Question:
Does julia's speed advantage over python make any difference for DSGE modeling?

When compared to Python the main selling point of Julia is its speed as it is often argued. However, from my own personal experience I never noticed any significant difference in speed between Julia and Python. If there is a trivial few seconds difference that would not matter practically. This could be problem for models using big-data but outside machine learning are there any (even large) DSGE models where this makes difference?

I am looking for some examples of significant differences between the two.

PS: Despite reference request tag I am happy to accept answer that showcases some examples directly.

Explanation: The Federal Reserve Bank of New York is using julia. We can check their reasons, which are potentially related to advantages of julia.

$\begingroup$

Julia is actually a lot faster than Python, also when running DSGE models.

The [ NY FED moved their DSGE model to Julia
](https://juliacomputing.com/case-studies/ny-fed/) because it allows them to:

>   * Estimate models 10x faster
>   * Complete 'solve' test 11x faster
>   * Reduce number of lines of code in half, saving time, increasing
> readability and reducing errors
>

The original results can be found [ here ](http://frbny-
dsge.github.io/DSGE.jl/latest/MatlabToJuliaTransition/) .

These speedups are compared to Matlab which the FED used before. However, with
regards to speed, Matlab should be quicker than Python for DSGE models (any
matrix statistics, iteration and recursion and so forth). That is also what
the first suggested paper in the accepted answer finds (I only looked at the
revised 2018 version). By the way, the conclusion in the paper reads as
follows:

> ... C++ is the fastest alternative, Julia offers great balance of speed and
> ease of use, and Python is too slow.

The screenshot below is directly from the paper. [ ![enter image description
here](https://i.sstatic.net/EANf4l.png) ](https://i.sstatic.net/EANf4l.png)

The slowest Julia implementation takes only 1.6% of the fastest Python
version.

The second paper (2020) essentially tests a model that runs only a few seconds
(less than 1 in Julia). [ ![enter image description
here](https://i.sstatic.net/yCY5ml.png) ](https://i.sstatic.net/yCY5ml.png)

Nonetheless, as soon as it's more than a fraction of a second (where compile
time latency of Julia will almost certainly be an issue), Julia is
significantly quicker. It may not be a difference you really feel or that
matters for you, because waiting for 10 or 15 seconds is essentially not a
deal breaker.

Unlike Python, Julia is significantly more complex when it comes to potential
code implementation. Everything that runs fast in Python is not Python, but C,
Fortran and co. Julia can also turn slow when type inference fails or the JIT
compiler has insufficient information to optimize effectively. If you notice
no speedup to Python, it is either because you use examples (or benchmark that
way) where compile time latency matters more than computation, or it is
inefficient code. I did some work a while ago on Julia's speed and comparison
to Python. I will copy paste some sections in case anyone is interested in
some details why Julia is actually fast.

In dynamic languages like Python, classes could be subclassed. This is also
possible in some statically typed languages that are object oriented such as
Java. For this reason, a single integer in ` Python 3.x ` actually contains
four pieces:

  * ` ob_refcnt ` , a reference count that helps Python silently handle memory allocation and deallocation
  * ` ob_type ` , which encodes the type of the variable
  * ` ob_size ` , which specifies the size of the following data members
  * ` ob_digit ` , which contains the actual integer value that we expect the Python variable to represent.

This means that there is some overhead in storing an integer in Python as
compared to an integer in say Julia or C. Python uses 28 bytes to store an
integer, Julia only 8 bytes.

A great feature of Julia is that types are extremely lightweight, and user-
defined types are exactly as performant as anything built-in: this is a big
difference to languages like Python where constructing a new instance of a
class is very expensive. The amount of data required to store a Struct (Class)
called Foo is the same as the amount of data required to store a pointer to a
string. At compilation, Julia (just like Fortran and C) doesn't have
additional overhead contrary to how an object (in say Python) is represented
in memory (includes type information, reference counter etc).

Julia:

[ ![enter image description here](https://i.sstatic.net/rfcFqm.png)
](https://i.sstatic.net/rfcFqm.png)

Python:

[ ![enter image description here](https://i.sstatic.net/WK8LXm.png)
](https://i.sstatic.net/WK8LXm.png)

You can see the massive overhead in Python. It's probably even better to say
that Julia isn't slow (not that it is fast), meaning it doesn't get in the way
of the hardware and lets the hardware do its job efficiently. Mathematically,
the integer 5 is exactly identical to the floating point 5.0, but it has a
different bitwise representation. This is why Types are important in
computers. Slow programming languages have a very hard time to know in advance
what types things are. So they test for all sorts of combinations to figure
out what routine to use to call the correct CPU instructions, because at the
lowest level, the microprocessor has to perform different instructions when
dealing with for example integers or floats. A microprocessor does not know
types. A CPU needs special instructions for all different types; e.g. signed
and unsigned integers, floats with single precision or double precision, or
combinations of floating points and integers, for which you will need
conversion (promotion) of types. Usually there will be different special
instructions for every possible type.

As long as your task is computational, Julia will always beat Python (provided
both are optimized). Where it starts to matter is when you really work with
lots of data and / or complex models.

For example look at the question [ Why is this task faster in Python than
Julia? ](https://stackoverflow.com/questions/70987896/why-is-this-task-faster-
in-python-than-julia) on stackoverflow. It is almost always code written in
non-performant ways if you get slow Julia code. Without any optimization, just
getting rid of compile time latency, resulted in Julia taking 8s vs 30s in
Python. Regarding the stackoverflow question, [ Quantinsti
](https://blog.quantinsti.com/julia-programming/) has some good tests for
Multiple operations on large datasets. For 100 groups of ~10,000,000 rows,
Python (pandas package) and R (dplyr package) resulted in an internal error
and out of memory error, respectively while Julia took 2.4 seconds the first
time and 1.8 seconds the second time.

Julia is fast because of its design decisions that allow a compiler to make
efficient code. This is achieved with type-stability through specialization
via multiple-dispatch as a core design decision. To illustrate this, you can
try to compute ` 2^3 ` .

In Julia, you can run ` @code_llvm ` as well as ` @code_native ` macros to
print the LLVM bitcodes as well as the native assembly instructions generated
for running the method matching the given generic function and type.

If you use ` @code_llvm exponential(2,3) ` as well as ` @code_llvm
exponential(2,3) ` and compared it to the 2^3 counterpart, you will be
surprised how messy the “manual” exponential solution is compared to Julia’s
built in.

Manual (ignoring almost half the output):

[ ![enter image description here](https://i.sstatic.net/5XNk7l.png)
](https://i.sstatic.net/5XNk7l.png)

Built-in (entire output):

[ ![enter image description here](https://i.sstatic.net/FR0qMl.png)
](https://i.sstatic.net/FR0qMl.png)

The built in solution is something you can decipher fairly quickly with some
basic assembly.

  * The lines beginning with ` ; ` are comments, and explain which section of the code the following instructions come from. Calling it with ` debuginfo=:none ` removes the comments in the assembly code
  * ` pushq ` , ` movq ` , ` subq ` and ` addq ` are to save stack frames, move content to or from [ registers ](https://en.wikipedia.org/wiki/64-bit_computing#Architectural_implications) (the suffix ` q ` is short for ` quad ` , which means 64-bit integer), allocate to registers and dealocate. Neither is important for our purpose. For short, a CPU operates only on data present in registers. These are small, fixed size slots (e.g. 8 bytes in size) inside the CPU itself. A register is meant to hold one single piece of data, like an integer or a floating point number.
  * ` movabsq ` is the so called [ Exponentiation by squaring ](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) . For example if you compute  $x^{15}$  , it will look like this

    x^15 = (x^7)*(x^7)*x
    x^7 = (x^3)*(x^3)*x
    x^3 = x*x*x

Or only the last line in our simple example above, which is  $x^3$  only.

The reason this works is that Julia's built in function made some clever
design decisions. For instance, ` x^-n ` works for an integer ` x ` and
literal ` n ` but not for expressions because Julia developers [ defined
](https://github.com/JuliaLang/julia/issues/20527) a special syntactic
treatment of literals.

  * The benefit is quick and reliable exponentiation for something like  $x^-3$  . The advantage is that [ literal powers ](https://docs.julialang.org/en/v1/base/math/#Base.:%5E-Tuple%7BNumber,%20Number%7D) automatically become type-stable, because they turn into a fixed number of * calls. This is why Julia now lowers ` x^-3 ` to ` inv(x)^3 ` .
  * The downside is that  $p = -3$  and  $x^p$  does not work and throws an error which seems potentially quite confusing. However, the ` x^literal ` has a different meaning than ` x^expression ` . In essence, referential transparency was sacrificed, and type stability "extended": That is why ` ^ ` to a literal integer power is different than raising to a variable with the same integer value.

**Note:** The crux here is that type-stability doesn’t mean that the type
returned by a function is the same as the input. It means that the type can be
inferred at every step of the way. If inv of an integer is always a floating
point number, then that’s type stable.

The problem however, is that most casual Python users will expect x^p to work
for p = -3.

Similarly, scope matters a lot. You can look at this simple function.

    b = 1.0
    function g(a)
        global b
        tmp = a
        for i in 1:1_000_000
            tmp = tmp + a + b
        end
        return tmp
    end

b is global here, which is like poison for performance because the type of a
global variable is never certain.

If you instead write

    function g(a, b)
        tmp = a
        for i in 1:1_000_000
            tmp = tmp + a + b
        end
        return tmp
    end

you are eliminating the global variable which

• reduces the number of allocations to zero (from 3000001 allocations: 45.78
MiB)
• speeds up execution and
• produces clean and fairly simple machine code.

For short, with some care, Julia can be on par with the fastest languages.

These allocations matter massively. On my private laptop for example, finding
a single file (including opening and closing the file) takes about 1.4
milliseconds. Accessing 1,000,000 integers from memory takes 75.7
milliseconds. So my RAM is almost 20,000 times faster than my disk. I ran this
with a [ reasonably fast
](https://ssd.userbenchmark.com/SpeedTest/1317771/E12S-512G-PHISON-SSD-B27B)
SSD but even the newer Optane technology disks are usually thousands of times
slower than RAM.

I ran a speed test between C, Python and Julia, which is based on a notebook
from an introductory [ MIT math course
](https://github.com/mitmath/18S096/blob/master/lectures/lecture1/Boxes-and-
registers.ipynb) .

It is a speed comparisons between C, Python and Julia by implementing a
**sum** function ` sum(a) ` , which computes

$$ \mathrm{sum}(a) = \sum_{i=1}^n a_i $$

for an array ` a ` with ` n ` elements. I compared built in ` sum ` functions
in Julia and Python along with hand-coded implementations in C, Python, and
Julia. If you are a Windows user and want to replicate this on your own, you
will need to install the MinGW (GCC/G++) compiler.

