Simulation
In appendix 10F of POE4, the authors conduct a Monte Carlo experiment comparing the performance of OLS and TSLS. The basic simulation is based on the model y = x …
Hausman Test
The Hausman test probes the consistency of the random effects estimator. The null hypothesis is that these estimates are consistent-that is, that the requirement of orthogonality of the model’s errors …
Time-Varying Volatility and ARCH Models: Introduction to Financial Econometrics
In this chapter we’ll estimate several models in which the variance of the dependent variable changes over time. These are broadly referred to as ARCH (autoregressive conditional heteroskedas - ticity) …
Cointegration
Two nonstationary series are cointegrated if they tend to move together through time. For instance, we have established that the levels of the Fed Funds rate and the 3-year bond …
Tobit
The tobit model is essentially just a linear regression where some of the observations on your dependent variable have been censored. A censored variable is one that, once it reaches …
ARCH and GARCH
The basic ARCH(1) model can be expressed as: yt = в + et (14.1) et|1t-i ~ N(0, ht) (14.2) ht = ao + aqe2_i (14.3) a0 > 0, 0 < …
APPLICABILITY AND DEFINITIONS
This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of …
Simultaneous Equations Models
In Chapter 11 of POE4 the authors present a model of supply and demand. The econometric model contains two equations and two dependent variables. The distinguishing factor for models of …
Seemingly Unrelated Regressions
The acronym SUR stands for seemingly unrelated regression equations. SUR is another way of estimating panel data models that are long (large T), but not wide (small N). More generally …
COLLECTIONS OF DOCUMENTS
You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a …
Error Correction
Cointegration is a relationship between two nonstationary, I(1), variables. These variables share a common trend and tend to move together in the long-run. In this section, a dynamic relationship between …
Selection Bias
Selection bias occurs when your sample is truncated and the cause of that truncation is correlated with your dependent variable. Ignoring the correlation, the model could be estimated using least …
Testing for ARCH
Testing for the presence of ARCH in the errors of your model is straightforward. In fact, there are at least two ways to proceed. The first is to estimate the …
VERBATIM COPYING
You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to …
The Reduced Form Equations
The reduced form equations express each endogenous variable as a linear function of every exogenous variable in the entire system. So, for our example Qi =пц + П21 psi + …
Qualitative and Limited Dependent Variable Models
16.1 Probit There are many things in economics that cannot be meaningfully quantified. How you vote in an election, whether you go to graduate school, whether you work for pay, …
Vector Error Correction and Vector Autoregressive Models: Introduction to Macroeconometrics
The vector autoregression model is a general framework used to describe the dynamic interrelationship between stationary variables. So, the first step in your analysis should be to determine whether the …
Using R for Qualitative Choice Models
R is a programming language that can be very useful for estimating sophisticated econometric models. In fact, many statistical procedures have been written for R. Although gretl is very powerful, …
Threshold ARCH
Threshold ARCH (TARCH) can also be estimated in gretl, though it requires a little programming; there aren’t any pull-down menus for this estimator. Instead, we’ll introduce gretl’s powerful mle command …
COPYING IN QUANTITY
If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document’s license notice requires Cover Texts, you …
The Structural Equations
The structural equations are estimated using two-stage least squares. The basic gretl commands for this estimator are discussed in Chapter 10. The instruments consist of all exogenous variables, i. e., …
Marginal Effects and Average Marginal Effects
The marginal effect of a change in xij on Pi is dF- = Ф(в 1 + в2Хі2 + взХіз)ві (16.2) where ф() is the standard normal probability density. That means …
Vector Error Correction and VAR Models
Consider two time-series variables, yt and xt. Generalizing the discussion about dynamic relationships in chapter 9 to these two interrelated variables yield a system of equations: yt =віо + Piiyt-i …
Some Basic Probability Concepts
In this chapter, you learned some basic concepts about probability. Since the actual values that economic variables take on are not actually known before they are observed, we say that …
Garch-in-Mean
The Garch-in-mean (MGARCH) model adds the equation’s variance to the regression function. This allows the average value of the dependent variable to depend on volatility of the underlying asset. In …
MODIFICATIONS
You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this …
Fulton Fish Example
The following script estimates the reduced form equations using least squares and the demand equation using two-stage least squares for Graddy’s Fulton Fish example. In the example, ln(quan) and ln(price) …
Standard Errors and Confidence Intervals for Marginal Effects
Obtaining confidence intervals for the marginal effects (and the AME) is relatively straightforward as well. To estimate the standard error of the marginal effect, we resort to the Delta method. …
Series Plots—Constant and Trends
Our initial impressions of the data are gained from looking at plots of the two series. The data plots are obtained in the usual way after importing the dataset. The …
Some Statistical Concepts
The hip data are used to illustrate computations for some simple statistics in your text. C.1 Summary Statistics Using a script or operating from the console, open the hip data, …
Pooling Time-Series and Cross-Sectional Data
A panel of data consists of a group of cross-sectional units (people, firms, states or countries) that are observed over time. Following Hill et al. (2011) we will denote the …
COMBINING DOCUMENTS
You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination …
Alternatives to TSLS
There are several alternatives to the standard IV/TSLS estimator. Among them is the limited information maximum likelihood (LIML) estimator, which was first derived by Anderson and Rubin (1949). There is …
Hypothesis Tests
Based on the soft drink example explored in section 8.7, suppose you want to test the hypothesis that the Coke and Pepsi displays have an equal but opposite effect on …
Selecting Lag Length
The second consideration is the specification of lags for the ADF regressions. There are several ways to select lags and gretl automates one of these. The basic concept is to …
