ENSAE Paris

Summary Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE ) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator. (JEL C21, C23, D72, J31, J51, L82)

A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value ; the membership function is monotonia on both sides of this mean value. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle. The practical use of fuzzified operations is shown to be easy, requiring no more computation than when dealing with error intervals in classic tolerance analysis. The field of applications of this approach seems to be large, since it allows many known algorithms to be fitted to fuzzy data.

This paper studies the links between productivity, innovation and research at the firm level. We introduce three new features: (i) A structural model that explains productivity by innovation output, and innovation output by research investment: (ii) New data on French manufacturing firms, including the number of European patents and the percentage share of innovative sales, as well as firm-level demand pull and technology push indicators; (iii) Econometric methods which correct for selectivity and simultaneity biases and take into account the statistical features of the available data: only a small proportion of firms engage in research activities and/or apply for patents; productivity, innovation and research are endogenously determined; research investment and capital are truncated variables, patents are count data and innovative sales are interval data. We find that using the more widespread methods, and the more usual data and model specification, may lead to sensibly different estimates. We find in particular that simultaneity tends to interact with selectivity, and that both sources of biases must be taken into account together. However our main results are consistent with many of the stylized facts of the empirical literature. The probability of engaging in research (R&D) for a firm increases with its size (number of employees), its market share and diversification, and with the demand pull and technology push indicators. The research effort (R&D capital intensity) of a firm engaged in research increases with the same variables, except for size (its research capital being strictly proportional to size). The firm innovation output, as measured by patent numbers or innovative sales, rises with its research effort and with the demand pull and technology indicators, either directly or indirectly through their effects on research. Finally, firm productivity correlates positively with a higher innovation output, even when controlling for the skill composition of labor as well as for physical capital intensity.

We examine the sales of French manufacturing firms in 113 destinations, including France itself. Several regularities stand out: (i) the number of French firms selling to a market, relative to French market share, increases systematically with market size; (ii) sales distributions are similar across markets of very different size and extent of French participation; (iii) average sales in France rise systematically with selling to less popular markets and to more markets. We adopt a model of firm heterogeneity and export participation which we estimate to match moments of the French data using the method of simulated moments. The results imply that over half the variation across firms in market entry can be attributed to a single dimension of underlying firm heterogeneity: efficiency. Conditional on entry, underlying efficiency accounts for much less of the variation in sales in any given market. We use our results to simulate the effects of a 10 percent counterfactual decline in bilateral trade barriers on French firms. While total French sales rise by around $16 billion (U.S.), sales by the top decile of firms rise by nearly $23 billion (U.S.). Every lower decile experiences a drop in sales, due to selling less at home or exiting altogether.

Abstract This book deals with a new generation of econometric methods leading to criterion functions without simple analytical expression. The difficulty often comes from the presence of integrals of large dimension in the probability density function or in the moments, and the idea is to circumvent this numerical difficulty by an approach based on simulation. The main methods considered are the methods of Simulated Moments, Simulated Maximum Likelihood, Simulated Pseudo‐Maximum Likelihood, Simulated Non‐Linear Least Squares, and Indirect Inference. These methods are applied to Limited Dependent Variables Models, to Financial Series, and to Switching Regime Models.

This paper compares the role innovation plays in productivity across four European countries, France, Germany, Spain, and the UK, using firm-level data from the internationally harmonized Community Innovation Surveys (CIS3). Despite a considerable number of national firm-level studies analysing this relationship, cross-country comparisons using micro data are still rare. We apply a structural model that describes the link between R&D expenditure, innovation output, and productivity (CDM model). Our econometric results suggest that overall the systems driving innovation and productivity are remarkably similar across these four countries, although we also find interesting differences, particularly in the variation in productivity that is associated with more or less innovative activities.

This paper studies a classical extension of the Black and Scholes model for option pricing, often known as the Hull and White model. Our specification is that the volatility process is assumed not only to be stochastic, but also to have long‐memory features and properties. We study here the implications of this continuous‐time long‐memory model, both for the volatility process itself as well as for the global asset price process. We also compare our model with some discrete time approximations. Then the issue of option pricing is addressed by looking at theoretical formulas and properties of the implicit volatilities as well as statistical inference tractability. Lastly, we provide a few simulation experiments to illustrate our results.