The C code is:

    C_code = """
    #include <stddef.h>
    double c_sum(size_t n, double *X) {
        double s = 0.0;
        for (size_t i = 0; i < n; ++i) {
            s += X[i];
        }
        return s;
    }
    """

    const Clib = tempname()   # make a temporary file

    # compile to a shared library by piping C_code to gcc
    open(`gcc -fPIC -O3 -msse3 -xc -shared -o $(Clib * "." * Libdl.dlext) -`, "w") do f
        print(f, C_code)
    end

Julia's

    function my_sum1(x)
        result = zero(eltype(x))
        for element in x
            result += element
        end
        return result
    end

Not only is the Julia code significantly easier, but also, unlike C, it works
in Julia for any type of array (any iterable that provides an ` eltype `
method).

Python (within a Julia Kernel using PyCall)

    py"""
    def mysum(a):
        s = 0.0
        for x in a:
            s = s + x
        return s
    """
    mysum_py = py"mysum"

The results are

[ ![enter image description here](https://i.sstatic.net/RBhSI.png)
](https://i.sstatic.net/RBhSI.png)

There are a few interesting aspects.

  * Starting with C, testing the function on an array of  $10^7$  random numbers in [0,1] gives a result of ≈ 10ms for summing these numbers, which means that we have about 1 billion additions per second. This sounds a lot, but is well below the clock-speed of 2.5GHZ my [ processor ](https://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i5-7300HQ+%40+2.50GHz&id=2922) has. This is because each Floating-Point addition needs to perform several additional calculations to load the next element of the array from memory, plus the time needed to access memory itself.
  * Probably most interesting is that Python's built in sum is fairly slow, even though the Python sum function is written in C (Julia's sum is built using only Julia). It takes almost 4x longer than the equivalent C code and allocates memory. Python code pays a price for being generic and being able to handle arbitrary iterable data structures. See above for memory allocation differences between Julia and Python. Therefore, there are not only the computations involving addition, but also the overhead from fetching each item from memory.
  * Julia equivalent of a Python list is a Vector{Any}: internally, this is an array of pointers to "boxes" that can hold any type (Any). This makes things much slower: each + computation on an Any value must dynamically look up the type of object, figure out what + function to call, and allocate a new "box" to store the result. If you run this logic in Julia, it is even slower than Python. This is the same problem as with the manual Numpy array implementation. Python is faster (better optimized for dealing) with untyped ` Any ` values. This is because Julia expects you to use "concretely" typed arrays in all performance-critical cases and why you should always avoid abstract types in Julia.
  * On the other hand, Numpy arrays can take advantage of the fact that all of the elements are of the same type. This is actually faster than C! The reason is that NumPy gets and extra turbo boost from exploiting [ SIMD instructions ](https://en.wikipedia.org/wiki/Streaming_SIMD_Extensions) .

You can run SIMD for C as well as Julia as well.

Julia

    function mysum(A)
        s = zero(eltype(A))
        @simd for a in A
            s += a
        end
        return s
    end

C

    const Clib_fastmath = tempname()   # make a temporary file

    # The same as above but with a -ffast-math flag added
    open(`gcc -fPIC -O3 -msse3 -xc -shared -ffast-math -o $(Clib_fastmath * "." * Libdl.dlext) -`, "w") do f
        print(f, C_code)
    end

    # define a Julia function that calls the C function:
    c_sum_fastmath(X::Array{Float64}) = ccall(("c_sum", Clib_fastmath), Float64, (Csize_t, Ptr{Float64}), length(X), X)

[ ![enter image description here](https://i.sstatic.net/ZoFTDl.png)
](https://i.sstatic.net/ZoFTDl.png)

However, once you work with SIMD, you really need to know what you do when you
implement and use this. Incorrect use of the @simd macro may cause unexpected
results.

While this may sound like esoteric computer science stuff, you can look at the
[ following question ](https://quant.stackexchange.com/a/63891/54838) to see
what can happen with floating point math results in a reasonable normal
situation. The most intriguing example demonstrating the dangers of floating
point math I have seen so far comes from [ Stefan Karpinksi
](https://discourse.julialang.org/t/array-ordering-and-naive-summation/1929) .
You can use this to illustrate the difference between left-to-right summation
and left-to-right summation with a @simd annotation.

Essentially, if you use this code snippet in Julia,

    function sumsto(x::Float64)
        0 <= x < exp2(970) || throw(ArgumentError("sum must be in [0,2^970)"))
        n, p₀ = Base.decompose(x) # integers such that `n*exp2(p₀) == x`
        [floatmax(); [exp2(p) for p in reverse(-1074:969) if iseven(n >> (p-p₀))]

        -floatmax(); [exp2(p) for p in reverse(-1074:969) if isodd(n >> (p-p₀))]]
    end

    s = rand()*10^6
    v = sumsto(s)

you order the random vector (10^6) from highest to lowest value. None of the
standard algorithms in Julia or Python provide the true sum, although
interestingly, in this example SIMD comes closest in this case. The reason is
that in the case of summation, strict left-to-right summation is actually one
of the least accurate algorithms, so putting @simd on the loop makes it faster
and more accurate at computing the true sum because SIMD largely allows for
reassociation of mathematically associative operations which are not actually
associative in floating point. This includes ` + ` and ` * ` . Generally, ` (a
+ b) + c ` can be evaluated as ` a + (b + c) ` instead, but this does not
compute the same thing for floating-point values.

The correct answer can be obtained with the [ Kahan-Babuska-Neumaier (KBN)
](https://en.wikipedia.org/wiki/Kahan_summation_algorithm) summation algorithm
for computing sums (and cumulative sums). This comes at a speed difference of
about 20x, which is why none of the conventional implementations uses it.

Bottom line is, in my opinion, that Julia is serving a niche market. While the
paper states that Julia comes with a great mix of speed and usability, the
main problem is that it is still quite a task to reach C (C++ or Fortran
speed) in Julia. If you require real speed, firms will prefer C++ (at least in
my field, quant finance, C++ is the by far most frequently used language, with
some niche products like OCAML used by Lexifi or Bloomberg's DLIB, which focus
on complex derivs). Most users don't need that speed because the models are to
small, or the data is not big enough. E.g. an everyday Bloomberg user could
never download as much data (BBG has a limit on daily data usage) that it
really makes a noticeable difference, just like ~150 seconds (compared to 2 in
Julia) don't make a huge difference if you run a DSGE model because there is
no need to rerun it every 3 minutes or at even shorter periods.

That said, packages are really developing in Julia, and charting
functionalities and the DataFrames package are really well done. You can look
[ here ](https://quant.stackexchange.com/a/69780/54838) to see how little code
is needed to make some kinda decent interactive charts (dynamic option PnL
charts).

Also, since the release of 1.0, you don't usually face issues with breaking
code due to deprecation anymore. If everyday datasets grow, and computational
power becomes more important for casual programmers, Julia could very well
become a big player (subjective opinion).


Question:
Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

I am given 𝑈(𝑥,𝑦,𝑧)=𝑥23𝑦13+𝑧
. I am asked to solve the following:

(i) Prove the convexity of these preferences (convex, strictly convex or neither?)
(ii) Solve for the Walrasian Demand?

For part 1, I calculated the determinant of the bordered hessian matrix and got 32081∗1𝑥23𝑦43
. Here I concluded that if x and y are greater than zero (This was not given to me I assumed this), then determinant is greater than zero so 𝑈
 must be quasi-concave and hence preferences are convex. Is this correct?

For part 2, I considered three cases.

Case 1: when 𝑧=0
 and 𝑥,𝑦>0
. This was just the Walrasian for the standard Cobb Douglas we are left with.

Case 2: when 𝑥
 or 𝑦=0
 and 𝑧>0
. All wealth is spent on z as well.

Case 3: 𝑥,𝑦,𝑧>0
. This I was unable to compute and did not know how to proceed.

Note: Budget constraint is standard 𝑃1𝑋+𝑃2𝑌+𝑃3𝑍=𝑊

For Case 3: I set up Lagrangian and used Kuhn Tucker Conditions:

23
*(𝑦𝑥)13−𝜆𝑃1≤0
13
*(𝑥𝑦)23−𝜆𝑃2≤0
1−𝜆𝑃3≤0
𝑥[23
*(𝑦𝑥)13−𝜆𝑃1]=0
𝑦[13
*(𝑥𝑦)23−𝜆𝑃2]=0
𝑧[1−𝜆𝑃3]=0
𝑊−𝑃1𝑋−𝑃2𝑌−𝑃3𝑍≥0
𝜆[𝑊−𝑃1𝑋−𝑃2𝑌−𝑃3𝑍]=0
Imposing 𝑥,𝑦,𝑧>0
 and Walras's law, I know that I can equate 1, 2, 3, and 7 to zero. Essentially I end up with an equation which says that at optimal Marginal Utility to Price Ratio of each good is same.

After simplifying by equating 𝜆
, I get this from 1, 2:

𝑥𝑃2=2𝑦𝑃1
.
My problem is that I can't solve for 𝑧
 as I can't get my budget constraint all in terms of one variable.

Explanation: The part 1 looks correct. For part 2, recall that Walrasian demand is the solution to utility maximization subject to budget constraint. One important step is to derive the Kuhn-Tucker conditions. We may check its definition and example.

$\begingroup$

For part (i), in complete rigor, you should also check [ the determinants of
all the leading principal minors of the bordered Hessian and make sure that
they have alternating signs
](https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/qcc/t#d:borderedHessian)
. Your final conclusion looks correct though.

For part (ii), recall that Walrasian demand is the solution to utility
maximization subject to budget constraint. So you should setup a Lagrangian,
derive the [ Kuhn-Tucker conditions
](https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/ktc/t)
, and then solve for  $x,y,z$  as functions of the prices and income. These
will be the Walrasian demands.


Question:
Test which functional form that best explains data

Tried asking this on Math Stack Exchange. Got no answer after a week, so trying here.

I had this question in an exam lately and I was not sure how to answer it. Now the exam is done, and I can't go back, but it's been in my head ever since and I'm really curious about the answer.

Suppose you have a data set, with variables:

𝑎𝑔𝑒
: A persons age

𝑎𝑔𝑒2
: age to the power of 2

And dummy variables: 𝐷45=(𝑎𝑔𝑒=45)
, 𝐷46=(𝑎𝑔𝑒=46)
 ... 𝐷55=(𝑎𝑔𝑒=55)
 etc.

And suppose you have two models, where

𝑦=𝛽1𝑥1+𝛽2𝑎𝑔𝑒+𝛽3𝑎𝑔𝑒2
and
𝑦=𝛽1𝑥1+𝛽2𝐷45+𝛽3𝐷46...𝛽22𝐷65

How would you guys test which of the functional forms in the two models best explains the data?

I suppose we are to test 𝛽𝑖=0
 for both models. But I am not sure.

What would you guys have done in this situation?

Kind regards

Explanation: We can test for the fit of the models using something like a likelihood ratio test, i.e. the ratio indicates the expression/fitness of the model.

