Reduced Form Parameters Research Articles

When Harry Bet with Sally: An Empirical Analysis of Multiple Peer Effects in Casino Gambling Behavior

In many consumption settings (e.g., restaurants), individuals consume products either alone or with their peers (e.g., friends). In this study, we propose a general framework for modeling peer effects by including two new peer effects: the exogenous peer effect (exogenous factors that could change the peer’s behavior) and the peer presence effect (when the peer is present but not consuming). We also include the well known endogenous peer effect. We develop an empirical model that allows us to identify all three effects simultaneously and apply the model to behavioral data from a casino setting. It is a simultaneous equation model with the structural parameters expressed as a function of the ratio of the reduced form parameters. This necessitates the use of the Minimum Expected Loss approach, allowing us to obtain consistent estimates at the individual level. Our data comprise detailed gambling activity for a panel of individuals at a single casino over a two-year period. Our results show that all three types of peer effects exist. These effects vary across individuals and exhibit considerable asymmetry within pairs of peers. We discuss how our results can help managers allocate resources more effectively and policy makers formulate regulatory guidelines with more complete information.

Bayesian and Frequentist Inference in Partially Identified Models

A large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite-dimensional reduced form parameter vector. It is used to analyze the dierences between frequentist confidence sets and Bayesian credible sets in partially identified models. A key dierence is that frequentist set estimates extend beyond the boundaries of the identified set (conditional on the estimated reduced form parameter), whereas Bayesian credible sets can asymptotically be located in the interior of the identified set. Our asymptotic approximations are illustrated in the context of simple moment inequality models and a numerical illustration for a two-player entry game is provided.

MEASUREMENT ERRORS AND CENSORED STRUCTURAL LATENT VARIABLES MODELS

We consider censored structural latent variables models where some exogenous variables are subject to additive measurement errors. We demonstrate that overidentification conditions can be exploited to provide natural instruments for the variables measured with errors, and we propose a two-stage estimation procedure. The first stage involves substituting available instruments in lieu of the variables that are measured with errors and estimating the resulting reduced form parameters using consistent censored regression methods. The second stage obtains structural form parameters using the conventional linear simultaneous equations model estimators.

Algebraic Theory of Indentification in Parametric Models

The paper presents the problem of identification in parametric models from the algebraic point of view. We argue that it is not just another perspective but the proper one. That is using our approach we can see the very nature of the identification problem, which is slightly different than that suggested in the literature. In practice it means that in many models we can unambiguously estimate parameters that have been thought as unidentifiable. This is illustrated in the case of Simultaneous Equations Model (SEM), where our analysis leads to conclusion that existing identification conditions, although correct, are based on the inappropriate premise: only the structural parameters that are in one–to–one correspondence with the reduced form parameters are identified. We will show that this is not true. In fact there are other structural parameters, which are identified, but can not be uniquely recovered from the reduced form parameters. Although we apply our theory only to SEM, it can be used in many standard econometric models.

Health insurance and the consumer bankruptcy decision: Evidence from expansions of Medicaid

Anecdotal evidence and several observational studies suggest that out-of-pocket medical costs are pivotal in a large fraction of consumer bankruptcy decisions. In this paper, we assess the contribution of medical costs to household bankruptcy risk by exploiting plausibly exogenous variation in publicly provided health insurance. Using cross-state variation in Medicaid expansions from 1992 to 2004, we find that a 10 percentage point increase in Medicaid eligibility reduces personal bankruptcies by 8%, with no evidence that business bankruptcies are similarly affected. We interpret our findings with a model in which health insurance imperfectly substitutes for other forms of financial protection, and we use the model to present simple calibration results which illustrate how our reduced-form parameter estimate affects the optimal level of health insurance benefits. We conclude with calculations which suggest that out-of-pocket medical costs are pivotal in roughly 26% of personal bankruptcies among low-income households.

