set identification via quantile restrictions in short panels this paper studies the identifying power of conditional quantile restrictions in short panels with flxed efiects in contrast to classical flxed efiects models with conditional mean restrictions conditional quantile restrictions are not preserved by taking difierences in the regression equation over time this paper shows however that a conditional quantile restriction in conjunction with a weak conditional independence restriction provides bounds on quantiles of difierences in time varying unobservables across periods these bounds carry observable implications for model parameters which generally result in set identiflcation the analysis of these bounds includes conditions for point identiflcation of the parameter vector as well as weaker conditions that result in identiflcation of individual parameter components

arithmetic of normal rees algebras two reasons drive this study of the arithmetical properties of blow up like algebras first one still lacks effective criteria for the rees algebra of an ideal to be normal and second there are several new phenomena related to torsionfree symmetric algebras of modules notably bundlesthat need clarification as yet another related question there is the description of the canonical modules of such algebras a necessary step in determining their gorenstein loci the main thread for these questions is the understanding of the divisor class group essentially defined by a pair made up of a morphism and a free subgroup of finite rank the behaviour of the mapping has puzzling

on the arithmetic and homology of algebras of linear type three modifications of the symmetric algebra of a module are introduced and their arithmetical and homological properties studied emphasis is placed on converting syzygetic properties of the modules into ideal theoretic properties of the algebras e g cohen macaulayness factoriality the main tools are certain fitting ideals of the module and an extension to modules of a complex of not necessarily free modules that we have used in studying blowing up rings

hilbert coefficients and the gorenstein property of the associated graded ring in this article we investigate the gorenstein property of the associated graded ring ga i of an ideal i in a gorenstein local ring a m of positive dimension we especially concentrate on the case where i is m primary assuming that the rees algebra of i is cohen macaulay we then give necessary and sufficient conditions for the gorensteiness of ga i in terms of the hilbert coefficients of i

instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings this paper reports estimates of the effects of jtpa training programs on the distribution of earnings the estimation uses a new instrumental variable iv method that measures program impacts on quantiles the quantile treatment effects qte estimator reduces to quantile regression when selection for treatment is exogenously determined qte can be computed as the solution to a convex linear programming problem although this requires first step estimation of a nuisance function we develop distribution theory for the case where the first step is estimated nonparametrically for women the empirical results show that the jtpa program had the largest proportional impact at low quantiles perhaps surprisingly however jtpa training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution

inference on counterfactual distributions counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics in this article we develop modeling and inference tools for counterfactual distributions based on regression methods the counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates for either of these scenarios we derive joint functional central limit theorems and bootstrap validity results for regression based estimators of the status quo and counterfactual outcome distributions these results allow us to construct simultaneous confidence sets for function valued effects of the counterfactual changes including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals these confidence sets can be used to test functional hypotheses such as no effect positive effect or stochastic dominance our theory applies to general counterfactual changes and covers the main regression methods including classical quantile duration and distribution regressions we illustrate the results with an empirical application to wage decompositions using data for the united states as a part of developing the main results we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution we show that distribution regression encompasses the cox duration regression and represents a useful alternative to quantile regression we establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals publication abstract

cohen macaulay rees algebras and degrees of polynomial relations e mail aron sunrnp vfba br 2 department of mathematics michigan state university east lansing mi 48824 usa e mail 21144bfu msu edu 3 department of mathematics rutgers university new brunswick nj 08903 usa e mail vasconce rings rutgers edu received 5 october 1993

blow up of straightening closed ideals in ordinal hodge algebras we study a class of ideals i in graded ordinal hodge algebras a these ideals are distinguished by the fact that their powers have a canonical standard basis this leads to hodge algebra structures on the rees ring and the associated graded ring furthermore from a natural standard filtration one obtains a depth bound for a in which under certain conditions is sharp for n large frequently one observes that in i n under suitable hypotheses it is possible to calculate the divisor class group of the rees algebra our main examples are ideals of virtual maximal minors and ideals of maximal minors fixing a submatrix

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

asymptotics for panel quantile regression models with individual effects this paper studies panel quantile regression models with individual fixed effects we formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals n and the number of time periods t jointly go to infinity the estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature nevertheless due to the non smoothness of the objective function we had to impose a more restrictive condition on t to prove asymptotic normality than that usually found in the literature the finite sample performance of the estimator is evaluated by monte carlo simulations

