Estimating Euler equations

In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of preference parameters. When utility is isoelastic and a sample covering a long time period is available, consistent estimates are obtained from the loglinearized Euler equation when the innovations to the conditional variance of consumption growth are uncorrelated with the instruments typically used in estimation. We perform a Montecarlo experiment, consisting in solving and simulating a simple life cycle model under uncertainty, and show that in most situations, the estimates obtained from the log-linearized equation are not systematically biased. This is true even when we introduce heteroscedasticity in the process generating income. The only exception is when discount rates are very high (e.g. 47% per year). This problem arises because consumers are nearly always close to the maximum borrowing limit: the estimation bias is unrelated to the linearization and estimates using nonlinear GMM are as bad. Across all our situations, estimation using a log-linearized Euler equation does better than nonlinear GMM despite the absence of measurement error. Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the discount factor is very high, is remarkably flat. This implies that claims that demographic variables in log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted

Consumption over the life cycle and over the business cycle

Consumption;Models

The demand for money, financial innovation, and the welfare cost of inflation: an analysis with household data

We use microeconomic data on households to estimate the parameters of the demand for currency derived from a generalized Baumol-Tobin model. Our data set contains information on average currency, deposits, and other interest-bearing assets; the number of trips to the bank; the size of withdrawals; and ownership and use of ATM cards. We model the demand for currency accounting for adoption of new transaction technologies and the decision to hold interest-bearing assets. The interest rate and expenditure flow elasticities of the demand for currency are close to the theoretical values implied by standard inventory models. However, we find significant differences between individuals with an ATM card and those without. The estimates of the demand for currency allow us to calculate a measure of the welfare cost of inflation analogous to Bailey's triangle, but based on a rigorous microeconometric framework. The welfare cost of inflation varies considerably within the population but never turns out to be very large (about 0.1 percent of consumption or less). Our results are robust to various changes in the econometric specification. In addition to the main results based on the average stock of currency, the model receives further support from the analysis of the number of trips to and average withdrawals from the bank and the ATM

The demand for money, financial innovation, and the welfare cost of inflation: an analysis with household data

We use microeconomic data on households to estimate the parameters of the demand for currency derived from a generalized Baumol-Tobin model. Our data set contains information on average currency, deposits, and other interest-bearing assets; the number of trips to the bank; the size of withdrawals; and ownership and use of ATM cards. We model the demand for currency accounting for adoption of new transaction technologies and the decision to hold interest-bearing assets. The interest rate and expenditure flow elasticities of the demand for currency are close to the theoretical values implied by standard inventory models. However, we find significant differences between individuals with an ATM card and those without. The estimates of the demand for currency allow us to calculate a measure of the welfare cost of inflation analogous to Bailey's triangle, but based on a rigorous microeconometric framework. The welfare cost of inflation varies considerably within the population but never turns out to be very large (about 0.1 percent of consumption or less). Our results are robust to various changes in the econometric specification. In addition to the main results based on the average stock of currency, the model receives further support from the analysis of the number of trips to and average withdrawals from the bank and the ATM

Booms and busts: consumption, house prices and expectations

Over much of the past 25 years, the cycles of house price and consumption growth have been closely synchronised. Three main hypotheses for this co-movement have been proposed in the literature. First, that an increase in house prices raises households’ wealth, particularly for those in a position to trade down the housing ladder, which increases their desired level of expenditure. Second, that house price growth increases the collateral available to homeowners, reducing credit constraints and thereby facilitating higher consumption. And third, that house prices and consumption have tended to be influenced by common factors. This paper finds that the relationship between house prices and consumption is stronger for younger than older households, which appears to contradict the wealth channel. These findings therefore suggest that common causality has been the most important factor behind the link between house price and consumption

Consumption over the life cycle and over the business cycle

The main aim of this paper is to assess the validity of the life cycle model of consumption. In particular, we address an issue that has recently received much attention, especially in the macroeconomic literature: that of "excess sensitivity" of consumption growth to income growth. We do this using a time series of cross sections and a novel and flexible parameterization of preferences. The former allows us to' address aggregation issues directly, while with the latter we can allow both the discount factor and the elasticity of intertemporal substitution eis to be affected by various observable variables and lifetime wealth. The main findings can be summarized as follows: (i) the excess sensitivity of consumption growth to labor income disappears when we control for demographic variables. This is true both at life cycle and business cycle frequencies. (ii) estimation of a flexible specification of preferences indicates that the elasticity of intertemporal substitution is a function of several variables, including the level of consumption. The eis increases with the level of consumption, as expected. (iii) the variables that change the eis are also important in explaining why we observe excess sensitivity over the business cycle. (iv) we are able to reconcile our results with those reported both in the macro and micro literature. (v) in our specification the elasticity of intertemporal substitution is not very well determined. This result, however, should be taken with care, as we have not made an effort to construct a 'preferred' specification, which would probably include additional controls for labor supply behavior. The evidence presented shows that the life cycle model cannot be easily dismissed. Indeed, we believe that the model does a good job at representing consumption behavior both over the life cycle and over the business cycle