External Habit Formation Research Articles

Utility-implied term structures of equity risk premia

The fundamental asset pricing problem is extended to the frequency domain for commonly used utility functional forms. For each class of utility functions, closed-form solutions are presented for the term structure of the equity risk premium. The term structure is flat for time separable one-period utility and uncorrelated external habit formation utility, downward sloping for internal habit formation utility, upward sloping for time preference (recursive) utility, and can be upward sloping, downward sloping, or flat for production-based utility. These results suggest how observed risk premium term structures can be mapped to linear time series models consistent with utility preference classes.

A mean field game approach to equilibrium consumption under external habit formation

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a log-normal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude some financial implications caused by consumption habits from a mean-field perspective. In each problem with n agents, we construct an approximate Nash equilibrium for the n-player game using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained.

A consumption-based term structure model of bonds and equity

In this study, I propose a consumption-based asset pricing model to capture the dynamic properties of term structures of bonds and equity. I extend the long-run risks model by introducing a mean-reversion of dividend growth and the external habit formation of a representative agent. The mean-reverting dividend growth generates a negative equity term premium, while the habit formation augments the equity premium and renders an upward-sloping bond yield curve, on average. In addition, fluctuations in the surplus consumption ratio and the conditional variance of consumption growth allow the model to reproduce pro-cyclical variations in bond and equity yield spreads and counter-cyclical variations in bond and equity term premiums, as observed in the U.S. data.

Research on the comparison effect of urban residents' consumption

As an important component of gross domestic product, expanded consumer spending is essential for promoting economic growth. To provide a realistic basis to support effective policy formulation to meet diversified consumption needs and enhance the fundamental role of consumption in economic development, this study constructs a multi-layer panel extended linear expenditure system (ELES) model that includes external habit formation (comparison effect). The study empirically analyses the comparison effect and causes using nested consumption data of urban residents from 31 provinces in China from 2002 to 2019. The results show that the comparison effect is relatively large for urban residents’ subsistence consumption expenditure. In contrast, the comparison effect in development and enjoyment consumption expenditure is smaller overall. Second, a widening income gap increases food and clothing comparison effects. Increased educational attainment reduces comparison effects on housing, health care and transport. Significant geographical differences in the comparison effect on various types of consumer spending are evident based on the degree of regional economic development. Finally, the study proposes policy recommendations of increasing residents’ income, raising educational levels and promoting balanced regional development. The most significant contribution of this study is the innovative multi-layer panel ELES statistical model which incorporates external habit formation theory to systematically analyse comparison effects and causes.

Psychological Needs, Physiological Needs and Regional Comparison Effects

This paper innovatively constructs a panel extended linear expenditure system (ELES) model including the theory of internal and external habit formation and analyzes the time effect of consumption habits and the regional differences of the comparison effects on rural residents in a variety of consumption expenditures from a temporal and spatial perspective. This research demonstrates the following. Firstly, overall, rural residents have least internal habits in terms of subsistence spending, followed by developmental spending and the most in enjoyment spending. Secondly, China’s rural residents consider the “actual use value” of commodities in “introverted” consumption expenditures; but in “export-oriented” consumption expenditures, besides the “actual use value” of the goods, they also seek to fulfill their “emotional demands”. Thirdly, there is the largest comparison effect on food and housing consumption expenditures for rural residents in coastal economic developed regions, and the smallest comparison effect on clothing, transportation, cultural and educational expenditures. It is the largest comparison effect on clothing and medical care expenditures for rural residents in underdeveloped regions of the central and western, and the smallest comparison effect on food and housing consumption expenditures.

Asset Pricing Implications Of The Mismatch Between Performance Window And Benchmark Duration

This paper studies the mismatch between asset managers' performance window and the time average of their benchmark dividend payouts, commonly referred to as duration. Our asset pricing equilibrium mechanism provides the first plausible theoretical foundation for the recent empirical findings showing that the risk premium, volatility, and Sharpe ratio on short-term dividend strips are higher than long-term dividend strips. These findings are at odds with the leading equilibrium asset pricing models, such as long-run risk, external habit formation, and rare disaster risk models. Our continuous-time setup admits precise closed-form expressions. We provide novel empirical evidence to support other model predictions.

Observational equivalence of balanced growth with external habit formation

AbstractThis paper investigates two scenarios in the external habit formation model with concave utility functions. When the utility function is weakly concave, there exists a unique history‐dependent balanced growth path (BGP) under a knife‐edge existence condition. When the utility function is strictly concave, a unique BGP exists under a more generic condition. I find that the BGPs in the two scenarios are observationally equivalent. The knife‐edge condition limits the applicability of the first scenario. The generic existence condition and the observational equivalence result mitigate this issue. I show that our model can help understand a variety of growth patterns of countries that differ in their fundamentals substantially.

