--- title: "EC306 Assignment 1: Child Care and Mothers' Labour Supply" author: "Your name, your student number" date: today format: pdf: fig-width: 6 fig-height: 3.5 include-in-header: text: | \usepackage{float} \floatplacement{table}{H} \floatplacement{figure}{H} execute: message: false warning: false --- ## Background Since 1997, Quebec has offered regulated child care at a low fixed daily fee: originally \$5 a day, and still under \$10 a day in 2019. Until 2021, parents in the rest of Canada mostly paid market prices that were many times higher. In 2021 the federal government began signing agreements with the other provinces and territories to bring average fees down to \$10 a day by 2026. Because the rest of Canada has been catching up since then, this assignment uses data from 2019. In the labour supply model, child care is a cost of working: a parent who takes a job has to pay for care during the hours they are away. Cheaper child care raises the net return to working, so we would expect it to draw parents of young children, and mothers especially, into the labour force. In this assignment you will look at whether the data are consistent with that prediction, and then think about whether the comparison you make can be read as causal. ## The data The data come from the Labour Force Survey public use microdata file for March 2019. The sample is everyone aged 25 to 54. | Variable | Description | |:-----------|:----------------------------------------------------------------| | `id` | Person identifier | | `province` | Province of residence | | `gender` | "Women+" or "Men+" | | `agegroup` | Five-year age group | | `educ` | Highest level of education | | `lfsstat` | Labour force status: "Employed, at work", "Employed, absent from work", "Unemployed", or "Not in labour force" | | `kidage` | Age of youngest child living with the person: "Under 6", "6 to 12", "13 to 17", "18 to 24", or "None under 25" | | `hours` | Usual weekly hours at all jobs (missing if not employed) | ## Instructions - Write your R code in the chunks provided. You can add more chunks if you need them. - When a question tells you to store a result under a particular name, such as `q2` or `gap_u6`, use exactly that name. Those objects are marked by computer, and a different name counts as missing. - Do not round the numbers you store. Round only when you display them. - Tables and graphs must be presentable: use `modelsummary()`, `datasummary()` or `datasummary_df()` for tables, and give every graph readable axis labels. Do not show a table by just printing a data frame. - The hints under each question point to sections of the R tutorial, the Introduction to R and Quarto page on the course website. Each section has a worked example of the step the hint describes, using different data. - Render the document after each question, not only at the end. - Every written answer goes under **Answer:**, and what it must cover is set out just above, under **Comment on the results**. - Each question is marked out of 5 from your PDF, using the rubric on the assignment page. The objects you are told to create are also checked by computer, for another 5 marks, so the assignment is out of 30. ## Setup Do not change this chunk or the next one. ```{r} #| label: setup library(tidyverse) library(modelsummary) ``` ```{r} #| label: load-data lfs <- read_csv("ec306assign1.csv") # Put the categories of kidage in their natural order, so tables and # graphs list them from youngest to oldest instead of alphabetically. lfs <- lfs |> mutate(kidage = factor(kidage, levels = c("Under 6", "6 to 12", "13 to 17", "18 to 24", "None under 25"))) glimpse(lfs) ``` ## Question 1 (5 marks) Create the following dummy variables and add them to `lfs`: - `lfp`: 1 if the person is in the labour force (employed and at work, employed but absent from work, or unemployed), 0 otherwise - `woman`: 1 if `gender` is "Women+", 0 otherwise - `quebec`: 1 if `province` is "Quebec", 0 otherwise - `kid_u6`: 1 if the person's youngest child is under 6 (`kidage` is "Under 6"), 0 otherwise Then make a table showing the mean, standard deviation, minimum, and maximum of the four dummy variables. *Hints.