The Labor Market Effects of a Refugee Wave

A. Sample Size and Measurement Error

Table 1 shows the number of observations for our preferred sample (constituted by all non-Cuban high school dropouts aged 19–65) in Miami. Using the March CPS (first column), it includes between 60 and 80 observations per year. The May-ORG CPS data set, available between 1973 and 1978, is somewhat smaller, with about 40 observations per year. However, beginning in 1979 and spanning the years during and after the Mariel Boatlift, the ORG CPS sample usually consists of around 150 observations per year.⁶ In Section V we discuss in detail how the small size of the March CPS data set affects the analysis of Borjas (2017), who focuses on a small subgroup of the population of high school dropouts. On average, the size of Borjas’ (2017) sample is between one-quarter and one-third of our preferred sample. He justifies the choice of such a restricted sample as measuring wages more precisely without the contamination from trends in women’s participation rates and transitions in early and late working life. However, those were national trends, unlikely to affect Miami in particular or to change abruptly after 1980. An individual-level regression including ethnic, gender, and age controls can address those differences, and using city-specific residuals, as we will do below in our empirical methodology, and Borjas (2017) also does for age-controls only, the analysis should not be affected by those demographic trends.

A second important lesson from Table 1 is that the pre-1979 samples are especially small and likely noisy. This suggests that when matching Miami to a control group of cities, whose labor market trends were similar before 1979, one should include as many years as possible to reduce the impact of measurement error. Data for Miami and other 43 metropolitan areas exist since 1973, so we choose that as the initial year of analysis.

Another argument in favor of relying on the May-ORG CPS data set is that the hourly and weekly wages figures are more accurate than the corresponding ones from the March CPS. The variation of measurement error in average wages across cities in the March CPS sample is much larger than in the May-ORG CPS sample. One way to show this is to assume that, for year 1979, the “true” average city log wages for the group of high school dropouts can be calculated using the 5 percent sample of the 1980 Census. From the Census data set, we calculate the log wage measure analogously to the March CPS by dividing the respondent’s total pre-tax wage and salary income for the past year by the number of weeks worked for the same period. First, we calculate average log weekly wages for our preferred sample in each of the 32 metropolitan areas available in all three data sets. Then, we calculate the difference of these average log wages in each metropolitan area, between the March CPS and the Census and between the ORG CPS and the Census. The measurement error in the March CPS has a standard deviation of 0.12 logarithmic points (about 12%), while for the ORG CPS it is equal to about half of that (0.07 log points, 7%). Consequently, differences in average measured wages across cities, which are the crucial statistics used in the SCM, will depend on differences in true mean and differences in measurement error.⁷ With average differences of measurement errors on the order of 15 percent, for the March CPS it will be impossible to separate true differences within the 15–20 percent level from differences in measurement error.

A final limitation of the March CPS in measuring weekly wages, especially of low-skilled individuals, was proved by Bollinger (1998) and Lemieux (2006). They showed that the March CPS wage data, based on the recollection of previous year annual salary and weeks worked, compounds recall and division errors that are particularly severe for people who are paid by the hour; this includes a large fraction of the high school dropouts who are the main subject of this analysis. People often have a difficult time recalling the exact actual number of hours worked last year, a figure used in constructing weekly wages. The impact of this measurement error will certainly be magnified in small samples, such as metropolitan-area-level subgroups in the March CPS. To the contrary, the May-ORG CPS sample, based on weekly wages recall from the last week of work, produces a less noisy and more reliable estimate of earnings for less educated individuals who are usually paid by the hour.

B. Number and Demographics of the Mariel Cubans

Table 2 shows the summary statistics as well as the aggregate count of immigrants and existing workers in Miami around the time of the Boatlift. In the first column, we present data relative to the labor force in Miami as of 1980 as measured in the Census. In the second one, we display the same characteristics for all Mariel Cubans identified in the 1990 Census as Cubans who arrived in the United States in 1980 and were 19 or older at arrival. In the last column, we do the same for Mariel Cubans who were still living in Miami as of 1990 and hence had likely settled there permanently.

We obtain a total of 54,196 working-age Mariel Cubans (by multiplying the Census personal weight by the number of observations in the 5 percent Census sample), 56 percent of whom lacked a high school degree. Of those, only 62 percent were in still in Miami as of 1990. Hence, either at arrival or in the successive years, about two out of five Mariel Cubans relocated to other places. The share of Cubans in Miami, in fact, peaks in 1981 and then declines between 1981 and 1985. As we show below, there is additional evidence in the CPS data for Miami that some of the Cubans who arrived in 1980 might have left the city in the following two to three years.

Overall, the statistics of Table 2 imply that the Mariel Boatlift produced an 18 percent increase in the number of high school dropouts in the Miami labor market, while it increased the other education groups by only 5 percent and the total Miami labor force by 8.4 percent. The last three lines of Table 2 show that among dropouts, the Mariel Cubans had a comparable share of women and young individuals to those in the existing Miami labor force.⁸

C. Measured Labor Supply Shift in Miami

Figure 1 shows the share of Cubans in Miami’s population, aged 19–65 (black lines), and in the population with no high school degree, aged 19–65 (lighter gray line), between 1973 and 1985. Panel A shows the March CPS data, while Panel B uses the May-ORG CPS. In both panels we observe a clear jump upwards of the Cuban share from “1979-Pre” to “1981-Post”, which is the mark of the Boatlift. In all figures, we adopt the convention to call “1979-Pre” the data relative to the last observation before the Mariel Boatlift and “1981-Post” the first data point certainly after all Mariel Cubans had arrived.⁹ The 1980 data in the May-ORG CPS are collected year round and include pre- and post-Boatlift information. Similarly, for the March CPS the wage data are yearly averages and in 1980 include pre and post. Hence, the reader should look at the difference 1979–1981 as the short-run impact of the Boatlift, with the idea that the 1980 data point is “during” the Boatlift.¹⁰

