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Predicting Output Growth and Inflation in Pakistan: The Role of Yield Spread.

Byline: Fida Hussain and Asif Mahmood

Abstract: This paper presents empirical evidence on the role of yield spread in predicting inflation and output growth in Pakistan. We also test the role of foreign interest rates in predicting inflation and output growth. Our results indicate that the yield spread in Pakistan does contain information to help predict output growth in the country. However, yield spread has no predictive content for inflation. Our results, for output growth as well as inflation, are consistent with findings of other studies for the case of emerging market economies.

Keywords: Yield Curve, Inflation, Output, Forecasting

1. Introduction

The yield curve or term structure of interest rate represents the relationship between the maturities and the yields of government securities. It contains useful information for future movement in inflation, economic activity and interest rates. The slope of the yield curve, the yield spread, is often used by financial market analysts and policy makers as an indicator of future economic activity and inflation.2 While empirical analysis generally confirms this attribute of yield spread, research on this has largely been done for advanced economies with very little focus on emerging countries.

Financial markets in Pakistan have undergone significant changes in the last two decades. Their integration with global markets has also increased, in terms of volume as well as transactions, in recent years. These developments have gradually increased the role of market interest rates in making future financial decisions. Now, policy makers and financial analysts in Pakistan often refer to changes in term structure of interest rates as reflecting changes in market expectations about future inflation, economic activity, and thus the monetary policy stance.

There is a consensus in literature that short-term interest rates in the economy are normally influenced by the monetary policy stance of the central bank, while long-term interest rates are believed to reflect market views on evolving macroeconomic conditions, particularly market expectations about output growth, inflation expectations, credit risks and expected real yields. The rationale is that financial variables are inherently forward looking as they rapidly assimilate developments in various sectors of the economy, which are usually not observable on real time basis. Fama (1975) argued that market uses all available information likely to have effects on future inflation while setting the nominal interest rates of one month to six months.3 Ang et al. (2006) found that about 85 percent of the variations in bond yields at shorter end are explained by innovations in macro factors and the movements in longer-end bond yields are mostly influenced by unobservable factors.

According to Evans and Marshal (2007), movements in long-term interest rates of almost all maturities are driven by developments in major sectors of the economy and changing path of key macroeconomic variables. This implies that the level and slope of the yield curve strongly leads to the changes in macroeconomic conditions.

To this end, a number of studies provide empirical evidence. In the earlier work, Fama (1975, 1977 and 1990) found the nominal interest rates leading the movements in US inflation during 1953-71 and yield spread being the "best single predictor of inflation". Latter, Mishkin (1988 and 1990) found that the yield spread is not very accurate in predicting short-term inflation but forecasts do get slightly better as the forecasting horizon increases.

According to Fisher hypothesis, the yield curve should contain information mainly about future path of inflation.4 However, a number of recent studies have shown that slope of the yield curve has a significant predictive power for changes in economic activity. The pioneer work demonstrating predictive power of the yield spread for real activity includes Stock and Watson (1989), Harvey (1991) and Estrella and Hardouvelis (1991).5 Most of these studies also show that yield spread performs quite well in predicting recessions. Findings of a survey of research on usefulness of the information content of term structure by Wheelock and Wohar (2009) show that most of the studies have found the term spread as useful indicator for predicting output growth and recessions 6 to 12 month in advance.

Besides having explanatory power for predicting inflation and economic activity, the literature shows that term structure of interest rates is often taken as an indicator of likely monetary policy stance. After the seminal work by Irving Fisher in 1930, Fama (1984a and 1984b) and Fama and Bliss (1987) provide empirical evidence that longer maturity forward interest rates help in forecasting distant future spot rates. Mishkin (1988), Frankel and Lown (1994), Moreno (2008) and, more recently, Wu and Xia (2018) find that term structure is helpful in predicting future short-term interest rates several months in advance. Mishkin's later studies show that term structure of nominal interest rates of up to 6-month maturities does provide information about the term structure of the real interest rates.

