15 On the Sources of Inflation in Kenya A Model-Based Approach

Andrew Berg, and Rafael Portillo
Published Date:
April 2018
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Michal Andrle, Andrew Berg, R. Armando Morales, Jan Portillo and Rafael Vlcek 

1 Introduction

Central banks in sub-Saharan Africa (SSA) have had a mixed inflation performance in recent years.1 On the one hand, since the early 2000s many countries in SSA have succeeded in re-anchoring inflationary expectations, reducing median inflation in the region from 15 per cent in 2000 to 6 per cent in 2006. As described in Chapter 1, this has taken place in the context of fiscal-based stabilization efforts, in which many countries adopted policy regimes centred on targets for reserve and broad money. While de facto flexibility was and has always been the norm—money targets are frequently missed in either direction—the adoption of such targets was meant to signal that the central bank was ‘holding the line’, i.e., that stabilization efforts were on track and that fiscal pressures on monetary policy were contained.

On the other hand, more recently SSA has experienced large swings in inflation.2 To a large extent, this reflects external factors. The region has been buffeted by large external shocks, starting with the first food and fuel crisis of 2007–08, spillovers from the global financial crisis in 2008–09, and the spike in commodity prices in 2010–11. However, an important question is the role that monetary policy may have played during these episodes, relative to the external factors. This is of particular importance to policymakers, as there is an acknowledgement that existing frameworks, with their emphasis on money targets and money target misses, have not provided a useful framework for thinking about external shocks and the role that policy may have played in amplifying them. In this chapter, we apply a model-based approach to answer this question, with an application to Kenya.

Central banks in advanced and emerging markets make use of a variety of models to study these types of questions. These models are typically New Keynesian, which embody the fairly general view that aggregate demand and monetary policy matter for output dynamics in the short run. At their core, they consist of a forward-looking IS equation, a hybrid Phillips curve, a monetary policy rule, and an uncovered interest parity equation.3 An important feature of these models is the emphasis on gaps in output and the real exchange rate—deviations between observed values and trend or potential components—as drivers of inflation. Considerable effort therefore goes toward distinguishing gaps from trends.

Our emphasis in this chapter is on disentangling the role of external factors versus the contribution of monetary policy decisions (and other domestic factors) in the dynamics of food and non-food inflation. To that end, we extend the standard framework by introducing two separate Phillips curves, one for food and one for non-food. The disaggregation requires that special attention be paid to various relative food prices: both the domestic and the international relative price as well as the deviation between the two. It also calls for a careful treatment of trends in these relative prices, which we explicitly undertake here, for two reasons. First, trends in relative prices have implications for the consistency between sectoral inflation rates and the inflation target (toward which headline inflation eventually converges). Second, deviations between relative prices and their trend becomes an important source of inflationary pressures, both sectorally and in the aggregate, as these gaps enter the Phillips curves directly.

The Kenyan case is representative of the challenges SSA countries have faced in recent years. As Figure 15.1 indicates, Kenya experienced large swings in inflation, first increasing to 16 per cent in mid-2008, falling back to under 4 per cent in mid-2010, only to increase again to almost 20 per cent at the end of 2011. While movements in international food prices account for some of these fluctuations, monetary policy may have also played a role, with short-term interest rates falling from 6 per cent in 2009 to about 1 per cent by early 2011.

Figure 15.1.Food and Non-food Inflation, Kenya

We filter selected macroeconomic data from Kenya through the model, in order to recover a model-based decomposition of most series into gap and potential/trend components. The filtration exercise also serves to recover the sequence of macroeconomic shocks that, according to the structure of the model and our own view of recent history, account for business cycle dynamics over the last few years. This allows us to discuss the quantitative significance of various factors (international shocks, monetary policy) in explaining inflation developments. This process is iterative: as we have a prior opinion on the relative importance of various shocks, we repeat the filtration to adjust the calibration of the model until a consistent view of the economy emerges; this iteration also helps us adjust our own views in light of the empirical evidence.

Our results are the following. We find that imported food shocks have accounted for some of the inflation dynamics in Kenya, both in 2008 but also recently. Domestic food shocks (harvest shocks) were also relevant. However, we also find that accommodative monetary policy played an important role, both in 2007–08 and more recently. In 2007–08, the CB experienced ‘good luck’: domestic inflationary pressures were compensated by disinflationary forces associated with the global recession, without a need for tightening. The 2011 inflationary spike was different, in that such forces were not present.4

We also find that the difference between actual short-term interest rates and what would be predicted on the basis of an interest rate rule provides a useful measure of the stance of policy, even in a country such as Kenya, which at the time did not have a meaningful policy rate to signal the stance of policy and was a de jure money targeter. This policy measure helps identify episodes of policy loosening, which subsequently resulted in large increases in inflation. Using monetary policy statements, we argue that the excessive accommodation stemmed to a large extent from pursuing monetary objectives, namely credit growth.

There has been very little work in applying these types of models to study inflation in low-income countries.5 It is sometimes argued that these models do not adequately capture the structure of these economies and the monetary transmission mechanism in place. Our results show otherwise, in that a careful application of these models can yield useful insights that are relevant for policy analysis.

The chapter is organized as follows. Section 2 introduces the model. Section 3 applies the model to Kenya. Section 4 discusses some possible reasons behind the monetary policy response in recent years and the validity of our model-based analysis for Kenya. Section 5 concludes.

2 The Model

In this section we describe the model. In terms of general notation, for any given variable x a bar (x¯) denotes that variable’s trend or potential value. A gap term added to the variable (xgap) denotes deviation from trend or potential. A delta (Δ) in front of the variable indicates changes from one period to the next, except for inflation rates, which are denoted with a π. Finally, an asterisk * denotes a foreign variable.

Before presenting the model it is useful to briefly mention its properties. The model is structural, in that each equation has economic interpretation, and general equilibrium, in that the model’s equations jointly determine the dynamics of inflation, output, short-term interest rates, and the real exchange rate. It is also stochastic: the system of equations is subject to various shocks, the variance of which can help derive measures of uncertainty in the baseline forecast. Expectations of future variables matter for macroeconomic outcomes and are rational, in the sense that they depend on the model’s own forecast. Despite these somewhat complex features, the core economics embedded in the model are simple: aggregate demand and supply shocks drive inflation but monetary policy provides the nominal anchor.

2.1 Price Indices and Relative Prices

We begin by defining price indices and various relative prices. First, the headline price index (ptcpi, all prices are in logs) is the weighted sum of food (ptf) and non-food prices (ptnf):

where w is the weight of food, πt is the quarterly inflation rate (annualized) and πt4 is the year-on-year inflation rate.