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Figure 1

Cubans in Miami as a Share of Total and of High School Dropout Population

Notes: We calculate the share of all those who define themselves as “Cuban” in the ethnicity question of the CPS. The population considered is the total number of individuals between 19 and 65. The high school dropout population includes those who do not have a high school degree in the age range 19–65. For the March CPS, we include the figure for March 1980 as “1979-Pre” and we interpolate the figure for “1980-Shock”, between 1979-Pre and 1981-Post. The vertical dashed bar corresponds to the last observation before the Mariel Boatlift happened.

Three facts emerge from Figure 1. First, the March CPS and May-ORG CPS data show similar shares of Cubans in the total population, but they are less consistent with each other for the share among high school dropouts. This indicates that there is significant noise and discrepancies between the May-ORG CPS and the March CPS statistics when the sample size is small. Second, both time series and samples show an increase between the “1979-Pre” and “1981-Post” data points. The 1979–1981 increase does not seem particularly large compared to the trends and year-to-year movements before and after. Considering May-ORG CPS figures, the 1979–1981 increase as a percentage of the population equals about six points, and as a percentage of high school dropouts, the increase was around 12 points.¹¹ Third, after initially increasing between 1979 and 1981, the share of Cubans decreased in the following four years (in both samples), and this effect was larger for the share among high school dropouts. In fact, in 1985 the share of Cubans among high school dropouts was back at percentage levels comparable to those of the pre-Boatlift period. This emphasizes the temporary nature of the shock.¹²

A. The Synthetic Control Method

The SCM, first introduced by Abadie and Gardeazabal (2003) and then further developed in Abadie, Diamond, and Hainmueller (2010, 2015), provides a systematic way of analyzing the impact of case-study events such as the Mariel Boatlift. Typically in these settings a single unit (often represented by a city or a region) experiences, at a point in time, an event (or treatment), while the rest do not. In order to evaluate whether the treatment had an impact on some outcomes in the treated unit, relative to what would have happened in its absence, the method formally identifies a control group called the synthetic control unit.

In our case, we consider J + 1 metropolitan areas indexed by j = 0, 1, 2 … J and denote Miami as 0, while we call the group of all the rest the “donor pool.” This is the group of 43 other cities (31 for the March CPS) in the United States for which data are consistently available in the Current Population Survey for the relevant time period. Then, we define a vector G₀ of dimension k × 1 whose elements are equal to the values of variables that help predict the wages of high school dropouts in Miami between 1972 and 1979. Similarly, we define a k × J matrix, G_J, in which row j is the sequence of values for the same variables and years relative to city j in the “donor pool.”

The SCM then identifies the vector of nonnegative weights W* = (w₁, …, w_J) that produces a convex combination of variables in cities in the donor pool, G_J, to approximate as close as possible, in terms of a quadratic error, the pretreatment vector of variables chosen for metropolitan area 0, G₀. In other words, it minimizes the difference between G₀ and G_JW

(1)

Once we have identified W* we can use it to calculate the posttreatment outcome variables for the synthetic control unit by weighting each city accordingly.¹³

Comparing the pre–post 1979 change in the outcome variable for Miami relative to the pre–post change for the Synthetic Control is the basis to evaluate if the treatment has had any effect. The synthetic control method hence produces a figure with two time series, one for the treated unit (Miami) and one for the synthetic control. In Section IV.A, we show these two lines for several wage and unemployment outcomes, and we visually examine the post-1979 differences in order to assess whether they are large relative to the pre-event differences (1972–1979).

We minimize the distance for the following variables in the pretreatment period: the outcome variable itself for selected pre-1979 years (and/or its average value), the share of low-skilled workers, the share of Hispanics, and the share of manufacturing workers in the labor force. These are all important characteristics in predicting the labor market outcomes of low-skilled workers.¹⁴ In robustness checks, we also match alternative variables, such as overall employment, wages growth, and low-skilled employment growth, which mirrors the analysis of Borjas (2017).

Given the noise and the small samples it is crucial to allow for as long a pretreatment period as possible. The most influential studies using the synthetic control method include more than 20 pre-event years (for example, Abadie, Diamond, and Hainmueller 2010, 2015). In our case, because data for Miami begin in 1973, the best we can do is to include six pre-event years of data. Most results are robust to variations in the selection of the synthetic control group, as long as one matches the whole 1973–1979 period. However, matching only on a very short pre-1979 period may produce control groups with very large pre-event differences between the treated unit and control, reducing the validity of the method.

B. Accounting for Differential Demographic Composition

It is well known that the average wages of different demographic groups, such as women, men, young, old, Hispanic, Black, and White workers, had different national trends in the 1970s and 1980s. Depending on the demographic composition, these trends may affect labor markets differentially, introducing confounding factors in the analysis. The commonly used method for reducing the potential confounding effects from differential demographic characteristics (age, gender, and ethnicity) is to adjust individual log wages by running the following regression

The (log) wage of individual i in metropolitan area j in year t, ln w_ijt, is regressed on a set of five-year age dummies Age_it, on a female dummy Female_i, dummies for Hispanic and Black Ethnic_i, three-year bin dummies Year_t, as well as the first three variables interacted with Year_t. This produces the residual, ϵ_ijt, that captures individual log wage variation once those aggregate trends are accounted for. We then average these residuals by city–year and treat them as outcome variables in several specifications of the empirical analysis.

