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National Statistical Institutes do still compile IO tables (see http://ec.europa.eu/eurostat/web/esa-supply-use-input-tables for EU versions, although these are 5-yearly as well). They're generally more interested in producing the Supply and Use tables (which are then transformed into input-output tables) due to their usefulness in balancing the 3 measures ...


5

Quick answer, as I'm on my phone, but product by product input output tables can be obtained from Eurostat for EU countries, and are probably your best bet. Individual countries may have more detail from their own National Statistical Institutes' websites. The production functions in these are derived under some fairly strong assumptions, though, and you'...


4

Something you didn't mention is that $x = Ax + y$ means that to produce one unit of $x$, you use $A$ unit of $x$. E.g. you need electricity to produce electricity. Under the condition that $1>|A|\geq0$ $(1-A)^{-1} = \sum_{k=0}^\infty A^k$ Which allows us to write $x = Ly = \left(\sum_{k=0}^\infty A^k \right)y$ Thus, for one unit of $y$, your (...


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Personal consumption expenditure (PCE) is the primary measure of consumer spending on goods and services in the U.S. economy. It accounts for about two-thirds of domestic final spending, and thus it is the primary engine that drives future economic growth. PCE shows how much of the income earned by households is being spent on current consumption as ...


4

Doing this more abstractly, let $Y_j\subseteq\mathbb{R}^n$ be a production set for $j=1,\ldots,m$ and let $$Y=Y_1+Y_2+\cdots+Y_N=\{y_1+y_2+\cdots+y_n|y_j\in Y_j, j=1,\ldots,m\}$$ be the aggregate production set. The standard result on when the aggregate production set is closed is the following: Theorem: Let $Y_j$ be closed and convex sets containing $0$ for ...


3

For a fully overview on the conditions for the sum of closed sets to be closed, see this note of Kim Border Recession cones I'll be working with subsets of $\mathbb{R}^n$. Let's start with some definitions. Def: A set $C$ is convex if for $x, y \in C$ and $\alpha \in [0,1]$, $\alpha x + (1-\alpha) y \in C$. Def: A set $K$ is a cone if for $x \in K$ and $\...


2

I am not sure exactly what you divided by what, but suppose your input-output table looks like this: $$ A = \left[ \begin{array}{lll} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array} \right] $$ If you proceed to divide the first column by $\sum\limits_i a_{i,1}$ the second by $\sum\limits_i ...


1

What intuition can the mathematical concept of an inverse (function, matrix) have? In a single-input monotonic production function $F(x) = q \implies x= F^{-1}(q)$ the operator $F^{-1}$ is the transformation mechanism that translates output to required input. A "change of units" calculator if you wish. Isn't this what $(I-A)^{-1}$ does in the case of the ...


1

The exports and imports in an input-output analysis should correspond to imports and exports as components of GDP so you can use those or some measures derived from them. For example, trade as a $\%$ of GDP is the sum of exports plus imports over GDP (i.e. $\frac{E+M}{Y}$, where $E$ is export, $M$ import and $Y$ GDP/output). Hence to calculate any comparable ...


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Open question: how would you best make such an estimate? Normally, if you would not care about closing the economy, such estimate would be simply done by calculation of real wages per hour and then based on prevailing prices of the necessities you could calculate how many hours would average worker need to work to afford them. However, the fact that you ...


1

I`d propose you to follow these steps: Set up the minimization cost problem (i.e. for a given output quantity $y$ minimize costs): \begin{align} \min_{H,L,K}& \quad sH + wL + rK \tag{1} \label{1}\\ \text{such that} &\quad \min\{H,L\} + \min\{H, K\}\geq y \tag{2} \label{2} \end{align} In principle you have 3 cases, depending on price of factors $(s,...


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Start with definitions: Production (possibilities) set: $Y$ which you know is convex Input requirement set: $V(y)=\{\mathbf{x}:(y,−\mathbf{x})∈Y\}$ On page 7. you can see: $\mathbf{y}\in Y$ and $\mathbf{y'} \in Y$ which then implies $t\mathbf{y}+(1-t)\mathbf{y'} \in Y$. Hint 1: What does it mean that $Y$ is a convex set? Okay, but what does that ...


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IOTs are usually derived from Supply and Use tables, which have an industry by commodity format. If you used these to derive your IOT, then you can use those to build your SAM, though note you need both the Supply AND Use tables for this. You end up with something that looks roughly like what you see on slide 7 here - with both commodity and activity (...


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Quasi-fixed labour costs are typically those associated with the number of workers rather than the number of hours they work, so things like recruitment costs training costs Commonly they are seen as fixed costs in the short run, but marginal costs in the long run. Other non-labour costs which have the same short run / long run distinction can also be ...


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The key to the answer is good data on Capital. There is a project (KLEMS), which is computing harmonised (i.e. comparable) information on capital, labour, energy, etc for many countries. At the moment it has information mainly on developed countries, but data for more developing countries are coming up. For example, this is a calculation of the capital-...


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Your conjecture seems unlikely. For example the unit matrix would show an economy where no new goods can be produced (it takes 1 unit of something to make 1 unit of that same thing). Yet the determinant of this matrix is 1. If we were to multiply the $3 \times 3$ unit matrix by say 10, the new determinant would be a 1000. But the economy did not get better, ...


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All right kids. You gave me the answer when Dismalscience wrote "this is still not a problem as long as the value of the good produced differs from the sum of the value of its inputs" ... actually, one of the branches had a complete set of zeros in the input table exept for one input and a zero in terms of production ... and another one had a complete set ...


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I didn't divided each column by the sum of the column. This would make no sence since the goal is to produce a technical coefficient matrix that links each input (row) needed by the industry (column) in order to produce their output. I divided each element of the input-output table by the total output of the branch, according to the method presented in ...


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