Most work related to predictive power of the yield spread has mainly focused on advanced countries. In case of emerging economies, however, the empirical literature related to ability of yield spread to predict both inflation and output can be considered as scarce with a few exceptions including a study by Mehl (2009).6 The study used a sample of 14 emerging economies to explore the usefulness of sample country's slope of the yield curve to forecast inflation and growth both for short and long run horizons. The findings show that the yield curve has information content in almost all countries in the sample while predicting output growth up to 2 years. However, yield spread could also predict inflation for half of countries. Being important driver of global economy, the study also found the significant role of the US interest rates in influencing the yield spread in selected emerging economies.

To our knowledge, the empirical work exploring the predictive power of yield spread in case of Pakistan is non-existent. The objective of this paper is to explore if yield spread in Pakistan could provide useful information about future inflation path and the direction of economic activity. For this purpose, we use standard methodologies surveyed by Stock and Watson (2003) and Mishkin (1990) for predicting both inflation and output growth up to 2 years. Given the importance and impact of changes in the US interest rates for emerging economies, we also attempt to explore this angle through empirical analysis. We perform forecasts evaluations to investigate the predictive power of yield spread while predicting output growth and inflation. To check the predictive power of yield spread in out-of-sample forecasts, we compare our results with simple Autoregressive (AR) model.

Our findings show that the yield spread is a predictor of output growth in Pakistan, particularly for horizons beyond 6 months and up to 2 years. Our findings also show that changes in the US interest rates (or yield spread) have significant impact on domestic interest rates in Pakistan, and its inclusion increases forecasted output growth associated with Pakistan's yield spread. This latter finding is in line with empirical results of Caceres et. al (2016).7 Unlike growth, however, we do not find the significant role of yield spread for predicting inflation in Pakistan. When compared to other emerging economies, inflation volatility and thus uncertainty in Pakistan appears to be high which may have confounded the results in case of inflation prediction.

The rest of the paper is organized as follows. Section 2 presents the stylized facts on bond market in Pakistan. We also discuss the trends in the yield spread and other macroeconomic indicators during last decade. Section 3 details the empirical framework for testing the predictive power of yield spread for inflation and output growth in Pakistan. Section 4 describes the data issues. Section 5 discusses the results and caveats while last section makes the concluding remarks.

2. Data Description and Stylized Facts

In Pakistan, the process of financial liberalization started in the early 1990s. The beginning of auction based system for government securities paved the way for development of bond market. First auction of both short-term treasury bills and longer term bonds were conducted in March 1991. After remaining successful in the earlier years, however, the Federal Investment Bonds (FIBs) lost their attractiveness. 8

Participation of financial institutions in bond auctions almost came to a standstill during fiscal year (FY) 1997-98 and bond auctions were subsequently suspended in June 1998. 9, 10 Government resumed the auctions of bonds in December 2000 with the introduction of Pakistan Investment Bonds (PIBs) to replace FIBs. Investors were found keen to invest in the new long term bonds. However, increased external inflows reduced government's financing needs from the domestic sources. 11 Resultantly, government issued bonds worth Rs12 billion only during FY2004-05 and FY2005-06. Although, issuance was increased gradually from FY2006-07 onwards, the average share of bonds in total outstanding government securities remained around 38.0 percent. The relatively higher dependence on short-term bills overtime did not allow the development of long-term liquid secondary market in Pakistan.12 Beginning from 1991 the government issued 6-month T-bills. After 1998, it also started issuing 3 and 12 month T-bills.

Figure 1 plots the trends in the inflation, output growth [proxy by changes in large-scale manufacturing (LSM) index] and yield spread - i.e. the difference between yield on 10-year bond and 3-month treasury bill in the secondary market.13 It could be observed that during the period from January 2003 to June 2004, the yield spread is positively sloped. This was the time when Pakistan's economy was witnessing substantial foreign capital inflows and inflationary pressures which started to build up from October 2003. Subsequently, banks' participation in both short and long term debt auctions declined as they were already getting attractive returns from the private lending. During July 2004 to December 2007, SBP increased its market interventions in its regular open market operations (OMOs). This put upward pressure on short-term market interest rates, which resulted into a negatively sloped yield curve.

Moreover, due to unprecedented increase in oil prices and subsequent pressure on Pak rupee-US dollar parity, the inflationary pressures emerged from December 2007 onwards. Subsequently, SBP geared up its policy tightening and increased the policy rate by 500 basis points in 2008.