C. Inference

A main drawback of the original analysis of the Mariel Boatlift by Card (1990) is neglecting aggregate city-specific idiosyncratic shocks in conducting statistical inference. This is problematic because it treats contemporaneous observations from different workers within the same labor market (and hence subject to the same labor demand shocks) as independent data while in fact they could be strongly correlated due to city-specific idiosyncratic shocks.¹⁵ We address this issue within the context of the SCM in two ways.

D. Others Methodological Considerations

The Mariel Boatlift was a one-time, unexpected shift in supply that took place mostly between March and July 1980. It was not a persistent policy change or a prolonged increase in immigration rates from Cuba. As shown in Figure 1, the share of Cubans among high school dropouts in Miami was back to pre-Boatlift levels by 1985. Hence, the bulk of the effect on employment and/or wages should be detected in years 1981 and 1982. After that, only transitional dynamics would be detected and should imply smaller effect than in 1981–1982 as the shock was temporary. Moreover, several other economic shocks (including a significant recession and a worsening of the war on drugs in 1982, which actively and differentially involved Miami) took place during the following decade, and Miami could have responded differently from any chosen control group. Differences between Miami and the control city after 1983 are likely caused by factors unrelated to the Boatlift. Consequently, any study of a labor market impact of the Mariel Boatlift should focus on the years 1981 and 1982.

A. Main Results

We show our main results in Figures 2 and 3. In each panel we present two time series lines, one for Miami (solid) and one for its synthetic control (dashed). To learn about the possible impact of the Boatlift, our focus will be on two features of the graphs. First, we assess the magnitude of the differences between Miami and the control between 1972 and 1979. This indicates how well our control group matches Miami pre-Boatlift. Second, relative to those, we eyeball the magnitude of the difference in the outcomes in the 1981–1982 period, when the Boatlift should have had its largest potential effect. In Panels A–C of Figure 2 and all panels of Figure 3, we present various wage measures, and in Panel D of Figure 2, we show the unemployment rate for low-skilled workers. The footnotes of each figure indicate the sample and the cities that enter the synthetic control and their associated weights. Notice that in every panel the synthetic control is constructed (at least partly) from cities not included in the Card (1990) control group (Los Angeles, Houston, Atlanta, and Tampa Bay–St. Petersburg). By construction we improve on his identification strategy because we match variables similar to the ones on which he based his choice of control group, and we make no arbitrary decision regarding which cities enter the control.

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Figure 2

Miami and Synthetic Control, Wages and Unemployment of Low-Skilled Workers

Notes: The data source is May-ORG CPS. Each panel shows the outcome variable for Miami (solid line) and the synthetic control (dashed line) in the period 1972–1991. The outcome variable is noted in the title of each panel. The sample for Panels A, B, and D is non-Cuban high school dropouts, age 19–65, not self-employed and in the labor force. The sample for Panel C removes the high school dropout restriction. Some time series are standardized to the same value in 1979. The cities with positive weight in the synthetic control are as follows. Panel A: New Orleans, LA 43.9%; New York City, NY 29.9%; Baltimore, MD 24.8%. Panel B: New Orleans, LA 43.2%; New York City, NY 30.1%; Baltimore, MD 24.9%. Panel C: Birmingham, AL 60.6%; Rochester, NY 28.6%; Nassau-Suffolk, NY 10.4%. Panel D: New Orleans, LA 48.4%; New York City, NY 30.9%; Albany-Schenectady-Troy, NY 19.5%; Cincinnati, OH 1.1%.

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Figure 3

Miami and Synthetic Control, Additional Outcomes of Low-Skilled Workers

Notes: The data source is May-ORG CPS. Each panel shows the outcome variable for Miami (solid line) and the synthetic control (dashed line) in the period 1972–1991. The outcome variable is noted in the title of each panel. The sample for Panels B, C, and D is non-Cuban high school dropouts, age 19–65, not self-employed and in the labor force. The sample for Panel A removes the high school dropout restriction. See Section III.B in the text for an explanation of the regression adjustment. The cities with positive weight in the synthetic control are as follows. Panel A: San Diego, CA 57.7%; Birmingham, AL 28.4%; Nassau-Suffolk, NY 13.8%. Panel B: Tampa–St. Petersburg, FL 64.6%; Anaheim, CA 25.2%. Panel C: Greensboro, NC 70.5%; Norfold–Portsmouth, VA 18.4%; Cincinnati, OH 7.3%; Buffalo, NY 3.8%. Panel D: Los Angeles, CA, Tampa Bay–St. Petersburg, FL; Houston, TX, Anaheim, CA.

We do not observe a drop in wages in Miami relative to its control in the 1980–1983 period in any of the panels in Figures 2 and 3. Panels A and B of Figure 2 show (log) weekly wage and hourly wages, respectively, taken as raw measures, that is, without regression adjustment. One may argue that the second measure is closer to capturing the marginal productivity (and hence price) of labor. However, we follow previous studies and consider weekly wages as our main variable of interest. These two panels show a reasonable, but noisy, Miami–control match for the pre-1979 period, a small positive difference in 1980 and 1981 for Miami relative to its control, and essentially no difference in 1982 and 1983. This difference is magnified in the longer run, after 1985. Panel C shows the path for the 15th (log) wage percentile of non-Cuban workers in Miami and its control. An advantage of using the wage percentile, relative to looking at the average wage of a small group (such as the high school dropouts), is that the sample used in estimating the statistic is larger. Hence, the results are less sensitive to extreme values and therefore less volatile. Confirming this, Panel C exhibits a better Miami–control match pre-1979 and also shows small positive differences between 1980 and 1983.

