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chapotraphouse @hexbear.net
sodium_nitride [any, any] @hexbear.net

Simulation model, version 2

This is a real big update to my simulation and reworks the entire logic of it. Though doing so allows me to investigate even more stuff. Check out the post on the old sim if you haven't seen it.

At this point, the sim has become so complex, I don't think I can explain it in as much depth as the previous one.

So I'll keep it simple and show you my assumptions, results, and code. There are 10 sectors in the economy this time (so the visualization has changed)

As always, "economic reproduction" is the condition where nobody in the economy gains or looses money by the end of the production period.

The code and pictures are in the comments.

Also, I'd like /u/Sebrof and /u/pancake@lemmygrad.ml to see this post.

Assumptions:

  1. There are no banks, governments, population growth or technological changes. None of these things are modeled yet since they distract from the point of the model, which is to see how labor prices and economic reproduction are related.

My next model will try to model these things to see if the relationship between labor prices and economic reproduction still holds

  1. The logic of this model is inverted to the last one. In the previous model, we started with a net output (sold to consumers) then calculated how much gross output would be needed (sold to consumers and to factories) to maintain this. This time, I randomly generate a gross output then compute a net output.
  2. I randomly generate 100,000 economies, each with its own technological level (the 10x10 A matrix), a set of prices (10x1 column vector), and employment in industries (10x1 vector). I assume everyone is employed. Also, this time, there is only 1 price vector per economy.
  3. For each economy, I randomly generate a "basket of consumption", which is the amount of products that its people will consume. I scale the basket so that it could be produced by half the labor of the economy, and keep the basket constant for all time.
  4. This time, there is foreign trade. If the economy produces more of a product than what is required for the basket, that's exports. Otherwise it imports.
  5. I simulate 100 time steps for each economy. Every time step, the sectors of the economy will update their prices and employment. There were many possible rules for choosing how these updates happened. I made it so that the sectors hire workers in proportion to how much money they have (divided by how much it costs to hire workers). Prices are scaled down as a sector grows (due to competition)
  6. Then I compute all the financial data (like revenues, wages, incomes, costs, trade imbalances, profits, etc) and plot it.

The important accounting identities are:

National income = Wages + trade balance

National income = Revenues of industry - Costs of industry (not including wages)

17 comments

  • have you considered taking bls input-output sector tables

    • I've tried looked into this with the world input output tables. But the time baseline on that is much smaller, but you gain a global view of the economy in exchange for just national views. In fact, using it to calculate labor exploitation is something that can be done, as well as tracing the flow of commodities between nations.

      In the world input output tables I've noticed that some nations lack labor data, like China. Idk why. So that may have to be imputed with a reasonable guess for some nations or compiled from other sources.

      When working with real input output tables the most important aspect of them is that they are set up differently from the input output tables you find in theory. I will explain in the next paragraoh In addition to the set up, they also have extra tidbits like taxes, tariffs (the most beautiful word in the dictionary, folks) government spending, gross fixed capital investment, etc. Those wouldn't be too hard to handle, though I would need help in understanding some of details if doing it alone.

      Now for the world input output tables, the given data isn't your typical input output table A where ai,j is the quantity flow of product i required as input for the production of a unit product of type j. Instead, the data is typically a monetary input output table. For the data, A is in money terms. So ai,j is the money flow of for product i paid to create one "dollar" output of product type j.

      You can still use the same equations you find in input output analysis, but one must keep in mind that instead of a vector of quantity flows (q or n) you are dealing with a vector of money flows such as gross or net product for each sector. The labor coefficients (l) or value vectors (v) are also in units of labor per dollar (or whatever currency gets used).

      Perhaps not all data is like this, but most of the input output table data i have found has this set up that is slightly different from how input output tables are set up and used in theory

      I think it would be cool to have some way of integrating those calculations into a network or the @hexatlas map

      I stalled out on that project as life got in the way. But most of the math is worked out. Given the data you can find how much labor one country consumes from another, and how much it gives in return by tracing labor inputs through this input output tables (i.e. a production network)

      Also, if you want to find profitability or wage data, one thing you would need to find data on or make assumptions about is productive labor vs unproductive

      Some sectors, like finance, insurance etc, are unproductive and simply take away from the surplus without producing any. But even productive sectors that create surplus, like manufacturing, are going to have some fraction of labor inputs that are included in the data but are not actually productive labor. Think management.