In August 2009, after abrupt movements in overnight repo rate, SBP adopted the interest rate corridor framework for monetary policy implementation. The purpose was to address short-term market interest rate volatility (i.e. overnight repo rate). Following this, market had adjusted its expectations about interest rate levels as slight upward trajectory could be observed in the yield spread in the earlier months. In FY16 yield spread increased despite decline in inflation. Such behavior, to some extent, could also be explained by the significant increase in PIB issuance in recent years.

Figure 2 exhibits the dynamic correlations of yield spread with year-on-year changes in headline inflation, which is calculated from the Consumer Price Index (CPI), and output growth in the last decade. Moreover, as discussed in previous section, correlation between the US and Pakistan yield spreads is also plotted. It could be seen that the yield spread in time t is positively correlated with output growth up to t+12 horizons. After peaking at t+3 months, the correlation starts moderating though with a lesser pace. Similarly, the US yield spread in time 't' is found positively correlated with the yield spread in Pakistan up to t+12 horizons. Similar as in case of output growth, the correlation increases up to 3 months in future after which it starts to decline gradually. However, in contrast to what theory says, the dynamic correlation with inflation is found to be negative for lags as well as leads.

3. Estimation Methodology

To investigate the usefulness of the slope of the yield curve in Pakistan as a predictor of domestic inflation and growth, we follow the methodology used by Estrella and Mishkin (1997), Hamilton and Kim (2002) and Stock and Watson (2003). The slope of the yield curve, denoted as Xt, is defined as the difference, in period t, between the yield on the long-term domestic government bond, denoted itl, and that on the short-term domestic treasury bill, denoted its.

(EQUATION)

In case of output growth, the forecasting begins from next one-month up to k-month ahead in order to see the predictive power of yield curve along various time horizons. The basic model is estimated as;

(EQUATION)

where Yt+kk represents output growth over next k months, Xt represents term spread at time t, and Iut+k represents error term. We use LSM index to proxy the output growth.

LSM is transformed such that,

(EQUATION)

The 1200/k is multiplied to standardize LSM growth in annualized form. Based on theoretical underpinnings discussed in the first section, the value of [beta]1 is expected to be positive in equation (1). Since the lagged output may be useful in forecasting the output growth, we estimate the model including the lags in (1), which are chosen by AIC. The criterion suggests inclusion of first lag in case of Pakistan.

For testing the predictive power of yield spread in case of headline CPI inflation (I) in Pakistan, the basic model is similar to that of output growth model as;

(EQUATION)

Likewise LSM growth, we transform the Itk as; Equation (2) is considered as 'inflation equation' where we want to see the predictive content of yield spread on inflation over the next k periods.

We also estimated 'change in inflation equation' as suggested by Mishkin (1990) and further refined and tested by Fama (1990), Mishkin (1991) and Jorion and Mishkin (1991). Basically, we investigate whether the current spread between m-period and n-period interest rates includes information about the change of inflation between periods m and n. It stems from the Fisher equation that the nominal interest rate in time t with maturity in period m (it,m) may be decomposed into an ex-ante real interest rate (rrt,m) in time t maturing in m and expected inflation (Et) over the next m-periods in time

it,m = EtIt,m + rrt,m (3)

The expected inflation over the next m-periods equals actual inflation (perfect foresight assumption) in the period plus the forecast error of inflation (Iut,m);

Et It,m = It,m + Iut,m (4)

By combining equations (3) and (4) we obtain;

It,m = it,m - rrt,m + Iut,m (5)

Since the objective of this study is to extract information about the future path of inflation embodied in the term structure, a similar equation for n-periods (m > n) must be subtracted from equation (5), which gives;

It,m - It,n = it,m - it,n - rrt,m + rrt,n + Iut,m - Iut,n (6)

After rewriting equation (6) into a regression form that will be used for empirical testing we obtain:

It,m - It,n = [alpha]m,n + [beta]m,n (it,m - it,n) + ut,m,n (7)

Equation (7) is considered as 'change in inflation equation.' If the null hypothesis [beta]m,n = 0 is rejected, the slope of the nominal yield spread (it,m - it,n) contains information about the change in the future inflation rate between periods n and m, and, at the same time, the slope of the nominal and the real yield spread does not move one for one in time. Moreover, if the null hypothesis [beta]m,n = 1 is rejected then the slope of the real yield spread is not constant over time and the slope of the nominal yield spread contains information about the real yield spread.

