Estimating Financial Conditions Index for India

Abstract

This article constructs financial condition indices (FCIs) for India and explores their predictive ability of business cycle. The estimated FCIs indicate substantial tightening in financial conditions in India since the global financial crisis barring a brief phase during 2010–11. Unlike in the literature, it shows the importance of standardising the financial variables by removing the influence of unit of measurement and not purging the influence of past economic activity as that improves the forecasting ability of FCI about business cycle. In predicting GDP growth, principal component analysis-based FCI outperforms vector autoregression-based FCI but both are better than OECD composite leading indicator, and indicate an upturn in business cycle in India in 2015–16.

JEL Classification: E5, E17, E44

Keywords

Financial conditions index vector autoregression principal component analysis

1. Introduction and a Brief Review of Literature

The severity of the impact of financial markets stress on the real economy during the global financial crisis, and the euro area sovereign debt crisis, has led to a renewed focus on identifying and assessing the macro-economic–financial linkages embodied in financial conditions. Financial condition is the current state of financial variables characterising the supply and demand of financial instruments relevant for economic activity, which, therefore, influence economic behavior and future economic state (Hatzius, Hooper, Mishkin, Schoenholtz, & Watson, 2010). They also characterise the functioning of the financial markets and access to credit by non-financial agents (Paries, Maurin, & Moccero, 2014). Thus, financial conditions have important influence on macroeconomic variables. Monetary policy focusing only on policy interest rate neglects the important role played by other financial variables, which in turn are influenced by the monetary policy stance. Further, while some important macroeconomic variables such as output gap and neutral interest rate are unobservable and others such as GDP growth and unemployment are available only with lags, most financial variables are readily observable at higher frequencies, and can thus provide crucial real time information to policymakers (Osorio, Pongsaparn, & Unsal, 2011). Therefore, policy makers assess financial conditions on an ongoing basis.

Measuring financial conditions, however, is not straightforward, given the complexity of the financial sector characterised by a wide range of financial variables with distinctive characteristics and predictive powers of economic activity that change over time. A wide range of financial variables are needed to evaluate the functioning of financial markets in real time, but it would be impractical to focus on each and every individual financial indicator separately. Thus, a summary statistics of financial variables in the form of a financial condition index (FCI) is often constructed to gauge the state of financial environment and the degree of strains in the financial system. Though the construction of a FCI is operationally appealing for monetary policy, it is analytically challenging, and consequently, in the literature, there are several methods of constructing it. However, they can be broadly categorised under two main approaches viz., weighted-sum approach and principal-components approach, with several variations within these two broad approaches.

In the weighted-sum approach, a weight is assigned to each variable considered in the index. One easy way is to assign equal weights to all the variables and obtain the FCI as a simple average (e.g., European Central Bank, 2009). The second method is to assign the weights based on the relative impact of each variable on real GDP or inflation. These weights are generated either through simulations of large-scale macroeconomic models or through the estimation of reduced-formed demand equations (IS curves) or vector autoregression (VAR) models (e.g., Beaton, Lalonde, & Luu, 2009; Swiston, 2008). In the second or principal component approach, a common factor which captures the greatest common variation in a group of financial variables is estimated. This common factor is interpreted as the unobserved common variable underlying the variation in the entire financial variables in the group.

Within these two broad approaches, estimates of FCI differ on two other aspects. First is in the control for endogeneity of the financial variables. Estimates of FCI such as in Hatzius et al. (2010) purge the financial variables from the influence of economic cycle on the ground that since FCI summarises the information about future state of the economy contained in the current financial variables, it should ideally measure only financial shocks or exogenous shifts. In other words, endogenous reflection or embodiment in financial variables of past economic activity that itself predicts future economic activity should be removed from the FCI. On the other hand, other estimates such as in Matheson (2012) and van Roye (2011) do not purge the financial variables. The purging is done either by removing the influence from the relevant variables before the construction of the FCI (Hatzius et al., 2010; Paries et al., 2014) or after the construction of FCI (Osorio et al., 2011). But in both the methods, the purging is carried out by regressing the normalised financial variables on current and lagged measures of economic activity such as GDP growth and inflation, and segregating the residual as the unexplained component for constructing the FCI.

