伍德里奇计量经济学 (9)

Intermediate Econometrics, Yan Shen 20
Caution in using of RESET
However, if the omitted variable have nonlinear expectations in the dependent variables, a significant RESET can indicate omitted-variable problem.

First, we regress the dependent variables on the independent variables, without any square terms.
Intermediate Econometrics, Yan Shen 7
Economics 20 - Prof. Anderson
Intermediate Econometrics, Yan Shen
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Drawbacks of adding square terms to detect functional form misspecification Some nonlinearities cannot be picked up by adding quadratic terms. For example, we may find a square term matters when using logs is more appropriate.
Housing Price Example(hprice1.dta)
This example is used for two purposes. First, log forms can be better in dealing with nonlinearities then using the level variables. Second, a significant RESET may indicate nonlinear effect of omitted variables, like the variable “assess” added in later.
Intermediate Econometrics, Yan Shen
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Functional Form Misspecification
Misspecifying the functional form of a model can have serious consequences. We may obtain biased or inconsistent estimators of the partial effects. One way out: to add quadratic terms of any significant variables to a model and to perform a joint test of significance.
Economics 20 - Prof. Anderson 2
Functional Form (continued)
First, use economic theory to guide you Think about the interpretation Does it make more sense for x to affect y in percentage (use logs) or absolute terms? Does it make more sense for the derivative of x1 to vary with x1 (quadratic) or with x2 (interactions) or to be fixed?
Theoretically, we can test joint exclusion restrictions to see if higher order terms or interactions belong to the model
It can be tedious to add and test extra terms. Many degrees of freedoms may be used.
Intermediate Econometrics, Yan Shen
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Ramsey’s RESET
A test of functional form is Ramsey’s regression specification error test (RESET)
RESET adds polynomials in the OLS fitted values to the original regression.
Economics 20 - Prof. Anderson 3
Functional Form Misspecification
A multiple regression model suffers from functional form misspecification when it does not properly account for the relationship between the dependent and the observed explanatory variables.
Also notice that the drawback of the RESET test is when the null is rejected, RESET does not suggest what to do in the next step.
Intermediate Econometrics, Yan Shen 21
0
200 400 legal income, 1986, $100s
600
Economics 20 - Prof. Anderson
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Plotting narr86 against ptime86
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Economics 20 - Prof. Anderson
5 10 mos. in prison during 1986
Intermediate Econometrics, Yan Shen
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Example: Modeling Crime(crime1.dta)
Dependent variable:

Narr86, # times arrested, 1986
Explanatory Variables：
pcnv proportion of prior convictions 以前被定罪比例 avgsen avg sentence length, mos. 平均判刑期限，单位：月 tottime time in prison since 18, mos. 18岁以来的服刑时间，单位：月 Ptime86 mos. in prison during 1986 1986年的服刑时间，单位：月 Intermediate Econometrics, Yan Shen
Intermediate Econometrics, Yan Shen
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Implementing RESET in Stata
STATA uses command ovtest after reg command. ŷ2 , ŷ3 , and ŷ4 are used in stata.
Intermediate Econometrics, Yan Shen
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Plotting narr86 against pncv
15 ቤተ መጻሕፍቲ ባይዱ 5 10
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.4 .6 proportion of prior convictions
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Economics 20 - Prof. Anderson
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Plotting narr86 against inc86
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9. Multiple Regression Analysis:
Specification and Data Problems
y = b0 + b1x1 + b2x2 + . . . bkxk + u
Economics 20 - Prof. Anderson
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Functional Form
We’ve seen that a linear regression can really fit nonlinear relationships Can use logs on RHS, LHS or both Can use quadratic forms of x’s Can use interactions of x’s How do we know if we’ve gotten the right functional form for our model?
Intermediate Econometrics, Yan Shen
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Cautions in Using RESET
RESET is good at detecting misspecifications in the form of nonlinearities, not general omitted variables.
Economics 20 - Prof. Anderson 16
Ramsey’s RESET
A significant F statistic suggests some sort of functional form problem.
The distribution of F is approximately F2,n-k3 in large samples under the null hypothesis and the G-M assumptions.
Wooldridge (1995) shows that RESET has no power for detecting omitted variables whenever they have expectations that are linear in the included independent variables.
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Implementing RESET in Stata
An alternative is to specify the option, rhs. In this case the power(幂) terms of all the explanatory variables instead of the fitted values are used in the test.

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Example: Modeling Crime
Explanatory variables
Qemp86 # quarters employed, 1986 1986年被雇佣季度数 inc86 legal income, 1986, $100s 1986年合法收入，单位：百美元 black =1 if black hispan =1 if Hispanic(西班牙裔)
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Adding Quadratic terms to significant Variables
Economics 20 - Prof. Anderson
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Drawbacks of adding square terms to detect functional form misspecification
Intermediate Econometrics, Yan Shen
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Ramsey’s RESET
RESET relies on a trick similar to the special form of the White test Instead of adding functions of the x’s directly, we add and test functions of ŷ So, estimate y = b0 + b1x1 + … + bkxk + d1ŷ2 + d1ŷ3 +error and test H0: d1 = 0, d2 = 0 using F~F2,n-k-3 or LM~χ22