Furthermore, to capture the effects of international financial linkages on movement of yield spread in Pakistan, we use the US yield spread data based on corresponding tenor rates. For this, we followed Mehl (2009) and tried to instrument the slope of the yield curve in Pakistan by using the US yield spread as an explanatory variable. 14 We then add the fitted series and residual from first stage regression as explanatory variable while predicting output growth and/or inflation in Pakistan. For example, we model the foreign linkage part for output growth prediction as follows:

(EQUATION) (8)

where Yt and et represent the fitted values and residual from first stage regression when yield spread from Pakistan is instrumented by the US yield spread. As suggested by Mehl (2009), with [beta]2 = 0 suggesting that movements in the yield spread of Pakistan have no residual information content for output growth beyond that was predicted by movements in the US yield spread. Otherwise, if [beta]2 a 0, this indicates that the yield spread in Pakistan does contain some information about future output growth.

4. Data

All the data series cover the period from January 2003 to June 2016.15 While inflation is calculated through headline consumer price index (CPI), the inflation for different tenors is annualized. Similar treatment is also carried out for LSM growth. Monthly average of Pak rupee revaluation rates (PKRV) are used for all interest rates series. US interest rates are used as foreign interest rates. 16 See table B2 in appendix B for further data descriptions.

5. Results and Discussion

Based on the empirical framework for this study, for both output growth and inflation, we divide our findings into three broad categories: (i) results from in-sample forecasts, (ii) results from pseudo out-of-sample forecasts and (iii) outcomes from the estimation capturing international financial linkages.

A. In-sample Forecast Results

i. Output growth

Table 1 reports the results from estimation of equation (1). It could be observed from the table that beyond 3-month horizon, yield spread measured through different interest rate tenors tend to predict output (LSM) growth in case of Pakistan. The estimates suggest that 1 percent steepening of yield spread - measured from 3-year and 3-month tenors -predicts increase in the LSM growth by 1.6 percent in the next 6 months. Similarly, a 1 percent steepening of a yield spread, made up of 10-year and 12-month interest rate tenor, predicts an increase in the LSM growth by 0.66 percent in the next 2 years. Importantly, it appears that predictive contents of yield spread decrease with increase in forecasting horizon. Also, across the yield spreads, spread between 10-year bond and 3-month treasury bill rates is found to be significant in all horizons beyond 3 months. These results are in line with findings from other emerging economies (Mehl, 2009).

Table 1: One-step ahead in-sample forecast for output growth

(From equation (1), 1 coefficients based on respective yield spread and output (LSM) growth horizon)

###Horizon###k=1###k=3###k=6###k = 12###k = 18###k = 24

Spread###month###months###months###months###months###months

3 year - 3 month###0.00###1.05###1.62###1.54**###0.94**###0.86**

3 year - 6 month###0.62###1.29###1.89*###1.71**###1.05**###0.99**

3 year - 12 month###0.24###1.25###1.72*###1.61**###0.93*###0.80**

5 year - 3 month###1.01###1.12###1.38*###1.41**###0.87**###0.77**

5 year - 6 month###1.48###1.25###1.51*###1.49**###0.93**###0.84**

5 year - 12 month###1.36###1.24###1.41**###1.44**###0.86**###0.79**

10 year - 3 month###1.29###1.10###1.18*###1.06**###0.73**###0.63**

10 year - 6 month###1.51###1.14###1.24**###1.09**###0.76**###0.67**

10 year - 12 month###1.48###1.16###1.08**###0.74**###0.74**###0.66***

No. of observations###160###158###155###149###143###137

ii. Inflation

Table 2 reports the results from equation (2) the 'inflation equation.' Unlike the findings in case of output growth, the results indicate that the yield spread is not a good predictor of inflation in Pakistan. Besides being statistically insignificant at almost each horizon, the sign of the estimated coefficients is negative, which is not in line with theoretical underpinnings about the information content of term structure about future inflation. Similar observations in case of inflation are also reported by Mehl (2009) for most of the other emerging economies. Mehl (2009) also identified inflation volatility, variations in risk premia, permanent and positive productivity shocks, and the lack of liquidity of the domestic debt market as main reasons which distort the information signals embodied in securities prices in emerging economies.

