Puerto Rico's minimum wage: Revisiting a price floor with bite


 Revisiting research from the 1990s from Castillo-Freeman and Krueger, I use the synthetic control method of Abadie et al. to estimate the impact of the most recent increase in the federal minimum wage on employment in Puerto Rico. I estimate that the employment/population ratio of various groups in Puerto Rico was significantly lower than that of a data-constructed synthetic Puerto Rico which did not raise its minimum wage. Placebo tests on other donor units, time periods, and population groups suggest that a significant portion of this gap is a result of the minimum wage. Groups with greater exposure to the minimum wage, such as teens and restaurant workers, experienced proportionally greater declines in employment. My results suggest an own-wage elasticity of employment in Puerto Rico of −0.68, higher than estimates from the mainland, which suggests that the employment response to minimum wages may be more dramatic at higher relative minimum wages.


Part I 1 Introduction
The employment effect, or lack thereof, of the minimum wage remains a contentious issue in empirical economics, but a significant amount of progress on the issue has been made since the dueling studies of Card and Krueger (1993) and Neumark and Wascher (1995). Modern research on the minimum wage generally finds an employment response that is negative, small, and mostly localized to groups such as teenagers (Wolfson and Belman (2019), Neumark and Shirley (2021)). However, most studies use variation in state and local minimum wages to identify the effect of the minimum, and states and localities in the United States have generally chosen minimum wages that are modest relative to their median wages. In Cengiz et al.'s (2019) comprehensive study of state level minimum wage changes, for example, the highest relative minimum wage was 59% of the median wage.
With current proposals to dramatically increase the federal minimum wage to $15/h being considered by policymakers, the current literature on the employment effects of the minimum wage may be ill-equipped to forecast the effects of much larger minimum wage increases. A federal minimum wage of $15/h would be 95% of the median wage in Mississippi and 87% of the median wage in West Virginia if implemented immediately, for example. Such an increase is far beyond those studied by the majority of the minimum wage literature. The employment effects of such a high minimum may be better gauged by looking to the US territory of Puerto Rico, which has been bound by the Federal Minimum wage since 1983. While Puerto Rico is wealthier than other Caribbean countries, with Gross Domestic Product (GDP) per capita in 2020 equal to roughly $31,000, compared to $9,000 in Jamaica, $18,000 in the Dominican Republic, and $25,000 in St. Kitts and Nevis, it is simultaneously poorer than the U.S. states with which it shares Federal Laws. GDP per capita for all states was $65,281, nearly double Puerto Rico's, and even the poorest states like Mississippi ($40,000) and West Virginia ($43,000) are still much wealthier than Puerto Rico. Average hourly earnings in Puerto Rico were equal to $12.21 in 2010, compared to $21.92 for the mainland United States, $17.74 for Mississippi,and $17.65 in West Virginia. This results in Puerto Rico having a relative minimum wage that is much higher than any other state. Most recently, in 2007, the Federal Minimum Wage was increased from $5.15/h, which was 59% of Puerto Rico's median wage at the time, to $7.25/h, 76% of the median wage. Estimating the effect of this increase on Puerto Rican employment might provide insight into whether the minimum wage has a modest disemployment effect even at higher relative levels.
This paper revisits the question of the minimum wage in Puerto Rico using the most recent increase in the federal minimum wage as a case study. Since there is no a priori sensible control group to use for Puerto Rico, such as a neighboring state with a higher minimum wage, I utilize Abadie et al.'s (2010) synthetic control method, constructing a plausible counterfactual for the path of Puerto Rican employment without the minimum wage increase using the labor markets of other nations, Puerto Rican industries less affected by the minimum wage increase, and cities on the mainland United States. Identification is threatened by the Great Recession of the late 2000s, which coincided with the minimum wage increase and was particularly pronounced in Puerto Rico. To combat this potential source of bias, I use triple differences strategies comparing the estimated employment effects of groups with differential exposure to the wage floor and find that groups with lower wage levels and thus more exposure to the minimum experienced proportionally larger relative decreases in employment. I also construct a synthetic Puerto Rico matching on fluctuations in pre-and post-treatment GDP per capita, rather than just pre-treatment employment, creating a counterfactual which experienced similar macroeconomic fluctuations during the post-treatment period. I find that the increase in the minimum wage lead to substantial reductions in Puerto Rican employment across all specifications. On average, my results suggest an own-wage elasticity of employment of -0.68, larger than estimates from previous studies of the minimum wage in the United States, which are generally in the −0.3 to −0.5 range. I discuss several reasons why the employment response to the minimum wage may have a non-constant elasticity. Alternative avenues by which employers may choose to adjust, such as cuts to hours or fringe benefits, have a limited capacity to absorb higher labor costs, leaving cuts to employment as the only remaining option at higher relative minimum wages. A higher minimum wage is also more likely to bind in the tradable goods sector, where employment is demonstrated to be much more sensitive to minimum wage increases due to more elastic product demand.
The remainder of the paper is organized as follows. Part II gives a brief summary of the state of the literature on the employment effects of minimum wages and previous investigations into Puerto Rico more specifically. Part III provides background on the minimum wage in Puerto Rico and provides evidence that the 2007 increase in the minimum lead to a large increase in hourly wage. Part IV explains the synthetic control method, and Part V presents my results. Finally, Part VI concludes.

