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一个面板回归，横截面26个，时间序列4年，一共5个自变量，有一个自变量（X1）在做FE时直接dropped，这个自变量针对每一个横截面，其4年数据时相同的，但不同横截面之间数据不相同。用cor看了相关系数，X1与Y相关系数有0.6，其他相关系数都不高。
通过做hausman test发现应选择随机效应而非固定效应，有两个问题：
1）既然应该是随机效应，固定效应的系数被dropped是否就无所谓了？
2）如果hausman test认为应该选择固定效应，是否可以直接把X1舍弃（文章重点关注的不是X1而是其他几个变量），是否存在问题？
非常非常感谢！
载入中......
由于个体效应 u_i 不随时间改变，因此若 x_it 包含了任何不随时间改变的变量，都会与 u_i 构成多重共线性，Stata会自动删除之。stata manual里面有详细说明
X1的确是不随时间变化，但我做过随机效应模型，而且hausman test表明是接受原假设，即采用随机效应模型，那这样是否就可以直接采用随机效应模型呢？
你自己说的这个自变量X1针对每一个横截面，其4年数据时相同的，很显然你的X1是虚拟变量，虚拟变量应该和其他譬如时间做交互，才能放入面板数据模型 ，进行回归，伍德里奇书上有，论坛里也有人说过，这个问题我也出现过。
建议用固定模型，实证中90%用的是固定模型。当然如果接受huasman检验，用随即模型也无可厚非
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本帖最后由 wanghaidong918 于
14:28 编辑
我做了如下的回归：
y=beta* X1+ gamma* X2+ epsilon
请问如何做t-test检验一下假设：
H0:& & beta+k*gamma&0
载入中......
就直接检验等式就可以了
Stata版版规
蓝色 发表于
就直接检验等式就可以了高手，能不能细一点，还是看不懂啊。我估计出了系数以后怎么用stata操作呢？谢谢啦！
help testnl& && && && && && && && && && && && && && && && && && && && && && && && && && && && && && && && && &dialog:&&testnl
-----------------------------------------------------------------------------------------------------------------------------
& & [R] testnl -- Test nonlinear hypotheses after estimation
& && &&&testnl exp=exp[=exp...] [, options]
& && &&&testnl (exp=exp[=exp...]) [(exp=exp[=exp...]) ...] [, options]
& & options& && && & description
& & -----------------------------------------------------------------------------------------------------------------------
& & mtest[(opt)]& &&&test each condition separately
& & nosvyadjust& && &carry out the Wald test as W/k ~ F(k,d); for use with svy estimation commands
& & iterate(#)& && & use maximum # of iterations to find the optimal step size
& & -----------------------------------------------------------------------------------------------------------------------
& & The second syntax means that if more than one constraint is specified, each must be surrounded by parentheses.
Description
& & testnl tests (linear or nonlinear) hypotheses about the estimated parameters from the most recently fitted model.
& & testnl produces Wald-type tests of smooth nonlinear (or linear) hypotheses about the estimated parameters from the most
& & recently fitted model.&&The p-values are based on the delta method, an approximation appropriate in large samples.
& & testnl can be used with svy estimation results, see [SVY] svy postestimation.
& & The format (exp1=exp2=exp3= ... ) for a simultaneous-equality hypothesis is just a convenient shorthand for (exp1=exp2)
& & (exp1=exp3), etc.
& & testnl may also be used to test linear hypotheses. test is faster if you want to test only linear hypotheses.&&testnl
& & is the only option for testing linear and nonlinear hypotheses simultaneously.
& & mtest[(opt)] specifies that tests be performed for each condition separately.&&opt specifies the method for adjusting
& && &&&p-values for multiple testing.&&Valid values for opt are
& && && && && & bonferroni& & Bonferroni's method
& && && && && & holm& && && & Holm's method
& && && && && & sidak& && && &Sidak's method
& && && && && & noadjust& && &no adjustment is to be made
& && &&&Specifying mtest without an argument, is equivalent to mtest(noadjust).
