Core Equation Structure

Each of the six countries/regions in GPM6 has a core set of behavioral equations specified to capture linkages between key macro variables, namely output, inflation, interest rates and exchange rates. Output, inflation and real interest rates are specified with reference to their steady-state equilibrium values. Leads and lags of selected variables are specified to capture the dynamic adjustment process. There is also a broad distinction between the modeling of G-3 and non-G-3 economies in the model, particularly with respect to the treatment of financial conditions - output in G-3 economies can be effected by episodes of domestic financial tightening/easing, whereas output in non-G-3 economies is not modeled to incorporate such a domestic channel (foreign financial shocks do have an effect on non-G-3 growth, however).

The output gap in each of the G3 countries is affected by deviations of the medium-term real interest rate (RR_t−1) from its equilibrium value $\left({\overline{RR}}_{t-1}\right)$, the four-quarter moving average of deviations of the real effective exchange rate (REER_t−1) from its equilibrium value $\left({\overline{REER}}_{t-1}\right)$, foreign demand (Ω_t),³ financial conditions (θ_t, known in the GPM as ‘bank lending tightening (BLT)’), commodity prices (κ_t) and two disturbance terms (${\epsilon }_t^{yy}$ and ${\epsilon }_t^y$):

Next, the inflation process (π_t) in the model is affected by the output gap, the four-quarter moving average of the real effective exchange rate gap $({REER}_t-{\overline{REER}}_t)$ and a disturbance term $\left({\epsilon }_t^{\pi }\right)$ as is the case elsewhere in GPM. Inflation dynamics are determined by a combination of backward- and forward-looking components which implicitly captures the underlying expectations-formation mechanism, together with rigidities in the price-setting process:

The monetary authority in a ‘standard’ block of the model adjusts the nominal short-term interest rate to ensure that inflation reverts to its target rate over time. The monetary policy reaction function is specified using an inflation-forecast-based rule that has an interest-rate smoothing component:

where RS_t is the short-term nominal interest rate, ${\overline{RR}}_t$ is the equilibrium short-term real interest rate, π4_t+3 is expected inflation (in year-on-year terms), π_target is the inflation target, y_t is the output gap, and ${\epsilon }_t^{RS}$ is a disturbance term.⁴

Turning to the exchange rate, uncovered interest-rate parity (UIP) links deviations in domestic and foreign interest rates to the expected change in the exchange rate. For all countries in the existing GPM6 model, the expected change in the exchange rate is determined by the forward solution of the model. This ensures that interest-rate differentials are consistent with exchange-rate changes projected by the model. The expected change in the exchange rate is determined by a combination of backward- and forward-looking components:

where (LZ) is the real bilateral exchange rate (viz. the USD), ${\epsilon }_t^{UIP}$ is a disturbance term, and LZ^e is a blend of the model-consistent expectation of LZ and a lag:⁵

This hybrid approach in modeling exchange-rate expectations in GPM allows us to capture better the dynamics of how exchange rates adjust empirically.

Modeling the Exchange-rate Regime

Beginning with the treatment of the exchange rate, we model the choice of exchange-rate regime as a policy variable in the following way:

Where ${LS}_{UIP}^{CH}$ is defined by:

So, ${LS}_{UIP}^{CH}$ is the nominal bilateral exchange rate that would prevail in order for uncovered interest-rate parity to hold at time t. Thus, policymakers can allow the nominal exchange rate $\left({LS}_t^{CH}\right)$ to float freely, in which case they follow the UIP condition (η_CH set equal to 0) as is the case elsewhere in the GPM, or can opt to manage the nominal exchange rate (η_CH non-zero). At present, η_CH is set equal to ⅔, thereby assigning a relatively large weight to exchange-rate management, while still allowing some fluctuations/pressures due to UIP.⁷

The path for the desired exchange rate $\left({LS}_{p,t}^{CH}\right)$ is assumed to be determined by the following equation:

This equation states that policymakers adjust the appreciation/depreciation of their desired nominal rate $\left({LS}_{p,t}^{CH}\right)$ according to two factors – first, they would allow any change in the bilateral equilibrium real exchange rate, $\mathrm{\Delta }{\overline{LZ}}_{t+1}^{CH}$ (adjusted for differences in the inflation target), to be passed through into the nominal rate. Secondly, they could accelerate (slow) the amount of appreciation if the output gap were to be positive (negative) according to the term ${\zeta }_{CH}{y}_t^{CH}$. In the current version of the model, we calibrate this term to be 0.2, which implies that the exchange-rate response to the output gap is modest.

