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ECO401H1 S LEC0101

Topics in Economic Policy

Winter 2022

Problem Set #2

Optimal Income Taxation

1. We saw in Lecture 4 that the mechanical increase in tax revenue for a small tax reform  about some earnings level  was equal to  where  is the average income of top bracket earnings. Furthermore, the behavioral response to the tax reduces tax revenue according to  where  is the elasticity of average income with respect to the net-of-tax rate. Argue intuitively why if the tax is set optimally,  has to hold.

2. If we solve for the optimal tax directly using , we get  . Notice that this depends on . One of Saez’s contributions was to examine the ratio  using empirical earnings distributions. Figure 2 from Saez (2001) shows that this ratio is roughly constant (and around 2) with respect to  in the top tail of the income distribution for  above $300,000. Using this fact, explain why Diamond and Saez (2011) argue that top incomes are distributed according to the Pareto distribution.

3. Suppose we assume that the elasticity  is roughly constant across earners at the top of the distribution. Argue why in this case the optimal marginal tax rate is the same over the range of very high incomes where the distribution is Pareto.

4. Veall (2012) argues that the Pareto parameter () for Canada is between 1.50 and 2.25. Consider [0.25,1] as a reasonable range for the elasticity  and conduct a sensitivity analysis illustrating the top marginal tax rate for various combinations of  and . How do these compare current values of the top marginal tax rate in Ontario? Make sure to combine provincial and federal income tax rates.

Introduction of the Universal Child Care Benefit (UCCB)

In this question, you will be asked to empirically evaluate the introduction of the Universal Child Care Benefit (UCCB) on the labour force participation of mothers with young children. Some additional information about the UCCB can be found here and here.

General questions:

1. Provide an overview of the UCCB. Be sure to document who is eligible to receive benefits. What was the rationale for its introduction? Were there competing policies advocated by other political parties around the same time?

2. Consider a difference-in-differences (DiD) estimator to examine the causal effect of the introduction of the UCCB on labour supply. First, show how one can implement the DiD using raw means only when there are no covariates. Second, show how you can use a saturated regression model to estimate the DiD. Be sure to discuss which parameter in the regression model corresponds to the DiD estimate.

3. What assumption(s) ensure that the DiD estimator will produce a valid (or “consistent”) estimate of the causal effect of the policy on the group that was treated? How could you test this assumption?

The following questions require that you use Stata to produce some regression-based estimates and graphs. You may also use R.

The data file “LFS_2001_2011.dta” is available on Quercus, as is a Stata .do file to help you get started. The dataset contains eleven year’s worth of data (2001-2011) from the Labour Force Survey (LFS). The LFS contains monthly observations for a representative sample of Canadians and asks them questions related to their participation in the labour force (e.g., whether they worked, how many hours, their wage, etc.). Here’s a list of variables that are included in the dataset:

You should use the “PS2_instructions.do” file as a starting point for your own code---it creates additional variables that you will need for the analysis, and it also contains some hints about how to calculate averages, generate graphs, and run regressions. Please make sure that you add your own code to the .do file so that it may be replicated by others.

4. Produce a figure that depicts the annual rates of labour force participation for working-aged married mothers with young children  (treatment group) and married mothers with older children (control group) over time. There should be two lines on the same plot, one for the treatment group and one for the control group. Interpret your figure and report your findings. In particular, comment on i) whether using married mothers with older children are a suitable control group and ii) whether the UCCB reform visually appears to have had an impact on labour supply for the treatment group. Include this figure in your written submission.

5. Produce a similar figure for working-aged single mothers with younger children (treatment group) and working-aged single mothers with older children (control group). Report your findings. In particular, comment on i) whether using single mothers with older children are a suitable control group and ii) whether the UCCB reform visually appears to have had an impact on labour supply for the treatment group. Include this figure in your written submission.

6. Calculate a difference-in-difference estimate for working-aged married mothers “manually” by calculating the average rates of labour force participation in the pre-UCCB and post-UCCB periods for married mothers with young children and married mothers with older children, respectively.

7. Calculate a difference-in-difference estimate for working-aged single mothers with younger and older children “manually”.

8. Using a regression model, estimate a difference-in-difference regression for working-aged married mothers and include that estimate in a table in your written submission. Comment on the size and the direction of the parameter of interest. Is the impact of the UCCB statistically significant and in the direction predicted by economic theory?

9. Estimate the regression model in #8 once again but this time include controls for the respondent’s age, highest level of education, and province of residence. We use controls when we may be concerned that the composition of our groups over time may be changing---for instance, it may be the case that the average level of education in one group is changing at a different rate. We can control for these changes in composition. Because these variables are coded as categories in the LFS, you can control for them using “i.variablename” in your regression---there’s an example in the .do file’s “hints” section. The “i.” in front of the variable ensures that Stata understands the variable is categorical. Include the estimate from a regression with controls in your table.

10. Estimate a difference-in-difference regression for working-aged single mothers and include that estimate in a table in your written submission. Comment on the size and the direction of the parameter of interest. Is the impact of the UCCB statistically significant and in the direction predicted by economic theory?

11. Estimate the regression model in #10 once again but include controls for the respondent’s age, highest level of education, and province of residence. Include that estimate in your table.

12. Based on the graphs you produced in part 4 and 5, does it seem like the assumptions needed for the difference-in-difference estimator to produce estimates of causal effects hold for married mothers? What about single mothers? Relate this discussion to the results you found from parts 8 and 10.

13. Describe how these difference-in-difference estimates might inform a cost-benefit analysis of the UCCB. What other kind of information might you need?

Please submit your written answers as a Word or PDF file, the .do file containing your code, and a .log file that shows your output.