In my dissertation, I propose the empirical method in testing the Life-Cycle/Permanent Income Model utilizing the concept of Cross-Euler equation. The Cross-Euler equation has an advantage over the standard Euler equation, in the sense that the cointegrating relationship is maintained even when the liquidity constraint is present in the agent's decision problem. Thus, by comparing the preference parameter estimates from the Cross-Euler equation to those from the standard Euler equation, it is possible to detect the existence of a liquidity constraint.
In Part 1 of my dissertation, I disaggregate the U.S. non-durable consumption expenditure into domestic and imported portions allowing for the additive-separable preference towards both goods. 1 compare parameter estimates from Cross-Euler and standard Euler equations to test for the misspecification in the intertemporal consumption pattern. As for the empirical result, the LR type test rejects the specification of the Euler equation for domestic goods, but does not reject it for imported non-durable goods. Since the model in Part I does not take into account for the aggregation problem over heterogeneous agents, it is not clear whether the misspecification in the Euler equation was caused by the liquidity constraint or not.
In Part II of my dissertation, 1 disaggregate the U.S. non-durable consumption expenditure into necessity and luxury goods expenditure. Since poorer agents are more likely to be constrained by the liquidity constraint, it is expected that the Euler equation will be violated in the case of necessity goods. This prediction is indeed confirmed by the empirical results. The results can be thought of as empirical evidence from the aggregated time series data that supports the existence of liquidity constraints in the U.S. economy. Next, in order to overcome the aggregation problem, the synthetic panel was constructed from the series of Consumer Expenditure Survey from 1984 to 1998. Again using the Cross-Euler equation approach, the test rejects the specification for low-education cohorts frequently, while accepting it for high-education cohorts. Taking the education level as a proxy for lifetime income, the test results were consistent with the view that poorer agents are more likely to be liquidity constrained.