This paper deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo techniques usually have difficulties with well-separated modes such as occur here; the Markov chain Monte Carlo sampler stays within a neighbourhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed on the Markov chain Monte Carlo sampler using tempered transitions based on Langevin algorithms. However, as the prior distribution does not distinguish between the different components, the posterior mixture distribution is symmetric and thus standard estimators such as posterior means cannot be used. Since this is also true for most non-symmetric priors, we propose alternatives for Bayesian inference for permutation invariant posteriors, including a cluster...

Abstract This article reports the results from a randomized experiment designed to evaluate the direct and indirect (displacement) impacts of job placement assistance on the labor market outcomes of young, educated job seekers in France. We use a two-step design. In the first step, the proportions of job seekers to be assigned to treatment (0%, 25%, 50%, 75%, or 100%) were randomly drawn for each of the 235 labor markets (e.g., cities) participating in the experiment. Then, in each labor market, eligible job seekers were randomly assigned to the treatment, following this proportion. After eight months, eligible, unemployed youths who were assigned to the program were significantly more likely to have found a stable job than those who were not. But these gains are transitory, and they appear to have come partly at the expense of eligible workers who did not benefit from the program, particularly in labor markets where they compete mainly with other educated workers, and in weak labor markets. Overall, the program seems to have had very little net benefits.

Abstract This paper attempts to enlarge the class of Threshold Heteroscedastic Models (TARCH) introduced by Zakoían (1991a). We show that it is possible to relax the positivity constraints on the parameters of the conditional variance. Unconstrained models provide a greater generality of the paths allowing for nonlinearities in the volatility. Cyclical behaviour is permitted as well as different relative impacts of positive and negative shocks on volatility, depending on their size. We give empirical evidence using French stock returns.

Summary Linear regressions with period and group fixed effects are widely used to estimate policie’s effects: 26 of the 100 most cited papers published by the American Economic Review from 2015 to 2019 estimate such regressions. It has recently been shown that those regressions may produce misleading estimates if the policy’s effect is heterogeneous between groups or over time, as is often the case. This survey reviews a fast-growing literature that documents this issue and that proposes alternative estimators robust to heterogeneous effects. We use those alternative estimators to revisit Wolfers (2006a).

We derive the implications from the absence of arbitrage in dynamic securities markets with bid-ask spreads. The absence of arbitrage is equivalent to the existence of at least an equivalent probability measure that transforms some process between the bid and the ask price processes of traded securities into a martingale. The martingale measures can be interpreted as possible linear pricing rules and can be used to determine the investment opportunities available in such an economy. The minimum cost at which a contingent claim can be obtained through securities trading is its largest expected value with respect to the martingale measures. Journal of Economic Literature Classification Numbers: G11, G12, G13, D52, and D90.