The second difference is in the exclusion of policy interest rate or a short-term interest rate from the set of financial variables constituting the FCI. FCI as estimated in Swiston (2008), which includes policy interest rate, can be interpreted as an extension of monetary conditions indices to account for more complex transmission mechanisms than those subsumed by policy interest rates and exchange rate changes (Paries et al., 2014). On the other hand, others such as Matheson (2012), Hatzius et al. (2010) and van Roye (2011) exclude policy interest rate from the FCI to segregate those transmission channels unaccounted for by the traditional monetary policy transmission mechanism emanating from policy interest rate.

In the Indian context, there are very few estimates of FCI that are publicly available. Kannan, Sanyal and Bhoi (2006) estimate only a monetary condition index (MCI), a narrow concept of FCI, consisting of interest rate and exchange rate, with the weights on these variables based on the estimate of an aggregate demand equation. The MCI is then obtained as the weighted-sum of deviations of interest rate and exchange from the base period. In another alternative specification, bank credit is also considered as an additional variable. They find that the estimated MCIs are able to track GDP growth more than inflation. Osorio et al. (2011) estimated FCIs for 13 Asian economies, including India, based on four financial variables using both weighted-sum approach and principal component analysis approach, and a combination of both by a simple average. In the PCA-based approach, the variables are also purged from the influence of business cycle to remove endogeneity problem. They find that interest rates and bank credit provide a greater contribution to their estimated FCIs, which is able to predict GDP growth in India. More recently, Shankar (2014) estimates FCI using PCA on 13 financial market variables encompassing four money market variables and three variables each from bond market, forex market and stock market. It finds a relatively high correlation between the FCI and growth in IIP and GDP, but does not conduct any formal test to establish the predictive ability of the estimated FCI of future economic activity.

In the above backdrop, this article attempts to construct FCI for India using both the weighted-sum approach based on VAR and principal component approach, and a linear combination of the estimated FCIs based on these two approaches. The predictive power on real GDP growth is then compared among these FCIs and vis-à-vis to that of OECD composite leading indicator (CLI) for India, as it is a commonly used indicator to gauge the future economic activity.

This article differs from the comparable earlier work in the following aspects. First, in the Indian context, it uses a larger dataset of higher frequency that extends to more recent period and employs an interpolated monthly GDP series based on Chow and Lin (1971). Specifically, we use more variables of higher frequencies (monthly) and longer time period as compared to that of Osorio et al. (2011), though they also employed both the VAR and PCA approaches. As for comparison with Shankar (2014), we also include quantity variables such as bank credit which are important determinants of financial conditions in India, employ VAR approach in addition to PCA approach. Second, while VAR-based estimates (e.g., Ho & Lu, 2013; Osorio et al., 2011) in the literature normalise the financial variables only by demeaning or subtracting the sample average, we, as an alternative, also standardise or remove the influence of unit of measurement by dividing the series with the standard deviation and compare their predictive ability of GDP growth. Third, it explores the importance of purging the influence of past economic activity from the FCI while assessing their predictive ability of future economic activity.¹ Thus, under both approaches two alternative FCIs, viz., purged and not purged, are estimated, and their predictive ability of GDP growth is compared. Last but not the least, with the purpose of FCI being to serve as a leading indicator of economic activity, we conduct three quarters (9 months) ahead forecast of GDP growth using the best-performing FCIs in terms of in-and out-of-sample forecast from among the estimates.²

The rest of the section is organised as in the following. Section 2 briefly explains the methodology under the two approaches. The description of the variables used for construction of FCIs and analysis of the behaviour of the estimated FCIs are presented in Section 3. The predictive powers of the FCIs of future economic activity are presented in Section 4. The summary and concluding remarks are provided in the final section.

2. Methodology

2.1. VAR-based FCI

In the weighted-sum approach, following Swiston (2008) and others, the weights are derived using a VAR model. This involves estimating the following system of equations.

X_{t} = A_{0} + \sum_{i = 1}^{n} A_{i} X_{t - i} + B Y_{t} + ε_{t}

(1)

where X and Y are vectors of endogenous and exogenous variables, respectively, while A and B are vectors of coefficients, and ε is a vector of error terms.

