RDP 2013-09: Terms of Trade Shocks and Incomplete Information 4. Response of the Economy to Terms of Trade Shocks

In this section I first show how incomplete information affects the response of the economy to terms of trade shocks and then discuss its implications for aggregate macroeconomic volatility.

4.1 Dynamic Responses to Terms of Trade Shocks

4.1.1 Transitory terms of trade shocks

Figure 3 shows the response of the economy to a positive one standard deviation transitory terms of trade shock. I focus first on the response of the economy when agents have incomplete information about the persistence of these shocks.

Initially, the shock increases the terms of trade by around 1.3 per cent. In subsequent quarters, the terms of trade decrease and after six years stabilise at their original level. The shock increases the price of the economy's output relative to the price of consumption and investment goods. This induces households to invest more and increases real wages, which leads to an expansion in labour supply and production. The employment boom is short-lived, however, and within two years employment falls below its trend level. This reflects the fact that the increase in the terms of trade makes households in the economy wealthier. As they receive disutility from working, households choose to convert some of their increased wealth into additional leisure. In contrast, the investment boom is more persistent and it takes five years for investment to return to trend. Output remains slightly above trend for a considerable period, reflecting the increase in the size of the economy's capital stock. The impact of the terms of trade boom on the trade balance is quite small, with an initial increase followed a few quarters later by a small decrease.

Consumption also responds positively to the shock before gradually reverting to trend. This response reflects two factors. First, the higher terms of trade increases the wealth of domestic residents. All other things equal, this would lead them to increase their consumption. However, to the extent that agents expect that some of the increase in the terms of trade will eventually dissipate, the shock also creates the expectation of a decrease in the price of the consumption good in terms of import prices.^[10] As the bond price in this model is exogenous and denominated in terms of importables, the expected decrease in the relative price of the consumption good increases the real interest rate faced by domestic households. This induces households to postpone consumption.^[11] The substitution effect of a higher real interest rate is greatest immediately following the shock, while in later quarters the income effects of greater wealth dominate the consumption response.

It is instructive to compare the response of the economy under incomplete information to its response under full information.^[12] In the full information case, the initial responses of employment and output are substantially larger than they are under incomplete information. That is, with full information, agents realise that the shock is transitory and bring forward production to take advantage of the temporarily high export prices. Meanwhile, the shock causes an initial contraction in consumption. This is larger than in the incomplete information case for two reasons. First, under full information agents are confident that the increase in the terms of trade will be short-lived. Consequently, the expected increase in their wealth is smaller than it would be if they anticipated that the terms of trade would be persistently higher. Second, fully informed agents are also confident that that the price of the home-produced consumption good relative to the imported good's price will decrease in the future. Consequently, the real interest rate is also higher under full information than it is under incomplete information. Both the smaller positive income effect and larger substitution effect will tend to depress consumption in the full information case relative to the incomplete information case.

In contrast, the increase in investment is smaller under full information. This largely reflects the impact of the capital adjustment costs, which dampen the response of investment to transitory shocks. Agents do not wish to pay large costs to expand the capital stock during a terms of trade boom and then to pay these costs again when the capital stock shrinks as commodity prices fall. The combination of a larger increase in output, smaller increase in investment and decrease in consumption implies a greater initial increase in the trade balance in the full information case compared to the incomplete information case. After two years, households start to draw down on the foreign assets that they accumulate through the increased trade balance, and use the proceeds to fund additional consumption.

The response of the economy under full information reflects a standard consumption smoothing response to a temporary increase in income. Agents produce more when the relative price of output is high and save part of the windfall to fund higher consumption when it is cheaper in the future. To understand the response of agents under incomplete information, it is necessary to examine their beliefs. These are illustrated in Figure 4. The left panel shows how agents' beliefs about the two components of the terms of trade shock, z_t and g_t, evolve following a transitory shock. Agents have some success in identifying the shock. They attribute over half of the 1.3 per cent increase in the terms of trade to the transitory shock and only a small proportion to the permanent shock.^[13] Agents are less successful in inferring the evolution of z_t and g_t in future periods. But they still correctly attribute most of the evolution in the terms of trade to transitory shocks.