The first relative price is the domestic price of food relative to non-food:

The second relative price is the domestic price of food relative to the international price of food measured in local currency:

where pt*f is the international price of food (in dollars) and st is the nominal exchange rate (shillings per dollars). devt measures the extent of the deviation between domestic and foreign food prices. As will be shown later, whether this deviation creates pressures for domestic food price inflation—in order to catch up with international prices—depends on whether the deviation reflects temporary or long-term factors.

The third relative price is the international price of food relative to the international CPI (pt*cpi):

The fourth relative price is the real exchange rate, which is given by the international CPI (measured in domestic currency) minus the domestic CPI:

Note that, by construction, all four relative prices are related, as follows:

The above relation also holds for the gaps and trend components of these relative prices. For reasons that will become clear later, we also define two alternative real exchange rate measures, a food and a non-food real exchange rate. Each of these relative prices can also be derived using zt and rlpt:

2.2 Trends in Relative Prices

All relative prices are decomposed into gap and trend components:

We only need to define stochastic processes for three relative price trends, as trends for the other relative prices will follow from the above relations. We assume first-order autoregressive processes in first (annualized) differences for the domestic relative price of food (rlp), the international relative price of food (rlp*), and the real exchange rate (z):

The above specification merits two comments. First, the trend value of devt(dev¯t) will drift, as implied by the stochastic trends of rlpt, rlpt*, and zt. This drift implies the long-run value of domestic food prices is unrelated to the long-run value of international food prices: trend changes in international relative food prices rlp*¯t will simply result in an equal and offsetting increase in dev¯t, without any implication for trend changes in domestic relative food prices rlp¯t. This is a stronger assumption than lack of cointegration. While this disconnect may seem extreme, it only applies to long-run movements in relative prices and not to gap movements, which—as we will see—account for much of the dynamics in international food prices in the last few years. As will be shown below, it is also based on the observed trend movements in devt.

Second, the existence of relative price trends has implications for the inflation rates of certain price indices, even if the inflation rate for the headline index is (eventually) determined by the inflation objective. As the relative price of food is either growing or decaying along a stochastic trend (depending on the sign of Δrlp¯t), nominal food prices will tend to grow at a different rate than non-food prices. Specifically, for any time-varying inflation objective π¯t, implicit targets for food and non-food inflation must be as follows:

In addition, the long-run (annualized) nominal rate of depreciation must be consistent with the process for trend real exchange rates and domestic and foreign inflation targets:

2.3 Output and Real Interest Rates

Quarterly (non-agricultural) output is divided into its gap and potential components,

where potential output follows a random walk with time-varying drift gt:

Thus there can be both i.i.d. and persistent shocks to the growth rate, which allows for more flexibility in matching the data. The output gap is given by a hybrid IS curve. It depends on real monetary conditions (rmc) and foreign demand (ygap*), as well as past and future output gaps:

Real monetary conditions are composed of the real interest rate gap (rrgap)—the difference between actual real interest rates (rstEt(πt+1cpi)) and neutral real interest rates (rr¯t)—and the real exchange rate gap:

Note that neutral rates follow an AR(1) process:

2.4 Phillips Curves

We introduce two Phillips curves: one for non-food prices and one for food prices. The non-food Phillips curve is of the form:



This specification allows temporary changes in imported inflation to have a direct effect on non-food inflation, as captured by the term λ2(πnf,timpπ¯timp). It also makes non-food inflation sensitive to expected future and lagged changes of itself, as well as changes in real marginal costs in the non-food sector (rmctnf). These are given by a weighted sum of the domestic output gap and the real exchange rate gap in terms of non-food prices.6

The Phillips curve for food prices has a similar structure:


In addition to a potentially different calibration, the main difference relative to non-food inflation is that real marginal costs also depend on temporary deviations between domestic and international food prices (devgapt). This extra term implies that temporary increases in international food prices will be inflationary, as they open a gap relative to domestic food prices that will be closed (in part) by increases in domestic food prices.7

2.5 Exchange Rate (UIP)

We assume that uncovered interest parity (UIP) holds:

where premt measures persistent movements in the risk premium associated with holding domestic currency, which follows an AR(1) process with coefficient ρprem, and ϵts measure one-time errors in exchange rate valuation. Real exchange rate expectations are allowed to deviate temporarily from rational expectations:

2.6 Monetary policy rule

We assume that the central bank moves the interest rate in response to endogenous developments in the economy, as follows:

The central bank also specifies a stochastic process for its inflation target:

While this specification may appear surprising—why would the central bank subject its inflation target to persistent fluctuations?—it is meant to capture relatively low-frequency movements in inflation. These movements tend to reflect changes in the central bank’s willingness to tolerate certain levels of inflation and have been proven to capture an important element of inflation dynamics in developed and emerging markets.8

2.7 Foreign Block

The dynamics of the model are complete with the foreign block, a set of six equations that describes the comovement of external variables:

and the process for the trend in the international relative price of food described earlier. Note that international food inflation is given by πt*f=πt*cpi+Δrlpt*.

3 Applying the Model to Kenya

Having described the model, we now present various model-based exercises for Kenya. We begin by describing Kenya’s recent experience. We then discuss the calibration and our dataset. We provide impulse response functions for selected shocks, and conclude with the filtration exercise, with an emphasis on two related issues: the decomposition of macro-variables into their trend and gap components, and the historical decomposition of recent business-cycle dynamics in Kenya by the relevant shocks.

3.1 Kenya: Inflation Developments and Monetary Policy 2007–11

Kenya has experienced large swings in inflation in recent years. Headline inflation accelerated from around 3 per cent at the beginning of 2007 to 16 per cent by mid-2008, and after having fully reversed by mid-2010, climbed again to almost 20 per cent by the end of 2011. Inflation dynamics were accounted for by both food and non-food (see Figure 15.1). Kenya is exposed to changes in imported food prices: 40 per cent of the total cereal consumption (of about 5 million metric tons, chiefly maize) is imported. This influence can be seen by comparing the Kenyan food price index (measured in dollars) with a price index of international food commodity prices (see Figure 15.2): the two series display considerable comovement, especially during the food crisis.9 Policy challenges were compounded by domestic shocks and the downturn of the global economy in the period 2007–09.

Figure 15.2.Domestic and International Food Prices (in US$)

Kenya’s de jure monetary policy anchor has traditionally been reserve money targeting. It is difficult to characterize the CBK’s de facto monetary policy framework, though there is considerable exchange rate flexibility. It maintained an inflation target of 5 ±2 per cent. Its reserve money targets have often been missed and subsequently adjusted. From 2009 to 2011, reserve growth was consistently higher than targeted, explained by the CBK in terms of its objective of increasing financial intermediation (through higher broad money growth) and thus supporting economic activity.