Modeling Monetary Policy

In addition to treating the exchange rate as a policy lever, we also need to consider other mechanisms employed by policy makers in China. As in other blocks of the GPM, nominal interest-rates are one such mechanism. However, in the China block of the model nominal rates are not set in the same manner as elsewhere in the model (solely in response to inflation and output); this is done in order to alleviate pressure on the exchange rate coming through the UIP channel. More specifically, we begin with a similar rule as we have for the exchange rate, in which interest-rate policy can be chosen according to the following equation:⁸

As we saw in the previous subsection, the UIP condition has been modified somewhat from the specification in other work on the GPM:

In particular, there is no longer a shock term associated with this equation $\left({\epsilon }_t^{UIP}\right)$. Instead, shocks enter the ${LS}_p^{CH}$ and ${RS}_p^{CH}$ equations directly.

Returning to equation (10), interest rates can: (i) respond freely so as to allow UIP to hold, which can be thought of as alleviating pressure on capital flows (ν^CH = 0); (ii) be set completely independent from what would be dictated by UIP and the exchange-rate policy (ν^CH = 1); or (iii) be set using some combination of the two approaches. In the present calibration of the model, we set ν^CH = 0.8, thereby allowing considerable autonomy in setting interest rates in response to domestic factors without great concern for the implications for the exchange rate. This parameter value yields sensible model properties, which broadly capture the recent dynamics of monetary policy decisions in China. Notionally, this equation can be thought of as suggesting that capital controls bind in China, but not completely, and so policy rates are set with some deference to the implications of exchange-rate policy for capital inflows. In fact, in recent years sterilization measures have been quite effective at curbing inflationary pressures associated with capital inflows (Ma, Xiandong, and Xi 2011). This has allowed interest rates to be set in response to domestic inflation and output, without too much concern for the implications for the managed exchange rate, and thus tends to support the calibrated value for ν^CH adopted here.

The policy-rate decision rule is similar to what appears elsewhere in GPM:

As in the other blocks, rates respond to deviations of expected inflation from some target and the output gap, and display some inertia. The calibrated parameter values in this equation (presented in the appendix) are meant to reflect the notion that: i) rates are somewhat less inert in China than in the G-3 countries; ii) the policy response to inflation is somewhat weaker than in the EU, but slightly above that in the US and Japan; and iii) the response to the output gap is also slightly weaker than in other blocks of the model. This last point partly reflects the fact that China is modeled as having multiple monetary-policy instruments at its disposal to smooth out fluctuations in its economy.

Unlike other economies in the GPM, monetary policy in China does not rely as heavily on the setting of nominal interest rates. As documented in Liu and Zhang (2010), and Laurens and Maino (2007), authorities in China rely on a mix of instruments when setting policy, including benchmark lending and deposit rates (proxied in our model by the nominal interest rate equation documented above), open-market operations, moral suasion, and the reserve-requirement ratio (REQR). In recent years, the REQR has gained favor as an instrument to sterilize the domestic money base from inflows associated with the exchange-rate regime, as discussed in Ma, Xiandong, and Xi (2011) and elsewhere. Indeed, as shown in Figure B (Appendix I), reserve requirements have been adjusted at much higher frequencies since 2005 or so in response to policy objectives. With this instrument playing an increasingly important role in describing the stance of policy in recent years, we include the following decision rule for the reserve-requirement ratio in this model:⁹

As with the interest-rate rule, ${REQR}_t^{CH}$ responds to expected inflation, the output gap, and it is a somewhat inert process. In addition, shocks to the interest rate will be accommodated by the REQR, to some degree, according to ${\nu }_4^{CH}({\epsilon }_t^{{RS}_{p,t}^{CH}}+{\epsilon }_t^{{RS}^{CH}})$. The calibrated parameter values in this version of the model place equal weights on the output gap and inflation deviations from target, and REQR is modeled as being slightly less inert than the interest rate.

