150 lines
4.5 KiB
Matlab
150 lines
4.5 KiB
Matlab
function [ya, yass, gya, gyass] = quarterly2annual(y,yss,GYTREND0,type,islog,aux)
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% function [ya, yass, gya, gyass] = quarterly2annual(y,yss,GYTREND0,type,islog,aux)
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% transforms quarterly (log-)level time series to annual level and growth rate
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% it accounts for stock/flow/deflator series.
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%
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% INPUTS
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% y quarterly time series
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% yss steady state of y
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% GYTREND0 growth rate of y
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% type 1 sum (default)
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% 2 average
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% 3 last period (Q4)
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% 4 geometric average
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% 5 annual price as quantity weighted average
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% 6 annual quantity from average price
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% 7 annual nominal from Q real and deflator
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% 8 annual ratio [e.g. trade balance to GDP]
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% islog 0 level (default)
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% 1 log-level
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% 2 growth rate Q frequency
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% aux optional input used when type>4
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%
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%
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% OUTPUTS
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% ya annual (log-)level
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% yass annual steadystate (log-)level
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% gya annual growth rate
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% gyass annual growth rate steadystate
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% Copyright (C) 2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if nargin ==0
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disp('[ya, yass, gya, gyass] = quarterly2annual(y,yss,GYTREND0,type,islog);')
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return
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end
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if nargin<4 || isempty(type)
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type=1;
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end
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if nargin<5 || isempty(islog)
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islog=0;
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end
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if isstruct(aux)
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yaux=aux.y;
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yauxss=aux.yss;
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islogaux=aux.islog;
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GYTREND0aux=aux.GYTREND0;
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typeaux=aux.type;
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if islogaux
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yaux=exp(yaux+yauxss);
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yauxss=exp(yauxss);
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yaux=yaux-yauxss;
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end
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elseif type > 4
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error('TYPE>4 requires auxiliary variable!')
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end
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if islog == 2
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% construct loglevel out of growth rate
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y = cumsum(y);
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yss=0;
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islog=1;
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end
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if islog == 1
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y=exp(y+yss);
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yss=exp(yss);
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y=y-yss;
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end
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switch type
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case 1
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yass = yss*(exp(-GYTREND0*3)+exp(-GYTREND0*2)+exp(-GYTREND0)+1);
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tmp = lagged(y,3)*exp(-GYTREND0*3)+lagged(y,2)*exp(-GYTREND0*2)+lagged(y,1)*exp(-GYTREND0)+y; % annualized level
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ya = tmp(4:4:end);
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case 2
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yass = yss*(exp(-GYTREND0*3)+exp(-GYTREND0*2)+exp(-GYTREND0)+1)/4;
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tmp = (lagged(y,3)*exp(-GYTREND0*3)+lagged(y,2)*exp(-GYTREND0*2)+lagged(y,1)*exp(-GYTREND0)+y)/4; % annualized level
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ya = tmp(4:4:end);
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case 3
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yass=yss;
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tmp = y;
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ya = tmp(4:4:end);
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case 4
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yass = yss*(exp(-GYTREND0*3/2));
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tmp = (lagged(y+yss,3)*exp(-GYTREND0*3).*lagged(y+yss,2)*exp(-GYTREND0*2).*lagged(y+yss,1)*exp(-GYTREND0).*(y+yss)).^(1/4); % annualized level
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tmp = tmp - yass;
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ya = tmp(4:4:end);
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case 5
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% nominal series
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yn = (y+yss).*(yaux+yauxss) - yss.*yauxss;
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[yna, ynass] = quarterly2annual(yn,yss.*yauxss,GYTREND0+GYTREND0aux,typeaux,0,0);
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% real series
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[yra, yrass] = quarterly2annual(yaux,yauxss,GYTREND0aux,typeaux,0,0);
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% deflator
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yass = ynass/yrass;
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ya = (yna+ynass)./(yra+yrass)-yass;
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case 6
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% nominal series
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yn = (y+yss).*(yaux+yauxss) - yss.*yauxss;
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[yna, ynass] = quarterly2annual(yn,yss.*yauxss,GYTREND0+GYTREND0aux,typeaux,0,0);
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% deflator
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[pa, pass] = quarterly2annual(yaux,yauxss,GYTREND0aux,2,0,0);
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% real series
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yass = ynass/pass;
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ya = (yna+ynass)./(pa+pass)-yass;
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case 7
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% nominal series
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yn = (y+yss).*(yaux+yauxss) - yss.*yauxss;
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[ya, yass] = quarterly2annual(yn,yss.*yauxss,GYTREND0+GYTREND0aux,typeaux,0,0);
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GYTREND0=GYTREND0+GYTREND0aux;
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case 8
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% numerator
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yn = y;
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[yna, ynass] = quarterly2annual(yn,yss,GYTREND0,typeaux(1),0,0);
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% denominator
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yd = yaux;
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[yda, ydass] = quarterly2annual(yd,yauxss,GYTREND0aux,typeaux(2),0,0);
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% ratio
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yass = ynass/ydass;
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ya = (yna+ynass)./(yda+ydass)-yass;
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GYTREND0 = GYTREND0 - GYTREND0aux;
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otherwise
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error('Wrong type input')
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end
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% annual growth rate
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gyass = GYTREND0*4;
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gya = (ya+yass)./(lagged(ya,1)+yass).*exp(4*GYTREND0)-1-gyass;
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if islog
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ya=log(ya+yass);
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yass=log(yass);
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ya=ya-yass;
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end
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