The effectiveness, or at least transparency, of monetary policy was hampered by the operational framework in place. The CBK maintained a so-called ‘policy rate’, meant to signal the stance of policy (the Central Bank rate, or CBR). In practice, the rate was not relevant for the financial system: sizeable injections of liquidity resulted in a large decline in interbank rates, which fell to 1 per cent while the CBR stood at 6 per cent. The CBK employed repo and reverse repo operations to manage liquidity, with the rates associated with these operations delinked to the CBR and moving in line with the interbank rate.

Inflation started to accelerate significantly in 2011, reaching almost 19 per cent in November. The Shilling depreciated by 15 per cent in the six months to November 2011 as inflation expectations deteriorated. Facing this instability, the CBK modified its operational framework in September 2011, with a view to making the CBR useful as a signal of policy. It increased the CBR to 18 per cent by December 2011 from 6.25 in September. In addition, the CBR became the pivot rate for both repos and reverse repos; i.e., these operations would take place at the CBR rate plus or minus a margin. Since this reform and policy shift, inflation has been declining steadily, though it remains above the 5 per cent target, standing at 13 per cent as of April 2012.

In sum, Kenya fits the description of many SSA central banks in IMF (2008): it pursued an inflation objective in the context of a managed float, but with a variety of instruments and intermediate targets, including some—uneven—attention to monetary aggregates. In this chapter we choose to simplify by characterizing the stance of policy in terms of a single interest rate, the construction of which we describe below. We return to this issue in the Discussion section.

3.2 Calibration and Data

3.2.1 Calibration

We present the calibration in Tables 15.115.3. Our choice is guided by several principles. First, some of the parameters of the model (average growth rates of relative prices and output, long-run value of equilibrium real interest rates, average inflation target) reflect Kenyan averages or, in the case of the inflation target, the explicit objective of the central bank. These parameters are straight-forward to calibrate.

Table 15.1.Calibration
Relative Prices and their Trends
wShare of food in the CPI0.36Kenya National Bureau of Statistics
Δrlp¯Trend growth rate, relative price of food6.5Historical average
θripPersistence, trend growth, relative price of food0.8System properties (S.P.)
ΔZ¯Trend growth rate, real exchange rate-4Historical average
θripPersistence, trend growth, real growth rate0.65S.P.
Output and Real Interest Rates
g¯Trend growth rate, non-agricultural GDP4Historical average
θgPersistence, trend growth, GDP0.5S.P.
β1Backward-looking parameter, IS curve0.6Implies real economic activity
β2Forward-looking parameter, IS curve0.1is relatively backward looking
β3Output sensitivity to real monetary cond. (rmc)0.15Weak interest rate channel
β4Weight of real exchange rate in rmc0.6Strong exchange rate channel
β5Output sensitivity to foreign demand0.15Relatively large
ρrr¯Persistence, equilibrium real interest rate0.75S.P.
rr¯Equilibrium real interest rate1Historical average
Non-Food Phillips Curve
λ1Forward-looking parameter0.4
λ2Exposure to imported food inflation0.05
λ3Sensitivity to real marginal cost (rmc)0.2
λ4Weight of output gap in rmc0.5
Food Phillips Curve
b1Forward-looking parameter0.5
b2Exposure to imported food inflation0.05
b3Sensitivity to real marginal cost (rmc)0.1
b4Weight of food real exchange rate gap in rmc0.1
b5Weight of food deviation gap in rmc0.7

Other parameters reflect our views about structural features of the Kenyan economy, relative to other economies. As there is an extensive literature applying these models to many advanced and emerging economies, these can serve as a starting point from which to build a Kenya-specific calibration.10 In the IS curve, the relatively large backward-looking term and small forward-looking term reflect our view that expectations of future developments play a relatively small role in output dynamics. The small sensitivity of output to interest rates (given by β3(1 – β4) = 0.06) is consistent with the view that the interest rate channel is likely to be small in LICs, while the relative importance of the real exchange rate gap in rmc indicates the exchange rate channel is relatively stronger.

Table 15.2.Calibration (continued)
Monetary Policy and Uncovered Interest Parity
ρpremAR parameter for country risk premium0.75S.P.
ϕForward-looking term in UIP0.85
γ1Interest rate smoothing in MP rule0.8
γ2Long-run MP response to inflation1.4
γ3Long-run MP response to output gap0
γ4Long-run MP response to nominal depreciation0.25
π¯Inflation target5
ρπ¯Persistence, inflation target0.85
Rest of the World
Δrlp¯*Trend growth rate, intl. relative price of food2Historical average
θripPersistence, trend growth, intl. relative price of food0.5S.P.
β1*Backward-looking parameter, IS curve0.5
β2*Forward-looking parameter, IS curve0.5
β3*Output gap sensitivity to real interest rate gap0.05
λ1*Forward-looking parameter, Phillips curve0.6
λ2*Sensitivity to output gap, Phillips curve0.06
γ1*Interest rate smoothing in MP rule0.75
λ2*Long-run MP response to inflation1.7
λ3*Long-run MP response to output gap0.25
ρpf*Persistence, international food price gap0.75
ρrr¯*Persistence, equilibrium real interest rate0.5
rr¯*Equilibrium real interest rate2.5Historical average

In the case of the two Phillips curves, non-food inflation is more sensitive to the output gap, with the sensitivity given by λ3λ4 = 0.1, than food inflation, with the sensitivity given by b3(1 – b4 – b5) = 0.02. The same holds regarding sensitivity to the real exchange rate: it equals λ3 (1 – λ4) = 0.1 in the non-food sector but only b3b4 = 0.04 in the food sector. This difference reflects our view that aggregate demand is crucial for understanding non-food inflation dynamics, and is less of a factor for food inflation. On the other hand, food inflation is quite sensitive to temporary gaps between international and domestic food prices (devgapt): a 1 per cent widening of the gap—ignoring expectations of future values of devgap—results in an immediate 0.07 per cent increase in food prices. The effect is twice as large (0.13) once expectations about future gaps are incorporated into current prices. The calibration of the monetary policy rule is relatively dovish, with large smoothing of interest rates and a relatively small response to increases in expected inflation. The calibration also allows for some response to nominal exchange rate movements (an important issue in LICs) but no response to the output gap. The calibration for the rest of the world is taken from applications of similar gap models to the US economy.