$\begingroup$

Notice that:  $$ y = \beta_1 x_1 + \beta_2 age + \beta_3 age^2 $$  is a more
restrictive model than:  $$ y = \delta_1 x_1 + \delta_2 D_{45} + \delta_3
D_{46} + \ldots $$  where you have a dummy for every age level.

To see this, take for example the case where age is  $a$  . Then the first
regression gives:  $$ y = \beta_1 x_1 + \beta_2 \times a + \beta_3 \times
(a)^2 $$  The second regression gives:  $$ y = \delta_1 x_1 + \delta_a. $$
where  $\delta_a$  is the coefficient of the dummy  $D_a$  .

So for  $\delta_1 = \beta_1$  and  $\delta_a = \beta_2 \times a + \beta_3
\times (a)^2$  the two are the same.

This means that the first regression is a special case of the second one where
we specify  $\delta_1 = \beta_1$  and  $\delta_a = \beta_2 a + \beta_3 a^2$  .

Given that the first regression is a restrictive version of the second one, in
principle, you could test for the fit of the first model versus the second
model using something like a likelihood ratio test [ wiki
](https://en.wikipedia.org/wiki/Likelihood-ratio_test) .


Question:
Why did Germany not suffer from Great Inflation in the 1970s/80s?

Comparing the inflation rate of some of the industrial countries around 1975 (Great Inflation) in between the two oil shocks of 1973 and 1979/80, it seems odd that most countries' inflation rate was very high at around 22%, whereas Germany does not seem to have suffered from such a high rate (at most 7% which is quite low compared to the others)

Why is that? Are there any reasons for that, f.ex. due to Germany leaving the Bretton Woods System in 1973? What are some reasonable explanations?

Explanation: This is related to the monetary policy conducted by Bundesbank.

$\begingroup$

There is actually a paper on this topic by [ Beyer et al (2009)
](https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp1020.pdf) titled ‘Opting out
of the great inflation: German monetary policy after the breakdown of Bretton
Woods’ that exactly addresses your question.

As the authors explain:

> During the turbulent 1970s and 1980s the Bundesbank established an
> outstanding reputation in the world of central banking. Germany achieved a
> high degree of domestic stability and provided safe haven for investors in
> times of turmoil in the international financial system… We derive an
> interest rate rule and show empirically that it approximates the way the
> Bundesbank conducted monetary policy over the period 1975-1998. We compare
> the Bundesbank's monetary policy rule with those of the FED and of the Bank
> of England. We find that the Bundesbank's policy reaction function was
> characterized by strong persistence of policy rates as well as a strong
> response to deviations of inflation from target and to the activity growth
> gap. In contrast, the response to the level of the output gap was not
> significant.

Basically, to sum up and bit oversimplify the paper, it was thanks to
Bundesbank’s masterful use of inflation expectation anchoring as well as
pursuing relativity tight monetary policy.

Moreover, Germany was viewed as a safe country for investors so it had capital
inflows that also helped.


Question:
Irreversibility in the Creation of Value

In his book The Origin of Wealth, Eric D. Beinhocker says that

A pattern of matter, energy, and/or information has economic value if the following three conditions are jointly met:

Irreversibility: All value-creating economic transformations and transactions are thermodynamically irreversible.
Entropy: All value-creating economic transformations and transactions reduce entropy locally within the economic system, while increasing entropy globally.
Fitness: All value-creating economic transformations and transactions produce artifacts and/or actions that are fit for human purposes.
These conditions seems pretty logical for me, particularly the "fitness" thing. However, I wonder about the "irreversibility" part: it sounds logical to state that, say, once a tree is transformed into a chair it cannot be turned into a tree again; so, making a chair is clearly irreversible. In the same vein, if a barber cut the hair of someone, he or she can not "uncut" it - irreversibility, of course.

But what if I was a doorman? My job would be to open a door for the others the whole day, which is a service that many people value to some extent, i.e., I would be creating some value in the economic sense of the term, right? But I can close the door as easily as I can open it, so it is something clearly reversible. Thus, it seems obvious I may do something "reversible" that is valued by someone - should I conclude Beinhocker is wrong or - I as suspect - I am missing something?

Explanation: This is about the understanding of Irreversibility. We need to check the concept of thermodynamic irreversibility.

$\begingroup$

The author talks about thermodynamic irreversibility. Thermodynamic
irreversibility exist any time that original conditions cannot be restored
without expenditure of energy. Opening and closing doors is thermodynamically
irreversible (eg see [ here
](https://en.m.wikipedia.org/wiki/Irreversible_process) ). Only actions where
there is no dissipation are thermodynamically reversible, as implied by the
laws of thermodynamics.

However, this being said Beinhocker uses extremely fringe definition of value.
In economics we do not typically define value in terms of thermodynamics.

In economics, the dominant theory of value is the subjective theory of value
that posits that things have value because individuals subjectively perceive
them to have value.


Question:
Why is there such a big difference of purchasing power toward Coca-Cola between Euro in France and USD in USA, comparing to Big-Mac?

I have an assignment that requires me to pick an item and use it to create my own price level index, similar to Big-Mac index.

In March 2021, the price of 0.5 litre Coca-Cola in France was 0.97 Euro and in the United States was 2.75 USD. Therefore, the “Coca-Cola exchange rate” was 2.84 USD per Euro. (Source: https://www.globalproductprices.com/France/coca_cola_price/)

However, in 2018 the price of Big-Mac in France was 4.2 Euro. Meanwhile, in the United States it costs only 5.65 dollars. This ratio is 1.35 USD per Euro, approximately half of the one derived from price of Coca-Cola. (Source: https://data.nasdaq.com/data/ECONOMIST/BIGMAC_FRA-big-mac-index-france, https://data.nasdaq.com/data/ECONOMIST/BIGMAC_USA-big-mac-index-united-states)

Explanation: Thie is likely to be related to the different taxation in the US and France. We can check the detailed data.

$\begingroup$

This could be for several reasons:

  1. this can be because coca-cola is tradable good whereas Big Mac is non-tradable. You would expect the law of one price to hold better for tradables than non-tradables. Even though the prices/wages in tradable sector affect those in non-tradable (e.g. Balassa-Samuelson effect), there is no good reason to assume the law of one price actually holds for non-tradables.

  2. Limitation of Big Mac or Coca-Cola etc indexes are that they also capture effect of local taxes, import duties, competition etc.

As far as data show the taxation in the US and France are not exactly same
(e.g. see [ OECD ](https://stats.oecd.org/Index.aspx?DataSetCode=CTS_ETR) and
[ USCIB ](https://www.uscib.org/value-added-tax-rates-vat-by-country/) ).

As pointed in the comments there are likely differences between level of
coopetition in US vs Fr retail, and fastfood.


Question:
What does chi p(q) mean?

It is a beginner question but I did not find a good explanation so I am asking here. Hope that I received the help from the community.

Today I run a joint null test individually like that

test (tau0=0) (tau1=0) (tau2=0)
And the result is

( 1)  tau0 = 0
 ( 2)  tau1 = 0
 ( 3)  tau2 = 0

           chi2(  3) =    1.12
         Prob > chi2 =    0.7717
I am wondering what does the numbers 2 and 3 in chi2(3) mean. I did a search from Wikipedia but I did not fully get it.

Explanation: This is related to chi-squared distribution with k degrees of freedom

$\begingroup$

This is most likely a [ $\chi^2$  distribution
](https://en.wikipedia.org/wiki/Chi-squared_distribution) with a degree of
freedom of 3. From Wikipedia:

> In probability theory and statistics, the chi-squared distribution [...]
> with k degrees of freedom is the distribution of a sum of the squares of k
> independent standard normal random variables.


Question:
How to compare investments with different risk and expected return?

Supposing I can choose to invest money in several different investments, each having

risk 𝜎𝑖
, for example, calculated as standard deviation
and expected return 𝑟𝑖
let's assume they have the same duration and same initial investment to keep things simpler
For example if 𝜎1=𝜎2
, I can easily choose the one for which 𝑟𝑖
 is greater. if for example 𝜎1=1.1𝜎2
 and 𝑟1=2𝑟2
, reasonably 𝑟1
 is better. From the above, I could decide to pick the investment for which 𝑟𝑖𝜎𝑖
 is greater. But this is just empirical and arbitrary. Is this method any good? Is there any more rigorous way of choosing between investments?

Explanation:
One approach is to approximate expected utility by a function
 of mean and variance

$\begingroup$

The trade-off between risk and expected returns depends on your own
preferences.

Assume that you are expected utility maximizer and let the return of the
investment be given by the random variable  $X$  . Your utility is given by.
$$ \mathbb{E}(u(X)) $$

Let  $\mu$  be the mean of  $X$  and let  $\sigma^2$  be the variance of  $X$
then taking a Taylor expansion of  $u(x)$  around  $u(\mu)$  gives:  $$ u(x)
\approx u(\mu) + u'(\mu)(x - \mu) + \frac{u''(\mu)}{2}(x - \mu)^2 $$  Taking
expectations on both sides gives:  $$ \begin{align*} \mathbb{E}(u(X)) &\approx
u(\mu) + u'(\mu)(\mu - \mu) + \frac{u''(\mu)}{2}\sigma^2,\\\ &= u(\mu) +
\frac{u''(\mu)}{2} \sigma^2.\\\ \end{align*} $$

So the higher the curvature of  $u$  (the more negative  $u''(\mu)$  ) the
more negative the second term will be. Intuitively, the curvature measures the
degree of aversion for uncertainty.

Remark that this approximation will only be good when  $X$  does not deviate
too much from the mean, so the Taylor expansion is good.

You can also take a Taylor approximation around zero. This gives:  $$
\begin{align*} u(x) \approx u(0) + u'(0) x + \frac{u''(0)}{2} x^2,\\\
\end{align*} $$  So:  $$ \mathbb{E}(u(X)) \approx u(0) + u'(0) \mu +
\frac{u''(0)}{2} (\sigma^2 + \mu^2) $$

See also the paper of [ Levy and Markowitz (1979), "Approximating Expected
Utility by a Function of Mean and Variance", American economic review, 69,
308-317 ](https://www.jstor.org/stable/1807366) .


Question:
IV regression: first stage in logs, second stage in levels?

I have a regression in levels, derived from theory.

I want to instrument one of the variables, but the best instrument I find has a weak correlation to the endogenous variable in levels, and a strong correlation in logs. Both are very heteroskedastic.

Is it possible to somehow instrument with the first stage in logs, and the second stage in levels?

Explanation: This is called forbidden regression. We need to check calculation and results there.

