Optimal Advertising: Nonlinear Combinations of Parameters
The optimal level of advertising, adverto, is defined in this example to be the amount that maximizes net sales. Andy will advertise up to the point where another dollar of …
Heteroskedastic-Consistent Standard Errors
The least squares estimator can be used to estimate the linear model even when the errors are heteroskedastic with good results. As mentioned in the first part of this chapter, …
Choosing a Functional Form
There is no reason to think that the relationship between food-exp and income is a linear one. In fact, it is likely to be nonlinear. A low wage earner might …
Adjusted R2
The adjusted R2 was introduced in chapter 5. The usual R2 is ‘adjusted’ to impose a small penalty when a variable is added to the model. Adding a variable with …
Another Test for Autocorrelation
Another way to determine whether or not your residuals are autocorrelated is to use an LM (Lagrange multiplier) test. For autocorrelation, this test is based on an auxiliary regression where …
Generating New Variables
In this manual, we will be generating new variables, computing statistics based on gretl output, and performing matrix calculations using gretl’s scripting language. That means we will be generating series, …
Prediction Interval
To generate a complete confidence interval for every year of schooling between 1 and 21 years, you can use the following script. The result looks very similar to Figure 4.15 …
Log-Linear Models with Indicators
In this example an indicator variable is included in a log-linear model. It is based on a wage example used earlier. ln(wage) = ві + P2educ + 5 female + …
Durbin-Watson Test
The Durbin-Watson statistic is produced with every time-series regression estimated by least squares. To access the p-value associated with the test, which is computed using the Imhoff procedure, use the …
Regression with an Indicator Variable
An indicator variable is a variable that can be equal to one of two possible values. Commonly, this an indicator variable can be a 1 or a 0. So for …
Basic Interactions of Continuous Variables
The basic model considered is pizza = ві + в2аде + вз income + e (5.14) It is proposed that as a person grows older, his or her marginal propensity …
Weighted Least Squares
If you know something about the structure of the heteroskedasticity, you may be able to get more precise estimates using a generalization of least squares. In heteroskedastic models, observations that …
Linear-Log Specification
The linear-log specification of the food expenditure model uses the natural logarithm of income as the independent variable: food-exp = ві + в2 ln (income) + e (4.6) Taking the …
Information Criteria
The two model selection rules considered here are the Akaike Information Criterion (AIC) and the Schwarz Criterion (SC). The SC is sometimes called the Bayesian Information Criterion (BIC). Both are …
Estimation with Serially Correlated Errors
In this section, several methods of estimating models with serially correlated errors will be explored. We will use least squares with robust standard errors to estimate regression models with serial …
GNUPLOT
At the end of each chapter that follows you will find listings of the entire gretl script used to generate the results that are contained in it. When a graph …
Log-Log Model
Finally, a log-log model is used. This functional form is often used to estimate demand equations as it implies a constant price elasticity for the commodity in question. This example …
Linear Probability
A linear probability model is a linear regression in which the dependent variable is an indicator variable. The model is estimated by least squares. E[yi] =1 x Pr(yi = 1) …
FGLS and Other Estimators
The feasible GLS estimator of the AR(p) model can be estimated using gretl in a number of ways. For first order autocorrelated models the ar1 command can be used. There …
Monte Carlo Simulation
The first step in a Monte Carlo exercise is to model the data generation process. This requires what Davidson and MacKinnon (2004) refer to as a fully specified statistical model. …
Log-Linear Model
In this example the simple regression first considered in chapter 4 is modified to include more variables and an interaction. The model adds experience to the model ln(wage) = ві …
Grouped Data
In our discussion of the Goldfeld-Quandt test we decided that wages in rural and metropolitan areas showed different amounts of variation. When the heteroskedasticity occurs between groups, it is relatively …
Using gret l for Principles of Econometrics, 4th Edition
The previous edition of this manual was about using the software package called gretl to do various econometric tasks required in a typical two course undergraduate or masters level econometrics …
Residual Plots
Inadvertently choosing an inappropriate functional form can lead to some serious problems when it comes to using your results for decision-making. There are a number of formal tests that one …
A gretl Function to Produce Model Selection Rules
Gretl offers a mechanism for defining functions, which may be called via the command line, in the context of a script, or (if packaged appropriately via the programs graphical interface. …
Bandwidth and Kernel
HAC is not quite as automatic as the heteroskedasticity consistent (HCCME) estimator in chapter 8. To be robust with respect to autocorrelation you have to specify how far away in …
Simple Linear Regression
In this chapter you are introduced to the simple linear regression model, which is estimated using the principle of least squares. 2.1 Simple Linear Regression Model The simple linear regression …
Multiple Regression Model
The multiple regression model is an extension of the simple model discussed in chapter 2. The main difference is that the multiple linear regression model contains more than one explanatory …
Treatment Effects
In order to understand the measurement of treatment effects, consider a simple regression model in which the explanatory variable is a dummy variable, indicating whether a particular individual is in …
Random Regressors and Moment Based Estimation
In this chapter you will learn to use instrumental variables to model’s parameters when its independent variables are correlated 10.1 Basic Model Consider the linear regression model Уі = ві …
Interval Estimation and Hypothesis Testing
In this chapter, I will discuss how to generate confidence intervals and test hypotheses using gretl. Gretl includes several handy utilities that will help you obtain critical values and p-values …
Goodness-of-Fit
Other important output is included in Table 5.1. For instance, you'll find the sum of squared errors (SSE) which gretl refers to as “Sum squared resid.” In this model SSE …
A Hetroskedasticity Function
A commonly used model for the error variance is the multipicative heteroskedasticity model. It appears below in equation 8.7. o2 = exp (ai + a2Zi) (8.7) The variable zi is …
What is Gretl?
Gretl is an acronym for Gnu Regression, Econometrics and Time-series Library. It is a software package for doing econometrics that is easy to use and powerful. It features a very …
Testing for Normality
Your book, Principles of Econometrics, discusses the Jarque-Bera test for normality which is computed using the skewness and kurtosis of the least squares residuals. To compute the Jarque- Bera statistic, …