      Anwar Shaikh and Tomak (spelling?) Actually have a paper and book about how to make these profitability calculations using BLS data. So that is a source. And Basu has a paper with an overview of quantitative methods in Marxism that also overviews it.

      To my knowledge, Shaikh's method aggregates data across sectors, but with an input output table the beauty is sectoral analysis.

    • No, I don't know what I'd do with them.

      Actually maybe I could use them to compute some things but that'd be a different investigation entirely.

      • i've been pondering if you can vaguely track industry profit/exploitation in them, but always get distracted. They can summarize labor,and they stretch for 50 years i think

  • I will be taking requests if someone wants me to generate data. I can change the number of sectors, the amount of wages. I can try different price seeking strategies, etc.

    Also, I never thought I'd reach the "post your research annonymously on Hexbear" stage of my academic career.

  • ' %%%%%%%%%%

     
            time = 100;
    n = 10;
    N = 100000;
    connectivity = (2*n)^0.5; %The average number of intermediate commodities that go into making a commodity
    threshold = connectivity/n;
    e_l = 0.025;                 %proportionality rate at which hirings change per timestep
    e_p = 0.025;                 %proportionality rate at which prices can change per timestep

    Data = zeros([5 N*time]); %Pre allocating data matrix. Necessary to speed up simulation
    Data_final = zeros([5 N]); %Pre allocating data matrix. Holds data on final time steps of each economy
    w = 0.5; %Percentage of national production that the economy aims to give to labor
    
    %%%%%%%%%%LOOP
    
    for i = 1:N

        %Generate random workforce distribution between sectors
        L = rand([n time])*0.998 + 0.001;
        L(:,1) = L(:,1)./sum(L(:,1));    %Normalise the population to 1

        %Randomly generate direct labor use
        l = rand([n 1])*0.998 + 0.001;
        
        %Technical matrix:
        A = rand([n n]);
        A = A.*(A<=threshold);
        a = (eye(n)-A)\eye(n); %Storing the productivity matrix so it doesn't have to be recalculated over and over

        while sum(sum(a<0))>0     %If a has negative components, regenerate the economy and try again
            A = rand([n n]);
            A = A.*(A<=threshold);
            a = (eye(n)-A)\eye(n);
        end

        %LTV prices calculation
        LTV = sum(a.*l)';

        %Consumption
        basket = rand([n 1]);
        basket = w*basket./(sum(basket.*LTV)); %Consumption is scaled so that it can be in theory satisfied by the work of half the workforce

        %net production
        %o = zeros([n time]);

        %net income of sectors + agregate measures (pre-allocation)
        M = zeros([n time]);
        trade_balance = zeros([1 time]);
        profit_var = zeros([1 time]);
        
        %Randomised prices are generated for starting timestep (pre-allocation)
        P = zeros([n time]);

        %P(:,1) = rand([n 1]);             %randomly generates a set of prices

        
        %P(:,1) = (eye(n) - A - Cw)\rand([n 1]);
        P(:,1) = rand([n 1]);

        for k = 1:time
            
            if k>1
                hirings = e_l*(M(:,k-1))/sum(basket.*P(:,k-1));  %New Hirings are in proportion to the income available divided by wages
                L(:,k) = L(:,k-1) + hirings;   
                L(:,k) = L(:,k).*(L(:,k)>=(0.001/n)) + (L(:,k)<(0.001/n))*(0.01/n);   %This puts a floor on the size of sectors. Helps prevent the code from exploding.
                P(:,k) = P(:,k-1).*(1 - e_p*(hirings./L(:,k-1)));  %If the size of a sector doubles, the price decreases by e_p percent (from competititon)
                
                L(:,k) = L(:,k)./sum(L(:,k));    
            end

            P(:,k) = P(:,k).*((P(:,k)>=(0.001))) + (P(:,k)<(0.001))*(0.01);   %This puts a floor on the price. Helps prevent the code from exploding.