$\begingroup$

What you are describing is the so called " _forbidden regression_ ", which (in
general) does not give consistent estimates. This is a summary of the [ notes
of Ben Williams
](https://benjamindwilliams.weebly.com/uploads/6/8/5/7/68575765/notesonforbiddenregressions.pdf)

Consider a (nonlinear) first stage regression of  $X$  on the instruments  $Z$
giving fitted values (e.g. using a log-log specification):  $$ \hat X = \hat
\mu(Z) $$  Consider the structural (causal) equation:  $$ Y = X'\beta + u $$
What you propose is to use  $\hat X : \hat \mu(Z)$  instead of  $X$  in the
second stage. This gives:  $$ \begin{align*} \hat \beta &= (\hat X' \hat
X)^{-1} \hat X Y,\\\ &= (\hat X' \hat X)^{-1} \hat X (X' \beta + u),\\\ &=
(\hat X' \hat X)^{-1} \hat X (\hat X' \beta) + (\hat X' \hat X)' \hat X'(X -
\hat X)'\beta + (\hat X' \hat X)^{-1}\hat X u,\\\ &= \beta + \underbrace{(\hat
X' \hat X)' \hat X'(X - \hat X)'\beta}_A + \underbrace{(\hat X' \hat
X)^{-1}\hat X u}_B, \end{align*} $$  If  $Z$  is a valid instrument, on can
expect that the  $B$  vanishes as  $\hat X = \hat \mu(Z)$  and by assumption
$\mathbb{E}(u|Z) = 0$  .

Now the  $A$  terms is the real problem. Notice that we can always write:  $$
X = \mathbb{E}(X|Z) + \eta,\\\ \text{ with } \mathbb{E}(\eta|Z) = 0 $$  (here
$\eta$  is simply  $X - \mathbb{E}(X|Z)$  ).

Then taking the middle part of the  $A$  term gives:  $$ \hat X'(X - \hat X) =
\hat X'(\mathbb{E}(X|Z) - \hat X) + \hat X'\eta,\\\ $$  The last term should
vanish as  $\mathbb{E}(\eta|Z) = 0$  . The first term however, will (in
general) only vanish if  $\hat X = \hat \mu(Z)$  is consistent for
$\mathbb{E}(X|Z)$  , which will be the case if  $\mu(Z)$  is a correct
specification of  $\mathbb{E}(X|Z)$  .

The usual 2SLS however is consistent as in this case:  $$ \hat X =
Z(Z'Z)^{-1}Z'X. $$  Then:  $$ \begin{align*} \hat X'(X - \hat X) &=
X'Z(Z'Z)^{-1}Z'(X - Z(Z'Z)^{-1}Z'X),\\\ &= X'Z(Z'Z)^{-1}Z'X -
X'Z(Z'Z)^{-1}Z'Z(Z'Z)^{-1}Z'X,\\\ &= X'Z(Z'Z)^{-1}Z'X - X'Z(Z'Z)^{-1}Z'X = 0
\end{align*} $$  So either you do normal 2SLS, which will be consistent if
$Z$  is uncorrelated with  $u$  or you can use what is called indirect least
squares.

  1. Regress  $X$  on  $Z$  using a nonlinear regression (e.g. loglinear regression).

  2. Use the fitted values  $\hat X = \hat \mu(Z)$  as instruments themselves in a 2SLS of  $Y$  on  $X$  . So run 2SLS with instruments  $\hat X = \hat \mu(Z)$  instead of  $Z$  . As  $\mu(Z)$  is a function of  $Z$  , we also have that  $\mathbb{E}(u|\mu(Z)) = 0$  , so these should be valid instruments.


Question:
How could you partition Household Food Expenditures into Producing Industries?

From the 2019 Consumer Expenditure Survey, the average household annual food expenditure was $8,169 for that year. There are subcategories such as "Food at Home" and "Food away from Home," but for simplicity, I'll keep the scope to annual household food expenditures.

I want to partition this $8,169 into the BEA industries (aggregation level is "summary") for the ultimate goal of assessing pollution impact. That is, if buying bread is related to a farm purchasing harvesting equipment, maybe some of those dollars should be allocated towards both farms and industrial machinery.

Here are a few immediately relevant BEA industry summaries:

111CA: Farms
113FF: Forestry, Fishing & Related activity (the fish is sold to markets?)
311FT: Food and Beverage & tobacco
445: Food and Beverage Stores
722: Food services and Drinking places
In my studies of the Leontief Input/Output model, one thought is just to pile all $8,169 into 311FT and let the "recipe" tell me how much that 111CA contributed, but that feels contradictory since it predicts 0 final demand at the household level for 111CA, when clearly that industry has a large GDP number.

So what is the best way to "attribute" the household expenditures on food into those industries?

Explanation: You should try to avoid mixing data sets unless you have a good way to bridge them. There are very precise methodologies used to construct each data set and mixing them can lead to nonobvious problems. You might consider looking at the BEA's IO tables at a more disaggregated level.

$\begingroup$

You should try to avoid mixing data sets unless you have a good way to bridge
them. There are very precise methodologies used to construct each data set and
mixing them can lead to nonobvious problems. You might consider looking at the
[ BEA's IO tables at a more disaggregated level
](https://www.bea.gov/industry/input-output-accounts-data) . For example, the
Use table shows Personal Consumption Expenditures at a granularity that you
might be interested in. For example, in the screenshot below it shows that in
2012, households consumed \$32 billion worth of goods from the "Vegetable and
melon farming" product category.

[ ![enter image description here](https://i.sstatic.net/ttNDd.png)
](https://i.sstatic.net/ttNDd.png)

At this level of disaggregation, you can see how much households purchased
from different kinds of product categories: restaurant goods, from frozen
foods, from snack food manufacturing, etc. You can also see how much each of
these industries purchased from each other product type category, etc.
Continuing with the example, you'll see that the Vegetable and melon farming
industry purchased \$106 billion worth of goods from "Farm machinery and
equipment manufacturing" product category.

[ ![enter image description here](https://i.sstatic.net/IeMqW.png)
](https://i.sstatic.net/IeMqW.png)

Note that I haven't stated that the Vegetable and melon farming industry
necessarily produces goods in the Vegetable and melon farming product
category. To get that information, you would have to explore the [ BEA supply
tables. ](https://www.bea.gov/industry/input-output-accounts-data) For those
interested, more information is in the answer to this other question: [
https://economics.stackexchange.com/a/47689/59
](https://economics.stackexchange.com/a/47689/59)

Hope this helps.

The link to the spreadsheet from the BEA is given here: [
https://apps.bea.gov/industry/xls/io-
annual/Use_SUT_Framework_2007_2012_DET.xlsx
](https://apps.bea.gov/industry/xls/io-
annual/Use_SUT_Framework_2007_2012_DET.xlsx)


Question:
Why is having a big corporation keep its money in foreign countries a bad thing in the public's eye?

I have been trying to dig deeper into corporate tax evasion, and how it works, to really determine if they're doing something bad or what. I don't know much about economics or politics, but I hear people all the time saying "tax the corporations! they are finding loopholes not to pay taxes and that is bad!" I don't understand why, and want to know what is going on and why people think it's bad.

For example, I read this:

The law installed a "territorial" system in which global corporations aren't taxed on foreign profit. The TCJA encourages them to reinvest it in the U.S. This benefits pharmaceutical and high-tech companies the most.3

Multinationals were taxed on foreign income earned under the prior "worldwide" system. They didn't pay tax until they brought the profits home. As a result, many corporations reinvested profits earned overseas into those markets. It was cheaper for them to borrow at low interest rates in the U.S. than to bring earnings home. As a result, corporations became debt-heavy in the U.S. and cash-rich in overseas operations.

Basically, if you go to the Cayman Islands and pay a low tax rate, somehow money you make there (I don't know how you "make money" in these foreign places if your real business is elsewhere), and you don't "bring it home" to the U.S.. Instead you leave it there and reinvest (into what, I don't know). This in theory means you can make money (somehow) and pay lower taxes on it (in the tax haven).

Can you explain how this works and why it is considered bad by some people on the left specifically? Why would they borrow money in the US and have cash in another country? How much money is a large corporation even borrowing? Basically, how does this work, what is an example?

Explanation: It is related to transfer pricing, where profit centers are set up to maximize firm profits.

$\begingroup$

Firms can always shift their profits from one tax territory to another via
various methods.

Consider a simplistic example, let’s say we have firm ABC that has most of its
business in Sweden. The owners of ABC can set up another parent company, let’s
say ABC global in some tax haven like Luxembourg. Afterwards they can transfer
some intellectual property (or other difficult to value assets - typically
some intangibles) to the ABC global.

Then when ABC Sweden manages to have to have let’s say 100,000€ profit, the
Luxembourg based ABC global will decide to lease the intellectual property (eg
logo) to ABC Sweden for 100,000€. This extra cost will cause ABC Sweden to
have zero profit in Sweden while now ABC global in Luxembourg gets 100,000€
profit that now will be taxed there at the their very low corporate taxes.

The above is just an oversimplified example of course, the methods how this is
done are always evolving as government regulators always play cat and mouse
game with corporations. If you want to know more details you can have look at
topics such as transfer pricing (see [ Alles,& Datar, 1998
](https://www.jstor.org/stable/2350664) or [ Hirshleifer, 1956
](https://www.researchgate.net/profile/Srikant-
Datar/publication/227447111_Strategic_Transfer_Pricing/links/09e41510fb40bca7f8000000/Strategic-
Transfer-Pricing.pdf) ).

Alternatively, and this what is directly referenced in that article, the
parent company even can be located in the US, and just let it’s foreign
daughter companies to reinvest profits they earn in each individual foreign
market (eg use that profit to buy new building, invest in R&D etc, or to build
a war chest). This still makes sense for the company, as A) doing so still
makes company more valuable and thus increases shareholder value, B) if they
build a war chest they can always bring that money home at some unspecified
future if US decides to lower its taxes (like the [ Trump tax cuts
](https://www.google.nl/amp/s/www.cnbc.com/amp/2019/03/27/us-companies-bring-
home-665-billion-in-overseas-cash-last-year.html) ).

Again the above is only very rough sketch of how this is done, the details
always evolve following current tax regulations that are changing virtually
every year in some small or bigger way around the world.

> Can you explain how this works and why it is considered bad by some people
> on the left specifically?

This is not an economics question but moral question, so you would do better
to ask this on philosophy stack exchange. This being said in short, answer
whether the above is bad or ok depends on your moral framework. On a
fundamental level this is not much different from ordinary people also trying
to optimize their tax rates by taking advantage of various loopholes (eg
people trying to claim as many deductions as possible or people avoiding VAT
by having friend with a business buy them the product for them - since
business get VAT rebates). So if you adopt some deontological (rules/action
based) ethics, which says trying to minimize your tax rate (within legal
bounds) is acceptable, then the (legal)corporate tax optimization should also
not be a moral issue.

