Tests for Gaussianity of the MAXIMA-1 CMB Map

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a r X i v :a s t r o -p h /0104248v 1 15 A p r 2001Tests for Gaussianity of the MAXIMA-1CMB MapJ.H.P.Wu 1,A.Balbi 2,3,4,J.Borrill 3,5,P.G.Ferreira 6,S.Hanany 3,7,A.H.Jaﬀe 1,3,8,A.T.Lee 3,4,9,B.Rabii 3,9,P.L.Richards 3,9,G.F.Smoot 3,4,8,9,R.Stompor 3,8,10,C.D.Winant 3,91Dept.of Astronomy,University of California,Berkeley,CA94720-3411,USA2Dipartimento di Fisica,Universit`a Tor Vergata,Roma,Via della Ricerca Scientiﬁca,I-00133,Roma,Italy3Center for Particle Astrophysics,University of California,Berkeley,CA94720-7304,USA4Lawrence Berkeley National Laboratory,Berkeley,CA94720,USA5National Energy Research Scientiﬁc Computing Center,Lawrence Berkeley National Laboratory,Berkeley,CA94720,USA6Astrophysics,University of Oxford,Oxford,OX13RH,UK7School of Physics and Astronomy,University of Minnesota/Twin Cities,Minneapolis,MN55455,USA8Space Sciences Laboratory,University of California,Berkeley,CA94720,USA 9Dept.of Physics,University of California,Berkeley,CA94720-7300,USA 10Copernicus Astronomical Center,Bartycka 18,00-716Warszawa,PolandGaussianity of the cosmological perturbations in the universe is one of the key predictions of standard inﬂation,but it is violated by other models of structure formation such as topological defects.We present the ﬁrst test of the Gaussianity of the cosmic microwave background (CMB)on sub-degree angular scales,where deviations from Gaussianity are most likely to occur.We apply the methods of moments,cumulants,the Kolmogorov test,the χ2test,and Minkowski functionals in eigen,real,Wiener-ﬁltered and signal-whitened spaces,to the MAXIMA-1CMB anisotropy data.We conclude that the data,which probe angular scales between 10arcminutes and 5degrees,are consistent with Gaussianity.A.Introduction :The anisotropy in the cosmic mi-crowave background (CMB)is arguably the cleanest cos-mic signal that preserves the intrinsic statistical proper-ties of cosmological perturbations [1].The recent obser-vations from MAXIMA-1[2]and BOOMERANG [3]have unambiguously detected a sharp peak in the CMB power spectrum.This has favored inﬂation [4]as the dominant mechanism for structure formation of the universe [5]as opposed to other candidates like topological defects [6].Another key prediction of standard inﬂation is that the distribution of cosmic perturbations are Gaussian,while other cosmological models such as isocurvature inﬂation (e.g.[7])and topological defects (e.g.[8])predict other-wise.Thus tests for the Gaussianity of CMB anisotropy data can discriminate between cosmological models.In addition,a Gaussian distribution is an important ingre-dient in the estimation algorithm of CMB power spec-tra [9,10],which has been used to produce the recent MAXIMA-1and BOOMERANG results [2,3].Adding the fact that the estimation of cosmological parameters [11–13]relies on the estimated CMB power spectra,it is important to verify the Gaussian distribution of the CMB.Tests for the Gaussianity of CMB data have been carried out by numerous authors,mainly using data from the Diﬀerential Microwave Radiometer (DMR)on the COsmic Background Explorer (COBE)[14].Sev-eral statistics were used including moments,cumulants,Minkowski functionals (which include genus,e.g.[15,16]),the three-point function (e.g.[17]),bispectrum (e.g.[18,19]),wavelet transform (e.g.[20]),etc.All these tests showed that the data were consistent with Gaussianity,except for a couple of results [19,20]that may have non-cosmological origins [21].In addition to the usual limitations from foreground contamination and instrumental noise,the 7◦angular resolution of the DMR data is not ideal for tests of Gaus-sianity.Angular resolution is an issue because the size of the causal horizon at last scattering is about one degree.Thus in a sky patch of super-degree size,there are many uncorrelated perturbations due to causality.As a result,the central limit theorem guarantees that the pre-last-scattering anisotropy on super-degree scales will tend to be Gaussian.Even if the post-last-scattering anisotropy is strong and non-Gaussian,it can be obscured by the pre-last-scattering contribution,which we expect to be Gaussian.Therefore a CMB map with sub-degree reso-lution can provide much more powerful tests for Gaus-sianity.Park et al.[22]recently used a genus test on the QMAP and Saskatoon data,which have a resolution of about 1.5◦,to show that they were consistent with Gaussianity.In this paper we report results from a series of Gaussianity tests on the MAXIMA-1CMB map [2],which provides anisotropy information on angular scales between 10′and 5◦.To optimize both the resolution and the signal-to-noise ratio for these tests,we shall use a map with 5972square pixels of 8′each [23].Using these high-quality data we probe for the ﬁrst time the Gaus-sianity of CMB anisotropy on sub-degree scales.A CMB sky is Gaussian if it is a realization of a pro-cess that is only speciﬁed by the two-point correlation function of a given cosmological model.However,be-cause we have only one realization of the CMB sky,it is not possible to exhaustively test the statistical prop-erties of the process that generated it.Therefore,we employ a Frequentist approach,testing the null hypoth-esis of Gaussianity for the inﬂationary model that best ﬁts the data.B.Karhunen-Lo`e ve transform :We consider the Karhunen-Lo`e ve (K-L)transform,sometimes called Prin-cipal ComponentAnalysis or the signal-to-noise eigen-mode transformation [24,9],because it enables us not only to transform the observed CMB map into uncor-related eigenmodes of known signal-to-noise ratios,and further to implement Gaussianity tests on the uncorre-lated modes.For the CMB,it is standard to model the data d ≡d i as a linear sum of uncorrelated signal s ≡s i and noise n ≡n i ,with the correlation matrix C ≡ dd T =S +N where S = ss T and N = nn T .In the noise-whitened space d (W)=N −1/2d ,all the eigenvalues of the noise matrix,N −1/2NN −1/2=I ,are simply unity.Thus the eigenvalues e S (W)of the noise-whitened signal matrix N −1/2SN −1/2represent the square of signal-to-noise ratios of each eigenmode.The coeﬃcients b (W)of the noise-whitened eigenmodes in a data set can be obtained by transforming d (W)to the ba-sis which diagonalizes N −1/2CN −1/2.These coeﬃcients are normally called the K-L coeﬃcients.We compute S using the CMB power spectrum of the best estimated cosmological model [11](Ωb =0.105,Ωc =0.595,ΩΛ=0.3,and h =0.53)and including the eﬀects introduced by the beam shape and the pixelization of the map [25].The matrix N is estimated from the tem-poral data [23].The resulting eigenvalues in the noise-whitened space are shown in Fig.1,sorted in descending order.The dot-dashed line indicates that only the ﬁrst639modes have signal-to-noise ratios e S (W) 1/2≥1.This number is well below our pixel number 5972.It is determined by the signal and noise levels and the observ-ing resolution (beam)of a data set,but is independent of the pixel number of the map when the pixel size is not larger than the observing resolution.A common technique to remove the information of non-cosmological interest in the map is Wiener ﬁltering,d WF =SC −1d .This is equivalent to weighting the eigen-modes with the ratios e S (W)/(e S (W)+1)(see Fig.1).The sum of these ratios for all the eigenmodes is 837,again well below the total number 5972of the eigenmodes.We shall employ this technique in section D to amplify the statistical signiﬁcance of the CMB signal in our map.The K-L transform can also be used to test for Gaussianity.If the underlying map is Gaussian,then the eigenvalue-normalized K-L coeﬃcients a (W)≡b (W)/(e S (W)+1)1/2should be a set of Gaussian variables with mean zero and variance one.We compute the a (W)of our data,and use the observed frequency distribu-tion to approximate its one-point probability distribution functions (PDF)p (ν),where νis the number of standard deviations from the mean,for both the entire 5972andCMB data (top),and the Wiener ﬁlter (bottom).