代写Econometric Analysis代做回归

日期：2024-03-29 02:12

Course Project Description

The Topic and Data

The topic is based on Kenkel and Terza (2001): The effect of physician advice on alcohol consumption

(http://dx.doi.org/10.1002/jae.596, also included in the kit), where a major task is to estimate the effect of advice on drinks. The data (KTDATA.DTA) and a do-file (kt-temp.do) for reading the data are provided.

This topic involves various issues that may be encountered in empirical research. The issues include endogeneity and some special data features. Mostly, these issues have been discussed in this course and two assignments. You should carry out this project using the tools and techniques

covered in our course (up to the end of Ch17.2) although they may not be perfect for the data.

You are not required to replicate the above Kenkel and Terza (KT) article (as some techniques and methods there are not covered in this course). You should use this article to gain a good

understanding of the topic, motivation, questions of interest, issues involved, and data to be analysed.

The Report

You should read Chapter 19 of Wooldridge to get insights about how to proceed with an empirical

project. You should report your analysis in the following 7 sections. You should limit your report to 8 pages (excluding the cover sheet).

1.   Introduction (1 page). You may discuss why the topic is of interest and how it is related to previous literature (referring to two or three related articles discussed in KT). You should outline the econometric issues, your modelling strategies, and provide a summary of your findings.

2.   Data (0.5 page). You may briefly describe the data, including the data source, variable definitions,  important descriptive statistics, and the main features of key variables. You should let readers see what you see as important.

3.   Conceptual Model (1 page). You may very briefly describe the empirical economic model, on which your econometric models are based. This can motivate your choice of regressors in the econometric models. You should read Section 2 of KT for this part.

4.   Econometric Models (2 pages). You may describe your econometric models in detail, and discuss

how you address various issues in econometric analysis (such as suspected endogeneity and data

features – drinks being nonnegative with many zeros and advice being binary). The main assumptions and estimation method for each econometric model should be briefly discussed. You may need to

complete this section in conjunction with your computation in Stata, which could involve many trial- and-error iterations. See also the “Econometric Analysis” section below.

5.   Empirical Results (2 pages). Your results and findings of econometric analysis should be presented in detail in this section. You may use tables for your presentation (e.g., similar to Table 17.3 of

Textbook). You should interpret your results properly, using the tools covered in this course.

Comparing results from different models is a good way to check if your findings are robust or

insensitive to the variations in models and assumptions. You may also want to present the results of relevant tests, which may justify or reject the models and assumptions you use. It is important to

comment on the merits and drawbacks of your econometric models, and discuss possible violation of your main assumptions and biases in your findings.

6.   Conclusions (0.5 page). You may reiterate your main findings here, and comment on possible policy implications. You may discuss briefly the remaining issues that you are unable to resolve, and you may comment on how you would like to tackle them.

7.   References (0.5 page). You should list your textbook (if it is used) and articles you have read and used as references.

Econometric Analysis

(a)  A goal of this project is for you to explore and apply the knowledge and tools you have learned so far (up to the end of Ch17.2) in a research project. You should be able to comment on the strength and weakness of your models and methods.

(b) You should briefly explain why some variables are included in, and others are excluded from, an    equation. Always pay attention to endogeneity: Is there endogeneity? Do I have valid instruments? Can I test the validity of instruments? Does endogeneity make a difference?

(c)  You should start with linear models. While not perfect, linear models can be regarded as a linear

approximation to the true model. It can also serve as a benchmark for comparisons. In particular, we understand well how endogeneity is handled in linear models.

(d) The method we test for endogeneity (see Ch15.5a) can also be used to estimate the regression

coefficients in the presence of endogeneity. This approach, known as “control function” method (see   p10-13 of Slides-W2-1b and p13 of Slides-W4-2b), can be extended to nonlinear models. Suppose we want to use  (x, Z1) to explain y, where Z1  is exogenous, and x is possibly endogenous. Note that Z1 may involve two or more variables (i.e., it can be a vector). You can think of y = dTinks and x = advice in this context.

Assume that the reduced-form equation for x can be either linear with x  = Z1π1  + Z2π2  + v, or  probit with x = Φ(Z1π1  + Z2π2) + v. Here, (Z1, Z2) are exogenous, (π1, π2) are parameters, Φ( ?) is the standard normal CDF, and v is an error term with E(v |Z1, Z2) = 0. Note that Z2  may involve two or more variables (i.e., it can be a vector).

Further, assume that the structural equation for y can be either linear with y = xy + Z1β + u, or  Tobit with y = max{0, xy + Z1β + u). For Tobit, u is an error term that is conditionally normal with u = θv + e, E(e |v, z1, z2) = 0, e ～ N(0, σ 2), and (y, β, θ) are parameters. The structure of u here    takes into account the possible correlation between u and v. The parameter θ can be used to test

whether x is exogenous (when θ  = 0, u and v are uncorrelated) or endogenous (when θ  ≠ 0, u and v are correlated).

It follows that the structural equation for y can be expressed as y = xy + Z1β + vθ + e for the

linear model, andy = max{0, xy + Z1β + vθ + e) for the Tobit model, where e is normally

distributed and uncorrelated with (x, Z1, Z2). Hence, if we were able to observe v, the OLS estimation would be applicable to the linear model and the maximum likelihood estimation would be applicable  to the Tobit model.

As we do not observe v, we use a two-step approach (control function approach). If models are correct, (y, β, θ) can be consistently estimated in two steps:

(i)  estimate the reduced-form. equation for x, either the linear model x = z1π1 + z2π2 + v or

the probit model x = Φ(z1π1 + z2π2) + v, and save the residual v;

(ii) estimate the structural equation (either linear or Tobit) replacing v by v.

However, the standard errors from Step (ii) can be incorrect because they are based on the first step

estimation. As we did not cover how to correct such standard errors, you may assume the standard errors from Step (ii) are good approximates to the true standard errors, and acknowledge this weakness.

For brevity, the above presentation does not include an intercept in the models. In your report, however, all models should include an intercept.

Stata Commands

For Stata commands, you may consult the Stata do-files (from Weeks 2 to Week 5) deposited in the

“Tutorials” folder on Moodle. You may also consult the do-files for Assignments 1 and 2. The following points should also be useful.

.    OLS estimation of linear model

regress x z1 z2

predict xhat  //Save fitted values

predict vhat, residuals  //Save residuals in vhat

test z2  //Test null hypothesis that coef on z2 is zero

.    2SLS estimation of linear model

ivregress 2sls y z1 (x=z2 z3) //2SLS using z2 and z3 as instruments for x predict yhat  //Save 2SLS fitted values

predict uhat, residuals  //Save residuals in uhat

.    Probit estimation

probit x z1 z2

predict xhat  //Save fitted values in xhat

generate vhat=x-xhat  //Save residuals in vhat

.    Tobit estimation

tobit y x z1

predict yhat, ystar(0,.)  //Save fitted values in yhat

margins, dydx(x) predict(ys(0,.))  //Find partial effect of x display r(rho)^2  //Display R-squared

.    Tobit estimation: Prefix a binary regressor x with “i.”

tobit y i.x z1

margins, dydx(i.x) predict(ys(0,.))  //Find partial effect of binary x