A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

Exogenous expectations on endogenous uncertainty: recursive equilibrium and survival

This paper analyses general equilibrium models with finite heterogeneous agents having exogenous expectations on endogenous uncertainty. It is shown that there exists a recursive equilibrium with the state space consisting of the past aggregate portfolio distribution and the current state of the nature and that it implements the sequential equilibrium. We establish conditions under which the recursive equilibrium is continuous. Moreover, we use the continuous recursive relation of the aggregate variables to prove that if the economy has two types of agents, the one who commits persistent mistakes on the expectation rules of the future endogenous variables is driven out of the market by the others with correct anticipations of the variables, that is, the rational expectations agents.

Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options

Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. And market expectations on financial variables may influence macroeconomic policy decisions. It can be useful also for corporate and financial institutions decision making. This paper uses the Liu et all (2007) approach to estimate the option-implied Risk-neutral densities from the Brazilian Real/US Dollar exchange rate distribution. We then compare the RND with actual exchange rates, on a monthly basis, in order to estimate the relative risk-aversion of investors and also obtain a Real-world density for the exchange rate. We are the first to calculate relative risk-aversion and the option-implied Real World Density for an emerging market currency. Our empirical application uses a sample of Brazilian Real/US Dollar options traded at BM&F-Bovespa from 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distribution and then the real-world density is obtained by means of the Liu et al. (2007) parametric risktransformations. The relative risk aversion is calculated for the full sample. Our estimated value of the relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this parameter for the Brazilian Economy, such as Araújo (2005) and Issler and Piqueira (2000). Our out-of-sample evaluation results showed that the RND has some ability to forecast the Brazilian Real exchange rate. Abe et all (2007) found also mixed results in the out-of-sample analysis of the RND forecast ability for exchange rate options. However, when we incorporate the risk aversion into RND in order to obtain a Real-world density, the out-of-sample performance improves substantially, with satisfactory results in both Kolmogorov and Berkowitz tests. Therefore, we would suggest not using the “pure” RND, but rather taking into account risk aversion in order to forecast the Brazilian Real exchange rate.

Uncertainty of aid inflows and the growth relationship

This paper contributes to the literature on aid and economic growth. We posit that it is not the levei of aid flows per se but the stability of such flows that determines the impact of aid on economic growth. Three measures of aid instability are employed. One is a simple deviation from trend, and measures overall instability. The other measures are based on auto-regressive estimates to capture deviations from an expected trend. These measures are intended to proxy for uncertainty in aid receipts. We posit that such uncertainty will influence the relationship between aid and investment and how recipient governments respond to aid, and will therefore affect how aid impacts on growth. We estimate a standard cross-country growth regression including the leveI of aid, and find aid to be insignificant (in line with other results in the literature). We then introduce measures of instability. Aid remains insignificant when we account for overall instability. However, when we account for uncertainty (which is negative and significant), we find that aid has a significant positive effect on growth. We conduct stability tests that show that the significance of aid is largely due to its effect on the volume of investment. The finding that uncertainty of aid receipts reduces the effectiveness of aid is robust. When we control for this, aid appears to have a significant positive influence on growth. When the regression is estimated for the sub-sample of African countries these findings hold, although the effectiveness of aid appears weaker than for the full sample.

The effects of uncertainty about the timing of deals on consumer behavior

I examine the effects of uncertainty about the timing of de aIs (i.e. temporary price cuts or sales) on consumer behavior in a dynamic inventory model of consumer choice. I derive implications for purchase behavior and test them empirically, using two years of scanner data for soft drinks. I fmd that loyal consumers' decisions, both about the allocation of their purchases over time and the quantity to be purchased in a particular deal, are affected by the uncertainty about the timing of the deal for the product. Loyal consumers buy a higher fraction of their overall purchases during de ais as the uncertainty decreases. This effect increases with an increase in the product' s share of a given consumer' s purchase in the same category or if the consumer stockpiles (i.e., is a shopper). During a particular deal, loyal shoppers increase the quantity they purchase the more time that has passed since the previous de aI, and the higher the uncertainty about the deals' timing. For the non-Ioyal consumers these effects are not significant. These results hold for products that are frequently purchased, like soft-drinks and yogurt, but do not hold for less frequentIy purchased products, such as laundry detergents. The fmdings suggest that manufacturers and retailers should incorporate the effects of deals' timing on consumers' purchase' decisions when deriving optimal pricing strategies.