However, the ideology of modern (liberal) left is underlined by Rawlsian moral
framework (or at least in literature that’s the basis for it, I doubt that
most people on either left or right know any moral philosophers) which is
governed by consequentialist Max-Min principle (although Rawls full framework
has [ non-consequentialist elements
](https://faculty.washington.edu/wtalbott/phil410/trrawls.htm) so technically
it is a hybrid moral framework for economics the Max-Min rule is the most
relevant part). Under this ethical system actions are good if they help to
maximize welfare for the poorest members of society. So under the Max-Min
principle it’s consequences that matter not rules. Taking advantage of tax
loopholes is fine if you are poor, but if you are rich corporation it is bad
as resources from those taxes could be redistributed to the poor (assuming
that the parameters of economy are such that this would still increase the
welfare of poor eg we are not already at the point where taxes are so high
that extra taxes cause so much distortions to the economy that it lowers
welfare of poor more than they gain from extra redistribution).


Question:
Filling gap in data with correlated series

I have two time series, of different length. A time series is GDP growth.

The gdp growth is the series I need, and it is also the longer series, but it has two gaps in two periods one after the other. The aggregate economic indicator is shorter, but it covers the period where I find the two gaps, and for the period in which both data are available, they are strictly correlated (r=0.94).

How could I fill these two gaps?

One possibility would be to use the autoregressive forecast. AR(1) describes quite well the series R²=0.91, and no significant autocorrelation in the residuals. But I do not think it is the optimal solution, because:

I have two gaps, the second gap will be filled with the two step ahead forecast, which is less precise,
I have data AFTER the point, and neglecting part of the information does not seem to be the best solution,
I have also some external information (the correlated series), which I could also exploit.
Which method would be the most appropriate?

Thanks for the tips!

Explanation: One possible approach is Catmull–Rom spline, where original set of points also make up the spline curve.

$\begingroup$

If I understood correctly the gap is in the middle of the data. In such cases
you should not use forecasts that extrapolate the data, but some interpolation
method.

If there is relatively large amount of variation in the data you would have
best results using something like [ Catmull–Rom spline
](https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Catmull%E2%80%93Rom_spline)
. Catmull–Rom spline has some nice properties (see [ here
](https://splines.readthedocs.io/en/latest/euclidean/catmull-rom-
properties.html) ). The main advantage of the Catmull-Rom spline is that all
real observations you have will become part of it and it allows you to
estimate missing points in non-linear way.

If you work in R you can easily implement it with [ splineCR
](https://rdrr.io/github/jedalong/PathInterpolatR/man/splineCR.html) , if you
work with Python you can have look at [ this github
](https://github.com/vmichals/python-algos/blob/master/catmull_rom_spline.py)
code. Nowadays you will find it also part of programs such as EViews or Stata.


Question:
Why isn't economic growth defined in terms of the increase in national wealth?

Economic growth is defined as the increase in production or output per unit time. Why isn't it instead defined in terms of the increase in national wealth?

Explanation: We need to figure out the definition of economy and wealth, and check whether they match.

$\begingroup$

Because the word _economic_ in economic growth refers to growth of economic
activity. By common definition (see [ Eurostat
](https://ec.europa.eu/eurostat/statistics-
explained/index.php?title=Glossary:Economic_activity) )

> An economic activity takes place when resources such as capital goods,
> labour, manufacturing techniques or intermediary products are combined to
> produce specific goods or services. Thus, an economic activity is
> characterised by an input of resources, a production process and an output
> of products (goods or services).

Wealth is an _accumulated_ difference between production and consumption over
time, since any production not consumed will eventually become part of wealth
(typically measured in terms of net assets).

Thus wealth is not in itself economic activity, as defined above, but rather
an accumulation of the output from the economic activity that society did not
decided to consume.


Question:
Are there any behavioral macro models with rigorous micro-foundations?

I am looking for some paper that tries to establish rigorous micro-foundations the behavioral New Keynesian (or any other) macro models.

This is surprisingly hard, most work on this topic (like De Grauwe 2012), simply starts already by setting up IS and LM curves and adding some sort of mix of rational and behavioral agents (mostly agents with non-rational expectations) on top of it. However, I can't find any paper that would provide full rigorous micro-foundations for such model (i.e. deriving IS and LM from the micro behavior of these rational and behavioral agents across time).

This is of course difficult, as without the rational expectations it is difficult to solve macro models, but on other hand it is hard to believe this issue would be ignored by the practitioners.

Consequently, my question is: are there any papers that establish rigorous micro-foundations for behavioral macro models?

Explanation:
The macro-models can be related to monetary and
fiscal policy. We need to find some micro-foundations.

$\begingroup$

[ Gabaix, X. (2020). A behavioral New Keynesian model. American Economic
Review, 110(8), 2271-2327.
](https://scholar.harvard.edu/files/xgabaix/files/behavioral_new_keynesian_model.pdf)
has microfoundation. And Gabaix has more papers that might interest you..


Question:
Is there any example for "pluralistic ignorance" in economics?

Today I read a paper recently written by Bursztyn, 2021 saying that

The origin, persistence, and rigidity of misperceptions about others can in principle be explained by different conceptual frameworks, such as stereotyping (e.g., Bordalo et al. 2016), motivated reasoning (e.g., Benabou and Tirole 2016), and pluralistic ignorance (e.g., Kuran 1997; Bursztyn, Egorov and Fiorin 2020; Bursztyn, Gonz´alez and Yanagizawa-Drott 2020)

From what I understand, pluralistic ignorance is

the situation in which almost all members of a group privately reject group norms, yet believe that virtually all other group members accept them

However, I still not yet got the idea of this behaviour, could you give me an example in economic or finance to understand it more?

Update: Adding a great explaination of "pluralistic ignorance" as suggested by @Lason

The term “pluralistic ignorance” was coined to describe the situation in which almost all members of a group privately reject group norms, yet believe that virtually all other group members accept them (Katz and Allport, 1931). Under such situations, individuals predict that they would lose social standing if they behaved as they wished. Behaving against the group norm could result in negative reactions from other ingroup members. Therefore, people are likely to follow perceived group norms to maintain positive impressions in their groups, even when they do not support the norms (Miller and McFarland, 1987; Miller and Prentice, 1994; Prentice and Miller, 1996; Geiger and Swim, 2016). In line with this idea, in situations of pluralistic ignorance, some people even actively enforce the perceived norms (i.e., publicly criticizing a “misfit” into accepting the norm), although they privately disapprove of the norms (Willer et al., 2009). Consequently, public behaviors of groups as a whole do not coincide with the majority of group members' private preferences under circumstances of pluralistic ignorance. Thus, the situation of pluralistic ignorance is well represented in the following sentence: “No one believes, but everyone believes that everyone else believes” (Krech and Crutchfield, 1948).

Explanation: This can be related to the perceptions/beliefs about the public of the Beliefs of the Public.

$\begingroup$

Pluralistic ignorance is a theory explaining why social practices continue to
be perpetuated when almost no individual seems to support them. When
pluralistic ignorance is at play, agents act in the way they envision others
want them to act, so as not to lose their social standing by acting as they
wished.

Some examples in the indirect economic world include: [ Heavy drinking in
college
](https://www.sciencedirect.com/science/article/abs/pii/S0065260108602385?via%3Dihub)
, [ Racial segregation perceptions ](https://academic.oup.com/poq/article-
abstract/40/4/427/1872200?redirectedFrom=fulltext) , and [ many others (see
references)
](https://www.frontiersin.org/articles/10.3389/fpsyg.2017.01508/full) .

I have not found or studied any example in finance, but I would argue that the
same logic applies and any experienced stockbroker or individual investor
would experience the negative effects of pluralistic ignorance; for example
each investor might not like a particular asset, but for reasons of their own,
they might think that everyone else _loves_ this asset, and thus is willing to
buy it or hold on to it. The outcome of this process is for the price of an
unlikeable asset to rise - conforming to the norm that each individual
unwillingly propagated.


Question:
Economic growth in a DSGE model, despite mean-zero shocks

The DSGEs I've seen have steady-states, and mean-zero shocks.

Can these predict growth in GDP / capital etc?

Is this possible despite them being equilibrium models, or do you have to completely change your approach and switch to a Solow-Swan-type model to predict GDP growth?

Explanation: These models typically have a particular kind of steady-state, which is, more precisely, called balanced growth path, where key indicators growth at the same constant rate.

$\begingroup$

**Yes, there are DSGE models that can be used for forecasting.**

These models typically have a particular kind of steady-state, which is, more
precisely, called _balanced growth path_ [ (BGP)
](https://en.wikipedia.org/wiki/Balanced-growth_equilibrium) . On the BGP (in
the absence of shocks), key indicators growth at the same constant rate. For
example, GDP, household consumption, investment all grow at 2% a year. This is
consistent with constant steady-state ratios of the indicators over GDP, for
example  $\frac{K}{Y}$  and  $\frac{C}{Y}$  would be constant, while
indicators grow at the same rate.

The rate itself is often built in as an assumption, based on economic priors
and analysis done outside of the DSGE model (for example estimates of labor-
productivity growth). Because of this fact, forecast of equilibrium growths
are not just boring, but not really forecasts. However, an economy is hardly
ever on its balanced growth path, so the strength of these models is in
describing the dynamics back towards equilibrium, for example after a shock to
global oil prices. Immediately after the shock hits, investment will typically
fall at a faster rate than GDP, and then grow faster after the impact has
bottomed out.

Note that these models need to be related to actual data via estimation, often
using the Kalman Filter to identify unobservable variables, such as the output
gap, and shocks (such as a technology shock).

To see how data can be related to model variables, consider the measurement
equation (assuming the use of a Kalman filter).  $Y$  is actual GDP in
quarterly frequency,  $\hat{y_t}$  is the deviation of output from its trend
level at time  $t$  , and 2% is the assumed annual growth rate. Then this can
be fed into the model as  $$ \log Y_t - \log Y_{t-1} - 0.005 = \hat{y}_t -
\hat{y}_{t-1} $$  This means in particular that the model solution can be
translated back into numbers that are consistent with actual data and hence
_can be used for forecasting_ .

_References:_ For an overall good and detailed example, see the [ ECB's New
Area Wide Model ](https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp944.pdf) . It
includes a section on model dynamics (4), and one on how assumptions are built
into the model (3.2 & 3.3). The references in that paper are also worth
checking out. For an even more modern version, see their new [ model
](https://www.ecb.europa.eu/pub/pdf/scpwps/ecb.wp2200.en.pdf) , which includes
many more financial market dynamics.


Question:
Do governments have to pay interest on government debt held by the central bank?

Through open market operations, the central bank may buy government debt to increase the money supply. Does the government need to pay interest on the debt held by the central bank, or does the debt become interest-free?

Explanation: We can check typical examples, e.g., whether federal reserve receives interest income from open market operations.

$\begingroup$

Yes, the government has to pay interest on debt even if it is held by the
central bank. That is true at least for major modern central banks.

For example, from a press [ release
](https://www.federalreserve.gov/newsevents/pressreleases/other20210111a.htm)
from the US Federal Reserve Board:

> Net income for 2020 was derived primarily from $100 billion in interest
> income on securities acquired through open market operations...