Modeling Output and Inflation

Ultimately, the three policy measures described above affect output in the following way:

Where,

So, the output gap in China is driven by a host of factors similar to those found elsewhere in the GPM, including oil prices (represented by ${\kappa }_t^{CH}$),¹⁰ the real effective exchange-rate gap, spillovers from foreign demand $\left({\mathrm{\Omega }}_t^{CH}\right)$, own leads and lags meant to capture expectations, habit persistence, etc. However, unlike in other country blocks, there are two policy variables that influence output - interest rates, and the reserve-requirement ratio. As in other emerging market economy blocks in the GPM, output is calibrated to display less inertia (lower value for ${\beta }_1^{CH}$), and there is a relatively important role for movements in the real exchange rate (higher value for ${\beta }_4^{CH}$) given that China is an open economy. The role of oil prices is similar to what is found in other GPM models - higher prices depress activity in the short run, given the relatively price inelastic nature of demand for oil by both producers and consumers. Foreign demand impacts China’s output gap in the same way as in GPM6 (through both the foreign output gap, and also foreign shocks $\left({\epsilon }_t^{yy}\right)$. However, although the structure of how spillovers work in the model is the same as in previous versions of the GPM, the calculation of the spillover coefficients (ω_i,j) has been changed slightly, for all countries in the model. The new spillover-calibration methodology is presented in Appendix VI.

The inflation process in the China block of the model also differs from the GPM6 setup (equation (2) above) in several ways. First, we model three components of inflation, namely core inflation ${\pi }_t^x$, domestic gasoline inflation ${\pi }_t^g$, and consumer food inflation ${\pi }_t^{\mathrm{cf}}$. ¹¹ Because of a lack of time series data on the weights of gasoline and food on the CPI basket, the respective weights are constant over time and calibrated to be 3 percent for gasoline ${\lambda }_2^s$ and 32 percent for domestic food $(1-{\lambda }_1^s-{\lambda }_2^s)$.¹² A shock to headline inflation $\left({\epsilon }_t^{\pi }\right)$ was added to capture measurement errors associated with these constant weights.

Second, we model the Phillips curve for core inflation as follows:

The most notable departure from the standard GPM setup is that we include the inflation target $\left({\pi }_t^T\right)$ on the right-hand side of the equation. This allows us to replicate better the inflation dynamics observed over the sample period (inflation has been remarkably well anchored throughout the sample period in China, despite some variation on other determinant variables). In our assessment, the behavior of core inflation over the sample period is at least partly a product of China’s large pool of surplus rural labor, which has likely held down industrial wages for much of the past decade (Das and N’Diaye, 2013). The other feature of the Phillips Curve equation in the China block of the model that is unique is the inclusion of both the four-quarter moving average of the real exchange-rate gap (as done elsewhere in the model), and the change in that gap. This last term was added to capture better the core inflation dynamics observed in the data.

Third, we assume that the domestic prices for gasoline and consumer food follow a simple structure: in the long run, those prices depend on crude oil costs, international food prices, taxes and other factor input costs as well as markups. Domestic prices for gasoline $\left({\pi }_t^g\right)$ and consumer food $\left({\pi }_t^{cf}\right)$ depend on movements in international prices $({\pi }_t^{oil\_d};{\pi }_t^{cf\_d})$, measured in domestic currency and other inputs costs such as labor, which we assume move in tandem with the inflation target $\left({\pi }_t^T\right)$.

