Moving average stochastic volatility models with application to inflation forecast

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical application involving US inflation we find that these moving average stochastic volatility models provide better in-sample fitness and out-of-sample forecast performance than the standard variants with only stochastic volatility.     

Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

Forecasts in times of crises

Financial crises pose unique challenges for forecast accuracy. Using the IMF’s Monitoring of Fund Arrangements (MONA) database, we conduct the most comprehensive evaluation of IMF forecasts to date for countries in times of crises. We examine 29 macroeconomic variables in terms of bias, efficiency, and information content to find that IMF forecasts add substantial informational value, as they consistently outperform naive forecast approaches. However, we also document that there is room for improvement: two-thirds of the key macroeconomic variables that we examine are forecast inefficiently, and six variables (growth of nominal GDP, public investment, private investment, the current account, net transfers, and government expenditures) exhibit significant forecast biases. The forecasts for low-income countries are the main drivers of forecast biases and inefficiency, perhaps reflecting larger shocks and lower data quality. When we decompose the forecast errors into their sources, we find that forecast errors for private consumption growth are the key contributor to GDP growth forecast errors. Similarly, forecast errors for non-interest expenditure growth and tax revenue growth are crucial determinants of the forecast errors in the growth of fiscal budgets. Forecast errors for balance of payments growth are influenced significantly by forecast errors in goods import growth. The results highlight which macroeconomic aggregates require further attention in future forecast models for countries in crises.     

Estimation and inference under economic restrictions

Estimation of economic relationships often requires imposition of constraints such as positivity or monotonicity on each observation. Methods to impose such constraints, however, vary depending upon the estimation technique employed. We describe a general methodology to impose (observation-specific) constraints for the class of linear regression estimators using a method known as constraint weighted bootstrapping. While this method has received attention in the nonparametric regression literature, we show how it can be applied for both parametric and nonparametric estimators. A benefit of this method is that imposing numerous constraints simultaneously can be performed seamlessly. We apply this method to Norwegian dairy farm data to estimate both unconstrained and constrained parametric and nonparametric models.     

Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation

We characterize full implementation of social choice sets in mixed-strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu–Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.     

The sampling distribution of forecasts from a first-order autoregression

Previous work on characterising the distribution of forecast errors in time series models by statistics such as the asymptotic mean square error has assumed that observations used in estimating parameters are statistically independent of those used to construct the forecasts themselves. This assumption is quite unrealistic in practical situations and the present paper is intended to tackle the question of how the statistical dependence between the parameter estimates and the final period observations used to generate forecasts affects the sampling distribution of the forecast errors. We concentrate on the first-order autoregression and, for this model, show that the conditional distribution of forecast errors given the final period observation is skewed towards the origin and that this skewness is accentuated in the majority of cases by the statistical dependence between the parameter estimates and the final period observation.     

Nonparametric state price density estimation using constrained least squares and the bootstrap

The economic theory of option pricing imposes constraints on the structure of call functions and state price densities. Except in a few polar cases, it does not prescribe functional forms. This paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions (such as monotonicity and convexity) within a single least squares procedure. The bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints. We apply the techniques to option pricing data on the DAX.     

Performance evaluation of the LDR and the PSH with forecast errors

Despite its ability to produce optimal solutions, the Linear Decision Rule (LDR) has not had a significant impact in the business environment. The Production Switching Heuristic (PSH), which has shown promising results when compared with the LDR, has experienced some business application because of its practicability and flexibility. During aggregate production planning, forecast errors are almost unavoidable, but the sensitivity of these models to such errors has not been thoroughly tested. Insufficient attention has been paid to truly understand the cost effects of forecast errors and other important interactions. The study investigates these issues by analyzing the results of 740 simulated problems.Using the famous “paint factory” cost data, the sensitivity of the LDR and the PSH are examined under various experimental conditions. The factors controlled at different levels are: forecast error mean, forecast error standard deviation, demand pattern, demand variability, and cost coefficients. The results show that 1) the PSH is generally less sensitive than the LDR to forecast errors, 2) both forecast error mean and standard deviation effectively measure the severity of forecast errors, and 3) underforecasts cause less cost penalty than overforecasts.The outcome of the study has helpful managerial implications for aggregate planning related decisionmaking. It suggests that the use of the PSH could result in potential cost savings even if significant forecast errors are envisioned as long as the period-to-period demand variability is not substantially high. Also, BIAS warrants more attention than MSE in evaluating the extent of forecast errors and their eventual cost impact on aggregate production planning.     

