M/Ph/dZddlmZddlZddlmZmZddlm Z ddl m Z m Z m Z ddlmZmZmZddlmcmZddlmZdd lmZdZd ZGd d e ZGd deZdZGdde ZGdde ZGddeZ Gdde Z!Gdde Z"GddeZ#d dZ$GddeZ%ee#edZ&dS)!a{Generalized Method of Moments, GMM, and Two-Stage Least Squares for instrumental variables IV2SLS Issues ------ * number of parameters, nparams, and starting values for parameters Where to put them? start was initially taken from global scope (bug) * When optimal weighting matrix cannot be calculated numerically In DistQuantilesGMM, we only have one row of moment conditions, not a moment condition for each observation, calculation for cov of moments breaks down. iter=1 works (weights is identity matrix) -> need method to do one iteration with an identity matrix or an analytical weighting matrix given as parameter. -> add result statistics for this case, e.g. cov_params, I have it in the standalone function (and in calc_covparams which is a copy of it), but not tested yet. DONE `fitonce` in DistQuantilesGMM, params are the same as in direct call to fitgmm move it to GMM class (once it's clearer for which cases I need this.) * GMM does not know anything about the underlying model, e.g. y = X beta + u or panel data model. It would be good if we can reuse methods from regressions, e.g. predict, fitted values, calculating the error term, and some result statistics. What's the best way to do this, multiple inheritance, outsourcing the functions, mixins or delegation (a model creates a GMM instance just for estimation). Unclear ------- * dof in Hausman - based on rank - differs between IV2SLS method and function used with GMM or (IV2SLS) - with GMM, covariance matrix difference has negative eigenvalues in iv example, ??? * jtest/jval - I'm not sure about the normalization (multiply or divide by nobs) in jtest. need a test case. Scaling of jval is irrelevant for estimation. jval in jtest looks to large in example, but I have no idea about the size * bse for fitonce look too large (no time for checking now) formula for calc_cov_params for the case without optimal weighting matrix is wrong. I do not have an estimate for omega in that case. And I'm confusing between weights and omega, which are *not* the same in this case. Author: josef-pktd License: BSD (3-clause) )lrangeN)optimizestats) approx_fprime)ModelLikelihoodModelLikelihoodModelResults)OLSRegressionResultsRegressionResultsWrapper)cache_readonly) _ensure_2dcNtj|S)z'just a shortcut to np.abs(x).max() )npabsmax)xs b/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/regression/gmm.pymaxabsrDs 6!99==??c>eZdZdZdfd ZdZdZdZddZxZ S) IV2SLSaU Instrumental variables estimation using Two-Stage Least-Squares (2SLS) Parameters ---------- endog : ndarray Endogenous variable, 1-dimensional or 2-dimensional array nobs by 1 exog : ndarray Explanatory variables, 1-dimensional or 2-dimensional array nobs by k instrument : ndarray Instruments for explanatory variables. Must contain both exog variables that are not being instrumented and instruments Notes ----- All variables in exog are instrumented in the calculations. If variables in exog are not supposed to be instrumented, then these variables must also to be included in the instrument array. Degrees of freedom in the calculation of the standard errors uses `df_resid = (nobs - k_vars)`. (This corresponds to the `small` option in Stata's ivreg2.) Nc2t|d\|_|_t|||jjd|jjdz |_t|jjd|j z |_ dS)NTr) r instrumentinstrument_namessuper__init__exogshapedf_residfloat k_constantdf_model)selfendogrr __class__s rrzIV2SLS.