(b)a (W)of the MAXIMA-1data (solid),the Gaussian expec-tation (dashed),and its 95%CRG (shaded).the ﬁrst 639modes (i.e.,those modes with signal domi-nating over noise).Both cases easily pass the χ2and the Kolmogorov tests for Gaussianity at 95%conﬁdence.In addition to the above tests,we also use Monte Carlo (MC)simulation to build a Gaussian reference frame for the Frequentist approach.We generate 100,000Gaussianrealizations,each of which is obtained by d MC i=C 1/2ij g j ,where g j is a Gaussian variable of mean zero and variance one.As a ﬁrst application,we use the MC simulation to ﬁnd the probability distribution of p (ν)at each νfor the entire 5972and the ﬁrst 639a (W).Fig.2shows that in both cases the real data lie well within the 95%conﬁdence regions of Gaussianity (hereafter CRG).We also compute the moments and cumulants of the ﬁrst 639a (W)up to tenth order,and they are all well within the 99%CRG.All these results support the conclusions not only that our map is consistent with Gaussianity,but also that our estimations of noise and CMB power spectrum (giving N and S respectively)are consistent with the data so as to provide the proper eigenmodes for the K-L transform.C.Minkowski functionals :The concept of Minkowski functionals is based on integral geometry.According to Hadwiger’s Theorem β+1Minkowski functionals are suf-ﬁcient to measure the morphology of a β-dimensional pattern.In the case of CMB we have β=2and thus need only three Minkowski Functionals.First we de-ﬁne the excursion set Q in a given CMB ﬁeld as the region in which the CMB amplitude d i is larger than a threshold:Q ≡Q (ν)={d i |(d i −µ)/σ>ν},where µ= d and σ2= d 2 −µ2.Then the surface densities v i (ν)≡V i (Q )/A of Minkowski functionals V i (Q )for aan oﬀset in the pixel positions every other row.(b)An example of a pixelized CMB map with the artiﬁcial pixel oﬀset. CMB patch of angular area A can be deﬁned asv0=14A∂Qdl,v2=12)/2,v1(G)=τ1/2exp(−ν2/2)/8σ,and v2(G)=τνexp(−ν2/2)/(2π)3/2σ2.We also note that the com-monly used one-point PDF p(ν)and genus g,or the‘Euler-Poincar´e characteristics’,are simply related to the Minkowski Functionals.For the two-dimensional CMB,we have p(ν)=−∂V0/A∂νand g=V2+V0/2π. Because the MAXIMA-1map has an irregular bound-ary and all pixels have a square shape lying on a regularlattice,we need a numerical scheme to approximate its Minkowski Functionals.For a given thresholdνand thusa given Q on the lattice,v0is simply the number of pixelsin Q divided by the total number of pixels in the map. Here v1is determined by the length of∂Q multipliedbyπ/4to correct for the square-pixel lattice eﬀect.To compute v2,weﬁrst induce oﬀset in the pixel positionsevery other row.As Fig.3(a)shows,this gives two types(I and II)of vertices.For each type,the integration of κin equation(1)can be easily obtained by examiningthe status of the neighboring four pixels(basically theintegration is determined by the change of the internal angle along∂Q).Fig.3(b)shows an example,where thepixels in Q are shaded and the one with no CMB data is labeled with a cross.In this case the verticesα1,α2,α3andα4have unambiguously αi(2κ/π)dl=−2,2,−1 and0respectively,while a confusion in this calculation would occur atα1andα2if there was no oﬀset every otherrow.We also notice that any bias possibly induced bythe above algorithms should disappear when the number of pixels is large,as in our case.We compute the v0(ν),v1(ν),and v2(ν)for both the entire map and the central37%(2209pixels,coveringIMA-1map(a)and the central part(b).The Gaussian ex-pectation obtained from the MC simulation(dashed),its95% CRG(shaded),and the analytic Gaussian forms(dotted). about6.3◦×6.3◦),expected to have the lowest noise.We use pixel sizes of8′,16′,and24′,the last two obtained by averaging the neighboring pixels of the original map. The results of all six cases lie within the95%CRG ob-tained from the MC simulation described earlier.Fig.4 shows the results of the two cases with8′pixels.We note that while the means of the MC simulation(dashed lines)are close to the analytical isotropic Gaussian forms (dotted lines)in(b1–b3),they deviate signiﬁcantly from each other in(a1–a3).This is due to the higher noise level near the edge of the map,contributing as an anisotropic component in the map(the RMS noise of the full map and the central part are about162µK and57µK respec-tively).We also note that some results(solid lines)appear to have systematic departure from the Gaussian expecta-tions¯v MCi(ν)(dashed lines).For example,(b3)shows the number of cold spots is less than the Gaussian ex-pectation.To determine whether these discrepancies are really systematic,weﬁrst deﬁneI i(ν)= ν−∞v i(ν′)−¯v MC i(ν′)−4−3−2−101234(−3.1,3.4)σand(−3.7,4.3)σrespectively.earlier,and the other is a new signal-whitening tech-nique d W=S1/2C−1d[26],which not only removes the anisotropy on scales where the noise dominates(as in Wienerﬁltering)but also equalizes the anisotropy am-plitudes on scales where the CMB signal dominates.The signal-whitening procedure will reveal in d W the features of the non-Gaussian components whose contribution in the CMB anisotropy dominates the Gaussian one within at least a range of the accessible scales[26].We apply theseﬁltering methods to both the real map(Fig.5)and the MC simulation,and then compute their Minkowski functionals.Weﬁnd that for both the entire map and the central part(as previously)the v i(ν)and I i(ν)of the ﬁltered maps are within the95%CRG.Fig.6shows re-sults of theﬁltered central maps.We also verify for both of theﬁltered maps that none of the pixels with ampli-tude outside the±2σrange coincides with the locations of any known radio or IRAS point sources[27].Thus we have no statistically signiﬁcant detection of localized non-Gaussianity in our data.E.Conclusion:We employ moments,cumulants,the Kolmogorov test,theχ2test,and Minkowski functionals in eigen,real,Wiener-ﬁltered and signal-whitened spaces to implement a total of82(not independent)hypothe-sis tests for Gaussianity(22in Sec.B,36in Sec.C,24 in Sec.D),and show that the MAXIMA-1CMB map is consistent with Gaussianity on angular scales between10′and5◦.This gives us conﬁdence in the Gaussian distri-bution used in our estimation of the CMB angular power spectrum[2],and consequently in the estimation of cos-mological parameters[11,13].Although our results are consistent with standard inﬂation and the CMB power spectrum of recent observations has favored inﬂation as the dominant mechanism for structure formation[5],the existence of topological defects is still possible.More so-phisticated methods or data with even higher resolution and signal to noise ratio will be required to fully explore and the signal-whitened(b)MAXIMA-1central map.this possibility.Acknowledgments—JHPW and AHJ acknowledge support from NASA LTSA Grant no.NAG5-6552and NSF KDI Grant no.9872979.PGF acknowledges sup-port from the Royal Society.RS and SH acknowledge support from NASA Grant NAG5-3941.BR and CDW acknowledge support from NASA GSRP Grants no.S00-GSRP-032and S00-GSRP-031.MAXIMA is supported by NASA Grant NAG5-4454and by the NSF through the Center for Particle Astrophysics at UC Berkeley,NSF co-operative agreement AST-9120005.[13]A.H.Jaﬀe et al,Phys.Rev.Lett.86,3475(2001)[14]G.F.Smoot et al.,Astrophys.J.396,L1(1992)[15]H.Minkowski,Mathematische Annalen57,447(1903);J.Schmalzing&K.M.G´o rski,Mon.Not.R.As-tron.Soc.297,355(1998)[16]G.F.Smoot et al.,Astrophys.J.437,1(1994);A.Kogutet al.,Astrophys.J.464,L29(1996)[17]X.Luo,Phys.Rev.D49,3810(1994);G.Hinshaw etal.,Astrophys.J.446,L7(1995)[18]A.F.Heavens,Mon.Not.R.Astron.Soc.299,805(1998)[19]P.G.Ferreira,J.Magueijo&K.M.Gorski,Astrophys.J.503,L1(1998)[20]J.Pando, D.Valls-Gabaud&L.-Z.Fang,Phys.Rev.Lett.81,4568(1998)[21]A.J.Banday,S.Zaroubi&K.M.Gorski,Astrophys.J.533,575(2000); B.C.Bromley&M.Tegmark,Astro-phys.J.524,L79(1999)[22]C.-G.Park et al.,astro-ph/0102406(2001)[23]R.Stompor et al.,in preparation.[24]C.W.Therrien,‘Discrete Random Signals and Statis-tical Signal Processing’,(Englewood Cliﬀs:Prentice-Hall),1992;J.R.Bond,m.32, 63(1995);J.R.Bond,Phys.Rev.Lett.74,4369(1995);M.Tegmark,A.Taylor&A.Heavens,Astrophys.J.480, 22(1997);E.F.Bunn&M.White,Astrophys.J.480,6 (1997)[25]J.H.P.Wu et al.,Astrophys.J.S.132,1(2001)[26]J.H.P.Wu,astro-ph/0012206(2000)[27]We thank R.Paladini for providing us with the data.。