We also allow for shocks to these prices $({\epsilon }_t^{{\pi }^g};{\epsilon }_t^{{\pi }^{cf}})$, which enter the equation with a negative sign, to better capture the intuition that a positive supply shock reduces gasoline/food prices and is good for economic activity. The parameter ${\iota }_2^g$ for gasoline is calibrated to be lower in China than in advanced economies, which is meant to capture the small pass-through from crude oil prices due to the regulatory structure of domestic gasoline prices in China. Domestic food prices, however, are assumed to follow international food prices more closely, with an important role for domestic shocks.

Modeling Commodity Prices in a Global Setting

Given China’s significant demand for commodities (in particular, oil and metals), this block of the model warrants further explanation. The block of real commodity prices for a generic commodity named Q, representing oil prices, food prices or metals, is defined by the following structure:¹³

The price at the world level of commodity, $Q_t^w$ (in logarithms and measured in US Dollars), is equal to the sum of the equilibrium level of its real commodity price, $\overline{Q_t^w}$, and the gap between the level of real prices and its equilibrium value q^w.

Then, the equilibrium value follows a simple stochastic process equal to its lagged value, the growth rate and a disturbance term representing shocks to the level of oil prices, ${\epsilon }_t^{\overline{Q^w}}$.

The growth rate is equal to lagged growth plus a term that links real commodity prices to potential GDP growth in the world, ${\iota }_4^Q{gspill}_t$ and a disturbance term representing shocks to the growth rate.

The gap in commodity prices is equal to its lagged value plus the effect of world output gap plus and a disturbance term.

In the case of oil, the calibration of ${\iota }_2^Q$ follows empirical studies which indicate that a one percent permanent decrease in the level of global output would reduce the world price of oil by about 9 percent in the short run and 3 percent in the long run.¹⁴ The price response is tempered over the longer term as firms cut back investment in oil production over time and consumers and firms substitute to less expensive energy options. For the cases of world metal and food prices, the calibration reflects the fact that these prices tend to be much less sensitive to changes in demand, and thus ${\iota }_2^Q$ is considerably lower. In the baseline calibration of GPM the price elasticity for oil is three times the magnitude of that for metals and nine times that for food.¹⁵

Stochastic Processes

As is done elsewhere in the GPM, we specify stochastic processes that govern the path of the unobservable variables in the model. The most important processes (those for potential output, the equilibrium real interest rate, the equilibrium reserve-requirement ratio, and the equilibrium real exchange rate) are largely the same as those used in previous GPM work (Carabenciov and others, 2008). These are presented in Appendix IV.

Impulse-Response Functions

When constructing a model to be used for policy analysis, arguably the most important consideration is the model’s properties, in particular the response of the model to shocks applied around the steady state. These responses are critical, since the behavior of the model in a projection or simulation environment will simply reflect the combined effect of the shocks applied to the model. If the results from simple simulations around the steady state are not intuitive, the model is of no use to policy makers since one cannot understand the channels through which a change in the outlook/scenario has come to pass. To ensure that our model is sensible, we scrutinize a set of impulse-response functions (IRFs) for the major shocks in the new China block of the model.

First, we consider a simple (one quarter) positive Chinese demand shock. Shown in Figure 1 (Appendix II), the shock increases demand by about one percent on impact - since this is a pure demand shock, and there is no response of supply/potential, the impact on the level of GDP and the output gap is also one percent. In response to this shock, and its impact on the output gap, inflation rises by slightly under ½ a percentage point. Given the deviations of output and inflation from their equilibrium and target levels, respectively, policy tightens to restore equilibrium. In China, this entails the use of several instruments simultaneously: first, the policy rate increases, by about 100 basis points. Second, the reserve-requirement ratio also rises, and also by about 100 basis points. Finally, the nominal exchange rate is allowed to appreciate slightly, though this happens only gradually over several quarters, which is consistent with the observed behavior of policy makers in China, who allow only sluggish changes in this rate. In the quarters following the shock, as the output gap returns to target and inflationary pressures subside, policies return to neutral.