In the VAR, GDP is necessarily included and policy rate excluded among the endogenous variables, as inclusion of GDP allows the dynamic interaction of business cycle with the financial variables, while exclusion of policy rate enables segregating the impact of traditional channel of monetary policy transmission. The weights of the financial variables in the FCI are obtained from the accumulated impulse responses of GDP to one standard deviation shock on each of the variables. To remove the sensitivity of VAR results on the ordering of variables, and also given the difficulty in identifying the relative sluggishness in the responses of financial variables that would determine the ordering of the variables in the VAR, generalised impulse responses are used.

Two alternative transformations of the financial variables are carried out, viz., (i) normalising the series by subtracting the sample average and (ii) dividing the demeaned series from (i) by the standard deviation to remove the influence of unit of measurement. The respective weights obtained from impulse responses are then applied to the two transformed variables to obtain FCIs as

F C I_{var} = \sum_{j = 1}^{m} w_{j} (x_{j, t} - {\hat{x}}_{j})

(2)

and

F C I_{var_m} = \sum_{j = 1}^{m} w_{j} ((x_{j, t} - {\hat{x}}_{j}) / S t d x_{j})

(3)

where w_j is the weight assigned to financial variable x_j, which is obtained as the cumulative response of GDP to one standard deviation shock to variable in concerned, ${\hat{x}}_{j}$ is the average and Stdx_j the standard deviation of financial variable x_j over the sample period. In other words, a financial variable enter both the FCIs as deviation from its sample mean to represent shocks to the variable at each point of time. However, in the second FCI, the influence of unit of measurement is also removed.

To address the issue of need for removing the influence of current and past economic activity pointed out in the literature, the FCIs obtained in equations 2 and 3 were purged from the influence of current and past economic activity through the following regression

F C I_{var} = c + \sum_{i = 0}^{n} g_{t = i} + ε_{t}

(4)

where ‘g_t’ is GDP growth, and i the number of lags. ε_t which is the residual is the purged FCI, denoted by FCI_{var_m_p} and FCI_{var_p}, respectively, for financial variables normalised and not normalised for magnitude.

2.2. Principal Component Analysis

In the PCA approach, the dimensionality of the underlying dataset is reduced by extracting the uncorrelated linear combinations of the variables that contains most of the variance. In other words, PCA models the variance structure of a set of observed variables using linear combinations of the variables themselves. The principal components of a set of variables are obtained by computing the Eigen value decomposition of the observed dispersion matrix of variables. The first principal component is the unit length linear combination of the original variables with maximum variance. The variance explained by the first principal component is the largest Eigen value of dispersion matrix. Subsequent principal components maximise variance among unit-length linear combinations that are orthogonal to the previous components and are uncorrelated with all the preceding components. Thus, principal components account for a progressively smaller share of variance of the original dataset, with bulk of the information having been summarised in the first few components.

Specifically, let X₁, X₂, …, X_n be the variables under consideration with dispersion matrix ∑ _nxn. The objective of PCA is to obtain a set of new variables say Y_i, with i = 1 to n, called the principal components, defined as linear combination of original variables such that Y₁ captures the largest proportion of the variability in the original data, Y₂ captures the next largest proportion of the variability, and Y₂ is uncorrelated with Y₁ and so on. In other words, PCA provides the vectors a₁, a₂, …, a_p (p < n) such that,

a^’_k * a_k = 1 for k = 1, …, p,

the variance of X*a_k is as large as possible; and

X *a_k and X *a_l are uncorrelated if k ≠ l.

It can be shown that the vectors a₁, a₂, … a_n are the Eigen vectors and Var(Y_k ) = Var(X*a_k) = λ_k is the Eigen value of dispersion matrix ∑ _{n x n}.

Usually, variability in the data can be adequately described by the first few principal components that are sufficient to consider as leading principal components for further analysis. In practice, principal components with Eigen value greater than unity are generally considered. Other criterion to select the leading principal components is to consider the first few principal components which explain at least 70 per cent of variation cumulatively. The selected principal components can be combined as weighted average to get the common factor Z_t using the weights as proportion of variation explained by individual principal component as

Z_{t} = \sum^{​} b_{i} * Y_{i, t}

(5)

where b_i = λ_i / ∑ λ_j, i=1,2, …, p and j=1,2, …, p

To obtain the FCI, the influence of past economic activity is then purged from the common factor Z_t by regressing it on current and lagged GDP growth as

Z_{t} = c + \sum_{i = 0}^{n} g_{t - i} + ε_{t}

(6)

where ε_t is the PCA-based purged FCI.

