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# Lucas GIRARD (CREST) – "Non-asymptotic confidence intervals in linear models / Quantifying several dimensions of residential segregation in France (1968-2019)"

**Microeconometrics Seminar: Every Tuesday**

Time: 03:00 pm – 4:15 pm

Date: 18th of May 2021

by visio

Lucas GIRARD (CREST) – “Non-asymptotic confidence intervals in linear models / Quantifying several dimensions of residential segregation in France (1968-2019)”

TWO papers in a single seminar : one is advanced and theoretical, the other is more in progress and empirical.

**Abstract**: The presentation will be split into two parts:

The first part will be devoted to a theoretical project, joint work with Alexis Derumigny (TU Delft) and Yannick Guyonvarch (Télécom Paris), about non-asymptotic confidence intervals (CIs) in linear models.

The prevalent way to conduct inference in applied economics stems from asymptotic results. As a case in point, the usual CIs for individual coefficients in linear regressions rely on the asymptotic normality of the t-statistic. Their properties are, therefore, only asymptotic and, in finite samples, involve an asymptotic approximation.

We consider the issue of constructing non-asymptotic CIs for individuals coefficients in linear regressions, i.e., whose probability of containing the true parameter is at least the nominal level for any sample size.

The existing tools to conduct non-asymptotic inference either rely on the normality of the error term or the independence between the error term and the observed covariates of the model. However, those assumptions may be restrictive in economic applications: normality rules out models with skewed or fat-tailed idiosyncratic shocks while independence does not allow for heteroskedasticity.

Using tools from Edgeworth expansions, we construct a novel CI with guaranteed coverage for any sample size under moment restrictions only (in particular, we require the distribution of errors conditional on covariates to have bounded kurtosis and fourth moment).

Besides, a common concern with non-asymptotic CIs is their conservative behavior: their actual coverage tends to exceed the desired nominal size. To (partly) address that issue, our CI has the same length asymptotically as the one based on the t-statistic, whose coverage equals its nominal level in the limit. In addition, some simulation exercises suggest it is quite informative compared to the usual asymptotic CI in practice.

The presentation will start on the simple example of inference on a scalar expectation to present basic notions contrasting asymptotic and non-asymptotic results.

In the second part, I will present some initial results on a new project about residential segregation in France.

The sampling scheme of the French Labor Force Survey happens to draw clusters of around thirty adjacent housing. Such clusters form relevant neighborhoods to study residential segregation provided the indices account for small-unit bias to be compared over time or across different dimensions of segregation (French versus non-French people; jobseekers versus workers; college graduates versus non-graduates, etc.). In this project, I try to construct long-term series of segregation indices to describe the evolution of residential segregation in France between 1968 and 2019 and compare the magnitude of segregation along several dimensions (nationality, ethnicity, education, socio-economic status, jobseekers/workers).

The presentation will also relate segregation indices to a more general problem, which is to quantify to which extent two groups tend to make different choices among a set of options, and explain the so-called “small-unit bias.”

**Organizers:
**

Benoît SCHMUTZ (Pôle d’économie du CREST)

Anthony STRITTMATTER (Pôle d’économie du CREST)

**Sponsors:**

CREST

**Microeconometrics Seminar: Every Tuesday**

Time: 03:00 pm – 4:15 pm

Date: 18th of May 2021

by visio

Lucas GIRARD (CREST) – “Non-asymptotic confidence intervals in linear models / Quantifying several dimensions of residential segregation in France (1968-2019)”

TWO papers in a single seminar : one is advanced and theoretical, the other is more in progress and empirical.

**Abstract**: The presentation will be split into two parts:

The first part will be devoted to a theoretical project, joint work with Alexis Derumigny (TU Delft) and Yannick Guyonvarch (Télécom Paris), about non-asymptotic confidence intervals (CIs) in linear models.

The prevalent way to conduct inference in applied economics stems from asymptotic results. As a case in point, the usual CIs for individual coefficients in linear regressions rely on the asymptotic normality of the t-statistic. Their properties are, therefore, only asymptotic and, in finite samples, involve an asymptotic approximation.

We consider the issue of constructing non-asymptotic CIs for individuals coefficients in linear regressions, i.e., whose probability of containing the true parameter is at least the nominal level for any sample size.

The existing tools to conduct non-asymptotic inference either rely on the normality of the error term or the independence between the error term and the observed covariates of the model. However, those assumptions may be restrictive in economic applications: normality rules out models with skewed or fat-tailed idiosyncratic shocks while independence does not allow for heteroskedasticity.

Using tools from Edgeworth expansions, we construct a novel CI with guaranteed coverage for any sample size under moment restrictions only (in particular, we require the distribution of errors conditional on covariates to have bounded kurtosis and fourth moment).

Besides, a common concern with non-asymptotic CIs is their conservative behavior: their actual coverage tends to exceed the desired nominal size. To (partly) address that issue, our CI has the same length asymptotically as the one based on the t-statistic, whose coverage equals its nominal level in the limit. In addition, some simulation exercises suggest it is quite informative compared to the usual asymptotic CI in practice.

The presentation will start on the simple example of inference on a scalar expectation to present basic notions contrasting asymptotic and non-asymptotic results.

In the second part, I will present some initial results on a new project about residential segregation in France.

The sampling scheme of the French Labor Force Survey happens to draw clusters of around thirty adjacent housing. Such clusters form relevant neighborhoods to study residential segregation provided the indices account for small-unit bias to be compared over time or across different dimensions of segregation (French versus non-French people; jobseekers versus workers; college graduates versus non-graduates, etc.). In this project, I try to construct long-term series of segregation indices to describe the evolution of residential segregation in France between 1968 and 2019 and compare the magnitude of segregation along several dimensions (nationality, ethnicity, education, socio-economic status, jobseekers/workers).

The presentation will also relate segregation indices to a more general problem, which is to quantify to which extent two groups tend to make different choices among a set of options, and explain the so-called “small-unit bias.”

**Organizers:
**

Benoît SCHMUTZ (Pôle d’économie du CREST)

Anthony STRITTMATTER (Pôle d’économie du CREST)

**Sponsors:**

CREST