Nonparametric Bayesian modelling of monotone preferences for discrete choice experiments

Discrete choice experiments are widely used to learn about the distribution of individual preferences for product attributes. Such experiments are often designed and conducted deliberately for the purpose of designing new products. There is a long-standing literature on nonparametric and Bayesian modelling of preferences for the study of consumer choice when there is a market for each product, but this work does not apply when such markets fail to exist as is the case with most product attributes. This paper takes up the common case in which attributes can be quantified and preferences over these attributes are monotone. It shows that monotonicity is the only shape constraint appropriate for a utility function in these circumstances. The paper models components of utility using a Dirichlet prior distribution and demonstrates that all monotone nondecreasing utility functions are supported by the prior. It develops a Markov chain Monte Carlo algorithm for posterior simulation that is reliable and practical given the number of attributes, choices and sample sizes characteristic of discrete choice experiments. The paper uses the algorithm to demonstrate the flexibility of the model in capturing heterogeneous preferences and applies it to a discrete choice experiment that elicits preferences for different auto insurance policies.     

Efficient estimation of probit models with correlated errors

Maximum Likelihood (ML) estimation of probit models with correlated errors typically requires high-dimensional truncated integration. Prominent examples of such models are multinomial probit models and binomial panel probit models with serially correlated errors. In this paper we propose to use a generic procedure known as Efficient Importance Sampling (EIS) for the evaluation of likelihood functions for probit models with correlated errors. Our proposed EIS algorithm covers the standard GHK probability simulator as a special case. We perform a set of Monte Carlo experiments in order to illustrate the relative performance of both procedures for the estimation of a multinomial multiperiod probit model. Our results indicate substantial numerical efficiency gains for ML estimates based on the GHK–EIS procedure relative to those obtained by using the GHK procedure.     

A combined random effect and fixed effect forecast for panel data models

When some of the regressors in a panel data model are correlated with the random individual effects, the random effect (RE) estimator becomes inconsistent while the fixed effect (FE) estimator is consistent. Depending on the various degree of such correlation, we can combine the RE estimator and FE estimator to form a combined estimator which can be better than each of the FE and RE estimators. In this paper, we are interested in whether the combined estimator may be used to form a combined forecast to improve upon the RE forecast (forecast made using the RE estimator) and the FE forecast (forecast using the FE estimator) in out-of-sample forecasting. Our simulation experiment shows that the combined forecast does dominate the FE forecast for all degrees of endogeneity in terms of mean squared forecast errors (MSFE), demonstrating that the theoretical results of the risk dominance for the in-sample estimation carry over to the out-of-sample forecasting. It also shows that the combined forecast can reduce MSFE relative to the RE forecast for moderate to large degrees of endogeneity and for large degrees of heterogeneity in individual effects.     

On implied volatility for options—Some reasons to smile and more to correct

We analyze the properties of the implied volatility, the commonly used volatility estimator by direct option price inversion. It is found that the implied volatility is subject to a systematic bias in the presence of pricing errors, which makes it inconsistent to the underlying volatility. We propose an estimator of the underlying volatility by first estimating nonparametrically the option price function, followed by inverting the nonparametrically estimated price. It is shown that the approach removes the adverse impacts of the pricing errors and produces a consistent volatility estimator for a wide range of option price models. We demonstrate the effectiveness of the proposed approach by numerical simulation and empirical analysis on S&P 500 option data.     