__init__dsy1;J1M1M.. %%% *TY_Q-?? dioa04?BCC rc6|j|_|j|_dSN)r&wendogrwexogr%s r initializezIV2SLS.initializensj Y rcdS)zNot implementedN)r%Xs rwhitenz IV2SLS.whitenrs rcR|j|j|j}}}tj|j|}tj|j|}tj||x|_}tj||x}}tj|j|} | |_ tj|j|} tj|j|} tj| | } tj | } tj| jtj| | |_ t|| |j }||_ ||_t|||_t%|S)aestimate model using 2SLS IV regression Returns ------- results : instance of RegressionResults regression result Notes ----- This returns a generic RegressioResults instance as defined for the linear models. Parameter estimates and covariance are correct, but other results have not been tested yet, to see whether they apply without changes. )normalized_cov_params)r&rrrdotTlinalgsolve xhatparamsxhatprodinvr3IVRegressionResultsexog_hat_paramsexog_hatr fit_results_ols2ndr )r%yrzztzztxr8FxhatFtFFtxFtyparamsFtxinvlfits rr>z IV2SLS.fitvsK& DItA!fQS!nnfQS!nn')ysC'@'@@*6!Z(((DfQS!nn fQS!nnfQS!nnc**s##%'VFHbfS&6I6I%J%J""4-1-GIII * "1d||//11'---rc>||j}tj||S)a Return linear predicted values from a design matrix. Parameters ---------- exog : array_like Design / exogenous data params : array_like, optional after fit has been called Parameters of a linear model Returns ------- An array of fitted values Notes ----- If the model as not yet been fit, params is not optional. rrr4r%rIrs rpredictzIV2SLS.predicts"& <9DvdF###rr)) __name__ __module__ __qualname____doc__rr-r1r>rO __classcell__r's@rrrJs2DDDDDD   ).).).X$$$$$$$$rrc8eZdZdZedZddZddZdS) r;a1 Results class for for an OLS model. Most of the methods and attributes are inherited from RegressionResults. The special methods that are only available for OLS are: - get_influence - outlier_test - el_test - conf_int_el See Also -------- RegressionResults c|jjj}| tjSt |j}tj|}t|}||=| ||j }|Sr)) modeldata const_idxrnanlenrIeyerf_testfvalue)r%rZk_vars restrictionidx_noconstantfvals rr_zIVRegressionResults.fvalueshJO-  6M%%F&..K#F^^Ny);;{>:;;BDKrNcR|jj|jj}}t||}|jj}|jt|z }|j|jz }tj |jj |z }|stj |}tj |} tj|tj| ||z } tj| |} | | |fS)zHausman's specification test See Also -------- spec_hausman : generic function for Hausman's specification test )rXr&rr r>r3ssrr\rIrr6pinvr9 matrix_rankr4rchi2sf) r%dofr&rresolsnormalized_cov_params_olsse2 params_diffcov_diff cov_diffpinvHpvals r spec_hausmanz IVRegressionResults.spec_hausmansj& tUD!!%%''$*L$F!j3u::%kFM1 9>>$*"5669RR 2)''11Cy~~h// F;|[ A A B B3 Fz}}Q$$$|r皙?c ddlm}m}m}||j\}} } } ||j\} } |jj}tj tj |j |}tj |}tj |d|dz }t|| | | | | ||d|_ddddgfd d gfd d d ddg }dd|jzgfdd|jzgfdd|jzgfdd|jzgfg}dd| zgfdd| zgfdd| zgfdd| zgfg}dd||jzgfdd|zgfdd| zgfd d|zgfg}||jjjd"zd#z}dd$lm}|}|||||||%|||||d&'||||||d %|S)(Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Default is `var_##` for ## in p the number of regressors title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results r) jarque_bera omni_normtest durbin_watson)jbjbpvskewkurtosisomniomnipvcondno mineigvalzDep. Variable:NzModel:NMethod:z Two Stagez Least SquareszDate:NzTime:NzNo. Observations:N)z Df Residuals:N)z Df Model:Nz R-squared:z%#8.3fzAdj. R-squared:z F-statistic:%#8.4gzProb (F-statistic):%#6.3gzOmnibus:z%#6.3fzProb(Omnibus):zSkew:z Kurtosis:zDurbin-Watson:zJarque-Bera (JB):z Prob(JB):z%#8.3gz Cond. No.N zRegression ResultsSummarygleftgrightynamexnametitleTrralphause_t)statsmodels.stats.stattoolsrwrxrywresidrXr+rr6eigvalshr4r5sortsqrtdictdiagnrsquared rsquared_adjr_f_pvaluer'rPstatsmodels.iolib.summaryradd_table_2colsadd_table_params)r%rrrrrwrxryr{r|r}r~rrr+eigvalsrtop_left top_right diagn_left diagn_rightrsmrys rsummaryzIVRegressionResults.summarys8 . . . . . . . . . .#.;t{#;#; D$$}T[11 f  )$$RVEGU%;%;<<''""WQZ/00 Rd#F6$+AJ000 -$ ./*+##/+' #X %=$>?'