            %Calculate gross output of industries
            O = L(:,k)./l;

            P(:,k) = P(:,k)./sum(O.*P(:,k));%Normalises these prices so that total economy wide revenue is always 1

            Cw = basket * l';
            profit_var(:,k) = var(((eye(n) - A - Cw)*P(:,k))./P(:,k));

            %Calculate net production
            o = O - A*O;       %Net production can be negative. We will assume the existence of imports
                                    %negative net production will show up as
                                    %negative sales (the external market is
                                    %selling to the economy)
    
            %Inter-industry sales
            R = O.*P(:,k);  %Market value of gross production by sector
            C = A' .*O*P(:,k); %Costs of inputs to production by sector
            
            %Industry to market sales
            S = o.*P(:,k); %Sales to consumers by sector
            Y = sum(S); %Total industry income from market sales
                        %Under balanced conditions, this income would be
                        %exactly matched by industry outflows to consumers
                        %(wages + dividends)
    
                        %Here it is assumed that the industry pays enough in
                        %(wages + dividends) to afford a fixed basket of 
                        % consumption.
    
                        %Any leftover income is the trade balance
    
            trade_balance(k) = sum((o - basket).*P(:,k));
    
            W = L(:,k).*(sum(basket.*P(:,k))); %Wages paid out vector by industry
            
            M(:,k) = R - C - W; %Net Income by industry
            
            M_per_worker = (1/n)*M./L(:,k); %I want to see if this givees any interesting results

            %Accounting identities
            % Y = sum(W) + trade_balance
            %Y = sum(R - C)

        end 
        %%%%%%%%%%%%%%Computing more time steps%%%%%%%%%%%%%%%%%%%%%%%%
        
        
        %%%%%%%%%%%%%Processing data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        %poopoo = LTV./LTV(1,:); 
        %Peepee = P./P(1,:); 

        ratios = P./LTV;
        ratios = log(ratios);
        ratios = ratios - mean(ratios);
        specific_price = sum(abs(ratios))/n;

        M = sum(abs(M));
        M_per_worker = sum(abs(M_per_worker));
        
        %specific_price = sum(abs(log(Peepee./poopoo)))/(n-1);

        % trade_balance; trade_intensity
        Data(:,(1+ (i-1)*time ):(i*time)) = [specific_price; M; M_per_worker; trade_balance; profit_var];
        Data_final(:,(1+ (i-1) ):(i)) = [specific_price(time); M(time); M_per_worker(time); trade_balance(time); (profit_var(time)).^0.5];
    
    end
    %%%%%%%%%%LOOP end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    resolution = 1001;
    scale = 1;
    
    ptsy = linspace(0, 1, resolution);
    ptsx = linspace(0, scale, resolution);
    %ptsx = linspace(-0.1, 5, 1001);
    %H = log(histcounts2(Data_final(2,:), Data_final(1,:), pts, pts));
    H = log(histcounts2(Data(2,:), Data(1,:), ptsy, ptsx));
    imagesc(ptsx, ptsy, H);
    axis xy;
    set(gca, 'XLim', ptsx([1 end]), 'YLim', ptsy([1 end]), 'YDir', 'normal');
    colormap copper
    a=colorbar;
    a.Label.String = "Density of simulation outcomes [natural log scale]";
    xlabel {Deviation from LTV prices [natural log scale]}
    ylabel {Deviation from reproduction [linear scale]}
    title {Absolute sector income vs LTV pricing}
    exportgraphics(gcf,"repro_inv_M10.png","Resolution",600);
    
    figure 
    ptsy = linspace(0, 1, resolution);
    ptsx = linspace(0, scale, resolution);
    %H = log(histcounts2(Data_final(3,:), Data_final(1,:), pts, pts));
    H = log(histcounts2(Data(3,:), Data(1,:), ptsy, ptsx));
    imagesc(ptsx, ptsy, H);
    axis xy;
    set(gca, 'XLim', ptsx([1 end]), 'YLim', ptsy([1 end]), 'YDir', 'normal');
    colormap copper
    a=colorbar;
    a.Label.String = "Density of simulation outcomes [natural log scale]";
    xlabel {Deviation from LTV prices [natural log scale]}
    ylabel {Deviation from reproduction (scaled by employment) [linear scale]}
    title {Per worker sector income vs LTV pricing}
    exportgraphics(gcf,"repro_inv_Mw10.png","Resolution",600);
    