Given that agents correctly identify transitory shocks as the main cause of the observed changes in the terms of trade, why do their reactions differ so much between the full information and incomplete information cases? The key to understanding this is to recall that the permanent shock increases the terms of trade in future periods as well as on impact. Hence, even a small initial increase in agents' beliefs about g_t can translate into a large increase in the expected long-run level of the terms of trade. To illustrate this, the right panel of Figure 4 shows the actual path of the terms of trade as well as agents' expectations about the evolution of the terms of trade calculated in the period when the shock hits, as well as after five and nine quarters. Although agents initially attribute only a small portion of the shock to the permanent component, agents initially believe that this small permanent shock is ultimately expected to leave the terms of trade 0.8 per cent above its initial level. In subsequent quarters, as the terms of trade starts to fall, agents revise down their expectations, but continue to believe that some of the increase in the terms of trade will be permanent. This explains why, in the incomplete information case, agents in the economy feel less urgency to work and save more in the near term to take advantage of the high terms of trade than they do in the full information case.

4.1.2 Permanent terms of trade shocks

Turning to the permanent shock, Figure 5 shows the economy's response to a one standard deviation shock to ε_g. The shock increases the terms of trade by 0.2 per cent on impact, and accumulates over time so that the terms of trade ultimately settles at around 1 per cent above its initial level. Focusing first on the incomplete information case, output and investment both increase following the shock. The expansion in output is initially small and accumulates over time. In contrast, the initial investment response is large, and then diminishes. While output and investment increase permanently following the shock, employment eventually returns to trend. It takes a long time to do so, however, and 15 years after the shock employment remains above trend. Consumption initially responds little to the shock, but then increases over time. Since the investment boom is larger than the increase in revenue from the higher terms of trade, the economy's trade balance decreases for some time following the shock, although it ultimately increases once the investment boom passes.

Once again, it is informative to examine the economy's response to the shock under full information. In this case, employment and output both decrease following the shock and only return to their initial level after two years. Following that, however, the response of output in the full and incomplete information cases are broadly similar. In contrast, the investment boom is larger than under incomplete information. This reflects the fact that, when agents are confident that the terms of trade will increase in the future, they are more willing to make long-term investments today. Agents also increase consumption by more under full information. A stronger response of consumption and investment, and weaker response of output, translates into a larger initial decline in the trade balance. This is offset by a stronger increase in the trade balance in future years.

Figure 6 shows agents' beliefs about the composition of the permanent shock under incomplete information. Agents make substantial errors in interpreting this shock. Initially, they attribute most of the increase in the terms of trade to changes in its transitory component. And even as the terms of trade increase further in future periods, agents continue to attribute only a small proportion of these changes to innovations to the persistent component of the terms of trade. Indeed, immediately following a permanent shock agents' expectations about the future evolution of the terms of trade (shown in the right-hand panel of Figure 6) aren't substantially different from their beliefs following a transitory shock. Agents expect that most, but not all, of the initial increase in the terms of trade will be permanent. As the terms of trade rise further in the future, agents revise up their estimate of the long-run level of the terms of trade. But they still fail to forecast subsequent increases. Or, put another way, the high estimated standard deviation of the noise shock means that agents struggle to distinguish between persistent and transitory terms of trade shocks in real time.

4.1.3 Noise shocks

As a further exercise, Figure 7 shows the response to a noise shock. Although it is difficult to assign a structural interpretation to this shock, it can be thought of as a signal that the terms of trade will increase permanently that ultimately proves to be unfounded. Agents respond to a noise shock because they cannot be sure that it is not genuine. In particular, agents consume more in anticipation of higher future income and invest more in anticipation of higher prices for their output in the future. In the near term, they also work and produce less, expecting that future increases in export prices will make such a decrease in production sustainable. Agents fund their additional consumption and investment by borrowing from abroad. This translates into a decrease in the trade balance. When they realise that the signal was misleading and that the terms of trade will not increase, agents are forced to draw back on consumption, and to work and produce more to repay their accumulated foreign borrowing.

Although one must be cautious about interpreting this shock, it is interesting that the behaviour of the economy is similar to that of an economy running a ‘bad’ current account deficit, of the type described by Blanchard and Milesi-Ferretti (2009), in which private saving decreases in anticipation of an income boom that does not occur.^[14]

4.2 Implications for Volatility

The previous section demonstrated how incomplete information alters the macroeconomic effects of permanent and transitory terms of trade shocks. In light of these results, one might wonder whether incomplete information makes the economy more or less sensitive to terms of trade shocks. Specifically, if agents have incomplete information about the persistence of terms of trade shocks, is the variance of macroeconomic variables higher or lower and do terms of trade shocks contribute more or less to macroeconomic volatility?