A possible explanation for the small wage effects is that wages were rigid in the years 1979–1982, and hence a negative demand shock for native workers did not translate into lower wages in Miami.¹⁷ In the presence of a supply shock and rigid wages, the result would be displacement and nonemployment of natives. If this explanation is correct, we would expect the inflow of Mariel Cubans to be associated with an increase in the unemployment rate of non-Cuban high school dropouts in Miami. Panel D of Figure 2 shows the unemployment rate of this group for Miami and the synthetic control. In the years after the shock, between 1980 and 1983, no significant difference between the unemployment rate in Miami and synthetic control arises. A caveat in this case is that the year-to-year volatility of unemployment in Miami before 1979 was quite large.

Next, in Figure 3, Panel A we show the behavior of the 20th (log) weekly wage percentile in Miami and the synthetic control, which is another measure of wage among less skilled workers in Miami. In Panels B and C we present the results for the regression-adjusted weekly and hourly wages for high school dropouts, respectively (as described in Section III.B). Any spurious behavior driven by national trends in the wages of women or Hispanics and Blacks or young-old workers affecting the previous figures is controlled for. All three panels show very small differences in the outcomes for 1980–1983 and a reasonably good pre-1979 match. Finally, in Panel D of Figure 3, we show the log weekly wage graph for high school dropouts, as in Panel A of Figure 2, using the control group of cities as used in Card (1990) (Los Angeles, Houston, Atlanta, and Tampa Bay–St. Petersburg). Again, no systematic difference between Miami and the control is discernible for the period 1980–1983. We also see that the control group chosen by Card (1990) produces a reasonably good pre-1979 match of low-skilled wages.

The key takeaway from Figures 2 and 3 is that the average labor market outcomes of low-wage workers and high school dropouts in Miami do not show any negative break or jump corresponding to the Mariel Boatlift relative to the control group. The pre-1979 match between the constructed control group and Miami is quite noisy, and hence one has to take these results with a grain of salt. There is, however, no unusually large difference in any outcome for Miami and the control during the 1980–1983 period, corresponding to the aftermath of the Boatlift.

B. Robustness Checks

1. Subsamples

In this section we begin exploring the sensitivity of the results to the selection of subsamples. A more systematic analysis of how choosing small subsamples affects the results is carried out in Section V. By restricting the focus to subsamples of high school dropouts we face the risk of introducing measurement error as the sample size drops. When we consider the May-ORG data set and our preferred sample, we still have more than 39 observations in Miami even before 1979. Hence, while we need caution, it can be interesting to separate across various demographic subgroups to check whether there is evidence of heterogeneous effects.

It is worth noting that, while the Mariel Cubans were disproportionately high school dropouts, they were rather similar in terms of age and gender composition to native dropouts. Hence, there is no clear reason why the Mariel Cubans should compete more closely in the labor market with one of these subgroups. Still, one may think that their impact was different for men than for women and for incumbent Hispanic (whose culture and language were similar) or Black workers. This may be the case if, for instance, the Mariel Cubans specialized in occupations that were in direct competition with males and with Hispanics. Figure 4 shows first the synthetic control analysis, when separating the labor force by gender between non-Hispanic men (Panel A) and women (Panel B). The outcome is log weekly wages of high school dropouts. While the time profiles of the wages in Panel A and B are different, and the year-to-year variation is large, we do not observe negative differences between Miami and the control between 1980 and 1983 in either group.

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Figure 4

Miami and Synthetic Control, Wages of Subsamples of High School Dropouts

Notes: The data source is May-ORG CPS. Each panel shows log weekly wages for Miami (solid line) and the synthetic control (dashed line) in the period 1973–1991. The sample is a separate subgroup of high school dropouts age 19–65, not self-employed and in the labor force. Panel A and B restrict the sample to males and females only, respectively. Panels C and D further restrict it to Hispanics only and Blacks only. Some time series are standardized to the same value in 1979. The cities with positive weight in the synthetic control are as follows. Panel A: Tampa–St. Petersburg, FL 92.6%; Greensboro, SC 6.3%; New York City, NY 1.1%. Panel B: Cincinnati, OH 66.8 %; Pittsburgh, PA 29.4%; Indianapolis, IN 3.8%. Panel C: Sacramento, CA 49.8%; Houston, TX 30.1%; Philadelphia, PA 20.1%. Panel D: Greensboro, NC 39.6%; Cincinnati, OH 19.8%; New York City, NY 15.8%; Seattle, WA, 9.7%; Birmingham, AL, 8.5%; New Orleans, LA 6.7%.

In Panels C and D of Figure 4 we perform the analysis for Hispanic and Black workers. This second group could be particularly exposed to the new immigrant competition as they may be more similar in terms of skills and occupational choices. Even in these cases, Miami and the control exhibit small differences (positive in the case of Hispanics) for wages between 1980 and 1983 and similar, albeit noisy, trends of average log wages in the 1970s. Overall, selecting the sample on one dimension (ethnicity or gender) at a time does not produce evidence of a negative post-1979 difference in wages between Miami and the control.