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

efficient semiparametric estimation of quantile treatment effects this paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics identification is achieved without requiring computation of the conditional quantiles of the potential outcomes instead the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems root n consistency asymptotic normality and achievement of the semiparametric efficiency bound are shown for that estimator a consistent estimation procedure for the variance is also presented finally the method developed here is applied to evaluation of a job training program and to a monte carlo exercise results from the empirical application indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates the monte carlo study shows that for a relatively small sample size the method produces estimates with good precision and low bias especially for middle quantiles

gorenstein associated graded rings of analytic deviation two ideals abstract this paper studies the question of when the associated graded ring g i n 0in in 1 of a certain ideal i in a local ring is gorenstein the main result implies for example that if a is a regular local ring 708 is a prime ideal in a with dim a p 2 and a p is a complete intersection in codimension one then the associated graded ring g p is gorenstein if and only if the reduction number of p is at most 1

the theory of d sequences and powers of ideals in this paper we study the question of finding depth r i given an ideal i in a commutative ring this problem is difficult in general even for simple examples depth r z can be difficult to compute brodmann has shown that for any commutative noetherian ring depth r z become stable for large n finding this value however is quite hard this problem originally arose through consideration of the following example suppose k is a field and x xij is an n

estimation of censored quantile regression for panel data with fixed effects this article investigates estimation of censored quantile regression qr models with fixed effects standard available methods are not appropriate for estimation of a censored qr model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity motivated by these limitations the article proposes estimators that are obtained by applying fixed effects qr to subsets of observations selected either parametrically or nonparametrically we derive the limiting distribution of the new estimators under joint limits and conduct monte carlo simulations to assess their small sample performance an empirical application of the method to study the impact of the 1964 civil rights act on the black white earnings gap is considered supplementary materials for this article are available online

linkage and the koszul homology of ideals 0 introduction let r be a local ring and i an ideal of r associated to i are several graded algebras the symmetric algebra of the module i sym i the rees algebra of i defined to be the algebra r i gn o inf and the associated graded algebra of i gr1 r rii g ii 2 in in 1 i i i our purpose in this paper is to study the behavior of these graded algebras when we change i through linkage recall the definition of linkage found in the paper of peskine and szpiro 22

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

gorenstein graded rings associated to ideals let a be a noetherian local ring with the maximal ideal m and dim a d let i 6 a be an ideal in a and s hta i this article studies the question of when the associated graded ring g i i 0 i i is gorenstein to state our result we set up some notation let be an integer such that d and let j be a reduction of i generated by elements a1 a2 a we denote by rj i the reduction number of i with respect to j the analytic spread of i is i dim a m a g i then s i we always assume that the generating set a1 a2 a of j is a basic generating set for j in the sense of aberbach huneke and trung aht which means that jiaq is a reduction of iaq for all q v i with i hta q here let v i be a set of prime ideals in a containing i and ji a1 a2 ai for 0 i by aht 7 2 there always exists a basic generating set for j if the field a m is infinite let

algebras of minors let i be an ideal of a noetherian ring r the rees algebra of i is the graded r algebra k 0ik the study of the properties of rees algebras and of the other blow up algebras has attracted the attention of many researchers in the last three decades for a detailed account of the theories that have been developed and of the results that have been proved the reader should consult the monograph of vasconcelos v in this paper we treat a special and interesting case the rees algebras of determinantal ideals and their special fibers let x xij be a generic matrix of size m n over a field k and let s be the polynomial ring k xij let it be the ideal of s generated by the minors of size t of x finally let t be the rees algebra of it and let at be the subalgebra of s generated by the t minors of x in the case of maximal minors i e t min m n the algebra at is nothing but the homogeneous coordinate ring of the grassmann variety which is known to be a

on the divisor class group of rees algebras let r be a normal noetherian domain and let i be an ideal whose associated graded ring gr r is reduced barshay 2 showed that under these conditions the rees algebra s r it r 0 it 0 izt2 a e r t is normal a much simpler proof was given later by huneke 111 let p r it t be the extended rees algebra then pt e r t t 1 is normal and p tp e gr r is reduced it follows that p itself is normal this implies easily the normality of s as well we are interested in the class group cl s of s to obtain a neat result we strengthen our hypothesis and assume that gr r is a domain hochster 6 showed in this case that p is factorial if r is so the only tool needed to prove this is the following elementary but powerful theorem of nagata