Table 2: One-step ahead in-sample forecast for CPI headline inflation

(From equation (2), 1 coefficients based on respective yield spread and inflation horizon)

###Horizon

###k=1###k=3###k=6###k=12###k=18###k=24

###month###months###months###months###months###months

###Spread

###3 year - 3 month###1.36###0.79###0.40###0.18###0.03###0.02

###3 year - 6 month###1.77###0.92###0.44###0.20###0.04###0.02

###3 year - 12 month###1.96###1.05###0.50###0.24###0.07###0.07

###5 year - 3 month###1.29###0.57###0.33###0.12###0.01###0.02

###5 year - 6 month###1.49###-0.63###-0.35###-0.12###-0.02###-0.03

###5 year - 12 month###1.60###-0.68###-0.38###-0.14###-0.03###-0.05

###10 year - 3 month###0.98###-0.31###-0.13###-0.04###0.01###-0.01

###10 year - 6 month###1.08###-0.33###-0.14###-0.04###0.01###-0.01

###10 year - 12

###1.14###-0.36###-0.15###-0.05###0.01###-0.02

###month

###No. of observations###160###158###155###149###143###137

Furthermore, to check the predictive power of yield spread for inflation, table 3 presents the estimation results for 'change in inflation' based on equation (7). Like findings from equation (2) where yield spread was found statistically insignificant, here again, it is found to be insignificant across all measures of spread and horizons. Moreover, except for change in inflation between 18 and 3 months in future, the coefficient has negative sign, which is again inconsistent with the theory.

Table 3: One-step ahead in-sample forecast for change in CPI headline inflation

(From equation (7), , coefficients based on respective yield spread and change () in inflation horizon)

###Horizon

###CPI =###CPI =###CPI =###CPI =###CPI =

###6 - 1 months###12 - 1 months###18 - 3 months###24 - 3 months###24 - 6 months

Spread

3 year - 3 month###-0.60###-0.33###0.31###0.07###0.10

3 year - 6 month###-0.57###-0.27###0.36###0.09###0.08

3 year - 12 month###-0.69###-0.42###0.41###0.05###0.05

5 year - 3 month###-0.42###-0.23###0.18###0.02###0.08

5 year - 6 month###-0.39###-0.19###0.21###0.03###0.07

5 year - 12 month###-0.45###-0.27###0.23###0.01###0.06

10 year - 3 month###-0.12###-0.08###0.07###-0.03###-0.01

10 year - 6 month###-0.09###-0.05###0.08###-0.02###-0.02

10 year - 12 month###-0.12###-0.09###0.09###-0.04###-0.03

No. of observations###155###149###143###137###137

B. Out-of-sample Forecast Results

To check the predictive power of yield spread, we perform out-of-sample forecasts across different tenors for k year ahead. However, we perform this analysis for output growth only as yield spread is not found to be a predictor of inflation rate in Pakistan. As suggested by Stock and Watson (2003), the predictive power of yield spread forecasting model would be examined by comparing root mean square error (RMSE) of spread models against the simple Autoregressive (AR) models which includes only lagged value of the dependent variable. The relative RMSE ratio is calculated as;

Relative RMSE ratio = RMSE of yield spread forecasting model / RMSE of AR model

The lower value of RMSE indicates better forecasting performance. The value of relative RMSE ratio below 1 would indicate that the yield spread based forecasting model outperforms simple AR model.

Table 4: Out-of-sample forecast results for output growth

(Relative RMSE ratio)

###Horizon

###k=6###k=12###k=18###k=24

###months###months###months###months

Spread

3 year - 3 month###1.10###0.92###1.51###2.56

3 year - 6 month###1.14###1.03###1.68###3.10

3 year - 12 month###1.17###1.17###1.78###3.48

5 year - 3 month###1.16###0.89###1.37###2.26

5 year - 6 month###1.20###0.97###1.47###2.51

5 year - 12 month###1.24###1.07###1.56###2.70

10 year - 3 month###1.22###0.92###1.26###1.69

10 year - 6 month###1.26###0.98###1.32###1.80

10 year - 12 month###1.31###1.07###1.40###1.92

Table 4 reports the relative RMSEs of out-of-sample forecast results for output growth and of simple AR models. For this exercise, we only select those horizons which were found to be significant based on table 1 results. In only 5 out of 36 cases the relative RMSE is below unity, indicating not so impressive performance of yield spread model than AR model. Also, all these relatively lower RMSEs were found while forecasting output growth for the next 12 months.

