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

Cystatin C and cardiovascular disease : A mendelian randomization study

BACKGROUND: Epidemiological studies show that high circulating cystatin C is associated with risk of cardiovascular disease (CVD), independent of creatinine-based renal function measurements. It is unclear whether this relationship is causal, arises from residual confounding, and/or is a consequence of reverse causation. OBJECTIVES: The aim of this study was to use Mendelian randomization to investigate whether cystatin C is causally related to CVD in the general population. METHODS We incorporated participant data from 16 prospective cohorts (n ¼ 76,481) with 37,126 measures of cystatin C and added genetic data from 43 studies (n ¼ 252,216) with 63,292 CVD events. We used the common variant rs911119 in CST3 as an instrumental variable to investigate the causal role of cystatin C in CVD, including coronary heart disease, ischemic stroke, and heart failure. RESULTS: Cystatin C concentrations were associated with CVD risk after adjusting for age, sex, and traditional risk factors (relative risk: 1.82 per doubling of cystatin C; 95% confidence interval [CI]: 1.56 to 2.13; p ¼ 2.12 1014). The minor allele of rs911119 was associated with decreased serum cystatin C (6.13% per allele; 95% CI: 5.75 to 6.50; p ¼ 5.95 10211), explaining 2.8% of the observed variation in cystatin C. Mendelian randomization analysis did not provide evidence for a causal role of cystatin C, with a causal relative risk for CVD of 1.00 per doubling cystatin C (95% CI: 0.82 to 1.22; p ¼ 0.994), which was statistically different from the observational estimate (p ¼ 1.6 105 ). A causal effect of cystatin C was not detected for any individual component of CVD. CONCLUSIONS: Mendelian randomization analyses did not support a causal role of cystatin C in the etiology of CVD. As such, therapeutics targeted at lowering circulating cystatin C are unlikely to be effective in preventing CVD. 

An Analysis of the Telecommunications Business in China by Linear Regression

In this paper, we study the influence of the National Telecom Business Volume by the data in 2008 that have been published in China Statistical Yearbook of Statistics. We illustrate the procedure of modeling “National Telecom Business Volume” on the following eight variables, GDP, Consumption Levels, Retail Sales of Social Consumer Goods Total Renovation Investment, the Local Telephone Exchange Capacity, Mobile Telephone Exchange Capacity, Mobile Phone End Users, and the Local Telephone End Users. The testing of heteroscedasticity and multicollinearity for model evaluation is included. We also consider AIC and BIC criterion to select independent variables, and conclude the result of the factors which are the optimal regression model for the amount of telecommunications business and the relation between independent variables and dependent variable. Based on the final results, we propose several recommendations about how to improve telecommunication services and promote the economic development.