& & nosvyadjust is for use with svy estimation commands.&&It specifies that the Wald test be carried out as W/k ~ F(k,d)
& && &&&rather than as (d-k+1)W/(kd) ~ F(k,d-k+1), where k = the dimension of the test, and d = the total number of sampled
& && &&&PSUs minus the total number of strata.
& & iterate(#) specifies the maximum number of iterations used to find the optimal step size in the calculation of
& && &&&numerical derivatives of the test expressions.&&By default, the maximum number of iterations is 100, but
& && &&&convergence is usually achieved after only a few iterations.&&You should rarely have to use this option.
& & In contrast to likelihood-ratio tests, different -- mathematically equivalent -- formulations of an hypothesis may lead
& & to different results for a nonlinear Wald test (lack of &invariance&). For instance, the two hypotheses
& && &&&H0: b1 = b2
& && &&&H0: exp(b1) = exp(b2)
& & are mathematically equivalent expressions but do not yield the same test statistic and p-value. In extreme cases, under
& & one formulation, one would reject H0, whereas under an equivalent formulation one would not reject H0.
& & Likelihood-ratio testing does satisfy representation invariance.
& && &&&. sysuse auto
& && &&&. generate weightsq = weight^2
& && &&&. regress price mpg trunk length weight weightsq foreign
& & Test one nonlinear constraint
& && &&&. testnl _b[mpg] = 1/_b[weight]
& & Test multiple nonlinear constraints
& && &&&. testnl (_b[mpg] = 1/_b[weight]) (_b[trunk] = 1/_b[length])
& & Test multiple nonlinear constraints separately, and adjust p-values using Holm's method
& && &&&. testnl (_b[mpg] = 1/_b[weight]) (_b[trunk] = 1/_b[length]), mtest(holm)
Saved results
& & testnl saves the following in r():
& & Scalars& &
& && &r(df)& && && & degrees of freedom
& && &r(df_r)& && &&&residual degrees of freedom
& && &r(chi2)& && &&&chi-squared
& && &r(p)& && && &&&significance
& && &r(F)& && && &&&F statistic
& & Matrices&&
& && &r(G)& && && &&&derivatives of R(b) see Methods and Formulas in [R] testnl.
& && &r(R)& && && &&&R(b)-q; see Methods and Formulas in [R] testnl.
& & Manual:&&[R] testnl
& & Online:&&[R] lincom, [R] lrtest, [R] nlcom, [R] test
Stata版版规
help nlcom& && && && && && && && && && && && && && && && && && && && && && && && && && && && && && && && && &&&dialog:&&nlcom
-----------------------------------------------------------------------------------------------------------------------------
& & [R] nlcom -- Nonlinear combinations of estimators
& & Nonlinear combination of estimators -- one expression
& && &&&nlcom [name:]exp [, options]
& & Nonlinear combinations of estimators -- more than one expression
& && &&&nlcom ([name:]exp) [([name:]exp) ...] [, options]
& & The second syntax means that if more than one expression is specified, each must be surrounded by parentheses.&&exp is
& && &&&any function of the parameter estimates that is valid syntax for testnl. However, exp may not contain an equal sign
& && &&&or a comma.&&The optional name is any valid Stata name and labels the transformation.
& & options& && & description
& & -----------------------------------------------------------------------------------------------------------------------
& && &level(#)& &
default is level(95)
& && &iterate(#)&&maximum number of iterations
& && &post& && &&&post estimation results
& & + noheader& & suppress output header
& & -----------------------------------------------------------------------------------------------------------------------
& & + noheader does not appear in the dialog box.
Description
& & nlcom computes point estimates, standard errors, test statistics, significance levels, and confidence intervals for
& & (possibly) nonlinear combinations of parameter estimates after any Stata estimation command.&&Results are displayed in
& & the usual table format used for displaying estimation results.&&Calculations are based on the &delta method&, an
& & approximation appropriate in large samples.