Also of interest is the response of oil prices - this positive demand shock in China entails increased demand for commodities, which pushes up the real oil price. The demand shock, and subsequent impact on commodity prices, also has implications for growth in other regions of the model. Figure 2 shows the impact of this same Chinese demand shock on growth in the other regions of the model. Not surprisingly, the largest effect is on the Emerging Asia block, given the important trade linkages between these countries and China. The next most important recipient of spillovers is Japan, given its integration in the region. Also of note are the small responses of the US, and euro area. Given that Chinese demand for US/EU exports is fairly limited, and both the US and EU are relatively large, relatively closed economies, this result appears sensible.

As for the response of demand in Latin America, there is a modest positive impact of the increase in Chinese demand, despite limited trade linkages between these two economies – this result comes from the increase in commodity prices associated with higher Chinese demand, which is a favorable development for the commodity-exporting countries in the Latin America block of the model.

Next, we examine a core-inflation shock in the China block of the model in Figure 3. Here, the shock is negative, with quarter-on-quarter inflation falling by one percentage point on impact. Given the relatively mild persistence in this process specified in the Phillips curve equation, inflation returns to target relatively quickly. Of course, policy also plays a role here, acting quickly to provide stimulus (lower policy rate and reserve-requirement ratio) thereby opening up a very slight positive output gap which aids the smooth transition of inflation back to target. As in the previous IRF, the slight increase in demand (this time generated endogenously as a result of looser policy, rather than by an exogenous shock) boosts oil prices slightly.

Although the role of monetary policy in the model (interest rates and reserve-requirement ratio) can largely be understood from examining the first two simple IRFs, we nevertheless proceed to examine an exogenous shock to each of these in turn. Beginning with the interest-rate IRF, in Figure 4 we see that for a 100 basis point exogenous increase in interest rates, the output gap is depressed by about 1/3 pp, at the trough. Note that it takes several quarters for the increase in the interest rate to have a noteworthy effect on output, which is consistent with the well-established concept that there is a lag in the transmission of monetary policy to the real economy. This policy shock also dies out somewhat slowly due to the inertia in the policy rate equation. The rest of the results in this Figure are as described in the previous IRFs: lower output (and hence output gap, given that supply is not responding in this scenario) depressed inflation and oil prices. Following the shock, policy rates actually reverse the initial shock by easing for a period of time, providing stimulus to boost activity and close the output gap.

Turning to the response of the model to a shock to the reserve-requirement ratio, in Figure 5 we see that an exogenous 100 basis point increase in this ratio (which is not attributable to equilibrium/trend developments, and is not accompanied or offset by policy rates) has a fairly limited impact on output, depressing the output gap by only 0.1pp, with a subsequent muted effect on inflation. Exchange rates are essentially held constant.

Finally, we turn to the effect of a policy-induced, exogenous, nominal exchange-rate shock in the model in Figure 6. If policy makers force the nominal rate to depreciate by about 1 percent relative to baseline, output in the model rises gradually, peaking at 0.2 percent above baseline. Counteracting the impetus from the nominal exchange rate depreciation are the responses of the interest rate and reserve-requirement ratio, which increase to return output to equilibrium. In addition, note that the nominal exchange rate is permanently lower, but that this is offset by a higher price level (increase in inflation rates with no subsequent payback) leaving the real exchange rate unchanged once the shock has run its course.

Empirical Fit

Although theoretical coherence is the most important criterion in assessing the validity of a policy model, once this is achieved empirical fit is of paramount importance. To investigate the empirical validity of the changes we have introduced in this version of the model, we compare the model for China documented in this paper with a ‘naive’ specification for China. More specifically, this naive specification for China uses the same equations as found elsewhere in the GPM6. As such, a comparison of empirical fit between this benchmark model and the one we have specified in this paper will provide insights on whether the modeling innovations introduced here (changes to the exchange-rate process, addition of reserve-requirement ratio, and additional anchoring of inflation associated with excess labor supply) do a better job of fitting the data than would the ‘standard’ equations used in the other blocks of the model.