* - Create the dummies with `mutate()`, and save the result back into `lfs`; otherwise the new variables are not kept. A comparison such as `province == "Ontario"` gives `TRUE` or `FALSE` for each person, and wrapping it in `as.numeric()` turns that into 1 or 0. See "Dummy variables" in the R tutorial. - Three of the four categories of `lfsstat` count as being in the labour force. You can join comparisons with `|` (or), or use `!=` (is not equal to) on the one category that does not count. See "Dummy variables" and "`filter()` — keep some rows" in the R tutorial. - Text has to match exactly, capitals and punctuation included. Run `count(lfs, lfsstat)` to see the exact spellings. - For the table, use `datasummary()` with the statistics `Mean`, `SD`, `Min` and `Max`. See "Tables" in the R tutorial. ```{r} #| label: q1-dummies # Add lfp, woman, quebec and kid_u6 to lfs here. ``` ```{r} #| label: q1-table ``` **Comment on the results.** What does the table tell you about the people in the sample? Before you write, review how to interpret the mean of a dummy variable. **Answer:** *Write your answer here.* ## Question 2 (5 marks) Keep only women. For each combination of `kidage` and `quebec`, calculate the labour force participation rate. That gives 10 rates: five child age groups, in Quebec and in the rest of Canada. Store the result in a data frame called `q2`, with the rates in a column called `lfp_rate`. Then make a bar chart of the participation rates, with the age of the youngest child on the horizontal axis and the Quebec and rest-of-Canada bars side by side. You do not need a table for this question: the graph presents the rates. *Hints.* - Do not overwrite `lfs` with the women-only data, because later questions need everyone. Use `filter()` to save the women in a new data frame called `women`; you will use it again in Questions 3 and 4. See "`filter()` — keep some rows" in the R tutorial. - The rates come from `group_by()` followed by `summarise()`, with both variables in `group_by()`. See "Grouping by two variables" in the R tutorial. - Give `q2` to `ggplot()`, not `women`. `geom_col()` draws the bars, `position = "dodge"` puts them side by side, and mapping `factor(quebec)` to `fill` colours them by province. Replace the 0 and 1 in the legend with words. See "Bar charts of results you have calculated" in the R tutorial. ```{r} #| label: q2-rates ``` ```{r} #| label: q2-graph ``` **Comment on the results.** What does the graph show? Describe how participation changes as the youngest child gets older, and how the gap between Quebec and the rest of Canada changes. **Answer:** *Write your answer here.* ## Question 3 (5 marks) Participation is only one way to adjust labour supply. The other is how many hours to work. Keep only women who are employed (at work or absent from work) and whose youngest child is under 6. Make a box plot of usual weekly hours (`hours`) for Quebec and for the rest of Canada. *Hints.* - Start from `women`, and save the filtered data as a new data frame to give to `ggplot()`. Conditions in `filter()` separated by commas must all hold, so you can write the condition on employment and the condition on the child separately. Two categories of `lfsstat` count as employed. See "`filter()` — keep some rows" in the R tutorial. - Put `factor(quebec)` on the horizontal axis and replace the 0 and 1 on the axis with words. Adding `outliers = FALSE` to `geom_boxplot()` leaves out the individual points beyond the whiskers, which otherwise crowd the graph. See the boxplot of men's and women's wages under "Graphs" in the R tutorial. ```{r} #| label: q3-graph ``` **Comment on the results.** Do employed mothers of young children in Quebec work more hours than those in the rest of Canada? How does the difference compare with the difference in participation you found in Question 2? **Answer:** *Write your answer here.