& & nlcom can be used with sv see [SVY] svy postestimation.
& & level(#) specifies the confidence level, as a percentage, for confidence intervals.&&The default is level(95) or as set
& && &&&by set level.
& & iterate(#) specifies the maximum number of iterations used to find the optimal step size in calculating numerical
& && &&&derivatives of the transformations with respect to the original parameters.&&By default, the maximum number of
& && &&&iterations is 100, but convergence is usually achieved after only a few iterations.&&You should rarely have to use
& && &&&this option.
& & post causes nlcom to behave like a Stata estimation (eclass) command.&&When post is specified, nlcom will post the
& && &&&vector of transformed estimators and its estimated variance-covariance matrix to e(). This option, in essence,
& && &&&makes the transformation permanent.&&Thus you could, after posting, treat the transformed estimation results in the
& && &&&same way as you would treat results from other Stata estimation commands.&&For example, after posting, you could
& && &&&redisplay the results by typing nlcom without any arguments, or use test to perform simultaneous tests of
& && &&&hypotheses on linear combinations of the transformed estimators.
& && &&&Specifying post clears out the previous estimation results, which can be recovered only by refitting the original
& && &&&model or by storing the estimation results before running nlcom and see [R] estimates store.
& & The following option is available with nlcom but is not shown in the dialog box:
& & noheader suppresses the output header.
Comparison with lincom
& & nlcom is a generalization of lincom that allows the estimation of nonlinear transformations of model parameters.&&In
& & cases where you are estimating one transformation and that transformation is linear, it is faster.
& & However, when estimating more than one linear transformation or combinations of linear and nonlinear transformations,
& & using nlcom has the added benefit that you can obtain the variance-covariance matrix (which is saved in r(V)) of the
& & joint transformation.&&lincom does not allow the simultaneous estimation of multiple linear combinations.
Remark on the manipulability of nonlinear Wald tests
& & In contrast to likelihood-ratio tests, different -- mathematically equivalent -- formulations of a hypothesis may lead
& & to different results for a nonlinear Wald test (lack of &invariance&). For instance, the two hypotheses
& && &&&H0: coefficient = 0
& && &&&H0: exp(coefficient) - 1 = 0
& & are mathematically equivalent expressions but do not yield the same test statistic and p-value. In extreme cases, under
& & one formulation, one would reject H0, whereas under an equivalent formulation one would not reject H0.
& & -------------------------------------------------------------------------------------------------------------------------
& && &&&. webuse regress
& & Fit linear regression model
& && &&&. regress y x1 x2 x3
& & Estimate the product of the coefficients on x2 and x3
& && &&&. nlcom _b[x2]*_b[x3]
& & Estimate the ratios of the coefficients on x1 and x2 and on x2 and x3 jointly
& && &&&. nlcom (ratio1: _b[x1]/_b[x2]) (ratio2: _b[x2]/_b[x3]), post
& & Test whether the two ratios from above are equal
& && &&&. test _b[ratio1] = _b[ratio2]
& & -------------------------------------------------------------------------------------------------------------------------
& && &&&. webuse sysdsn3
& & Fit maximum-likelihood multinomial logit model
& && &&&. mlogit insure age male nonwhite site2 site3
& & Estimate the ratio of the coefficients on the male dummy in the Prepaid and Uninsure equations
& && &&&. nlcom [Prepaid]_b[male] / [Uninsure]_b[male]
& & -------------------------------------------------------------------------------------------------------------------------
Saved results
& & nlcom saves the following in r():
& & Scalars& && &&&
& && &r(N)& && && && && & number of observations
& && &r(df_r)& && && && & residual degrees of freedom
