cross section and ct of abdomen at l5 level

... Photosynthetic activity, chloroplast ultrastructure, and leaf characteristics of high- and low-light plants and of sun and shade leaves Photosynth Res 2, 115-141 light E.M (1986) Correlation of activity and ... aboveground) was similar to that at level 1; only the appressed/non-appressed membrane ratio was initially somewhat higher than at level Leaves at level maintained high rates uptake throughout the ... climatic conditions but had a lower rate of C0 uptake and an appressed/non-appressed membrane ratio of about In the present study, a tion was found between negative correla- N P and the ratio of...

Ngày tải lên: 09/08/2014, 03:24

... number followed by section number and, sometimes, subsection number Therefore, Section 6.3 refers to Section in Chapter 6, and Section 13.8.3 refers to Subsection of Section in Chapter 13 By always ... Expectations and Related Concepts in Econometrics The Role of Conditional Expectations in Econometrics Features of Conditional Expectations 2.2.1 Definition and Examples 2.2.2 Partial E¤ects, ... econometrics tend to be high -level treatments that focus on general approaches to estimation, thereby attempting to cover all data configurations— including cross section, panel data, and time series—in...

Ngày tải lên: 06/07/2014, 08:20

... summary of properties of conditional expectations 1.2 1.2.1 The Stochastic Setting and Asymptotic Analysis Data Structures In order to give proper treatment to modern cross section and panel data ... random sampling, it is important to know what it allows and what it rules out Random sampling is often reasonable for cross section data, where, at a given point in time, units are selected at ... we must choose a stochastic setting that is appropriate for the kinds of cross section and panel data sets collected for most econometric applications Naturally, all else equal, it is best if...

Ngày tải lên: 06/07/2014, 08:20

... scalars u and v and a random vector x, suppose that Eðu j x; vÞ is a linear function of ðx; vÞ and that u and v each have zero mean and are uncorrelated with the elements of x Show that Eðu j ... most general statement needed in this book Suppose that w is a random vector and y is a random variable Let x be a random vector that is some function of w, say x ¼ fðwÞ (The vector x could simply ... combination of the two (depending on the nature of y) It follows that the conditional expectation operator has the same linearity properties as the unconditional expectation operator, and several...

Ngày tải lên: 06/07/2014, 08:20

... Limiting Behavior of Estimators and Test Statistics In this section, we apply the previous concepts to sequences of estimators Because estimators depend on the random outcomes of data, they are properly ... square root of the appropriate diagonal ele^N ment of V =N The asymptotic standard errors can be loosely thought of as estimating ^ the standard deviations of the elements of yN , and they are ... repeated application of Lemma 3.2 (see Problem 3.2) lemma 3.3: Let fZN : N ¼ 1; 2; g be a sequence of J Â K matrices such that ZN ¼ op ð1Þ, and let fxN g be a sequence of J Â random vectors...

Ngày tải lên: 06/07/2014, 08:20

... consistency of OLS is that the expected outer product matrix of x has full rank, so that there are no exact linear relationships among the regressors in the population This is stated succinctly as ... bŠ2 , and use the facts that sample averages are Op ð1Þ when ^ 2xi ui ð b ^ expectations exist and that b À b ¼ op ð1Þ Assume that all necessary expectations exist and are finite.] 4.5 Let y and ... also the linear projection, Theorem 4.1 also shows that OLS consistently estimates conditional expectations that are linear in parameters We will use this fact often in later sections There are a...

Ngày tải lên: 06/07/2014, 08:20

... various interactions of these with year of birth and state of birth—are very weak, and they are too numerous relative to their contribution in explaining years of education One lesson is that, even ... sense that Eðq j z1 Þ ¼ 0, but that y2 and q may be correlated Let z2 be a vector of instrumental variable candidates for y2 Suppose it is known that z2 appears in the linear projection of y2 ... combination of interest, say y a1 b1 þ a2 b2 þ Á Á Á þ aK bK , and then to write one of the bj in terms of y and the other elements of b Then, substitute into the equation of interest so that y...

Ngày tải lên: 06/07/2014, 08:20

... observations are correlated because of unobserved strata e¤ects, estimation and inference are much more complicated A model with strata -level covariates and within-strata correlation is yis ¼ x is ... for systematic di¤erences in the response and explanatory variables across states If we are interested in the e¤ects of variables measured at the strata level, and the individual observations are ... Pooled Cross Sections over Time A data structure that is useful for a variety of purposes, including policy analysis, is what we will call pooled cross sections over time The idea is that during...

Ngày tải lên: 06/07/2014, 08:20

... independent cross sections in Section 6.3 The estimator in equation (7.17) is for the same cross section units sampled at di¤erent points in time Theorem 7.1 shows that the POLS estimator is consistent ... products and vectorization For conformable matrices D, E, and F, recall that vecðDEFÞ ¼ ðF n DÞ vecðEÞ, where vecðCÞ is the vectorization of the matrix C [That is, vecðCÞ is the column vector ... appropriate for applications But for derivations we will often need to indicate the equation for a generic cross section unit i When we study the asymptotic properties of various estimators of the...

Ngày tải lên: 06/07/2014, 08:20

... of estimates in addition 202 Chapter to the statistical significance of test statistics Hausman (1983, p 435) shows how to construct a statistic based directly on the 3SLS and 2SLS estimates of ... Linear System of Equations We now discuss estimation of a general linear model of the form yi ¼ Xi b þ u i ð8:11Þ where yi is a G  vector, Xi is a G  K matrix, and u i is the G  vector of errors ... crucial fact that some elements of xg are thought to be correlated with ug for at least some g For each equation we assume that we have a set of instrumental variables, a  Lg vector zg , that are...

