Betting on odds on Favorites as an Optimal Choice in Cumulative Prospect Theory

It is well known that the parametric version of Cumulative Prospect theory (CPT) proposed by Kahneman and Tversky (1979) and Tversky and Kahneman (1992) (KT) can explain gambling at actuarially unfair odds on long shots due to the over weighting of small probabilities. However betting on odds favorites appears problematic. We demonstrate using a parametric model of Cumulative Prospect Theory that nests that of Kahneman and Tversky that if agents are risk averse enough over gains and risk-seeking enough over losses then they will gamble on odds on chances at actuarially unfair odds even when there is no probability distortion. This previously unappreciated fact is interesting since many experimental results suggest that some respondents are very risk averse over gains.

Some implications of a quartic loss function

Motivated by a central banker with a symmetric but non-quadratic loss function, we show in this note that the approximations of two plausible loss functions of this type will include a quartic term. For skewed distributions, we establish that such a loss function implies a systematic inflation bias even when the bank targets the natural rate. Moreover, we show that the weights in an optimal combination of forecasts will differ from that under quadratic loss. We illustrate these differences using simulated data and data from the Livingston Surveys of Professional Forecasters.

Testing for central bank independence and inflation using the wild bootstrap

This paper reviews the relationship between Central Bank Independence (CBI) and Inflation both in high income economies (as proposed in Campillo and Miron 1997 and Temple 1998) and in developing countries (as proposed in Brumm 2006)1 when a variety of Heteroskedasticity Consistent Covariance Matrix Estimators as well as the wild bootstrap are employed.Inflation Central bank independence Wild bootstrap

The Central Bank Inflation Bias in the Presence of Asymmetric Preferences and Non-Normal Shocks

We investigate the nature of the inflation bias in a model that exhibits asymmetries in preferences and non–normality in shocks but simplifies to the classic Barro-Gordon problem as a special case. The inflation bias is shown to depend on the trade-off between preference, structural and the scale and shape parameters of the model.

NONLINEAR PPP UNDER THE GOLD STANDARD

Hegwood and Papell (2002) conclude on the basis of analysis in a linear framework that long-run purchasing power parity (PPP)\ does not hold for sixteen real exchange rate series, analyzed in Diebold, Husted, and Rush (1991) for the period 1792-1913, under the Gold Standard. Rather, purchasing power parity deviations are mean-reverting to a changing equilibrium -a quasi PPP (QPPP) theory. We analyze the real exchange rate adjustment mechanism for their data set assuming a nonlinear adjustment process allowing for both a constant and a mean shifting equilibrium. Our results confirm that real exchange rates at that time were stationary, symmetric, nonlinear processes that revert to a non-constant equilibrium rate. Speeds of adjustment were much quicker when breaks were allowed.Purchasing Power Parity, ESTAR, Bootstrapping.

THE PROCESS FOLLOWED BY PPP DATA. ON THE PROPERTIES OF LINEARITY TESTS

Recent research has reported the lack of correct size in stationarity test for PPP deviations within a linear framework. However, theoretically well motivated nonlinear models, such as the ESTAR, appear to parsimoniously fit the PPP data and provide an explanation for the PPP ¿puzzle¿. Employing Monte Carlo experiments we analyze the size and power of the nonlinear tests against a variety of nonstationary hypotheses. We also fit the ESTAR model to data from high inflation economies. Our results provide further support for ESTAR specification.ESTAR, Real Exchange Rate, Size, Linearity Test.

TEMPORAL AGGREGATION OF AN ESTAR PROCESS: SOME IMPLICATIONS FOR PURCHASING POWER PARITY ADJUSTMENT

Nonlinear models of deviations from PPP have recently provided an important, theoretically well motivated, contribution to the PPP puzzle. Most of these studies use temporally aggregated data to empirically estimate the nonlinear models. As noted by Taylor (2001), if the true DGP is nonlinear, the temporally aggregated data could exhibit misleading properties regarding the adjustment speeds. We examine the effects of different levels of temporal aggregation on\ estimates of ESTAR models of real exchange rates. Our Monte Carlo results show that temporal aggregation does not imply the disappearance of nonlinearity and that adjustment speeds are significantly slower in temporally aggregated data than in the true DGP. Furthermore, the autoregressive structure of some monthly ESTAR estimates found in the literature is suggestive that adjustment speeds are even faster than implied by the monthly estimates.ESTAR, Real Exchange Rate, Purchasing Power Parity, Aggregation.

A NEW ANALYSIS OF THE DETERMINANTS OF THE REAL DOLLAR-STERLING EXCHANGE RATE: 1871-1994

Nonlinear models of deviations from PPP have recently provided an important, theoretically well motivated, contribution to the PPP puzzle. In recent work the equilibrium level has been modeled either as constant or as time varying with very similar statistical fits and very different economic implications. The high persistence of both PPP deviations and the proxy variables for the equilibrium real rate might create a problem of spurious coefficient significance. This paper investigates the possibility of spurious regression within nonlinear models of PPP. Monte Carlo experiments show that standard critical values are not appropriate in such a context. To illustrate we consider the real Dollar-Sterling exchange rate over the period 1871-1994. Due to many exchange rate regime changes over the sample period we employ a Bootstrap methodology that preserves the original structure of the estimated residuals and obtain new critical values of the coefficient estimates. A nonlinear (ESTAR) process with a time varying equilibrium proxied by relative wealth and relative income per capita seems to parsimoniously fit the data. Our results provide further evidence for the nonlinear model with a shifting equilibrium and the implied speed of adjustment is found to be substantially faster than previously reported in the literature.ESTAR, Purchasing Power Parity, Bootstrapping

Cumulative prospect theory and gambling

Whilst Cumulative Prospect theory (CPT) provides an explanation of gambling on longshots at actuarially unfair odds, it cannot explain why people might bet on more favoured outcomes. This paper shows that this is explicable if the degree of loss aversion experienced by the agent is reduced for small-stake gambles (as a proportion of wealth), and probability distortions are greater over losses than gains. If the utility or value function is assumed to be bounded, the degree of loss aversion assumed by Kahneman and Tversky leads to absurd predictions, reminiscent of those pointed out by Rabin (2000), of refusal to accept infinite gain bets at low probabilities. Boundedness of the value function in CPT implies that the indifference curve between expected-return and win-probability will typically exhibit both an asymptote (implying rejection of an infinite gain bet) and a minimum at low probabilities, as the shape of the value function dominates the probability weighting function. Also the high probability section of the indifference curve will exhibit a maximum. These implications are consistent with outcomes observed in gambling markets.