高尔基英文简介

⾼尔基英⽂简介玛克西姆·⾼尔基，前苏联作家、诗⼈，评论家，政论家，学者。

下⾯是店铺为你整理的⾼尔基英⽂简介，希望对你有⽤! 玛克西姆·⾼尔基简介 Maxime Golgi, formerly known as Alexei Maximevich Bishkek. Former Soviet writers, poets, critics, political commentators, scholars. Gol is based on the March 16, 1868 was born in the Volga River under the town of Nautilogro a carpenter family. At the age of 4, his father died, and he spent his childhood with his mother in his grandfather's house. At the age of 10, Golgi began to make a living independently. He has been an apprentice, porters, gatekeepers, bread workers, etc., to experience the suffering of the lower people. During this period, he studied hard and began to explore the truth of transforming society. In 1884, he participated in the populist party group, read the works of populist writers and Marx's works, and actively engaged in revolutionary activities. In 1905, Gorky joined the Russian Social Democratic Labor Party. In 1906, Golgi was commissioned by Lenin, from Finland to the United States for revolutionary activities, published in the United States novel "mother". After settling in Capri Island, Italy. In 1913, Golgi returned from Italy, engaged in proletarian cultural organization work, presided over the "Pravda" literary column. After the October Revolution of 1917, there was a contradiction between Gorky and Lenin and the new regime, accompanied by the chaos, destruction, anarchism and various violent incidents of the revolution. In October 1921, due to the disease, also due to differences with the Bolshevik regime, Gorky went abroad to recuperate. In 1928, Gorky returned to the Soviet Union, under the arrangement of Stalin, he made two long-distance travel in Russia after the decision to return home to settle down. In 1934 was elected chairman of the Association. After returning to the Golgi as a flag of the Soviet cultural sector, for the Soviet culture to do a lot of work. But the Soviet Union in the 1930s all the problems that made him and Stalin and the reality of politics has always maintained a certain distance. June 18, 1936, Golgi disease died. 玛克西姆·⾼尔基⼈物经历 Early experience March 28, 1868, Alexei Maximilian Bishopov (Maxime Golgi) was born in the next Nuo Ke Ge Luo De (formerly known as Golgi City) a woodworking family. In 1871, when Golgi was 4 years old his father died, with his mother to live in grandparents home. In 1879, Gorky 11 years old to "human" independent living, had been apprenticeship, porters, bread workers and so on. In the 1880s, Gorky participated in the intellectual learning team of intellectuals in the Kazan Mountains. In 1883, Gorky began to wander life. 1884 living in Kazan, the late nineteen eighties and early 90s roaming all over Russia, a wide range of understanding of the people; In 1889, after being arrested for participation in secret revolutionary organizations, the release was still monitored by the Constitutional Police. Writing the way In 1892, published in the "Caucasus" with Golgi Maxim (meaning the greatest pain) the pseudonym published debut novel "Margar Qudela", in the local press when editing, journalists, from the focus on writing. In 1895, Golgi published a romantic short story "Yi Jigir old woman" and "song of the song", praised the love of freedom, longing for the bright and heroic performance of the strong personality, the desire to fight the passion. In 1898, Golgi's first collection of two sets of "essays and short stories" come out, from the famous Russian and European literary world attracted wide attention at home and abroad. In 1899, Gorky completed the first novel "Foma Golgyev". At the turn of the 19th and 20th centuries, the two novels of "Foma Golgyev" and "Three", through the broader reality picture, focused on revealing the theme of the exploration of young hero life. At the beginning of the twentieth century, Gorky's creation turned to drama, reflecting the social contradictions in the most rapid, direct and concise manner. From 1900 onwards, Gorky participated in and served the work of knowledge publishers, through the publication of "knowledge" series united at that time Russia has a large number of democratic tendencies of the writer. In 1901, on the eve of the first major revolution in Russia, when the revolutionary movement of the masses was soaring, the tsar reactionary government intensified the repression of the people, and it was time for the revolution and the counter-revolution to wrestle. Golgi to participate in the demonstration of Petersburg, personally felt the workers movement, student movement majestic momentum, witnessed the tsarist government crackdown on student movement brutal crimes. He wrote the prose poem "Swallow Sword" (renamed "Swallow") in order to warmly praise the pioneer of the proletarian revolution, expose the tsarist reactionary government, criticize the opportunists and the bourgeois liberals. The revolutionary storm is coming soon, inspiring people to meet the great battle, this is a proletarian revolutionary battle of the text and carol, by Lenin's enthusiasm praise. In 1901, Gorky also wrote the first script "Little Citizen", exposing the contradictions between bourgeois conservatives and liberals, shaping the image of the first revolutionary proletarian (revolutionary worker Neil) in the history of world literature. In 1901, the Goyle was arrested for demonstrations in Petersburg. After being released from prison by the revolutionary party commissioned the establishment of secret printing, for the second time arrested, was exiled. 1902, wrote the script "at the bottom", which is the author through 20 years to observe the tramp life summary, is Gorky drama masterpiece. In 1905, it was the beginning of the second stage of Golgi's thought and creative development (before and after the 1900-1909 revolution). During the fierce revolutionary situation, Gorky joined the revolutionary movement as a soldier, and his house became the armed uprising in 1905 One of the positions. As Golgi actively participated in the revolutionary movement, and Lenin met and joined the Bolshevik Party, the world view of a qualitative leap in the creation and more consciously for the proletarian revolutionary cause, and strive to create new heroes, write higher than life, Better, more beautiful things come. In 1905, during the Russian revolution, Gorky actively engaged in the proletarian revolutionary struggle, joined the Russian Social Democratic Labor Party, and met with Lenin. In the early days of the outbreak of the revolution, he wrote as an eyewitness as a witness to the tsarist government, and called on the people to fight, and actively participated in the publication of the "New Life" and the "Battle Newspaper" of the Social Democratic Labor Party. The insurgents plan funds and weapons. During this period he also published a lot of political theory, which "talk about the small public habits," a profound analysis of small social habits of social roots, psychological characteristics and its harm to the cause of the revolution. In 1906, Golgi secretly left Russia to the United States, where he proclaimed the revolution, raised funds for the party, wrote the political commentary "My Visit", which exposes and criticizes the capitalist system, and features "in the United States", the script "enemies". The script "The Enemy" and the novel "Mother" in the same year marked the creation of a new peak. "Mother" in the history of world literature has epoch-making significance. These two works are the foundation of Russian proletarian literature. In the spring of 1907, he participated in the Fifth Congress of the Russian Democratic Labor Party in London. Since then, he and Lenin established a close connection and deep friendship. 1906 1908 published in the novel novel "confession", by Lenin's serious criticism. At that time, he published some papers and monographs "Russian literature history" and so on, also contains different degrees of "concept compound", "experience organization" and the creation of the wrong view. With the help of Lenin's criticism, he gradually raised his awareness from the advance group. 1901 ~ 1910, has written "small people" "bottom" "enemies" "summer", "the children of the sun" "barbarians" and many other important social and political script, some of which reflect the struggle on thedeath line The life of the poor people, and some expose the spiritual emptiness of the intellectuals and the bourgeois philistine. In the "Little Citizen" a play for the first time described the advanced workers Neil's glorious image. The script was staged, warmly welcomed by the revolutionary people, causing the tsarist government to fear. 1911 - 1913 years, complete the story set "Italian fairy tale". 1911 - 1917, completed the "Russian fairy tale". 1912-1917, completed "Ross Travels". In 1913, he created the first "childhood" of the autobiographical trilogy. In 1913, returned to the motherland, presided over the "Pravda" literary column, engaged in cultural organization and literary activities. In 1916, published autobiographical trilogy of the second "in the world". Recuperate In the summer of 1921, Golgi disease relapsed to seek medical treatment until 1928, basically living in Sorrento, Italy. While he recuperates, he has done a great deal of work to train young writers and unite different styles of writers through letters and meeting visitors to try to resist the "left" and sectarian errors of some groups such as Lap. He also works hard to create and write a memoir "Leo Tolstoy" and close-up "Lenin" to complete the "my university", depicting the writer from the bottom of life to the revolutionary road, the workers looking for the truth, the pursuit of a bright process. In 1922, published "my university". In 1925, Golgi in the disease to complete the novel "Ardamonov husband's career." This description depicts the evolution of a family of three generations from the broad historical context of the Russian serfdom reform to the October Revolution in the mid-19th century, showing the inevitable decline of the bourgeoisie from a psychological and moral point of view. In 1928, after the return of Gorky, twice to travel around the country to visit, witnessed the vigorous development of the socialist construction of the motherland, enthusiasm, wrote a long report of the literature "Soviet travel". elderly life In 1931, Golgi settled in Moscow. In his later years, the script "Yegor Brechoff and others" and "Tosci Gayev and others" demonstrated the decline of capitalism and the victory of socialism; the novel "Klim Samkin The life of the Russian society in the 40 years before the October Revolution, with an individualist intellectuals as the central figure reflects the growth of revolutionary forces; "on the socialist realism" and a series of papers, advocate the socialist realism The In 1934, Gorky presided over the first congress of the Soviet writers, and was elected the first president of the Soviet Writers Association. June 18, 1936 at 2:30, Gorky left the world at the age of 68 years old.。