(T5F*F)GH$x$+'=&>@+h.F-GH "HtO#45'(V*;)<=D 12"X%8$9: )8mmDK6P6P+P*QR+hm_=#ho%67#h&7%89  =J(1C7:NNE 655555wyy T) %U%  A A A d%uE#'  ) ) ) TK %U "  $ $ $  rr)NNNrt)rPrQrRrSr r_rsrr/rrr;r;sh   ^ Biiiiiirr;a Options for GMM --------------- Type of GMM ~~~~~~~~~~~ - one-step - iterated - CUE : not tested yet weight matrix ~~~~~~~~~~~~~ - `weights_method` : str, defines method for robust Options here are similar to :mod:`statsmodels.stats.robust_covariance` default is heteroscedasticity consistent, HC0 currently available methods are - `cov` : HC0, optionally with degrees of freedom correction - `hac` : - `iid` : untested, only for Z*u case, IV cases with u as error indep of Z - `ac` : not available yet - `cluster` : not connected yet - others from robust_covariance other arguments: - `wargs` : tuple or dict, required arguments for weights_method - `centered` : bool, indicates whether moments are centered for the calculation of the weights and covariance matrix, applies to all weight_methods - `ddof` : int degrees of freedom correction, applies currently only to `cov` - maxlag : int number of lags to include in HAC calculation , applies only to `hac` - others not yet, e.g. groups for cluster robust covariance matrix ~~~~~~~~~~~~~~~~~ The same options as for weight matrix also apply to the calculation of the estimate of the covariance matrix of the parameter estimates. The additional option is - `has_optimal_weights`: If true, then the calculation of the covariance matrix assumes that we have optimal GMM with :math:`W = S^{-1}`. Default is True. TODO: do we want to have a different default after `onestep`? ceZdZdZdZ dfd ZdZddZddZ ddZ ddZ d dZ d!dZ dZ d"dZ d#dZ d$dZdZd%dZd&dZd&dZxZS)'GMMa Class for estimation by Generalized Method of Moments needs to be subclassed, where the subclass defined the moment conditions `momcond` Parameters ---------- endog : ndarray endogenous variable, see notes exog : ndarray array of exogenous variables, see notes instrument : ndarray array of instruments, see notes nmoms : None or int number of moment conditions, if None then it is set equal to the number of columns of instruments. Mainly needed to determine the shape or size of start parameters and starting weighting matrix. kwds : anything this is mainly if additional variables need to be stored for the calculations of the moment conditions Attributes ---------- results : instance of GMMResults currently just a storage class for params and cov_params without it's own methods bse : property return bse Notes ----- The GMM class only uses the moment conditions and does not use any data directly. endog, exog, instrument and kwds in the creation of the class instance are only used to store them for access in the moment conditions. Which of this are required and how they are used depends on the moment conditions of the subclass. Warning: Options for various methods have not been fully implemented and are still missing in several methods. TODO: currently onestep (maxiter=0) still produces an updated estimate of bse and cov_params. GMMResultsNnonec |||}t|||||jd|_|||_n&||jd|_nt j|_|||_n&||jd|_nt j|_|j |d|_ dS)z maybe drop and use mixin instead TODO: GMM does not really care about the data, just the moment conditions )missingrrNrư>) _check_inputsrrr nobsnmomsrr[k_params__dict__update epsilon_iter) r%r&rrk_momsrrkwdsr's rrz GMM.__init__s'' E::  g%  ' ' ' KN  DJJ  ##)!,DJJDJ  $DMM  # JqMDMMFDM T""" rc|?tj|}|jd|jdkrtd|S)Nrz*instrument is not the same length as endog)rasarrayr ValueError)r%rr&offsets rrzGMM._check_inputssC  !Z ++F|A%+a.00 !MNNNrc|jj}|=t|t|kr||j_dStdt|t|kr$|t| d|j_dSt|t|kr2dt t|D|j_dSdS)N param_names has the wrong lengthcg|]}d|zS)zp%2dr/).0is r z(GMM._fix_param_names..s#K#K#K1FQJ#K#K#Kr)rYxnamesr\rrange)r%rI param_namesrs r_fix_param_nameszGMM._fix_param_namess!  "6{{c+....#.     !CDDD6{{S[[((#)3v;;,--#8    Vs6{{**#K#Kc&kk8J8J#K#K#K    +*rc|||_n|j}|t|kr||j_dSt d)aset the parameter names in the model Parameters ---------- param_names : list[str] param_names should have the same length as the number of params k_params : None or int If k_params is None, then the k_params attribute is used, unless it is None. If k_params is not None, then it will also set the k_params attribute. Nr)rr\rYrr)r%rrs rset_param_nameszGMM.set_param_namessL  $DMM}H s;'' ' '*DI   ?@@ @r covr/Tbfgsc f|} | |} |||i}d|vrd|d<|dks|dkrT| tj|} n|d} || | ||} | } n>|| |||||| \} } tj| } |dkr|| || } |j} |||d } | | d t|j || | || | }||_ |S)ac Estimate parameters using GMM and return GMMResults TODO: weight and covariance arguments still need to be made consistent with similar options in other models, see RegressionResult.get_robustcov_results Parameters ---------- start_params : array (optional) starting value for parameters ub minimization. If None then fitstart method is called for the starting values. maxiter : int or 'cue' Number of iterations in iterated GMM. The onestep estimate can be obtained with maxiter=0 or 1. If maxiter is large, then the iteration will stop either at maxiter or on convergence of the parameters (TODO: no options for convergence criteria yet.) If `maxiter == 'cue'`, the the continuously updated GMM is calculated which updates the weight matrix during the minimization of the GMM objective function. The CUE estimation uses the onestep parameters as starting values. inv_weights : None or ndarray inverse of the starting weighting matrix. If inv_weights are not given then the method `start_weights` is used which depends on the subclass, for IV subclasses `inv_weights = z'z` where `z` are the instruments, otherwise an identity matrix is used. weights_method : str, defines method for robust Options here are similar to :mod:`statsmodels.stats.robust_covariance` default is heteroscedasticity consistent, HC0 currently available methods are - `cov` : HC0, optionally with degrees of freedom correction - `hac` : - `iid` : untested, only for Z*u case, IV cases with u as error indep of Z - `ac` : not available yet - `cluster` : not connected yet - others from robust_covariance wargs` : tuple or dict, required and optional arguments for weights_method - `centered` : bool, indicates whether moments are centered for the calculation of the weights and covariance matrix, applies to all weight_methods - `ddof` : int degrees of freedom correction, applies currently only to `cov` - `maxlag` : int number of lags to include in HAC calculation , applies only to `hac` - others not yet, e.g. groups for cluster robust has_optimal_weights: If true, then the calculation of the covariance matrix assumes that we have optimal GMM with :math:`W = S^{-1}`. Default is True. TODO: do we want to have a different default after `onestep`? optim_method : str, default is 'bfgs' numerical optimization method. Currently not all optimizers that are available in LikelihoodModels are connected. optim_args : dict keyword arguments for the numerical optimizer. Returns ------- results : instance of GMMResults this is also attached as attribute results Notes ----- Warning: One-step estimation, `maxiter` either 0 or 1, still has problems (at least compared to Stata's gmm). By default it uses a heteroscedasticity robust covariance matrix, but uses the assumption that the weight matrix is optimal. See options for cov_params in the results instance. The same options as for weight matrix also apply to the calculation of the estimate of the covariance matrix of the parameter estimates. NdisprrcueFr:weights optim_method optim_args)maxiterstart_invweightsweights_methodwargsrr)rr)rhas_optimal_weightsr)r)rXrIrr options_otherr) fitstartrr6rf start_weightsfitgmmfititer fitgmm_cu _weights_curresults_class_dict results_classresults)r% start_paramsr inv_weightsrrrrrstartrrIweights_rrs rr>zGMM.fit+sx =MMOOE   K  J  # #!"Jv  a<<7e++&)..55,,,77[[.:z!SSFHH"ll53:0:$<> >  * ")--(( ) ) )y*E'' '%'' 'rc|i}|dkr tj}n?