4B.1 Sign restrictions on impulse responses

C O M M O D I TY M A R K E TS CHAPTER 4 249

(4B.5)

Relating equation (4B.4) to equation (4B.5), we consider the matrix B = PQ as a valid candidate. B should also satisfy the sign restrictions in table 4B.1. A positive demand shock on impact will raise the real price of oil or metals and stimulate oil or metal production, but it will lower global economic activity. A positive supply shock will lower oil or metal production on impact. It also will lower global economic activity while increasing the real price of oil or metals.

Note that these commodity demand and supply shocks differ materially from the global demand and supply shocks modeled in Charnavoki and Dolado (2014) and Ha, Kose, and Ohnsorge (2019). In these approaches, an increase in economic activity and commodity prices can reflect either a global demand or global supply shock, depending on movements in global inflation (table 4B.2). Either of these two global shocks drives up commodity demand, consistent with the definition of a commodity demand shock used here and in Kilian and Murphy (2014). Both here and in Kilian and Murphy (2014), a simultaneous increase in economic activity, commodity production, and prices reflects a commodity demand shock. An oil or metal supply shock is associated with an increase in oil or metal prices and a decline in economic activity and commodity production.

We simulate impulse responses based on a candidate B. The candidate B is retained if the resulting impulse responses meet the sign restrictions, otherwise it is discarded.

The integrated steps are as follows:

1. Estimate an unrestricted VAR and find Zg. Implement Cholesky decomposition to extract P.

2. Draw a random orthogonal matrix Q and compute B = PQ.

3. Compute impulse responses using B calculated in step 2. If all implied impulse response functions satisfy the sign restrictions, retain B. Otherwise discard B.

4. Repeat the first two steps 50,000 times, recording each B that satisfies the restrictions, and record the corresponding impulse response functions (table 4B.3).

About one-fifth of the draws are discarded.

TABLE 4B.1 Sign restrictions on impulse responses

Oil or metal production

Supply shocks Demand shock'

Global economic activity

Real price of oil or metals +

Source: World bank.