2. Different control groups

In the panels of Figures 2–4 we chose the synthetic control so as to best match a common set of variables and the outcome pre-1980. This results in a somewhat different synthetic control group for each panel. We now show that small variations in the choice of the control group do not change the visual impression obtained from those figures. In Figure 5 we present the same outcomes as in Figure 2, but now comparing Miami to a fixed set of control cities (New York, Nassau-Suffolk, New Orleans, and Tampa–St. Petersburg), which is the set of cities most frequently selected by the synthetic control method (for both the ORG CPS and the March CPS) when matching share of high school dropouts, share of Hispanics, share of manufacturing, plus outcome variables in the 1972–1979 period. The figures show, as expected, a worse match of the pre-1980 trend on average, but they confirm the result of no negative difference (rather a positive one) between Miami and the control log wages between 1980 and 1983 (see Panels A and B for wages of high school dropouts and Panel C for wages at the 15th percentile). Similarly, only small differences in unemployment rates are observed between Miami and this fixed control group between 1980 and 1983, and they are comparable with those pre-1979 (Panel D). Although the choice of the control group is important, as one needs to approximate as closely as possible the pre-1979 trends in labor market outcomes, Figure 5 shows that the results are not sensitive to small differences in the choice of the best matching set for each variable. Nevertheless, as we will see in Section V below, one can be misled when selecting a control group that only matches a very short pre-event period (such as 1977–1979), as short-run idiosyncratic noise may be masking the pre-event trend behavior of labor market variables. It is always important, as a check of validity, to look at the 1972–1979 match of the outcome variables between Miami and the synthetic control.

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Figure 5

Miami and Fixed Control, Wages and Unemployment of Low-Skilled Workers

Notes: The data source is May-ORG CPS. Each panel shows the outcome variable for Miami (solid line) and the synthetic control (dashed line) in the period 1972–1991. The outcome variable is noted in the title of each panel. The sample for Panels A, B and D is a non-Cuban high school dropouts age 19–65, not self-employed and in the labor force. The sample for Panel C removes the high school dropout restriction. The set of available cities in the control group is restricted to New York, Nassau–Suffolk, New Orleans and Tampa–St. Petersburg. The associated weights are as follows: Panel A: Tampa–St. Petersburg, FL 67.7%, New York City, NY 30.9; Panel B: Tampa–St. Petersburg, FL 69.0%, New York City, NY 31.0%; Panel C: New Orleans, LA 75.9%, New York City, NY 24.1%; Panel D: Tampa–St. Petersburg, FL 44.5%, New York City, NY 31.9; Nassau–Suffolk, NY 23.3%.

3. Using March CPS data

In Section II we argued that the small size and the measurement and recall error in the March CPS may introduce significant noise in the average wages in Miami. Nevertheless, in this section, we show how the synthetic control analysis performs when we use our sample in the March CPS.

In Figure 6, we simply show the Miami and control comparison for some outcomes as we did in Figures 2 and 3, but now measured in the March CPS. The sample, exactly as in the previous section, consists of non-Cuban high school dropouts aged 19–65. We observe similar patterns as the ones from ORG CPS. Panel A represents log weekly wages (we do not calculate hourly wages in the March CPS) and shows a negative difference for Miami relative to control in 1981–1982, no difference in 1983, and then a quite large difference in 1986. While the difference in 1981–1982 seems larger than in pre-1979, it seems also driven by an increase of average wage in the control group (specific to this sample), as much as by a decrease of average wage in Miami. Panels B and C show that such difference is not visible in the 15th and 20th wage percentile time series. Moreover, even in Panel A a simple continuation of the pre-1979 trend for Miami would show little difference with the actual wages in Miami up to 1985. The unemployment rate in Panel D shows no post-1979 difference between Miami and the control. However, we can observe sizable differences in Panel D before 1979, which imply that the noise in the data prevent a precise pre-1979 match for the unemployment rate. In sum, the preponderance of evidence in Figures 2–5 does not show differences in the labor market outcomes of less skilled incumbent workers of Miami relative to the synthetic control during the post-Mariel period.

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Figure 6

Miami and Synthetic Control, Wages and Unemployment of Low-Skilled Workers, March CPS Sample

Notes: The data source is March CPS. Each panel shows the outcome variable for Miami (solid line) and the synthetic control (dashed line) in the period 1972–1991. The outcome variable is noted in the title of each panel. The sample for Panels A and D are non-Cuban high school dropouts age 19–65, not self-employed and in the labor force. The sample for Panels B and C remove the high school dropout restriction. The cities with positive weight in the synthetic control are as follows. Panel A: Cincinnati–Hamilton, OH/KY/IN 37.1%; Atlanta, GA 32.3%; New Orleans, LA 18.5%; Tampa–St. Petersburg, FL 12.0%. Panel B: New York City, NY 51.8%; San Diego, CA 38.2%; Riverside, CA 10.0%. Panel C: San Diego, CA 50.7%; New York, NY 41.9%; Tampa–St. Petersburg, FL 4.6%; Los Angeles–Long Beach, CA 2.8%. Panel D: Denver, CO 65.8%; Cincinnati–Hamilton, OH/KY/IN 30.3%; San Diego, CA 3.95.

C. Regression Results

In Table 3 we show the β_P coefficients from Regression 2 with their respective standard errors. If the Mariel shock had any labor market effect, this should be captured primarily by the coefficient β_81–82 that shows the average difference between Miami and the synthetic control arising in 1981 and 1982 once the 1979 difference is set to zero, as the reference year, and we exclude the 1980 observation.¹⁸ Just as importantly, our framework allows us to quantify the pre-1979 differences between the two cities. Specifically, the estimates of β_73–75 and β_76–78 provide validation for how well the two cities track each other before the shock. Statistically significant pre-1979 differences would cast doubt on our control group as they will imply systematic differences between Miami and the control, even before the Boatlift. The subsequent coefficients β_83–85, β_86–88, and β_89–91 complete the picture.

