The linked system of seven national Inforum models is described here. The principles of the linkage are set out. Similarity in software implementation is fundamental, while diversity in the structure of the input–output tables is tolerated and variety in economic content encouraged. The flow of information on prices and imports among the models is fundamental to the linking mechanism. The structure and functional forms used in linkage is laid out in detail. An application of the system to study the mutual destruction of a protectionist trade war concludes the paper.

http://inforumweb.umd.edu/papers/publishedwork/articles/esr91-04.pdf

The INFORUM International System

We examine the asymptotic behaviour of confidence regions in identifiable one-dimensional parametric models with smooth likelihood function and information equal to zero at a critical point of the parameter space. Confidence regions are based on inversion of the likelihood ratio test statistic and of some common forms of the score and Wald test statistics. For fixed parameter values other than the critical point, all these statistics have limiting X 2 (1) distributions, but for most of them the convergence is not uniform near the critical point. When it is not, confidence regions based on inverting the tests, using the X 2 (1) approximation, do not asymptotically have the nominal level. The exception to this lack of locally uniform convergence occurs with the score test standardised by expected, rather than observed, information. For the regions based on the score test standardised by observed information and on the likelihood ratio test, conservative procedures that do not rely on the X 2 (1) approximation can be developed, but they are much too conservative near the critical parameter value. The regions based on the Wald tests have asymptotic level less than 1/2, regardless of the procedure used. Our results suggest that no procedure based solely on the likelihood function will be satisfactory. Whether or not this is the case is an open problem. A simulation study illustrates the results of this paper.

Confidence regions when the Fisher information is zero

Value-added taxes and other indirect taxes pose a special challenge to the I–O model builder. Because they affect price formation, they should be included in a model with a developed nominal side. This paper describes the treatment of indirect taxes in the Italian table. It recognizes that firms are not always able to deduct all VAT paid on inputs. It outlines the treatment of indirect taxes in INTIMO.

Value-Added Taxes and Other Indirect Taxes in an EEC Country Model: The Italian Case

The structure and diversity of microbial communities is intrinsically hierarchical due to the shared evolutionary history of their constituents. This history is typically captured through taxonomic assignment and phylogenetic reconstruction, sources of information that are frequently used to group microbes into higher levels of organization in experimental and natural communities. Connecting community diversity to the joint ecological dynamics of the abundances of these groups is a central problem of community ecology. However, how microbial diversity depends on the scale of observation at which groups are defined has never been systematically examined. Here, we used a macroecological approach to quantitatively characterize the structure and diversity of microbial communities among disparate environments across taxonomic and phylogenetic scales. We found that measures of biodiversity at a given scale can be consistently predicted using a minimal model of ecology, the Stochastic Logistic Model of growth (SLM). This result suggests that the SLM is a more appropriate null-model for microbial biodiversity than alternatives such as the Unified Neutral Theory of Biodiversity. Extending these within-scale results, we examined the relationship between measures of biodiversity calculated at different scales (e.g., genus vs. family), an empirical pattern predicted by the Diversity Begets Diversity (DBD) hypothesis. We found that the relationship between richness estimates at different scales can be quantitatively predicted assuming independence among community members.Contrastingly, only by including correlations between the abundances of community members (e.g., as the consequence of interactions) can we predict the relationship between estimates of diversity at different scales. The results of this study characterize novel microbial patterns across scales of organization and establish a sharp demarcation between recently proposed macroecological patterns that are not and are affected by ecological interactions. 

Investigating macroecological patterns in coarse-grained microbial communities using the stochastic logistic model of growth

Abstract The structure and diversity of microbial communities is intrinsically hierarchical due to the shared evolutionary history of community members. This history is typically captured through taxonomic assignment and phylogenetic reconstruction, sources of information that are frequently used to group microbes into higher levels of organization in experimental and natural communities. Connecting community diversity to the joint ecological dynamics of the abundances of these groups is a central problem of community ecology. However, how diversity and dynamics depend on the scale of observation at which groups are defined has never been systematically examined. Here, we used a macroecological approach to quantitatively characterize the structure and diversity of microbial communities among disparate environments across taxonomic and phylogenetic scales. We found that measures of biodiversity at a given scale can be consistently predicted using predictions derived from a minimal model of ecology, the Stochastic Logistic Model of growth (SLM). Extending these within-scale results, we examined the relationship between measures of biodiversity calculated at different scales (e.g., genus vs. family), an empirical pattern predicted by the Diversity Begets Diversity (DBD) hypothesis. We found that the relationship between richness estimates at different scales can be quantitatively predicted assuming independence among community members. Contrastingly, only by including correlations between species abundances (e.g., as consequence of interactions) can we predict the relationship between estimates of diversity at different scales. The results of this study characterize novel microbial patterns across scales of organization and establish a sharp demarcation between recently proposed macroecological patterns that are not and are affected by ecological interactions. 

/pdf/macroecological-patterns-in-coarse-grained-microbial-19zvnasx.pdf

Macroecological patterns in coarse-grained microbial communities

The new estimates of imports and exports equations for Italy have been done for providing the Irnterindustry Italian Model (INTIMO) of a suitable set of equations since the model has expanded including besides the original real side (Grassini,l982) the blocks of the price equation and the income side. An input-output model with real and price sides integrated requires in fact a careful definition of the prices influencing the final demand components of the real side in order to preserve the simultaneity among the variables determined inside its blocks; this implies a clear link between the producers’ prices determined in the price side of the model and the prices considered as explanatory variables in the imports and exports equations.

On Modeling Foreign Trade in an Input—Output Model of an Open Economy

In the paper we propose a way to test the null hypothesis h(θ)=0 when the information matrix is singular. The approach is based on the introduction of a quadratic penalty log-likelihood function with the penalty parameter close to zero (but not zero). This slight change of the log-likelihood allows to obtain a consistent estimator close to the maximum likelihood estimator and whose limiting distribution is Normal with variance-covariance matrix given by the Moore-Penrose pseudoinverse of the information matrix. This result allows to obtain an asymptoticx 2-distribution that may be used in hypothesis testing when the infonnation matrix is singular.

Hypothesis testing when the information matrix is singular

We face an indeterminate parameters problem when there are two sets of parameters, x and g, say, such that the null hypothesis H0:x=x0 makes the likelihood independent of g. A consequence of indeterminacy is the singularity of the information matrix. For this problem the standard results, such as the asymptotic chi-squared distribution of the Wald test statistic, are generally false. In the paper we propose an estimator of the parameters of interest, x, so that a Wald-type test statistic can be used for testing H0. Such an estimator is obtained through the maximization of a modified (penalized) log-likelihood function. We show that a solution to the (penalized) likelihood equation is consistent and asymptotically normally distributed with variance-covariance matrix approximated by the Moore-Penrose pseudoinverse of the information matrix. These properties allow one to construct a Wald-type test statistic useful for inferential purposes.

/pdf/inference-in-the-indeterminate-parameters-problem-54idflsfzj.pdf

Inference in the indeterminate parameters problem

In general, the exact distribution of a convolution of independent gamma random variables is quite complicated and does not admit a closed form. Of all the distributions proposed, the gamma...

An approximation to the convolution of gamma distributions

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On Modeling Foreign Trade in an Input—Output Model of an Open Economy

Hypothesis testing when the information matrix is singular

Inference in the indeterminate parameters problem

An approximation to the convolution of gamma distributions