betareg (version 3.2-1)

LossAversion: (No) Myopic Loss Aversion in Adolescents

Description

Data from a behavioral economics experiment assessing the extent of myopic loss aversion among adolescents (mostly aged 11 to 19).

Usage

data("LossAversion", package = "betareg")

Format

A data frame containing 570 observations on 7 variables.

invest

numeric. Average proportion of tokens invested across all 9 rounds.

gender

factor. Gender of the player (or team of players).

male

factor. Was (at least one of) the player(s) male (in the team)?

age

numeric. Age in years (averaged for teams).

treatment

factor. Type of treatment: long vs. short.

grade

factor. School grades: 6-8 (11-14 years) vs. 10-12 (15-18 years).

arrangement

factor. Is the player a single player or team of two?

Details

Myopic loss aversion is a phenomenon in behavioral economics, where individuals do not behave economically rationally when making short-term decisions under uncertainty. Example: In lotteries with positive expected payouts investments are lower than the maximum possible (loss aversion). This effect is enhanced for short-term investments (myopia or short-sightedness).

The data in LossAversion were collected by Matthias Sutter and Daniela Glätzle-Rützler (Universität Innsbruck) in an experiment with high-school students in Tyrol, Austria (Schwaz and Innsbruck). The students could invest X tokens (0-100) in each of 9 rounds in a lottery. The payouts were 100 + 2.5 * X tokens with probability 1/3 and 100 - X tokens with probability 2/3. Thus, the expected payouts were 100 + 1/6 * X tokens. Depending on the treatment in the experiment, the investments could either be modified in each round (treatment: "short") or only in round 1, 4, 7 (treatment "long"). Decisions were either made alone or in teams of two. The tokens were converted to monetary payouts using a conversion of EUR 0.5 per 100 tokens for lower grades (Unterstufe, 6-8) or EUR 1.0 per 100 tokens for upper grades (Oberstufe, 10-12).

From the myopic loss aversion literature (on adults) one would expect that the investments of the players (either single players or teams of two) would depend on all factors: Investments should be

• lower in the short treatment (which would indicate myopia),

• higher for teams (indicating a reduction in loss aversion),

• higher for (teams with) male players,

• increase with age/grade.

See Glätzle-Rützler et al. (2015) for more details and references to the literature. In their original analysis, the investments are analyzes using a panel structure (i.e., 9 separate investments for each team). Here, the data are averaged across rounds for each player, leading to qualitatively similar results. The full data along with replication materials are available in the Harvard Dataverse.

Kosmidis and Zeileis (2024) revisit the data using extended-support beta mixture (XBX) regression, which can simultaneously capture both the probability of rational behavior and the mean amount of loss aversion.

References

Glätzle-Rützler D, Sutter M, Zeileis A (2015). No Myopic Loss Aversion in Adolescents? -- An Experimental Note. Journal of Economic Behavior & Organization, 111, 169--176. tools:::Rd_expr_doi("10.1016/j.jebo.2014.12.021")

Kosmidis I, Zeileis A (2024). Extended-Support Beta Regression for [0, 1] Responses. 2409.07233, arXiv.org E-Print Archive. tools:::Rd_expr_doi("10.48550/arXiv.2409.07233")

See Also

betareg

Examples

options(digits = 4)

## data and add ad-hoc scaling (a la Smithson & Verkuilen)
data("LossAversion", package = "betareg")
LossAversion <- transform(LossAversion,
  invests = (invest * (nrow(LossAversion) - 1) + 0.5)/nrow(LossAversion))


## models: normal (with constant variance), beta, extended-support beta mixture
la_n <- lm(invest ~ grade * (arrangement + age) + male, data = LossAversion)
summary(la_n)

# \donttest{
la_b <- betareg(invests ~ grade * (arrangement + age) + male | arrangement + male + grade,
  data = LossAversion)
summary(la_b)

la_xbx <- betareg(invest ~ grade * (arrangement + age) + male | arrangement + male + grade,
  data = LossAversion)
summary(la_xbx)

## coefficients in XBX are typically somewhat shrunken compared to beta
cbind(XBX = coef(la_xbx), Beta = c(coef(la_b), NA))


## predictions on subset: (at least one) male players, higher grades, around age 16
la <- subset(LossAversion, male == "yes" & grade == "10-12" & age >= 15 &  age <= 17)
la_nd <- data.frame(arrangement = c("single", "team"), male = "yes", age = 16, grade = "10-12")

## empirical vs fitted E(Y)
la_nd$mean_emp <- aggregate(invest ~ arrangement, data = la, FUN = mean)$invest 
la_nd$mean_n <- predict(la_n, la_nd)
la_nd$mean_b <- predict(la_b, la_nd)
la_nd$mean_xbx <- predict(la_xbx, la_nd)
la_nd

## visualization: all means rather similar
la_mod <- c("Emp", "N", "B", "XBX")
la_col <- unname(palette.colors())[c(1, 2, 4, 4)]
la_lty <- c(1, 5, 5, 1)
matplot(la_nd[, paste0("mean_", tolower(la_mod))], type = "l",
  col = la_col, lty = la_lty, lwd = 2, ylab = "E(Y)", main = "E(Y)", xaxt = "n")
axis(1, at = 1:2, labels = la_nd$arrangement)
legend("topleft", la_mod, col = la_col, lty = la_lty, lwd = 2, bty = "n")


## empirical vs. fitted P(Y > 0.95)
la_nd$prob_emp <- aggregate(invest >= 0.95 ~ arrangement, data = la, FUN = mean)$invest
la_nd$prob_n <- pnorm(0.95, mean = la_nd$mean_n, sd = summary(la_n)$sigma, lower.tail = FALSE)
la_nd$prob_b <- 1 - predict(la_b, la_nd, type = "probability", at = 0.95)
la_nd$prob_xbx <- 1 - predict(la_xbx, la_nd, type = "probability", at = 0.95)
la_nd[, -(5:8)]

## visualization: only XBX works well
matplot(la_nd[, paste0("prob_", tolower(la_mod))], type = "l",
  col = la_col, lty = la_lty, lwd = 2, ylab = "P(Y > 0.95)", main = "P(Y > 0.95)", xaxt = "n")
axis(1, at = 1:2, labels = la_nd$arrangement)
legend("topleft", la_mod, col = la_col, lty = la_lty, lwd = 2, bty = "n")
# }