We begin by showing a comparison of the goodness of fit (using root-mean-squared errors) between the two models, over several different forecast horizons (one, four, eight, and twelve quarters ahead), for the key variables in the model (real GDP growth, inflation, interest rates, and the exchange rate) in Table 1 of Appendix III. On balance, the results are quite favorable for the innovations adopted in this paper. In particular, the short-term (one quarter ahead) fit of real GDP growth is dramatically better (‘current’ model’s RMSEs are 0.76 of the ‘naive’ model’s errors), without any notable deterioration in the forecast performance at longer horizons. The fit of the inflation equation is considerably better across all forecast horizons, and the fit of the exchange-rate forecast is remarkably better at all horizons. The lone area in which the model’s forecast performance has deteriorated is for policy rates at longer time horizons.

Figures I-III of Appendix III present the China model’s unconstrained forecasts of real GDP growth, inflation, the exchange rate, and policy rates, beginning in three different time periods: 2009q1, 2010q1, and 2011q1. These plots show how the model would have projected these variables, subject to the information available at the beginning of each time period (in other words, assuming no further ‘shocks’ over the forecast period).

Beginning with the first projection period (2009q1 onwards) in Figure I we see that growth had fallen sharply in China as the global financial crisis was in full swing. In response to this weak growth environment, the model would have suggested that policy rates should be lowered to provide stimulus - in fact, interest rates would have been projected to trough quite near the level at which they ultimately did trough (actual realization of data shown in with a dashed line). The easing in policy conditions would have been expected to generate firmer growth, though the model was unable to predict how rapid the ultimate recovery would end up being - massive fiscal stimulus measures undertaken by policymakers in response to the crisis boosted China’s growth to well over 15 percent (q/q saar - staff calculations) by 2009q2. Given that the model does not include equations to capture fiscal policy, this information was ‘missed,’ thereby preventing the model from capturing the sharpness of the recovery. In light of the model’s expectation that the output gap would take about a year to close, inflation was projected to remain muted. Regarding the exchange rate, the model does not capture the fact that policy makers returned to pursuing a strict peg during the crisis period.

Proceeding to the next forecast period (2010q1 - Figure II), we see that the model would have performed very well on several fronts. First, as a result of a return to solid growth and some gradual improvement in external demand conditions, the exchange-rate peg was once again abandoned in early 2010, and the model’s projection for the exchange rate over the two-year forecast period considered here was quite accurate. Next, the model would have expected policymakers to tighten rates starting in early 2010 in response to strong growth conditions, and this would have been expected to slow activity somewhat in coming years. However, in reality policy was not tightened in China, as authorities chose to allow growth to proceed at a more rapid pace. Although the model struggles to capture the precise dynamics of inflation over the forecast period (a very standard result in projection models, given the volatile nature of this variable), it does capture the broad evolution of inflation over the 2010-12 period very well.

Finally, we consider the forecast period starting in 2011q1 (Figure III). At this point, the property market was expanding rapidly, and authorities were beginning to take measures to cool the economy (raising policy rates and reserve requirements, as well as implementing policies to restrict investment in real estate) and would continue to do so throughout 2011. As we saw in Figure II, the model for China was already calling for moderately tighter policy in early 2010, and so by 2011q1 the model saw the need for much more tightening, given that policy had remained essentially unchanged for much of 2010. Examining Figure III, we can see that the model would have projected somewhat more tightening in policy rates, and somewhat less tightening in reserve requirements than what actually ended up occurring, but the net amount of tightening projected by the model between the two measures seems to have been fairly accurate. As a result of this projected, necessary tightening in policy conditions, growth would have been expected to slow, and inflation would have been expected to ease – the model’s projections over the next two years were quite accurate for both of these variables. As in the forecast that began in 2010q1, the model’s projection of exchange rates over the 2011q1 to 2013q1 period was also quite prescient.