Helle Bunzel

Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch -Singer Hypothesis

We propose tests for hypotheses on the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data, and they are robust to strong serial correlation. The data can contain a unit root and still have the correct size asymptotically. The tests that we analyze are standard heteroscedasticity autocorrelation robust tests based on nonparametric kernel variance estimators. We analyze these tests using the fixed-b asymptotic framework recently proposed by Kiefer and Vogelsang. This analysis allows us to analyze the power properties of the tests with regard to bandwidth and kernel choices. Our analysis shows that among popular kernels, specific kernel and bandwidth choices deliver tests with maximal power within a specific class of tests. Based on the theoretical results, we propose a data-dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang. We apply the recommended test to the logarithm of a net barter terms of trade series and we find that this series has a statistically significant negative slope. This finding is consistent with the well-known Prebisch–Singer hypothesis.

A Nonstandard Empirical Likelihood for Time Series

Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though nonstandard, data-blocking rule which uses a data block of every possible length. Consequently, the method does not involve the usual block selection issues and is also anticipated to exhibit better coverage performance. Its nonstandard blocking scheme, however, induces nonstandard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi-square one, but is distribution-free and can be reproduced through straightforward simulations. Numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard BEL.

Choosing to Keep up with the Joneses

Does a rise in income inequality induce people to work harder to stay in the rat race (“keep up with the Joneses”) or to simply drop out? We investigate this issue in a simple new framework in which heterogeneous ability agents get extra utility if their consumption keeps up with the economy’s average. The novelty is that agents are allowed to choose whether they want to stay in or drop out of the rat race. We show that sufficiently high ability agents choose to keep up with the Joneses and they enjoy higher consumption but lower leisure than those who don’t. When income inequality rises in a mean-preserving manner, average leisure in the economy may fall. Our analysis touches on the question, why are Americans working so much compared to the Europeans? We posit that higher income inequality in the US, by inducing more people to join the rat race there, may be partly responsible for the transatlantic leisure divide.

Resurrecting Equilibria through Cycles

In an overlapping generations model, momentary equilibria are defined as points that lie on the intergenerational offer curve, i.e., they satisfy agents’ optimality conditions and market clearing at any date. However, some dynamic sequences commencing from such points may not be considered valid equilibria because they asymptotically violate some economic restriction of the model. The literature has always ruled out such paths. This paper studies a pure-exchange monetary overlapping generations economy in which real balances cycle forever between momentary equilibrium points. The novelty is to show that segments of the offer curve that have been previously ignored, can in fact be used to produce asymptotically valid cyclical paths. Indeed, a cycle can bestow dynamic validity on momentary equilibrium points that had erstwhile been classified as dynamically invalid.

FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS

This note uses fixed bandwidth (fixed-b) asymptotic theory to suggest a new approach to testing cointegration parameters in a single-equation cointegration environment. It is shown that the standard tests still have asymptotic distributions that are free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous.This paper provides a new approach to testing cointegration parameters in a single-equation cointegration environment. The novelty is in improving over the well-known heteroscedasticity and autocorrelation consistent (HAC) robust standard errors using fixed bandwidth (fixed-b) asymptotic theory and adapting it to the cointegration environment. It is shown that the standard tests still have asymptotic distributions free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous. Using asymptotic power and finite sample size simulation experiments, specific practical and user-friendly recommendations regarding kernel and bandwidth choices are made. Finite sample simulations comparing the size and power of the tests using the fixed-b asymptotics to some of the currently popular tests are performed. These simulations confirm that the well-known size distortion of the standard tests can be greatly reduced. Alternatively, one can obtain greater power with much the same level of size distortion, depending on the choice of kernel and bandwidth. Finally, the newly developed tests are employed to investigate the standard money-demand relationship for US data

Fixed bandwidth asymptotics in single equation models of cointegration with an application to money demand

This note uses fixed bandwidth (fixed-b) asymptotic theory to suggest a new approach to testing cointegration parameters in a single-equation cointegration environment. It is shown that the standard tests still have asymptotic distributions that are free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous.This paper provides a new approach to testing cointegration parameters in a single-equation cointegration environment. The novelty is in improving over the well-known heteroscedasticity and autocorrelation consistent (HAC) robust standard errors using fixed bandwidth (fixed-b) asymptotic theory and adapting it to the cointegration environment. It is shown that the standard tests still have asymptotic distributions free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous. Using asymptotic power and finite sample size simulation experiments, specific practical and user-friendly recommendations regarding kernel and bandwidth choices are made. Finite sample simulations comparing the size and power of the tests using the fixed-b asymptotics to some of the currently popular tests are performed. These simulations confirm that the well-known size distortion of the standard tests can be greatly reduced. Alternatively, one can obtain greater power with much the same level of size distortion, depending on the choice of kernel and bandwidth. Finally, the newly developed tests are employed to investigate the standard money-demand relationship for US data

Do the Joneses make you financially vulnerable

This paper studies a model economy populated with agents of differing incomes that get a utility boost when their consumption keeps up with their neighbors, the proverbial Joneses. The resulting utility function is non-concave. In this setup, participation in a fair consumption lottery has the potential to make some agents ex-ante better off but more financially vulnerable. More people of different incomes join the lottery pool when the ‘kick’ from keeping up increases. Worsening income inequality may increase the number of financially vulnerable people. The analysis offers broad-brushstroke insights into the connection between inequality and financial vulnerability. This paper studies a model economy populated with agents of differing incomes that get a utility boost when their consumption keeps up with their neighbors, the proverbial Joneses. The resulting utility function is non-concave. In this setup, participation in a fair consumption lottery has the potential to make some agents ex-ante better off but more financially vulnerable. More people of different incomes join the lottery pool when the ‘kick’ from keeping up increases. Worsening income inequality may increase the number of financially vulnerable people. The analysis offers broad-brushstroke insights into the connection between inequality and financial vulnerability.

Voting for Income‐Immiserizing Redistribution in the Meltzer–Richard Model

This paper argues that income received via redistributive transfers, unlike labor income, requires no direct sacrifice of leisure; this makes it attractive to many voters even if it leaves them poorer. This point is made within the classic Meltzer and Richard (1981) model wherein heterogeneous voters evaluate an income-redistribution program that finances a lump-sum transfer to all via a distorting income tax. The political-equilibrium policy under majority rule is the tax most preferred, utility-wise, by the median voter. She, and many poorer voters, may support income redistribution that, ironically, leaves them poorer in income terms but with higher utility.

Immiserizing Redistribution: Voting to Get Poorer in the Meltzer-Richard Model

In the classic Meltzer and Richard (1981) model, the canonical model of income redistribution in democracies, voters, heterogeneous on the sole dimension of idiosyncratic productivity, evaluate an income-redistributive program that pays everyone a lump-sum income subsidy financed by a distorting income tax levied on all. The political-equilibrium policy under majority rule is the tax rate most preferred (in a utility sense) by the median voter. The larger the gap between the median and mean income, the larger is the scale of income redistribution favored by the median voter. But does the median voter actually end up with more income post redistribution? We establish, somewhat ironically, that the median voter (and many poorer voters) in the Meltzer-Richard model may support income redistribution that leaves them poorer in income terms. Indeed, the basis for their support may not be more income but more leisure. The analysis spotlights the fact that transfer income, unlike labor income, requires no direct sacrifice of leisure.