Ngày tải lên: 06/07/2014, 08:20

... equation (9.42) In fact, any number of functions of z1 and z2 can be added to the instrument list The fact that this argument is faulty is fortunate because our identification analysis in Section ... equation to be a wage o¤er equation rather than a labor demand equation.) 0 Let b 1 ðg1 ; d1 Þ be the ðG þ MÞ Â vector of structural parameters in the first equation With a normalization restriction ... work as a function of the exogenous factors, demographics, and unobservables; the other has crime as a function of these same factors Of course, it is always possible that factors treated as exogenous...

Ngày tải lên: 06/07/2014, 08:20

... variance of uit , a case often relevant for applications (As l approaches unity, the precision of the random e¤ects estimator approaches that of the fixed e¤ects estimator, and the e¤ects of time-constant ... variables’’ means that each element of x it varies over time for some cross section units Often there are elements of x it that are constant across time for a subset of the cross section For example, ... su fact, l similar estimates from fixed e¤ects and random e¤ects Even with small T, random e¤ects can be close to fixed e¤ects if the estimated variance of ci is large relative to the estimated...

Ngày tải lên: 06/07/2014, 08:20

... Population on Crime Rates): In order to estimate the causal e¤ect of prison population increases on crime rates at the state level, Levitt (1996) uses instances of prison overcrowding litigation ... reasonable Keane and Runkle (1992) argue that panel data models for testing rational expectations using individual -level data generally not satisfy the strict exogeneity requirement But they satisfy sequential ... crime rates and prison population, or, more precisely, in the growth rates, makes OLS estimation of equation (11.27) generally inconsistent Using the violent crime rate and a subset of the data...

Ngày tải lên: 06/07/2014, 08:20

... consists of xi and yi , the ith draw from the population on x and y What allows us to estimate yo when it indexes Eð y j xÞ? It is the fact that yo is the value of y that minimizes the expected squared ... class of estimators Let qðw; yÞ be a function of the random vector w and the parameter vector y An M-estimator of y o solves the problem N À1 yAY N X qðwi ; yÞ ð12:8Þ i¼1 ^ assuming that a solution, ... estimator clearly depends on the sample fwi : i ¼ 1; 2; ; Ng, but we suppress that fact in the notation The objective function for an M-estimator is a sample average of a function of wi and...

Ngày tải lên: 06/07/2014, 08:20

... observation i Note that li ðy Þ is a random function of y, since it depends on the random vector ðx i ; yi Þ By taking the expected value of expression (13.12) and using iterated expectations, ... score of li ðy Þ evaluated at the restricted estimates y partial derivatives of li ðy Þ with respect to each of the P parameters, but then we 398 Chapter 13 evaluate this vector of partials at the ... serially correlated Estimation of the asymptotic variance of the partial MLE is not di‰cult In fact, we can combine the M-estimation results from Section 12.5.1 and the results of Section 13.5 to...

Ngày tải lên: 06/07/2014, 08:20

... statistic is based on the square estimator using weighting matrix L limiting distribution of the score of the unrestricted objective function evaluated at the restricted estimates, properly standardized: ... the score of an objective function (evaluated at yo ) and A is the expected value of the Jacobian of the score, again evaluated at yo (We suppress an ‘‘o’’ subscript here, as the value of the true ... outer product of the scores s and s1 equals the expected Jacobian of s (evaluated at yo ) In Section 12.5.1 we claimed that the GIME plays a role in e‰ciency, and Lemma 14.1 shows that it does...

Ngày tải lên: 06/07/2014, 08:20

... e¤ects of attending a Catholic high school on the probability of attending college, allowing the Catholic high school indicator to be correlated with unobserved factors that a¤ect college attendence ... that, in nonlinear models, we usually want to estimate partial e¤ects and not just parameters For the purposes of obtaining the directions of the e¤ects or the relative e¤ects of the explanatory ... discuss estimation of the random e¤ects probit model, we should be sure we know what we want to estimate As in Section 15.7.1, consistent estimation of b means that we can consistently estimate the...

Ngày tải lên: 06/07/2014, 08:20

... by the same multiplicative factor This fact allows us—both in data-censoring applications and corner solution applications—to estimate the relative e¤ects of any two explanatory variables The ... the estimates of b from standard Tobit and Tobit with heteroskedasticity But when Eð y j x; y > 0Þ and Eðy j xÞ are of interest, we should look at estimates of these expectations with and without ... we can estimate Eðci Þ and evaluate the partial e¤ects at the estimated mean value We will also see how to estimate the average partial e¤ects Rather than cover a standard random e¤ects version,...

Ngày tải lên: 06/07/2014, 08:20

... including tests and corrections Section 17.7 treats sample selection and the related problem of attrition in panel data Stratified sampling, which arises out of sampling design, is covered in Section 17.8 ... general treatment allows elements of x to be correlated with u Rather than obtaining a random sample—that is, a sample representative of the population—we only use data points that satisfy certain ... parents’ education (motheduc, fatheduc) and husband’s education as IVs In addition, Sample Selection, Attrition, and Stratified Sampling 569 we need some variables that a¤ect labor force participation...

Ngày tải lên: 06/07/2014, 08:20

... than the fixed e¤ects Poisson estimator that we cover in Section 19.6.4.) Count Data and Related Models 673 A quasi-MLE random e¤ects analysis keeps some of the key features of assumptions (19.60)–(19.62) ... i ; bo Þ and note that, under assumptions (19.3) and (19.7), ui2 À so mðx i ; bo Þ is uncorrelated with any function of x i Let hðx i ; b Þ be a  Q vector of functions of x i and b, and consider ... elasticity, and obtain its standard error (Assume that the full set of FEP assumptions hold.) Count Data and Related Models 683 19.11 a For a random draw i from the cross section, assume that (1)...

Ngày tải lên: 06/07/2014, 08:20