Finally, the last set of parameters are calibrated in part based on the model’s ability to deliver plausible interpretations of recent macro dynamics. The parameters that fall in this category are primarily the AR coefficients of most exogenous variables, as well as the variances of the shocks which are listed in Table 15.3. As is explained in Appendix 15B, the filtration exercise depends on the relative variance of the shocks, since there are more shocks than observables, so the choice of these as well as the AR coefficients help determine the model’s account of Kenya’s business cycle.11 To pin down these parameter values, we start with an initial calibration, assess the model-based decomposition of the data, and iterate until the model-based story looks plausible.12

Table 15.3.Calibration (continued)
Monetary Policy and Uncovered Interest Parity
σrlp¯Volatility, dom. relative food price trend2S.P.
σz¯Volatility, real exchange rate trend shocks3S.P.
σy¯Volatility, potential output growth shocks1.5S.P.
σgz¯Volatility, potential output drift shocks1S.P.
σygapVolatility, output gap shocks1S.P.
σrr¯Volatility, equilibrium real interest rate shocks0.7S.P.
σπnfVolatility, dom. non-food shocks1.5S.P.
σπnfVolatility, dom. food shocks2.5S.P.
σsVolatility, UIP shocks3.5S.P.
σpremVolatility, risk premium shocks3.5S.P.
σrsVolatility, monetary policy shocks1.5S.P.
σπ¯Volatility, inflation targets1S.P.
σygap*Volatility, US output gap shocks0.3S.P.
σrs*Volatility, US monetary policy shocks0.3S.P.
σπ¯*Volatility, US equilibrium real interest rate shocks0.08S.P.
σπ*Volatility, US CPI shocks1.5S.P.
σrlp¯*Volatility, intl. relative food price trend shocks0.35S.P.
σrlpgap*Volatility, intl. relative food price gap shocks0.3S.P.

Several additional points are worth making about calibration. As mentioned above, the calibration is assessed in part on the plausibility of the model-based interpretation of recent events (our focus here). There are other dimensions which we do not discuss in this chapter which are equally important, such as the forecasting properties of the model, both in-sample and out-of-sample.13 Second, we must acknowledge that considerable judgement is involved in this exercise as there is no unique way of calibrating the model, and therefore of interpreting the data. This is a general property of calibrated exercises. Third, there is a somewhat wide range of parameters which will yield broadly similar results, so it is not necessary to obsess over excessively precise calibration values. In addition, the range of possible parameter values is also limited by the fact that the model must have a unique rational expectations equilibrium. For example, the Taylor principle—the idea that real interest rates must increase in the event of a persistent surge in inflation—places a lower bound on γ2*. We will discuss the implications of an alternative calibration for the interpretations of recent events below.

3.2.2 Data

The data are described in Appendix 15A. The data are of mixed frequency, and go from the beginning of 2000 to 2011. Two series are worth discussing in some detail. The short-term interest rate used in the model—monthly series, averaged into quarters—differs from the CBK policy rate, since the latter did not reflect the true stance of monetary policy for reasons discussed in Part II (Figure 15.3 presents the various rates). Instead, we choose the rate that best captures the policy stance. From 2000:1 to 2009:1, and from 2011:5 to 2011:6, we use the repo rate as the central bank was mainly withdrawing liquidity from the money market. From 2009:3 to 2011:4 we use the reverse repo rate since the central bank was mainly injecting liquidity. In 2009:2 we used the average of the two, as the central bank was engaging in both operations during that month.

Figure 15.3.Short-Term Interest Rates, Kenya

The second series of interest is the CPI series and its components. There have been various changes in methodology in the construction of price indices in Kenya. Previous CPI inflation series suffered from upward biases, especially in food price inflation, in part reflecting the use of a chained arithmetic mean formula (the ‘Carli’ index). The Kenya National Bureau of Statistics switched to a geometric mean formula in 2009, for both food and non-food prices, and retroactively revised the aggregate CPI index (but not the sub-indexes) up to 2005. To construct a consistent series that would go back to the beginning of our sample, we estimated a bias coefficient from the period where the alternative indices (from the two methodologies) overlap and applied the correction to the older series.14

3.3 Impulse Response Analysis

We begin our assessment of the model by analysing how a 1 per cent temporary increase in international relative food prices (ϵtrlpgap*=1) affects Kenyan inflation. The purpose of this exercise is to highlight various aspects of the transmission mechanism.

Figure 15.4 plots impulse responses for international food price inflation as well as domestic food and CPI inflation (all presented on a year-on-year (YoY) basis) for two cases. Results are presented in deviations, i.e., movements in inflation rates above or below their long-run value. By construction, temporary changes to international relative food prices have very short-lived effects on international food inflation, since they result in one time increases in the food price level, which then declines over time. This is reflected in the large drop in YoY international food price inflation after four quarters. However, the effect on domestic inflation is longer-lived, since it takes longer for the increase to be (incompletely) passed on to domestic food prices.

Figure 15.4.Impulse Response Functions, ϵtrlpgap*=1

In the first case (left quadrant), we assume that monetary policy does not respond and that the nominal exchange rate does not depreciate.15 The increase in inflation can be thought of as the first-round effect of shocks to international food prices. In this case, the shock has a large effect on food inflation but no effect on non-food, so the impact on headline is given by the weight of food in the CPI. In the second case (right quadrant), we allow for monetary policy to respond, in which case the central bank raises interest rates as inflation increases. This policy tightening leads to an incipient decline in the output gap, which, all else equal, creates pressures for both non-food and food inflation to decrease. In addition, the increases in interest rates results in a temporary appreciation of the currency, which also reduces inflation by reducing production costs in both sectors. The increase in inflation is therefore smaller.

Note that the direct effect of monetary policy can also be analysed with a monetary policy shock (ϵtRS=1), shown in Figure 15.5. Consistent with the previous discussion, the shock results in an increase in the output gap, a decline in both components of inflation and a nominal and real depreciation.

Figure 15.5.Impulse Response Functions, ϵtRS=1

We do not show impulse responses for all shocks, for the sake of brevity. A general result is that all non-trend shocks have an effect on inflation since they affect gap terms, and the monetary policy response will play a role in the propagation of the shock.16 Shocks to trend components are not inflationary, with two exceptions. The first exception is a positive shock to the trend component of the domestic relative price of food (ϵtrlp¯=1), not shown. In this case, there would be an increase in the food inflation rate, a decrease in non-food inflation rate, but no change in the headline inflation rate (and no monetary policy response). The second exception concerns a shock to equilibrium real interest rates (ϵtrr¯,notshown), which would have an impact on economic activity and inflation because of the slow adjustment in the monetary policy rule. Actual real interest rates would not keep up with equilibrium rates, thus opening a gap in real monetary conditions.