The VAR-based FCIs from equation 4 and PCA-based FCI from equation 6 are then averaged to obtain the average FCI (FCI_average), which has the characteristics of both the approaches, so as to check whether a combination of the two approaches enhances the predictive power on future economic activity than the individual approach.

3. Data and Estimation Results of the Financial Condition Indices

The time period considered is from March 2002 to September 2014 of monthly frequency. The details of data sources for the various macro and financial market variables used in the construction of FCIs are listed in Annexure 1.

3.1. VAR-based FCI

For the purpose, old GDP series (GDP data with 2004–05 as base) which is available at quarterly frequency was converted into monthly frequency using Chow and Lin’s (1971) method based on the behaviour of 3-month moving average of IIP (see Annexure 2).³ Nominal variables were converted to real terms by deflating with GDP deflator derived from the converted nominal and real monthly GDP series by the method mentioned above. Barring spread and policy rate, all other variables, both endogenous and exogenous, variables were converted into growth over 12 months or year-on-year growth, rendering effective time period for estimates of FCI from March 2003 to September 2014. The exogenous variables controlling for external factors in the VAR are US stock market volatility (VIX) and index of industrial production (IIP) in the US. A lag length of one was selected for the VAR based on Schwartz Bayesian Criterion (SBC), as this criterion makes an adjustment of degrees of freedom (Bayoumi & Darius, 2011).

In the VAR, among several prospective financial variables, we considered only those financial variables on whose shock the accumulated responses of GDP were found to be statistically significant as shown in Figure 1.

Figure 1.

Source: Authors’ estimates.

It is observed that the direction of the responses are as expected, perhaps barring that of real effective exchange rate (REER), the increase, or appreciation, of which leads to improvement in GDP growth. But in the Indian case this is plausible for several reasons. One, India being not so much export dependent, while imports being quite price inelastic due to higher share of crude oil that appreciation in REER could lead to decline in net imports and thus GDP growth. Second, REER appreciation following capital inflows due to gain in confidence in the economy could, by improving the financial resources available for investment, enhance GDP growth. Third, REER appreciation in India, which more often than not follows from large capital inflows, would indicate easing financial conditions.

Thus, the endogenous variables finally included in the VAR are real GDP, REER, real bank credit (NFC), spread in 10-year G-sec yield between India and US (SPREAD), real money supply (M3), and real equity prices (SENSEX). Consequently, the financial variables constituting the FCI are REER, NFC, SPREAD, M3, and SENSEX, with the weights assigned to them being the accumulated responses of GDP growth to the respective one standard deviation shock of these variable over 6 to 12 months.

The estimated FCI along with the contributions of individual financial variables are shown in Figure 2. It can be seen that the contribution of these five financial variables to the aggregate FCI varied over the sample period. Exchange rate and equity prices have been important contributors to swings in the overall financial conditions, which could be attributed to the important role of capital flows (portfolio) in easing financial conditions via fluctuations in exchange rate and stock prices. While quantity variables viz., money supply and bank credit have also been important contributors to overall financial conditions, they at times moved in the opposite direction to exchange rate and stock prices. For instance, during the global financial crisis of 2008–09 when the overall financial conditions tighten drastically, reflected in the falling equity prices and large currency depreciation, money supply, and bank credit eased, while during 2010–11 with improvement in the overall financial conditions on economic rebound and capital inflows, money supply, and bank credit tightened. On the whole, the estimated FCI shows easy financial conditions during 2003 to mid-2008, barring around end-2004, while succeeding period is largely characterised by tight financial conditions barring a brief phase of economic recovery during 2010–11 following global financial crisis.

Figure 2.

Source: Authors’ estimates.

3.2. Principal Component Analysis

Based on the literature, different indicators of financial conditions are chosen, broadly classified into quantity, spread, and price variables. Since banks play a major role in the financial system in India and to real sector of the economy, non-food credit extended by banks is considered an important financial variable, with increase in it indicating easing financial conditions. Another closely related financial variable considered is the money supply (M3), with increase in it again reflecting easing financial conditions. Further, recognising the growing importance of financial market in the funding of corporate firms, capital raised by corporate (both public issues and private placements) is considered as another quantity variables, with increase in it representing easing financial conditions.

