A Note on Proxy Variables and Instrument Variable Regression

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Firm relocation and firm profits : Evidence from the Swedish wholesale trade sector

This study analyses the effects of firm relocation on firm profits, using longitudinal data on Swedish limtied liability firms and employing a difference-in-differnce propensity score method in the empirical analysis. Using propensity score matching, the pre-relocalization differneces between relocating and non-relocating firms are balanced. In addition to that, a difference-in-difference estimator is employed in order to control for all time-invariant unobserved heterogeneity among firms. For matching, nearest neighbour matching, using the one-, two- and three nearest neighbours is employed. The balanacing results indicate that matching achieves a good balance, and that similar relocating and non-relocating firms are being compared. The estimated average treatment on the treatment effects indicate thats relocations has a significant effect on the profits of the relocating firms. In other words, firms taht relocate increase their profits significantly, in comparison to what the profits would be had the firms not relocated. This effect is estimated to vary between 3 to 11 percentage points, depending on the lenght of the analysed period after relocation. 

Novel Statistical Methods in Quantitative Genetics : Modeling Genetic Variance for Quantitative Trait Loci Mapping and Genomic Evaluation

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Essays on firm dynamics in the Swedish wholesale trade sector

This thesis consists of a summary and five self-contained papers addressing dynamics of firms in the Swedish wholesale trade sector. Paper [1] focuses upon determinants of new firm formation in the Swedish wholesale trade sector, using two definitions of firms’ relevant markets, markets defined as administrative areas, and markets based on a cost minimizing behavior of retailers. The paper shows that new entering firms tend to avoid regions with already high concentration of other firms in the same branch of wholesaling, while right-of-the-center local government and quality of the infrastructure have positive impacts upon entry of new firms. The signs of the estimated coefficients remain the same regardless which definition of relevant market is used, while the size of the coefficients is generally higher once relevant markets delineated on the cost-minimizing assumption of retailers are used. Paper [2] analyses determinant of firm relocation, distinguishing between the role of the factors in in-migration municipalities and out-migration municipalities. The results of the analysis indicate that firm-specific factors, such as profits, age and size of the firm are negatively related to the firm’s decision to relocate. Furthermore, firms seems to be avoiding municipalities with already high concentration of firms operating in the same industrial branch of wholesaling and also to be more reluctant to leave municipalities governed by right-of-the- center parties. Lastly, firms seem to avoid moving to municipalities characterized with high population density. Paper [3] addresses determinants of firm growth, adopting OLS and a quantile regression technique. The results of this paper indicate that very little of the firm growth can be explained by the firm-, industry- and region-specific factors, controlled for in the estimated models. Instead, the firm growth seems to be driven by internal characteristics of firms, factors difficult to capture in conventional statistics. This result supports Penrose’s (1959) suggestion that internal resources such as firm culture, brand loyalty, entrepreneurial skills, and so on, are important determinants of firm growth rates. Paper [4] formulates a forecasting model for firm entry into local markets and tests this model using data from the Swedish wholesale industry. The empirical analysis is based on directly estimating the profit function of wholesale firms and identification of low- and high-return local markets. The results indicate that 19 of 30 estimated models have more net entry in high-return municipalities, but the estimated parameters is only statistically significant at conventional level in one of our estimated models, and then with unexpected negative sign. Paper [5] studies effects of firm relocation on firm profits of relocating firms, employing a difference-in-difference propensity score matching. Using propensity score matching, the pre-relocalization differences between relocating and non-relocating firms are balanced, while the difference-in-difference estimator controls for all time-invariant unobserved heterogeneity among firms. The results suggest that firms that relocate increase their profits significantly, in comparison to what the profits would be had the firms not relocated. This effect is estimated to vary between 3 to 11 percentage points, depending on the length of the analyzed period.