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ItemCharitable Giving in the Laboratory: Advantages of the Piecewise Linear Public Goods GameMenietti, M ; Recalde, M ; Vesterlund, L ; Scharf, K ; Tonin, M (The MIT Press, 2018)The vast majority of US households make significant charitable contributions. When examining the effectiveness of the mechanisms fundraisers use to solicit such funds, it is often essential that researchers elicit or control the donor’s return from giving. While much can be gained from examining data on actual donations, insights on giving increasingly result from laboratory studies. An advantage of the laboratory is that it permits control of the donor’s return from giving and thus facilitates the identification of donor motives as well as their responses to different fundraising or solicitation strategies (see Vesterlund 2016 for a review).
ItemInverse test confidence intervals for turning-points: A demonstration with higher order polynomialsLye, JN ; Hirschberg, JG ; Terrell, D ; Millimet, D (Emerald Publishing, 2012)In this chapter we demonstrate the construction of inverse test confidence intervals for the turning points in estimated nonlinear relationships by the use of the marginal or first derivative function. First, we outline the inverse test confidence interval approach. Then we examine the relationship between the traditional confidence intervals based on the Wald test for the turning-points for a cubic, a quartic and fractional polynomials estimated via regression analysis and the inverse test intervals. We show that the confidence interval plots of the marginal function can be used to estimate confidence intervals for the turning points that are equivalent to the inverse test. We also provide a method for the interpretation of the confidence intervals for the second derivative function to draw inferences for the characteristics of the turning-point. This method is applied to the examination of the turning points found when estimating a quartic and a fractional polynomial from data used for the estimation of an Environmental Kuznets Curve. The Stata do files used to generate these examples are listed in the appendix along with the data.