Optimal inflation persistence: Ramsey taxation with capital and habits

Ramsey models of fiscal and monetary policy featuring time-separable preferences and a fixed supply of capital predict highly volatile inflation with no serial correlation. In this paper, we show that an otherwise-standard Ramsey model that incorporates capital accumulation and habit persistence predicts highly persistent inflation. The result depends on increases in either the ability to smooth consumption or the preference for doing so. The effect operates through the Fisher relationship: a smoother profile of consumption implies a more persistent real interest rate, which in turn implies persistent optimal inflation. Our work complements a recent strand of the Ramsey literature based on models with nominal rigidities. In these latter models, inflation volatility is lower than in the baseline model but continues to exhibit little persistence. We quantify the effects of habit and capital on inflation persistence and also relate our findings to recent work on optimal fiscal policy with incomplete markets.     

A present value test of habits and the current account

Forecasts derived from standard intertemporal current account (ICA) models generally fail to match the volatility of actual current accounts. This paper offers a solution to the “excess volatility” problem of standard ICA models by incorporating consumption habits into the standard model. The model, as developed in the paper, shows that significant habit formation implies increased current account volatility, as sluggishness is introduced into the consumption adjustment process that follows income shocks. A theory-consistent measure of the degree of habit formation is estimated using GMM. The estimated habit parameter is found to be statistically significant in six of eight quarterly samples.     

Habit formation and the persistence of monetary shocks

The dynamic effects and relative importance of monetary shocks in the US business cycle are studied using a sticky-price dynamic stochastic general equilibrium model with habit formation and capital adjustment costs. The model is estimated via maximum likelihood using data on output, real money balances, and the nominal interest rate. Econometric results indicate that the model has a strong internal propagation mechanism that can explain the persistent and hump-shaped response of US output and consumption to monetary shocks.     

Risk preferences in multi-period consumption models, the equity premium puzzle, and habit formation utility

The relationship between the relative risk aversion measure for the utility function for consumption and that for the value function for wealth is a derived relationship whose properties depend on how consumption and wealth are defined and measured. This fact together with information concerning estimates for these two relative risk aversion measures is used to give another perspective on the equity premium puzzle, and to explain why it is that the habit formation utility function is effective in eliminating that puzzle. A time separable utility function that can serve as an alternative to the assumption of habit formation is also presented.     

Deep Habits,Price Rigidities,and the Consumption Response to Government Spending

This paper studies two frictions, good‐specific habit formation and price rigidities, used in theoretical models to generate the crowding‐in of consumption by expansionary government spending observed in the data. Both frictions generate countercyclical price markups, rising wages, and ensuing consumption–leisure substitution to overcome the negative wealth effect of the fiscal expansion. I demonstrate that while they independently support the rise of consumption, when used together the two frictions exert opposing pressures on the markup and the wage, weakening consumption–leisure substitution. Crucially, when price stickiness is high enough in an economy with “deep” habits, consumption is crowded out by the fiscal expansion.     

Consumption Habits in a New Keynesian Business Cycle Model

Consumption habits have become an integral component in new Keynesian models. However, consumption habits can be modeled in a host of different ways and this diversity is reflected in the literature. I examine whether different approaches to modeling consumption habits have important implications for business cycle behavior. Using a standard New Keynesian business cycle model, I show that, to a first-order log-approximation, the consumption Euler equation associated with the additive functional form for habit formation encompasses the multiplicative function form. Empirically, I show that whether consumption habits are internal or external has little effect on the model's business cycle characteristics.     

Revisiting asset pricing under habit formation in an overlapping-generations economy

By incorporating habit formation into an overlapping-generations economy, we show that the middle-aged consumers’ savings decision has a substantial impact on the equity premium. The higher incentive for savings for the middle-aged, resulting from the habit formation preference, causes an even higher demand for bonds and a lower demand for equity, which eventually generates a lower risk-free rate and a higher required return for holding equity than does the framework of non-habit forming models. Calibration results verify that the habit formation setting, together with an OLG framework is capable of yielding lower bond returns and higher equity returns than the standard CRRA utility models, and the borrowing constraint imposed on the young-aged consumers amplifies the positive effect of habit formation on the equity premium. The findings imply that habit formation preferences within the overlapping-generations framework under the borrowing-constrained economy can provide a more improved explanation of the equity premium puzzle.     

Expectations, learning and macroeconomic persistence

Monetary DGSE models under rational expectations typically require large degrees of features as habit formation in consumption and inflation indexation to match the inertia of macroeconomic variables.This paper presents an estimated model that departs from rational expectations and nests learning by economic agents, habits, and indexation. Bayesian methods facilitate the joint estimation of the learning gain coefficient together with the ‘deep’ parameters of the economy.The empirical results show that when learning replaces rational expectations, the estimated degrees of habits and indexation drop closer to zero, suggesting that persistence arises in the model economy mainly from expectations and learning.     

