Immigration surplus couldn’t be a world GDP increase of 60%, but could be 7%

Global gains from open borders shaded area shows immigration surplus

The immigration surplus made concrete, on paper:

  • North’s gain from Southern workers, trapezoid B, equals South’s loss, trapezoid C.
  • North’s total gain, trapezoid AB, is bigger than South’s loss, trapezoid C. The difference is the total immigration surplus: trapezoid AB‘s shaded portion, which is triangle A.
  • This is idealized with migration costless; and with poor Southern immigrants suddenly producing like rich Northern natives; and with migration continuing when Northern natives’ wages fall.

Immigration surplus has been called a world GDP increase of 60%

To get a better grasp of the issues at hand, it is best to begin with a description of the basic model.

As in the generic study in the literature, the removal of immigration restrictions (combined with the assumption of costless mobility) would lead to a huge increase in world GDP. Specifically… world GDP would increase by $40 trillion, almost a 60 percent increase. Moreover, these gains would accrue each year after the migration occurs, so that the present value of the gains nears one quadrillion dollars!

…if only countries would stop being countries.

Immigration surplus that big would take exodus of 95%, productivity leap, native wages down 40%

The simulation implies that 2.6 billion workers, or 95 percent of the workforce in the South, will move. If these workers bring along their families, the 95 percent mobility rate implies that nearly 5.6 billion persons would move from the South to the North.

For immigration to generate substantial global gains, it must be the case that billions of immigrants can move to the industrialized economies without importing the “bad” organizations, social models, and culture that led to poor economic conditions in the source countries in the first place.

The formation of social networks among migrants could substantially lower the costs of migration for the second or third billionth mover. But congestion costs in the receiving countries could also increase exponentially, making it harder to resettle that marginal migrant.

The earnings of the North’s native workforce fall by almost 40 percent, and the earnings of Southern workers increase by 143 percent.

A little humility about what we actually know would seem to be a prerequisite before anyone proposes a breathtaking rearrangement of the world order. …it seems likely that a particular [immigration] policy is chosen because that choice leads to the greatest benefits and/or smallest costs in that place and at that time.[1]

Immigration surplus could plausibly come from emigration of 12%, with productivity lag

In this paper, we quantify the effect of a complete liberalization of cross-border migration on the world GDP and its distribution across regions.

As for desired migration, we aggregate four waves of the Gallup World Poll survey… About 290,000 adults from 142 countries were questioned about their desired migration and preferred country of destination. These countries are representative of about 97 percent of the world population.

Data on potential migration reveal that the number of people in the world who have a desire to migrate is around 400 million. For the year 2000, we identify 274.5 million desiring migrants aged 25 and over. Adding them to the effective migrants gives a total stock of 386.1 million potential migrants (i.e., 12.1 percent of the population).

Most of these desiring migrants originate in poor countries and want to relocate to rich countries.

The main regions of origin are Asia (30 percent of the total, including China and India), sub-Saharan Africa (17 percent), Latin America (14 percent), and the Middle East and Northern Africa (8 percent).

In terms of destinations, a vast majority want to emigrate to an OECD, high-income country (27 percent to the United States, 26 percent to Europe, and 16 percent to Canada, Australia, and New Zealand). Other important destinations are Japan, Singapore, Saudi Arabia, and the United Arab Emirates.

It is widely documented that many immigrants with higher education tend to find jobs in occupations typically staffed by less-educated natives… Highly educated immigrants trained in developing countries, in particular, are likely to be less productive in high-skill jobs than natives with similar educational degrees.

Plausible immigration surplus in the first generation could be world GDP increase of 7%

…when total factor productivity (TFP) is an increasing function of the proportion of college graduates in the country’s labor force… in the medium term… (i.e., over one generation)… liberalizing migration increases the world GDP by… in the range of 7.0 percent…[2]


  1. Borjas, George J. “Immigration and globalization: A review essay.” Journal of Economic Literature 53.4 (2015): 961-974.
  2. Docquier, Frédéric, Joël Machado, and Khalid Sekkat. “Efficiency gains from liberalizing labor mobility.” The Scandinavian journal of economics 117.2 (2015): 303-346.

Climate model bias is incentivized in science, economics, and politics

Lower-Atmosphere Temperatures Predicted by United Nations' Intergovernmental Panel on Climate Change (IPCC) Models and Measured by Satellites and Weather Balloons Demonstrate Climate Model Bias

Figure 64.1. Lower-Atmosphere Temperatures Predicted by United Nations’ Intergovernmental Panel on Climate Change (IPCC) Models and Measured by Satellites and Weather Balloons

Climate model bias is naturally selected by government-funded science

An accurate cost-benefit analysis can only be done if there is a reliable forecast for climate change and its specific impacts.

The… federal Interagency Working Group (IWG)… by relying on the output from published general circulation models (GCM) that simulate future climate as carbon dioxide is added to the atmosphere, is saying that those models are sufficient. They are not. The most logical interpretation of the ongoing (and increasing) disparity between the collectively modeled and observed temperatures (as shown in Figure 64.1 [above]) is that the forecast models are simply too sensitive to carbon dioxide changes.