semiparametric instrumental variable estimation of treatment response models this article introduces a new class of instrumental variable iv estimators for linear and nonlinear treatment response models with covariates the rationale for focusing on nonlinear models is that if the dependent variable is binary or limited or if the effect of the treatment varies with covariates a nonlinear model is appropriate in the spirit of roehrig econometrica 56 1988 433 identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest one virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well defined approximation to a treatment response function under functional form misspecification in contrast to some usual iv models heterogeneity of treatment effects is not restricted by the identification conditions the ideas and estimators in this article are illustrated using iv to estimate the effects of 401 k retirement programs on savings

on the gorenstein property of rees and form rings of power of ideals in this paper we determine the exponents n for which the rees ring r in and the form ring gra in are gorenstein rings where i is a strongly cohen macaulay ideal of linear type including complete and almost complete intersections or an m primary ideal in a local ring a with maximal ideal m given an ideal i in a local ring a m it is well known that the cohenmacaulayness of the rees algebra r i implies the cohen macaulayness of all rees algebras r in the same is true for the form rings gra i and gra in see 3 2 7 8 and 8 8 5 in this paper we show that in contrast to the cohenmacaulay property the gorenstein property of r in and gra in only holds for special exponents n if in particular gra i is gorenstein and r i is cohen macaulay it turns out that these special exponents are closely related to the a invariant of the form ring gra i mainly under this aspect we prove some results concerning the gorenstein property of rees and form rings of powers of i strongly cohen macaulay ideals of linear type including almost complete intersections in gorenstein rings ii m primary ideals in cohen macaulay rings and iii equimultiple prime ideals p m in a generalized cohen macaulay ring our investigations are essentially based on the explicit computation of the a invariants of form and rees rings see 2 for the above classes of idealsusing a structure theorem for the canonical module of r i in 7 we can determine in 3 the exponents n 1 for which r in and gra in are gorenstein rings see in particular theorem 3 5 a more geometrical interpretation of the results in 3 is the observation that in these situations the gorenstein property of proj r i can be deduced from the gorenstein property of a certain veronesean subring r in of r i it might be an interesting question when the gorenstein property of a blow up proj r i is inherited to an appropriate rees ring r j with proj r j proj r i over speca in 4 part i we characterize for cohen macaulay or gorenstein rings a the gorenstein property of r md i i 1 2 3 by conditions on the received by the editors june 30 1991 and in revised form april 10 1992 1991 mathematics subject classification primary 13d03 13h10 13h15 secondary 14b05 14b 1 5 1994 american mathematical society 0002 9947 94 1 00 25 per page

on the canonical module of the rees algebra and the associated graded ring of an ideal the investigations of this paper originate in the following question suppose i is an ideal of a local gorenstein ring r m whose associated graded ring gr r is cohenmacaulay under which extra conditions is gr r actually a gorenstein ring hochster shows in 151 that gr r is a gorenstein ring if r is factorial and gr r is a domain hochster s arguments work as well if one only requires r to be a gorenstein ring however the condition that gr r is a domain cannot be weakened much in fact we given an example of a local complete intersection r m whose associated graded ring gr r is a reduced cohen macaulay ring but not a gorenstein ring the question when gr r is a gorenstein ring has a more satisfying answer for ideals i generated by a d sequence for which r i is a cohen macaulay ring d sequences were introduced and studied by huneke their relevance in the study of powers of ideals was shown by huneke in 161 for further investigations on d sequences the reader is referred to 111 now given an ideal i generated by a d sequence and such that r i is cohenmacaulay we show that gr r is a gorenstein ring if and only if i is strongly cohen macaulay again the notion strongly cohen macaulay was introduced by huneke it means that the koszul homology of a system of generators of i is cohen macaulay huneke showed in 191 that any ideal in the linkage class of a complete intersection is strongly cohen macaulay this result provides us with plenty of interesting examples the main subject of the paper however is the study of the canonical module of gr r and of the rees algebra r if r zr 12t2 sr t in 14 the canonical class os of the rees algebra s r zr was determined under the assumption that i is