Innovation-ownership-and-profitability

Innovation,ownership and pro ﬁtabilityJames H.Love a ,⁎,Stephen Roper b ,Jun Du aa Economics and Strategy Group,Aston Business School,Aston University,Birmingham,B47ET,UKbCentre for Small and Medium Sized Enterprises,Warwick Business School,University of Warwick,Coventry,CV47AL,UKa b s t r a c ta r t i c l e i n f o Article history:Received 5March 2007Received in revised form 4April 2008Accepted 15November 2008Available online 27November 2008JEL classi ﬁcation:O32F14L60Keywords:Innovation Ownership Pro ﬁtabilityQuantile regression IrelandNorthern IrelandThis paper considers the relationship between innovation,ownership and pro ﬁtability for a panel of manufacturing plants in Ireland and Northern Ireland.Previous literature suggests that innovators are persistently more pro ﬁtable than non-innovators,but little is known about how this link is moderated by external versus domestic ownership.We consider the link between innovation and pro ﬁts separately for indigenous innovators and non-innovators and externally-owned plants.We also consider the determinants of innovation over the distribution of plant-level pro ﬁtability,and ﬁnd that the determinants of pro ﬁtability –including innovation and external ownership –vary over the distribution from low to high pro ﬁtability plants.We ﬁnd support for the view that innovators and non-innovators have different pro ﬁtability determinants,and that the pro ﬁtability of externally-owned plants depends on very different factors to those of indigenously-owned enterprises.©2008Elsevier B.V.All rights reserved.1.IntroductionResearch on the link between (product)innovation and pro ﬁtability at the ﬁrm or establishment level suggests that innovators are persistently more pro ﬁtable than non-innovators (Geroski et al.,1993;Leiponen,2000;Ce ﬁs and Ciccarelli,2005).This may arise because innovators,due perhaps to their market position,are able to protect their new products from the competition which normally erodes such pro ﬁts,or because innovating ﬁrms are able to introduce multiple innovations over time,and are therefore able to maintain high pro ﬁts although the pro ﬁt effect of any individual innovation may be transitory.The empirical evidence here is mixed.Both Geroski et al.(1993)and Leiponen (2000),for instance,conclude that the pro ﬁtability effects of individual innovations are relatively transitory,and that innovators are persistently more pro ﬁtable than non-innovators because they have superior internal capabilities.By contrast,in an analysis of the US pharmaceutical industry,Roberts (1999)ﬁnds evidence of a ‘conveyor belt ’of new products,each of which provides only a temporary monopoly position,but which collectively result in persistently high pro ﬁts among innovating ﬁrms.In the case of economies such as Ireland,where a signi ﬁcant element of productive capacity is externally owned,making general inferences about the relationship between innovation and pro ﬁt-ability is complicated by two further issues.First,foreign-owned enterprises tend to be more productive (and by implication more pro ﬁtable)than their indigenous counterparts (Stone and Peck,1996;Grif ﬁth et al.,2004)largely because they are more technologically advanced (Oulton,2001).1So,there may be differences between the pro ﬁtability of indigenous and foreign plants regardless of their product innovation performance.Secondly there is evidence of a link between foreign ownership and innovation,with the balance of evidence suggesting that externally-owned ﬁrms are generally more likely to be innovative than indigenously-owned ﬁrms in terms of both products (Harris and Trainor,1995;Love and Ashcroft,1999),and their adoption of new process technologies (Hewitt-Dundas et al.,2005).Thus,not only may innovators be different from non-innovators in terms of their organisational or internal capabilities aside from innovation,but externally-owned plants may be differentInternational Journal of Industrial Organization 27(2009)424–434⁎Corresponding author.E-mail addresses:j.h.love@ (J.H.Love),stephen.roper@ (S.Roper),j.du@ (J.Du).1Birnie and Hitchens (1998),for example,comparing Census of Production data from Ireland and the UK,suggest that in 1989:manufacturing productivity in externally-owned ﬁrms in Ireland was 69%above that of externally-owned ﬁrms in the UK,while indigenously-owned ﬁrms in Ireland lagged 8%behind indigenously-owned ﬁrms in the UK;the productivity differential between externally-owned and indigenously owned ﬁrms in Ireland was 178%compared to 52%in the UK.Similarly,Cassidy (2004)in his recent review of Irish productivity growth concludes that:‘Ireland ’s superior productivity performance in manufacturing has been largely a consequence of two factors,namely higher productivity growth in the high-technology sectors than the European average and also a greater degree of specialisation in these sectors'(p.93).0167-7187/$–see front matter ©2008Elsevier B.V.All rights reserved.doi:10.1016/j.ijindorg.2008.11.001Contents lists available at ScienceDirectInternational Journal of Industrial Organizationj o u r na l ho m e p a g e :w w w.e l s ev i e r.c o m /l o c a t e /i j i ofrom indigenously-owned plants partly as a result of innovation performance,complicating the innovation–proﬁtability relationship.In this paper we consider the relationship between innovation and proﬁtability for a large sample of manufacturing plants in Ireland and Northern Ireland.The economies of both Ireland and Northern Ireland are heavily weighted towards externally-owned enterprises with,for example,50.5%of employment and81.9%of value added being accounted for by externally-ownedﬁrms in manufacturing and tradable services in Ireland in2005(Forfas, 2006).2So,in order to allow for these differences,we consider not only the link between innovation and proﬁts but do so separately for innovators and non-innovators,and for indigenously-owned and externally-owned plants.3Because of the tendency for considerable enterprise-level heterogeneity in performance even within industries(Bartelsman and Doms,2000;Goddard et al., 2006),we also consider the determinants of innovation over the distribution of plant-level proﬁtability,andﬁnd that the determi-nants of proﬁtability–including the impact of innovation and external ownership–vary over the distribution from low to high proﬁtability plants.Our analysis also provides support for the view that innovators have different capabilities from non-innovators, even among indigenous plants,and that it is these capabilities, rather than innovation per se,that explains their superior proﬁt-ability.In addition,however,weﬁnd that externally-owned plants have a quite different set of proﬁtability determinants from indi-genously-owned plants,and that this is not related directly to innovation being conducted in the Irish plant.2.Linking ownership,innovation and proﬁtabilityThis section brieﬂy reviews the empirical evidence on the three sets of relationships that are relevant to the present research:the link between innovation and proﬁtability;the link between external ownership and performance;and,the link between external owner-ship and innovation.We develop a simple model linking these three inﬂuences which provides the basis for our empirical analysis.2.1.Innovation and proﬁtabilityA considerable empirical literature has considered the link between R&D inputs,innovation andﬁrm proﬁtability.The consensus is overwhelmingly of a positive relationship,but with some debate about the precise nature of the relationship.Using UKﬁrm-level data from1972–83,Geroski and Machin (1992)and Geroski et al.(1993)ﬁnd that there are positive effects of ﬁrm-level innovation on proﬁts,but these are relatively small and transitory.Indirect effects are larger and more long lasting:that is,it is the process of innovation that really matters for proﬁtability(i.e.the transformation of internal capabilities),rather than the returns from individual innovations.The fact that innovators persistently earn higher proﬁts than non-innovators is a result of three components:a small,transitory difference associated with the production of speciﬁc innovations;a substantial permanent difference(improved capabil-ities though the process of innovating);and a large cyclical component (non-innovators'proﬁt margins are more sensitive to trade cycle than those of innovators).Subsequent studies have built on this work,particularly on the idea that the process of innovation helps build the internal capabilities ofﬁrms.Another UK study,this time for the period 1988–92,alsoﬁnds that innovators are persistently more proﬁtable than non-innovators,and that the gap is greater between persistent innovators and non-innovators(Ceﬁs and Ciccarelli,2005).Ceﬁs and Ciccarelli(2005)alsoﬁnd that innovation has a positive effect on proﬁtability which decreases over time(i.e.there is a decay effect).Using data for Finnish manufacturingﬁrms,Leiponen(2000)is able to assess the proﬁtability effects of both process and product innovation,andﬁnds that while process innovation has a positive effect on proﬁtability product innovation has a negative effect. Leiponen alsoﬁnds that the proﬁtability of innovators and non-innovators are determined by different factors,with competencies built on knowledge-based factors being much more important for innovators.Canadian data appear to conﬁrm the positive relationship between R&D/innovation and proﬁing data on278quoted Canadian companies,Hanel and St-Pierre(2002)ﬁnd thatﬁrm-level R&D capital has a positive(but lagged)effect on proﬁtability,and that this effect is especially strong in sectors in which theﬁrm is able to appropriate the results of its own R&D activity i.e.where there is effective patent protection.This latterﬁnding raises the issue of whether the persistently higher proﬁts of innovators relative to non-innovators arises becauseﬁrms introduce new products which are somehow protected from the competition which normally erodes such proﬁts (an anti-competitive effect)or becauseﬁrms successfully introduce multiple innovations over time,and so are able to maintain high proﬁts although the proﬁt effect of any individual innovation is transitory(an innovation effect).Roberts(1999)speciﬁcally examines these competing explana-tions for US pharmaceuticalﬁrms from1977to1993,andﬁnds strong support for the latter effect:US pharmaceuticalﬁrms are adept at bringing forward a conveyor belt of new products each of which provides only a temporary monopoly position,but which collectively provide persistently high proﬁts at theﬁrm level.There is little support for the anti-competitive hypothesis in this sector: however,there may be some doubt about the generalisability of Roberts'ﬁndings.The pharmaceuticals industry is one largely predicated on the continuous search for new products,which is not a feature of other industries.For example,using a large database of innovations over the period1945–82,Geroski et al.(1997)look for evidence of‘dynamic economies of scale’i.e.the possibility that increases in the volume of innovations produced by aﬁrm in one time period increases the likelihood that it will continue to innovate subsequently.Theyﬁnd very little evidence that innovative activity is self-sustaining:it is very rare forﬁrms to innovate persistently, and even the ones that do so do not innovate over long periods.2.2.External ownership and performanceThere is strong theoretical and empirical evidence of a positive link between external ownership and business performance.The tradi-tional starting point for considering the determinants of foreign direct investment(FDI)from the perspective of theﬁrm involves the assumed possession of some competitive or‘ownership’advantage, often knowledge-based.The public good nature of theseﬁrm-speciﬁc assets may make international exploitation of the advantage by contractual means hazardous,thus giving an incentive to engage in FDI(Buckley and Casson,1976;Dunning,1988;Horstmann and Markusen,1996).The consensus of the empirical literature supports the view that externally-owned plants are more productive than their indigenous2The extent of externally-owned productive capacity in Northern Ireland is less clear with publishedﬁgures identifying724foreign-ownedﬁrms operating in Northern Ireland in2005(DETI,2005).Around a third of these plants are owned by ﬁrms with headquarters in Ireland and a further quarter by USﬁrms.Noﬁgures are published,however,for the number of plants in Northern Ireland owned by UKﬁrms with headquarters in other regions(see Hewitt-Dundas et al.,2005for a more detailed discussion).3For Ireland,a nation state,the terms‘externally-owned’and‘foreign-owned’are of course synonymous.For Northern Ireland,‘externally-owned’plants include all those which are‘foreign-owned’but also those which are headquartered in other UK regions. Throughout the paper our discussion relates to this wider group of externally-owned plants.425J.H.Love et al./an.27(2009)424–434counterparts,even within advanced industrialised economies (Caves,1996;Oulton,2001;Grifﬁth et al.,2004).There are a few caveats,however.Globerman et al.(1994),for example,ﬁnd that multinationals in Canada are not signiﬁcantly more productive than Canadian domestically ownedﬁrms after controlling for capital intensity and size,hence they suggest that the superior perfor-mance of externally-owned plants is due to their high capital intensity and large size.Drifﬁeld and Girma(2003)ﬁnd that although externally-ownedﬁrms in the UK are more productive, they pay higher wages to an extent that outweighs the productivity advantages.A substantial body of academic research has recognized and documented the contribution of multinationalﬁrms to the Irish economy(e.g.Barry and Bradley,1997;Love and Roper,2001;Görg and Strobl,2002,2003;Girma et al.,2004;Cassidy et al.,2005).For example,Cassidy et al.