3.4 Filtering Kenyan Data through the Model

We now use the model to interpret the joint movement of macro variables in Kenya. To do so, we filter the data through the model using the Kalman smoother described in Appendix 15B. The Kalman filter and smoother are recursive algorithms used to estimate a sequence of unobserved state variables whose dynamics are described by a state space model—a vector autoregression of order one (VAR(1))—based on the observations of a sequence of other variables which are linearly related to them. In our case, the state variables are trend and gap components and the shocks—their dynamics are jointly described by the VAR(1) representation of the model solution—and the observables are the actual series.

The use of the Kalman smoother to estimate trends and gaps implies that the estimates at any point in time draw on information from the entire sample, e.g., the estimate of the output gap in 2005:Q1 depends on movements in inflation (and other observed variables) from both before and after 2005:Q1. This feature is convenient when trying to understand historical episodes, though it also implies that the economist doing the exercise can have a clearer picture of past macro developments than policymakers at the time.

We will focus primarily on two main outputs: a decomposition of most series into a trend (or potential) and a gap component, and a decomposition of the current value of any variable into the different shocks responsible for its dynamics.

3.4.1 Decomposition into Trends and Gaps

We begin the analysis by looking at the model’s four main relative prices (zt, rlpt,(zt,rlp,rlpt*,devt), devt which are displayed in Figure 15.6. Kenya’s real exchange rate (zt) has appreciated over time (see upper left quadrant), which in the model is accounted for by a smooth trend appreciation. The real exchange rate also displays some noticeable spikes, especially in 2008, accounted for by movements in the gap (the difference between the two series). The international relative price of food (rlpt*, bottom left quadrant) also displays a relatively smooth positive trend, with large movements in the gap. Of particular interest are the large increase in international food prices in 2007–08 and the more recent spike, which in our model are mainly accounted for by shocks to the international food price gap, although the trend also increased.

Figure 15.6.Trend/Gap Decomposition, Relative Prices

A different story emerges for the domestic relative price of food (rlpt, upper right quadrant). The trend component also increases over time, though it slows down at the onset of the 2007–08 period before accelerating after that. The actual domestic relative price of food falls in early 2007, so that most of the increase in food inflation observed in 2008 can be interpreted as catching up relative to the trend. rlpt falls below trend again in 2010, though the gap is smaller. The deviation between domestic and foreign food prices (devt, bottom right quadrant) oscillates widely, with the 2007–08 crisis—and the more recent spike—opening up large negative gaps. Given the role of devt in the food Phillips curve, we can foresee these gaps will be inflationary.

Figure 15.7 plots the time series for GDP. Output experienced fast growth during 2003–07, with a 6 per cent average growth and 7 per cent peak in 2007, before dropping to 2 per cent in 2008–09. Given our assumption about the volatility of shocks to potential, potential output displays a smooth path, although it accounts for most of the growth observed in 2003–06. Most of the acceleration and deceleration of output around 2007 is explained by movements in the output gap, which peaks during that time but then contracts until it closes in mid-2009, in the midst of the global financial crisis. The gap opens up again from 2010 onwards.

Figure 15.7.Trend/Gap Decomposition, GDP

Finally, the real interest rate (see Figure 15.8) displays large movements: largely positive from 2001 to early 2003, then largely negative until mid-2005 and again from mid-2007 until the end of the sample. Most of these movements are accounted for by movements in the real interest rate gap.

Figure 15.8.Trend/Gap Decomposition, Real Interest Rates

In sum, the trend/gap decomposition has identified various periods with sizeable gaps in output, relative prices, and real interest rates. As these gaps have inflationary effects, in the next subsection we account for some of them and for the resulting changes in inflation in terms of the model’s shocks.

3.4.2 Decomposition into Shocks

With the help of the Kalman smoother, we decompose the dynamics of each series—both observed and unobserved—into the different estimated shocks and initial conditions (see Appendix 15B). Since we have eighteen different shocks, we regroup them into seven groups for convenience:

  • Shocks that hit the output gap: ϵtygap,ϵtrr¯.
  • Shocks that hit sectoral inflation rates: ϵtπf,ϵtπnf,ϵtrlp¯.
  • Shocks that affect the international relative price of food: ϵtrlp¯*,ϵtrlpgap*.
  • Shocks related to monetary policy: ϵtRS,ϵtπ.
  • Shocks that directly affect the exchange rate: ϵtS,ϵtprem,ϵtz¯.
  • Shocks that originate in the rest of the world: ϵtygap*,ϵtπ*,ϵtRS*,ϵtrr¯*.
  • Other (initial conditions).17

The regrouping should not be interpreted too strictly, as some of the groups can overlap: some shocks to the exchange rate reflect changes in international market conditions and may be related to developments in the world economy. More generally, the model remains highly stylized and is likely to miss other transmission mechanisms which may be important in certain historical episodes. Estimated shocks may therefore comove as a result.

It is important to reiterate that shocks affect the model variables in a number of ways. In some cases, the effect is straightforward to understand. For example, shocks to the output gap will have a direct positive effect on that variable. In other cases, the interpretation is not simple. For example, shocks that persistently raise inflation would in principle have a positive impact on the output gap since, by raising expected inflation, they lower the real interest rate. However, this effect is more than offset by the fact that monetary policy endogenously responds to increases in inflation, which then tightens real monetary conditions and results in a real appreciation, both of which reduce the output gap. It is important for the model’s user to understand the different channels through which shocks affects variables.

Finally, an important caveat to the shock-based analysis is the importance of own shocks, i.e., shocks that directly affect an observed variable (like temporary shocks to food and non-food inflation ϵtπfandϵtπnf). In general, these will soak up two types of movements in that variable. The first type of movement has an economic interpretation, e.g., negative shocks to the food harvest will result in an increase in food inflation, and will show up in ϵtπf. The second type of movement captures any high frequency dynamics in that variable without a clear economic interpretation, and which is most likely due to the fact that the model is highly stylized. The latter type may result in an overstatement of the relative important of own shocks. We will therefore complement this analysis with alternative representations of the filtration exercise.

Figure 15.9 shows the shock decomposition for the output gap. Three main features emerge. First, an important share of output gap fluctuations is explained by developments in the international economy: the positive gap of the mid-2000s is driven in part by strong international output, with the deceleration of the economy in mid-2008 mainly due to the effects of the global financial crisis, and the recovery since mid-2010 supported by the relative improvement in the US economy. Second, output gap shocks account for much of the economic boom in 2007, associated in part with the increase in the fiscal deficit during that period.18 Third, the Kenyan economy was supported by an accommodating monetary policy (ϵtRS<0,ϵtπ>0) from mid-2008 onwards, which helped offset some of the fallout from the global financial crisis. This monetary support became expansionary once the international economy recovered.

