riv (version 2.0-5)

earthquake: Alaskan earthquakes data

Description

The dataset contains information about 62 Alaskan earthquakes that occured between 1969-1978 (Fuller, 1987). The goal is to see how the earthquake strength, measured in terms of the true value of the body waves, \(x^{*}\), impacts on the amplitude of the surface waves of the earthquake (\(Y\)). However, we do not observe \(x^{*}\) but \(X\), which is the logarithm of the seismogram amplitude of longitudinal body waves measured at some observation stations, i.e., \(x_i=x^{*}_i+u_i\), for \(i=1,\dots,62\), where \(u_i\) is the measurement error of each observation. Thus, in the regression \(Y_i=a+b*X_i+e_i\), the covariate \(X\) is an endogenous covariate. We can consistently estimate the regression parameters using instrumental variables estimators. The logarithm of maximum seismogram trace amplitude at short distance, \(W\), can be used as an instrument.

The first column in the dataset is the response (Y), the second column is the endogenous variable (X), and the third column is the instrument (W).

Usage

data(earthquake)

Format

A data frame with 62 observations on the following 3 variables.

Y

a numeric vector of the logarithm of the seismogram amplitude of 20 second waves.

X

a numeric vector of the logarithm of the seismogram amplitude of longitudinal body waves.

W

a numeric vector of the logarithm of maximum seismogram trace amplitude at short distance.

References

COHEN-FREUE,G.V. and ZAMAR,R.H. (2005). A Robust Instrumental Variables Estimator.

Examples

# NOT RUN {
data(earthquake)
plot(earthquake$X, earthquake$Y, xlab="X", ylab="Y")
# }