Especulative (sic) attack on exchange rate target zone regime : the uncertainty case

We present a continuous time target zone model of speculative attacks. Contrary to most of the literature that considers the certainty case, i.e., agents know for sure the Central Bank behavior in the future, we build uncertainty into the madel in two different ways. First, we consider the case in whicb the leveI of reserves at which the central bank lets the regime collapse is uncertain. Alternatively, we ana1ize the case in which, with some probability, the government may cbange its policy reducing the initially positive trend in domestic credito In both cases, contrary to the case of a fixed exchange rate regime, speculators face a cost of launching a tentative attack that may not succeed. Such cost induces a delay and may even prevent its occurrence. At the time of the tentative attack, the exchange rate moves either discretely up, if the attack succeeds, or down, if it fails. The remlts are consistent with the fact that, typically, an attack involves substantial profits and losses for the speculators. In particular, if agents believed that the government will control fiscal imbalances in the future, or alternatively, if they believe the trend in domestic credit to be temporary, the attack is postponed even in the presence of a signal of an imminent collapse. Finally, we aIso show that the timing of a speculative attack increases with the width of the target zone.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .

Labor supply, risk aversion and economic refrom in China

Economic reform in China has created a small, but fast-growing private sector that has spurred rapid productivity growth. Growth of the private sector is predicated upon continued labor movements away from state-run industries and into private firms. This paper presents a theory of labor market sectoral choice demonstrating that three factors determine private sector labor supply-the difference in wages between the state and private sectors, private sector wage risk and risk aversion. Estimation of the model using survey data provides strong support for the theory. We find that the riskiness of private sector earnings has a greater effect in discouraging workers from taking jobs in private firms than the wage premi um has in attracting workers.

Asymmetric auctions and risk aversion within independent private valoues

We study tournaments with many ex-ante asymmetric (heterogeneous) contestants as an independent-private-values all-pay auction. The asymmetry is either with respect to the distribution of valuations for the prize or the risk preferences. By characterizing equilibria in tnonotone strategies we show that tournaments \:vith man~y heterogenous contestants are qualitatively distinct. First, with two (or many ex-ante identical) participants, a contestant always exerts some effort with positive probability. In contrast, with many asymmetric participants, one 1night not exert any effort at all, even if there is a positive probability that he has the highest valuation among ali. Second, in tournan1ents with t'wo (o r n1any ex-ante h01nogenous) contestants, equilibrium effort densities are decreasing. This prediction is at odds with experimental evidence that shows the empírica! density might be increasing at high effort levels. V\.lith rnany heterogeneous contestants, however. the increasing bid density is consistent with an equilibrium behavior.

Asymetric price adjustment and loss aversion

Ajuste assimétrico de preço é observado em diversos mercados, notavelmente varejo de gasolina: um aumento de custo é passado para os consumidores mais rápido do que uma redução. Eu desenvolvo um modelo de busca dos consumidores que gera essa predição sob aversão à perda. Uma fração dos consumidores ignora os preços no mercado e pode adquirir informação a um custo, o que permite que as firmas tenham lucro com dispersão de preços. Ajuste assimétrico de preço emerge se os consumidores são aversos a perdas em relação a um preço de referência. Custos mais altos tornam os consumidores mais dispostos a procurar, mas também diminui as chances de encontrar preços baixos, gerando uma relação custo-preço convexa.