Measuring core inflation in Italy comparing aggregate vs. disaggregate price data

This paper focuses on the core inflation measurement in Italy using univariate (national-level inflation) vs. multivariate (city-level inflation) models during the period 1970–2006. We derive algebraic expressions that allow comparison between the reduced form parameters of univariate and multivariate local level models in the context of contemporaneous and temporal aggregation. We illustrate the relevance of these theoretical results for the empirical analysis of time series. Using Italian data, we find that multivariate and univariate models extract similar core inflation measures when analyzing the moderate-low inflation period. In contrast, the two competing models yield different trends when modeling the Great Inflation period.

Structural time series models and aggregation: some analytical results

This paper derives the analytical relationships between structural and reduced form parameters of the local linear trend model with correlated shocks. The results are also valid in the context of temporal aggregation of local level and local linear trend models with their corresponding ARIMA(0, 1, 1) and ARIMA(0, 2, 2) reduced forms.

THE POLITICAL ECONOMY OF INTERGENERATIONAL INCOME MOBILITY

The intergenerational elasticity of income is considered one of the best measures of the degree to which a society gives equal opportunity to its members. While much research has been devoted to measuring this reduced-form parameter, less is known about its underlying structural determinants. Using a model with exogenous talent endowments, endogenous parental investment in children, and endogenous redistributive institutions, we identify the structural parameters that govern the intergenerational elasticity of income. The model clarifies how the interaction between private and collective decisions determines the equilibrium level of social mobility. Two societies with similar economic and biological fundamentals may have vastly different degrees of intergenerational mobility depending on their political institutions. We offer empirical evidence in line with the predictions of the model. We conclude that international comparisons of intergenerational elasticity of income are not particularly informative about fairness without taking into account differences in politico-economic institutions. (JEL E24, J62, J68, P16)

COMPARATIVE FISCAL RESPONSE EFFECTS OF DEBT RELIEF: AN APPLICATION TO AFRICAN HIPCS

AbstractAs part of the efforts of the international donor community to scale up aid to Africa, substantial debt relief has been granted in recent years through the Heavily Indebted Poor Countries (HIPC) Initiative and its successor, the Multilateral Debt Relief Initiative. This paper tries to assess, for a sample of 24 African countries that have at least reached decision point status in the HIPC Initiative, to what extent this debt relief has created fiscal space in recipient country budgets, and what, on average, the actual fiscal response effects have been, relative to other types of aid. Inspired by the fiscal response literature, we model public finance behaviour as a system of structural equations and estimate the reduced form parameters in a Vector Autoregressive framework. In general, we are unable to find evidence that debt relief might provoke no or even perverse fiscal responses. On average, debt relief affects public finance behaviour in a desired way, with effects being most similar to those of its most direct substitute, programme grants.

Stress-testing Financial Systems: An Overview of Current Methodologies

This paper reviews the state-of-the-art of macro stress-testing methodologies. Substantial progress has been made both in the econometric analysis of financial soundness indicators and in the simulation of value-at-risk measures to assess system-wide vulnerabilities. However, a number of methodological challenges still remain concerning the correlation of market and credit risks over time and across institutions, the limited time horizon generally used for the analysis and the potential instability of reduced-form parameter estimates because of feedback effects. Further research in this area might also focus on how to use macro stress-testing techniques as an operational tool to incorporate financial stability considerations into monetary policy decision-making.

Takeup, social multipliers and optimal social insurance

This paper examines the optimal provision of unemployment insurance (UI) in a framework that accounts for behavioral responses along both the intensive and extensive margins. Two formulations of takeup are considered: in the first, individuals face a takeup cost that is exogenous; in the second, the cost depends endogenously on the takeup rate. Such endogenous costs to takeup lead to a social multiplier, a reduced-form parameter summarizing the strength of social interactions. This paper derives a formula for the optimal replacement rate in terms of the takeup and duration elasticities, and the social multiplier. The formula is applied by estimating the social multiplier using policy variation in UI benefit levels. The results suggest that social multiplier effects account for 35% of the total effect of UI on takeup and yield an optimal replacement rate around 60% of pre-unemployment wages, 20% higher than previous estimates.