Additionally, Congress should direct that all SCC calculations take into account the massive increase in global food production (valued at $3.2 trillion since 1950) that is a direct result of increasing atmospheric concentrations of carbon dioxide, as well as the nearly global increase in green vegetative matter. The current models used by the IWG to determine the SCC are woefully insufficient on these accounts.

A remarkable finding published in 2016 by the Royal Society, the national academy of science of the United Kingdom, may explain the time and money spent. It shows that the way we reward scientists is producing, in the authors’ words, increasingly “bad science.” A corollary is that, if the federal government suddenly disburses enormous amounts of funding for a given field, as it has for climate studies, then the quality of research will decline significantly.

Climate model bias makes for government-friendly economic analyses

Proponents of a carbon dioxide tax… cite something called the “social cost of carbon” (SCC). The Obama administration’s SCC was generated by a federal Interagency Working Group (IWG) that ignored specific… Office of Management and Budget (OMB)… directives with regard to the determination of the SCC and its use in cost-benefit analysis of federal actions.

“For regulatory analysis, you should provide estimates of net benefits using both 3 percent and 7 percent”—with a discount rate of 7 percent representing “an estimate of the average before-tax rate of return to private capital in the U.S. economy” and 3 percent reflecting the low case. Had the IWG included a 7 percent discount rate as guided by the OMB, they would have arrived at a substantially lower estimate of the SCC—some 80 percent (or more) below the current IWG mean SCC value.

“Your analysis should focus on benefits and costs that accrue to citizens and residents of the United States.” Yet the administration’s IWG reports (and subsequently relies upon) a value of the SCC determined from the accumulation of costs projected to occur across the globe while burying the U.S. domestic costs (which are estimated to be only 7 to 23 percent of the global value).

Climate model bias is used to weaken property rights and build dependence

…the Paris Agreement on climate change… states, “Developed country Parties shall provide financial resources to assist developing country Parties with respect to both mitigation and adaptation in continuation of their existing obligations under the Convention.”

“Continuous and enhanced international support shall be provided to developing country Parties.”

“Developed country Parties shall biennially communicate indicative quantitative and qualitative information related to paragraphs 1 and 3 of this Article, as applicable, including, as available, projected levels of public financial resources to be provided to developing country Parties” [emphasis added].

Climate model bias is used to promote bigger government

First and foremost, Congress should turn down any legislative proposals for a tax on carbon dioxide emissions, erroneously called a “carbon tax” by proponents. Such a tax would be as insidious as the income tax, which began as a very small levy but ultimately evolved into the fiscal and byzantine morass that it is today.

Legislators will never give up an equivalent amount of revenue that they could spend on desired projects. …we can’t “expect three trillion dollars to walk down K Street unmolested” by special interests and lobbies.[1]


  1. Michaels, Patrick J. and Paul C. Knappenberger. “Global Warming and Climate Change.” Cato Handbook for Policymakers, 8th ed., Cato Institute, 2017, pp. 627-636.

Calculating impact of change for simple models is intuitive

Odometer as integral, which illustrates calculating impact of change

Calculating impact of change of a car [1]

Calculating impact of change is the second of calculus’s two principal operations

…the two principal symbols that are used in calculating… are:

  1. d which merely means “a little bit of.”
    Thus dx means a little bit of ..
  2. ∫ which is merely a long S, and may be called (if you like) “the sum of.”
    Thus ∫ dx means the sum of all the little bits of x… Ordinary mathematicians call this symbol “the integral of.” Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dx‘s, (which is the same thing as the whole of x). The word “integral” simply means “the whole.” When you see an expression that begins with this terrifying symbol, you will henceforth know that it is put there merely to give you instructions that you are now to perform the operation (if you can) of totalling up all the little bits that are indicated by the symbols that follow. That’s all.

Calculating impact of change means calculating a curve’s footprint

Like every other mathematical operation, the process of differentiation may be reversed; thus, if differentiating y = x4 gives us dy/dx= 4x3; if one begins with dy/dx = 4x3 one would say that reversing the process would yield y = x4. But here comes in a curious point. We should get dy/dx = 4x3 if we had begun with any of the following: x4, or x4 + a, or x4 + c, or x4 with any added constant. So it is clear that in working backwards from dy/dx to y, one must make provision for the possibility of there being an added constant, the value of which will be undetermined until ascertained in some other way.

One use of the integral calculus is to enable us to ascertain the values of areas bounded by curves.

Let AB… be a curve, the equation to which is known. That is, y in this curve is some known function of x. Think of a piece of the curve from the point P to the point Q.

Let a perpendicular PM be dropped from P, and another QN from the point Q. Then call OM = x1 and ON = x2, and the ordinates PM = y1 and QN = y2. We have thus marked out the area PQNM that lies beneath the piece PQ. The problem is, how can we calculate the value of this area?

Calculating impact of change one strip at a time

The secret of solving this problem is to conceive the area as being divided up into a lot of narrow strips, each of them being of the width dx. The smaller we take dx, the more of them there will be between x1 and x2. Now, the whole area is clearly equal to the sum of the areas of all such strips. Our business will then be to discover an expression for the area of any one narrow strip, and to integrate it so as to add together all the strips.