|dkrtj}|j|d<n"|dkr tj}nt d||j|fddi|S) aestimate parameters using continuously updating GMM Parameters ---------- start : array_like starting values for minimization Returns ------- paramest : ndarray estimated parameters Notes ----- todo: add fixed parameter option, not here ??? uses scipy.optimize.fmin Nrrrrrrr/)rrrscore_currgmmobjective_cu)r%rrrrs rrz GMM.fitgmm_cus.  J 4   II V # # *I#'=Jx U " " )II=>> >y-uLL2LLLLrc4tj|jS)z+Create identity matrix for starting weights)rr]r)r%r:s rrzGMM.start_weights+svdj!!!rc|||}tjtj|||S)aL objective function for GMM minimization Parameters ---------- params : ndarray parameter values at which objective is evaluated weights : ndarray weighting matrix Returns ------- jval : float value of objective function ) momcond_meanrr4)r%rIrmomss rrzGMM.gmmobjective/s5"  ((vbfT7++T222rcD||}||||}tj|}||_tjtj|d||dS)a, objective function for continuously updating GMM minimization Parameters ---------- params : ndarray parameter values at which objective is evaluated Returns ------- jval : float value of objective function )rrr)momcondcalc_weightmatrixrr6rfrr4mean)r%rIrrrrrs rrzGMM.gmmobjective_cuFs ||F##,,T.38-:: )..--"vbfTYYq\\733TYYq\\BBBrcg|_|j}||d} n|} | } t|D]} | } tj| } ||| ||} || }||||| } | dkrt| |z |j krn| }| | fS)aiterative estimation with updating of optimal weighting matrix stopping criteria are maxiter or change in parameter estimate less than self.epsilon_iter, with default 1e-6. Parameters ---------- start : ndarray starting value for parameters maxiter : int maximum number of iterations start_weights : array (nmoms, nmoms) initial weighting matrix; if None, then the identity matrix is used weights_method : {'cov', ...} method to use to estimate the optimal weighting matrix, see calc_weightmatrix for details Returns ------- params : ndarray estimated parameters weights : ndarray optimal weighting matrix calculated with final parameter estimates Notes ----- NTrrrrrIr ) historyr rrrr6rfrr rr)r%rrrrrrrr wwinv_newitwinvresgmmrs rrz GMM.fititer^sH ,  #""t",,AA A ..  BD t$$A[[ ,6!88F76??D--d=K49&.JJHAvv&%0043DDDEEqyrc .|j\}}trtd|d|vo|d }|s|}n||z }|dkrmt j|j|} d|vrH|ddkr| ||jz z} n trtd|d| ||dz z} n| |z} n|dkrd|vrtd |d} t j | d z} t j|j||z } td | d zD]?} | | | t j|| d j|d | z|| z z z } @n,|d krC|d} d |vr |d } ntj } | |d <tj || | } | |z} n|dkr||}|r||dz}|j}t j|j|t j|j||z } d|vrF|ddkr| ||jz z} nAtrtd|d| ||dz z} n| |z} ntd| S)a> calculate omega or the weighting matrix Parameters ---------- moms : ndarray moment conditions (nobs x nmoms) for all observations evaluated at a parameter value weights_method : str 'cov' If method='cov' is cov then the matrix is calculated as simple covariance of the moment conditions. see fit method for available aoptions for the weight and covariance matrix wargs : tuple or dict parameters that are required by some kernel methods to estimate the long-run covariance. Not used yet. Returns ------- w : array (nmoms, nmoms) estimate for the weighting matrix or covariance of the moment condition Notes ----- currently a constant cutoff window is used TODO: implement long-run cov estimators, kernel-based Newey-West Andrews Andrews-Moy???? References ---------- Greene Hansen, Bruce z momcov wargscenteredrddofrz momcov ddof flatkernelmaxlagzflatkernel requires maxlagrNhackernel)nlags weights_funciidrzweight method not available)r rrr rr4r5rronesrsmcovweights_bartlett S_hac_simple get_errorr)r%rrrrIrrrmoms_rrhrrurs rr zGMM.calc_weightmatrixsTz f  * /5 ) ) )"e+EE*4E0EF 'EE499;;&E U " "uw&&A=J..