A 2015 article on the Farm Bureau's website states:

Half of all workers on U.S. dairy farms are immigrants, and the damage from losing those workers would extend far beyond the farms, nearly doubling retail milk prices and costing the total U.S. economy more than $32 billion, according to a new report commissioned by the National Milk Producers Federation.

According to an analysis at Progressive Dairy, out of the 3.40 a consumer pays for a gallon of milk at the supermarket, 1.53 goes to the farmer. In terms of hundredweight, the numbers are 39.40 cwt and 17.85 cwt.

According to a survey of dairy farms in the Northeast, the labor costs of running a dairy farm in terms of cost/hundredweight were [also] about 3.40 (with variations by herd size, etc).

Various sources put the hourly wage for illegals on dairy farms between 10.00 and 14.00 dollars per hour. Let's assume a dairy farmer hires only illegals and he pays them 12.00 per hour. Then they are all deported. In order to attract quality legal workers to take their places, lets say he needs to pay 24.00 per hour and that the full amount of that cost is passed directly to the consumer.

Since 24.00 is twice 12.00, we can multiply the labor share of a dairy farm's expenses per hundredweight by 2 which equals 6.80 and then add the increase into the farmer's share of the consumer's dollar / hundredweight, or 17.85 + 3.40 = 21.25.

A gallon of milk weighs about 8.6 pounds which means there are about 11.63 gal of milk in a hundredweight. So we take the 3.40 new labor costs and divide between the 11.63, which is a .29 per gallon increase.

So, the next time you bought a gallon of milk it would be 3.69, up from 3.40--a very far cry from "nearly doubling".

Question: How can we analyze the veracity of the claim that milk prices would double at the retail level if all the illegals were deported?

The article was a press release from the "National Milk Producers Federation", which is located in the heart of dairy country, Arlington, VA.

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    $\begingroup$ I think you have asked this exact same thing before and it was pointed out that you make a lot of assumptions in your example. $\endgroup$
    – Giskard
    Sep 30 '17 at 10:56
  • $\begingroup$ I see that jmbejara suggested reposting this question after it was edited to be clearer about what the actual question is. I agree that there is a clear question here, and I think we should have someone on the site capable of writing a good answer, so I'd vote to keep this one open. $\endgroup$
    – Ubiquitous
    Sep 30 '17 at 15:26
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    $\begingroup$ @Ubiquitous Really? "How is it this outfit isn't lying to us? Why would economists lie?" This is a clear question? I would have no problem with this question 1) without the hyperbole and 2) without the totally made up example in which labor costs double but somehow the cost share of labor stays the same. $\endgroup$
    – Giskard
    Sep 30 '17 at 19:57
  • $\begingroup$ @densep I agree the question is unnecessarily hyperbolic, but the underlying query "Is this claim that deportation of illegal immigrants would double some consumer price?" seems to be a valid and interesting econ question to me. The example looks to me like a fair (if, perhaps, flawed) attempt at thinking this problem through systematically, and I think a good answer would confront this head-on. But anyone who thinks differently can vote to close the question. $\endgroup$
    – Ubiquitous
    Sep 30 '17 at 20:54
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    $\begingroup$ My reservations about this question are clear to me. This site is not a soapbox to rail against the evils of media or institutions or whatnot. Useful questions must be framed in a way that asks what tools can be used to analyze an idea, economic statement, etc. It should not assume the truth/falseness of a statement and ask why people would disagree with the asker's position. Framing questions neutrally is an important part of maintaining an impartial atmosphere and I will edit the question to reflect this as best I can. $\endgroup$
    – Kitsune Cavalry
    Oct 5 '17 at 3:26

It is worth noting that OP's original question before I edited it asked, "why would economists lie to us?" This already leaves a poor taste in my mouth; such a question is loaded enough as it is, only good for picking fights. The author stated at the bottom of the Progressive Dairy article is a lawyer, not an economist, and seems to be the basis for some of your figures in your analysis. The article from the Texas A&M AgriLife study cited by the Farm Bureau/NMPF did have economists writing on the topic, which I'll discuss briefly later.

Related to denesp's comment on cost of labor share, consider the firm's cost of milk production:

$$p_L q_L + \sum^n_{i = 1} p_iq_i = C$$

The cost $C$ is made up of the cost of labor (price of labor times quantity of labor) plus the cost of all other factors of production. The labor share of cost that was mentioned by OP would be:

$$\frac{p_L q_L}{C} \equiv \boxed{s_L = \frac{p_L q_L}{p_L q_L + \sum^n_{i = 1} p_iq_i}}$$

Suppose as in the hypothetical that the cost of labor doubles. OP argues that then,

we can multiply the labor share of a dairy farm's expenses per hundredweight by 2

but this is clearly not true from a mathematical standpoint.

$$2s_L \neq \frac{(2p_L) q_L}{(2p_L) q_L + \sum^n_{i = 1} p_iq_i}$$

More than this, it also assumes there are no cross-price effects. That is, if the price of one good changes, it will not change the quantity demanded of other factors of production. If there is any sort of substitutability OR complementarity between labor and any other factor of production, this cannot hold. Empirically, low-skill/blue-collar labor is a complement to high skill labor and a substitute with capital.