C. Impact of international financial linkages in predicting output growth in Pakistan17

Based on equation (8), table 5 presents the results for the influence of international integration of domestic financial markets in Pakistan. As discussed above, we use the yield spread calculated using interest rates on US bonds and T-bills to proxy the impact of international financial linkages. We selected the US economy as Pakistan - like many other emerging economies - has strong trade and financial linkages with the US economy. Economic developments in the US economy have both direct and indirect effects on the Pakistan's economy, say through Pakistan's exports demand and thus economic activity. Based on this, it could be observed from table 5 that when yield spreads in Pakistan is instrumented by the US yield spreads, the results for 6 to 24 months forecasting horizons is not only found to be statistically significant but also explains most variations in LSM growth, i.e. [beta]2 = 0 based on Wald test.

Table 5: Impact of international financial linkages in predicting output growth in Pakistan

(estimated coefficients - from equation (8))

###Horizon###k = 6 months###k = 12 months###k = 18 months###k = 24 months

Spread###[beta]1###[beta]2###[beta]1###[beta]2###[beta]1###[beta]2###[beta]1###[beta]2

3 year - 3 month###2.52***###-3.01###2.15***###-1.06###1.24**###-0.37###1.17***###-0.34

5 year - 3 month###1.92***###-2.30###1.81***###-0.77###1.08***###-0.39###0.95***###-0.19

10 year - 3 month###1.52***###-2.51###1.31***###-1.09###0.84***###-0.32###0.74***###-0.28

Wald test (2 =0)###Yes###Yes###Yes###Yes

Specifically, the results indicate that when yield spread in Pakistan is instrumented by the US yield spread, the predicted output growth for Pakistan increases, compared to results presented in Table 1. For instance, when predicting output growth for next 6 month, using an instrumented yield spread, we find that a 1 percent increase in spread is associated with an increase in the output growth in the range of 1.5 percent to 2.5 percent across different tenors. However, using the same tenors but without incorporating the impact of US interest rates, Table 1 shows that a 1 percent increase in yield spreads is associated with an increase in the output growth in Pakistan in range of 1.2 percent to 1.6 percent at next 6 months horizon. Similar results are found at longer horizons as well.

Overall, while our empirical results do support the hypotheses that yield spread is a good indicator of predicting output growth in Pakistan over next two years, the results for inflation, however, remained insignificant throughout the study for different specifications. As highlighted, in general, similar observations are also found by Mehl (2009) in most of the emerging economies. Two reasons are identified for this diverging behavior for the yield spread prediction in case of emerging economies by Mehl (2009): shallow bond markets and volatility in inflation. Both seem relevant for the case of Pakistan as well. Let us see in some details.

During the last ten years, the average turnover ratios for short-term bills and longer term bonds are 0.88 and 0.20 in Pakistan, respectively.18 The relatively illiquid bond market indicates the existence of high liquidity premium in Pakistan. In fact, when compared to most other emerging and regional economies, the bond market size in Pakistan is quite small (Figure 3). McCauley and Remolona (2000) suggests that the outstanding government bonds must exceed around US$100-200 billion in order to sustain a liquid government bond market. According to this criterion, it can be observed that Pakistan is far behind in comparison to most emerging markets.

Besides the shallow bond market, there are also certain demand-side factors affecting predictive power of yield spread in case of inflation. Inflation uncertainty (or volatility) is one of these prime factors. The empirical evidence indicate that lower inflation uncertainty decreases the term premium while higher inflation uncertainty leads to higher term premiums (Wright 2011).

Figure 4 depicts that inflation has been relatively more volatile in Pakistan in the last decade compared to most of the other emerging economies.

6. Concluding remarks

The paper attempts to explore the leading indicator attributes of the yield spread in Pakistan, particularly in the context of predicting inflation and output growth by using standard methodologies used in economic literature. Results show that the yield spread in Pakistan can be used as an indicator of future output growth in Pakistan. The paper also investigates the influence of international financial linkages using the changes in the US interest rates. Results show that the use of the US yield spread as an instrument results in increased output growth forecast compared to the case when Pakistan's yield spread is used without such instrument.