Figure 15.9.Shock Decomposition, Output Gap

A related pattern emerges for non-food inflation (see Figure 15.10).19 Shocks to non-food prices account for some of its movements. The benign international environment also helps account for some of the non-food movements, especially during the global financial crisis. But more importantly, non-food prices have been consistently buoyed by accommodating monetary policy, which resulted in the large acceleration in inflation observed in 2011.

Figure 15.10.Shock Decomposition, Non-Food Inflation

The dynamics of food inflation (Figure 15.11) are somewhat different. Domestic food price shocks play an important role, reflecting the importance of shocks to the domestic food harvest such as the drought of 2008–09. More importantly, international food price shocks explain an important fraction of the upswing/downswing/upswing of food prices, while monetary conditions have again played a role. These two dynamics are then aggregated into headline inflation (Figure 15.12), with international conditions—including international food prices—but more importantly accommodating monetary policy being the two key factors.

Figure 15.11.Shock Decomposition, Food Inflation

Figure 15.12.Shock Decomposition, Headline Inflation

We conclude this subsection with an analysis of nominal depreciation (Δs) relative to its long-run value—given by Δs¯ —presented in Figure 15.13. The large depreciation observed in 2009 is accounted for by the shocks to monetary policy mentioned earlier, as well as shocks to the risk premium possibly associated with the worsening of the external environment during that time. The external improvement contributes to the nominal appreciation observed in early 2010. However, since then monetary policy and exchange rate shocks—the latter possibly associated with additional balance of payment pressures from the higher food and fuel import bill—resulted in the depreciation of the currency.

Figure 15.13.Shock Decomposition, Nominal Depreciation

3.4.3 A Model-Based Interpretation of Monetary Policy

We now present an alternative representation of the model’s results for the short-term interest rate (Figure 15.14). We compare observed interest rates with the path predicted by the model in the absence of the variable’s own shock, which we refer to as ‘KF Predicted’. We also present an alternative decomposition, based on the terms that enter the interest rate rule. Overall, the model-predicted interest rate tracks the actual interest rate relatively closely, which indicates the interest rate rule and the model more broadly (in its current calibration) do a reasonable job of accounting for interest rate dynamics.

Figure 15.14.Central Bank Rate—Repo Rates

However, since mid-2007, actual interest rates are consistently below those predicted by the model, with the difference due to the negative shocks to monetary policy described above. The gap is most prominent in 2008–09, where the model called for a policy tightening which did not take place. The gap opens up again starting in mid-2010 for similar reasons, though the widening is smaller. In sum, the application of the model to Kenya identifies a prolonged period of policy accommodation, which had important implications for inflation in 2008 and 2011.

In terms of the factors that describe the model’s implied path for interest rates, we observe that most of the persistence in interest rates is due to the smoothing factor in the policy rule. The increase in interest rates predicted by the model in 2008–09 and in 2011 is due to the increase in inflation observed during those periods, as well as the nominal depreciation in the first episode, whereas the decrease in rates in between is due to the decline in inflation.

3.5 Sensitivity Analysis

As previously mentioned, the model-based interpretation of the data depends crucially on the calibration of the model parameters, including the variances of the shocks. We now briefly discuss how alternative calibrations change the interpretation of recent history. In particular, we make the assumption that the variance of the monetary policy shock (σrs) and the variance of the shock to the inflation target (σπ¯) are almost zero. This is an extreme assumption, but it illustrates how to use the plausibility (or lack thereof) of the story that emerges from the filtration exercise to help inform the calibration. The comparison between the baseline and the alternative calibration are shown in Figure 15.15.

Figure 15.15.Sensitivity Analysis, Alternative Calibration

Imposing the absence of monetary policy shocks implies that the interest rate level observed in the data is perfectly accounted for by the interest rate rule. This has a number of implications. In the post-2008 period, the sustained decrease in interest rates coincides with an inflationary surge in 2010–11, and a corresponding increase in inflation expectations. Making the inflationary surge consistent with declining interest rates requires that some of the unobserved variables in the interest rate rule offset inflationary pressures. Given that the inflation target is forced to remain constant (σπ¯=0), the equilibrium interest rate does the adjustment. The filtration therefore interprets 2008–11 as a period of large decline in equilibrium real interest rates (by as much as 1,000 basis points). In turn, this decline in equilibrium rates opens up a large gap in real monetary conditions and hence results in a largely negative output gap. It also results in positive shocks to aggregate demand to avoid too large a decrease in the output gap. In addition, a large negative output gap requires potential output (not shown) to be considerably higher. Finally, inflation is no longer accounted for by monetary policy shocks; instead, the bulk of the surge in inflation post-2010 is interpreted as supply-side shocks.

We can disregard this story as implausible. Among other things it requires that equilibrium/trend real interest rates make large swings, which is inconsistent with the idea that this variable should be relatively smooth. It also requires that the combination of low interest rates, increasing inflation and output acceleration post-2010 be unrelated. A more plausible story must therefore allow some role for monetary policy shocks.20

4 Discussion

The use of the model for policy analysis has yielded various insights into the drivers of inflation in Kenya. One such insight is the role of excessively accommodating monetary policy in recent years. In this section we discuss some likely factors behind the policy stance during this period.

Monetary policy operates in an environment of considerable uncertainty and incomplete information. The central bank must rely on current and leading indicators that are noisy and may not reveal a clear picture until incipient inflationary pressures have built up, in which case it is too late to offset the impact on actual inflation given the lags in the transmission of monetary policy. Because of these information lags, central banks often find themselves responding to the inflationary effects of past shocks rather than responding to new developments. In the case of sub-Saharan Africa, these challenges are compounded by the scarcity of high frequency indicators.

An additional challenge for monetary policy is the management of multiple objectives, either explicit and implicit. While most if not all central banks place price stability as their primary objective, they also attempt to support economic growth and—at times—financial sector development and credit growth. While these objectives are sometimes consistent, they can also conflict with one another. In addition, because excessively tight or accommodating policies do not immediately show up in high inflation, it may take time before the central bank can realize the inconsistency. A related challenge is that the legacy of monetary aggregate targeting can at times lead to inconsistent views about the stance of policy if broad money growth appears consistent with previously set targets; even though interest rates may be too high or too low.

In the case of Kenya, the central bank loosened its policy in response to the global financial crisis of 2008–09, which had resulted in lower economic growth, contributed to a large decrease in inflation, and had negative implications for the growth of domestic credit. The policy loosening was maintained beyond this period, however, with rates continuously declining and reaching 1 per cent by the end of 2011.