However, although modern central banks are in their decision making
independent from the government, they are still public entities (or equivalent
to such), and profits (if there are any) will ultimately be transferred back
to the government. So, to the extent that profits are due to the holding of
government debt, the government will get a rebate on interest paid.


Question:
Large National Debt by borrowing money from foreign sources

I have a question about the greater severity of large national debt caused by borrowing from foreign sources.

I am reading a book about elementary Economics and am currently on a chapter discussing the strengths and weaknesses of demand-side policies.

The book (A-level Economics, Anderton, 2015, pp. 204) states the following:

Keynesian economics states that so long as a government can print money to finance its deficit without fueling inflation or borrow money from the financial markets, then the National Debt is not a problem for the short term. Nearly all economists, however, would argue that, in the long term, large National Debts can be a problem particularly if they are financed mainly by borrowing money from foreigners.

However, I am struggling to understand how they can be worse than borrowing from domestic debt markets (if I have stated the correct market i.e. from a domestic lender).

My understanding was that if the debt was financed through printing more money, and had to pay off the loans to a foreign lender, it would find it harder to reduce the supply of money via reversing quantitative easing i.e. selling bonds back into the bond market, so impending inflation in the long term would occur.

However, the book does not qualify its statement regading large National Debt as above so I am not sure what the justification is for Anderton's statement above.

Why would large National Debts financed by foreign lenders be a greater problem than domestic lenders if the problem was to be solved by printing more money?

Explanation: The central question is to ask for a comparison between domestic and foreign debt.

$\begingroup$

The statement should be ideally subjected to several caveats because there is
a lot of heterogeneity between how difficult it is to manage external debt
among nations (e.g. developed vs developing nations, country in monetary union
vs country outside monetary union etc), but generally it is argued that:

  1. Foreign debt is usually (but not always) also denominated in foreign currency. In the past sometimes people even used words 'foreign debt' and 'debt denominated in foreign currency' interchangeably ( [ Vasishtha, 2007 ](https://www.bankofcanada.ca/wp-content/uploads/2010/02/wp07-33.pdf) ) even though that of course is not accurate as you can have foreign debt denominated in domestic currency, and domestic debt denominated in foreign currency. Still just the fact that some scholars sometimes slipped and used the terms interchangeably indicates that often foreign owned debt is denominated in foreign currency. Such debt is more difficult to manage because it can't be easily monetized.

  2. Foreign and domestics creditors are different, for many countries, foreign investors will be large international hedge funds or other governments or international organizations like IMF, whereas domestic creditors are typically domestic firms or individuals. It is easier for large international organization to try to sue government, or to do reputational damage to the government which will make its future borrowing costs higher ( [ Vasishtha, 2007 ](https://www.bankofcanada.ca/wp-content/uploads/2010/02/wp07-33.pdf) ).

On the other hand, domestic creditors are at the mercy of the government.
Since from creditor's perspective the government debt is an asset, government
can always decide to raise taxes on the income domestic creditors earn from
these assets (thereby recouping portion or all interest paid on the domestic
debt), or levy some wealth tax that will in effect force domestic creditors to
in effect hand portion of their assets (and debt is an asset for creditor) to
the government. To be fair in principle there are ways how domestic government
can tax foreign entities as well but it's much more difficult (see discussion
of that in [ Gros 2011 ](https://voxeu.org/article/external-versus-domestic-
debt-euro-crisis) ).


Question:
Krugman article - Government debt helps avoid a destructive scramble for cash?

I was just reading this Krugman article which contains the words...

I’ve already mentioned that having at least some government debt outstanding helps the economy function better. How so? The answer, according to MIT’s Ricardo Caballero and others, is that the debt of stable, reliable governments provides “safe assets” that help investors manage risks, make transactions easier and avoid a destructive scramble for cash.

Now the "help investors manage risks" part I can understand, but "make transactions easier" and "avoid a destructive scramble for cash" are a mystery to me.

Explanation: This is related to the fact that government debt has positive impact on market liquidit. We need to find related literature to support this.

$\begingroup$

This is because there is strand of literature that suggests government debt
has positive impact on market liquidity (eg see [ Grobety 2018
](https://www.sciencedirect.com/science/article/pii/S0261560618300470?casa_token=fD0WcDXUE7QAAAAA:oG-
tMAWmua78NAZSGRn3wJmxl4HHlFPWAak1YFpptrA_BG4wqwNBY-RB-Ypvbsn0k7q_uaoWWg) ).
When Krugman talks about scramble for cash he likely refers to lack of
liquidity which is clearly bad for business. Also more liquidity makes
transactions easier because it’s easier to find buyer for your asset.

However, I think Krugman is a bit prone to over-dramatization, and while there
is some good empirical work supporting the result, it is not completely beyond
critique.


Question:
Is "avoiding being the bearer of bad news" an example of the "principal-agent problem"?

For example:

A king designs a bridge, and he unknowingly does a bad job. He asks an engineer for her opinion, but the engineer fears that if she tells the truth, the dictator will be angry with her.

More generally, I'm thinking of situations in which the principal requests feedback/information from the agent, but fear of retribution prevents the latter from being honest.

It seems like a reasonable example of the principal-agent problem, with conflicting incentives, but I wasn't sure if this situation had its own name.

Explanation: We need to check the definition of principal-agent problem and see whether this example satisfies.

$\begingroup$

I think it is. [ Intelligent economist
](https://www.intelligenteconomist.com/principal-agent-problem/) site states:

> The Principal Agent Problem occurs when one person (the agent) is allowed to
> make decisions on behalf of another person (the principal). In this
> situation, there are issues of moral hazard and conflicts of interest.

> The agent usually has more information than the principal. This difference
> in knowledge is known as asymmetric information. The consequence is that the
> principal does not know how the agent will act. Also, the principal cannot
> always ensure that the agent acts in the principal’s best interests. This
> departure from the principal’s interest in the agent’s interest is called an
> “agency cost.”

  * In the example you mention the agent can make decision on behalf of principal (approve or reject design).

  * Agent has more information than principal.

  * Interest of agent and principal are not aligned. Principal wants honest answer, agent wants to keep her head. So there is conflict of interest.

If it has all features of principal agent problem I think it qualifies.


Question:
The geometry of cities (reference request)

I am interested in reading up on the geometry of cities: what explains their ‘shape’ (e.g. why is the population often distributed in a rough circle)? I imagine that this is a question with some literature. Does anyone know of the classic papers? Textbook recommendations also appreciated!

P.S. While I would be happy to read about empirical work on this, I am mainly interested in the topic from the theory side.

Explanation: This is related to the economics of space and time.

$\begingroup$

If you want a highbrow mathematical economics take on the topic, you can take
a look at the 1977 book "The Economics of Space and Time" by Arnold M. Faden.
You can find a review of the book by Hal Varian [ here
](https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-
society-new-series/volume-1/issue-2/Review--Arnold-M-Faden-The-economics-of-
space-and/bams/1183544087.full) .


Question:
Was there any currency backed by other metals than gold, silver or copper?

Was any other metal than gold, silver or copper ever in history used to back a currency?

Explanation: Other types of metal can include bronze, e.g., the coin once used in central Italy.

$\begingroup$

[ Spartan iron coins
](https://www.jstor.org/stable/1086107?seq=1#metadata_info_tab_contents) .

Roman bronze coins: [ Aes Grave ](https://en.wikipedia.org/wiki/Aes_grave)

Chinese bronze coins: [ Ban liang
](https://en.wikipedia.org/wiki/Ancient_Chinese_coinage#Ban_Liang_coins) (one
type was bronze, not all)

A non-metal "currency" backed by various industrial metals: the cryptocurrency
[ Tiberius coin ](http://www.cda.org.uk/2019/10/tiberius-cryptocurrency-
backed-by-metals/) .


Question:
Non CES Production Functions
I know CES production functions dominate economics, but I was curious, why? I've never seen a research paper or presentation utilize any form of a production function that is not CES.

why is imposing CES so important in our models?

Explanation: It is helpful to assess the intrinsic links between production and factor substitution, e.g., CES functions

$\begingroup$

> (1) why is imposing CES so important in our models?

Because although its relatively quite general (relatively to some other widely
used production functions like Cobb-Douglas - which is a special case of CES)
it is still easy to estimate with parametric models and generally CES
production functions are easy to work with ( [ McFadden 1963
](https://academic.oup.com/restud/article-
abstract/30/2/73/1517685?redirectedFrom=fulltext) ).

Until very recently you need Cobb-Douglas, or some CES, with its unitary
elasticity of substitution due to the normalization problem which precluded
people from applying even more general form. For example, as discussed in [
Klump et al (2011) ](https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp1294.pdf)
[emphasis mine]:

> Until recently, the application of production functions with non-unitary
> substitution elasticities (i.e., non Cobb Douglas) was hampered by empirical
> and theoretical uncertainties. As has recently been revealed,
> “normalization” of production functions and production-technology systems
> holds out the promise of resolving many of those uncertainties and allowing
> considerations as the role of the substitution elasticity and biased
> technical change to play a deeper role in growth and business-cycle
> analysis. Normalization essentially implies representing the production
> function in consistent indexed number form. **Without normalization, it can
> be shown that the production function parameters have no economic
> interpretation since they are dependent on the normalization point and the
> elasticity of substitution itself** . This feature significantly undermines
> estimation and comparative-static exercises, among other things.

The above issue leads to bias in estimation (especially in parametric models)
so its quite a serious issue. This is because, we can only use observable data
for estimation but capital and labor are measured in completely different
units (aside from the problem that we actually have no way of accurately
measuring capital in the first place). CES or Cobb-Douglass with unitary fixed
elasticity gets around the issue by the virtue of elasticity of substitution
being 1, and because the differences in units get absorbed into the scaling
constant.

But what even more, as the above cited paper discussed, the problem of
normalization was essentially solved for CES even with non-unitary
elasticities making it even so more desirable function to use. This is quite
important since empirically elasticity of substitution is generally below
unity (e.g. have a look at [ Chirinko et al. 1999
](https://www.sciencedirect.com/science/article/abs/pii/S0047272799000249?casa_token=2-aYd3UIB1oAAAAA:S_dVDrAU0IptuS1-HZRgyVQ2ila5vbSTiw5ZTF_erpUFvZol2xmJdY9Qvmt-
q_mXxQzXdp74r5Q) , [ Klump et al. 2007 ](https://direct.mit.edu/rest/article-
abstract/89/1/183/57638/Factor-Substitution-and-Factor-Augmenting) , [ Leon-
Ledesma et al. 2010
](https://www.aeaweb.org/articles?id=10.1257/aer.100.4.1330) ).

