Cross-equation Restrictions Research Articles

A Revealed Preference Approach to Identification and Inference in Producer-Consumer Models

This article provides a new identification result for a large class of models in which consumers participate in production. I show that consumer preferences are necessary and sufficient to identify production functions through cross-equation restrictions implied by first-order conditions. In addition, I derive a nonparametric revealed preference characterization of the class of models that exhausts its empirical implications. Finally, I use a novel and easy-to-apply inference method that is valid under partial identification. This method can be used to statistically test the model, can deal with any type of latent variables (e.g., measurement error), and can be combined with standard exclusion restrictions. Using data on shopping expenditures and shopping intensity from the NielsenIQ Homescan Dataset, I show that a doubling of shopping intensity decreases prices paid by about 15 % . At the same time, I find that search costs are significant, hence, largely diminishing benefits of price search.

Estimating robustness

I estimate and evaluate a model with a representative agent who is concerned that the persistence properties of her baseline model of consumption and inflation are misspecified. Coping with model uncertainty, she discovers a pessimistically biased worst-case model that dictates her behavior. I combine interest rates and aggregate macro series with cross-equation restrictions implied by robust control theory to estimate this worst-case distribution and show that (1) the model's predictions about key features of the yield curve are in line with the data, and (2) the degree of pessimism underlying these findings is plausible. Interpreting the worst-case as the agent's subjective belief, I derive model implied interest rate forecasts and compare them with analogous survey expectations. I find that the model can replicate the dynamics and average level of bias found in the survey.

Dividend Momentum and Stock Return Predictability: A Bayesian Approach

A long tradition in macro-finance studies the joint dynamics of aggregate stock returns and dividends using vector autoregressions (VARs), imposing the cross-equation restrictions implied by the Campbell-Shiller (CS) identity to sharpen inference. We take a Bayesian perspective and develop methods to draw from any posterior distribution of a VAR that encodes a priori skepticism about large amounts of return predictability while imposing the CS restrictions. In doing so, we show how a common empirical practice of omitting dividend growth from the system amounts to imposing the extra restriction that dividend growth is not persistent. We highlight that persistence in dividend growth induces a previously overlooked channel for return predictability, which we label ``dividend momentum.'' Compared to estimation based on OLS, our restricted informative prior leads to a much more moderate, but still significant, degree of return predictability, with forecasts that are helpful out-of-sample and realistic asset allocation prescriptions with Sharpe ratios that out-perform common benchmarks.

Implications of household-level evidence for policy models: the case of macro-financial linkages

AbstractMacroeconomic policy models should track the different channels of monetary transmission, providing a framework for Monetary Policy Committees. They should also be useful for assessing risks to financial stability, including for designing macroprudential stress tests and instrument settings in the new macroprudential toolkits. Current policy models, including the ‘semi-structural’ non-DSGE econometric models such as FRB-US, are seriously deficient in these respects, failing to capture the credit channel and the role of real estate in the financial accelerator that operated in the global financial crisis, and in key transmission channels in the recovery. Furthermore, developments in economic theory, greatly encouraged by new evidence, have rendered redundant the previously accepted micro-foundations for household behaviour in these policy models.A multi-purpose policy model needs to include a household-housing sub-system. This should contain a consumption function broadly consistent with the micro-evidence with equations for permanent income, for the balance sheet drivers, and for residential investment. To capture the credit channel, this block of the model needs to embed common credit conditions in the equations. Sub-system estimation is required to impose the cross-equation restrictions implied by these common factors.

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.

Testing for a common Phillips curve in common monetary area of Southern Africa

PurposeThis paper sets out to investigate whether the four members of the common monetary area (CMA) regime experience similar inflation-unemployment dynamics as explained by the Phillips Curve phenomenon.Design/methodology/approachThis study uses a combination of seemingly unrelated regression (SUR) and Copula based marginal regression techniques to investigate existence of a common Phillips curve (PC) between members of the CMA. Model estimation was done using country specific annual time series data for inflation, unemployment and imports spanning from 1980 to 2014.FindingsWe find evidence of contemporaneous correlation between the residuals of individual CMA PC equations and a statistically significant trade-off between inflation and unemployment for all CMA countries. Wald test results of cross-equation restrictions reveal a 9.94% chance of a common unemployment coefficient for CMA countries.Originality/valueTogether, the results of the SUR and Gaussian Copula techniques provide mixed and inconclusive evidence to support the existence of a common PC among CMA member states. This study is the first of its kind in examining this phenomenon for currency board regimes like CMA, and one of the very few among emerging market economies.

Macro-Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including long-run risk models and (time-varying) rare-disaster risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro-finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross-equation restrictions. For empirical application, we apply the proposed conditional specification test to evaluate a time-varying rare-disaster risk model and construct data-driven robust model uncertainty sets. The supplemental appendix can be found at: https://ssrn.com/abstract=3609598. The additional materials can be found at: https://ssrn.com/abstract=3787125.