1 Introduction.- 1.1 The Development of ARCH Models.- 1.2 Book Content.- 2 Linear and Nonlinear Processes.- 2.1 Stochastic Processes.- 2.2 Weak and Strict Stationarity.- 2.3 A Few Examples.- 2.4 Nonlinearities.- 2.4.1 Portmanteau Statistic.- 2.4.2 Some Implications of the White Noise Hypothesis..- 2.5 Exercises.- 3 Univariate ARCH Models.- 3.1 A Heteroscedastic Model of Order One.- 3.1.1 Description of the Model.- 3.1.2 Properties of the Innovation Process ?.- 3.1.3 Properties of the Y Process.- 3.1.4 Distribution of the Error Process.- 3.2 General Properties of ARCH Processes.- 3.2.1 Various Extensions.- 3.2.2 Stationarity of a GARCH(p, q) Process.- 3.2.3 Kurtosis.- 3.2.4 Yule-Walker Equations for the Square of a GARCH Process.- 3.3 Exercises.- 4 Estimation and Tests.- 4.1 Pseudo Maximum Likelihood Estimation.- 4.1.1 Generalities.- 4.1.2 The i.i.d. case.- 4.1.3 Regression Model with Heteroscedastic Errors.- 4.1.4 Regression Model with ARCH Errors.- 4.1.5 Application to a GARCH Model.- 4.1.6 Stochastic Variance Model.- 4.2 Two Step Estimation Procedures.- 4.2.1 Description of the Procedures.- 4.2.2 Comparison of the Estimation Methods under Conditional Normality.- 4.2.3 Efficiency Loss Analysis.- 4.3 Forecast Intervals.- 4.4 Homoscedasticity Test.- 4.4.1 Regression Models with Heteroscedastic Errors.- 4.5 The Test Statistic Interpretation.- 4.5.1 Application to Regression Models with ARCH or GARCH Errors.- Appendix 4.1: Matrices I and J.- Appendix 4.2: Derivatives of the Log-Likelihood Function and Information Matrix for a Regression Model with ARCH Errors.- 4.6 Exercises.- 5 Some Applications of Univariate ARCH Models.- 5.1 Leptokurtic Aspects of Financial Series and Aggregation.- 5.1.1 The Normality Assumption.- 5.1.2 The Choice of a Time Unit.- 5.2 ARCH Processes as an Approximation of Continuous Time Processes.- 5.2.1 Stochastic Integrals.- 5.2.2 Stochastic Differential Equations.- 5.2.3 Some Equations and Their Solutions.- 5.2.4 Continuous and Discrete Time.- 5.2.5 Examples.- 5.2.6 Simulated Estimation Methods.- 5.3 The Random Walk Hypothesis.- 5.3.1 Description of the Hypothesis.- 5.3.2 The Classical Test Procedure of the Random Walk Hypothesis.- 5.3.3 Limitations of the Portmanteau Tests.- 5.3.4 Portmanteau Tests with Heteroscedasticity.- 5.4 Threshold Models.- 5.4.1 Definition and Stationarity Conditions.- 5.4.2 Homoscedasticity Test.- 5.4.3 Qualitative ARCH Models.- 5.4.4 Nonparametric Approaches.- 5.5 Integrated Models.- 5.5.1 The IGARCH(1,1) Model.- 5.5.2 The Persistence Effect.- 5.5.3 Weak and Strong Stationarity.- 5.5.4 Example.- 5.6 Exercises.- 6 Multivariate ARCH Models.- 6.1 Unconstrained Models.- 6.1.1 Multivariate GARCH Models.- 6.1.2 Positivity Constraints.- 6.1.3 Stability Conditions.- 6.1.4 An Example.- 6.1.5 Spectral Decompositions.- 6.2 Constrained Models.- 6.2.1 Diagonal Models.- 6.2.2 Models with Constant Conditional Correlations.- 6.2.3 Models with Random Coefficients.- 6.2.4 Model Based on a Spectral Decomposition.- 6.2.5 Factor ARCH Models.- 6.3 Estimation of Heteroscedastic Dynamic Models.- 6.3.1 Pseudo Maximum Likelihood Estimators.- 6.3.2 Asymptotic Properties of the Pseudo Maximum Likelihood Estimator.- 6.3.3 Model with Constant Conditional Correlations.- 6.3.4 Factor Models.- 7 Efficient Portfolios and Hedging Portfolios.- 7.1 Determination of an Efficient Portfolio.- 7.1.1 Securities and Portfolios.- 7.1.2 Mean Variance Criterion.- 7.1.3 Mean Variance Efficient Portfolios.- 7.2 Properties of the Set of Efficient Portfolios.- 7.2.1 The Set of Efficient Portfolios.- 7.2.2 Factors.- 7.3 Asymmetric Information and Aggregation.- 7.3.1 Incoherency of the Mean Variance Approach.- 7.3.2 Study of the Basic Portfolios.- 7.3.3 Aggregation.- 7.4 Hedging Portfolios.- 7.4.1 Determination of a Portfolio Mimicking a Series of Interest.- 7.4.2 A Model for the Call Seller Behavior.- 7.4.3 The Firm Behavior.- 7.5 Empirical Study of Performance Measures.- 7.5.1 Performances of a Set of Assets.- 7.5.2 Improving the Efficiency.- 7.5.3 Estimation of the Efficient Portfolio and its Performance in the Static Case.- Appendix 1: Presentation in Terms of Utility.- Appendix 2: Moments of the Truncated Log-Normal Distribution.- Appendix 3: Asymptotic Properties of the Estimators.- 7.6 Exercises.- 8 Factor Models, Diversification and Efficiency.- 8.1 Factor Models.- 8.1.1 Linear Factor Representation.- 8.1.2 Representation with Endogenous Factors.- 8.1.3 Structure of the Conditional Moments.- 8.1.4 Cofactors.- 8.1.5 Characterization with the Matrix Defining the Endogenous Factors.- 8.2 Arbitrage Theory.- 8.2.1 Absence of Arbitrage Opportunities.- 8.2.2 Diversification and Pricing Model.- 8.2.3 Diversification and Risk Aversion.- 8.3 Efficiency Tests and Diversification.- 8.3.1 Ex-Ante Efficiency.- 8.3.2 Ex-Post Efficiency.- 8.4 Conditional and Historical Performance Measures.- 8.4.1 The Dynamics of a Model with Endogenous Factors.- 8.4.2 Tests for Ex-Ante Efficiency and Performances...- 8.5 Exercises.- 9 Equilibrium Models.- 9.1 Capital Asset Pricing Model.- 9.1.1 Description of the Model.- 9.1.2 Market Portfolio.- 9.1.3 The CAPM as a Factor Model.- 9.1.4 Spectral Decomposition of the Moments.- 9.1.5 Time Dependent Risk Aversion.- 9.2 Test of the CAPM.- 9.2.1 Some Difficulties.- 9.2.2 Testing Procedures in a Static Framework.- 9.2.3 Test for Efficiency of the Market Portfolio in a Dynamic Framework with Constant Betas.- 9.2.4 Tests in the General Case.- 9.3 Examples of Structural Models.- 9.3.1 A Model with Speculative Bubbles.- 9.3.2 The Consumption Based CAPM.