While very low interest rates should have acted as a signal that monetary policy was excessively accommodative, the central bank justified its stance in its December 2011 Monetary Policy Statement by emphasizing objectives for monetary and credit aggregates: ‘The programmed growth in money supply … was considered adequate to support economic growth through expansion of credit to private sector … Generally, broad money supply, M3, remained within the set target. Credit to private sector increased, which was virtually on target’ (Monetary Policy Statement, Dec. 2010, p. 3). It is worth noting that reserve money growth was also indicative of expansionary policies, as this variable was overshooting its target consistently through 2011.21 Despite the overshooting of reserve money, as broad money and credit aggregates were in line with their targets, the perception was that monetary policy would have ‘no effect on demand-driven inflation’ (MPS, p. 3). This state of affairs may have been compounded by the sustained decline in inflation between late 2008 and mid-2010.

In hindsight, the targets for broad money and credit were based on an optimistically low assumption for broad money velocity and optimistic assumptions about the credit growth rates consistent with stable inflation. More generally, had the policy regime placed more emphasis on interest rates as indicating the stance of policy and less emphasis on credit growth and other quantitative targets, a clearer picture about the stance of policy may have emerged.

4.1 Is it Valid to Use Interest Rate Rules to Study Monetary Policy in Kenya?

From a methodological point of view, a related question to the above discussion is whether it is valid to apply a model with an interest rate rule to a de jure money targeter such as Kenya, in which, as the above discussion suggests, the stance of monetary policy has been influenced at times by objectives for monetary aggregates, and where policy rates did not provide clear guidance about the stance of policy. We provide several answers to this important question.

First, models are gross simplifications of reality and will inevitably miss many aspects that may be important. In our model we abstract from monetary and credit aggregates, and money targets, and focus exclusively on interest rates. Although these other aspects of policy are important, we believe that the right short-term interest rates provide a useful summary of variations in real financial conditions in Kenya, as emphasized in the previous section.

Second we believe that the Taylor principle is an essential component of monetary policy, regardless of the policy framework. Concerns with other objectives may mask this relation in the short run, but it must eventually hold if inflation expectations are to be anchored. This was the case for the CBK, which by the end of 2011 raised real interest rates by several hundred points to stabilize inflation, a policy tightening similar in magnitude to the one prescribed by our model.22 So modelling monetary policy as a rule in which the Taylor principle must eventually hold seems the correct approach to us.

Third, because of the relevance of the Taylor principle, deviations between the interest rate rule and the actual level of interest rates provide a useful measure of the stance of policy, which can then help in understanding the dynamics of inflation. This can be seen in our model simulations, in that the sustained deviation between interest rates and the level implied by the rule coincides with the increase in inflation observed in 2008 and 2011. This further validates the use of the policy rule as a way of thinking about monetary policy.

Fourth, it could be the case, however, that what the model identifies as shocks are actually systematic responses to achieve other objectives, e.g., hitting money targets. In this case, an important aspect of monetary policy would be left outside the model, which could invalidate the exercise. In Chapter 16, we study frameworks that include a systematic role for money targets and apply it to Kenya and find that this is not the case, i.e., that despite Kenya’s de jure money targeting framework, there is no systematic relation between the monetary policy stance and money targets or money target deviations, even if there have been periods such as in 2010–11 when targets have mattered. We therefore conclude that monetary policy analysis in Kenya can be done, at least to a first approximation, in stylized models such as ours in which monetary policy is captured with an interest rate rule and which abstract from credit and money growth. We believe these insights may also apply to other countries with similar frameworks, but we leave such an analysis for future work.

5 Conclusion

In this chapter we have provided a framework for forecasting and policy analysis for low-income countries, with an application to Kenya. In particular, we have extended the standard framework to include an explicit role for food prices, by introducing two separate Phillips curves (one for food and one for non-food), and by paying special attention to the domestic and foreign relative food prices (both trend and gap component).

We have filtered key macroeconomic series from Kenya through the model to recover a model-based decomposition of most series into trend and gap components, and to discuss the quantitative significance of various factors (international shocks, monetary policy) in driving inflation. We find that, while imported food price shocks have accounted for some of the inflation dynamics in Kenya, both in 2008 but also recently, an accommodative monetary policy also played an important role. We believe the model’s ability to provide a plausible interpretation of recent events in Kenya, validates the use of these types of models for policy analysis in low-income countries.

Appendix 15A: Data Series
VariableData UsedSourceRemarks
sMarket rate, Shilling/DollarIMF IFS
rsRepo, reverse Repo ratesCBKRepo rate (2000:1 2009:1,2011:5 2011:6),

Reverse repo (2009:3 2011:4),

Avg repo and reverse repo 2009M2
yNon-Agricultural GDPKNBSInterpolated, smoothed with an HP filter (λ = 0.8)
pcpiCPIKNBS, IMF staff
pfFood Price IndexKNBS, IMF staff
pnfNon-food Price IndexKNBS
rs*Fed Funds rateIMF IFS
rr¯*US equilibrium real interest ratesIMF modelling group
ygap*US Output GapIMF IFSUS GDP, HP filtered.
p*fInternational Food Commodity IndexFAO
Appendix 15B: Solving and Using the Model

Solving and Simulating the Model

The actual model is a linear semi-structural forward-looking model, with model-consistent expectations, of the form F(Xt-1,Xt,Xt+1,εt|θ) – 0, where Xt denotes the vector of endogenous variables, εt are exogenous variables (shock innovations, of which there are k), and θ denotes the parameters of the model. The model is solved using a variant of the Blanchard and Kahn algorithm (see Blanchard and Kahn, 1982), implemented using the IRIS Toolbox for Matlab.23

Kalman Filter and Smoother

To estimate the model’s structural shocks and unobserved variables, we proceed as follows. First, we present the solution of the model in state space representation:

where Σε is the variance covariance matrix of the shock innovations.24 Model variables Xt are linearly related to observed variables Yt (inflation, output, exchange rates, etc.) via a measurement equation:

where ηt indicates potential noise in the relation (and Ση denotes the noise covariance). Note that in the case of our model ηt 0.

We then apply the Kalman filter to the data, using the system 1–2. The Kalman filter is a recursive algorithm used for updating estimates of the sequence of Xt and εt based on observations of Yt. It can be summarized by the following sequence (see Hamilton, 1995: ch. 13):

Pt+1|t is mean square error of the estimate X^t+1|t. The recursion is initiated with X^1|0=E(X1)andvec(P1|0)=[Ir2(TT)]1vec(Q), where Q – R’ΣεR.