(2005)analyse productivity determinants using Irish plant-level survey data over1999–2002for plants with at least10employees.Theyﬁnd that both domestic and foreign-owned exporting plants tend to be more productive(in TFP terms)than their non-exporting counterparts,with the results being stronger for foreignﬁrms than domestic ones.And,Girma et al.(2004)compare the productivity of purely domestic plants,domestic exporters and domestic multinationals in Ireland,andﬁnd evidence that the distribution of performance of domestic multinationals dominates that of other groups ofﬁrms.42.3.External ownership and innovationConceptually,the literature on the link between external ownership and innovation suggests the effect could be positive or negative,depending on whether the beneﬁcial effects of access to group resources outweigh the potentially detrimental‘branch plant’effect.Externally-owned plants may have access to techno-logical resources such as access to large-scale R&D facilities ope-rated by the parent,or to proprietary knowledge developed by the parent(Brugger and Stuckey,1987).5Alternatively,access may be available to a wide range of non-scientiﬁc resources such asﬁnance, an international marketing organisation through which new products can be diffused,or through patenting or other support functions.On the other hand,the‘branch plant’literature suggests that externally-owned plants are less likely to have in-situ R&D facilities on which innovation crucially depends.For example,early work by Malecki(1980)and Howells(1984)suggests that the location of R&D is likely to be heavily inﬂuenced by corporate decisions,with basic scientiﬁc research,for example,typically assumed to be the most scale-intensive activity and therefore more likely to be centralised by the parent company than applied re-search and development work.The limited empirical evidence on this issue appears to suggest that,on balance,a positive effect of external ownership on innovation is likely.Harris and Trainor(1995)conclude that externally-owned plants in Northern Ireland are more likely to innovate,at least in part because they devote more resources to R&D.This conclusion is supported by Love et al.(1996)and Love and Ashcroft(1999),whoﬁnd evidence that foreign-owned manufac-turing plants in Scotland(but not other UK-owned plants)are more likely to innovate than their indigenous counterparts.In an analysis of innovation among UK,German and Irish manufacturing plants, Love and Roper(2001)ﬁnd that external ownership generally has a negative effect on innovation intensity(number of innovations per employee);in Germany and Ireland,however,external ownership is positively associated with innovation success(the proportion of sales attributable to new products).The implication is that although plants which are externally owned tend to make relatively fewer innovations than indigenously owned enterprises,these innovations are typically more successful commercially.The consensus from these three separate strands of literature appears to be as follows.First,innovation is positively linked to proﬁtability.Although the precise nature of the relationship is unclear, it appears to be linked to the superior capabilities of innovators. Secondly,externally-owned enterprises generally perform better than domestically-owned enterprises(although this is not always the case), and Ireland has beneﬁted considerably from the employment and spillover effects of this superior performance.Andﬁnally,externally-owned plants are more likely to innovate,but may not innovate more, than indigenous plants.A straightforward representation of these interactions is as follows:πit=β0+β1I it+β2O it+β3X it+μitð1aÞI⁎it=α0+α1O it+α2S it+e itð1bÞwhereπi is proﬁtability of plant i at time t,I it is innovation,O it is plant ownership,X it is a vector of other determinants of proﬁtabi-lity,S it a vector of other determinants of innovation,and we anticipateβ1,β2,α1N0.Although simple,this formulation has two desirable features.First,it allows for both effects of ownership identiﬁed in the empirical literature:the direct effect of(external) ownership on proﬁtability and its indirect effect through innova-tion.Secondly,it allows for the possibility of innovators having systematically better proﬁtability performance than non-innova-tors,perhaps as a result of superior capabilities.Eqs.(1a)and(1b) can therefore be thought of in terms of a treatment model in which I it,the endogeneous binary decision variable,is assumed to stem from the unobserved latent variable I it⁎.The decision to obtain the treatment(i.e.the decision to innovate)is made according toI it=1;if I⁎itN00;otherwise;whereεit is the error term of Eq.(1b),andµit andεit are assumed to follow a bivariate normal distribution with mean zero andcovariance matrixσρρ1.In the empirical analysis we use a model based on the formulation above to estimate the impact of ownership and innovation on proﬁtability for a large sample of Irish manufacturingﬁrms.3.Data and estimation procedureOur empirical analysis is based on data from the Irish Innovation Panel(IIP)which provides information on the innovation,technology adoption,ownership and performance of manufacturing plants throughout Ireland and Northern Ireland over the period1991–2002.The IIP comprises four linked surveys conducted using similar postal survey methodologies,sampling frames provided by the economic development agencies in Ireland and Northern Ireland, and questionnaires with common questions.Each survey covers the innovation activities and performance of manufacturing plants with 10or more employees over a three year period with an average survey4Note,however,that this may be more an issue of multi-nationality than of foreignownership.5The evidence suggests that Ireland beneﬁts disproportionately from this type ofinward knowledge or technology transfer.OECD providesﬁgures on the TechnologyBalance of Payments(TBOP)which reﬂects the balance of inward and outwardknowledge transfer through patents,licensing etc.Countries such as Finland andDenmark with historically higher levels of business and university R&D both havesmall positive TBOPs(c.0.1%of GDP)while Ireland has a TBOP deﬁcit( inwardtransfer)equivalent to10.5%of GDP.426J.H.Love et al./an.27(2009)424–434response rate of34.5%.6In our analysis here we use the second,third and fourth waves of the survey covering the period1994–2002,with descriptive statistics given in Table1a.As a result of the separate sampling process for the various waves the panel is unbalanced,with 2002observations from1494plants.7The empirical implementation of the treatment model follows the standard literature in terms of dependent and independent variables. The proﬁtability Eq.(1a)uses a simple market structure–ﬁrm performance model augmented by indicators of innovation and ownership and other characteristics which are known to be linked to proﬁtability such as plant vintage and capital intensity(Geroski et al.,1993;Leiponen,2000).Following the innovation production function literature(Crépon et al.,1998;Lööf and Heshmati,2002; Roper et al.,2008),the innovation Eq.(1b)allows for R&D and other sources of knowledge inputs as well as ownership and scale effects. The empirical model is thus of the form:logπit=θ0+θ1M jt+θ2I it+θ3O it+θ4C it+μitð2aÞI⁎it=/0+/1SIZE it+/2RD it+/3KS it+/4O it+e it;I it=1;if I ⁎itN00;otherwiseð2bÞThe set of market structure variables(M jt)comprises three elements.Theﬁrst is a Herﬁndahl index measured by the sum of squares of plants’market share in terms of sales in each two-digit industrial sector(j)in each wave of the IIP survey(HHI).The second market structure indicator is a measure of the average innovation intensity of the two-digit sector of which the plant is part(measured as the mean proportion of total sales derived from products newly introduced in the last three years).Andﬁnally,we employ a series of two-digit dummy variables to capture other sectoral variations such as appropriability conditions.Innovation(I it)in the IIP is represented by two variables.For theﬁrst (binary)variable an innovator was deﬁned as an establishment which had introduced any new or improved product or process during the previous three years.Over the whole sample,62.5%of plants were product innovators while59.2%were process innovators(Table1a). Notably,however,the overlap between the group of product and process innovators was not complete:around70.2%of product innovators were also process innovators,with75.3%of process innovators also being product innovators.The second innovation output measure is the proportion of plants'total sales(at the end of each three year period) derived from products newly introduced during the previous three years.This variable–‘innovation success’–reﬂects not only plants' ability to introduce new products to the market but also their short-term commercial success.On average,15.1%of plants'sales were derived from new products across the IIP(Table1a).Indicators of ownership(O it)are dummy variables representing externally-owned plants with headquarters in the UK,US and elsewhere respectively.Other plant characteristics(C it)include measures of employment size,age,capital intensity,export intensity,labour qualiﬁca-tions,and market share(proportion of sales per two-digit sector).The innovation Eq.(2b)includesﬁrm size(SIZE)and its square,R&D (RD it),external knowledge sourcing activitities(KS it),and ownership status(O it).Four different types of external knowledge sourcing activity which are found to shapeﬁrms'innovation behaviour are included:forward linkages to customers(Joshi and Sharma,2004);backward links to either suppliers or external consultants(e.g.Horn,2005;Smith and Tranﬁeld,2005);horizontal linkages to either competitors or through joint ventures(Hemphill,2003;Link et al.,2005);and linkages to universities or other public research centres(Roper et al.,2004).To test the likely causal effect of ownership on innovation suggested in the literature,we allow for theﬁrm's ownership status in the decision-making process of engaging in innovation.The measure of proﬁtability is also derived from the IIP and is deﬁned as sales less the cost of materials,labour and capital inputs.Average proﬁtability across theﬁnal three waves of the IIP was£1.83m,or20%of sales.Two notes of caution are worth highlighting,however,about our proﬁtability indicator.First,it is clear from Table1a and b and previous studies that the heterogeneity of proﬁt rates even within sectors can be substantial reﬂecting evidence of substantial variations inﬁrm perfor-mance within Irish industries(Anyadike-Danes and Heller,2006). Second,there is substantial evidence of issues relating to transfer pricing in externally-owned businesses in Ireland.This can substantially distort both the cost of inputs purchased by plants–particularly inputs or technology‘purchased’by Irish plants from their parent companies–and/or the value of sales made by externally-owned Irish plants to other group plants or the marketing and sales units of theirﬁrms.For example, if an Irish branch is not fully charged for the cost of such external activities,this will artiﬁcially raise its recorded value-added or pro-ductivity.To achieve this they can supply inputs to the Irish branch from other parts of theﬁrm at relatively low prices,or they can sell products from the Irish branch to other parts of theﬁrm at relatively high prices.In either case this would tend to artiﬁcially raise the recorded level of value-added or turnover per employee in the Irish branch,a pattern which may be encouraged by relatively low rates of corporation tax in Ireland.Table1b shows descriptive statistics separately for non-innovators versus innovators and indigenously-owned versus externally-owned plants respectively.There is a strong similarity in the patterns of charac-teristics:innovators/externally-owned plants are larger,more capital intensive,have more highly qualiﬁed staff,are more export intensive and have higher market shares than non-innovating/indigenous plants. Innovators are also nearly twice as likely to be externally-owned as non-innovators,and externally-owned plants are signiﬁcantly more likely than indigenously-owned plants to be innovators,illustrating the links between innovation and external ownership.However,there is no evi-dence of proﬁtability differences between the groups:indeed the mean proﬁtability is almost identical between the different groups,although with a large degree of heterogeneity in proﬁtability performance.Two main econometric issues arise in operationalising Eqs.(2a)and (2b):potential endogeneity of the innovation output measures,and heterogeneity in performance outcomes.The potential endogeneity of Table1aSummary statistics—whole sample.Variable N Mean SDProﬁt(£000)15361834.6515998.553 Proﬁt margin(%,proﬁt/turnover)15360.2090.192 Employment(number)1977113.187248.544 Vintage(years)192532.28830.437 Capital intensity(capital investment per employee)1661 5.29413.954 Percentage of staff with degree(%)18779.09912.025 Export intensity(exports as proportion of sales)19190.2660.346 Market share(in sales in each sector and wave)17700.0060.022 Externally-owned plants(%)20020.3300.470 Externally-owned plants with head quarter in the UK20020.0600.237 Externally-owned plants with head quarter in the US20020.0940.292 Externally-owned plants with head quarter inother countries20020.0880.284Herﬁndahl Index(HHI,sum of squares of plants'marketshare in each sector and wave)20020.0220.066 Average product innovation success(in total sales)20020.1550.062 Source:Irish Innovation Panel,Waves2,3and4.6Details of each wave of the survey can be found in Roper et al.(1996),Roper and Hewitt-Dundas(1998),Roper and Anderson(2000),Roper et al.(2004).7The unbalanced nature of the panel means we cannot be sure if non appearance of a plant in a particular wave is a result of non-response or closure.This means that issues such as e.g.survivor bias cannot be explicitly accounted for in the estimation. However,it also means that other potential issues such as persistent difference in performance through time are unlikely to bias the results.427J.H.Love et al./an.27(2009)424–434。