Avoiding arbitrary exclusion restrictions using ratios of reduced-form estimates

We show how to obtain coherent structural-form (SF) exclusion restrictions using the reduced-form (RF) parameter ratios. It will be shown that an over-identified SF corresponds to a group of regressors sharing the same RF ratio value; those regressors should be excluded jointly from the SF. If there is no group structure, then the SF is just-identified; in this case, however, it is no longer clear which regressor should be excluded. Hence, just-identified SF’s are more arbitrary than over-identified SF’s in terms of exclusion restrictions. This is in stark contrast to the notion that the former is less arbitrary than the latter, because the former excludes fewer regressors. We formalize these points, and then suggest to find the number of modes in the estimated RF ratios as a way to find groups in the ratios. For this purpose, an informal graphical method using a kernel nonparametric method and a formal modality test are employed. An empirical example with selling price in a residential real estate market and duration on the market as two endogenous variables is provided.

A comparative analysis of macro stress-testing methodologies with application to Finland

This paper reviews the state-of-the-art of macro stress-testing methodologies. We assess the progress made both in the econometric analysis of balance sheet indicators and in the simulation of value-at-risk measures to assess system-wide vulnerabilities. To illustrate the main analytical approaches in the literature, we estimate two different models for stress-testing purposes using data for Finland over the time period from 1986 to 2003. The Finnish experience in the early 1990s appears particularly suited for macro stress-testing as it includes a severe recession with significantly higher-than-average default rates and banks’ loan losses. We highlight a number of methodological challenges that still remain concerning in particular the correlation of market and credit risks over time and across institutions, the limited time horizon generally used for macro stress-testing and the potential instability of reduced-form parameter estimates because of feedback effects.

Simultaneous equations in ordered discrete responses with regressor‐dependent thresholds

Summary The parameters of ordered discrete response (ODR) models are identified only up to a positive scale. In this paper, we examine the identification issue for simultaneous equations with ODR, where the well-known identification problem in simultaneous equations of recovering structural-form parameters from reduced-form parameters is compounded with the ODR identification problem. We allow the thresholds in ODR to be regressor dependent as well as constant; the former is particularly challenging because threshold parameters get mixed with regression parameters, adding one more dimension to the identification problem. We also explore a cross-equation restriction on threshold differences, under which the structural form parameters are fully identified as if the dependent variables are continuously distributed. An empirical example with farm–household joint labour supply is provided to illustrate the identification issues, to show how our proposals work and to apply tests devised for the threshold constancy and cross-equation restrictions.

Semiparametric three‐step estimation methods for simultaneous equation systems

AbstractThis paper proposes a new method for estimating a structural model of labour supply in which hours of work depend on (log) wages and the wage rate is considered endogenous. The main innovation with respect to other related estimation procedures is that a nonparametric additive structure in the hours of work equation is permitted. Though the focus of the paper is on this particular application, a three‐step methodology for estimating models in the presence of the above econometric problems is described. In the first step the reduced form parameters of the participation equation are estimated by a maximum likelihood procedure adapted for estimation of an additive nonparametric function. In the second step the structural parameters of the wage equation are estimated after obtaining the selection‐corrected conditional mean function. Finally, in the third step the structural parameters of the labour supply equation are estimated using local maximum likelihood estimation techniques. The paper concludes with an application to illustrate the feasibility, performance and possible gain of using this method. Copyright © 2005 John Wiley & Sons, Ltd.

