Linguistic Distance, Languages of Work and Wages of Immigrants in Montreal

Abstract

We use the Levenshtein linguistic distance measure to explore the question of whether the distance between an immigrant’s mother tongue and a Canadian official language (English or French) has an impact on his/her economic integration into the labor market. Using microdata from the master files of the 2001 and 2006 Canadian censuses and from the 2011 National Household Survey, we investigate the relationship between linguistic distance and the intensity of use of English and French at work in the Montreal metropolitan area. That region is characterized by the presence of sizeable French- and English-speaking communities, as well as by a large number of immigrants from a wide variety of linguistic backgrounds. Those elements of linguistic diversity interact in the environment of English being the lingua franca. We find that linguistic distances between immigrants’ mother tongues and English and French have an important impact on the relative intensities of use of the two Canadian official languages at work. We further investigate the role of the languages used at work on the earnings of immigrants by estimating earnings functions. We find that the use of both French and English is remunerated positively in the labor market, but that using English at work has a larger impact on earnings.

Appendix

Calculation of the Levenshtein Linguistic Distance

The following explanation of the computation of the linguistic distance is based on the work of Petroni and Serva (2010). The ASJP linguistic distance is computed by using a list of 40 words in each language having similar meanings. The list includes, for example, words describing body parts, animals, plants, nature, verbs, adjectives, and pronouns that are used universally across languages. It was originally based on the 100-item “Swadesh list” (Swadesh 1952), but was reduced to 40 items that were shown to suffice. To calculate the distances, the lexical similarities of all pairings of languages are compared using an algorithm called the “Levenshtein distance” (LD), which is calculated as the minimum number of edits (deletions, substitutions or insertions) required to transform a word from one language into another. To provide a very simple illustration, the Levenshtein distance between the French word “allo” to its corresponding English word “hello” is equal to two, the transformation of one word into the other cannot be effectuated with fewer than two edits.

• 1. allo hllo (substitution of ‘a’ with ‘h’)

• 2. hllo hello (insert ‘e’ after ‘h’)

A normalized measure of the Levenshtein distance (LDN) needs to be provided in order to account for the word lengths, because longer words inherently require more edits to be executed. The normalization is performed by dividing the LD between similar words in two different languages by the number of characters of the longer of the words in whichever language applies. The LDN between the words with meaning i in two languages labelled Q and W is equal to:

$$ LDN\left({Q}_i,{W}_i\right)=\frac{LD\left({Q}_i,{W}_i\right)}{L\left({Q}_i{W}_i\right)} $$

where LD(Q_i, W_i) is the Levenshtein distance between Q_i and W_i, and L(Q_iW_i) is the number of characters of the longer word. The total linguistic distance (involving all words) between a pair of languages is then calculated by measuring the average distance of all n words for those languages as follows.

$$ LDN\left(Q,W\right)=\frac{1}{n}\sum \limits_{i=1}^n LDN\left({Q}_i,{W}_i\right) $$

where Q_i and W_i correspond to the word i in languages Q and W. Finally, to account for word lexical similarity resulting from merely pure coincidence (as opposed to pure etymology), the program provides a further normalized measure labelled the Levenshtein distance normalized divided (LDND) between pairs of languages. It is obtained by dividing the LDN(Q, W) by the “global distance”, where the “global distance” (GD) is the average distance between two languages using only pairs of words with different meanings. This quantity is expressed as:

$$ GD\left(Q,W\right)=\frac{1}{n\left(n-1\right)}\sum \limits_{i\ne k}^n LDN\left({Q}_i,{W}_k\right) $$

The LDND is the final measure of linguistic distance, which is obtained by dividing the LDN(Q, W) between pairs of languages with their respective values of GD(Q, W). It is employed in our empirical analysis, and is written as:

$$ LDND\left(Q,W\right)=\frac{LDN\left(Q,W\right)}{GD\left(Q,W\right)} $$