Sources of current account fluctuations in Taiwan: 1989–2015

In this paper, we use a small open economy model with nontradable goods and time-varying interest rates to investigate the sources of fluctuations in Taiwan’s current account. The correlation coefficient between the implied path of the current account generated from our model and the actual current account data exceeds 0.9, while tests of the cross-equation restrictions also support the model-implied present value relationship between the current account and other macroeconomic variables. We find the consumption smoothing channel, based on the discounted sum of the expected future net output growth, is the main channel for current account adjustment in Taiwan. Expected changes in the real effective exchange rate also account for much of the variation in the current account.

Heteroscedastic stratified two-way EC models of single equations and SUR systems

A relevant issue in panel data estimation is heteroscedasticity, which often occurs when the sample is large and individual units are of varying size. Furthermore, many of the available panel data sets are unbalanced in nature, because of attrition or accretion, and micro-econometric models applied to panel data are frequently multi-equation models. The general least squares estimation of the heteroscedastic stratified two-way error component (EC) models of both single equations and seemingly unrelated regressions (SUR) systems (with cross-equation restrictions) on unbalanced panel data is considered. The derived heteroscedastic estimators of both single equations and SUR systems improve the estimation efficiency.

Market Capitalization, Corporate Payouts, and Expected Returns

This paper examines the present value framework that links market capitalization to non-dividend cash flows (i.e., share repurchases and issuances) beyond the conventional price–dividend relationship. We show that total (dividend plus non-dividend) cash flows can account for a large fraction of both price and return variations by using tests of cross-equation restrictions on vector autoregression (VAR), impulse response functions, and variance decomposition of unexpected returns. These results come from the fact that total cash flow shocks exhibit a strong negative correlation with payout yield shocks. Non-dividend cash flows help to reconcile our findings with previous literature that prices move substantially relative to dividends.

Equilibrium voluntary disclosures, asset pricing, and information transfers

We study a firm’s manager’s voluntary disclosure decisions and those disclosure decisions’ asset pricing, cost of capital, and information transfer effects in a model where investors trade multiple securities. We: develop new asset pricing formulas when the manager makes no disclosure that impose testable cross-equation restrictions on firms’ market values; develop a wide array of comparative statics; obtain surprising findings about nondisclosure’s effects on investors’ perceptions of uncertainty about firms’ future cash flows; develop simple, interpretable expressions for firms’ cost of capital; and show how no disclosure by one firm generates informational externalities on other firms.

An analytical approach to new Keynesian models under the fiscal theory

This article illustrates a widely applicable frequency-domain methodology to solving multivariate linear rational expectations models. As an example, we solve a prototypical new Keynesian model under the assumption that primary surpluses evolve independently of government liabilities, a regime in which the fiscal theory of the price level is valid. The resulting analytical solution is useful in characterizing the cross-equation restrictions and illustrating the complex interaction between the fiscal theory and price rigidity. We also highlight some useful by-products of such method which are not easily obtainable for more sophisticated models using time-domain methods.

News, Noise, and Tests of Present Value Models

This paper develops a present value model of stock prices in which agents receive a noisy signal about the future economic fundamentals. The noisy signal serves two purposes. First, the noise in the signal generates temporary price fluctuations which are unrelated to economic fundamentals. Second, the noisy signal drives a wedge between the information set of agents and econometricians, which poses substantial challenges for econometrics testing of market efficiency. By employing conventional econometric analyses, an outside econometrician unknowingly conditions on a smaller information set than the agents. As a result, he might find that stock prices are excessively volatile and wrongly reject the cross-equation restrictions implied by the underlying economic model. I show that rationality restricts the contribution of noise to price fluctuations. My estimates show that the US stock market were indeed reacting rationally to news, and the variation in price-dividend ratio is mostly driven by noise and movements in discount rates, and almost nothing from movements in expected dividend growth.

Oil Price Elasticities and Oil Price Fluctuations

We study the identification of oil shocks in a structural vector autoregressive (SVAR) model of the oil market. First, we show that the cross-equation restrictions of a SVAR impose a nonlinear relation between the short-run price elasticities of oil supply and oil demand. This relation implies that seemingly plausible restrictions on oil supply elasticity may map into implausible values of the oil demand elasticity, and vice versa. Second, we propose an identification scheme that restricts these elasticities by minimizing the distance between the elasticities allowed by the SVAR and target values that we construct from a survey of relevant studies. Third, we use the identified SVAR to analyze sources and consequences of movements in oil prices. We find that (1) oil supply shocks and global demand shocks explain 50 and 35 percent of oil price fluctuations, respectively; (2) a drop in oil prices driven by supply shocks boosts economic activity in advanced economies, whereas it depresses economic activity in emerging economies; and (3) the selection of oil market elasticities is essential for understanding the source of oil price movements and to measuring the multipliers of oil prices on economic activity.

