticity
Financial time-series such as foreign exchange rates, inflation rates and stock prices may exhibit some volatility which varies over time. In the case of inflation or foreign exchange rates this …
Dynamic Panel Data Models
The dynamic error components regression is characterized by the presence of a lagged dependent variable among the regressors, i. e., yit = %,t-1 + xitP + hi + Vit, i …
Testing Linear Versus Log-Linear Functional Form
yi -- j=1 /3j[14]ij + XyS=1 YsZis + ui І — 1) 2)-- In many economic applications where the explanatory variables take only positive values, econometricians must decide whether a …
Multinomial Choice Models
In many economic situations, the choice may be among m alternatives where m > 2. These may be unordered alternatives like the selection of a mode of transportation, bus, car …
Single Equation Estimation: Two-Stage Least Squares
In matrix form, we can write the first structural equation as yi = Yiai + Xifi1 + ui = ZiSi + ui (11.34) where y1 and u1 are (T x …
Comparing Biased and Unbiased Estimators
Suppose we are given two estimators в1 and в2 of в where the first is unbiased and has a large variance and the second is biased but with a small …
Empirical Illustration
Baltagi, Griffin and Xiong (2000) estimate a dynamic demand model for cigarettes based on panel data from 46 American states over 30 years 1963-1992. The estimated equation is ln Cit …
Generalized Least Squares
9.1 Introduction This chapter considers a more general variance covariance matrix for the disturbances. In other words, u ~ (0, a2In) is relaxed so that u ~ (0, a2Q) where …
Unordered Response Models
There are m choices each with probability nii, ni2,..., nim for individual i. yij = 1 if individual i chooses alternative j, otherwise it is 0. This means that £%£ …
Spatial Lag Dependence
An alternative popular model for spatial lag dependence considered in Section 9.9 is given by: y = pWy + Хв + є where є ~ IIN(0, a2), see Anselin (1988). …
Diagnostic Tests for Linear Regression Models
Variable addition tests suggested by Pagan and Hall (1983) consider the additional variables Z of dimension (T x r) and test whether their coefficients are zero using an F-test from …
Program Evaluation and Difference-in-Differences Estimator
Suppose we want to study the effect of job training programs on earnings. An ideal experiment would assign individuals randomly, by a flip of a coin, to training and non-training …
Special Forms
If the disturbances are heteroskedastic but not serially correlated, then Q = diag[a2]. In this case, P = diagOi], P-1 = Q-1/2 = diag[1/oi] and Q-1= diag[1/a2]. Premultiplying the regression …
The Censored Regression Model
Suppose one is interested in the amount one is willing to spend on the purchase of a durable good. For example, a car. In this case, one would observe the …
Test for Over-Identification Restrictions
We emphasized instrument relevance, now we turn to instrument exogeneity. Under just - identification, one cannot statistically test instruments for exogeneity. This choice of exogenous instruments requires making an expert …
Limited Dependent Variables
13.1 Introduction In labor economics, one is faced with explaining the decision to participate in the labor force, the decision to join a union, or the decision to migrate from …
Test of Hypotheses
In order to test H0; Ев = r, under the general variance-covariance matrix assumption, one can revert to the transformed model (9.3) which has a scalar identity variance-covariance matrix and …
The Truncated Regression Model
The truncated regression model excludes or truncates some observations from the sample. For example, in studying poverty we exclude the rich, say with earnings larger than some upper limit yu …
Hausman’s Specification Tes
A critical assumption for the linear regression model y = X@ + u is that the set of regressors X are uncorrelated with the error term u. Otherwise, we have …
Functional Form: Logit and Probit
Having pointed out the problems with considering the functional form F as linear, we turn to two popular functional forms of F, the logit and the probit. These two c. …
Empirical Example
Table 3.2 gives (i) the logarithm of cigarette consumption (in packs) per person of smoking age (> 16 years) for 46 states in 1992, (ii) the logarithm of real price …
Springer Texts in Business and Economics
This book is intended for a first year graduate course in econometrics. I tried to strike a balance between a rigorous approach that proves theorems, and a completely empirical approach …
Heteroskedasticity
Violation of assumption 2, means that the disturbances have a varying variance, i. e., E(u2) = a2, i = 1,2,... ,n. First, we study the effect of this violation on …
Descriptive Statistics
In Chapter 4, we will consider the estimation of a simple wage equation based on 595 individuals drawn from the Panel Study of Income Dynamics for 1982. This data is …
Restricted MLE and Restricted Least Squares
Maximizing the likelihood function given in (7.16) subject to R/3 = r is equivalent to minimizing the residual sum of squares subject to R/3 = r. Forming the Lagrangian function …
Multiple Regression Analysis
4.0 Introduction So far we have considered only one regressor X besides the constant in the regression equation. Economic relationships usually include more than one regressor. For example, a demand …
What Is Econometrics?
1.1 Introduction What is econometrics? A few definitions are given below: The method of econometric research aims, essentially, at a conjunction of economic theory and actual measurements, using the theory …
Autocorrelation
Violation of assumption 3 means that the disturbances are correlated, i. e., E(щUj) = aj = 0, for i = j, and i, j = 1,2,...,n. Since ui has zero …
Simple Linear Regression
3.1 Introduction In this chapter, we study extensively the estimation of a linear relationship between two variables, Yi and Xi, of the form: Yi = a + вХі + Ui …
Some Useful Matrix Properties
This book assumes that the reader has encountered matrices before, and knows how to add, subtract and multiply conformable matrices. In addition, that the reader is familiar with the transpose, …
Least Squares Estimation
As explained in Chapter 3, least squares minimizes the residual sum of squares where the residuals are now given by ei = Yi — 2 — £K=2 PkXki and 2 …
A Brief History
For a brief review of the origins of econometrics before World War II and its development in the 1940-1970 period, see Klein (1971). Klein gives an interesting account of the …
Distributed Lags and Dynamic Models
6.1 Introduction Many economic models have lagged values of the regressors in the regression equation. For example, it takes time to build roads and highways. Therefore, the effect of this …
Least Squares Estimation and the Classical Assumptions
Least squares minimizes the residual sum of squares where the residuals are given by ei = Yi — 2 - (3Xi i = 1,2,...,n and 2 and в denote guesses …
Regression Diagnostics and Specification Tests
8.1 Influential Observations1 Sources of influential observations include: (i) improperly recorded data, (ii) observational errors in the data, (iii) misspecification and (iv) outlying data points that are legitimate and contain …