计量经济学导论CH13习题答案

CHAPTER 13TEACHING NOTESWhile this chapter falls under “Advanced Topics,” most of this chapter requires no more sophistication than the previous chapters. (In fact, I would argue that, with the possible exception of Section 13.5, this material is easier than some of the time series chapters.)Pooling two or more independent cross sections is a straightforward extension of cross-sectional methods. Nothing new needs to be done in stating assumptions, except possibly mentioning that random sampling in each time period is sufficient. The practically important issue is allowing for different intercepts, and possibly different slopes, across time.The natural experiment material and extensions of the difference-in-differences estimator is widely applicable and, with the aid of the examples, easy to understand.Two years of panel data are often available, in which case differencing across time is a simple way of removing g unobserved heterogeneity. If you have covered Chapter 9, you might compare this with a regression in levels using the second year of data, but where a lagged dependent variable is included. (The second approach only requires collecting information on the dependent variable in a previous year.) These often give similar answers. Two years of panel data, collected before and after a policy change, can be very powerful for policy analysis. Having more than two periods of panel data causes slight complications in that the errors in the differenced equation may be serially correlated. (However, the traditional assumption that the errors in the original equation are serially uncorrelated is not always a good one. In other words, it is not always more appropriate to used fixed effects, as in Chapter 14, than first differencing.) With large N and relatively small T, a simple way to account for possible serial correlation after differencing is to compute standard errors that are robust to arbitrary serial correlation and heteroskedasticity. Econometrics packages that do cluster analysis (such as Stata) often allow this by specifying each cross-sectional unit as its own cluster.108SOLUTIONS TO PROBLEMS13.1 Without changes in the averages of any explanatory variables, the average fertility rate fellby .545 between 1972 and 1984; this is simply the coefficient on y84. To account for theincrease in average education levels, we obtain an additional effect: –.128(13.3 – 12.2) ≈–.141. So the drop in average fertility if the average education level increased by 1.1 is .545+ .141 = .686, or roughly two-thirds of a child per woman.13.2 The first equation omits the 1981 year dummy variable, y81, and so does not allow anyappreciation in nominal housing prices over the three year period in the absence of an incinerator. The interaction term in this case is simply picking up the fact that even homes that are near the incinerator site have appreciated in value over the three years. This equation suffers from omitted variable bias.The second equation omits the dummy variable for being near the incinerator site, nearinc,which means it does not allow for systematic differences in homes near and far from the sitebefore the site was built. If, as seems to be the case, the incinerator was located closer to lessvaluable homes, then omitting nearinc attributes lower housing prices too much to theincinerator effect. Again, we have an omitted variable problem. This is why equation (13.9) (or,even better, the equation that adds a full set of controls), is preferred.13.3 We do not have repeated observations on the same cross-sectional units in each time period,and so it makes no sense to look for pairs to difference. For example, in Example 13.1, it is veryunlikely that the same woman appears in more than one year, as new random samples areobtained in each year. In Example 13.3, some houses may appear in the sample for both 1978and 1981, but the overlap is usually too small to do a true panel data analysis.β, but only13.4 The sign of β1 does not affect the direction of bias in the OLS estimator of1whether we underestimate or overestimate the effect of interest. If we write ∆crmrte i = δ0 +β1∆unem i + ∆u i, where ∆u i and ∆unem i are negatively correlated, then there is a downward biasin the OLS estimator of β1. Because β1 > 0, we will tend to underestimate the effect of unemployment on crime.13.5 No, we cannot include age as an explanatory variable in the original model. Each person inthe panel data set is exactly two years older on January 31, 1992 than on January 31, 1990. This means that ∆age i = 2 for all i. But the equation we would estimate is of the form∆saving i = δ0 + β1∆age i +…,where δ0 is the coefficient the year dummy for 1992 in the original model. As we know, whenwe have an intercept in the model we cannot include an explanatory variable that is constant across i; this violates Assumption MLR.3. Intuitively, since age changes by the same amount for everyone, we cannot distinguish the effect of age from the aggregate time effect.10913.6 (i) Let FL be a binary variable equal to one if a person lives in Florida, and zero otherwise. Let y90 be a year dummy variable for 1990. Then, from equation (13.10), we have the linear probability modelarrest = β0 + δ0y90 + β1FL + δ1y90⋅FL + u.The effect of the law is measured by δ1, which is the change in the probability of drunk driving arrest due to the new law in Florida. Including y90 allows for aggregate trends in drunk driving arrests that would affect both states; including FL allows for systematic differences between Florida and Georgia in either drunk driving behavior or law enforcement.(ii) It could be that the populations of drivers in the two states change in different ways over time. For example, age, race, or gender distributions may have changed. The levels of education across the two states may have changed. As these factors might affect whether someone is arrested for drunk driving, it could be important to control for them. At a minimum, there is the possibility of obtaining a more precise estimator of δ1 by reducing the error variance. Essentially, any explanatory variable that affects arrest can be used for this purpose. (See Section 6.3 for discussion.)SOLUTIONS TO COMPUTER EXERCISES13.7 (i) The F statistic (with 4 and 1,111 df) is about 1.16 and p-value ≈ .328, which shows that the living environment variables are jointly insignificant.(ii) The F statistic (with 3 and 1,111 df) is about 3.01 and p-value ≈ .029, and so the region dummy variables are jointly significant at the 5% level.(iii) After obtaining the OLS residuals, ˆu, from estimating the model in Table 13.1, we run the regression 2ˆu on y74, y76, …, y84 using all 1,129 observations. The null hypothesis of homoskedasticity is H0: γ1 = 0, γ2= 0, … , γ6 = 0. So we just use the usual F statistic for joint significance of the year dummies. The R-squared is about .0153 and F ≈ 2.90; with 6 and 1,122 df, the p-value is about .0082. So there is evidence of heteroskedasticity that is a function of time at the 1% significance level. This suggests that, at a minimum, we should compute heteroskedasticity-robust standard errors, t statistics, and F statistics. We could also use weighted least squares (although the form of heteroskedasticity used here may not be sufficient; it does not depend on educ, age, and so on).(iv) Adding y74⋅educ, , y84⋅educ allows the relationship between fertility and education to be different in each year; remember, the coefficient on the interaction gets added to the coefficient on educ to get the slope for the appropriate year. When these interaction terms are added to the equation, R2≈ .137. The F statistic for joint significance (with 6 and 1,105 df) is about 1.48 with p-value ≈ .18. Thus, the interactions are not jointly significant at even the 10% level. This is a bit misleading, however. An abbreviated equation (which just shows the coefficients on the terms involving educ) is110111kids= -8.48 - .023 educ + - .056 y74⋅educ - .092 y76⋅educ(3.13) (.054) (.073) (.071) - .152 y78⋅educ - .098 y80⋅educ - .139 y82⋅educ - .176 y84⋅educ .(.075) (.070) (.068) (.070)Three of the interaction terms, y78⋅educ , y82⋅educ , and y84⋅educ are statistically significant at the 5% level against a two-sided alternative, with the p -value on the latter being about .012. The coefficients are large in magnitude as well. The coefficient on educ – which is for the base year, 1972 – is small and insignificant, suggesting little if any relationship between fertility andeducation in the early seventies. The estimates above are consistent with fertility becoming more linked to education as the years pass. The F statistic is insignificant because we are testing some insignificant coefficients along with some significant ones.13.8 (i) The coefficient on y85 is roughly the proportionate change in wage for a male (female = 0) with zero years of education (educ = 0). This is not especially useful since we are not interested in people with no education.