& & Matrices& && &
& && &r(b)& && && && && & vector of transformed coefficients
& && &r(V)& && && && && & estimated variance-covariance matrix of the transformed coefficients
& & If post is specified, nlcom also saves the following in e():
& & Scalars& && &&&
& && &e(N)& && && && && & number of observations
& && &e(df_r)& && && && & residual degrees of freedom
& && &e(N_strata)& && && &number of strata L, if used after svy
& && &e(N_psu)& && && && &number of sampled PSUs n, if used after svy
& & Macros& && && &
& && &e(cmd)& && && && &&&nlcom
& && &e(predict)& && && & program used to implement predict
& && &e(properties)& && & b V
& & Matrices& && &
& && &e(b)& && && && && & vector of transformed coefficients
& && &e(V)& && && && && & estimated variance-covariance matrix of the transformed coefficients
& && &e(V_srs)& && && && &simple-random-sampling-without-replacement (co)variance hat V_srswor, if svy
& && &e(V_srswr)& && && & simple-random-sampling-with-replacement (co)variance hat V_srswr, if svy and fpc()
& && &e(V_msp)& && && && &misspecification (co)variance hat V_msp, if svy and available
& & Functions& && &
& && &e(sample)& && && &&&marks estimation sample
& & Manual:&&[R] nlcom
& & Online:&&[R] lincom, [R] predictnl, [R] test, [R] testnl
Stata版版规
help test, help testparm& && && && && && && && && && && && && && && && && && && && && && && && && &&&dialogs:&&test&&testparm
-----------------------------------------------------------------------------------------------------------------------------
& & [R] test -- Test linear hypotheses after estimation
& & Basic syntax& &(see [R] anova postestimation
& && && && && && &&&see [MV] manova postestimation for test after manova)
& && &&&test coeflist& && && && && && && && && &(Syntax 1)
& && &&&test exp=exp[=...]& && && && && && && & (Syntax 2)
& && &&&test [eqno] [: varlist]& && && && && &&&(Syntax 3)
& && &&&test [eqno=eqno[=...]] [: varlist]& && &(Syntax 4)
& && &&&testparm varlist [, equal equation(eqno)]
& & Full syntax
& && &&&test (spec) [(spec) ...] [, test_options]
& & test_options& && && &description
& & -----------------------------------------------------------------------------------------------------------------------
& & Options
& && &mtest[(opt)]& && &&&test each condition separately
& && &coef& && && && && & report estimated constrained coefficients
& && &accumulate& && && & test hypothesis jointly with previously tested hypotheses
& && ¬est& && && && &&&suppress the output
& && &common& && && && &&&test only variables common to all the equations
& && &constant& && && && &include the constant in coefficients to be tested
& && &nosvyadjust& && && &carry out the Wald test as W/k ~ F(k,d); for use with svy estimation commands
& && &minimum& && && && & perform test with the constant, drop terms until the test becomes nonsingular, and test without
& && && && && && && && && &the constant on highly technical
& & + matvlc(matname)& &&&save the variance- programmer's option
& & -----------------------------------------------------------------------------------------------------------------------
& & + matvlc(matname) does not appear in the dialog box.
& & varlist and varname may contain time- see tsvarlist.
& && && && &Syntax 1 tests that coefficients are 0.
& && && && &Syntax 2 tests that linear expressions are equal.
& && && && &Syntax 3 tests that coefficients in eqno are 0.
& && && && &Syntax 4 tests equality of coefficients between equations.
& && &&&spec is one of
& && && && &coeflist
& && && && &exp=exp[=...]}
& && && && &[eqno][: varlist]
& && && && &[eqno1=eqno2[=...]][:&&varlist]
& && &&&coeflist is
& && && && &varlist
& && && && &[eqno]varname [[eqno]varname...]
& && && && &[eqno]_b[varname] [[eqno]_b[varname]...]
& && &&&exp is a linear expression containing
& && && && &varname
& && && && &_b[varname]
& && && && &[eqno]varname
& && && && &[eqno]_b[varname]
& && &&&eqno is
& && && && &##
& && && && &name
& & Distinguish between [], which are to be typed, and [], which indicate optional arguments.