Generally, risk premium embedded in various interest rates would indicate relative degree of financial stress—with increase in spreads reflecting this increasing stress or tightening financial conditions and vice versa. We use different measures of spreads from short-end to long-end with a view to capture stress in various segments of financial markets. First, the spread between 3-month Treasury bill and weighted average call rate is used as a proxy for financial tightness in financial institutions, as during tight financial conditions, the inter-bank market may dry up and lead to higher spread between inter-bank overnight rate and 3-month Treasury bill. Stress in other segments of financial markets is captured through longer-term spreads: (i) the spread between 10-year government bond yield and 3-month Treasury yield in India, (ii) sovereign credit risk measured by the spread between 10-year government bond yields in India over the US government bond of equal maturity—higher spread reflecting tighter financial conditions, and (iii) corporate credit risk measured by spread between 10-year AAA rated corporate bond yield and the 10-year government bond yield, with the rise in these spreads indicating tighter financial conditions.

Among the price variables, we consider equity prices (Sensex), as a higher equity price is expected to be associated with loose financial conditions. On the other hand, volatility in equity prices could reflect stress in the financial market—higher the volatility, the greater the stress in financial market. To capture it, we include volatility in stock market return, measured by 2-month moving average of standard deviation of daily stock return. Finally, the impact of external sector on financial conditions is sought to be captured through the movement in nominal effective exchange rate (NEER), with appreciation in it reflecting easing financial conditions due to higher capital inflows.

All the variables are standardised, that is, they are demeaned and divided by the standard deviation. Barring volatility and spread variables, all the quantity and price variables viz., bank credit, M3, capital raised by corporate, Sensex, and NEER are measured on year-on-year basis. Further, variables are suitably modified such that spread and volatility are taken with negative sign so that an increase in any series indicates easing of financial conditions.

PCA resulted in four principal components explaining around 76 per cent of variance cumulatively. Table 1 provides the loading factors of the selected four principal components reflecting the importance of different variables. First principal component is dominated by NEER, equity prices, money supply, capital raised by corporate and foreign spreads, while second principal component is influenced by domestic spreads, and quantity variables viz., non-food credit, capital raised by corporate and money supply.⁴

Table 1.
Loading Factors of Principal Components

PC1 PC2 PC3 PC4

Non-food credit 0.17 0.28 0.38 0.30

Money supply 0.34 0.30 –0.51 0.15

NEER 0.45 –0.07 0.19 –0.20

Sensex 0.43 –0.24 0.22 0.07

Capital raised 0.34 0.30 –0.51 0.15

Equity volatility 0.20 –0.54 –0.20 0.14

Domestic spread (10 years) –0.29 0.46 –0.02 –0.38

Foreign spread (10 years) 0.32 0.26 0.43 0.01

Spread between TB-3M and WACR –0.13 0.24 0.16 0.70

Spread between 10-year G-Sec and TB-3M –0.33 –0.22 –0.08 0.42

Eigen values 2.97 1.92 1.73 1.03

Share of total variance explained 29.70 19.20 17.30 10.30

	PC1	PC2	PC3	PC4
Non-food credit	0.17	0.28	0.38	0.30
Money supply	0.34	0.30	–0.51	0.15
NEER	0.45	–0.07	0.19	–0.20
Sensex	0.43	–0.24	0.22	0.07
Capital raised	0.34	0.30	–0.51	0.15
Equity volatility	0.20	–0.54	–0.20	0.14
Domestic spread (10 years)	–0.29	0.46	–0.02	–0.38
Foreign spread (10 years)	0.32	0.26	0.43	0.01
Spread between TB-3M and WACR	–0.13	0.24	0.16	0.70
Spread between 10-year G-Sec and TB-3M	–0.33	–0.22	–0.08	0.42
Eigen values	2.97	1.92	1.73	1.03
Share of total variance explained	29.70	19.20	17.30	10.30

Source: Authors’ estimates.

