One of the CLRM assumptions is: there is no perfect multicollinearity-no exact linear relationships among explanatory variables, Xs, in a multiple regression. In practice, one rarely encounters perfect multicollinearity, but cases of near or very high multicollinearity where explanatory variables are approximately linearly related frequently arise in many applications

The models we discussed are models that are linear in parameters; variables Y and Xs do not necessarily have to be linear The price elasticity of demand~the log-linear models The rate of growth~semilog model Functional forms of regression models which are linear in parameters, but not necessarily linear in variables:

Assumptions of the classical Linear Model (Clm) e So far, we know that given the Gauss Markov assumptions, OLS IS BLUE e In order to do classical hypothesis testing we need to add another assumption(beyond the Gauss-Markov assumptions) Assume that u is independent of x,x2…,xk and u is normally distributed with zero mean and variance 0: u- Normal(0, 02) Economics 20- Prof anderson

Ch. 24 Johansen's mle for Cointegration We have so far considered only single-equation estimation and testing for cointe- gration. While the estimation of single equation is convenient and often consis- tent, for some purpose only estimation of a system provides sufficient information This is true, for example, when we consider the estimation of multiple cointe- grating vectors, and inference about the number of such vectors. This chapter examines methods of finding the cointegrating rank and derive the asymptotic

Ch. 22 Unit root in Vector Time series 1 Multivariate Wiener Processes and multivari- ate FCLT Section 2.1 of Chapter 21 described univariate standard Brownian motion W(r) as a scalar continuous-time process(W: rE0, 1-R). The variable W(r) has a N(O, r)distribution across realization, and for any given realization, w(r) is continuous function of the date r with independent increments. If a set of k such independent processes, denoted

The Normal Distribution: the distribution of a continuous r.v. whose value depends on a number of factors, yet no single factor dominates the other. 1. Properties of the normal distribution: 1)The normal distribution curve is symmetrical around its mean valueu. 2)The PDF of the distribution is the highest at its mean value but tails off at its extremities

Definition (1) Econometrics: economic measurement. (2) Econometrics: the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena. (3) Econometrics: the result of a certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend

where a subscribed element of a matrix is always read as arou, column. Here we confine the element to be real number a vector is a matrix with one row or one column. Therefore a row vector is Alxk and a column vector is AixI and commonly denoted as ak and ai,respec- tively. In the followings of this course, we follow conventional custom to say that a vector is a columnvector except for

Ch. 20 Processes with Deterministic Trends 1 Traditional Asymptotic Results of OlS Suppose a linear regression model with stochastic regressor given by Y=x!3+e,t=1,2,…,T,;B∈R or in matrix form y=xB+E We are interested in the asymptotic properties such as consistency and limiting

Ch. 19 Models of Nonstationary Time Series In time series analysis we do not confine ourselves to the analysis of stationary time series. In fact, most of the time series we encounter are nonstationary. How to deal with the nonstationary data and use what we have learned from stationary model are the main subjects of this chapter 1 Integrated Process