& & Although not shown in the syntax diagram, parentheses around spec are required only with multiple specifications.
& & Also, the diagram does not show that test may be called without arguments to redisplay the results from the last test.
Description
& & test performs Wald tests for simple and composite linear hypotheses about the parameters of the most recently fitted
& & model.
& & test supports svy estimators, carrying out an adjusted Wald test by default in such cases.&&test can be used with svy
& & estimation results, see [SVY] svy postestimation.
& & testparm provides a useful alternative to test that permits varlist rather than a list of coefficients (which is often
& & nothing more than a list of variables), allowing the use of standard Stata notation, including '-' and '*', which are
& & given the expression interpretation by test.
& & test and testparm perform Wald tests.&&For likelihood-ratio tests, see [R] lrtest.&&For Wald-type tests of nonlinear
& & hypotheses, see [R] testnl.&&To display estimates for one-dimensional linear or nonlinear expressions of coefficients,
& & see [R] lincom and [R] nlcom.
& & See [R] anova postestimation for test after anova.
& & See [MV] manova postestimation for test after manova.
Options for testparm
& & equal tests that the variables appearing in varlist, which also appear in the previously fitted model, are equal to
& && &&&each other rather than jointly equal to zero.
& & equation(eqno) is relevant only for multiple-equation models such as mvreg, mlogit, and heckman.&&It specifies the
& && &&&equation for which the all-zero or all-equal hypothesis is tested.&&equation(#1) specifies that the test be
& && &&&conducted regarding the first equation #1.&&equation(price) specifies that the test concern the equation named
& && &&&price.
Options for test
& && &&&+---------+
& & ----+ Options +--------------------------------------------------------------------------------------------------------
& & mtest[(opt)] specifies that tests be performed for each condition separately.&&opt specifies the method for adjusting
& && &&&p-values for multiple testing.&&Valid values for opt are
& && && && && & bonferroni& & Bonferroni's method
& && && && && & holm& && && & Holm's method
& && && && && & sidak& && && &Sidak's method
& && && && && & noadjust& && &no adjustment is to be made
& && &&&Specifying mtest without an argument is equivalent to mtest(noadjust).
& & coef specifies that the estimated constrained coefficients be displayed.
& & accumulate allows a hypothesis to be tested jointly with the previously tested hypotheses.
& & notest suppresses the output.&&This option is useful when you are interested only in the joint test of several
& && &&&hypotheses, specified in a subsequent call of test, accumulate.
& & common specifies that when you use the [eqno1=eqno2[=...]] form of spec, the variables common to the equations eqno1,
& && &&&eqno2, etc., be tested.&&The default action is to complain if the equations have variables not in common.
& & constant specifies that _cons be included in the list of coefficients to be tested when using the [eqno1=eqno2[=...]]
& && &&&or [eqno] forms of spec.&&The default is not to include _cons.
& & nosvyadjust is for use with svy estimation commands.&&It specifies that the Wald test be carried out as W/k ~ F(k,d)
& && &&&rather than as (d-k+1)W/(kd) ~ F(k,d-k+1), where k = the dimension of the test and d = the total number of sampled
& && &&&PSUs minus the total number of strata.
& & minimum is a highly technical option.&&It first performs the test with the constant added.&&If this test is singular,
& && &&&coefficients are dropped until the test becomes nonsingular.&&Then the test without the constant is performed with
& && &&&the remaining terms.
& & The following option is available with test but is not shown in the dialog box:
& & matvlc(matname), a programmer's option, saves the variance-covariance matrix of the linear combinations involved in the
& && &&&suite of tests.&&For the test of the linear constraints L*b = c, matname contains L*V*L', where V is the estimated
& && &&&variance-covariance matrix of b.