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

A flexible parametric approach for estimating switching regime models and treatment effect parameters

In this paper, we propose a flexible, parametric class of switching regime models allowing for both skewed and fat-tailed outcome and selection errors. Specifically, we model the joint distribution of each outcome error and the selection error via a newly constructed class of multivariate distributions which we call generalized normal mean–variance mixture distributions. We extend Heckman’s two-step estimation procedure for the Gaussian switching regime model to the new class of models. When the distributions of the outcome errors are asymmetric, we show that an additional correction term accounting for skewness in the outcome error distribution (besides the analogue of the well known inverse mill’s ratio) needs to be included in the second step regression. We use the two-step estimators of parameters in the model to construct simple estimators of average treatment effects and establish their asymptotic properties. Simulation results confirm the importance of accounting for skewness in the outcome errors in estimating both model parameters and the average treatment effect and the treatment effect for the treated.     

Combining Forecasts from Nested Models*

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local‐to‐zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error‐minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach.     

Heterogeneous treatment effects: Instrumental variables without monotonicity?

Imbens and Angrist (1994) were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables. More recently, Heckman and Vytlacil (1999) suggested the estimation of a variety of treatment effect parameters using a local version of their approach. We investigate the sensitivity of the respective estimates to random departures from monotonicity. Approximations to the respective bias terms are derived. In an empirical application the bias is calculated and bias corrected estimates are obtained. The accuracy of the approximation is investigated in a Monte Carlo study.     

Combining VAR and DSGE forecast densities

A popular macroeconomic forecasting strategy utilizes many models to hedge against instabilities of unknown timing; see (among others) Stock and Watson (2004), Clark and McCracken (2010), and Jore et al. (2010). Existing studies of this forecasting strategy exclude dynamic stochastic general equilibrium (DSGE) models, despite the widespread use of these models by monetary policymakers. In this paper, we use the linear opinion pool to combine inflation forecast densities from many vector autoregressions (VARs) and a policymaking DSGE model. The DSGE receives a substantial weight in the pool (at short horizons) provided the VAR components exclude structural breaks. In this case, the inflation forecast densities exhibit calibration failure. Allowing for structural breaks in the VARs reduces the weight on the DSGE considerably, but produces well-calibrated forecast densities for inflation.     

Determinants and Dynamics of Current Account Reversals: An Empirical Analysis

We use panel probit models with unobserved heterogeneity, state dependence and serially correlated errors in order to analyse the determinants and the dynamics of current account reversals for a panel of developing and emerging countries. The likelihood‐based inference of these models requires high‐dimensional integration for which we use efficient importance sampling. Our results suggest that current account balance, terms of trades, foreign reserves and concessional debt are important determinants of current account reversal. Furthermore, we find strong evidence for serial dependence in the occurrence of reversals. While the likelihood criterion suggest that state dependence and serially correlated errors are essentially observationally equivalent, measures of predictive performance provide support for the hypothesis that the serial dependence is mainly due to serially correlated country‐specific shocks related to local political or macroeconomic events.     

Forecast Encompassing and Parameter Estimation*

A desirable property of a forecast is that it encompasses competing predictions, in the sense that the accuracy of the preferred forecast cannot be improved through linear combination with a rival prediction. In this paper, we investigate the impact of the uncertainty associated with estimating model parameters in‐sample on the encompassing properties of out‐of‐sample forecasts. Specifically, using examples of non‐nested econometric models, we show that forecasts from the true (but estimated) data generating process (DGP) do not encompass forecasts from competing mis‐specified models in general, particularly when the number of in‐sample observations is small. Following this result, we also examine the scope for achieving gains in accuracy by combining the forecasts from the DGP and mis‐specified models.     

Adaptive learning forecasting,with applications in forecasting agricultural prices

We introduce a new forecasting methodology, referred to as adaptive learning forecasting, that allows for both forecast averaging and forecast error learning. We analyze its theoretical properties and demonstrate that it provides a priori MSE improvements under certain conditions. The learning rate based on past forecast errors is shown to be non-linear. This methodology is of wide applicability and can provide MSE improvements even for the simplest benchmark models. We illustrate the method’s application using data on agricultural prices for several agricultural products, as well as on real GDP growth for several of the corresponding countries. The time series of agricultural prices are short and show an irregular cyclicality that can be linked to economic performance and productivity, and we consider a variety of forecasting models, both univariate and bivariate, that are linked to output and productivity. Our results support both the efficacy of the new method and the forecastability of agricultural prices.