Now think of any one of the strips. It will be like this: being bounded between two vertical sides, with a at bottom dx, and with a slightly curved sloping top.

Suppose we take its average height as being y; then, as its width is dx, its area will be y dx. And seeing that we may take the width as narrow as we please, if we only take it narrow enough its average height will be the same as the height at the middle of it. Now let us call the unknown value of the whole area S, meaning surface. The area of one strip will be simply a bit of the whole area, and may therefore be called dS. So we may write

area of 1 strip = dS = y ∙ dx.

If then we add up all the strips, we get

total area S = ∫ dS = ∫ y dx.

Calculating impact of change from start to finish

…how do you find an integral between limits, when you have got these instructions?

First, find the general integral thus:

∫ y dx,

and, as y = b + ax2 is the equation to the curve…,

∫ (b + ax2) dx

is the general integral which we must find.

Doing the integration in question by the rule…, we get

bx +(a/3)x3 + C;

and this will be the whole area from 0 up to any value of x that we may assign.

Therefore, the larger area up to the superior limit x2 will be

bx2 + (a/3)x23 + C;

and the smaller area up to the inferior limit x1 will be

bx1 + (a/3)x13 + C.

Now, subtract the smaller from the larger, and we get for the area S the value,

area S = b(x2 – x1) + (a/3)( x23 – x13).

This is the answer we wanted.

All integration between limits requires the difference between two values to be thus found. Also note that, in making the subtraction the added constant C has disappeared.

Calculating as simple as possible and no simpler

“Calculus made Easy” shows how… easy most of the operations of the calculus really are. The aim of this book is to enable beginners to learn its language, to acquire familiarity with its endearing simplicities, and to grasp its powerful methods of solving problems…[2]

It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.[3]


  1. Keisler, H. Jerome. Elementary calculus: An infinitesimal approach. Courier Corporation, 2012, p. xi.
  2. Thompson, Silvanus Phillips. Calculus made easy. 2nd ed., enlarged, MacMillan, 1914.
  3. Einstein, Albert. “On the method of theoretical physics.” Philosophy of science 1.2 (1934): 163-169.

Calculating rate of change for simple models is commonsense

Speedometer as derivative, which illustrates calculating rate of change

Calculating rate of change of a car [1]

Calculating rate of change is the first of calculus’s two principal operations

…the two principal symbols that are used in calculating… are:

  1. d which merely means “a little bit of.”
    Thus dx means a little bit of x; or du means a little bit of u.
  2. ∫ which is merely a long S, and may be called (if you like) “the sum of.”
    Thus ∫ dx means the sum of all the little bits of x… That’s all.

In ordinary algebra which you learned at school, you were always hunting after some unknown quantity which you called x or y; or sometimes there were two unknown quantities to be hunted for simultaneously. You have now to learn to go hunting in a new way; the fox being now neither x nor y. Instead of this you have to hunt for this curious cub called dy/dx. The process of finding the value of dy/dx is called “differentiating.” But, remember, what is wanted is the value of this ratio when both dy and dx are themselves indefinitely small.

Calculating rate of change means calculating a curve’s local slope

It is useful to consider what geometrical meaning can be given to the differential coeffcient. In the first place, any function of x, such, for example, as x2, or √x, or ax + b, can be plotted as a curve…

Consider any point Q on this curve, where the abscissa of the point is x and its ordinate is y. Now observe how y changes when x is varied. If x is made to increase by a small increment dx, to the right, it will be observed that y also (in this particular curve) increases by a small increment dy (because this particular curve happens to be an ascending curve). Then the ratio of dy to dx is a measure of the degree to which the curve is sloping up between the two points Q and T. If… Q and T are so near each other that the small portion QT of the curve is practically straight, then it is true to say that the ratio dy/dx is the slope of the curve along QT.

Calculating rate of change just takes a little algebra and common sense

Now let us see how, on first principles, we can differentiate some simple algebraical expression. Let us begin with the simple expression y = x2. Let x, then, grow a little bit bigger and become x + dx; similarly, y will grow a bit bigger and will become y + dy. Then, clearly, it will still be true that the enlarged y will be equal to the square of the enlarged x. Writing this down, we have:

y + dy = (x + dx)2.

Doing the squaring we get:

y + dy = x2 + 2x∙dx + (dx)2.

Remember that dx meant a bit—a little bit—of x. Then (dx)2 will mean a little bit of a little bit of x; that is… it is a small quantity of the second order of smallness. It may therefore be discarded as quite inconsiderable in comparison with the other terms. Leaving it out, we then have:

y + dy = x2 + 2x∙dx.

Now y = x2; so let us subtract this from the equation and we have left

dy = 2x∙dx.

Dividing across by dx, we find

dy/dx= 2x.

Now this is what we set out to find. The ratio of the growing of y to the growing of x is, in the case before us, found to be 2x.


  1. Keisler, H. Jerome. Elementary calculus: An infinitesimal approach. Courier Corporation, 2012, p. xi.
  2. Thompson, Silvanus Phillips. Calculus made easy. 2nd ed., enlarged, MacMillan, 1914.