Part II 2 Prior Research
Research on the employment effects of the minimum wage is as voluminous as it is controversial. As Neumark and Shirley (2021) summarize: depending on what one reads about how economists summarize the evidence, one might conclude that: (1) it is not well-established that higher minimum wages do not reduce employment, (2) the evidence is very mixed with effects centered on zero with no basis for a strong conclusion one way or the other, or (3) most evidence points to adverse employment effects (p. 2). In general, however, the evidence seems to be synthesized into supporting an employment effect of the minimum wage that is negative, small, and localized within subgroups such as teens and high school dropouts. In their meta-analysis summarizing the past 15 years of research on the employment effects of the minimum wage, Wolfson and Belman (2019) summarize the consensus range of elasticities of teen employment to the minimum wage as being −0.13 to −0.07, implying that a 10% increase in the minimum wage decreases employment among teenagers by between 1.3% and 0.7%. Neumark and Shirley's (2021) meta-analysis reaches similar conclusions, with a median elasticity of −0.11. The majority of this research relies on evidence from the United States, where crossstate differentials in the minimum wage generate natural experiments useful for identifying the employment effect. The average US minimum is 39% of the median wage and the largest minima are just above 50% of the median (Cengiz et al., 2019).
The idea of using Puerto Rico to examine the effects of a high relative minimum wage is not a new one. Santiago (1986) sought to examine the employment and unemployment effects of the minimum wage in Puerto Rico soon after the gap between the continental and Puerto Rican minima closed around 1983. Using multivariate time series techniques and transfer functions, Santiago concluded that the empirical findings suggest that both disemployment and unemployment effects resulted from the post-1974 minimum wage policy … consistent with theoretical hypothesis (p. 308). Soon after the revival in interest in minimum wage research in the 1990s, Castillo-Freeman and Freeman (1991) published research on the minimum wage's effect in Puerto Rico, primarily utilizing time-series data for their analysis. The authors found significant impacts on employment, concluding that-Imposing the U.S.-level minimum reduced total island employment by 8-10% compared to the level that would have prevailed had the minimum been the same proportion of average wages as in the United States. In addition, it reallocated labor across industries, greatly reducing jobs in low-wage sectors that had to raise minima substantially to reach federal levels (p. 178). The strongest evidence that the minimum wage had a negative effect on employment in Puerto Rico comes from an aggregate time series analysis. The weakest evidence comes from cross-industry analyses. In general, however, I think one would have to consider the evidence surprisingly fragile … perhaps the conclusion that one should reach from the review of evidence is that the jury is still out on Puerto Rico's experience (p. 23).

Castillo-Freeman and
In the 14 years since then, statistical techniques for casual inference have come a long way, but the evidence from Puerto Rico still lies unexamined with a fresh set of statistical eyes. Dube and Zipperer (2015) only cite the Freeman and Krueger papers in a 2015 report on Puerto Rico, and David Neumark noted in 2018 that "surprisingly, to the best of my knowledge the evidence from Puerto Rico has not been revisited" (p. 9).
Beyond Puerto Rico, Gregory and Zierahn (2020) study another instance of a high relative minimum wage. In 2006, Germany's minimum wage for roofers increased, leading to a statutory minimum wage that was equal to or even exceeded the median wage in low-wage areas in eastern Germany. The authors conclude that the minimum wage caused the wages of low-skilled East Germans to increase by 5-6%, but also caused employment among that group to decline by 3.5%, suggesting an own-wage elasticity of −0.58 to −0.70.