International trade and “Catching up with the Joneses”: Are the consumption patterns convergent?

We use a dynamic international trade model to analyse the implications of international trade for agents’ preferences and economic growth. This model is based on the home market effect with external habit formation (“catching up with the Joneses”) and “learning by doing” in production. We demonstrate the following: the historical composition of consumption in countries determines industrialization after trade; the preferences of agents converge after trade, independent of the economic results; and the welfare effects of trade may be positive or negative depending on trading partner characteristics. In some scenarios, autarky is strictly preferred to trade. Thus, international trade does not necessarily imply greater welfare, as is the typical result in a static context under CES preferences.

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.

Consumption Fluctuations and Expected Returns

ABSTRACTThis paper introduces a novel consumption‐based variable, cyclical consumption, and examines its predictive properties for stock returns. Future expected stock returns are high (low) when aggregate consumption falls (rises) relative to its trend and marginal utility from current consumption is high (low). We show that the empirical evidence ties consumption decisions of agents to time variation in returns in a manner consistent with asset pricing models based on external habit formation. The predictive power of cyclical consumption is not confined to bad times and subsumes the predictability of many popular forecasting variables.

DSGE-MODEL FOR RUSSIAN ECONOMY WITH BANKS ANDFIRM-SPECIFIC CAPITAL IN CORONAVIRUS PANDEMIC

The article presents a dynamic stochastic general equilibrium model (DSGE-model) for the Russian economy. The model describes the behavior of the following macroeconomic agents: households, real sector, banking sector, Central Bank, as well as the interactions between them and the world. Household modeling uses the external habit formation approach to account for the inertia of preferences. To model the real sector, we abandoned the most common approach which assumes that the decision on investments is made by the households as the owners of production factors. Instead, we took the firm-specific capital approach which assumes that the decision on investment is made by the firms themselves. The study also considers that in Russia, fixed assets are mostly invested from the firms' own funds. To account for the investment inertia in the fixed asset in a real sector model, the expenditures are transferred to the commissioning of new facilities, the Calvo model is applied to describe the price setting under the monopolistic competition. A banking sector which defines the loan and debt interest rates to the key Central Bank interest rate is chosen to be a link between the households and firms in the model. The Taylor equation is used to describe the monetary policy of the Bank of Russia under the inflation targeting, while an inertia factor is included into the equation with the uncovered interest parity for the budget rule which regulates the purchases (or sales) of the currency by the National Welfare Fund. The final linearized model is a system of 23 difference equations with rational expectations. Based on the proposed model, calculations were made and key macroeconomic indicators were forecasted for 2020–2021 on a quarterly basis for the Russian economy. The calculations account for the relevant recessionary factors: oil price fall, oil production cut in OPEC+ deals, quarantine measures aimed to prevent the spread of the corona virus infection, anti-recessionary measures of the RF Government. The findings show that the economic downturn in 2020 can be from 5 to 7% under COVID-19 pandemic. Growth in 2021 is estimated to be within 3–5%. The developed model can be used for scenario projecting for the Russian economy, upgrading the monetary policy of the Bank of Russia, and for developing applied quarterly projection models (QPM). The model could be further modified by including more elements: decomposing the household sector into the Ricardian and non-Ricardian ones, identifying the resources industries and industries in the real sector which manufacture the invested goods, including the key taxes and budget expenses into the model. One more promising area is to analyze the equilibrium of the interest rates when large firms could accumulate their own financial resources. This prerequisite decreases the demand for the bank loans from the real sector and, thus, leads to lower, including the negative, interest rates. The proposed approach enhances the quality of a DSGE model as a predictive tool for making the political and managerial decisions. Keywords mathematical modeling of economy, structural macroeconometrics, dynamic stochastic general equilibrium models, DSGE models, rational expectations, inflation targeting, monetary policy, budget rule, Taylor equation, scenarios projection, COVID-caused crisis, COVID-19 pandemic. Acknowledgements The author thanks A.B. Polbin, the Deputy Head of the Macroeconomic Modeling Department in Gaidar Institute for Economic Policy for valuable comments and recommendations during the model development.

Up- and downside variance risk premia in global equity markets

This paper provides novel insights into the dynamic properties of variance and semivariance premia. Considering nine international stock market indices, we find consistent evidence of significantly negative total and downside (semi)variance premia of around -15 bps per month. These premia almost exclusively compensate investors for the risk of extreme negative returns. We also document pronounced downside semivariance premia for longer times to maturity, while the term structure of the total variance premium is upward sloping for all of the considered indices. The slope is driven by upside semivariance premia which are positive over long horizons. They can only be negative in adverse states, characterized by high uncertainty and high risk aversion. We show that a general equilibrium model featuring external habit formation and “bad environment-good environment” dynamics for consumption and dividends can explain many of these stylized facts and highlight the economic mechanisms.