All of this walks around a bigger issue. The article in question makes a claim about the effect of disemployment on doubling milk prices. It does not say that it will come about by doubling labor prices, so the argument posed above is just a strawman. That is, it may very well be that doubling labor price would not double the final price of milk, but that is not what the article is arguing.

That said, I don't particularly like the analysis done in the Texas A&M AgriLife study cited either. Ultimately, it has no inference/causal modelling and is just a survey with some summary statistics, with a lot of questionable assumptions. There is like one price elasticity in that whole analysis as I could see, and its use was not compelling.

The lazy way to interpret this is to just say the methods of the study are bad and that its conclusions have no value and only serve to mislead the public. I don't think this is particularly true either. Private sector market analysis is definitely in some ways less stringent than publishing in, say, an economics journal however.

So what can we do?

The long, boring, rigorous way to estimate the impact of a large shock to the labor supply is to look at labor demand and labor supply simultaneously.

Consider an extremely simple set of linear estimations:

$$\ln(L_s) = \alpha_s \ln(w) + \vec{\beta}_s \vec{Z} + \epsilon_s$$ $$\ln(L_d) = \alpha_d \ln(w) + \vec{\beta}_d \vec{X} + \epsilon_l$$

Where $Z$ is a vector of control variables/supply shifters (e.g. non-labor income), and $X$ is the same but for demand. Notice that labor, $L$ and wage, $w$ are endogenously determined, which nudges us towards the use of IV estimation, rather than the typical OLS.

Labor Demand:

From here you'd have to think about what kind of functional form production should take: $Y = f(K, L, \cdots)$, where $K$ is capital, and you can put in some other factors if you want (legal labor vs illegal labor perhaps?), and derive conditional factor demands, which you can plug into the equation for cost which gets some $C(w, r, \cdots, Y)$, with $r$ representing the rental rate of capital.

Applying Shephard's Lemma, you can then derive the elasticities of substitution between two different factors of production, which are used to calculate the cost shares of of each production factor, and eventually, we can then find the own-price elasticity of the factors, used to help estimate $\alpha_d$.

Labor Supply:

Similar line of thought, but with a specification of utility and working with Frisch elasticities.

Plugging in the data (number of laborers, capital stock on farms, etc.) could prove difficult or impossible without existing data of course.

This is obviously a very rough sketch for an empirical framework for analyzing labor supply, but it is a foundation for analyzing all sorts of shocks to the labor supply. For a more detailed analysis, you can refer to Cahuc, Carcillo, and Zylberberg and their first few chapters on labor supply and labor demand.

Sometimes in the economic literature, undertaking a more detailed study like this requires a lot of funding and time, with in mind particularly the hassle of data. People want practical policy answers in the short run, particularly in the private sector. With limited resources, sometimes studies like the ones you've looked at provide "second-best results" and that is the analysis we have to work with. The productive, honest thing to do with studies that take on partisan issues is to think about how to feasibly improve them and ask specifically about how to look at the research being done on the topic.

There are plenty of voices accusing all manner of partisan research/analysis as misleading, and still plenty polemics out there who would waste their time writing polemics. It is not for this site.

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    $\begingroup$ Kitsune, you are a legend. excellent answer! $\endgroup$
    – EconJohn
    Oct 8 '17 at 3:02
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    $\begingroup$ Notwithstanding the impressive jargon you wield, the study is nevertheless misleading. The lobbyists are lying in order to influence public policy for the financial benefit of their clients to the detriment, necessarily, of the public good. Your analysis has the practical effect of exclusion. It is meant to retain membership for the initiated in an exclusive club, not to solve problems or add wisdom or insight to human activity. All your analysis did was add complications until the question was complicated enough to be rendered impenetrable to the lay person. Is that the goal of the economist? $\endgroup$
    – CWill
    Oct 8 '17 at 15:29
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    $\begingroup$ This is an academic site primarily for professional economists, but all I used was high achool algebra to address your particular argument. The layperson who is uninterested in the math does not have to necessarily understand how to make a whole new study on milk prices. Just that a better way exists. I have taken a fair side where I've acknowledged the shortcomings of the article you disliked, but if you are only here to belittle our profession, this site is not for you. $\endgroup$
    – Kitsune Cavalry
    Oct 8 '17 at 17:03

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