(ii) What we want to estimate is θ0 = δ0 + 12δ1; this is the change in the intercept for a male with 12 years of education, where we also hold other factors fixed. If we write δ0 = θ0 - 12δ1, plug this into (13.1), and rearrange, we getlog(wage ) = β0 + θ0y85 + β1educ + δ1y85⋅(educ – 12) + β2exper + β3exper 2 + β4union + β5female + δ5y85⋅female + u .Therefore, we simply replace y85⋅educ with y85⋅(educ – 12), and then the coefficient andstandard error we want is on y85. These turn out to be 0ˆθ = .339 and se(0ˆθ) = .034. Roughly, the nominal increase in wage is 33.9%, and the 95% confidence interval is 33.9 ± 1.96(3.4), or about 27.2% to 40.6%. (Because the proportionate change is large, we could use equation (7.10), which implies the point estimate 40.4%; but obtaining the standard error of this estimate is harder.)(iii) Only the coefficient on y85 differs from equation (13.2). The new coefficient is about –.383 (se ≈ .124). This shows that real wages have fallen over the seven year period, although less so for the more educated. For example, the proportionate change for a male with 12 years of education is –.383 + .0185(12) = -.161, or a fall of about 16.1%. For a male with 20 years of education there has been almost no change [–.383 + .0185(20) = –.013].(iv) The R -squared when log(rwage ) is the dependent variable is .356, as compared with .426 when log(wage ) is the dependent variable. If the SSRs from the regressions are the same, but the R -squareds are not, then the total sum of squares must be different. This is the case, as the dependent variables in the two equations are different.(v) In 1978, about 30.6% of workers in the sample belonged to a union. In 1985, only about 18% belonged to a union. Therefore, over the seven-year period, there was a notable fall in union membership.(vi) When y85⋅union is added to the equation, its coefficient and standard error are about -.00040 (se ≈ .06104). This is practically very small and the t statistic is almost zero. There has been no change in the union wage premium over time.(vii) Parts (v) and (vi) are not at odds. They imply that while the economic return to union membership has not changed (assuming we think we have estimated a causal effect), the fraction of people reaping those benefits has fallen.13.9 (i) Other things equal, homes farther from the incinerator should be worth more, so δ1 > 0. If β1 > 0, then the incinerator was located farther away from more expensive homes.(ii) The estimated equation islog()price= 8.06 -.011 y81+ .317 log(dist) + .048 y81⋅log(dist)(0.51) (.805) (.052) (.082)n = 321, R2 = .396, 2R = .390.ˆδ = .048 is the expected sign, it is not statistically significant (t statistic ≈ .59).While1(iii) When we add the list of housing characteristics to the regression, the coefficient ony81⋅log(dist) becomes .062 (se = .050). So the estimated effect is larger – the elasticity of price with respect to dist is .062 after the incinerator site was chosen – but its t statistic is only 1.24. The p-value for the one-sided alternative H1: δ1 > 0 is about .108, which is close to being significant at the 10% level.13.10 (i) In addition to male and married, we add the variables head, neck, upextr, trunk, lowback, lowextr, and occdis for injury type, and manuf and construc for industry. The coefficient on afchnge⋅highearn becomes .231 (se ≈ .070), and so the estimated effect and t statistic are now larger than when we omitted the control variables. The estimate .231 implies a substantial response of durat to the change in the cap for high-earnings workers.(ii) The R-squared is about .041, which means we are explaining only a 4.1% of the variation in log(durat). This means that there are some very important factors that affect log(durat) that we are not controlling for. While this means that predicting log(durat) would be very difficultˆδ: it could still for a particular individual, it does not mean that there is anything biased about1be an unbiased estimator of the causal effect of changing the earnings cap for workers’ compensation.(iii) The estimated equation using the Michigan data is112durat= 1.413 + .097 afchnge+ .169 highearn+ .192 afchnge⋅highearn log()(0.057) (.085) (.106) (.154)n = 1,524, R2 = .012.The estimate of δ1, .192, is remarkably close to the estimate obtained for Kentucky (.191). However, the standard error for the Michigan estimate is much higher (.154 compared with .069). The estimate for Michigan is not statistically significant at even the 10% level against δ1 > 0. Even though we have over 1,500 observations, we cannot get a very precise estimate. (For Kentucky, we have over 5,600 observations.)13.11 (i) Using pooled OLS we obtainrent= -.569 + .262 d90+ .041 log(pop) + .571 log(avginc) + .0050 pctstu log()(.535) (.035) (.023) (.053) (.0010) n = 128, R2 = .861.The positive and very significant coefficient on d90 simply means that, other things in the equation fixed, nominal rents grew by over 26% over the 10 year period. The coefficient on pctstu means that a one percentage point increase in pctstu increases rent by half a percent (.5%). The t statistic of five shows that, at least based on the usual analysis, pctstu is very statistically significant.(ii) The standard errors from part (i) are not valid, unless we thing a i does not really appear in the equation. If a i is in the error term, the errors across the two time periods for each city are positively correlated, and this invalidates the usual OLS standard errors and t statistics.(iii) The equation estimated in differences islog()∆= .386 + .072 ∆log(pop) + .310 log(avginc) + .0112 ∆pctsturent(.037) (.088) (.066) (.0041)n = 64, R2 = .322.Interestingly, the effect of pctstu is over twice as large as we estimated in the pooled OLS equation. Now, a one percentage point increase in pctstu is estimated to increase rental rates by about 1.1%. Not surprisingly, we obtain a much less precise estimate when we difference (although the OLS standard errors from part (i) are likely to be much too small because of the positive serial correlation in the errors within each city). While we have differenced away a i, there may be other unobservables that change over time and are correlated with ∆pctstu.(iv) The heteroskedasticity-robust standard error on ∆pctstu is about .0028, which is actually much smaller than the usual OLS standard error. This only makes pctstu even more significant (robust t statistic ≈ 4). Note that serial correlation is no longer an issue because we have no time component in the first-differenced equation.11311413.12 (i) You may use an econometrics software package that directly tests restrictions such as H 0: β1 = β2 after estimating the unrestricted model in (13.22). But, as we have seen many times, we can simply rewrite the equation to test this using any regression software. Write the differenced equation as∆log(crime ) = δ0 + β1∆clrprc -1 + β2∆clrprc -2 + ∆u .Following the hint, we define θ1 = β1 - β2, and then write β1 = θ1 + β2. Plugging this into the differenced equation and rearranging gives∆log(crime ) = δ0 + θ1∆clrprc -1 + β2(∆clrprc -1 + ∆clrprc -2) + ∆u .Estimating this equation by OLS gives 1ˆθ= .0091, se(1ˆθ) = .0085. The t statistic for H 0: β1 = β2 is .0091/.0085 ≈ 1.07, which is not statistically significant.(ii) With β1 = β2 the equation becomes (without the i subscript)∆log(crime ) = δ0 + β1(∆clrprc -1 + ∆clrprc -2) + ∆u= δ0 + δ1[(∆clrprc -1 + ∆clrprc -2)/2] + ∆u ,where δ1 = 2β1. But (∆clrprc -1 + ∆clrprc -2)/2 = ∆avgclr .(iii) The estimated equation islog()crime ∆ = .099 - .0167 ∆avgclr(.063) (.0051)n = 53, R 2 = .175, 2R = .159.Since we did not reject the hypothesis in part (i), we would be justified in using the simplermodel with avgclr . Based on adjusted R -squared, we have a slightly worse fit with the restriction imposed. But this is a minor consideration. Ideally, we could get more data to determine whether the fairly different unconstrained estimates of β1 and β2 in equation (13.22) reveal true differences in β1 and β2.13.13 (i) Pooling across semesters and using OLS givestrmgpa = -1.75 -.058 spring+ .00170 sat- .0087 hsperc(0.35) (.048) (.00015) (.0010)+ .350 female- .254 black- .023 white- .035 frstsem(.052) (.123) (.117) (.076)- .00034 tothrs + 1.048 crsgpa- .027 season(.00073) (0.104) (.049)n = 732, R2 = .478, 2R = .470.The coefficient on season implies that, other things fixed, an athlete’s term GPA is about .027 points lower when his/her sport is in season. On a four point scale, this a modest effect (although it accumulates over four years of athletic eligibility). However, the estimate is not statistically significant (t statistic ≈-.55).(ii) The quick answer is that if omitted ability is correlated with season then, as we know form Chapters 3 and 5, OLS is biased and inconsistent. The fact that we are pooling across two semesters does not change that basic point.If we think harder, the direction of the bias is not clear, and this is where pooling across semesters plays a role. First, suppose we used only the fall term, when football is in season. Then the error term and season would be negatively correlated, which produces a downward bias in the OLS estimator of βseason. Because βseason is hypothesized to be negative, an OLS regression using only the fall data produces a downward biased estimator. [When just the fall data are used, ˆβ = -.116 (se = .084), which is in the direction of more bias.] However, if we use just the seasonspring semester, the bias is in the opposite direction because ability and season would be positive correlated (more academically able athletes are in season in the spring). In fact, using just theβ = .00089 (se = .06480), which is practically and statistically equal spring semester gives ˆseasonto zero. When we pool the two semesters we cannot, with a much more detailed analysis, determine which bias will dominate.