Estimating the elasticity of intertemporal substitution taking into account the precautionary savings motive

This paper estimates the elasticity of intertemporal substitution for U.S. aggregate time series data, taking into account the precautionary savings motive. By making use of a recursive utility function, we estimate an Euler equation, via GMM. This procedure leads consumption growth rate to depend on asset returns, and on a time-varying variance, which captures the precautionary motive. When significant, the elasticity of intertemporal substitution estimates ranges from 0.4 to 1.8, which are higher than most of the results found in the literature. Furthermore, the evidence suggests that consumers react to risk; however, the contribution of precautionary motive to consumption growth seems to be limited.     

Prudent consumers: New evidence from the Consumer Expenditure Survey

Using Consumer Expenditure Survey data from 1986 to recent years, this study examines whether or not the precautionary saving motive is an important force governing consumer behavior. A time series model is obtained by aggregating a log-linearized Euler equation across households, in which the cross-sectional variance of consumption growth represents income uncertainty. The test uses an alternative measure of consumption that excludes some problematic expenditure items from the conventional measure and finds strong evidence for the presence of the precautionary motive. This result is in sharp contrast with the findings of previous cross-sectional estimations using the same data set. It is argued that cross-sectional estimations may be seriously affected by measurement errors whereas the current estimation is not.     

ESTIMATING TEMPTATION AND COMMITMENT OVER THE LIFE CYCLE

This article estimates the importance of temptation for consumption smoothing and asset accumulation in a life‐cycle model. We use two complementary estimation strategies: first, we estimate the model‐implied Euler equation; second, we match liquid and illiquid wealth accumulation using the method of simulated moments. In both cases, we find that the utility cost of temptation is one‐quarter of the utility benefit of consumption. Further, temptation is crucial for correctly estimating the elasticity of intertemporal substitution (EIS): EIS estimates are biased downward when ignoring temptation. Finally, the model only matches the share of illiquid wealth if temptation is in the preference specification.     

Loss aversion in aggregate macroeconomic time series

Prospect theory has been the focus of increasing attention in many fields of economics. However, it has scarcely been addressed in macroeconomic growth models—neither on theoretical nor on empirical grounds. In this paper we use prospect theory in a stochastic optimal growth model. Thereafter, the focus lies on linking the Euler equation obtained from a prospect theory growth model of this kind to real macroeconomic data. We will use generalized method of moments (GMM) estimation to test the implications of such a non-linear prospect utility Euler equation. Our results indicate that loss aversion can be traced in aggregate macroeconomic time series.     

The evolution of consumer preferences in Poland

This note investigates a change of consumer preferences in Poland in the period of 1996–2016. I use the Euler equation–generalized method of moments (GMM) to estimate the structural parameters of the aggregate consumption function to show that consumers in Poland significantly change their attitude to risk during the global financial crisis, when the estimate of the risk-aversion parameter becomes very high, while otherwise close to zero suggesting near risk neutrality. Also, the subjective trade-off between consumption today and tomorrow undergoes an evolution towards lower ‘impatience’. Over-identifying restrictions are tested and the null hypothesis of validity of instruments is not rejected. The stability over time of the estimated parameters is tested and rejected. The evolution of preferences is shown through recursive estimates of the deep parameters, too.     

Time preference and savings behaviour

A number of studies have examined various determinants of savings rate. This article contributes to this literature by empirically testing whether the time preference (discounting behaviour) is another important determinant of savings rate. To this end, we estimate the hyperbolic Euler equation using the generalized method of moments (GMM) to examine whether the short-run discount factor can account for savings behaviour. The empirical results show that people exhibit short-run patience (impatience) when savings rate increases (decreases), which is in line with the theoretical prediction. This result implies that the time preference also plays an important role in determining savings behaviour. Various sets of instruments and different sample periods do not reverse the main finding.     

Private consumption,public consumption and liquidity constraints in developing countries: some empirical evidence

This paper extends the empirical work of Giovannini (1983, 1985) in seeking to identify the elasticity of substitution in consumption in developing countries using the Euler equation approach. Allowing for liquidity constraints in capital markets which force a percentage of aggregate consumption growth to track income growth to track income growth, we report static and time-varying estimates of this percentage and the elasticity of intertemporal substitution, as well as estimates of substitution between private and public consumption and implied utility function parameters. Our results suggest that liquidity constraints are a pervasive feature of developing country consumption data and that the elasticity of intertemporal substitution is near-zero for the majority of countries considered.     

