Centre de Recherche en Économie et Statistique

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)

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.

This paper develops a new method to uncover the causal effect of trust on economic growth by focusing on the inherited component of trust and its time variation. We show that inherited trust of descendants of US immigrants is significantly influenced by the country of origin and the timing of arrival of their forebears. We thus use the inherited trust of descendants of US immigrants as a time-varying measure of inherited trust in their country of origin. This strategy allows to identify the sizeable causal impact of inherited trust on worldwide growth during the twentieth century by controlling for country fixed effects. (JEL N11, N12, N31, N32, O47, Z13)

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.

In this paper we present inference methods which are based on an ‘incorrect’ criterion, in the sense that the optimization of this criterion does not directly provide a consistent estimator of the parameter of interest. Moreover, the argument of the criterion, called the auxiliary parameter, may have a larger dimension than that of the parameter of interest. A second step, based on simulations, provides a consistent and asymptotically normal estimator of the parameter of interest. Various testing procedures are also proposed. The methods described in this paper only require that the model can be simulated, therefore they should be useful for models whose complexity rules out a direct approach. Various fields of applications are suggested (microeconometrics, finance, macroeconometrics).

The deviance information criterion (DIC) introduced by Spiegelhalter et al.(2002) for model assessment and model comparison is directly inspired by linear and generalised linear models, but it is open to different possible variations in the setting of missing data models, depending in particular on whether or not the missing variables are treated as parameters. In this paper, we reassess the criterion for such models and compare different DIC constructions, testing the behaviour of these various extensions in the cases of mixtures of distributions and random effect models.

International audience

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.

We document that, in a cross section of countries, government regulation is strongly negatively correlated with measures of trust. In a simple model explaining this correlation, distrust creates public demand for regulation, whereas regulation in turn discourages formation of trust, leading to multiple equilibria. A key implication of the model is that individuals in low-trust countries want more government intervention even though they know the government is corrupt. We test this and other implications of the model using country- and individual-level data on trust and beliefs about the role of government, as well as on changes in beliefs during the transition from socialism.

International audience

This paper deals with the trace regression model where $n$ entries or linear\ncombinations of entries of an unknown $m_1\\times m_2$ matrix $A_0$ corrupted by\nnoise are observed. We propose a new nuclear norm penalized estimator of $A_0$\nand establish a general sharp oracle inequality for this estimator for\narbitrary values of $n,m_1,m_2$ under the condition of isometry in expectation.\nThen this method is applied to the matrix completion problem. In this case, the\nestimator admits a simple explicit form and we prove that it satisfies oracle\ninequalities with faster rates of convergence than in the previous works. They\nare valid, in particular, in the high-dimensional setting $m_1m_2\\gg n$. We\nshow that the obtained rates are optimal up to logarithmic factors in a minimax\nsense and also derive, for any fixed matrix $A_0$, a non-minimax lower bound on\nthe rate of convergence of our estimator, which coincides with the upper bound\nup to a constant factor. Finally, we show that our procedure provides an exact\nrecovery of the rank of $A_0$ with probability close to 1. We also discuss the\nstatistical learning setting where there is no underlying model determined by\n$A_0$ and the aim is to find the best trace regression model approximating the\ndata.\n

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappé et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

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...

International audience

Engineering the water dissociation sites of MoS₂ nanosheets can efficiently enhance the electrocatalytic hydrogen evolution under alkaline conditions.

International audience

We construct company panel data sets for manufacturing firms in Belgium, France, Germany, and the United Kingdom, covering the period 1978–1989. These data sets are used to estimate empirical investment equations, and to investigate the role played by financial factors in each country. A robust finding is that cash flow and profits terms appear to be both statistically and quantitatively more significant in the United Kingdom than in the three continental European countries. This is consistent with the suggestion that financial constraints on investment may be relatively severe in the more market-oriented U.K. financial system.

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.