Each column in Table 3 corresponds to an outcome variable/specification. The header indicates the corresponding panel and figure, as well as the outcome variable in the regression. Some consistent features of the estimates are worth pointing out. First, none of the β_81–82 coefficients for the wage variables is negative and larger than its standard error. Most point estimates (Columns 2–5) are positive, and they reveal that Miami had a small positive difference relative to its synthetic control after the Boatlift. Given the estimated coefficients and standard errors, there is no support for a significant negative effect. For the unemployment rate (Column 6) we estimate a positive coefficient β_81–82 after the Boatlift. However, this value is not very different from the estimates of β_73–75 and β_76–78. This suggest similar behavior of dropouts’ unemployment before and after 1980 in Miami and Control.

Second, the estimated coefficients β_76–78 in Columns 2–5 are, for the most part, smaller than their standard errors. This is a more formal way of checking that Miami and its synthetic control move together to a reasonable extent, in the pre-Boatlift period, validating our identification strategy. The pre-1979 coefficients are smaller for the percentile wages (Columns 3 and 4), implying that for those variables the pre-1979 Miami–control fit is better. Note that the estimates are simply a quantification of the differences between the Miami–control time series represented in Figures 2 and 3 standardizing the difference to zero in 1979 (which the graphs do not necessarily do). Third, the standard errors for the wage regressions are not small (between 0.03 and 0.04 log points), and differences in the order of few percentage points would be difficult to measure precisely. Year-to-year fluctuations of 5–6 percent seem common both before and after 1979, and it is hard to say whether this is actually due to the Boatlift or measurement error.

D. Inference Results

Panels A–D of Figure 7 show the simulated differences treatment–control for Miami and the other 43 cities, analyzing non-Cuban high school dropouts’ log weekly and hourly wages (Panels A and B), log wages at the 15th percentile of wage distribution (Panel C), and the unemployment rate of non-Cuban high school dropouts (Panel D). The dark line in each panel corresponds to Miami–control differences, while each of the lighter ones corresponds to one of the 43 cities’ difference from the synthetic control.¹⁹ Panels A and B show that Miami’s average high school dropout wage in 1981–1982 had a positive difference relative to its synthetic control, and large vis-à-vis the simulated range in 1981–1982, while its differences look within the range of idiosyncratic variation after that year. Panels C and D show that for the 15th wage percentile and for the high school dropout unemployment rate, Miami is rather average and within the range of simulated differences any year post-1979. Notice that the range of simulated idiosyncratic noise in the sample is large. For instance, log weekly and hourly wages show a range of idiosyncratic noise spanning the interval between −20 and +20 log points. Let us emphasize once again that with this degree of noise it may be hard to identify effects on the order of five or six percentage points.²⁰

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Figure 7

Miami and 31 Metro Areas, Simulated Permutations

Notes: The data source is May-ORG CPS. Each graph reports deviations between synthetic control and treated group, assuming a treatment in 1980, for 44 metropolitan areas. The bold line represents Miami. Panel A shows the graph for the logarithm of weekly wages; Panel B shows it for the logarithm of hourly wages. Panel C shows the 15th percentile of log weekly wages, and Panel D the unemployment rate. The sample in Panel A, B, and D includes non-Cuban, high school dropouts, 19–65 years old from the May-ORG CPS. In Panel C the 15th percentile is calculated on all non-Cuban workers between 19 and 65 years old from the May-ORG CPS. Miami is excluded from constructing the synthetic controls. The lines are standardized to the same value in 1979.

A. The Figures

1. March CPS sample

Panels A and B of Figure 8 show a simple way of visualizing the key finding in Borjas (2017) and reconciling it with our results and those of Card (1990). The dashed line shows the average log weekly wage of high school dropouts in Miami from the March CPS sample that includes male, non-Hispanic workers, age 25–59. Panel A reproduces exactly the Miami wage path reported in Figure 6, Panel A of Borjas (2017), with two small modifications. First, we do not “smooth” the data with a moving average. The goal is to find a sharp short-run change in wages right around year 1980. Therefore, we do not want to contaminate the data by averaging observations before and after the Mariel Boatlift. Second, we draw the vertical bar in 1979, the last observation before the Boatlift. The dashed line in Panel A shows the very large dip in wages, which occurs slowly after 1980. This is the fundamental feature of the data that drives Borjas (2017) to argue in favor of a large effect of the Boatlift. The pre-1979 line is too short to infer the pre-1979 behavior (1977–1979) of wages. However, the fact that one observation (1977) is above and the other one (1978) below the 1979 point produces an impression of no clear (or rather flat) wage trend before 1979.

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Figure 8

Reconciling Borjas (2017)’s Visual Evidence with Ours, March CPS and May-ORG CPS

Notes: Panels A and C show the log wages (weekly for Panel A and hourly for Panel C) for high school dropouts in Miami as presented in Borjas (2017). The sample is non-Hispanic men, not self-employed, in the labor force, age 25–59. Panel B shows the same time series of 27 different subsamples of dropouts, based along the gender (male, female, or both), ethnicity (Hispanic, non-Hispanic, or both) and age (young/old, prime age or both) dimensions. Borjas (2017)’s sample choice is displayed in dashed line, with ours in black solid line, and the rest 25 subsamples are split depending on the average number of observations for Miami in the period 1978–1982 as follows: very light gray (0–20 observations), gray (20–40 observations), and dark gray (40+ observations). The time series are standardized to the same value in 1979.