A comparison of two methods for estimating income uncertainty with an application to aggregate consumption behaviour

Econometric theory now provides various techiniques for estimating the variance of a variable for which only a single. Observation is available at each sample point. This paper compares the autoregressive conditional heteroskedastic (ARCH) and linear moment (LM) estimated of the variance of disposable labour income as measures of income uncertainty. Consumer theory postulates a negative relationship between uncertainty about future income and current consumption. Using quarterly post-world war II data with income modelled as a random walk with drift, both ARCH and LM estimates of the variance of income are included in a standard specification of the consumption function. It is found that while noth the ARCH and LM estimates of income uncertainty provide essentially the same predicted reduction in consumption growth as uncertainty increases the LM estimates yield a statistically significant influence on consumption while the ARCH estimated do not. However, both uncertainty measures provide a statistically significant imporvement in the specification of the consumption function relative to estimating the equation in the absence on an uncertainty measure. Thus, recent advances in estimation techniques, for post-world waf II data, show that the uncertainty theorists of over two decades ago were correct, that is estimation of a consumption function in the absence of an uncertainty measure relults in an equation with a biased estimate of the marginal propensity to consume as well as biased estimates of coefficients for all other included variables (see e.g. Leland, 1968, PP. 470-472).     

经济转轨与城镇化进程中的居民消费行为特征——对1396户城镇家庭的实证分析

基于中国9个省1396户城镇家庭的面板数据,运用系统广义矩估计法对一个包括习惯形成和不确定性的欧拉方程进行估计以考察家庭消费是否跨时演进,研究结果表明,偏好的设定偏误是传统的生命周期——持久收入模型不能很好地诠释中国城镇家庭消费决策的一个原因,在解释消费决策的影响因素时假定偏好的跨时可分性会得出错误的结论,城镇居民消费偏好的跨时不可分性以及由收入和支出不确定性引发的预防性储蓄动机是导致居民消费倾向持续偏低的重要原因。     

Estimation of Dynamic Panel Data Sample Selection Models

This paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule, when the latent equations contain strictly exogenous variables, lags of the dependent variables, and unobserved individual effects. We derive a set of conditional moment restrictions which are then exploited to construct two-step GMM-type estimators for the parameters of the main equation. In the first step, the unknown parameters of the selection equation are consistently estimated. In the second step, these estimates are used to construct kernel weights in a manner such that the weight that any two-period individual observation receives in the estimation varies inversely with the relative magnitude of the sample selection effect in the two periods. Under appropriate assumptions, these "kernel-weighted" GMM estimators are consistent and asymptotically normal. The finite sample properties of the proposed estimators are investigated in a small Monte-Carlo study.     

Efficient estimation of macroeconomic equations with unobservable states

Macroeconomic equations, such as the consumption Euler equation, New Keynesian Phillips curve, and Taylor rule, are regularly estimated on an individual basis. However, such relations also jointly determine equilibrium, which may contain unobservable states. This paper shows how to utilize such an equilibrium model to improve the efficiency of individual estimators. In comparison with existing related approaches, this simple framework lends itself naturally to modern medium scale dynamic stochastic general equilibrium models. Not only does the derived estimator exhibit smaller asymptotic variance than equation-by-equation GMM, it also tends to be less prone to small sample distortions from weak identification.     

Empirical demand systems incorporating intertemporal consumption dynamics

This article presents and estimates demand systems by explicitly incorporating intertemporal consumption behavior as summarized by the Euler equation. Demand systems are characterized by two indirect utility functions which are effectively globally regular and can better approximate nonlinear Engel curves. Furthermore, an exact and nonlinear Euler equation is derived without a log approximation. This equation is estimated jointly with the demand functions by a careful implementation of the orthogonality conditions using generalized method of moments. We illustrate the techniques by estimating the demand system and Euler equation for Australian aggregate data. Results generally indicate that the proposed methods are promising. The estimated rate of time preference is fairly small while the restrictions producing the moment equations are not rejected. Estimated Frisch price elasticities, which are relevant in an intertemporal setting, appear reasonable, and the intertemporal elasticity of substitution for consumption is found to be small, which are consistent with the findings in earlier studies.     

Intertemporal consumption with directly measured welfare functions and subjective expectations

Euler equation estimation of intertemporal consumption models requires many, often unverifiable assumptions. These include assumptions on expectations and preferences. We aim at reducing some of these requirements by using direct subjective information on respondents’ preferences and expectations. The results suggest that individually measured welfare functions and expectations have predictive power for the variation in consumption across households. Furthermore, estimates of the intertemporal elasticity of substitution based on the estimated welfare functions are plausible and of a similar order of magnitude as other estimates found in the literature. The model favored by the data only requires cross-section data for estimation.     

