Category Using gret l for Principles of Econometrics, 4th Edition

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 data on U. S. and Australian GDP are found in the gdp. gdt file and were collected from 1970:1 – 2004:4.[76] Open the data and set the data structure to quarterly time-series using the setobs 4 command, start the series at 1970:1, and use the —time-series option.

open "@gretldirdatapoegdp. gdt" setobs 4 1970:1 —time-series

One purpose of the plots is to help you determine whether the Dickey-Fuller regressions should contain constants, trends or squared trends. The simplest way to do this is from the console using the scatters command.

scatters usa diff(usa) aus diff(aus)

The scatters command produces multiple graphs, each ...

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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, hip. gdt, and issue the summary command. This yields the results shown in Table C.1. This gives you the mean, median, mini­Summary Statistics, using the observations 1-50 for the variable ‘y’ (50 valid observations)

Mean

Median

Minimum

Maximum

Standard deviation C. V.

Skewness Ex. kurtosis

Table C.1: Summary statistics from the hip data

mum, maximum, standard deviation, coefficient of variation, skewness and excess kurtosis of your variable(s). Once the data are loaded, you can use gretl’s language to generate these as well. For instance, scalar y_bar = mean(y) yields the mean of the variable y...

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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 number of cross-sectional units by N and the number of time periods we observe them as T.

In order to use the predefined procedures for estimating models using panel data in gretl you have to first make sure that your data have been properly structured in the program. The dialog boxes for assigning panel dataset structure using index variables is shown below:

Panel data (stacked time series)

716 cross-sectional units observed over 5

о iUse index variab es

To use this method, the data have to include variables that identify each individual and time period...

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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 all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy...

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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 renewed interest in LIML because evidence indicates that it performs better than TSLS when instruments are weak. Several modifications of LIML have been suggested by Fuller (1977) and others. These estimators are unified in a common framework, along with TSLS, using the idea of a k-class of estimators. LIML suffers less from test size aberrations than the TSLS estimator, and the Fuller modification suffers less from bias. Each of these alternatives will be considered below.

In a system of M simultaneous equations let the endogenous variables be y1,y2,… ,yM...

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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 the probability of buying Coke. If a store has both displays, the net effect on Coke purchases is zero.

The model is:

Pr(Cokei = 1) = Ф(ві + e2pratio + fi3disp_coke + P4disp. pepsi) (16.6)

The null and alternative hypotheses are:

Ho : вз – в4 = 0 Hі : вз – в4 = 0

The simplest thing to do is use the restrict statement as shown below:

1 open "@gretldirdatapoecoke. gdt"

2 list x = pratio disp_coke disp_pepsi const

3 probit coke x

4 restrict

5 b[3]+b[4]=0

6 end restrict

This works exactly as it did in linear regression. The outcome in gretl is:

Restriction:

b[disp_pepsi] + b[disp_coke] = 0 Test statistic: chi"2(1) = 5...

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