(iii) The variables sat, hsperc, female, black, and white all drop out because they do not vary by semester. The intercept in the first-differenced equation is the intercept for the spring. We have∆= -.237 + .019 ∆frstsem+ .012 ∆tothrs+ 1.136 ∆crsgpa- .065 seasontrmgpa(.206) (.069) (.014) (0.119) (.043) n = 366, R2 = .208, 2R = .199.Interestingly, the in-season effect is larger now: term GPA is estimated to be about .065 points lower in a semester that the sport is in-season. The t statistic is about –1.51, which gives a one-sided p-value of about .065.115(iv) One possibility is a measure of course load. If some fraction of student-athletes take a lighter load during the season (for those sports that have a true season), then term GPAs may tend to be higher, other things equal. This would bias the results away from finding an effect of season on term GPA.13.14 (i) The estimated equation using differences is∆= -2.56 - 1.29 ∆log(inexp) - .599 ∆log(chexp) + .156 ∆incshrvote(0.63) (1.38) (.711) (.064)n = 157, R2 = .244, 2R = .229.Only ∆incshr is statistically significant at the 5% level (t statistic ≈ 2.44, p-value ≈ .016). The other two independent variables have t statistics less than one in absolute value.(ii) The F statistic (with 2 and 153 df) is about 1.51 with p-value ≈ .224. Therefore,∆log(inexp) and ∆log(chexp) are jointly insignificant at even the 20% level.(iii) The simple regression equation is∆= -2.68 + .218 ∆incshrvote(0.63) (.032)n = 157, R2 = .229, 2R = .224.This equation implies t hat a 10 percentage point increase in the incumbent’s share of total spending increases the percent of the incumbent’s vote by about 2.2 percentage points.(iv) Using the 33 elections with repeat challengers we obtain∆= -2.25 + .092 ∆incshrvote(1.00) (.085)n = 33, R2 = .037, 2R = .006.The estimated effect is notably smaller and, not surprisingly, the standard error is much larger than in part (iii). While the direction of the effect is the same, it is not statistically significant (p-value ≈ .14 against a one-sided alternative).13.15 (i) When we add the changes of the nine log wage variables to equation (13.33) we obtain116117 log()crmrte ∆ = .020 - .111 d83 - .037 d84 - .0006 d85 + .031 d86 + .039 d87(.021) (.027) (.025) (.0241) (.025) (.025)- .323 ∆log(prbarr ) - .240 ∆log(prbconv ) - .169 ∆log(prbpris )(.030) (.018) (.026)- .016 ∆log(avgsen ) + .398 ∆log(polpc ) - .044 ∆log(wcon )(.022) (.027) (.030)+ .025 ∆log(wtuc ) - .029 ∆log(wtrd ) + .0091 ∆log(wfir )(0.14) (.031) (.0212)+ .022 ∆log(wser ) - .140 ∆log(wmfg ) - .017 ∆log(wfed )(.014) (.102) (.172)- .052 ∆log(wsta ) - .031 ∆log(wloc ) (.096) (.102) n = 540, R 2 = .445, 2R = .424.The coefficients on the criminal justice variables change very modestly, and the statistical significance of each variable is also essentially unaffected.(ii) Since some signs are positive and others are negative, they cannot all really have the expected sign. For example, why is the coefficient on the wage for transportation, utilities, and communications (wtuc ) positive and marginally significant (t statistic ≈ 1.79)? Higher manufacturing wages lead to lower crime, as we might expect, but, while the estimated coefficient is by far the largest in magnitude, it is not statistically different from zero (tstatistic ≈ –1.37). The F test for joint significance of the wage variables, with 9 and 529 df , yields F ≈ 1.25 and p -value ≈ .26.13.16 (i) The estimated equation using the 1987 to 1988 and 1988 to 1989 changes, where we include a year dummy for 1989 in addition to an overall intercept, isˆhrsemp ∆ = –.740 + 5.42 d89 + 32.60 ∆grant + 2.00 ∆grant -1 + .744 ∆log(employ ) (1.942) (2.65) (2.97) (5.55) (4.868)n = 251, R 2 = .476, 2R = .467.There are 124 firms with both years of data and three firms with only one year of data used, for a total of 127 firms; 30 firms in the sample have missing information in both years and are not used at all. If we had information for all 157 firms, we would have 314 total observations in estimating the equation.(ii) The coefficient on grant – more precisely, on ∆grant in the differenced equation – means that if a firm received a grant for the current year, it trained each worker an average of 32.6 hoursmore than it would have otherwise. This is a practically large effect, and the t statistic is very large.(iii) Since a grant last year was used to pay for training last year, it is perhaps not surprising that the grant does not carry over into more training this year. It would if inertia played a role in training workers.(iv) The coefficient on the employees variable is very small: a 10% increase in employ increases hours per employee by only .074. [Recall:∆≈ (.744/100)(%∆employ).] Thishrsempis very small, and the t statistic is also rather small.13.17. (i) Take changes as usual, holding the other variables fixed: ∆math4it = β1∆log(rexpp it) = (β1/100)⋅[ 100⋅∆log(rexpp it)] ≈ (β1/100)⋅( %∆rexpp it). So, if %∆rexpp it = 10, then ∆math4it= (β1/100)⋅(10) = β1/10.(ii) The equation, estimated by pooled OLS in first differences (except for the year dummies), is4∆ = 5.95 + .52 y94 + 6.81 y95- 5.23 y96- 8.49 y97 + 8.97 y98math(.52) (.73) (.78) (.73) (.72) (.72)- 3.45 ∆log(rexpp) + .635 ∆log(enroll) + .025 ∆lunch(2.76) (1.029) (.055)n = 3,300, R2 = .208.Taken literally, the spending coefficient implies that a 10% increase in real spending per pupil decreases the math4 pass rate by about 3.45/10 ≈ .35 percentage points.(iii) When we add the lagged spending change, and drop another year, we get4∆ = 6.16 + 5.70 y95- 6.80 y96- 8.99 y97 +8.45 y98math(.55) (.77) (.79) (.74) (.74)- 1.41 ∆log(rexpp) + 11.04 ∆log(rexpp-1) + 2.14 ∆log(enroll)(3.04) (2.79) (1.18)+ .073 ∆lunch(.061)n = 2,750, R2 = .238.The contemporaneous spending variable, while still having a negative coefficient, is not at all statistically significant. The coefficient on the lagged spending variable is very statistically significant, and implies that a 10% increase in spending last year increases the math4 pass rate118119 by about 1.1 percentage points. Given the timing of the tests, a lagged effect is not surprising. In Michigan, the fourth grade math test is given in January, and so if preparation for the test begins a full year in advance, spending when the students are in third grade would at least partly matter.(iv) The heteroskedasticity-robust standard error for log() ˆrexpp β∆is about 4.28, which reducesthe significance of ∆log(rexpp ) even further. The heteroskedasticity-robust standard error of 1log() ˆrexpp β-∆is about 4.38, which substantially lowers the t statistic. Still, ∆log(rexpp -1) is statistically significant at just over the 1% significance level against a two-sided alternative.(v) The fully robust standard error for log() ˆrexpp β∆is about 4.94, which even further reducesthe t statistic for ∆log(rexpp ). The fully robust standard error for 1log() ˆrexpp β-∆is about 5.13,which gives ∆log(rexpp -1) a t statistic of about 2.15. The two-sided p -value is about .032.(vi) We can use four years of data for this test. Doing a pooled OLS regression of ,1垐 on it i t r r -,using years 1995, 1996, 1997, and 1998 gives ˆρ= -.423 (se = .019), which is strong negative serial correlation.(vii) Th e fully robust “F ” test for ∆log(enroll ) and ∆lunch , reported by Stata 7.0, is .93. With 2 and 549 df , this translates into p -value = .40. So we would be justified in dropping these variables, but they are not doing any harm.。

The Symptoms,Signs and Basic Diagnostic Techniques for Dermatoses

These are punctusted or linear abrasions produced by mechanical means such as scratching.
(7)Secondary lesions-fissures

These are linear clefts through the epidermis or into the dermis.
nikolsky‘s sign
method
shiatsu
On one side of the finger push blister， blister along the thrust direction.
shiatsu
Finger gently press blister wall ,blister fluid to move around
(8)Primary –cysts
Secondary lesions

These skin lesions represent evolutionary,or complication-related changes,producted by scratching,stimulants or infections over the course of the dermatoses.
1~minutes
Across the site in uplift group that pale wind line ， because of edema which is caused by histamine and bradykinin,etc.
nikolsky‘s sign

It is a skin condition in which the top layers of the skin slip free from the lower layers when slightly rubbed,A postive result may be present in patients with toxic epidermal necrolysis or with certain autoimmune bullous diseases.

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Tests for Gaussianity of the MAXIMA-1 CMB Map

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高尔基英文简介

Innovation-ownership-and-profitability

计量经济学导论CH13习题答案

The Symptoms,Signs and Basic Diagnostic Techniques for Dermatoses

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