Implications of habit formation for optimal monetary policy

We study the implications for optimal monetary policy of introducing habit formation in consumption into a general equilibrium model with sticky prices. Habit formation affects the model's endogenous dynamics through its effects on both aggregate demand and households’ supply of output. We show that the objective of monetary policy consistent with welfare maximization includes output stabilization, as well as inflation and output gap stabilization. We find that the variance of output increases under optimal policy, even though it acquires a higher implicit weight in the welfare function. We also find that a simple interest rate rule nearly achieves the welfare-optimal allocation, regardless of the degree of habit formation. In this rule, the optimal responses to inflation and the lagged interest rate are both declining in the size of the habit, although super-inertial policies remain optimal.     

Expected Returns and Habit Persistence

Using a consumption-based asset pricing model with infinite-horizonnonlinear habit formation, Campbell and Cochrane (1999) showthat low consumption in surplus of habit should forecast highexpected returns. This article argues that the finite-horizonlinear habit model also implies an inverse relation betweenexpected returns and surplus consumption. This article alsopresents empirical evidence, which indicates that expected returnson stocks and bonds vary with surplus consumption implied bythe habit models. The volatility of returns and the reward tovolatility are also related to surplus consumption. However,less than 30% of the predictable variation of expected returns,using standard lagged information variables, is attributed tosurplus consumption.     

Price Stability in Economies with Habit Persistence

This paper shows that the divine‐coincidence does not hold in a sticky price model with external habit if a time‐varying tax rate on labor income is not implemented to fully eliminate the time‐varying distortions associated with external habit and monopoly power in goods market. The required labor income tax rate is inversely related to the risk‐free real interest rate and the markup in the goods market, but it is proportional to the degree of external habit. Under this circumstance, the optimal monetary policy commands a countercyclical interest rate, having a perfect negative correlation with tax rate in the sticky price model with external habit. If a time‐invariant tax is the only fiscal instrument, then the degree of external habit entails a gap between the private marginal rate of substitution between consumption and labor and the social marginal rate of substitution, generating an endogenous trade‐off between the stabilization of welfare‐relevant output gap and inflation. Under this circumstance, price stability is not the optimal policy. The monetary policy authority should optimally try to undo the time‐varying distortions associated with external habit and monopoly power in goods market by deviating from price stability.     

Habit formation,surplus consumption and return predictability: International evidence

On an international post World War II dataset, we use an iterated GMM procedure to estimate and test the Campbell and Cochrane (1999, By force of habit: a consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251.) habit formation model with a time-varying risk-free rate. In addition, we analyze the predictive power of the surplus consumption ratio for future stock and bond returns. We find that, although there are important cross-country differences and economically significant pricing errors, for the majority of countries in our sample the model gets empirical support in a variety of different dimensions, including reasonable estimates of risk-free rates. Further, for the majority of countries the surplus consumption ratio captures time-variation in expected returns. Together with the price-dividend ratio, the surplus consumption ratio contains significant information about future stock returns, also during the 1990s. In addition, in most countries the surplus consumption ratio is also a powerful predictor of future bond returns. Thus, the surplus consumption ratio captures time-varying expected returns in both stock and bond markets.     

Propagation Mechanisms for Government Spending Shocks: A Bayesian Comparison

The inability of a simple real business cycle model to predict a rise in consumption in response to increased government expenditures, observed in many empirical studies, has stimulated the development of alternative theories of government spending shocks. Using the Bayesian approach, we evaluate the quantitative performance of five extant models, and find that neither of the considered transmission mechanisms for government spending helps improve the fit of the baseline model. Moreover, we find that consumption decreases in all estimated models in response to a rise in government spending.     

Saving-based asset-pricing

This paper explores the implications of a novel class of preferences for the behavior of asset prices. Following a suggestion by Marshall (1920), we entertain the possibility that people derive utility not only from consumption, but also from the very act of saving. These “saving-based” preferences are related to models of habit formation and the spirit of capitalism, but incorporate the feature that people have anticipatory habits because they care about the future accumulation of wealth. We derive the Euler equations for these preferences and estimate them with GMM. Our estimates suggest that the preference for saving is economically significant.     

