[Agents are assumed to have smooth preferences with natural boundary conditions. For large regular economies, satisfying an indeconposability conditions, it is shown that core allocations and competitive allocations converge to each other with a rate inversely proportional to the number of agents m. To the extent that the indecomposability condition is harmless, 1/m can be regarded as the normal rate of convergence. However, if indifference surfaces are allowed to have kinks, 1/m cannot be regarded as normal. This is treated in Part II [6].]

The author demonstrates that despite variables that are integrated, the fundamental issues on structural equation modeling raised by the Cowles Commission remain valid and standard estimation and testing procedures can still be applied. A basic framework linking the multiple time series model and the dynamic simultaneous equation model is provided and implications under the long-run cointegrating relations are discussed. Conditions for identifying both the short-run dynamics and long-run equilibrium conditions are given. Limiting properties of the least squares and simultaneous equation estimators under cointegration are derived. Implications for hypothesis testing are also discussed.

[This paper is concerned with the identification and estimation of the parameters in a dynamic simultaneous equations model with stationary disturbances when both the endogenous and exogenous variables are subject to random measurement errors. A frequency domain approach is suggested to fully utilize the information contained in the data. The first part of this paper explores the identification criteria. The second part of this paper suggests estimation methods for such a model. Both full information and limited information estimation methods are studied and their respective gains and losses are evaluated.]

[The model extlesstex-math extgreater$Y_\it\= extbackslashSigma _\k\( extbackslashbeta _\k\+ extbackslashdelta _\ik\+y_\tk\)x_\ikt\= extbackslashvarepsilon _\it\$ extless/tex-math extgreater with extlesstex-math extgreater$ extbackslashdelta _\ik\$ extless/tex-math extgreater and extlesstex-math extgreatery_\tk\ extless/tex-math extgreater random is considered as a means of pooling the time series of a cross-section sample. The model is placed in a mixed analysis of variance framework. Relationships between various estimation criteria are derived and their asymptotic properties compared. Some implementation problems are also discussed.]

[This paper constructs a life-cycle model of the consumer's allocation process in which the capital market is imperfect and the consumption bundle at each instant includes both durable and nondurable goods. The nondurables are instantaneously consumed at the moment of purchase, while the durable good is accumulated and yields a flow of services over its lifetime. The durable investment is assumed to be irreversible. The consumer's optimal allocation program is shown to vary between the periods of borrowing and lending with each phase defining a different relationship between consumption and the "truncated" permanent income.]

[In this paper, the authors develop a simultaneous equation model of birth rates composed of four estimated equations. This work differs from past research in that it considers the simultaneous relationship between birth rates and income and includes the cost of fertility as an explanatory factor. This cost is measured by the female labor participation rate under the assumption that income foregone due to fertility is a significant opportunity cost.]

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments, generalized empirical likelihood, minimum distance, and semi-parametric estimators. The consistency/lack-of-consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic sizes (in a uniform sense) of standard and identification-robust tests and CS's are established. The results are applied to the ARMA(1, 1) time series model estimated by ML and to the nonlinear regression model estimated by LS. In companion papers, the results are applied to a number of other models.

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including (time‐varying) rare‐disaster risk models and long‐run risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro‐finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross‐equation restrictions. We apply the proposed conditional specification test to the evaluation of a time‐varying rare‐disaster risk model and the construction of robust model uncertainty sets.