$./AA=neFm<<<$v./AAT  | + +u$$ !=>>>8_F ##Auw&&t+A1VAX&& I IadRVE!""IKss<<<QGH Iu $ $8_F5  $X $5 ".h"50<>>>A IAA u $ $v&&A QVVAYYJz|Z0044RVAC^^DDtKA=J..$./AA=neFm<<<$v./AAT :;; ;rc~||}|j\|_|_|dS)z- mean of moment conditions, r)r r nobs_momsrr )r%rIr s rrzGMM.momcond_mean(s5 ,,v&&&-m# ||Ar-C6?c|j}|r*t|||t||| zdz }nt|||}|S)a=gradient of moment conditions Parameters ---------- params : ndarray parameter at which the moment conditions are evaluated epsilon : float stepsize for finite difference calculation centered : bool This refers to the finite difference calculation. If `centered` is true, then the centered finite difference calculation is used. Otherwise the one-sided forward differences are used. TODO: looks like not used yet missing argument `weights` )epsilonr )rr)r%rIr+rr gradmomss rgradient_momcondzGMM.gradient_momcond3sk&#  G%fgwGGG!&'G8DDDEFGHHH%VWgFFFHrc:t||j|f||}|S)Scorerrr+)rr)r%rIrr+rderivs rrz GMM.scoreQs0fd&7wj'/BBB rc8t||jd||}|S)zScore cur/r0)rr)r%rIr+rr1s rrz GMM.score_cuXs.fd&:'/BBB r)NNrr))NrNrr/TrN)NrN)rNT)rr/)r Nrr/rN)rr/N)r)T)NT)rPrQrRrSrrrrrr>rrrrrrr rr-rrrTrUs@rrrs22h!MFJ!!!!!!>LLLL$AAAA0>B.0&*26WWWWr='='='='@%M%M%M%MN""""333.6; CCCC0:>AG#EEEEPCE!%D<rrceZdZdZdZdZedZedZdZ dd Z e d Z d Z dZdZddZdS)rzjust a storage class right nowFc|j||jj|_tj|_||_dSr)) rrrXrrinfr! _cov_paramscov_params_default)r%rrs rrzGMMResults.__init__fsF T"""JO  "&"2"2"4"4rcL|j|j|jS)zObjective function at params)rXrrIrr,s rqz GMMResults.qns z&&t{DLAAArc*|j|jjzS)z"nobs_moms attached by momcond_mean)r:rXr(r,s rjvalzGMMResults.jvalssv ,,,rc d|vr |j|d<d|vr|jd|d<d|vr|jd|d<|j|j}|j|j}|j||fi|}|S)Nrrr)rrrXr-rIr calc_cov_params)r%rr,r covparamss rr7zGMMResults._cov_paramsxs $   JDM 4 ' '%)%78H%ID! "  , ,*.*<=R*SD& ':..t{;;z!!$+..(D(x@@4@@ rNTrr/c |jd}||j}n |r|} n#|j||||j} |rht jt j|j t jt j| |} nt j|j |} t jt j| |} t jt j| t jt j| | | j | } | |z S)acalculate covariance of parameter estimates not all options tried out yet If weights matrix is given, then the formula use to calculate cov_params depends on whether has_optimal_weights is true. If no weights are given, then the weight matrix is calculated with the given method, and has_optimal_weights is assumed to be true. (API Note: The latter assumption could be changed if we allow for has_optimal_weights=None.) rNr) r rrXr rIrr6r:r4r5) r%rr,r use_weightsrrrromegahatrgwgwginvs rr>zGMMResults.calc_cov_paramss+"z!} ? lGG   DHHz3304?M6;7;{ 4DDH  U)--xz$&F29==+B+BH$M$M!O!OPPCC G,,BY]]26"h#7#788F&rvb(/C/CRT(J(JKKVTTC4xrc*|S)z2standard error of the parameter estimates )get_bser,s rbse_zGMMResults.bse_s||~~rc dtjtj|jdi|S)a*standard error of the parameter estimates with options Parameters ---------- kwds : optional keywords options for calculating cov_params Returns ------- bse : ndarray estimated standard error of parameter estimates r/)rrdiag cov_params)r%rs rrFzGMMResults.get_bses0wrwt666677888rc|j}|jj}|jj|z }|t j|||fS)zoveridentification test I guess this is missing a division by nobs, what's the normalization in jval ? )r<rIsizerXrrrhri)r%jstatnparamsdfs rjtestzGMMResults.jtestsA +" Z  'ejmmE2..22rc|j}|jj}|j}|jj}||z }||z }|dkr| }| }|tj|||fS)aoveridentification test for comparing two nested gmm estimates This assumes that some moment restrictions have been dropped in one of the GMM estimates relative to the other. Not tested yet We are comparing two separately estimated models, that use different weighting matrices. It is not guaranteed that the resulting difference is positive. TODO: Check in which cases Stata programs use the same weigths r)r<rXrrrhri)r%otherjstat1k_moms1jstat2k_moms2jdiffrOs r compare_jzGMMResults.compare_jso*"+# w  66BGEejmmE2..22rrtc2|\}}}ddddgfdddg}dd |zgfd d |zgfg} ||jjjd zdz}ddlm} | } | ||| |||| |||||j| S)rvrrrrrrrz Hansen J:rzProb (Hansen J):rNrResultsrrrr) rPrXr'rPrrrrr) r%rrrrjvaluejpvaluejdfrrrrs rrzGMMResults.summarys8 $zz||,$(##/ "Hv$5#68(8g+=*>?   =J(1C7)CE 655555wyy T)#(U  D D D d%uE$(J  0 0 0 r)NFTrr/r)rPrQrRrSrrr r:r<r7r>propertyrGrFrPrXrr/rrrras(( E555BB^B--^-4INBFJL2222hX 999 3 3 33338>>>>>>rrc8eZdZdZdZdZd dZdZd dZd Z dS) IVGMMaS Basic class for instrumental variables estimation using GMM A linear function for the conditional mean is defined as default but the methods should be overwritten by subclasses, currently `LinearIVGMM` and `NonlinearIVGMM` are implemented as subclasses. See Also -------- LinearIVGMM NonlinearIVGMM IVGMMResultscJtj|jjdS)zCreate array of zerosrrzerosrr r,s rrzIVGMM.fitstartXx *+++rTctj|jj|j}|jjd}|r||z Stj||z S)zStarting weightsr)rr4rr5r r6rf)r%r:zzrs rrzIVGMM.start_weights\sS VDO%t 7 7$Q'  -9 9>>"t),, ,rc<|j||z S)zGet error at params)r&rO)r%rIs rr#zIVGMM.get_erroreszDLL0000rNc>||j}tj||S)zGet prediction at paramsrMrNs rrOz IVGMM.predictis <9DvdF###rcT|j}|||dddfzS)zError times instrumentN)rr#)r%rIrs rr z IVGMM.momcondps-_ DNN622111d7;;;rr3r)) rPrQrRrSrrrr#rOr r/rrr`r`Gsz  #M,,,----111$$$$<<<<||j}tj||Sr)rMrNs rrOzLinearIVGMM.predicts <9DvdF###rc h|j|j}}tj|j| |jz }|Sr))rrrr4r5r)r%rIrrrAr,s rr-zLinearIVGMM.gradient_momconds0y$/1F13NN?TY.rc ,|j|j}}|jd}||}dt j|j||t j|j|z}|||zz}|S)Nr)rrr get_errorsrr4r5) r%rIrrrrArr&rs rrzLinearIVGMM.scores|y$/1wqz OOF # #RVAC^^'' BF13NN(C(CDDD  r)NNr))rPrQrRrSrrOr-rr/rrrlrlvse<++++\$$$$     rrlcJeZdZdZdZfdZd dZd dZ d dZd Z xZ S) NonlinearIVGMMa7 Class for non-linear instrumental variables estimation using GMM The model is assumed to have the following moment condition E[ z * (y - f(X, beta)] = 0 Where `y` is the dependent endogenous variable, `x` are the explanatory variables and `z` are the instruments. Variables in `x` that are exogenous need also be included in z. `f` is a nonlinear function. Notation Warning: our name `exog` stands for the explanatory variables, and includes both exogenous and explanatory variables that are endogenous, i.e. included endogenous variables Parameters ---------- endog : array_like dependent endogenous variable exog : array_like explanatory, right hand side variables, including explanatory variables that are endogenous. instruments : array_like Instrumental variables, variables that are exogenous to the error in the linear model containing both included and excluded exogenous variables func : callable function for the mean or conditional expectation of the endogenous variable. The function will be called with parameters and the array of explanatory, right hand side variables, `func(params, exog)` Notes ----- This class uses numerical differences to obtain the derivative of the objective function. If the jacobian of the conditional mean function, `func` is available, then it can be used by subclassing this class and defining a method `jac_func`. TODO: check required signature of jac_error and jac_func cJtj|jjdS)Nrrcr,s rrzNonlinearIVGMM.fitstartrerc N||_tj|||fi|dSr))funcrr)r%r&rrr|rr's rrzNonlinearIVGMM.__init__s3 j99D99999rNc@||j}|||Sr))rr|rNs rrOzNonlinearIVGMM.predicts" <9Dyy&&&rTcDt||j|jf||}|S)Nr0)rr|r)r%rIrrrr+r1s rjac_funczNonlinearIVGMM.jac_func!s3fdityl'/BBB rc<|||ddd}| S)NTr0)r)r%rIrrrr+rs r jac_errorzNonlinearIVGMM.jac_error*s1==td)-!