Part III 3 Background
When the United States created its first national minimum wage through the Fair Labor Stan- It's possible that, although the statutory minimum wage for Puerto Rico is high, it's actual effect on workers' wages was mitigated by noncompliance on the part of employers. Perhaps workers shift into more informal work arrangements were the minimum wage is not in effect in reaction to the higher price floor. If this were the case, then Puerto Rico may actually be an inappropriate case study for examining the employment effect of the minimum wage. One way to test this possibility is to compare the distribution of hourly wages in Puerto Rico just before and just after the minimum wage increase. If the increase really did result in higher wages, then where δ at and δ st are the levels of the dependent variable in the actual and synthetic treated unit at time t.
After constructing the treatment effects using the synthetic control for the treated units, statistical significance can be determined by running placebo tests. By estimating the same model on each untreated donor unit, while disallowing the treated unit to be used as a donor, one can generate a distribution of effect sizes for the placebo unit. If the size of the treatment effect for the treated unit is much larger than those generated for the untreated units, than it is unlikely that the estimated effect was the result of chance. If the distribution of placebo effects at time t is 1 , PL t jt j then the two-sided and one-sided p-values for period t are: If some placebo units have poor matches than the p-values may be too conservative. Galiani and Quistor (2017) recommend two methods for adjusting p-values for the quality of pre-treatment t. The first of these is that donor units which exceed a certain pre-treatment RMSE can be dropped from the distribution α 1 PL t for the calculation of the p-values; alternatively, all effects can be divided by the pre-treatment t to generate pre-treatment adjusted p-values.
One final test for significance is the placebo date test, where a model for the treated unit is estimated with the same parameters except for the treatment period. If the effects seen during the initial estimation are causally related to the treatment, then one should expect small and insignificant differences between the actual and synthetic unit following the placebo date.  Using the International Labor Organization's modeled estimate of the employment to population ratio for workers 15-24, as well as data from the World Bank on income per capita, GDP growth, and share of the population within the 15-24 year old range, I construct a synthetic control for Puerto Rico using 197 other countries as donors. The synthetic control algorithm, unsurprisingly, placed high weights on countries geographically close to Puerto Rico (Suriname) or at similar levels of economic development (Gabon), but also, somewhat puzzlingly, placed a high weight on Norway (Tables 2 and 3). Puerto Rico experienced a substantial decline in teen and young adult employment relative to synthetic control, with employment in this group being, on average, 30.3% lower in Puerto Rico following the phase-in of the minimum wage ( Figure 5). In addition, Abadie's placebo test indicates high levels of significance, with results being significant at the 1% level following the completion of the minimum wage's phase in (Table S1). In addition, a placebo treatment date of 2000 for Puerto Rico yields treatment effects that are small and statistically insignificant; this is exactly what should be expected if the decline was related to the minimum wage increase (Table S2). By dividing the estimated treatment effect on the log/employment population ratio, −0.303, by the percent increase in the minimum wage, 0.4, we can find the elasticity of teen/young adult employment to the minimum wage implied by these results to be −0.74 The elasticity implied by the triple differences approach is −1.2, again substantially larger in magnitude than estimates from the mainland United States.

Limited Donor Pool
One alternative approach is to address concerns regarding the potential donor pool countries, given that Norway in particular seems an inappropriate control ex ante, by limiting the pool of donor countries to only those which are a priori sensible. In order to maintain a stock of placebo countries that is as large as possible, the donor pool was limited by dropping only inappropriate nations chosen by the synthetic control algorithm until the chosen donors for synthetic Puerto Rico had intuitive appeal. After dropping several western European countries, the synthetic control procedure placed high weights on the tropical island nations of Barbados and Comoros, with the remaining weight coming from Sri Lanka and the mainland United States (Tables 4 and 5). The limited donor pool reduced the size of the treatment effect, from an average of 30% to 16%, implying an elasticity of -0.4. Statistical significance varies, with evidence of a disemployment effect being strongest in the years following the completion of the phase-in of the minimum wage (p = 0.04) (Table S4).
Finally, we can apply the triple differences approach to the limited donor pool by estimating treatment effects on total employment in Puerto Rico with a limited donor pool and subtracting. Total employment in Puerto Rico was 9.1% lower than the limited donor pool synthetic control following the phase-in of the minimum wage (Table S5). Adjusting for the   Table 2. When the two are compared in Figure 6, Puerto Rico's GDP grows faster than synthetic Puerto Rico's during the pre-treatment period, while the two are mostly parallel during the post-treatment period. It's unclear from this examination alone whether or not the Great Recession is confounding the previous results.  Puerto Rico that comes as close as possible to experiencing the same macroeconomic fluctuations as actual Puerto Rico (Table 6). Then, we can compare the path of employment in this new synthetic Puerto Rico to employment on the actual island.
As seen in Figure 7a and Table S6, output in the GDP matched synthetic Puerto Rico closely follows that of the actual island. When comparing trends in employment in Figure 7b,  teen/young adult employment in the GDP matched synthetic Puerto Rico is substantially higher than in actual Puerto Rico in both the pre-treatment and post-treatment periods. Thus, rather than calculating the treatment effect by taking the difference between synthetic and actual Puerto Rico in the post-treatment period, it's more appropriate in this case to compute a simple difference-in-differences estimator using the following linear regression model:

Cross-Industry Comparisons
Recalling Krueger's finding that the weakest evidence for a disemployment effect of the minimum wage in Puerto Rico came from cross-industry comparisons, any exploration of the minimum wage's effect on Puerto Rico should utilize a similar technique. Additionally, since this approach only uses Puerto Rican industries as donors, there is less concern about Puerto Rican specific shocks contaminating the results. Using data from the Bureau of Labor Statistics' State and Area Employment Hours and Earnings program, my initial approach is to construct a synthetic control for the accommodation and food industry using all other island industries where the minimum wage is less likely to bind as donors (Figure 8).
The synthetic control algorithm constructed the synthetic accommodation and food industry using the health, retail, education, and professional services industries (Tables 7 and 8).
Comparing the accommodation and food industry to its synthetic counterpart shows total employment was, on average, 8.5% lower after that minimum wage was phased in (Figure 9). Unlike with results for teens, raw placebo p-values for the cross-industry synthetic controls generally failed to reach statistical significance (0.07 < p < 0.31). However, these results become significant or approach significance for all periods if the p-values are adjusted for the quality of the per-treatment t (Table S7). In addition, a placebo date test using Q4 2000 as the treatment date yielded treatment effects that were small and statistically insignificant (Table S8).
To find the elasticity of accommodation and food industry employment to the minimum wage, we first need to find the coverage of the minimum wage in the constructed synthetic accommodation and food industry. By summing the products of each industry's share of the synthetic control and the share of workers earning $7.25/hour or below in each industry, we can find that the synthetic accommodation and food industry had an effective coverage of 47%, compared to the actual accommodation and food industry's 69%. The elasticity of accommodation and food employment to the minimum wage implied by this approach is thus

Cross-City Comparisons
One additional strategy to identify the employment effect for bound industries is to con- The employment/population ratio in San Juan's accommodation and food industry was found to be 9% lower than synthetic control on average following the phase-in of the minimum wage ( Figure 10). Fortunately, none of the three MSAs chosen as donors were bound by the minimum wage increase, so the implied elasticity is ε The effects vary in their significance (0.02 < p < 0.37) depending on the post-treatment period (0.01 < p < 0.93) (Table S10), but this variance in significance may partially be the result of the fact that the data was not available with seasonal adjustments (Table S9).
As an alternative, a synthetic Accommodation and Food industry using US MSAs was constructed using log employment, rather than the log employment/population ratio as the dependent variable of interest. In this case, the synthetic control procedure selected Miami FL, Tampa FL, Trenton NJ, and Tucson AZ as the donor cities comprising the synthetic San Juan restaurant industry (Tables 11 and 12). This specification also yielded a better pre-treatment  t than the previous synthetic control using the employment population ratio, without the concerning divergence between actual and synthetic employment observed in late 2006 prior to the wage increase that was previously observed. On average, employment in the San Juan restaurant industry was 4% lower than its synthetic counterpart, with effects also varying in significance depending on the post-treatment period (0.01 < p < 0.93) (Table 10). Unlike the specification detailed in Table 9, some of the donor cities used to construct the synthetic San Juan restaurant industry were bound by the minimum wage increase. Using the values in Table 11  Puerto Rico to a greater degree than among affected workers in the continental United States.
There are multiple theoretical reasons why the elasticity of employment to the minimum wage may decrease at higher relative minimum wages. As Clemens (2021)

Part VII 8 Conclusion
This paper contributes to the extensive literature on the employment effects of minimum wages by focusing on the 2007 increase in Puerto Rico's minimum wage, which led to a relative minimum wage for the island nation that was significantly higher than any found in the continental United States and thus affected the wages of a greater number of workers. Results indicate that employment in Puerto Rico fell relative to a data-constructed synthetic counterfactual following the phase-in of the higher minimum wage. Furthermore, employment for more affected subgroups like teens and restaurant workers fell more sharply proportional to their higher minimum wage coverage (Table S11). Estimated elasticities of employment to the minimum wage for groups in Puerto Rico were higher than those found from studies of the mainland US, but elasticities of employment to the own wage were also larger than consensus estimates from the mainland. This may be due to the fact that RMS are less able to adjust along non-employment margins such as hours or fringe benefits at higher relative minimum wages, and that which would all be affected by Puerto Rican specific macroeconomic shocks. Secondly, in the results using international comparisons in Part V, Section 1, I find that the estimated treatment effect of the minimum wage was smaller for all workers than for teenage workers with higher levels of exposure to the minimum. The estimated employment elasticity from the triple differences approach was actually larger than the one obtained through international comparisons alone, which is the opposite of what would be expected if an island specific shock was biasing the results. Finally, even when I create a synthetic Puerto Rico matching entirely on fluctuations in pre-and post-treatment output and growth, which assumes that the minimum wage increase had no effect on GDP levels or growth, I still find evidence of declines in employment.

Availability of Data and Material
All data used is available through the Bureau of Labor Statistics, the Census Bureau, IPUMS, and the World Bank.

Competing Interests
The author certifies that he has no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Funding
Not Applicable.

Authors' Contributions
Not Applicable.