Panel B reproduces the exact same wage path as Panel A, as a thick dashed line, but now it embeds it into more information about the average wages of high school dropouts in Miami before and after the Boatlift. Specifically, we extend the sample back to 1972, and we add the paths of average log wages of all the comparable subgroups among workers with no high school degree in Miami, standardized to be equal in 1979. Namely, we consider partitions of gender into male and female, of ethnicity into Hispanic-non-Cuban and non-Hispanic, and of age into prime (25–59 years old) and marginal (19–24 and 59–64 years old). Then we consider all 27 possible subgroups within the population of dropout workers in Miami that one can obtain selecting all possible combinations of individuals in one or both of the subgroups for each of the three characteristics.²¹ We plot the average weekly log wage of each of these subgroups using light shades of gray for the subgroups with 20 observations or fewer, with mid-gray shades for those with 20–40 observations, and with dark gray for those with 40 or more observations. The only other lines are Borjas’ (2017) sample, in thick dashed, and our preferred sample in thick solid. Borjas’ (2017) sample belongs to the subgroups with less than 20 observations (light gray). Our preferred sample, by including both groups for each of the three characteristics, is the largest one and belongs to the subgroups with 40 plus observations (dark gray). Finally, with a thick black dashed and dotted line, we denote the linear pre-1979 trend for the wage of the largest (and least noisy) dropout group extended to 1991.

Three clear facts emerge from Panel B of Figure 8. First, all subgroups with fewer than 40 observations (mid-gray and light gray) and particularly those with 20 observations or less (light gray plus the dashed Borjas’ [2017] sample) show very large fluctuations, before and after 1979, above and below the average trend of the group. The great dispersion and year-to-year variability of those averages seem to derive from measurement error, as they are more extreme the smaller those groups are, and they are largest in 1984 and 1985, when the Miami March CPS sample is smallest (see Table 1). The larger groups (including our preferred sample, the samples of Hispanic/non-Hispanic and men/women and prime age and that of Non-Hispanic and Men/Women and all ages) have much smaller year-to-year variation and follow a downward trend with much smaller fluctuations around it. The Borjas (2017) sample happens to be one with a large negative difference relative to the trend both before and after 1979, especially in the 1985–1986 period, and then a dramatic reversal with a positive difference in 1989–1991. Other small subgroups have similarly large differences, but some of them are positive in the 1985–1986 period. The Hispanic women group, for instance, is the one with a large double-spiked positive jump in 1983 and 1985. Let us also emphasize that the small sample bias problem, when considering subsamples, applies also to the control cities, not just to Miami. In the Borjas (2017) sample some of the cities in the control group (San Diego and San Jose) have samples with fewer than 15 observations between 1978 and 1982.

Second, Panel B of Figure 8 shows that the average wage of high school dropouts in Miami was on a significant downward trend from 1972–1979. Importantly, in order to capture such a trend, especially for the small and noisy subgroups, it is crucial to consider the whole 1972–1979 period. Limiting one’s attention to the behavior of Miami’s labor markets in the 1977–1979 period, as Borjas (2017) does when selecting control groups, implies that short-term fluctuations and measurement error can obscure the actual longer-run trend.

Third, if one can identify a group of two to three years in which the differences of the wage of some subgroups, above or below the average preexisting trend, are largest, those would be the years 1984–1986. Some sharp spikes (both upwards and downwards) emerge in those years. The years 1980–1982, which should show the largest short-run effect of the Mariel Boatlift, show instead smaller differences, especially if one excludes the very small subgroups. The years 1984–1986 were those when the Miami sample of the March CPS was smallest (fewer than 60 including all high school dropouts) and hence larger variation may simply come from smaller samples.²²

In summary, the drop in wages for non-Hispanic men age 25–59 in March CPS relative to its pre-1979 trend, which constitutes Borjas’ (2017) key piece of evidence, when embedded in a complete picture of all subgroups, appears to be a likely manifestation of measurement error that affects the smaller subgroups.²³

B. Choice of the Control Group

The remaining differences between our results and the Borjas (2017) results, which are relevant when looking at the regression analysis particularly for the May-ORG CPS sample, derive from the choice of the control group. Borjas (2017) matches either overall or low-skilled employment growth or these along with low-skilled wage growth between Miami and the controls during the 1977–1979 period. Namely, he pools the 1977–1978 data and the 1979–1980 data and estimates the growth between these two data points (based on four years). The four cities most similar to Miami are then chosen as controls. The year-to-year variability of wage data shown above, however, should warn us of the risk of basing the match only on the three years before the event and the year of the event.

Table 4 illustrates the sensitivity of the relative performance of Miami in terms of employment growth with respect to the choice of the period: 1977–1978 to 1979–1980, a one-year-earlier comparison 1976–1977 to 1978–1979, or the whole 1972–1979 period. The first three columns of Table 4 rank cities according to those three different employment growth rates. Borjas (2017) insists that Miami had robust labor market performance before 1979. However, this is only true when using the 1977–1978 to 1979–1980 growth (first column of Table 4, Miami is ninth out of 32 cities). The rate one year earlier (second column of Table 4) shows much slower growth of Miami (19th out of 32 cities), and the overall 1972–1979 rate shows Miami as one of the slower performers (25th out of 32). Notice also that the four closest cities to Miami (italicized in Table 4) are different depending on which period we consider. A control group based on only three years before 1980 risks selecting cities that do not match at all the Miami labor market trends before 1980. In addition, Miami was the worst performer in the 1972–1979 period among all the available 32 cities in terms of average wage growth (last column of the Table 4). Hence, when considering the full 1972–1979 trend, Miami seems to show slow employment growth, slow overall wage growth, and declining dropout wages.