Modeling Nonlinear Autoregressive Distributed Lag Models: A New Approach

It is a common practice in econometrics that estimation is carried out in terms of the reduced form parameters and the structural form parameters are retrieved using the functional relationship between structural form parameters and the reduced form parameters. The reduced form of many useful economic models is a nonlinear distributed lag model (NLADL) with error structure which may have autocorrelation. In addition, the relationship between the reduced form and the structural parameters is often nonlinear and in a ratio form. In such situations existing sampling theory estimation procedures result in estimators for the structural parameters which do not have finite moments and do not possess optimal sampling properties. As an alternative, we propose a two step Bayesian estimation method. The Bayesian method has great potential and allows us to obtain the posterior probability density functions of all parameters of interest. In particular, its application for the analysis of adaptive expectation partial adjustment models for which the reduced form is a NLADL model, has been found extremely useful. An application to Nerlove’s supply response function supports the proposed methodology.

ON THE ASYMPTOTIC DISTRIBUTION OF IMPULSE RESPONSE FUNCTIONS WITH LONG-RUN RESTRICTIONS

This paper adopts a two-step technique to estimate vector error correction models and provides the asymptotic distribution of the impulse response functions of such a system. The method combines two popular tools in econometrics, namely, vector autoregressive cointegration analysis in the first step and vector autoregression analysis in the second. The proposed model structure is very general in the sense that all just-identifying or overidentifying schemes that can be expressed as linear restrictions on either the contemporaneous or long-run impact of the shocks are allowed for. The long-run restrictions complicate the derivation of the asymptotic distribution of the parameter estimates as these restrictions are a function of the reduced form parameters. Consequently, the asymptotic distribution involves an extra partial derivative. This paper adopts a two-step procedure to estimate vector error correction models and provides the asymptotic distribution of the impulse response functions of such a system even if those contain long-run restrictions. The method combines two popular tools in econometrics, namely, vector autoregressive cointegration analysis and vector autoregressions. Vector autoregression (VAR) analysis has become a popular tool in empirical macroeconomics and finance. An important element in these models is the identification of independent shocks. Originally (Sims, 1980) a Choleski decomposition of the covariance matrix of the residuals was used for this purpose, thereby implicitly assuming a recursive causal ordering. Later on, structural VAR models were developed, in which the identifying restrictions are explicitly derived from theory. These restrictions can involve either contemporaneous relationships (Blanchard and Watson, 1986; Bernanke, 1986;

From the Help Desk: Polynomial Distributed Lag Models

Polynomial distributed lag models (PDLs) are finite-order distributed lag models with the impulse–response function constrained to lie on a polynomial of known degree. You can estimate the parameters of a PDL directly via constrained ordinary least squares, or you can derive a reduced form of the model via a linear transformation of the structural model, estimate the reduced-form parameters, and recover estimates of the structural parameters via an inverse linear transformation of the reduced-form parameter estimates. This article demonstrates both methods using Stata.

CONSISTENT ESTIMATION IN COINTEGRATED VECTOR AUTOREGRESSIVE MODELS WITH NONLINEAR TIME TRENDS IN COINTEGRATING RELATIONS

This paper studies the consistency of the Gaussian maximum likelihood estimator in a cointegrated vector autoregressive model with nonlinear time trends in cointegrating relations. The results are proved in a coordinate free framework that readily allows for general nonlinear parameter restrictions and makes it possible to show the consistency of reduced form parameter estimators without assuming identifiability of underlying structural parameters. Various consistency results for structural parameter estimators can then be obtained by imposing suitable identification conditions for the parameters of interest but not necessarily for nuisance parameters. Orders of consistency are also obtained because they are needed to develop a related asymptotic theory of statistical inference.

Bias and Sensitivity of Multipliers

Multipliers measure the derivatives of endogenous variables with respect to exogenous shocks and are functions of the structural parameters of an economic model. Substitution of the structural parameter estimates yields a so-called derived estimate for a multiplier or any reduced-form parameter. Derived estimates are biased. This paper presents first-order approximations to the biases and sensitivities of multipliers. The good performance of a flawed formula in input–output analysis is illuminated.