    figure 
    
    ptsy = linspace(-1, 1, resolution);
    ptsx = linspace(0, scale, resolution);
    %H = log(histcounts2(Data_final(4,:), Data_final(1,:), pts, pts));
    H = log(histcounts2(Data(4,:), Data(1,:), ptsy, ptsx));
    imagesc(ptsx, ptsy, H);
    axis xy;
    set(gca, 'XLim', ptsx([1 end]), 'YLim', ptsy([1 end]), 'YDir', 'normal');
    colormap copper
    a=colorbar;
    a.Label.String = "Density of simulation outcomes [natural log scale]";
    xlabel {Deviation from LTV prices [natural log scale]}
    ylabel {Trade balance [linear scale]}
    title {Trade balance vs LTV pricing}
    exportgraphics(gcf,"repro_inv_T10.png","Resolution",600);

    figure 
    
    ptsy = linspace(0, 2.5, resolution);
    ptsx = linspace(0, scale, resolution);
    %H = log(histcounts2(Data_final(5,:), Data_final(1,:), pts, pts));
    H = log(histcounts2(Data(5,:), Data(1,:), ptsy, ptsx));
    imagesc(ptsx, ptsy, H);
    axis xy;
    set(gca, 'XLim', ptsx([1 end]), 'YLim', ptsy([1 end]), 'YDir', 'normal');
    colormap copper
    a=colorbar;
    a.Label.String = "Density of simulation outcomes [natural log scale]";
    xlabel {Deviation from LTV prices [natural log scale]}
    ylabel {STD of profitability rates of sectors}
    title {Profit STD vs LTV pricing}
    exportgraphics(gcf,"repro_inv_p10.png","Resolution",600);

    '

  • This is really neat. And also very pretty. It's a great visualization of a fairly complex idea

  • The graphs:

    Each graph has 10 million points, There are 100 points (1 for each time step) for 100,000 economies

    Graph 1: The average deviation of sectorial income (Revenue - Costs - Wages) from reproduction vs average deviation of prices from LTV.

    Graph 2: Graph 1, but the incomes of each sector are given per worker

    Graph 3: The trade balance of each economy at each time step

    Graph 4: The variability of profit rates between different sectors

    • Interpretation of the graphs.

      Graph 1: We still see the same result. When the prices of an economy are at those predicted by the LTV, the income of every sector shrinks to 0, leading to perfect economic reproduction. However, we see that many economies have economic reproduction even without LTV prices. I have a hypothesis for this. Some of the randomly generated economies in the simulation are "disconnected", meaning that the different industries don't buy and sell to each other. In this case, the effect of prices of one industry on another are minimum, so the prices stop mattering much.

      Graph 2: Same as graph 1, but the shape of the curve is different. Not really sure what to say about this

      Graph 3: I found it very interesting that no matter how much I tried to increase the wages (at one point, I had a wage basket 2 times bigger than what the economy could actually produce on its own), the trade balance remained stubbornly positive for the overwhelming majority of the data points.

      This could happen because the sectors were reorganizing themselves to exploit comparative advantage, even though I never coded them to do this!

      Say the people of the country were consuming 1 million tons of grain, and 100,000 cars every time step. Producing a car takes 1 person-year, and producing a ton of grain takes 0.1 person years. This level of consumption would then require 2 million person-years of labor (1 million for the cars, 1 million for the grains).

      Even if there were only 1.5 million people in the economy, they could, for example, spend all their labor producing cars. So they would make 150,000 cars and export 50,000 cars. If the price of the cars is much higher than the price of grains, they could just exchange the cars for enough grains while still maintaining a trade surplus.

      This was one of the most surprising results I saw from this model.

      Graph 4: This here was to test an assumption that many economists make about the economy. They assume that the profit rates of industries equalise over time. However, in my simulation at least, this never happens. There is like an invisible floor to how low the differences in profit rates can get.

17 comments