Use the data in OPENNESS for this exercise. (i) Because...

Use the data in OPENNESS for this exercise. (i) Because log(pcinc) is insignificant in both $(16.22)$ and the reduced form for open, drop it from the analysis. Estimate $(16.22)$ by OLS and IV without log $(p c i n c) .$ Do any important conclusions change? (ii) Still leaving log(pcinc) out of the analysis, is land or log(land) a better instrument for open? (Hint: Regress open on each of these separately and jointly.) (iii) Now, return to $(16.22) .$ Add the dummy variable oil to the equation and treat it as exogenous. Estimate the equation by IV. Does being an oil producer have a ceteris paribus effect on inflation?

Use the data in OPENNESS for this exercise.
(i) Because log(pcinc) is insignificant in both $(16.22)$ and the reduced form for open, drop it from the analysis. Estimate $(16.22)$ by OLS and IV without log $(p c i n c) .$ Do any important conclusions change?
(ii) Still leaving log(pcinc) out of the analysis, is land or log(land) a better instrument for open? (Hint: Regress open on each of these separately and jointly.)
(iii) Now, return to $(16.22) .$ Add the dummy variable oil to the equation and treat it as exogenous. Estimate the equation by IV. Does being an oil producer have a ceteris paribus effect on inflation?

Key Concepts

Ordinary Least Squares (OLS) Estimation

OLS is a method for estimating the coefficients in a linear regression model by minimizing the sum of squared differences between observed and predicted values. It provides unbiased estimates under certain assumptions, and it serves as a benchmark against which more advanced methods, like instrumental variables estimation, are compared.

Instrumental Variables (IV) Estimation

IV estimation is used when one or more regressors in a model are endogenous, meaning they are correlated with the error term, which can lead to biased OLS estimates. Instruments are variables that are correlated with the problematic regressors but uncorrelated with the error term. This method helps obtain consistent estimates despite the presence of endogeneity.

Instrument Relevance and Validity

The effectiveness of an instrument relies on two properties: relevance and exogeneity. Relevance means the instrument must be strongly correlated with the endogenous regressor, while exogeneity means that the instrument is not correlated with the error term in the structural equation. Assessing these properties is crucial for ensuring that the IV estimates are reliable.

Specification Changes and Model Selection

Model specification involves determining which variables to include in the regression analysis to best capture the relationship of interest. Dropping an insignificant variable or selecting between different transformations (such as levels versus logarithms) can affect the efficiency and interpretation of estimates. Specification tests and diagnostics are conducted to ensure that such changes do not alter the fundamental conclusions of the analysis.

Dummy Variables in Regression Analysis

Dummy variables are used to incorporate categorical information into regression models by assigning binary values (0 or 1) to indicate the absence or presence of a particular attribute. When included in a regression, they allow for the estimation of a ceteris paribus partial effect of categorical factors, controlling for other variables in the model.

Transcript

00:01 All right, hey guys, and welcome to another econometrics tutorial, and this is going to be another one on simultaneous equations.

00:08 So we're going to be using a data set from wildridge called openness, which looks at the openness of a country, which they measure as imports as a percent of gdp, and comparing it to average inflation.

00:24 And then they have a bunch of other variables as indicator variables that we can use.

00:29 So, it's a simultaneous equation problem because inflation and openness the way that they have it.

00:35 Imports will affect inflation, and inflation can also affect imports.

00:40 So they affect each other.

00:41 In our case, we're going to be looking at inflation as the dependent variable and openness as the independent variable.

00:48 And we're going to just take one of the indicator variables, and we're just going to see if it has any influence on openness.

00:56 So we're going to put in per capita income and use the logarithmic form of that.

01:04 And we're going to see what we get here as our beta 2.

01:11 So let's run that.

01:13 So for our beta 2, let's just run the entire section actually.

01:17 May as well.

01:19 So for our base beta 2 using the log of per capita income, we get a beta 2.

01:28 Negative 0 .21.

01:33 And then if we go ahead and just remove that to see if it really has any effect on openness and inflation, we get a beta 2 that is extremely similar next to the same.

01:47 So this is a neat little example.

01:50 You don't really need to include it if it has no effect on the main thing you're looking at, which it doesn't really.

01:56 So it's pointless to include.

01:59 So we won't from now on.

02:01 Next, we're going to do an instrumental variable test using land as an instrument, and we're going to use two forms.

02:10 We're going to use land, just the regular form of land, and then the logarithmic form of land.

02:20 So let's go ahead and run the instrumental variable test for the...

02:26 Actually, no, we should probably...

02:27 We'll do log first.

02:28 So for the logarithmic form of land, is it a week...

02:33 Weak instrument? no...