Misspecification and Expectations Correction in New Keynesian DSGE Models

This paper focuses on the dynamic misspecification that characterizes the class of small-scale New Keynesian models currently used in monetary and business cycle analysis, and provides a remedy for the typical difficulties these models have in accounting for the rich contemporaneous and dynamic correlation structure of the data. We suggest using a statistical model for the data as a device through which it is possible to adapt the econometric specification of the New Keynesian model such that the risk of omitting important propagation mechanisms is kept under control. A pseudo-structural form is built from the baseline system of Euler equations by forcing the state vector of the system to have the same dimension as the state vector characterizing the statistical model. The pseudo-structural form gives rise to a set of cross-equation restrictions that do not penalize the autocorrelation structure and persistence of the data. Standard estimation and evaluation methods can be used. We provide an empirical illustration based on USA quarterly data and a small-scale monetary New Keynesian model.

Multiple local optima for seemingly unrelated regression models

This paper provides an example of multiple local maxima to the likelihood function for a seemingly unrelated regression (SUR) model with a cross equation restriction. Since this is the least complex of the various structural equations models (SEM) and since maximum likelihood is often the preferred technique for SEM the problem of multiple local maxima is expected to be pervasive.

The Misspecification of Expectations in New Keynesian Models: A DSGE-VAR Approach

This paper tests the ability of popular New Keynesian models, which are traditionally used to study monetary policy and business cycles, to match the data regarding a key channel for monetary transmission: the dynamic interactions between macroeconomic variables and their corresponding expectations. In the empirical analysis, we exploit direct data on expectations from surveys. To explain the joint evolution of realized variables and expectations, we adopt a DSGE-VAR approach, which allows us to estimate all models in the continuum between the extremes of an unrestricted VAR, on one side, and a DSGE model in which the cross-equation restrictions are dogmatically imposed, on the other side. Moreover, the DSGE-VAR approach allows us to assess the extent, as well as the main sources, of misspecification in the model. The paper’s results illustrate the failure of New Keynesian models under the rational expectations hypothesis to account for the dynamic interactions between observed macroeconomic expectations and macroeconomic realizations. Confirming previous studies, DSGE restrictions prove valuable when the New Keynesian model is exempted from matching observed expectations. But when the model is required to match data on expectations, it can do so only by moving away, and hence substantially rejecting, DSGE restrictions. Finally, we investigate alternative models of expectations formation, including examples of extrapolative and heterogeneous expectations, and show that they can go some way toward reconciling the New Keynesian model with the data. Intermediate DSGE-VAR models, which avail themselves of DSGE prior restrictions, return to fit the data better than the unrestricted VAR. Hence, the results overall point to misspecification in the expectations formation side of the DSGE model, more than in the structural microfounded equations.

Bootstrapping DSGE Models

This paper explores the potential of bootstrap methods in the empirical evaluation of dynamic stochastic general equilibrium (DSGE) models and, more generally, in linear rational expectations models featuring unobservable (latent) components. We consider two dimensions. First, we provide mild regularity conditions that su¢ ce for the bootstrap Quasi-Maximum Likelihood (QML) estimator of the structural parameters to mimic the asymptotic distribution of the QML estimator. Consistency of the bootstrap allows to keep the probability of false rejections of the cross-equation restrictions under control. Second, we show that the realizations of the bootstrap estimator of the structural parameters can be constructively used to build novel, computationally straightforward tests for model misspecification, including the case of weak identification. In particular, we show that under strong identification and bootstrap consistency, a test statistic based on a set of realizations of the bootstrap QML estimator approximates the Gaussian distribution. Instead, when the regularity conditions for inference do not hold as e.g. it happens when (part of) the structural parameters are weakly identified, the above result is no longer valid. Therefore, we can evaluate how close or distant is the estimated model from the case of strong identification. Our Monte Carlo experimentations suggest that the bootstrap plays an important role along both dimensions and represents a promising evaluation tool of the cross-equation restrictions and, under certain conditions, of the strength of identification. An empirical illustration based on a small-scale DSGE model estimated on U.S. quarterly observations shows the practical usefulness of our approach.

Solving generalized multivariate linear rational expectations models

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paper—an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.

Smooth coefficient estimation of a seemingly unrelated regression

This paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model. We discuss the imposition of cross-equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection. A test of correct functional form for the entire system of equations is also constructed. Asymptotic and finite sample results are given. We illustrate our estimator by applying it to a cost system for US commercial banks. Our results show that most of the banks are operating under increasing returns to scale, but that returns to scale decrease with bank size.