The synthetic control method, matching variables during the 1972–1979 period, captures a group of cities with similarly slow labor markets. The control group in Borjas (2017), based on three years only, selects cities that are very different from Miami when the whole 1972–1979 performance is considered. The bolded cities (Anaheim, San Diego, and San Jose) appear both in the Borjas (2017) synthetic and employment placebos.²⁴ However, they experience really strong labor market indicator growth according to all measures except for the one used in his paper. It is then not surprising that wages in Miami are on a lower trajectory post-1980, relative to those.

To show that this matters in the May-ORG CPS analysis, Figure 9 shows the log hourly wages (Panel A) and the log weekly wages (Panel B) for Miami using Borjas’ (2017) sample (solid line). We also present the behavior of our synthetic control, based on matching variables in the whole 1972–1979 period (dashed line), and the Borjas (2017) synthetic control based on matching variables in the 1977–1979 period (dotted line). While our control matches reasonably well the pre-1979 trend and fluctuations of the Miami wages, the Borjas (2017) synthetic control shows very large pre-1979 differences with Miami, especially in 1976 and 1977. These differences continue after 1979, and the Borjas (2017) control group deviates upwards from the continued downward trend that both Miami and our control, once aligned at the 1979 value, show after 1979. Therefore, matching only on the 1977–1979 period tends to select cities whose labor market outcomes and wages do not match properly the negative 1972–1979 Miami trend before the event.

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Figure 9

Comparison between the Borjas (2017) and Our Synthetic Controls

Notes: Each panel shows the outcome variable for Miami (solid line), the Borjas (2017) synthetic control (dotted line), and our synthetic control (dashed line) in the period 1972–1991. The outcome variable and the data set are noted in the title of each panel. The sample is non-Hispanic men, not self-employed, in the labor force, age 25–59. The time series are standardized to the same value in 1979.

C. The Regressions

In Table 5, we use the insight gained from the comparisons above to reconcile the regression estimates in Table 5 of Borjas (2017), showing large negative coefficients for β_81–83 dummy with our null or positive coefficient shown in Table 2 above. The table shows the estimates of the Miami period dummies for the March CPS sample (upper panel of the Table) and the May-ORG CPS (lower panel). The first column shows our replication of exactly the regressions performed by Borjas estimating differences of Miami dropouts wages from the synthetic control in the post-1980 subperiods. We include initially, in Column 1, exactly the Borjas sample and specification including the moving-average smoothing, the omission of year 1980 from the regression, and the choice of control group (which we select to be his synthetic control group). The estimate of Column 1 reproduces the large negative estimate for the β_81–83 coefficient (and following years) with relatively small standard errors. We focus on the β_81–83 coefficient as this would be the most likely to be affected by the Boatlift. The estimate of Column 1 is −0.327 (SE 0.068) close to Borjas (2017, Table 5, Panel A, Column 4), which equals −0.257, with SE 0.077. Then, in Column 2 we extend the data back to 1972, and we include dummies to capture differences between Miami and Control in the pre-1979 period, relative to 1979. This establishes 1979 as a reference year and allows us to evaluate whether there were large Miami–control differences before the Boatlift, which is a diagnostic measure on the quality of the control group. The β_81–83 coefficient becomes −0.247 (SE 0.052), and we estimate a large positive coefficient with a small standard error on β_72–75, denoting a quite imprecise match of the pre-1979 trend. Then, in Column 3, we remove the moving-average smoothing of the data. This further reduces the estimate of the β_81–83 coefficient to −0.147 and, most importantly, increases significantly the standard error to 0.103. The data are now much more variable year-to-year, and this is reflected by the standard errors. The moving-average smoothing was artificially reducing those errors by smoothing the year-to-year variation of the data. In Column 4, we introduce our sample including male and female, non-Cuban workers aged 19–65, and, in Column 5, we introduce our synthetic control group, based on 1972–1979 matching of variables. In both cases, the estimates of the β_81–83 coefficient are smaller than in Column 3, and the pre-1979 coefficients are much smaller and within their standard error. The final specification of Column 5 shows a point estimate of −0.11 for the β_81–83 coefficient and a standard error of 0.068. While likely the standard error is underestimated because we are not accounting for the fact that the variables are constructed, it is clear that such coefficient would not be significant at standard confidence levels.

The lower part of the table shows the same progression for the estimates obtained from the May-ORG CPS data. Column 1 reproduces the result of Table 6 Panel B Column 4 of Borjas (2017) obtaining a point estimate of −0.200 (SE 0.029) on the β_81–83 coefficient. Then, we see a progressively smaller negative estimate when including the pre-trend coefficients (Column 2) and dropping the moving-average smoothing (Column 3). These specifications also show the large pre-1979 differences between Miami and the control captured by the large point estimates of the dummies. Afterward, using May-ORG CPS we see that the point estimate of the β_81–83 coefficient becomes positive in Columns 4 and 5. Finally, the last coefficient is similar to Column 1 of Table 3 (the differences are due to a slightly different definition of the time dummies). To emphasize the improvement from the introduction of our control, notice that in Column 5 the estimates on both the pre-1979 coefficients is small and nonsignificant. The final specification shows a positive difference for the Miami–control between 1981 and 1983 of about 4.9 percent with a standard error of 4.8 percent.