Unlike output growth, however, we could not find any role of yield spread in predicting inflation in Pakistan. This finding about inflation deserves attention. We think, apart from expectations, term premium in Pakistan is also influenced by day-to-day movements in liquidity and the argument of shallow market cannot be ruled out in this regard. Another observation worth recording is absence of inflation indexed bonds and lack of inflation expectation surveys in the past that limit market's capacity to form expectations over a longer horizon. Therefore, market expectations seem not to be varying significantly for the longer horizon compared to those in shorter horizon.

Overall, like any empirical analysis, this study also carries some caveats and limitations that provide room for further empirical investigation and research. The theoretical identification of financial market behavior and the role of yield curve, in the context of emerging economies in predicting economic activity and inflation, can be a good contribution.

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Appendix A

Shapes of the yield curve and their economic interpretations

Yield curve or term structure of interest rates represents the relationship between the maturities and the yields of government securities. As represented in figure A1, there are three main types of yield curve shapes: normal, inverted and flat (or humped). A normal yield curve is one in which longer maturity bonds have a higher yield compared to shorter-term bonds. An inverted yield curve is one in which the shorter-term yields are higher than the longer-term yields. In a flat or humped yield curve, the shorter- and longer-term yields are very close to each other.

A positively (or upward) sloping yield curve is considered to be a signal of expansion of economic activities and rising inflation expectations in the economy in near term. A negatively (or downward) sloping yield curve suggests lower inflation expectations and slowdown in economic activity in the medium to long-run. A flattening of the yield curve, which means short-term rates are almost same as the long-term interest rates, indicates uncertainty about economic conditions. A humped yield curve means the yields on medium-term bonds is relatively higher than the short- and long-term bonds. While higher yields on medium tenor bonds relative to shorter tenor bonds indicates increase in inflation and better prospects for economic activity over the medium term, flat yields on longer-tenor bonds shows the inflation to fall without any significant change in economic activity in the long run.

From the theories establishing the relationship between short and long term bond yields, which give the yield curve a particular shape, long-term interest rate or long term bond yield is thought to contain useful information concerning future inflation and economic activity. The liquidity preference theory states that investors demand higher return on longer term bonds due to being less liquid relative to shorter term bonds which could easily be converted into transaction balances. Thus yields on longer term bonds is usually higher than on the shorter term bonds as investors tend to charge a liquidity premium for holding long-term bonds. This liquidity premium is thought to be influenced by investors' expectations about uncertainties surrounding future path of macroeconomic fundamentals having bearing on liquidity of the bonds.

According to the expectation theory, also known as the Fisher hypothesis, long term interest rates are the average of current and expected short term interest (at the time of maturity of the bond or investment) plus a term premium. These suggest the positively slopped yield curve under the normal economic conditions.19

Any change in the slope, which means disproportionate change in short and long term yields, and position of the yield curve, that is proportionate change in short and long term yield, reflects the change in market's perception about future short-term interest rates and uncertainty surrounding their investment. These are, in turn, influenced by investor's changing expectations about future inflation and economic activity. For instance, increase in long-term bond yields might be due to investors' expectation of higher future short-term interest rate and thus inflation. Similarly, investors' changing perception about the risk premium could reflect future path of economic activity influencing liquidity of the bond or financial conditions of the debtor.

Steepening of the yield curve i.e. increase in long-term rates relative to short-term rates or people's preferences for holding shorter tenor bonds and charging a premium for holding relatively less liquid longer tenor bonds, appears to suggest that inflation is expected to rise in the future.20 This means that future short-term rates to be higher than the current rates or central bank to adopt tight monetary policy in future. Alternative lower short-term rates relative to long-term rates also suggests that monetary policy is expansionary at the moment, which is perceived to provide boost to economic activity over the medium term. In other words, the real interest rates i.e. current interest rate adjusted for expected inflation, are low or negative, which encourage households and businesses to spend more and thus provides boost to economic activity. Given that market participants expect the future economic activity to pick up and Philips relationship to hold, then inflation would also be expected to increase.