//yrc X|j}|jd}|||ddd}| }||}dt jt j|j||t j|j|z} | ||zz} | S)NrT)rr+rrv)rr rr#rr4r5) r%rIrrrArjac_urr&rs rrzNonlinearIVGMM.score3s OwqzvwT4(,.. F NN6 " "RVBF13NNG4488QHHH  rr))NTN) rPrQrRrSrrrOrrrrTrUs@rryrys''X,,, ::::: ''''>BrrycTeZdZdZedZedZedZdS)razResults class of IVGMMc@|j|jS)z Fitted values)rXrOrIr,s r fittedvalueszIVGMMResults.fittedvaluesJsz!!$+...rc*|jj|jz S) Residuals)rXr&rr,s rresidzIVGMMResults.residPsz$"333rcF|j|jzdS)zSum of square errorsr)rsumr,s rrezIVGMMResults.ssrVs! TZ',,Q///rN)rPrQrRrSr rrrer/rrraraFsk  //^/ 44^4 00^000rracp||z }||z }|stj|}tj|}tj|tj||}t j||} tj|} || || fS)aHausmans specification test Parameters ---------- params_e : ndarray efficient and consistent under Null hypothesis, inconsistent under alternative hypothesis params_i : ndarray consistent under Null hypothesis, consistent under alternative hypothesis cov_params_e : ndarray, 2d covariance matrix of parameter estimates for params_e cov_params_i : ndarray, 2d covariance matrix of parameter estimates for params_i example instrumental variables OLS estimator is `e`, IV estimator is `i` Notes ----- Todos,Issues - check dof calculations and verify for linear case - check one-sided hypothesis References ---------- Greene section 5.5 p.82/83 ) rr6rgrfr4rrhrir) params_eparams_i cov_params_e cov_params_irjrnrorprqrrevalss rrsrs^sBh&Kl*H .i##H--9>>(++L {BF<==>>A :==C D I  x ( (E dC rc6eZdZdZfdZdZdZddZxZS) DistQuantilesGMMz Estimate distribution parameters by GMM based on matching quantiles Currently mainly to try out different requirements for GMM when we cannot calculate the optimal weighting matrix. c t||d|_|d|_|_d|vrt jgdx|_}n|dx|_}t jfd|dzD|_t|j|_ |_||_ ||_ t||_d|_dS) Ngh㈵>distfnpquant)g{Gz?rtg?g?g333333?g?gffffff?gGz?c:g|]}tj|Sr/)rscoreatpercentile)rpr&s rrz-DistQuantilesGMM.__init__..s2 / / /a 7q A A / / /rd)rXr)rrrrr&rarrayrxquantr\rrrrr)r%r&rrrrr's ` rrzDistQuantilesGMM.__init__s j111 8n   4  #%8,R,R,R#S#S SDK&&#'> 1DK&h / / / /#)#: / / /00 %%   $!---  rc|j}t|dr||j}ndg|jzddgz}t j|S)N _fitstartrgg?)rhasattrrr&numargsrr)r%rrs rrzDistQuantilesGMM.fitstarts[ 6; ' ' 1$$TZ00EEC&"R0Ez%   rct|dkr|\}}nt|dkr|\}}}n |j|j}}|jj|g|R|z }t j|S)amoment conditions for estimating distribution parameters by matching quantiles, defines as many moment conditions as quantiles. Returns ------- difference : ndarray difference between theoretical and empirical quantiles Notes ----- This can be used for method of moments or for generalized method of moments. r )r\rrrcdfr atleast_2d)r%rIlocscaler pqxqcdfdiffs rr zDistQuantilesGMM.momconds" v;;!  JC [[A   & E3 dkB!$+/".v...3}W%%%rNFc|tj|j}||}||j_i|j_ddi|j_|j||}||j_ | |||j_ |jj d|i|jS)afit without estimating an optimal weighting matrix and return results This is a convenience function that calls fitgmm and covparams with a given weight matrix or the identity weight matrix. This is useful if the optimal weight matrix is know (or is analytically given) or if an optimal weight matrix cannot be calculated. (Developer Notes: this function could go into GMM, but is needed in this class, at least at the moment.) Parameters ---------- Returns ------- results : GMMResult instance result instance with params and _cov_params attached See Also -------- fitgmm cov_params N)rrr)rrr) rr]rrrrIrrrJrrr<r)r%rrrrIr7s rfitoncezDistQuantilesGMM.fitonces4 ?fTZ((G5))$  &6u%= "l--g:M.OO  '  --fg>>  "))+@AT*UVVV|r)NNF) rPrQrRrSrrr rrTrUs@rrrsu!!!!!< ! ! !&&&B))))))))rr)rrarr))'rSstatsmodels.compat.pythonrnumpyrscipyrrstatsmodels.tools.numdiffrstatsmodels.base.modelrrr #statsmodels.regression.linear_modelr r r %statsmodels.stats.sandwich_covariancesandwich_covariancer statsmodels.tools.decoratorsr statsmodels.tools.toolsrrrrr; _gmm_optionsrrr`rlryrarsrrr/rrrs//d-,,,,,!!!!!!!!333333MMMMMMMMMMKKKKKKKKKK555555555777777......  n$n$n$n$n$_n$n$n$bjjjjj+jjjb6 py y y y y %y y y zbbbbb'bbbL,<,<,<,<,