Edward C. Norton

Interaction terms in logit and probit models

Abstract The magnitude of the interaction effect in nonlinear models does not equal the marginal effect of the interaction term, can be of opposite sign, and its statistical significance is not calculated by standard software. We present the correct way to estimate the magnitude and standard errors of the interaction effect in nonlinear models.

School and neighborhood characteristics associated with school rates of alcohol, cigarette, and marijuana use.

Previous research has noted that schools vary in substance use prevalence rates, but explanations for school differences have received little empirical attention. We assess variability across elementary schools (N = 36) in rates of early adolescent alcohol, cigarette, and marijuana use. Characteristics of neighborhoods and schools potentially related to school prevalence rates are examined, as well as whether these characteristics have independent effects or whether neighborhood characteristics are mediated by school characteristics. Neighborhood and school characteristics were measured using student, parent, and archival data. The findings show substantial variation across schools in substance use. Attributes of neighborhoods and schools are statistically significantly related to school rates of lifetime alcohol use, lifetime cigarette use, and current cigarette use. Contrary to expectations, lifetime alcohol and cigarette use rates are higher in schools located in neighborhoods having greater social advantages as indicated by the perceptions of residents and archival data. Neighborhood effects are expressed both directly and indirectly through school characteristics. The findings are discussed in light of contagion and social disorganization theories.

Interaction terms in nonlinear models

OBJECTIVES To explain the use of interaction terms in nonlinear models. STUDY DESIGN We discuss the motivation for including interaction terms in multivariate analyses. We then explain how the straightforward interpretation of interaction terms in linear models changes in nonlinear models, using graphs and equations. We extend the basic results from logit and probit to difference-in-differences models, models with higher powers of explanatory variables, other nonlinear models (including log transformation and ordered models), and panel data models. EMPIRICAL APPLICATION: We show how to calculate and interpret interaction effects using a publicly available Stata data set with a binary outcome. Stata 11 has added several features which make those calculations easier. LIMDEP code also is provided. CONCLUSIONS It is important to understand why interaction terms are included in nonlinear models in order to be clear about their substantive interpretation.

Long-term Survival Following Partial vs Radical Nephrectomy Among Older Patients With Early-Stage Kidney Cancer

CONTEXT Although partial nephrectomy is the preferred treatment for many patients with early-stage kidney cancer, recent clinical trial data, which demonstrate better survival for patients treated with radical nephrectomy, have generated new uncertainty regarding the comparative effectiveness of these treatment options. OBJECTIVE To compare long-term survival after partial vs radical nephrectomy among a population-based patient cohort whose treatment reflects contemporary surgical practice. DESIGN, SETTING, AND PATIENTS We performed a retrospective cohort study of Medicare beneficiaries with clinical stage T1a kidney cancer treated with partial or radical nephrectomy from 1992 through 2007. Using an instrumental variable approach to account for measured and unmeasured differences between treatment groups, we fit a 2-stage residual inclusion model to estimate the treatment effect of partial nephrectomy on long-term survival. MAIN OUTCOME MEASURES Overall and kidney cancer-specific survival. RESULTS Among 7138 Medicare beneficiaries with early-stage kidney cancer, we identified 1925 patients (27.0%) treated with partial nephrectomy and 5213 patients (73.0%) treated with radical nephrectomy. During a median follow-up of 62 months, 487 (25.3%) and 2164 (41.5%) patients died following partial or radical nephrectomy, respectively. Kidney cancer was the cause of death for 37 patients (1.9%) treated with partial nephrectomy, and 222 patients (4.3%) treated with radical nephrectomy. Patients treated with partial nephrectomy had a significantly lower risk of death (hazard ratio [HR], 0.54; 95% CI, 0.34-0.85). This corresponded with a predicted survival increase with partial nephrectomy of 5.6 (95% CI, 1.9-9.3), 11.8 (95% CI, 3.9-19.7), and 15.5 (95% CI, 5.0-26.0) percentage points at 2, 5, and 8 years posttreatment (P < .001). No difference was noted in kidney cancer-specific survival (HR, 0.82; 95% CI, 0.19-3.49). CONCLUSION Among Medicare beneficiaries with early-stage kidney cancer who were candidates for either surgery, treatment with partial rather than radical nephrectomy was associated with improved survival.