One can imagine why either outcome might be possible. Under incomplete information, agents' forecasts of future terms of trade movements are likely to be less accurate than if they have full information. As agents in the model make consumption and investment decisions in a forward-looking manner, these mistakes may force them to adjust their consumption patterns and expand or contract their investment projects. Moreover, under full information, agents do not respond to terms of trade noise shocks. On the other hand, the impulse responses in Figures 3 and 5 suggest that the response of output, consumption, employment and the trade balance to both transitory and persistent terms of trade shocks is more muted under incomplete information than it is under full information, although the investment response appears more volatile.

It turns out that, at the estimated parameter values, the model suggests that incomplete information reduces macroeconomic volatility and diminishes the importance of terms of trade shocks as a source of macroeconomic fluctuations. We can see this in Table 3, which compares the standard deviations of the growth rates of output, consumption, investment and the trade balance in the data and in the model. Under incomplete information, the model suggests a degree of macroeconomic volatility broadly comparable to that seen in the data. Under full information, the standard deviation of output growth increases by around a quarter, while the volatility of consumption growth and the trade balance double. In contrast, the volatility of investment increases under incomplete information.

The intuition for this result comes from the fact that, under full information, transitory terms of trade shocks cause large changes in the timing of production and consumption, but comparatively modest changes in investment. If agents expect that an increase in the terms of trade will be temporary, they will work and produce more to maximise income while prices are high. In contrast, permanent shifts in the terms of trade induce smaller intertemporal changes in production and consumption.^[15] However, when agents are unable to observe the persistence of shocks, they react more cautiously to temporary terms of trade shocks. As the measured variance of these transitory shocks is high, this caution reduces macroeconomic volatility. The increase in the volatility of investment in the incomplete information case is largely due to the existence of capital adjustment costs in the model. Under full information, agents are unwilling to pay these costs in response to temporary shocks and will choose a smooth path for investment in response to permanent shocks. In contrast, imperfectly informed agents will invest more during transitory terms of trade booms and, after initially under-investing during the early stages of persistent booms, will increase investment rapidly when commodity prices remain high.

Table 3 also shows the proportion of the variance of each of the variables explained by terms of trade shocks.^[16] Under incomplete information, terms of trade shocks explain a relatively modest proportion of the variance of output and consumption, but a large proportion of the variance of investment and the trade balance. Terms of trade noise shocks also account for a large portion of the variance of consumption and the trade balance. In the absence of noise shocks, the terms of trade becomes a much more important driver of the variances of output growth and consumption and a smaller driver of investment. The contribution of terms of trade shocks to the variance of the trade balance also increases. There is also a change in the relative contribution of transitory and permanent terms of trade shocks, with the relative contribution of permanent shocks to investment increasing and to the trade balance decreasing.

These results help to reconcile the conflicting results of Broda (2004) and Mendoza (1995) regarding the importance of terms of trade disturbances as a source of macroeconomic fluctuations. The baseline results correspond to Broda's finding that terms of trade shocks explain a relatively modest proportion of output volatility. In contrast, the results under the assumption of full information are much closer to those in Mendoza, who also assumes that agents have full information about the persistence of terms of trade shocks.

Footnotes

In log-linear terms, , so that the CPI is proportional to the terms of trade in this model. The transitory terms of trade shock increases the CPI on impact, but agents expect deflation in subsequent periods as the terms of trade decline. [10]

It should be noted that while this mechanism is general, the sign and magnitude of the consumption response are sensitive to the parameterisation of the utility function. For example, in a similar model, Mendoza (1995) assumes an intertemporal elasticity of substitution of 2.6, which causes consumption to increase following a transitory terms of trade shock. [11]

To calculate the response under the full information case, I use the parameter estimates from Table 2 but set the standard deviation of the terms of trade noise shocks, σ_h, equal to zero. In Section 6 I re-estimate the model parameters under the assumption of full information. [12]

Letting the symbolˆrefer to agents' beliefs about the components of the terms of trade, the sum of and does not equal the change in the terms of trade because agents also adjust their beliefs regarding following the shock. Specifically, on impact, is equal to around −0.8, so that . [13]

Examining the behaviour of household and firm expectations in the lead up to balance of payments crises to see whether this mechanism is empirically relevant would be a useful avenue for further research. [14]

Permanent shifts may, however, cause changes in the sectoral composition of output, for example between the tradeables and non-tradeables sectors or among tradeable industries. Examining these changes is not the focus of this paper and is left for future research. [15]

The remainder of the variance not explained by terms of trade shocks is explained by productivity. [16]