The common factor which summarises the information contained in the current financial variables is constructed by summing the selected principal components weighted by the share of total variability explained by them as defined in equation 5. The importance of individual variable in the common factor is reflected by the weighted loading across the four principal components. It is seen that foreign spread, non-food credit, NEER, and equity return contributed more to the common factor than the other variables (Figure 3).

The FCI is then estimated by purging the influence of GDP growth using equation 6 with lag length determined by SBC. The FCIs based on standardised financial variables and not purged under both the approaches viz., FCI_var_m and FCI_pc (based on equations 3 and 5) indicate a largely easy financial conditions in the pre-crisis period and tight financial conditions in the post-crisis period (Figure 4)⁵—any reading below zero indicates tight financial conditions and vice versa. The two FCIs are highly correlated (correlation of 0.61), with the correlation being significantly higher during the post-crisis period than the pre-crisis period. The average of the two FCIs (FCI_average) closely tracks PCA-based FCI as the loading factors in PCA-based FCI, in general, are found to be far larger than the weights in VAR-based FCI derived from the accumulated impulse responses.

Figure 3.

Source: Authors’ estimates.

Figure 4.

Source: Authors’ estimates.

4. Assessing the Predcitive Power of the Indices

As mentioned above, usefulness of a FCI lies in its ability to predict or serve as the lead indicator of economic activity, which in our case, is represented by GDP growth over 12 months. We do this in several steps. First, observe whether there is co-movement between the FCIs and GDP growth through graphical presentation and correlation. Second, conduct Granger causality test to check whether or not the FCIs cause GDP growth. Third, conduct in-sample and out-of-sample forecast to assess the FCIs’ predictive ability of future GDP growth by estimating the following equation.

G D P_{t + h} = α + \sum_{i = 1}^{m} β_{i} G D P_{t + 1 - i} + γ F C I_{t} + \in ​_{t}

(7)

where ‘h’ is the forecast horizon and ‘FCI’ is the estimated financial conditions index For in-sample forecast, we first estimate the autoregressive (AR) equation in equation 7, that is, GDP growth on its own lag for the concerned forecast horizon over the sample period. The AR equation is then augmented with FCI, and check for (i) whether the coefficient of FCI is statistically significant and (ii) how much the explanatory power, in terms of R-bar square, improves with the inclusion of FCI.

For out-of-sample forecast, both the AR equation and equation 7 are estimated for a shortened sample period, and these estimations are used to forecast the GDP growth over the remaining sample period. The respective forecasted values of GDP growth are compared with the actual values, and the root mean square errors (RMSEs) are calculated. The estimated RMSE for the AR equation and equation 7 are then compared, with lower RMSE for equation 7 than AR equation, a ratio lower than one, indicating better predictive ability of FCI.

Starting with VAR-based FCI with standardised financial variables, that is, demeaned financial variables scaled by standard deviation, it could be seen from Figure 5 that the individual and combined FCIs tend move in the same direction with that of GDP growth. During more recent period, one can discern some gaps in the movement of individual indices and GDP growth. However, the movement in some of the individual indices is in the opposite directions that they negate each other to a fair extent that the co-movement between the combined FCI and GDP growth improves significantly. For instance, while SENSEX indicates easing of financial conditions since around the beginning of 2012, bank credit and spread, on the other, point to tightening of financial conditions around the same time. In other words, the FCI_var_m, by aggregating/combining the information content in various financial indicators, tracks the GDP growth better than the individual FCIs.

Figure 5.

Source: Authors’ estimates.

The other alternative aggregate FCIs also show co-movement with GDP growth, though with varying degrees. However, there are significant differences between the purged and not purged FCIs, particularly for VAR-based FCIs. For instance, for more recent period, the purged FCIs indicate a much better financial condition than those FCIs which are not purged that the co-movement with GDP growth, which does not show a significant turnaround, is much weaker for the former than the latter (Figure 6). This observation could indicate that purging the influence of past economic activity from the FCI does not necessarily improve the predictive ability of FCI of future economic activity, which is further explored below.

Figure 6.

Source: Authors’ estimates.

