Model

Consumer

CES, Dixit and Stiglitz (1977) type model

\[ \begin{align} U_{i} & = C^{\alpha_{i}}_{i}F^{1-\alpha_{i}}_{i} \\ F_{i} &= \left( \sum_{j=1}^{N} \beta_j^{\frac{1}{\sigma}} x_j^{\frac{\sigma -1 }{\sigma}} \right) ^\frac{\sigma}{\sigma - 1} \end{align} \] Relative demand: \[ \frac{x_j}{x_k} = \frac{\beta_j}{\beta_k} \left( \frac{p_k}{p_j} \right)^\sigma \]

Summing over all products we obtain: \[ m = \sum_{j=1}^{N} p_j x_j = \left( \sum_{j=1}^{N} \frac{\beta_j}{\beta_k} p_j^{1-\sigma}\right) p_k^\sigma x_k \]

Marshallian demand: \[ \begin{align} x_k &= \frac{m p_k^{-\sigma}}{\sum_{j=1}^{N} \frac{\beta_j}{\beta_k}p_j^{1-\sigma}} \\ &= \frac{\beta_k m}{p_k^\sigma} \left( \sum_{j=1}^{N} \beta_j p_j^{1-\sigma} \right)^{-1} \\ &= \frac{\beta_k m}{P} \left( \frac{P}{p_k}\right)^\sigma \end{align} \] Expenditure share: \[ s_j = \beta_j \left( \frac{P}{p_j}\right)^{\sigma-1} \]
Holding price constant, an increase in \(\beta\) increases the associated expenditure share.

Producer

Assume single product firms engaging in Bertrand price competition

Profit function:

\[ \pi_i = p_i x_i - c_i x_i - F_i \]

F.O.C

\[ \begin{align} 0 &= x_i + p_i \frac{\partial x_i}{\partial p_i} - c_i \frac{\partial x_i}{\partial p_i} \\ c_i &= \left( 1 + \frac{1}{\varepsilon_d}\right)p_i \\ &= \left( 1 - \frac{1}{\sigma}\right)p_i \end{align} \]

Product \(i\) is imported if profit is higher than fixed cost

\[ (p_i - c_i)x_i \geq F_i \]

Equilibrium (assuming identical consumers):

\[ \frac{F_i}{p_i -c} = \frac{\beta_i m}{P} \left( \frac{P}{p_i}\right)^\sigma \]

Challenges in identifying changes in consumer’s preferences:

• Variety of goods is endogenous

• Hard to distinguish between preference and cost channels

Nevertheless, an increase in migrant flow is theorised to lead to an increase in consumption share

Data

• Nielsen consumer panel dataset
  • Detailed information on household shopping trips, purchases and amount spent
  • Used 2011 cross-section containing 62,000 households. Focus on white, non-hispanic, expenditure in 8 categories:
    • canned seafood, canned vegetables, dry mix, frozen, pasta, ready-to-serve, sauces, spices
  • Merged with products attributes dataset
• Recipe corpus
  • Scraped 6275 recipes with 25 different geographical region tags from allrecipe.com
  • Combined with data from 165 recipe books’ indexes.
• Foreign born data
  • Used 5-year 2006-2010 ACS and 1980 census data from NHGIS
  • Additional robustness test conducted over choice of dataset

Data

• 65,600 unique UPC codes in the initial dataset

• Merged UPC codes to type description and product description fields depending on which provide more information to create a vector of search text

• Excluded the following categories: misc. sauces, sandwich spreads meat, extracts, vegetables onion instant, multipack, soup

• Product description fields are quite sparse and contain basic information on product characteristic / flavour e.g. “mahi mahi mango marinaded”, “fajita seasoning”, “beans”

• Search text is subsequently merged with the TF-IDF dataset to create geographical region weights for 47,000 UPC codes

• Search text is merged to two versions of the recipe TF-IDF scores, single word and word pairs

• The word pair score is used if such a merge exists, otherwise the single word match with the highest maximum score is used e.g. “fajita seasoning” would be given the TF-IDF score of “fajita seasoning” if it exists, else it would be assigned the maximum of “fajita” and “seasoning”

Measuring region-linked expenditure shares

• Implemented a bag-of-words model commonly used in document classification problems

• Similar studies using text classification include Antweiler and Frank (2004) and Gentzkow and Shapiro (2010)

• Term frequency - inverse document frequency (TF-IDF) method:
  • Use the relative frequency of words/ingredients for a particular region as a signal of importance
  • “Normalise” the term frequencies by the inverse document frequency to down-weight common words

\[ TF\text{-}IDF_{t,d} =\frac{f_{t,d}}{\sum_{t'\in d}f_{t',d}} \cdot log \frac{N}{n_{t}+1} \]

• where \(f_{t,d}\) is the frequency in which term \(t\) appears in document \(d\)

• \(N\) is the total number of documents in the corpus and \(n_{t}\) is the total number of documents where term \(t\) is found

• The TF-IDF approach is commonly used in document classification problems and usually out performs multinomial naive bayes (Kibriya et al. 2004)

Word frequencies from the recipe dataset

Visualising TF-IDF scores

From TF-IDF scores to weights

• Calculate TF-IDF scores for recipe and book dataset (\(\rho\)=0.77) and take the simple average
• Match the TF-IDF scores to the product attribute dataset and normalise scores across each product
• Use the weights to calculate linked-expenditure shares
• Sample of products

Empricial Strategy

\[ Exp\_share_{ij} = \rho FB\_share_{ij} + \mu ln\_dist_{ij} + \lambda_{i} + \gamma_{j} +\epsilon_{ij} \]

• Control for unobserved variation at the county(\(i\)) and geographical-region(\(j\)) level as well as log great circle distance between county and region.

• Omitted variable problem not a main concern. While many factors affect foreign-born share, few, if any are correlated with local food expenditure share

• Potential “peer effects” endogeneity concerns(Angrist 2014) e.g. similar preferences between parent and child of common ancestry

• Solution: restrict the foreign-born share sample to non-European countries

Empricial Strategy

• Measurement error is still a large source of concern

• Use 1980 foreign-born share as an instrument

• Foreign enclave idea (Card 2001; Ottaviano and Peri 2006). Exploit persistent migrant flow patterns that are plausibly orthogonal to consumption

• Furthermore, the time period also coincides with the liberalisation of U.S. migration policy

• The Immigration and Naturalization Act of 1965 replaced the national origins quota with a category system

• Distribution of the initial wave of migrant plausibly exogenous to consumption

• Policy change resulted in mass migration primarily from Central America and Asia (Chiswick and Hatton 2003; Abramitzky and Boustan 2016)

Discussion

• The greater the number of Asian migrants to a particular county, the less likely it is for a native to purchase related supermarket goods

• By contrast, there is a positive relationship between non-Asian migrantion and consumption share

• These results are consistent across OLS and IV specifications and are robust to various methods of constructing expenditure shares and regional aggregations

• The positive relationship between share of foreign born of non-Asian origin and local expenditure may be due to the peer effect endogeneity problem

• Potential violation of the exclusion restriction: the recent migration wave also significantly expanded the availability and quality of outside food options

• Cross-substitution patterns could result in households substituting home-cooked food for outside consumption or perhaps there is a higher standard of what constitutes authentic Asian food and supermarket produce may not make the standard

Appendix (distribution of asian foreign-born)

Appendix (distribution of asian foreign-born )

Appendix (distribution of product weights)