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

Testing Equivalence of Two Regions

The question arises, is the wage equation different for the south than for the rest of the country? There are two ways to do this in gretl. One is very easy and the other not so easy, but makes for a useful example of how to use loops to create interactions among variables.

A Chow test is used to test for structural breaks or changes in a regression. In other words, one subsample has different intercept and slopes than another. It can be used to detect structural breaks in time-series models or to determine whether, in our case, the south’s wages are determined differently from those in the rest of the country. The easy method uses gretl’s built-in chow command to test for a change in the regression...

Read More

Multiplier Analysis

Multiplier analysis refers to the effect, and the timing of the effect, of a change in one variable on the outcome of another variable. The simplest form of multiplier analysis is based on a finite distributed lag model

Подпись: (9.19)yt = a + во Xt + PlXt-1 + в2 Xt-2 +——– + в Xt-q + et

Подпись: dE (yt) dxt-s Подпись: es Подпись: (9.20)

The estimated coefficients from this model can be used to produce impact, delay and interim multipliers. The impact multiplier is the impact of a one unit change in xt on the mean of yt. Since X and y are in the same time period the effect is contemporaneous and therefore equal to the initial impact of the change. The s-period delay multiplier is

is the effect of a change in x s-periods in the past on the average value of the dependent variable in the current period...

Read More

Estimating Nonlinear Relationships

Since economic relationships are often not linear, we often need to allow for the possibility that the independent and dependent variable are nonlinearly related. Consider the following simple regression

price = ві + e2sqft + e (2.7)

The parameter, fi2 measures the expected change in price given an additional square foot of living space in the home. As specified, this marginal effect is the same for homes of every size. It might make more sense to allow the size of this marginal effect to depend on the size of the house. Larger houses also tend to be more luxurious and therefore another square foot of living area might add more to the average home price. This can be modeled by using a quadratic term in the model.

price = a1 + a2sqft2 + e (2.8)

The marginal effect of another square foot i...

Read More

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 expenditure adds at least one dollar of additional sales-and no more. At this point the marginal effect is equal to one,

e3 + 2^4 adverto = 1 (5.8)

Подпись: A = adverto Подпись: 1 - вз 2в4 Подпись: (5.9)

Solving advert in terms of the parameters

which is nonlinear in the parameters of the model. A consistent estimate of the optimal level of advertising can be obtained by substituting the least squares estimates for the parameters on the right-hand side. Estimating the standard error via the Delta method requires some calculus, but it is quite straightforward to do in gretl.

The Delta method is based on a first-order Taylor’s series expansion of a function that inv...

Read More

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, the problem with using least squares in a heteroskedastic model is that the usual estimator of precision (estimated variance-covariance matrix) is not consistent. The simplest way to tackle this problem is to use least squares to estimate the intercept and slopes and use an estimator of least squares covariance that is consistent whether errors are heteroskedastic or not. This is the so-called heteroskcedasticity robust estimator of covariance that gretl uses.

Подпись: 1 2 3 4 5 Подпись: ols food_exp const income modeltab add ols food_exp const income modeltab add modeltab show image261

In this example, the food expenditure data is used to estimate the model using least squares with both the usual and the robust sets of standard ...

Read More