Alternative identification strategies

In Identification strategy 2 (refer Table 3on page 41), the negative restriction on the impact of FTS shock to surplus ratio, which was included in Identification strategy 1, is removed. In place of that, a zero restriction is imposed on the Surplus ratio on impact from the FTS shock. The impact of FTS shock on Real rates is still kept, as it was in Identification strategy 1, at positive for the impact horizon, i.e., the shock period and the next period. In addition, the response of the Surplus ratio in the identification strategy 2 has a Zero restriction on impact from Monetary policy shock as well.

Changes in identification strategy 2 can be summarised in the following way.

An increase in FTS is restricted to a positive impact on Price of risk and Real rates, Monetary policy shock is restricted to have a positive impact on Real rates, and both FTS and Monetary shock are orthogonal to the Surplus ratio.

Whereas, in this strategy, the impact restrictions for TFP shocks are unchanged from Identification strategy 1 and are orthogonal to both FTS and Monetary policy shock. The responses of the variable of interest, which is Investment or any other macro variable, are kept agnostic.

The impulse responses to FTS shocks under Identification strategy 2, which are plotted as dashes in Figure 16 on page 69, are not significantly different from the responses to Identification strategy 1, which are represented by a solid line with its 68% confidence band is shaded in the same fig. 16. The decline in Investments is severe and keeps around -2% for around 10 quarters. The impulse responses in

6 . 1 A lt e r n at i v e i d e n t i f i c at i o n s t r at e g i e s 69

Figure 16: Sensitivity of impulse responses to identification strategies

0 10 20 30

Strategy 1 Strategy 2 Strategy 3

Notes: Sensitivity of impulse responses to FTS shocks under identification with Benchmark Strategy 1 (Solid) with responses from Strategy 2 (Dash) and Strategy 3 (Triangles). Data: 1983:Q1 to 2019:Q3. 68% confidence band of Benchmark strategy is shaded in light green. Y-axis label is percentage points and X-axis label is Time (in quarters) horizon after the shock. ‘Cons (NDur+Svc)’ is Consumption of Non-durable goods and Services. ‘Res’ is residential, ‘Non-Res’ is non-residential, and ‘Rel.Price of Inv’ is Relative price of investment good in terms of consumption good.

key business cycle variables of interest such as hours, output, and consumption are immediate (See Figure 16) and are shaped in an inverse hump. The reduction in Consumption (non-durables and services) and the Surplus ratio is delayed by 2 periods, and the response is now less severe than it was in identification strategy 1. The response of the Surplus ratio stabilizes to pre-shock level as Habits fall in line with Consumption. The median response reaches a minimum of only -0.04%, which is due to the differences in identifying restrictions between Strategy 1 and Strategy 2. More importantly, the response of TFP is muted for around 10 periods and is nearly as severe as it was during the identification strategy 1. This exercise in identification strategy 2 shows that the Surplus ratio restriction was not driving the future decay in TFP. Instead, it further supports the argument that the FTS shocks predate, by a significant period, an imminent fall in TFP.

Identification strategy 3 is different from identification strategy 2 and strategy 1 concerning restrictions based on FTS shocks. The restriction imposed (in strategy 1 and 2) on the real rate response to be less than zero on the FTS shock impact is removed, and this variable is made unrestricted to the FTS shock. But the zero restrictions to TFP and Surplus ratio variables are kept, as they were in Identification strategy 2. Therefore Price of risk (Bond minus Equity prices) is the only variable that is restricted to increase on the impact of a positive FTS shock.

The impact restrictions for TFP shocks are unchanged and are kept the same as they were in identification strategy 1 and identification strategy 2. The monetary shock has restrictions for only the Real rate to be positive for the impact period (shock period and the next period) horizon and has zero restrictions on the impact of the TFP series and the Surplus ratio. The impact response from the variable of interest is unrestricted and kept agnostic.

Thus Identification strategy 3 is a way to distinguish between the responses of FTS and Monetary Shocks. By removing the restriction on Real rate upon the impact of FTS shocks, we would like to ascertain if the shocks that we have identified are FTS shocks and are not driven by some exogenous shocks that impact both FTS and Monetary policy shocks similarly.

The results from identification strategy 3 are represented by triangles in Fig-ure 16 on page 69. They differ from our findings from the results of the first 2 identification strategies. Once we take out the impact restriction on Real rate to be positive for an FTS shock, the real rates’ median response is only slightly pos-itive +0.1% on impact, whereas the fall in CPI upon impact from the FTS shock is -0.2%. This result should not be puzzling as it shows that the jump in Real