Examples after single-equation estimation except anova
& && &&&. webuse census4
& && &&&. regress brate medage medagesq reg2-reg4
& & Test coefficient on reg3 is 0
& && &&&. test reg3=0
& & Shorthand for the previous test command
& && &&&. test reg3
& & Test coefficient on reg2=coefficient on reg4
& && &&&. test reg2=reg4
& & Stata will perform the algebra, and then do the test
& && &&&. test 2*(reg2-3*(reg3-reg4))=reg3+reg2+6*(reg4-reg3)
& & Test that coefficients on reg2 and reg3 are jointly equal to 0
& && &&&. test (reg2=0) (reg3=0)
& & The following two commands are equivalent to the previous test command
& && &&&. test reg2 = 0
& && &&&. test reg3 = 0, accumulate
& & Test that the coefficients on reg2, reg3, and reg4 are all 0; testparm understands a varlist
& && &&&. testparm reg2-reg4
& & In the above example, you may substitute any single-equation estimation command (such as clogit, logistic, logit, and
& & ologit) for regress.
Examples after anova
& && &&&. webuse census4
& && &&&. anova brate medage medagesq reg2 reg3 reg4, continuous(medage medagesq)
& & Test coefficient on reg3 is 0
& && &&&. test _coef[reg3[1]]=0
& & Shorthand for the previous test command
& && &&&. test reg3
& & Test coefficient on reg2=coefficient on reg4
& && &&&. test _coef[reg2[1]]=_coef[reg4[1]]
& & Test that the coefficients on reg2 and reg3 are jointly equal to 0
& && &&&. test _coef[reg2[1]]=0, notest
& && &&&. test _coef[reg3[1]]=0, accumulate
& & Test that the coefficients on reg2, reg3, and reg4 are all 0; you cannot use testparm after anova
& && &&&. test _coef[reg2[1]]=0, notest
& && &&&. test _coef[reg3[1]]=0, accumulate notest
& && &&&. test _coef[reg4[1]]=0, accumulate
Examples after multiple-equation estimation commands
& && &&&. sysuse auto
& && &&&. sureg (price foreign mpg displ) (weight foreign length)
& & Test significance of foreign in the price equation
& && &&&. test [price]foreign
& & Test that foreign is jointly 0 in both equations
& && &&&. test [price]foreign [weight]foreign
& & Shorthand for the previous test command
& && &&&. test foreign
& & Test a cross-equation constraint
& && &&&. test [price]foreign = [weight]foreign
& & Alternative syntax for the previous test
& && &&&. test [price=weight]: foreign
& & Test all coefficients except the intercept in an equation
& && &&&. test [price]
& & Test that foreign and displ are jointly 0 in the price equation
& && &&&. test [price]: foreign displ
& & Test that the coefficients on variables that are common to both equations are jointly 0
& && &&&. test [price=weight], common
& & Simultaneous test of multiple constraints
& && &&&. test ([price]: foreign) ([weight]: foreign)
Saved results
& & test and testparm save the following in r():
& & Scalars& &
& && &r(p)& && && &&&two-sided p-value
& && &r(F)& && && &&&F statistic
& && &r(df)& && && & test constraints degrees of freedom
& && &r(df_r)& && &&&residual degrees of freedom
& && &r(dropped_i)& &index of ith constraint dropped
& && &r(chi2)& && &&&chi-squared
& && &r(ss)& && && & sum of squares (test)
& && &r(rss)& && && &residual sum of squares
& && &r(drop)& && &&&1 if constraints were dropped, 0 otherwise
& & Macros& &
& && &r(mtmethod)& & method of adjustment for multiple testing
& & r(ss) and r(rss) are defined only when test is used for testing effects after anova.
& & Manual:&&[R] test
& & Online:&&[R] anova, [R] anova postestimation, [R] lincom, [R] lrtest, [R] nlcom, [R] testnl
Stata版版规
蓝色 发表于
help test, help testparm& && && && && && && && && && && && && && && && && && && && && && && && && &...真是太谢谢啦！
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