Lastly, estimation of production functions is riddled beyond belief with
endogeneity issues. One way how to solve the endogeneity issues is to look to
theory for guidance of how to set up model (especially how to properly specify
the error term) to avoid these issues (e.g. see the work of [ Olley Pakes 1996
](https://web.archive.org/web/20211112161908/https://www.jstor.org/stable/2171831?seq=1#page_scan_tab_contents)
, [ Levinsohn-Petrin 2000 ](https://www.nber.org/papers/w7819) or [ Ackerberg,
Caves and Frazer 2015
](https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA13408?casa_token=YITxPu4O2wIAAAAA:_unIEQBPoYb8iN9nOKznktKIty_F4MYARvYO2UkwTKD93PSMR3jUOWt6PQqOreVP4MYenrWaUP4F
--o) ). But lot of these theoretical results are derived assuming CES
production function, so you can't just use theoretical result derived assuming
CES production to model the structure of the error term and nothing else.

>   2. are there any serious papers or methods that allow for a non-CES
> production function?
>

Well yes, there are a lot of papers that apply translog production function
which allows elasticity of substitution to change ( [ Heathfield, Wibe 1987
](https://link.springer.com/chapter/10.1007/978-1-349-18721-8_6) ). If you
just put [ translog production function estimation into google scholar
](https://scholar.google.com/scholar?hl=en&as_sdt=0,5&q=translog%20production%20function%20estimation)
you will get a lot of examples.

However, estimating translog production function parametrically can be
problematic because relative to CES or Cobb-Douglass you have to estimate
quite a lot of parameters to make it work. Especially if you want to include a
lot of factors of production the number of parameters virtually explodes
(Pavelescu, 2011), and this is a problem given the tendency of including more
and more factors in recent years (e.g. materials, different types of capital
and so on).


Question:
What is the "moderator for the relationship" in interactive regression model?

I have an interactive regresison model as below:

𝑌𝑖,𝑡=𝛽0+𝛽1
𝐷𝑖
 + 𝛽2
𝑃𝑖,𝑡
 + 𝛽3
(𝐷𝑖
𝑃𝑖,𝑡
) + other covariates + error terms

In this model, why 𝐷𝑖
 is called as the moderator for the relationship between 𝑃𝑖,𝑡
 and 𝑌𝑖,𝑡

Explanation: We need to check the definition of the moderating variable.

$\begingroup$

Because [ moderator variables ](https://www.statisticshowto.com/moderating-
variable/) are by definition variables that affect the strength of the
relationship between one variable and another variable, and that is exactly
what interaction effect does (it allows  $P$  to have different effect
depending on whether  $D=1$  or  $D=0$  ).

This is actually not terminology used widely in economics, but it is used
widely in [ psychology ](https://www.psychologyinaction.org/psychology-in-
action-1/2015/02/06/mediating-and-moderating-variables-explained) and some
other fields (although I seen it used in few behavioral economics papers). In
economics, outside few specific subfields people usually call it interaction
term.


Question:
Did Capitalism and Adam Smith Support a Central Bank?

Does Adam Smith and Capitalism support a Central Bank/Federal Reserve?

I am trying to read through the book "Wealth of Nations" to understand. Having a central/regulatory figure dictate supply and interest rates, seems less laissez faire. However curious if Adam Smith has any documentation on this subject.

Explanation: We can check his opinions about the role state/government in banking.

$\begingroup$

> Does Adam Smith ... support a Central Bank/Federal Reserve?

Adam Smith was firmly in favor of central banking (although not necessarily in
the same way as understood today). In Chapter 3 Book 4 of The Wealth of
Nations he writes:

> “In order to remedy the inconvenience to which this disadvantageous exchange
> must have subjected their merchants, such small states, when they began to
> attend to the interest of trade, have frequently enacted, that foreign bills
> of exchange of a certain value should be paid not in common [coin] currency,
> but by an order upon, or by a transfer in the books of a certain bank,
> established upon the credit, and under the protection of the state”.

Regarding the Federal Reserve, it is impossible to say. Fed is not just
central bank but also research institution and it does banking regulation and
supervision. Adam Smith, contrary to widely held beliefs was not principally
anti-regulation, in fact in WoN he supports all sorts of pragmatic regulations
such as the act of navigation which he rigorously defended.

As argued by [ Reisman (1998) ](https://www.jstor.org/stable/40752070)
[emphasis mine]:

> Adam Smith was not a single-minded advocate of a laissez-faire market in
> which the minimal State had no more than a protective function. Rather, he
> was a pragmatic social thinker who in each case selected the tool that was
> the best suited to his meta-objective of rapid economic growth. .... **In
> Wealth of Nations . . . laissez-faire becomes only a qualified presumption
> rather than a hard-and-fast rule**

Given his pragmatic stance on regulation, and that according to our best
modern understanding banking regulation is essential, [ Tarullo, 2019
](https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.33.1.61) ) he would likely
not oppose it, although without inventing time machine we can only conjecture
what he would say. In addition, central bank does not fulfill the same role in
present day fiat monetary system as it did under gold standard. Again, save of
having time machine we can just conjecture how he would respond to that. Smith
in his writing does not directly address fiat money systems, these became
commonplace only during 20th century (there are arguably few historical
exceptions (see Peter Bernholz (2003). Monetary Regimes and Inflation:
History, Economic and Political Relationships) but Smith does not discuss
these, and he might not have been even aware of such systems.

> Does ... Capitalism support a Central Bank/Federal Reserve?

  1. Capitalism is name for economic/social system. A system has no will it cannot support anything. That is like asking if solar system supports banning smoking in public places.
  2. If you are interested in knowing if having central bank is consistent with capitalism that depends on your definition of capitalism. The word capitalism is typically not used in economics as it is very poorly defined and it can mean anything (there are scholars that consider [ USSR capitalist ](https://en.wikipedia.org/wiki/State_capitalism) country). For example, Mankiws principles of economics have word capitalism printed only three times (in a textbook of over 850 pages), and all of those three times, two are quotes from newspapers and one is from a quote from Churchill used in introduction to one chapter.

However, if you wish to use the dictionary definition of capitalism (from [
Merriam-Webster ](https://www.merriam-webster.com/dictionary/capitalism) ):

> : an economic system characterized by private or corporate ownership of
> capital goods, by investments that are determined by private decision, and
> by prices, production, and the distribution of goods that are determined
> mainly by competition in a free market

then central banks or Fed are fully consistent with capitalist system. The
description above talks about system that is just characterized by private
ownership, and where the distribution of goods is _mainly_ determined by
competition in free market. Thus, having central bank or even whole sectors
like let's say healthcare, controlled by government is fully consistent with
capitalism provided the economy _mainly_ relies on free market.

However, under some different specific definitions of capitalism the above may
not hold. Since capitalism is poorly defined and value laden term it is best
to just avoid it as done throughout most of modern economic literature (or if
you have to use it it is best to refer to some specific definition).


Question:
Is it always a trade off between efficiency and equity?

Is there any situations where we can achieve both equity and efficiency? I'm thinking of Covid 19 vaccine program which is run by Goverment. Although the cost for the program is paid by the money from taxes, it still helps with economic growth right? (in my mind, it's like if people are saved they will have a normal life and buy stuffs, which will boost the production) Or is there anything wrong in my mind?

Explanation: One example could be the emigration from poor countries to rich countries. This enhances equity. We need to check whether this also benefits efficiency, e.g., gain of GDP.

$\begingroup$

> Is it always a trade off between efficiency and equity?

No there is not always trade-off between efficiency and equity, but equity
does not simply mean government spends some money on something in presence of
progressive tax system (that is extremely naïve view and there are myriad of
examples where programs that do that exacerbate inequality).

Equity is one of the words that laymen throw around so much that it is
practically meaningless in non-technical debate, but _in economics_ equity is
defined as having more equal or fair outcomes (see Feldman 1987). In
economics, when it comes to equity, the most focus is placed on income, wealth
or consumption inequality (see the discussion in Atkinson (2015) Inequality).

There are some examples where equity and efficiency go hand in hand. For
example, if we consider equity in global sense (not just national) we have
solid evidence that free migration is both good for efficiency. It could by
reasonable estimates double world's GDP (see [ Clemens, 2011
](https://www.aeaweb.org/articles?id=10.1257/jep.25.3.83) ) which would be
good for efficiency, and from global perspective it would help to reduce
world's income inequality, (albeit it may worsen national-level ones) as it
would significantly raise incomes and wealth of poor migrants and thus likely
reduce global income inequality (see some layman friendly discussion of that
in [ Peterson 2013 ](https://www.e-ir.info/2013/05/01/international-migration-
and-global-economic-inequality/) ).

Alternative simple textbook example of situation where there is no equity-
efficiency tradeoff, would be Pigouvian tax on something consumed
predominantly by rich, like flying. Flying creates an awful lot of pollution,
and Pigouvian tax would thus be efficient as it would correct for the
externality (that airlines without tax can pollute for free), and to an extent
that richer people fly more often, it would probably reduce consumption
inequality somewhat.

Of course, the ones above are just example, there are more cases. Atkinson
(2015) source mentioned above has a nice overview of some cases where there is
little or none efficiency equity tradeoff in chapter 9 (although note that in
earlier chapters he warns that not all examples are generally accepted by all
economists since some are controversial).

However, covid-19 vaccine program is not necessarily good example of that.
Covid-19 is particularly dangerous to people who are older ( [ Piroth et al
2020 ](https://www.sciencedirect.com/science/article/pii/S2213260020305270) ),
for example wealth inequality increases with life expectancy as older people
are expected to have more wealth due to growth dynamics ( [ Vandenbroucke,
2016) ](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2754973) , and
when old people pass to an extent they have more than one child they spread
out their wealth around making society more equitable.

What even more, as [ Deaton (2021) ](https://www.nber.org/papers/w28392)
argues:

> There is a widespread belief that the COVID-19 pandemic has increased global
> income inequality, reducing per capita incomes by more in poor countries
> than in rich. This supposition is reasonable but false. Rich countries have
> experienced more deaths per head than have poor countries; their better
> health systems, higher incomes, more capable governments and better
> preparedness notwithstanding. The US did worse than some rich countries, but
> better than several others. Countries with more deaths saw larger declines
> in income. There was thus not only no trade-off between lives and income;
> fewer deaths meant more income. As a result, per capita incomes fell by more
> in higher-income countries.

If equity would be goal, then from global perspective the best course of
action would be to ship as much vaccines to poor countries and let covid-19
ravage richer countries. What even more, in general research shows that
pandemics like that of bubonic plague in the past or other large catastrophes
(like large scale wars) were great equalizers (e.g. see [ Alfani 2017
](https://onlinelibrary.wiley.com/doi/10.1111/ehr.12652) ; [ Milanovic 2016
](https://www.nature.com/articles/537479a) ; [ Piketty and Saez 2014
](https://science.sciencemag.org/content/344/6186/838.abstract) ), so these
actually help equity (at least along income and wealth lines). There are some
that argue that covid-19 might be somewhat different (e.g. see [ Sayed & Peng
2021 ](https://link.springer.com/article/10.1007/s43546-021-00059-4) ) but it
is more likely than not that it will reduce inequality globally, at least
along wealth and income. However, it is precisely in the rich countries where
pandemic and lockdowns that were imposed as a response to it create the
largest efficiency loses so from pure efficiency perspective vaccines are more
important.