strongly cohen macaulay schemes and residual intersections this paper studies the local properties of closed subschemes y in cohen macaulay schemes x such that locally the defining ideal of y in x has the property that its koszul homology is cohen macaulay whenever this occurs y is said to be strongly cohen macaulay in x this paper proves several facts about such embeddings chiefly with reference to the residual intersections of y in x the main result states that any residual intersection of y in x is again cohen macaulay introduction our purpose in this paper is to investigate a property of a closed subscheme y in a noetherian cohen macaulay scheme x which we call strong cohen macaulayness this is a local property which we first describe for a local ring let x spec r where r is a cohen macaulay local ring and let y spec r i

cohen macaulay rees algebras and their specialization the rees algebra of an ideal j in a commutative ring r is by definition the graded algebra where t is an indeterminate in this paper we are concerned with proving that certain rees algebras are cohen macaulay and with answering under strong hypotheses the question if r s n is a factor ring of s and i jr when is i r a specialization of j s that is when is the natural epimorphism r a j s r i r an isomorphism these questions have interest partly because if s and s j s are cohen macaulay then so is gr s s j j j 16 1 and under these hypotheses if n is perfect and r s j s i r then r and 7 1 r are cohen macaulay too thus gr r is cohen macaulay and its torsion freeness and normality for exmple can be characterized in terms of analytic spreads as in 161 see section 3 for details we deal with the specialization question in section 1 it is answered for the case where as above s and 2 j s are cohen macaulay and n is 202

quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods abstract this paper shows that the conditional quantile treatment effect on the treated is identified under i a conditional distributional difference in differences assumption and ii a new assumption that the dependence the copula between the change in untreated potential outcomes and the initial level of untreated potential outcomes is the same for the treated group and untreated group we consider estimation and inference with discrete covariates and propose a uniform inference procedure based on the exchangeable bootstrap finally we estimate the effect of increasing the minimum wage on the distribution of earnings for subgroups defined by race gender and education

on rings with linear resolutions let r denote a positively graded noetherian ring over a field k r eori with r k and m the irrelevant maximal ideal generated by forms of degree 1 or let r be the m adic completion of such a ring if we consider x as a homomorphic image of a polynomial ring resp of a power series ring over k with a homogeneous defining ideal one may ask whether r has a minimal linear resolution as an s module cohen macaulay rings r of maximal embedding dimension e g have a linear resolution as sally showed in 9 she also proved formulas for the hilbert series hr and the poincari series pi pz schenzel lo later characterized cm rings r with a linear resolution and called these rings extremal he also gave formulas for hr and pi s goto see 3 1 below proved besides other facts the linearity of the resolution for buchsbaum rings of maximal embedding dimension i e edim r dim r e r i r 1 i r denotes the invariant of the buchsbaum ring r and a formula for hh in section 1 we generalize these results and characterize rings with a linear resolution which have a parameter system that forms a d sequence in the buchsbaum case we then show that the h pi and pf of such rings are determined by the embedding dimension the krull dimension the dimensions of the local cohomology modules as k vector spaces and what we call the type of r in section 2 we determine all buchsbaum rings r k r of maximal embedding dimension and multiplicity 2 sally proved in 8 that for a local cm ring r m of maximal embedding dimension the associated graded ring is also cm of maximal embedding dimension goto showed a similar result for buchsbaum rings of

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

partial distributional policy effects in this paper we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest both fixed and infinitesimal changes are considered we show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed but are typically only partially identified if its distribution is discrete for the latter case we derive informa tive bounds making use of the available information we also discuss estimation and inference

instrumental quantile regression inference for structural and treatment effect models we introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference these methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes we describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it we focus our discussion of inference on tests of distributional equality constancy of effects conditional dominance and exogeneity we apply the procedures to characterize the returns to schooling in the u s