* ## Question 4 (5 marks) The Quebec gap for mothers of young children in Question 2 may not all be due to child care. Quebec could differ from the rest of Canada in other ways, such as its labour market or attitudes toward women working, that raise participation for *all* Quebec women. Women whose youngest child is not under 6 rarely need daycare, so the Quebec gap for them estimates that general difference. Subtracting it from the gap for mothers of young children gives a **difference-in-differences** estimate of the effect of child care. For example, with made-up numbers: | Participation rate | Quebec | Rest of Canada | Quebec minus rest of Canada | |:------------------------------|-------:|---------------:|----------------------------:| | Youngest child under 6 | 80% | 70% | 10 points | | All other women | 85% | 81% | 4 points | | **Difference in differences** | | | **6 points** | **(a)** Using women only, calculate the four participation rates by `quebec` and `kid_u6`, the same way as in Question 2, and present them in a table. Then calculate the following, and store each as a single number without rounding: - `gap_u6`: the Quebec minus rest-of-Canada participation gap for women whose youngest child is under 6 - `gap_other`: the same gap for all other women (`kid_u6 == 0`) - `did`: `gap_u6 - gap_other` *Hints.* - `datasummary_df()` turns a data frame of results, such as your four rates, into a presentable table. See "Tables" in the R tutorial. - For `gap_u6`, `gap_other` and `did`, store each of the four rates as its own object first, under a name of your choosing, then subtract. - Each rate is the mean of `lfp` for one group of women. Square brackets pick out a group: `women$lfp[women$quebec == 1]` is `lfp` for every Quebec woman, and `&` adds a second condition. See "Picking out elements" and "Functions" in the R tutorial. ```{r} #| label: q4a-table ``` ```{r} #| label: q4a ``` **Comment on the results.** Report the three numbers in percentage points (0.05 is 5 percentage points) and explain what each one means. What has to be true for `did` to measure the effect of Quebec's child care policy? **Answer:** *Write your answer here.* **(b)** Using women only, estimate the regression $$ lfp_i = \beta_0 + \beta_1 quebec_i + \beta_2 kid\_u6_i + \beta_3 (quebec_i \times kid\_u6_i) + \epsilon_i $$ and store it as `q4_model`. Present the results in a table with `modelsummary()`. *Hint.* Estimate it with `lm()`, using `women` as the data. In an R formula, `quebec * kid_u6` includes both variables and their product. See "Interactions" in the R tutorial. ```{r} #| label: q4b ``` **Comment on the results.** Interpret each of the four coefficients. How does $\beta_3$ compare with `did` from part (a)? **Answer:** *Write your answer here.* ## Question 5 (5 marks) **(a)** Estimate the same regression for men, and store it as `q5_model`. Present both regressions side by side in one table, with the columns labelled "Women" and "Men". Part (a) needs no written answer; you will use the results in part (b). *Hints.* - You need a men-only data frame, made the same way as `women`. - `modelsummary()` accepts a list of models, and the names you give the elements of the list become the column headings. See "Presenting results" in the R tutorial. ```{r} #| label: q5 ``` **(b)** **Comment on the results.** Is `did` a causal estimate of the effect of Quebec's child care policy on mothers' participation? In your answer, consider: - what the result for men tells you; - other ways Quebec differs from the rest of Canada that could affect parents of young children. One example: the LFS counts a parent on parental leave, with a job to return to, as "employed, absent from work"; - in 2021 the other provinces began cutting their child care fees toward \$10 a day. If you repeated this analysis with data from 2025, what would you expect to happen to `did`, and why? **Answer:** *Write your answer here.* ## Use of generative AI If you used a generative AI tool for any part of this assignment, name the tool and describe what you used it for. If you did not use one, say so. *Write your statement here.* ## Before you submit This chunk lists any required objects that are still missing. It should say "All required objects found" before you submit. ```{r} #| label: check #| echo: false required <- c("lfs", "q2", "gap_u6", "gap_other", "did", "q4_model", "q5_model") missing <- required[!sapply(required, exists)] if (exists("lfs")) { missing_cols <- setdiff(c("lfp", "woman", "quebec", "kid_u6"), names(lfs)) if (length(missing_cols) > 0) missing <- c(missing, paste0("lfs$", missing_cols)) } if (length(missing) == 0) { cat("All required objects found\n") } else { cat("Still missing:", missing, sep = "\n ") } ```