The Kalman filter provides the best estimate of Xt using information up until time t. For many purposes, including for the filtration exercise presented in the text, it is useful to construct an estimate of Xt using the entire sample. This can be done using the Kalman smoother, another recursive algorithm which starts backwards from the last observation:


and Pt|T is the mean square error of the smoothed estimate X^t+1|T. A smoothed estimate of the structural shocks, ϵ^t|T, can also be derived as follows:

When there are as many shocks as observed variables, and the observed variables are linearly independent, it is possible to recover the estimates of the unobserved variables without drawing on the covariance matrix of the shocks. For example, if ηt – 0, R is an identity matrix and Z is invertible, then the Kalman filter recursion reduces to:

which does not depend on Q. In general, however, there are more structural shocks—number of elements in εt and ηt—than observed macroeconomic variables (Yt). In this case the estimate of X^t1|t depends on the stochastic specification of the model, i.e. the covariance matrices of η, ε. In economic terms this implies that both the impulse response behavior of the model and the assumed variance of structural shocks will determine the plausibility of particular drivers of the economy. In this case the actual interpretation of the data will depend on both the deterministic (parameters) and stochastic parameterizations (variances). For example, the assumption that the volatility of shocks to potential output is large relative to the shocks to the output gap, combined with the assumption that the output gap is not very sensitive to real monetary conditions will result in a very small output gap, with the bulk of output movements accounted for by movements in potential. The assumption about variances is therefore key, as discussed in the text.

Shock decomposition Having estimates of exogenous shocks and initial conditions allows us to carry out a decomposition of the path of observed (and state) variables in terms of exogenous shocks. This can be done by solving (1)-(2) backwards, resulting in the following relation.

By construction, Yt is the result of the sequence of shocks, recovered with the smoother (TtτRε̂τ|T) and the lingering effect of initial conditions (Tτt0X0|T). In the case of the estimated unobserved state variables X^t|T., a similar decomposition yields:

Note that the contribution of shocks can be further disaggregated into the different elements of ε = (ε1,…, εk), i.e., the different structural shocks:

where Mj is a matrix that has 1 in its jth row and zeros elsewhere. By construction, the contribution of each shock and the initial conditions add up to account all of the dynamics of any given variable at any point in time. Figures 15.915.13 in the main text show such a decomposition applied to both observed variables (inflation, exchange rates) and unob served variables (the output gap).25


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1Printed with permission of South African Journal of Economics (2015), 83(4), 475–505.
2See World Economic Outlook Fall 2011, Chapter 3.
3See Berg, Karam, and Laxton (2006) for an overview of the standard model.
4In the working paper version of this chapter, we undertake several forecasting exercises. Most notably, we perform an out-of-sample forecast to identify where the economy—and therefore policy—was likely headed given the inflationary pressures at the time, starting from where our data ends (third quarter 2011). Interestingly, our exercise indicated that short-term interest rates needed to increase, i.e., policy needed to be tightened to offset these inflationary pressures, which is exactly what the Central Bank of Kenya (CBK) implemented by the end of 2011. The coincidence between the latter response and the models forecast validates the use of the model for policy analysis in LICs.
5Several chapters in this book represent exceptions.
6In an appendix to the working paper version of this chapter, we show that the specification of the two Phillips curves in the model can be derived from micro-foundations. In the case of non-food inflation, the Phillips curve can be derived by assuming that the production of non-food requires a domestic input, e.g., labour, and imported goods. In this case, changes in the domestic cost of production are captured by changes in the output gap, while changes in the imported cost are represented by the real exchange rate gap. Note that, in two sector models, what is inflationary in each sector is not the real exchange rate gap per se but the cost of imported goods relative to prices in that sector, which is why znf gapt enters the equation and not zgapt.
7In the separate appendix mentioned earlier, we show that this additional term can be micro- founded by assuming that the production of the domestic food basket also requires imported food, in addition to domestic labour and imported non-food items.
9Cointegration between the two series is rejected. Regressing the Kenyan index on the international one (in first differences) generates a pass-through coefficient of 0.36.
10For example, a simpler but related version of this model was estimated for South Africa using Bayesian methods. See Harjes and Ricci (2006).
11For example, we picked the variances of the shocks to potential or trend values to be such that they resulted in relatively smooth trends. Otherwise, the trends would absorb large part of the business cycle movements of variables such as output, relative prices, and interest rates.
12It is feasible to estimate the model through Bayesian methods (as for example in Berg et al., 2010, the working paper version of Chapter 8, for a similar model). However, for operational purposes the iterative process is preferable, at least at first. It helps the operator understand the mechanisms of the model and in particular the mapping between calibrations and the interpretation of history. It also allows the operator to embody views of the transmission mechanism derived from other sources, such as the judgement of policymakers. And it avoids the danger of’overfitting’, in particular of attempting to fit episodes when the operator knows (or should know) that there really were large unexpected and un-modeled events, e.g. fiscal shocks, movements in the risk premium from global events, or droughts or riots that temporarily drove food prices.
13In the working paper version of this chapter we find that the model makes reasonable forecasts, especially out-of-sample.
14Our measure of output (non-agricultural GDP) was available at annual frequency; it was interpolated using the Chow-Lin procedure. We apply an HP filter with a very small λ (λ 0.8), to remove some of the noise that resulted from the interpolation. This helps make the series slightly smoother and avoids forcing the model to provide a structural interpretation for every small jump in the series. An alternative, more cumbersome, approach would have been to explicitly model the noise in the series as part of the broader model.
15To generate this scenario, we simulate a subset of the model where the output gap is always set to zero and the nominal interest rate stays constant, in which case the nominal exchange rate—through uncovered interest parity—does not depreciate. As actual real interest rates are declining, this exercise implicitly assumes a decrease in equilibrium real interest rates to keep the output gap closed.
16One such shock is the one that appears in the food Phillips curve. This shock can capture variations in food inflation due to temporary real factors, such as large variations in the weather that affect the production of food, or changes in food tariffs, subsidies or taxes. Understanding how these factors affect food inflation—and by how much—is an important area of research and merits further work.
17As previously discussed, shocks to potential output do not affect inflation and are therefore ignored in this analysis.
18Development expenditure increased by 60 per cent.
19Inflation variables are de-meaned.
20As an additional exercise, we also compared the baseline with an alternative calibration in which the sensitivity of aggregate demand to real monetary conditions (β3) is divided by 10, and the volatility of shocks to potential output (output gap) is magnified (reduced). In this case, most of the variations in output are accounted for shocks to potential, which greatly reduces the role of aggregate demand (and monetary policy shocks) in accounting for inflation dynamics. We also find this alternative interpretation to be implausible for reasons similar to the one discussed above.
21See Monetary Policy Statement by Central Bank of Kenya, December 2011.
22We describe the policy tightening in more detail in Chapter 5.
24As there are many alternative space representations to represent the model solution, we can assume, without loss of generality, that Xt and εt have the same dimension, and that R is invertible.
25Implementation of the Kalman filter and smoother is also readily available in the IRIS Toolbox for Matlab.

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