Accounting for Innovation and Measuring Innovativeness: An Illustrative Framework and an Application by Jacques Mairesse and Pierre Mohnen. Published in volume 92, issue 2, pages 226-230 of American Economic Review, May 2002

Abstract Data in many different fields come to practitioners through a process naturally described as functional. Although data are gathered as finite vector and may contain measurement errors, the functional form have to be taken into account. We propose a clustering procedure of such data emphasizing the functional nature of the objects. The new clustering method consists of two stages: fitting the functional data by B‐splines and partitioning the estimated model coefficients using a k ‐means algorithm. Strong consistency of the clustering method is proved and a real‐world example from food industry is given.

Abstract The increased adoption of fertilizer and improved seeds are two key aspects to raising the level of land productivity in Ethiopian agriculture. However, the adoption and diffusion of such technologies has been slow. We use data from Ethiopia between 1999–2009 to examine the role of learning from extension agents versus learning from neighbors for both improved seeds and fertilizer adoption. We combine farmers' spatial networks with panel data to identify these influences, and find that while the initial impact of extension agents was high, the effect wore off after some time, in contrast to learning from neighbors.

Abstract We identify the impact of intermediate goods markets imperfections on productivity downstream. Our empirical specification is based on a model of multifactor productivity (MFP) growth in which the effects of upstream competition can vary with distance to frontier. This model is estimated on a panel of fifteen OECD countries and twenty industries over 1985 to 2007. Competitive pressures are proxied with industry product market regulation data. We find evidence that anticompetitive upstream regulations have significantly curbed MFP growth over the past fifteen years, and more strongly so for observations that are close to the productivity frontier.

Summary We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ-dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments pyt∣y1:t−1,θ and rejuvenates the θ-particles through a resampling step and a Markov chain Monte Carlo update step. In state space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x-dimension, for any fixed θ. This motivates the SMC2 algorithm that is proposed in the paper: a sequential Monte Carlo algorithm, defined in the θ-dimension, which propagates and resamples many particle filters in the x-dimension. The filters in the x-dimension are an example of the random weight particle filter. In contrast, the particle Markov chain Monte Carlo framework that has been developed by Andrieu and colleagues allows us to design appropriate Markov chain Monte Carlo rejuvenation steps. Thus, the θ-particles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and non-sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x-particles. We contrast our approach with various competing methods, both conceptually and empirically through a detailed simulation study, and based on particularly challenging examples.

Abstract Using plant-level data from France, we document a potential cost of political connections for firms that is not offset by other benefits. Politically connected CEOs alter corporate employment decisions to help (regional) politicians in their re-election efforts by having higher job and plant creation rates, and lower rates of destruction in election years, especially in politically contested areas. There is little evidence that connected firms benefit from preferential access to government resources, such as subsidies or tax exemptions. Connected firms are less profitable in the cross-section and also experience a drop in profitability when a connected CEO comes to power.