A search-theoretic explanation for the negative correlation between labor income and impatience

Lawrance (1991) has shown, through the estimation of consumption Euler equations, that subjective rates of impatience (time preference) in the U.S. are three to Öve percentage points higher for households with lower average labor incomes than for those with higher labor income. From a theoretical perspective, the sign of this correlation in a job-search model seems at Örst to be undetermined, since more impatient workers tend to accept wage o§ers that less impatient workers would not, thereby remaining less time unemployed. The main result of this paper is showing that, regardless of the existence of e§ects of opposite sign, and independently of the particular speciÖcations of the givens of the model, less impatient workers always end up, in the long run, with a higher average income. The result is based on the (unique) invariant Markov distribution of wages associated with the dynamic optimization problem solved by the consumers. An example is provided to illustrate the method.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

In this paper we revisit the relationship between the equity and the forward premium puzzles. We construct return-based stochastic discount factors under very mild assumptions and check whether they price correctly the equity and the foreign currency risk premia. We avoid log-linearizations by using moments restrictions associated with euler equations to test the capacity of our return-based stochastic discount factors to price returns on the relevant assets. Our main finding is that a pricing kernel constructed only using information on American domestic assets accounts for both domestic and international stylized facts that escape consumption based models. In particular, we fail to reject the null hypothesis that the foreign currency risk premium has zero price when the instrument is the own current value of the forward premium.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

We build a pricing kernel using only US domestic assets data and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our stochastic discount factor as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by pricing Lustig and Verdelhan (2007)'s foreign currency portfolios. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

Using information on US domestic financial data only, we build a stochastic discount factor—SDF— and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our SDF as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by pricing Lustig and Verdelhan (2007)’s foreign currency portfolios. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

Using information on US domestic financial data only, we build a stochastic discount factor—SDF— and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our SDF as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by comparing this out-of-sample results with the one obtained performing an in-sample exercise, where the return-based SDF captures sources of risk of a representative set of developed and emerging economies government bonds. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.

The forward and the equity-premium puzzles: a straightforward test of whether they are two symptoms of the same illness

We build a stochastic discount factor—SDF— using information on US domestic financial data only, and provide evidence that it accounts for foreign markets stylized facts that escape SDF’s generated by consumption based models. By interpreting our SDF as the projection of the pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. In our tests, we address predictability, a defining feature of the Forward Premium Puzzle—FPP— by using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations both in the equity and the foreign markets.

A note on the forward and the equity-premium puzzles: two symptoms of the same illness?

We build a stochastic discount factor—SDF— using information on US domestic financial data only, and provide evidence that it accounts for foreign markets stylized facts that escape SDF’s generated by consumption based models. By interpreting our SDF as the projection of the pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. In our tests, we address predictability, a defining feature of the Forward Premium Puzzle—FPP— by using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations both in the equity and the foreign markets.

Testing consumption optimality using aggregate data

The objective of this paper is to test for optimality of consumption decisions at the aggregate level (representative consumer) taking into account popular deviations from the canonical CRRA utility model rule of thumb and habit. First, we show that rule-of-thumb behavior in consumption is observational equivalent to behavior obtained by the optimizing model of King, Plosser and Rebelo (Journal of Monetary Economics, 1988), casting doubt on how reliable standard rule-of-thumb tests are. Second, although Carroll (2001) and Weber (2002) have criticized the linearization and testing of euler equations for consumption, we provide a deeper critique directly applicable to current rule-of-thumb tests. Third, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Asset-Pricing Equation, since the latter is a linear function of individual returns. Fourth, aggregation of the nonlinear euler equation forms the basis of a novel test of deviations from the canonical CRRA model of consumption in the presence of rule-of-thumb and habit behavior. We estimated 48 euler equations using GMM, with encouraging results vis-a-vis the optimality of consumption decisions. At the 5% level, we only rejected optimality twice out of 48 times. Empirical-test results show that we can still rely on the canonical CRRA model so prevalent in macroeconomics: out of 24 regressions, we found the rule-of-thumb parameter to be statistically signi cant at the 5% level only twice, and the habit ƴ parameter to be statistically signi cant on four occasions. The main message of this paper is that proper return aggregation is critical to study intertemporal substitution in a representative-agent framework. In this case, we fi nd little evidence of lack of optimality in consumption decisions, and deviations of the CRRA utility model along the lines of rule-of-thumb behavior and habit in preferences represent the exception, not the rule.

