by mode but not trade costs Assume that traders choose the mode of least cost

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(by mode) but not trade costs . Assume that traders choose the mode of least cost for any route, subject to idiosyncratc shocks. This gives us a discrete choice framework. Concretely, assume that trade costs for each mode are an increasing function of distance: exp ( a m d ij , m + b m + tm ) where tm is a trader-mode specific idiosyncratic shock. 3. We observe the mode-specific bilateral trade shares. Using the discrete choice framework and these observed trade shares, we can estimate the relative cost of each mode of travel. We can also compute the average cost per route. 4. Use a gravity equation combined with observed total bilateral trade flows between regions to pin down the trade elasticity (the gravity equation incorporates non-geographic trade costs). ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 30 / 39
Estimate A and u I Theorem 3 in the paper: Theorem For any { w i , L i , τ i , j } i , j S where τ i , j is symmetric in i , j , there exists unique (up to scale) positive functions A i and u i such that w i and L i are the regular spatial equilibrium for the geography { w i , L i , τ i , j } . I One can start from observed wages, population and trade costs and back out the unique (up to scale) productivity and amenity functions that rationalize the observed equilibrium. I These are the endogenous productivity and amenity functions that rationalize the observed equilibrium, not the exogenous ¯ A ( i ) and ¯ u ( i ). I Note: to run counterfactuals, one must know how A i and u i respond endogenously to population, ie α , β , which the procedure does not identify. Here, they take values borrowed from the literature for α , β . ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 31 / 39
Running Counterfactuals I Use similar solving method for calibration and counterfactuals: I For estimation: start from observed { w i , L i , τ i , j } i , j S and calibrated α, β, σ and back out ¯ A ( i ) and ¯ u ( i ) I For counterfactuals, hold constant ¯ A ( i ) and ¯ u ( i ) and calibrated elasticities and change τ 0 i , j to get at counterfactual w 0 i , L 0 i and welfare W 0 I Equivalently, directly write the model in changes (exact hat algebra ˆ x = x 0 x ) and sidestep formally backing out ¯ A ( i ) and ¯ u ( i ). Knowing how trade costs change: ˆ τ i , j = τ 0 i , j τ i , j , directly solve for ˆ w i , ˆ L i , ˆ W ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 32 / 39
Observed population L ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 33 / 39
Observed wages ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 34 / 39
Fraction of Income explained by Geographic Location I Model-based decomposition: γ 1 σ - 1 ln Y ( i ) = C w + C L + (1 - β ) ln ¯ A ( i ) + (1 + ) ln ¯ u ( i ) - (2 + - β ) ln P ( i ) . I How much of the R-squared is explained by variation in P i ? I P i sufficient statistics for geographical location I Results depend on α and β : between 20% and 70% ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 35 / 39
Removing the Interstate Highway System: Counterfactual I Methodology: recompute the equilibrium with new matrix τ ij recomputed without the ISH, holding ¯ A i and ¯ u i constant I (Again, do so for various α , β ) ECON280D. Spring 2018. C. Gaubert Lecture 3.2 Equilibrium, Estimation, Counterfactuals 36 / 39
Removing the Interstate Highway System: Price Index I Results: price index increases most in the Rocky mountain (more economic remoteness) ; least e.g. in California that has alternative transportation