Calibration for Decomposition Analysis

Decomposition analysis provides a systematic way of explicitly separating the individual and the interactive effects of simultaneous shocks. Unlike O'Rourke's simulations, it requires all the significant mechanisms of change to be modelled and to be consistent with both an initial and a final equilibrium. The information available to economic historians about the net result of simultaneous changes is used to find values for unknown parameters. Typically not all of the values for the initial and final shock/policy parameters are known. The absence of information about the full set of policy shocks and the new equilibrium makes forward simulation the only option

available to policy modellers. For economic historians, however, knowledge of the ex

post equilibrium can be used to find unknown values for some of the shock or policy

46 If capital accumulation was a factor o f change, the conclusions from sim ulations with price shocks only should be that the effect o f the combination o f Famine and capital accumulation was im portant to the Irish economy.

parameters. While some of the values for these parameters, such as tax rates or quota allotments, will be known since they will be available from published data, others, such as technological change parameters, are seldom available from data and must be calibrated.'’7 Calibration in this context uses information about the second equilibrium, to find values for the unknown policy or shock parameters.

Calibration for decomposition analysis becomes a two stage process. In the first stage, the initial equilibrium is used to find values for those parameters that remain constant in the initial and final equilibria - the time invariant parameters. Let Y‘denote

the initial equilibrium, and let p* be the known, initial period values of the policy and shock parameters. If F is the system of equations that characterises the model, the first stage in the calibration is the standard procedure given in Chapter 2. It finds values for the vector of time-invariant parameters, a , such that

F(a, p*) = Y*. (5.1)

The second stage finds values for the unknown second period policy or shock parameters. Let Y” denote the second period equilibrium values, let 0" be the vector

of exogenously specified second period policy parameter values which are known from data, and let A.“ be the unknown second period policy or shock parameters. The second stage o f calibration finds values for X." such that when the model is solved using those 47

47 Harley and C rafts (1998), however, do not calibrate technology param eters from the 1770 benchmark data, but instead use exogenously specified values.

calibrated values and the values for 0**, the second equilibrium is returned as the model solution:

F(o, X**, 0") = Y " (5.2)

As with the calibration of the static a parameters, the calibration of the unknown transition parameters assumes that modelled economy represents a deterministic system: once the elements of 0" have been exogenously specified, the values of the calibrated transitional parameters, X*\ absorb all of the residual changes in the economy. Such an assumption would be reasonable for a historical problem in which the main determinants of change are known.48

This use of the second observation for the calibration of applied general equilibrium models is rare. One recent example, which does not fall under the traditional domain of economic history, is Hill (1995) who isolates the injury to the Canadian economy, measured by employment changes, caused by changes in the world price of imports. In the period 1972 -1980, the Canadian economy was subjected to changing tax rates, factor endowments, preferences and technology as well as world price shocks. Hill specifies changes to tax rates, factor endowments and world prices from statistical publications, but calibrates preference and technical change parameters

48 An alternative approach would be to specify a priori the number of transitional parameters in the model and then to calibrate the model to both equilibria under some least squares minimization criterion. Implicit in such an approach is the idea that the two equilibria are not true equilibrium representations of the economy.

so that when all the shocks are introduced to the 1972 economy, the 1980 benchmark data are reproduced as a solution to the system. In the counterfactual simulation, Hill allows all the changes to take place, but fixes the world price of industry output so that the share of domestic goods in domestic consumption remains at 1972 levels. The impact of the trade shocks is obtained from comparing the actual trade shock inclusive data to the counterfactual, trade shock free solution.

Although economic historians have not used a second observation to infer values for the parameters of their models, they have made use of information about the actual economic changes to test the performance of their model. This testing is undertaken by introducing all the known shocks to the model, solving, and comparing the model solution to the post-change observation. Typically, no formal testing criterion is applied. The modeller subjectively compares the magnitudes and directions of change arising from the model and asserts whether or not they are consistent with observed changes.

Hence, O’Rourke (1994), who explores the effects of repealing the Corn Laws on Irish agriculture, calibrates a model to data for the period 1856-1860, and in an initial exercise, exogenously introduces the actual wage and price shocks for the period 1956-1860 to 1874-76, together with a shock for the decline in the demand for potatoes. The simulation outcomes are compared to observed changes, and upon inspection, are deemed sufficiently close that the model can be used as an accurate representation of the economic process. The counterfactual is then undertaken by simulating the wage and potato demand shocks as before, but without the Repeal-based price shocks.

O'Rourke concludes from these simulations that the Repeal led to a large reduction in agricultural labour demand in Ireland.

Thus, O'Rourke and others who employ applied general equilibrium models to

explore problems in economic history, have exploited their information about ex post

equilibria to test their models, but they have not made full use of this information in their model specification. Decomposition analysis is a methodology that does make use o f this information. It offers the possibility for a richer systematic understanding of the causes of economic change, especially since the ways in which simultaneous shocks interact with one another has remained unexplored in economics. Knowledge of a second equilibrium opens this topic to investigation by modellers.