Question:
What is social science and discussion about Type II error preference?

Today, my senior lecturer in economics and finance class teaching about laws impact companies' operation told us one sentence "Also keep in mind that in (at least social) science, we care (try to avoid) about Type II (making a claim on some new finding while it is actually not true), more than Type I error (rejecting some new findings while it is actually true). "

From this link, the definition of social science is: "Social science is, in its broadest sense, the study of society and the manner in which people behave and influence the world around us."

Based on this definition, why economics relating to social science, and what is other than social science

Explanation: We need to check more discussions/research on the linkage between economics, science and social science.

$\begingroup$

> Based on this definition, why economics relating to social science, and what
> is other than social science?

There is actually no clear cut consensus on where Economics belongs (although
it is fair to say most would likely put it into category of social science).
Some authors consider it to be science, some social science, some even moral
science, and some even argue it should have its own category. A good paper
that tries to answer this question for economics is [ Hudson (2017)
](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5640760/) . As Hudson writes:

> Is economics a science or a social science? Arguments have been made for
> both orientations, i.e. that economics is a social science (Frey 1999), a
> science (Frey 1999) and even a moral science (Schabas 2009). In terms of
> sciences it has been linked with physics, with many physicists doubling as,
> or transforming into, economists and a subpart of physics, econophysics,
> specifically evolving which deals with economics (Stanley et al. 1999).
> There are also links with biology (Marshall 1920; Daly 1968). Frey (1999)
> argues economics is a social science as it is part of those sciences which
> deal with actual problems of society, i.e. it is the subject matter which
> makes it a social science. However, he also points out that in practice
> economists tend to fill the journals with axioms, lemmas and proofs, i.e.
> they adopt what they perceive as a scientific, and particularly a
> mathematical, methodology. Mayer (1980) argues that economists act as though
> economics is a hard science and this is reflected by their sophisticated use
> of mathematics. However, he then goes on to argue that econometrics is not
> sufficiently advanced to enable us to test theories as a hard scientist
> would.

But this being said, as mentioned in my first paragraph most would call it
social science as its main focus are societal issues (although you can have 1
person Robinson Crusoe economy, typically economies involve large groups of
people).

> Why he can make the claim above regarding Type I and Type II in social
> science?

I do not think there is any rigorous defense of such claim. In any science if
you care about the science itself both type I and type II errors are equally
problematic. You should ask your professor for why he thinks that, but I do
not think that you can rigorously defend such position.

I guess in some _specific_ circumstances you could defend the claim. If we
test if some food is poisonous then you should do everything you can about
avoiding type II error (e.g. saying the food is not poisonous when it actually
is), since if you commit type II error you get someone poisoned, whereas if
you commit type I error you just think some safe food is poisonous, but
assuming you have plenty of other food options that you know are safe you wont
starve and you won't kill anyone.

You could probably set up similar policy scenarios in the subfield of policy
economics, but extending that claim about type I and type II error to all
social science or even all economics is hardly defensible (if anything I can
think of far more examples from medicine which is not considered social
science).


Question:
What is the difference between Impression Management and Signaling Theory?

I'm interested in theories on how organisations shape their stakeholders' (especially consumers' and investors') perceptions and decisions. I read about Impression Management and Signaling Theory. They seam to be quite similar and I'm unsure when to apply which of them and where they differ. I could not find an article comparing both theories. Signaling Theory is especially for cases with information asymmetry but it seams like Impression Management is also more common in cases with scare information on one side.

Explanation: We need to check the definitions of impression management and signaling theory.

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I don't believe those two terms are used in the same spheres.

To me, an economic theorist, [ signaling
](https://en.wikipedia.org/wiki/Signalling_\(economics\)) plays a role in
models with asymmetric information when the informed party moves first and the
uninformed player reacts, treating the first action as a signal about the
private information. This idea goes back to [ Spence
](https://en.wikipedia.org/wiki/Michael_Spence) , and also plays a role in
biology with non-human interaction.

In contrast, [ impression management
](https://en.wikipedia.org/wiki/Impression_management) is (maybe just to me)
an umbrella term for all kinds of behavior aiming at improving the perception
("image") of something. I would use it loosely like "public relations" and not
with a formal definition in context of a mathematical model in mind (as
opposed to signaling). Because the history of thought is so different, both
terms are difficult to compare. The idea goes back to the sociological book "
[ The Presentation of Self in Everyday Life
](https://en.wikipedia.org/wiki/The_Presentation_of_Self_in_Everyday_Life) "
and there is no mathematical model. Impression management is essentially his
"self-presentation theory, which suggests that people have the desire to
control the impressions that other people form about them." (from the
Wikipedia entry)


Question:
Have the deregulation measures that caused the 2007-2008 crisis been rolled back?

The 2007-2008 financial crisis was largely attributed to several deregulation measures, especially the Gramm-Leach-Bliley act. Have any of these measures been rolled back after the crisis, or new ones introduced to prevent a similar crisis?

Explanation: We first need to check whether deregulation is the root cause of recession, i.e., it may only be the the symptom but not the disease. Then we can find more discussions about the inability of existing institutions.

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Actually, in the literature Great Recession itself is not attributed primarily
to financial deregulation. Financial deregulation played a significant and
extremely important role in the Great Recession, but saying it's the primary
cause of the Great Recession would be exaggeration. It is generally agreed
that root causes of the Great Recession were not just financial deregulation
but also macroeconomic imbalances, underlying moral hazard issues inherent in
the finance sector, past bailouts, changes in the tax code that incentivize
more leverage and also some macro policy mistakes. The deregulation was
additional catalyst that exacerbate the above but it is generally agreed that
that it is very difficult to pin Great Recession on single primary cause (see
Eichengreen Hall of Mirrors, [ Stiglitz 2009
](https://www8.gsb.columbia.edu/faculty/jstiglitz/sites/jstiglitz/files/2009_Interpreting_Causes.pdf)
, [ Verick et al 2010
](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1631069) or [
Jagannathan et al 2010
](https://www.sciencedirect.com/science/article/pii/S1042957312000277?casa_token=BxyUO4ePGIoAAAAA:pBiPcZeUL-2Xtuz9RLZSjPNaafvtetrEtDjFOVp77hbYp1VbmAPg9U7cl8VzFWHQCWzAa3qr45AW)
). Even when it comes to the deregulation itself, the role of Gramm-Leach-
Bliley Act is not settled and disputed (see [ Wallison 2010
](https://link.springer.com/chapter/10.1007/978-1-4419-6637-7_2) ). It can be
argued it contributed to the Too Big To Fail problem that further exhibited
moral hazard but far more important was deregulation that allowed banks to
become extremely overleveraged such as SECs 2004 decision to allow more
leverage or completely somehow letting shadow banks to fly under the radar. In
fact literature shows universal banks (which were prohibited by Glass-
Steagall) are not important contributors to financial instability e.g. see [
Dietrich et al 2012
](https://www.sciencedirect.com/science/article/pii/S106297691200004X?casa_token=fEMlx7Y85_QAAAAA:yvLSCG6mEqCJWoCIxdUT3v8AYk9m1nOoDjgdbsm4Ee9JwhLsni5dOMApHSCFZOgLIG0MKUnmbi8r)
).

Now getting to your main question, measuring financial regulation across time
is tricky business since you cannot simply just count the number of laws.
However, there is consensus that the financial regulation has increased
significantly since 2009 ( [ Rashid, 2019 ](https://mpra.ub.uni-
muenchen.de/93447/1/MPRA_paper_93447.pdf) ; [ Tarullo 2019
](https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.33.1.61) )

Some of the new regulations are similar to the old ones. For example, 2010
Dodd-Frank act can be said to be somewhat inspired by the Glass-Steagall in
some provisions, even though as explained by Tarullo (2019) Dodd-Frankt
largely eschewed the old regulatory solutions and did not reintroduce
separation of commercial and investment banking (as discussed above that is
likely not main problem when it comes to financial stability anyway).

Consequently, modern bank regulation is fundamentally different from the old
one (at least in the US), reflecting progress of the science on this issue.
Modern banking regulation places emphasis not just on microprudential
policies, but on macroprudential policies, systemic stability, stress testing
etc and the idea of clamping down on universal banking was more or less
eschewed.

For example, the Dodd-Frank focuses quite a lot on macroprudential policies
and systemic stability and later amendments (e.g. Collins amendment ) also
pushed for more stringent capital requirements for large banks (Tarullo 2019).
Basel III (which is international regulation but it affects US as well - at
least some provisions do) also significantly improves the capital standards of
banks.

Moreover, the stress-test introduced by Dodd-Frank and administered by Fed got
more stringent and risk sensitive over time ( Hirtle and Lehnert 2014).

Shadow banking is one area where the modern regulation is seriously lacking
(Tarullo 2019), but that is not to say that Glass-Steagall could solve that
issue. The problem with shadow banks is that they are technically not banks
even though they behave like banks and due to various issues such as
regulatory arbitrage they are extremely difficult to regulate.

Consequently, to sum up yes the financial regulation since the Great Recession
has increased, some of the new rules were based on the old, but for most part
the old regulatory framework was eschewed because in retrospective it was not
so great anyway (Glass-Steagall virtually completely ignores macroprudential
issues which are now agreed to be _extremely_ important). Rather the new
regulation is based on our current science and understanding of the market
failures and issues in the financial sector, which is actually to a certain
degree informed by the lessons learned from the Great Recession.


Question:
Bootstrap always valid under asymptotic Normality?

If an estimator is known to have an asymptotically normal distribution, is that sufficient for the bootstrap to be valid?

It seems that is must be, but in 20 minutes of Googling I have come up empty on a proof.

Explanation: With asymptotic normality, we will need define nonparametric bootstrap samples.

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Theorem 2.1 in [ Horowitz (2019)
](https://arxiv.org/ftp/arxiv/papers/1809/1809.04016.pdf) is what you are
looking for


Question:
Has monopoly theory incorporated network effects as a source of monopoly?

I studied industrial organization for my Econ. Ph.D. four decades ago. At that time industrial organization had no way to incorporate 'network effects' into monopoly theory. With the advent of social media (especially Facebook) since then accusations of monopoly power against social media are heard daily. Has someone articulated a theory of network effects as the source of monopoly?

Many thanks.

Explanation: We first need to figure out the definition of network effects, and then understand how/why they link to monopoly.

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Here's a solid example of it in formal literature, with about 1k citations:
[ Competition with Switching Costs and Network Effects
](https://www.sciencedirect.com/science/article/pii/S1573448X06030317) by
Joseph Farrell and Paul Klemperer

The general thought of the article is that customers who are "locked in" to a
particular product can lead to competitors preferring to separate markets
rather than competing with one another. To be pedantic, they are not full
monopolies (but they're certainly not classically competing either).