Testing consumption optimality using aggregate data

This paper tests the optimality of consumption decisions at the aggregate level taking into account popular deviations from the canonical constant-relative-risk-aversion (CRRA) utility function model-rule of thumb and habit. First, based on the critique in Carroll (2001) and Weber (2002) of the linearization and testing strategies using euler equations for consumption, we provide extensive empirical evidence of their inappropriateness - a drawback for standard rule- of-thumb tests. Second, we propose a novel approach to test for consumption optimality in this context: nonlinear estimation coupled with return aggregation, where rule-of-thumb behavior and habit are special cases of an all encompassing model. We estimated 48 euler equations using GMM. At the 5% level, we only rejected optimality twice out of 48 times. Moreover, out of 24 regressions, we found the rule-of-thumb parameter to be statistically significant only twice. Hence, lack of optimality in consumption decisions represent the exception, not the rule. Finally, we found the habit parameter to be statistically significant on four occasions out of 24.

Do equity and foreign currency risk premiums display common patterns?

In da Costa et al. (2006) we have shown how a same pricing kernel can account for the excess returns of the S&:P500 over the US short term bond and of the uncovered over the covered trading of foreign government bonds. In this paper we estimate and test the overidentifying restrictiom; of Euler equations associated with "ix different versions of the Consumption Capital Asset Pricing I\Iodel. Our main finding is that the same (however often unreasonable) values for the parameters are estimated for ali models in both nmrkets. In most cases, the rejections or otherwise of overidentifying restrictions occurs for the two markets, suggesting that success and failure stories for the equity premium repeat themselves in foreign exchange markets. Our results corroborate the findings in da Costa et al. (2006) that indicate a strong similarity between the behavior of excess returns in the two markets when modeled as risk premiums, providing empirical grounds to believe that the proposed preference-based solutions to puzzles in domestic financiaI markets can certainly shed light on the Forward Premium Puzzle.

A equação de Euler e a IS: estimações para o Brasil

Neste artigo estudamos a relação entre a taxa de juros e o hiato do produto no Brasil através da estimação de modelos Novo-Keynesianos. Para tanto, estimamos os modelos por três métodos: (1) método generalizados dos momentos, (2) máxima verossimilhança utilizando dados de expectativa divulgados pelo Banco Central do Brasil e (3) máxima verossimilhança utilizando variáveis de expectativa estimadas por um modelo VAR. As conclusões são altamente dependentes do método de estimação. Ao utilizar (1), os resultados indicam uma relação espúria entre a taxa de juros real e o hiato. Entretanto, as conclusões originadas de (2) indicam que somente o hiato defasado seria uma variável relevante para a nossa especificação. Ao estimar o modelo por (3), as estimativas corroboram os resultados obtidos com o método generalizados dos momentos.

A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

Testing the optimality of aggregate consumption decisions: is there rule-of-thumb behavior?

Consumption is an important macroeconomic aggregate, being about 70% of GNP. Finding sub-optimal behavior in consumption decisions casts a serious doubt on whether optimizing behavior is applicable on an economy-wide scale, which, in turn, challenge whether it is applicable at all. This paper has several contributions to the literature on consumption optimality. First, we provide a new result on the basic rule-of-thumb regression, showing that it is observational equivalent to the one obtained in a well known optimizing real-business-cycle model. Second, for rule-of-thumb tests based on the Asset-Pricing Equation, we show that the omission of the higher-order term in the log-linear approximation yields inconsistent estimates when lagged observables are used as instruments. However, these are exactly the instruments that have been traditionally used in this literature. Third, we show that nonlinear estimation of a system of N Asset-Pricing Equations can be done efficiently even if the number of asset returns (N) is high vis-a-vis the number of time-series observations (T). We argue that efficiency can be restored by aggregating returns into a single measure that fully captures intertemporal substitution. Indeed, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Pricing Equation, since the latter is a linear function of individual returns. This forms the basis of a new test of rule-of-thumb behavior, which can be viewed as testing for the importance of rule-of-thumb consumers when the optimizing agent holds an equally-weighted portfolio or a weighted portfolio of traded assets. Using our setup, we find no signs of either rule-of-thumb behavior for U.S. consumers or of habit-formation in consumption decisions in econometric tests. Indeed, we show that the simple representative agent model with a CRRA utility is able to explain the time series data on consumption and aggregate returns. There, the intertemporal discount factor is significant and ranges from 0.956 to 0.969 while the relative risk-aversion coefficient is precisely estimated ranging from 0.829 to 1.126. There is no evidence of rejection in over-identifying-restriction tests.

A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás