The Cross-Euler Equation Approach to testing for the Liquidity Constraint: Evidence from Macro and Micro Data

In this paper, we propose a new empirical method in testing for the existence of liquidity constraint utilizing the concept of Cross-Euler equation. The Cross-Euler equation represents the optimal consumption pattern of a good in the current period to another good at a future period. It can be interpreted as the composite optimal condition that embeds both intertemporal and intratemporal optimal consumption relationships into one 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. We adopt standard two goods version of Life-Cycle model to study the consumption behavior of necessity goods and luxury goods. First, based on the aggregate data, the test rejects the null of no liquidity constraints for necessity goods, while accpeting the null for luxury goods. Since, by construction, large share of necessity goods are consumed by poor households, it is possible to interpret the results as evidence that poorer households are likely to be liquidity constrainted. Next, we construct synthetic panel data from the Consumer Expenditure Survey where households have been classified to cohorts by their ages and educational attainments. Again, taking the Cross-Euler equation approach in testing for the liquidity constraints, the test rejected the null of no liquidity constraint for low-education cohorts, while accepting the null for high-education cohorts. Taking an education level as a proxy for permanent income, the test results were consistent with the view that poorer agents are more likely to be liquidity constrained.