Why have physical activity levels declined among Chinese adults? Findings from the 1991-2006 China health and nutrition surveys

Between 1991 and 2006, average weekly physical activity among adults in China fell by 32%. This paper discusses why total and occupational physical activity levels have fallen, and models the association between the rapid decline and various dimensions of exogenous community urbanization. We hypothesize that a) physical activity levels are negatively associated with urbanization; b) urbanization domains that affect job functions and opportunities will contribute most to changes in physical activity levels; and c) these urbanization domains will be more strongly associated for men than for women because home activities account for a larger proportion of physical activity for women. To test these hypotheses, we used longitudinal data from individuals aged 18-55 in the 1991-2006 China Health and Nutrition Surveys. We find that physical activity declines were strongly associated with greater availability of higher educational institutions, housing infrastructure, sanitation improvements and the economic wellbeing of the community in which people function. These urbanization factors predict more than four-fifths of the decline in occupational physical activity over the 1991-2006 period for men and nearly two-thirds of the decline for women. They are also associated with 57% of the decline in total physical activity for men and 40% of the decline for women. Intervention strategies to promote physical activity in the workplace, at home, for transit and via exercise should be considered a major health priority in China.

How Hospital Ownership Affects Access to Care for the Uninsured

This article addresses the effect of hospital ownership on the delivery of service to uninsured patients. It compares the volume of uninsured patients treated in for-profit and nonprofit hospitals by regarding hospital ownership and service as endogenous. Instrumental variable estimates are used to predict the percentage of patients who are uninsured, controlling for hospital ownership and service. The study shows that when for-profit and nonprofit hospitals are located in the same area, they serve an equivalent number of uninsured patients, but for-profit hospitals indirectly avoid the uninsured by locating more often in better-insured areas.

Controlling for the endogeneity of peer substance use on adolescent alcohol and tobacco use

This study examines whether the effects of peer substance use on adolescent alcohol and tobacco use are due to endogeneity of adolescents selecting their peer group. We analyzed data collected for a longitudinal analysis of a drug-use prevention programme for upper elementary school students. We used a two-step probit regression to control for the potentially endogenous explanatory variable peer substance use. Rigorous tests of endogeneity and the validity of the instrumental variables showed that controlling for the endogeneity of peer substance use to reduce bias is not worth the reduction in mean squared error in these data. Peer substance use has a positive and significant effect on adolescent substance use for both drinking and smoking. These results imply that peer influence is empirically more important than peer selection (endogeneity) in our sample of adolescents in grades 6-9. Living in a single-parent family was by far the strongest predictor of adolescent drinking and smoking.

Weight and wages: fat versus lean paychecks

Past empirical work has shown a negative relationship between the body mass index (BMI) and wages in most cases. We improve on this work by allowing the marginal effect of non-linear BMI groups to vary by gender, age, and type of interpersonal relationships required in each occupation. We use the National Longitudinal Survey of Youth 1979 (1982-1998). We find that the often-reported negative relationship between the BMI and wages is larger in occupations requiring interpersonal skills with presumably more social interactions. Also, the wage penalty increases as the respondents get older beyond their mid-twenties. We show that being overweight and obese penalizes the probability of employment across all race-gender subgroups except black women and men. Our results for the obesity-wage association can be explained by either consumers or employers having distaste for obese workers.

Choosing Between and Interpreting the Heckit and Two-Part Models for Corner Solutions

This article addresses certain poor practices commonly seen in the applied health economics literature regarding the use of the Heckit and the two-part model. First, many articles invoke the Heckit to solve a supposed selection problem associated with masses of zero values in continuous variables, despite the fact that it has been shown elsewhere that no such selection problem exists when modeling observed actual, as opposed to latent potential, outcomes. Second, many applications incorrectly formulate the marginal effect tests in the Heckit and two-part model, thus undermining central conclusions. Finally, many researchers use a t-test of the inverse Mills coefficient to choose between the Heckit and two-part models despite its poor performace; we propose instead an adapted empirical mean square error test.

Adverse Selection, Bequests, Crowding Out, and Private Demand for Insurance: Evidence from the Long-term Care Insurance Market

Adverse selection, moral hazard, and crowding out by public insurance have all been proposed as theoretical reasons for why the market for private long-term care insurance has been slow to evolve in the U.S. Using national samples of the elderly and near elderly, this study investigates which is most important. The data contain direct measures of risk aversion, expectations of future nursing home use and living to old age, and the bequest motive. For both groups, we find evidence of adverse selection, and, for the elderly, crowding out of private long-term care insurance by Medicaid. However, we do not find that demand for such insurance is motivated either by bequest or exchange motives.