Consumption Fluctuations and Expected Returns

This paper introduces a novel consumption-based variable, cyclical consumption, and examines its predictive properties for stock returns. Future expected stock returns are high (low) when aggregate consumption falls (rises) relative to its trend and marginal utility from current consumption is high (low). We show that the empirical evidence ties consumption decisions of agents to time-variation in returns in a manner consistent with asset pricing models based on external habit formation. The predictive power of cyclical consumption is not confined to bad times and subsumes the predictability of many popular forecasting variables.

Asset Return Dynamics under Habits and Bad Environment–Good Environment Fundamentals

We introduce a “bad environment–good environment” (BEGE) technology for consumption growth in a consumption-based asset pricing model with external habit formation. The model generates realistic non-Gaussian features of consumption growth and fits standard salient features of asset prices including the means and volatilities of equity returns and a low risk-free rate. BEGE dynamics additionally allow the model to generate realistic properties of equity index options prices and their comovements with the macroeconomic outlook. In particular, when option-implied volatility is high—as measured, for instance, by the VIX index—the distribution of consumption growth is more negatively skewed.

Asset Return Dynamics Under Habits and Bad-Environment Good-Environment Fundamentals

We introduce a “bad environment–good environment” (BEGE) technology for consumption growth in a consumption-based asset pricing model with external habit formation. The model generates realistic non-Gaussian features of consumption growth and fits standard salient features of asset prices including the means and volatilities of equity returns and a low risk-free rate. BEGE dynamics additionally allow the model to generate realistic properties of equity index options prices and their comovements with the macroeconomic outlook. In particular, when option-implied volatility is high—as measured, for instance, by the VIX index—the distribution of consumption growth is more negatively skewed.

Asset Return Dynamics under Habits and Bad-Environment Good-Environment Fundamentals

We introduce a "bad environment-good environment" (BEGE) technology for consumption growth in a consumption-based asset pricing model with external habit formation. The model generates realistic non-Gaussian features of consumption growth and fits standard salient features of asset prices including the means and volatilities of equity returns and a low risk free rate. BEGE dynamics additionally allow the model to generate realistic properties of equity index options prices, and their comovements with the macroeconomic outlook. In particular, when option-implied volatility is high, as measured for instance by the VIX index, the distribution of consumption growth is more negatively skewed.

Asset Return Dynamics Under Habits and Bad-Environment-Good Environment Fundamentals

We introduce a bad environment-good environment (BEGE) technology for consumption growth in a consumption-based asset pricing model with external habit formation. The model generates realistic non-Gaussian features of consumption growth and fits standard salient features of asset prices including the means and volatilities of equity returns and a low risk free rate. BEGE dynamics additionally allow the model to generate realistic properties of equity index options prices, and their comovements with the macroeconomic outlook. In particular, when option implied volatility is high, as measured for instance by the VIX index, the distribution of consumption growth is more negatively skewed.

Relative Consumption: The Strength of Internal and External Habits

This paper investigates the presence and strength of internal and external habit formation in consumption, using monthly household data. The habit hypothesis is used to explain empirical regularities in macroeconomics and finance. Empirical studies based on aggregate data (macro-evidence) leave the micro-behavior unexplored. The micro-evidence is inconclusive and primarily based on food consumption data. Unfortunately, food consumption is a bad proxy for total consumption — mainly, because food consumption preferences differ considerably from consumption preferences of other goods (Shea (1994)). Thus, I use total household consumption data to test the Euler equations of an additive habit formation model. There is evidence for internal and external habits; the external habit effect is about three times larger than the internal effect. Extensions to alternative habit coefficients are provided.

NONPARAMETRIC IDENTIFICATION OF POSITIVE EIGENFUNCTIONS

Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk–return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models. This paper provides identification conditions for positive eigenfunctions in nonparametric models. Identification is achieved if the operator satisfies two mild positivity conditions and a power compactness condition. Both existence and identification are achieved under a further nondegeneracy condition. The general results are applied to obtain new identification conditions for external habit formation models and for positive eigenfunctions of pricing operators in dynamic asset pricing models.

Habit Formation and Risk-free Rate Puzzle

This paper deals with risk-free rate puzzle when the agent shows external habit formation, using different sorts of instruments that are used for proxies as a risk-free rate. It is found that upon instruments, risk free rate puzzle is vulnerable to the proxies selected; this fact ascribes to the partial solution to that puzzle. In addition, the external habit ratio model in contrast with time separable preferences exclusively contributes to the description of observed behavior of secular instruments. In particular, the degree of time-nonseparability of the former plays a remarkable role in solving out the discrepancy between observed and derived rate, lowering theoretical interest rate into the bottom of observed rate within reasonable risk aversion.