Translog Demand PE Model of Tariff Changes
S. Schreiber, 8/8/2019
This industry-specific partial equilibrium (PE) model of trade policy quantifies the economic impacts of a tariff change on prices and quantities. Instead of CES preferences, this model uses transcendental logarithmic (translog) preferences originally proposed by Christensen, Jorgenson, and Lau (1975) and made popular in recent times by Feenstra and others. There are three sources of supply to a single market: domestic shipments (d), subject imports (s) and non-subject imports (n). The market operates under the perfect competition assumption. 

The user inputs translog demand parameters, price elasticities of supply, original and new tariff rates, and initial expenditure and price data on domestic shipments, subject imports, and non-subject imports. The user can modify data inputs in the simulation by changing the values in the ORANGE - shaded lines in the notebook below. The spreadsheet will  update the estimated changes in economic outcomes that are reported in the GREEN - shaded cells once the user selects "Evaluate Notebook" under "Evaluation" in the Menu above. The own- and cross-price elasticity values populate in BLUE.
   
This model is provided as a generic analytical tool, and the data and parameter values are fictional and illustrative. Actual data and parameter values should be supplied by the user based on the industry and market to which the model is applied. The model is the result of ongoing professional research of USITC staff and may be updated. The model is not meant to represent in any way the view of the U.S. International Trade Commission or any of its individual Commissioners. The model is posted to promote the active exchange of ideas between USITC staff and experts outside the USITC and to provide useful economic modeling tools to the public.
In[681]:= ClearAll[f];
Demand Parameters
Coefficient on interaction of log prices of domestic and subject import goods
In[682]:= gammads=-0.4;
Coefficient on interaction of log prices of domestic and non-subject import goods
In[683]:= gammadn=-0.3;
Coefficient on interaction of log prices of subject import and non-subject import goods
In[684]:= gammasn=0;
Coefficient on interaction of log prices of subject import and domestic goods (restricted)
In[685]:= gammasd=gammads;
Coefficient on interaction of log prices of non-subject and domestic goods (restricted)
In[686]:= gammand=gammadn;
Coefficient on interaction of log prices of non-subject and subject import goods (restricted)
In[687]:= gammans=gammasn;
Coefficient on log price of domestic good (restricted)
In[688]:= gammadd=-(gammads+gammadn);
Coefficient on log price of subject import good (restricted)
In[689]:= gammass=-(gammasd+gammasn);
Coefficient on log price of non-subject import good  (restricted)
In[690]:= gammann=-(gammand+gammans);
Price Elasticities of Supply
Price elasticity of supply, domestic production
In[691]:= ed=2;
Price elasticity of supply, subject imports
In[692]:= es=10;
Price elasticity of supply, non-subject imports
In[693]:= en=10;
Policy Shocks
Initial Tariff
In[694]:= ts0=0.0;
Revised Tariff
In[695]:= ts1=0.10;
Data Inputs for Initial Equilibrium
Value of Domestic Shipments
In[696]:= vd0 = 70;
Value of Subject Imports
In[697]:= vs0 =20;
Value of Non-Subject Imports
In[698]:= vn0 = 10;
Price of Domestic Shipments
In[699]:= pd0 = 1;
Price of Subject Imports
In[700]:= ps0 = 1;
Price of Non-Subject Imports
In[701]:= pn0 = 1;
In[702]:= qd0 = vd0/pd0;
In[703]:= qs0 = vs0/(ps0(1+ts0));
In[704]:= qn0 = vn0/pn0;
Calibration of Parameters
In[705]:= M = vd0+vs0+vn0;
The formulas below impose a common translog restriction that sum alpha_i = -1
In[706]:= alphaD = -(vd0/M)-gammadd Log[pd0/M]+((gammadd+gammand+gammasd) vd0 Log[pd0/M])/M-gammadn Log[pn0/M]+((gammadn+gammann+gammasn) vd0 Log[pn0/M])/M-gammads Log[(ps0 (1+ts0))/M]+((gammads+gammans+gammass) vd0 Log[(ps0 (1+ts0))/M])/M;
In[707]:= alphaS = -(vs0/M)-gammasd Log[pd0/M]+((gammadd+gammand+gammasd) vs0 Log[pd0/M])/M-gammasn Log[pn0/M]+((gammadn+gammann+gammasn) vs0 Log[pn0/M])/M-gammass Log[(ps0 (1+ts0))/M]+((gammads+gammans+gammass) vs0 Log[(ps0 (1+ts0))/M])/M;
In[708]:= alphaN = -(1/M)(M-vd0-vs0-gammadd M Log[pd0/M]-gammasd M Log[pd0/M]+gammadd vd0 Log[pd0/M]+gammand vd0 Log[pd0/M]+gammasd vd0 Log[pd0/M]+gammadd vs0 Log[pd0/M]+gammand vs0 Log[pd0/M]+gammasd vs0 Log[pd0/M]-gammadn M Log[pn0/M]-gammasn M Log[pn0/M]+gammadn vd0 Log[pn0/M]+gammann vd0 Log[pn0/M]+gammasn vd0 Log[pn0/M]+gammadn vs0 Log[pn0/M]+gammann vs0 Log[pn0/M]+gammasn vs0 Log[pn0/M]-gammads M Log[(ps0 (1+ts0))/M]-gammass M Log[(ps0 (1+ts0))/M]+gammads vd0 Log[(ps0 (1+ts0))/M]+gammans vd0 Log[(ps0 (1+ts0))/M]+gammass vd0 Log[(ps0 (1+ts0))/M]+gammads vs0 Log[(ps0 (1+ts0))/M]+gammans vs0 Log[(ps0 (1+ts0))/M]+gammass vs0 Log[(ps0 (1+ts0))/M]);
In[709]:= bd = qd0 pd0^-ed;
In[710]:= bs = qs0 ps0^-es;
In[711]:= bn = qn0 pn0^-en;
Calculation of Uncompensated Elasticities of Demand
In[712]:= etadd = -1 + (gammadd/(vd0/M)- (gammads+gammadd+gammadn))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[712]= -2.
In[713]:= etass = -1 + (gammass/(vs0/M)- (gammass+gammasd+gammasn))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[713]= -3.
In[714]:=  etann = -1 + (gammann/(vn0/M)- (gammans+gammand+gammann))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[714]= -4.
In[715]:= etads = (gammads/(vd0/M)- (gammads+gammadd+gammadn))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[715]= 0.571429
In[716]:= etadn = (gammadn/(vd0/M)- (gammads+gammadd+gammadn))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[716]= 0.428571
In[717]:= etasn = (gammasn/(vs0/M)- (gammasn+gammasd+gammass))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[717]= 0.
In[718]:= etasd = (gammasd/(vs0/M)- (gammasn+gammasd+gammass))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[718]= 2.
In[719]:= etand = (gammand/(vn0/M)- (gammann+gammand+gammans))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[719]= 3.
In[720]:= etans = (gammans/(vn0/M)- (gammann+gammand+gammans))/(-1+(gammads+gammans+gammass)Log[(ps0(1+ts0))/M]+(gammadn+gammann+gammasn) Log[pn0/M]+(gammadd+gammand+gammasd)Log[pd0/M])
Out[720]= 0.
Changes in Equilibrium Prices and Quantities
In[721]:= qd = bd pd^ed;
In[722]:= qs = bs ps^es;
In[723]:= qn = bn pn^en;
In[724]:= EQd1=(qd pd)/M== ((alphaD + (gammads Log[(ps(1+ts1))/M] + gammadn Log[pn/M]+gammadd Log[pd/M]))/((alphaD+alphaN+alphaS)+(gammads+gammans+gammass)Log[(ps(1+ts1))/M]+(gammadn+gammann+gammasn) Log[pn/M]+(gammadd+gammand+gammasd)Log[pd/M]));
In[725]:= EQs1=(qs ps(1+ts1))/M== ((alphaS + (gammass Log[(ps(1+ts1))/M] + gammasn Log[pn/M]+gammasd Log[pd/M]))/((alphaD+alphaN+alphaS)+(gammads+gammans+gammass)Log[(ps(1+ts1))/M]+(gammadn+gammann+gammasn) Log[pn/M]+(gammadd+gammand+gammasd)Log[pd/M]));
In[726]:= EQn1=(qn pn)/M== ((alphaN + (gammans Log[(ps(1+ts1))/M] + gammann Log[pn/M]+gammand Log[pd/M]))/((alphaD+alphaN+alphaS)+(gammads+gammans+gammass)Log[(ps(1+ts1))/M]+(gammadn+gammann+gammasn) Log[pn/M]+(gammadd+gammand+gammasd)Log[pd/M]));
In[727]:= FindRoot[{EQd1,EQs1,EQn1},{pd,pd0}, {ps,ps0},{pn,pn0}]
Out[727]= {pd->1.01078,ps->0.979195,pn->1.00228}
In[728]:= pd1 = pd /.%;
In[729]:= ps1 = ps/.%%;
In[730]:= pn1 = pn/.%%%;
In[731]:= qd1 =bd pd1^ed;
In[732]:= qs1 = bs ps1^es;
In[733]:= qn1 = bn pn1^en;
% Change in price of domestic shipments
In[734]:= ((pd1-pd0)100)/pd0
Out[734]= 1.0783
% Change in producer price of subject imports
In[735]:= ((ps1-ps0)100)/ps0
Out[735]= -2.08049
% Change in consumer price of subject imports
In[736]:= ((ps1(1+ts1)-pd0(1+ts0))100)/(pd0(1+ts0))
Out[736]= 7.71146
% Change in producer price of non-subject imports
In[737]:= ((pn1-pn0)100)/pn0
Out[737]= 0.22783
% Change in the quantity of domestic shipments
In[738]:= ((qd1-qd0)100)/qd0
Out[738]= 2.16823
% Change in the quantity of subject imports
In[739]:= ((qs1-qs0)100)/qs0
Out[739]= -18.9614
% Change in the quantity of non-subject imports
In[740]:= ((qn1-qn0)100)/qn0
Out[740]= 2.3018