Computation and Analysis of Multiple Structural-Change Models

In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least-squares operations of order O(T 2) for any number of breaks. Our method can be applied to both pure and partial structural-change models. Secondly, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. We present simulation results pertaining to the behavior of the estimators and tests in finite samples. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program available upon request for non-profit academic use.

Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

It is well known that standard asymptotic theory is not valid or is extremely unreliable in models with identification problems or weak instruments [Dufour (1997, Econometrica), Staiger and Stock (1997, Econometrica), Wang and Zivot (1998, Econometrica), Stock and Wright (2000, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. One possible way out consists here in using a variant of the Anderson-Rubin (1949, Ann. Math. Stat.) procedure. The latter, however, allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, which in general does not allow for individual coefficients. This problem may in principle be overcome by using projection techniques [Dufour (1997, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. AR-types are emphasized because they are robust to both weak instruments and instrument exclusion. However, these techniques can be implemented only by using costly numerical techniques. In this paper, we provide a complete analytic solution to the problem of building projection-based confidence sets from Anderson-Rubin-type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are required for building the confidence intervals. We also study by simulation how “conservative” projection-based confidence sets are. Finally, we illustrate the methods proposed by applying them to three different examples: the relationship between trade and growth in a cross-section of countries, returns to education, and a study of production functions in the U.S. economy.

The role of porcine reproductive and respiratory syndrome (PRRS) virus structural and non-structural proteins in virus pathogenesis.

Porcine reproductive and respiratory syndrome (PRRS) is an economically devastating viral disease affecting the swine industry worldwide. The etiological agent, PRRS virus (PRRSV), possesses a RNA viral genome with nine open reading frames (ORFs). The ORF1a and ORF1b replicase-associated genes encode the polyproteins pp1a and pp1ab, respectively. The pp1a is processed in nine non-structural proteins (nsps): nsp1a, nsp1b, and nsp2 to nsp8. Proteolytic cleavage of pp1ab generates products nsp9 to nsp12. The proteolytic pp1a cleavage products process and cleave pp1a and pp1ab into nsp products. The nsp9 to nsp12 are involved in virus genome transcription and replication. The 30 end of the viral genome encodes four minor and three major structural proteins. The GP2a, GP3 and GP4 (encoded by ORF2a, 3 and 4), are glycosylated membrane associated minor structural proteins. The fourth minor structural protein, the E protein (encoded by ORF2b), is an unglycosylated membrane associated protein. The viral envelope contains two major structural proteins: a glycosylated major envelope protein GP5 (encoded by ORF5) and an unglycosylated membrane M protein (encoded by ORF6). The third major structural protein is the nucleocapsid N protein (encoded by ORF7). All PRRSV non-structural and structural proteins are essential for virus replication, and PRRSV infectivity is relatively intolerant to subtle changes within the structural proteins. PRRSV virulence is multigenic and resides in both the non-structural and structural viral proteins. This review discusses the molecular characteristics, biological and immunological functions of the PRRSV structural and nsps and their involvement in the virus pathogenesis.