A Quantitative Comparison of Sticky-Price and Sticky-Information Models of Price Setting

I estimate sticky-price and sticky-information models of price setting for the United States via maximum-likelihood techniques, reaching several conclusions. First, the sticky-price model fits best, and captures inflation dynamics as well as reduced-form equations once hybrid-behavior is allowed. Second, the importance of hybrid behavior in sticky-price models is potentially consistent with a role for some information imperfections, such as sticky information, as a complement to nominal price rigidities. Finally, the favorable results herein for the hybrid sticky-price model when evaluated by statistics that summarize the relative fit of different models is consistent with the existing literature that is both supportive and dismissive of such models, as this literature has largely ignored fit in evaluating such models. Many previous studies have focused on ancillary issues, such as the standard errors associated with certain parameters or Granger-causality tests that may not provide much information about sticky-price models.     

The Slow Adjustment of Aggregate Consumption to Permanent Income

This paper investigates the relationship between aggregate consumption and permanent income using a new approach to the estimation of cointegrated systems that builds on Stock and Watson's common stochastic trends representation. The permanent and transitory movements in aggregate income and consumption are estimated directly using the Kalman filter and are allowed to be correlated. This approach avoids any implicit restriction that permanent income be as smooth as consumption. Instead, permanent income appears to be relatively volatile, with consumption adjusting toward it only slowly over time. These results provide a clear rejection of the standard version of the permanent income hypothesis and are suggestive of alternative theories of consumption behavior such as habit formation or precautionary savings.     

What do technology shocks tell us about the New Keynesian paradigm?

Researchers have used unanticipated changes to monetary policy to identify preference and technology parameters of macroeconomic models. This paper uses changes in technology to identify the same set of parameters. Estimates based on technology shocks differ substantially from those based on monetary policy shocks. In the post-World War II United States, a positive technology shock reduces inflation and increases hours worked, significantly and rapidly in both cases. Relative to policy shock identification, technology shock identification implies: (i) long duration durability in preferences instead of short duration habit, (ii) built-in inflation inertia disappears and price flexibility increases. In response to technological improvement, consumption durability increases hours worked because households temporarily increase labor supply to accumulate durables towards a new, higher steady state level. Limited nominal rigidities allow inflation to fall because firms are able to immediately cut prices when households’ labor supply increases. Finally, we consider alternative data constructions and econometric specifications; we find that (i) and/or (ii) hold in nearly every case.     

Multiple BGPs in a Growth Model with Habit Persistence

This paper establishes multiple balanced growth paths in an otherwise standard, competitive growth model without externality or distortions and with households' preference dependent upon how his/her consumption compares to a habit stock formed by his/her own past consumption. The key feature in our model is that consumption forms habits in combination with existing habits. This model establishes multiple equilibria because habit persistence induces an internal, intertemporal complementarity effect among consumption flows, with current consumption reinforcing future consumption. As a result, there exist two balanced-growth paths, with one path exhibiting low consumption and habits and high economic growth, and the other path exhibiting high consumption and habits and low growth that is not necessarily a development trap. Both steady states are saddles, but global indeterminacy arises where a high balanced growth path co-exists with a low balanced growth path where the two equilibrium paths cannot be pareto ranked and history need not matter for the selection of the equilibrium path.     

Seasonality and Consumption-Based Asset Pricing

Most of the evidence on consumption-based asset pricing is based on seasonally adjusted consumption data. The consumption-based models have not worked well for explaining asset returns, but with seasonally adjusted data there are reasons to expect spurious rejections of the models. This paper examines asset pricing models using not seasonally adjusted aggregate consumption data. We find evidence against models with time-separable preferences, even when the models incorporate seasonality and allow seasonal heteroskedasticity. A model that uses not seasonally adjusted consumption data and nonseparable preferences with seasonal effects works better according to several criteria. The parameter estimates imply a form of seasonal habit persistence in aggregate consumption expenditures.     

Procyclicality of the comovement between dividend growth and consumption growth

Duffee (2005) shows that the amount of consumption risk (i.e., the conditional covariance between market returns and consumption growth) is procyclical. In light of this “Duffee Puzzle,” I empirically demonstrate that the conditional covariance between dividend growth (i.e., the immediate cash flow part of market returns) and consumption growth is (1) procyclical and (2) a consistent source of procyclicality in the puzzle. Moreover, I solve an external habit formation model that incorporates realistic joint dynamics of dividend growth and consumption growth. The procyclical dividend-consumption comovement entails two new procyclical terms in the amount of consumption risk via cash flow and valuation channels, respectively. These two procyclical terms play an important role in generating a realistic magnitude of consumption risk. In contrast to extant habit formation models, the conditional equity premium no longer increases monotonically when a negative consumption shock arrives because it might lower the amount of risk while increasing the price of risk.