As an alternative explanation of yield curve steepening, Ang et al. (2006) note that risk premium is counter cyclical and tends to increase on longer tenor bonds in periods of slowdown in economic activity. This is because demand for longer tenor bonds usually decreases during recession, resulting in higher price. Therefore, steepening of the yield curve i.e. increase in long-term rates relative to short-term rates might purely be due to increase in risk premium, reflecting market's concerns about a possible slowdown in economic activities in future. These could also incorporate the likely fiscal position of the government, in particular the overall debt levels and its financing. In such case, steepening of the yield curve might indicate recession in the long-term.

Against this, a negatively sloped or "inverted" yield curve suggests lower inflation expectations and slowdown in economic activity in the medium to long-run. The intuitive argument is that higher short-term rates relative to long term suggests that monetary policy is currently tight in real terms, i.e. real interest rates are positive or relatively high at the moment, which is likely to bring inflation down in future. It also means that current high (real) interest rates encourage households to postpone current consumption for higher consumption in future and businesses to hold their expansion plans, which is likely to affect the real economic activity negatively.

In the same vein, a flattening of the yield curve, which means short-term rates are almost same as the long-term interest rates, indicates uncertainty about economic conditions. It also suggests a likely transition in economy from high inflation expectations - recovery in economic activity to low inflation expectations - slowdown in economic activity, and vice versa. Interpreting a humped yield curve, which means the yields on medium-term bonds is relatively higher than the short- and long-term bonds, is quite difficult. While higher yields on medium tenor (3 to 5 years) bonds relative to shorter tenor bonds indicates increase in inflation and better prospects for economic activity over the medium term, flat/inverted yields on longer-tenor bonds suggest a decline in inflation without any significant change in economic activity in the long run.

Appendix B

Table B1: Granger Causality Test p-values

###H0: US's yield does not Granger Cause###H0: Pakistan's yield does not Granger

###Null Hypothesis

###Pakistan's yield spread###Cause US's yield spread

###Lags

###2###4###6###2###4###6

###Spread

###3 year - 3 month###0.00 ***###0.00 ***###0.00 ***###0.27###0.52###0.68

###3 year - 6 month###0.00 ***###0.00 ***###0.00 ***###0.27###0.33###0.49

###5 year - 3 month###0.00 ***###0.00 ***###0.00 ***###0.16###0.36###0.45

###5 year - 6 month###0.00 ***###0.00 ***###0.01 ***###0.33###0.46###0.55

###10 year - 3 month###0.00 ***###0.00 ***###0.00 ***###0.26###0.47###0.57

###10 year - 6 month###0.01 ***###0.00 ***###0.00 ***###0.38###0.60###0.76

Table B2: Descriptive Statistics of the Selected Variables

###Mean###Median###Maximum###Minimum###Std. Dev.###Source

Interest rates - Pakistan, in percent per annum

###3-month###8.75###9.23###13.45###1.10###3.44

###6-month###8.86###9.27###13.73###1.12###3.46

###12-month###9.02###9.39###14.06###1.37###3.41

###FMA, SBP

###3-year###9.77###10.12###15.52###2.55###3.17

###5-year###10.20###10.40###16.01###3.61###2.94

###10-year###10.79###11.21###16.56###4.60###2.59

Yield spreads - Pakistan, in percentage points

###3 year - 3 month###1.02###0.83###3.58###-0.81###0.75

###3 year - 6 month###0.92###0.71###3.11###-0.83###0.71

###3 year - 12 month###0.75###0.55###2.70###-0.83###0.67

###5 year - 3 month###1.45###1.15###4.69###-0.75###0.98

###5 year - 6 month###1.35###1.07###4.23###-0.77###0.95###FMA, SBP

###5 year - 12 month###1.18###0.94###3.81###-0.77###0.91

###10 year - 3 month###2.04###1.73###6.17###-0.63###1.31

###10 year - 6 month###1.94###1.66###5.71###-0.61###1.30

###10 year - 12 month###1.77###1.49###5.29###-0.61###1.25

Yield spreads - US, in percentage points

###3 year - 3 month###0.72###0.82###2.06###-0.57###0.52###Federal

###5 year - 3 month###1.24###1.39###2.81###-0.60###0.77###Reserve

###10 year - 3 month###2.05###2.22###3.69###-0.52###1.09###Bank

Inflation and output growth, in percent

Headline CPI inflation - yoy###8.95###8.51###24.86###1.32###4.86

###PBS

LSM growth - yoy###6.11###4.50###44.62###-19.71###8.90
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