Euler equation errors

The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. When evaluated on cross-sections of stock returns, the model generates economically large unconditional Euler equation errors. Unlike the equity premium puzzle, these large Euler equation errors cannot be resolved with high values of risk aversion. To explain why the standard model fails, we need to develop alternative models that can rationalize its large pricing errors. We evaluate whether four newer theories at the vanguard of consumption-based asset pricing can explain the large Euler equation errors of the standard consumption-based model. In each case, we find that the alternative theory counterfactually implies that the standard model has negligible Euler equation errors. We show that the models miss on this dimension because they mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. By contrast, a simple model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in severe recessions, produces violations of the standard model's Euler equations and departures from joint lognormality that are remarkably similar to those found in the data.     

The Impact of Inequality and Redistribution on Growth

In this paper, we reassess the impact of inequality on growth. The majority of previous papers have employed (system) GMM estimation. However, recent simulation studies indicate that the problems of GMM when using non‐stationary data such as GDP have been grossly underestimated in applied research. Concerning predetermined regressors such as inequality, GMM is outperformed by a simple least‐squares dummy variable estimator. Additionally, new data have recently become available that not only double the sample size compared to most previous studies, but also address the substantial measurement issues that have plagued past research. Using these new data and an LSDV estimator, we provide an analysis that both accounts for the conditions where inequality is beneficial or detrimental to growth and distinguishes between market‐driven inequality and redistribution. We show that there are situations where market inequality affects growth positively while redistribution is simultaneously beneficial.     

Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

We propose a generalized method of moments (GMM) estimator with optimal instruments for a probit model that includes a continuous endogenous regressor. This GMM estimator incorporates the probit error and the heteroscedasticity of the error term in the first‐stage equation in order to construct the optimal instruments. The estimator estimates the structural equation and the first‐stage equation jointly and, based on this joint moment condition, is efficient within the class of GMM estimators. To estimate the heteroscedasticity of the error term of the first‐stage equation, we use the k‐nearest neighbour (k‐nn) non‐parametric estimation procedure. Our Monte Carlo simulation shows that in the presence of heteroscedasticity and endogeneity, our GMM estimator outperforms the two‐stage conditional maximum likelihood estimator. Our results suggest that in the presence of heteroscedasticity in the first‐stage equation, the proposed GMM estimator with optimal instruments is a useful option for researchers.     

流动性约束和不确定性状态下的预防性储蓄研究-中国城乡居民的消费特征分析

该文利用我国城乡时间序列数据,对城乡居民的消费特征做了新的探索.我们对引入预期收入增长的对数线性欧拉方程和二阶泰勒近似的欧拉方程进行了估计,结果说明,当期收入仍是决定我国居民消费的主要因素,消费的随机游走假说不成立;城镇居民比农村居民有更强的预防性储蓄动机.1990年代中期以来持续走低的收入增长率直接抑制了消费需求的增长,而仍然偏紧的流动性约束和日益增强的不确定性增大了预防性储蓄动机.     

Testing for asymmetries in the preferences of the euro-area monetary policymaker

This article tests for asymmetries in the preferences of the euro-area monetary policymaker with 1995:1–2005:2 data from the latest update of the European Central Bank's (ECB's) Area-wide database. Following the relevant literature, we distinguish between three types of asymmetry: precautionary demand for expansions, precautionary demand for price stability and interest rate smoothing asymmetry. Based on the joint generalized method of moments (GMM) estimation of the Euler equation of optimal policy and the aggregate supply-aggregate demand (AS-AD) structure of the macroeconomy, we find evidence of precautionary demand for price stability in the preferences revealed by the monetary policymaker. This type of asymmetry is consistent with the ECB's definition of price stability and with the priority of credibility-building by a recently created monetary authority.     

Consumption smoothing in Russia1

Using a panel from the Russian Longitudinal Monitoring Survey (1994–2004), this paper investigates to what extent Russian households have been able to maintain their living standards while suffering income shocks. Consumption smoothing is modelled by means of an equilibrium correction mechanism, which disentangles short‐run dynamics and long‐run equilibrium adjustments. GMM estimation is used to control for individual household effects in the presence of dynamics. Additionally, we differentiate between food and non‐food consumption, positive and negative shocks, rural and urban areas, and several levels of poverty risk. We find that dynamics are important in the consumption equation, and that estimates are sensitive to imputation errors in home food production. No strong claims can be made regarding heterogeneity in smoothing behaviour.     

A note on the asymptotic lower bound for the covariance matrix of the GMM estimator of the parameters of agents' utility functions

This paper derives under simplifying assumptions an explicit expression for the lower bound on the asymptotic variance of the GMM estimate of the curvature parameter of the CRR utility function. Numerical calculations indicate that qualitative conclusions reached on the basis of the expression are reliable indicators of what can be expected in complicated estimation situations where explicit formulae are not available.