set identification of the censored quantile regression model for short panels with fixed effects this paper studies identification and estimation of a censored quantile regression model for short panel data with fixed effects using the redistribution of mass idea we obtain bounds on the conditional distribution of differences of the model across periods under conditional quantile restrictions together with a weak conditional independence assumption along the lines of rosen 2012 the inversion of the distribution bounds characterizes the sharp identified set via a set of inequalities based on conditional quantile functions due to the presence of censoring some of the inequalities defining the identified set hold trivially and have no identification power moreover those trivial inequalities cause a difficulty in estimating the identified set to deal with the issue we propose a two step estimation method where the first step consists of excluding trivial inequalities and the second step performs minimization of a convex criterion function using the remaining inequalities we establish asymptotic properties of the set estimator and also consider sufficient conditions under which point identification can be attained

approximation complexes of blowing up rings ii this paper is a sequel to 111 where we studied the relationships that hold between the arithmetical properties of the rees ring 9 i and the symmetric algebra sym l of an ideal i and some of their fibers and the depth properties of the koszul homology modules h i r on a set of generators of i the connection between these objects is realized by certain differential graded algebras the so called approximation complexes that are built out of ordinary koszul complexes these compiexes show however different sensitivities being acyclic in situations much broader than the usual context of regular sequences it has been found that certain extensions thereof d sequences and proper sequences play here that role of acyclic sequence the interplay between sequences and approximation complexes will be a basic point of view here where we give

identification of panel data models with endogenous censoring this paper analyzes the identification question in censored panel data models where the censoring can depend on both observable and unobservable variables in arbitrary ways under some general conditions we derive the tightest sets on the parameter of interest these sets which can be singletons represent the limit of what one can learn about the parameter of interest given the model and the data in that every parameter that belongs to these sets is observationally equivalent to the true parameter we consider two separate sets of assumptions motivated by the previous literature each controlling for unobserved heterogeneity with an individual specific fixed effect the first imposes a stationarity assumption on the unobserved disturbance terms along the

landesman lazer type results for second order hamilton jacobi bellman equations we study the boundary value problem f d2u du u x u f x u in u 0on where the second order differential operator f is of hamilton jacobi bellman type f is sub linear in u at infinity and rn is a regular bounded domain we extend the well known landesman lazer conditions to study various bifurcation phenomena taking place near the two principal eigenvalues associated to the differential operator we provide conditions under which the solution branches extend globally along the eigenvalue gap we also present examples illustrating the results and hypotheses

the dilworth number of artin gorenstein rings 1let a be an artin local ring the dilworth number of a is defined to be the supremum of p z for ideals z in a where p is the minimal number of generators in my paper 4 i developed some methods to compute this number when a is homogeneously graded over a field k and especially if a is gorenstein and ch k 0 i showed that it is the dominating case that the dilworth number is attained by a power of the maximal ideal in such a case we shall say that a has the sperner property in the present paper we consider artin rings a m not necessarily graded and compare the dilworth number of a and that of gr a and it will be shown that the main result of 4 is valid without the assumption that the rings are homogeneous our main result is theorem 7 where we prove that most artin gorenstein rings have the sperner property actually we prove a stronger result which says that it has the weak stanley property to explain the term most we represent an artin gorenstein ring a in the

links of prime ideals and their rees algebras abstract in a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in gorenstein rings are equimultiple ideals with reduction number 1 this led to the construction of large families of cohen macaulay rees algebras the first goal of this paper is to extend this result to arbitrary cohen macaulay rings the means of the proof are changed since one cannot depend so heavily on linkage theory we then study the structure of the rees algebra of these links more specifically we describe their canonical module in sufficient detail to be able to characterize self linked prime ideals in the last section multiplicity estimates for classes of such ideals are established

on ideals of minors fixing a submatrix abstract let m be a n m matrix with entries in a noetherian ring r and let m be the submatrix of m consisting of the first r columns r n 1 consider the ideal jr m of n n minors of m involving the columns of m we obtain the primary decomposition and the homological dimension of jr m in the generic case the proofs rely heavily on the methods and the theory of weak d sequences and straightening laws as a byproduct we obtain exact conditions under which jr m is generated by a d sequence and also a complete picture of the blowing up algebras of jr m in that case the latter proofs rely on recent methods developed by several authors such as those of sliding depth approximation complexes cohen macaulay residual intersections to close the discussion we construct a free resolution of jr m when m n 1 the case r n 1 had been treated before by the present authors a side curiosity herein obtained is an example of a nonperfect radical 3 generated ideal of codimension 2 whose associated graded ring is a cohen macaulay reduced ring that is not gorenstein examples of this sort do not seem to abound