The co-movements between the FCIs and GDP growth are confirmed by the statistically significant correlations, which also reveal several interesting points (Table 2). First, the cross-correlations are higher with FCIs as the lagged variable—ranging from 2 to 12 months—than GDP growth as the lagged variable, suggesting that the FCIs are the leading indicators of GDP growth rather than vice versa. Second, cross-correlations with FCIs as the lag variable are higher than the corresponding contemporaneous correlations, also indicating the potential leading indicator property of these FCIs. Third, purging leads to significant lowering of cross-correlation coefficients, further suggesting that removing the influence of past economic activity from the FCIs perhaps leads to loss of information and lowers the predictive ability of future economic activity. Fourth, standardised FCIs have a much higher cross correlation with GDP growth than non-standardised FCIs obtained from demeaned financial variables not scaled by standard deviation.⁶ Fifth, all the alternative FCIs, baring FCI_var_p, have higher correlations with GDP growth than the correlation between CLI and GDP growth, suggesting that the estimated FCIs could be better leading indicators than CLI.

Table 2.

Correlation Between GDP Growth and FCIs

FCI	Contemporaneous	Cross Correlation
		FCI Lagged Variable		GDP Lagged Variable
	Value	Value	Lags	Value	Lags
FCI_var_m	0.65*	0.70*	3	0.63*	1
FCI_var_m_p	N.A.	0.52*	3	0.35*	2
FCI_var	0.61*	0.66*	2	0.58*	1
FCI_var_p	N.A.	0.42*	3	–0.34	10
FCI_PC	0.57*	0.65*	4	0.59*	1
FCI_PC_p	N.A.	0.57*	12	0.32*	2
FCI_average	0.58*	0.66*	3	0.60*	1
CLI	0.13	0.51*	8	–0.14	9

Source: Authors’ estimates.

Note: * denote significance at 1% level.

Granger causality tests reported in Table 3 show that when the FCIs are not purged from the influence of current and past economic activity, the causality is unidirectional from FCIs to GDP growth. However, when purged, the causality turns bidirectional in all the VAR-based FCIs, while for PCA-based FCI, the causality remains unidirectional from FCI to GDP growth.⁷ The average FCI, which is not purged, and CLI also have a unidirectional causality on GDP growth. These results while reinforcing the earlier results on the potential predictive power of these estimated FCIs on future economic activity, at the same time, indicate that purging, rather than enhancing, could lower the predictive ability.

Table 3.

Grange Causality

Null Hypothesis	Based on Cross-correlation Lags		Six Lags
	Chi-square	P-value	Chi-square	P-value
GDP does not Granger Cause FCI_var_m	0.72	0.54	1.06	0.39
FCI_var_m does not Granger Cause GDP	9.10	0.00	4.25	0.00
GDP does not Granger Cause FCI_var_m_p	5.61	0.00	2.11	0.06
FCI_var_m_p does not Granger Cause GDP	9.53	0.00	3.82	0.00
GDP does not Granger Cause FCI_var	1.36	0.26	1.37	0.26
FCI_var does not Granger Cause GDP	11.78	0.00	3.86	0.00
GDP does not Granger Cause FCI_var_p	4.11	0.01	3.38	0.00
FCI_var_p does not Granger Cause GDP	6.92	0.00	4.77	0.00
GDP does not Granger Cause FCI_pc	1.37	0.25	1.01	0.42
FCI_pc does not Granger Cause GDP	6.42	0.00	3.32	0.00
GDP does not Granger Cause FCI_pc_p	0.59	0.85	1.11	0.36
FCI_pc_p does not Granger Cause GDP	2.41	0.01	3.30	0.00
GDP does not Granger Cause FCI_average	1.35	0.26	1.01	0.42
FCI_average does not Granger Cause GDP	8.11	0.00	3.44	0.00
GDP does not Granger Cause CLI	1.12	0.35	1.18	0.32
CLI does not Granger Cause GDP	1.90	0.07	1.96	0.08

Source: Authors’ estimates.

Note: Six lags were chosen given the central forecast horizon for predictive performance of six months in the following.

Finally, the formal tests for relative predictive performance were carried through in-sample and out-of-sample forecast by estimating equation 7. Three forecast horizons of 3, 6, and 9 months were set over the sample period from 2003:3 to 2014:9. The optimum lag length of the AR process was determined by SBC, and the same lag length was adopted for the FCIs so as to have a fair comparison of the predictive performance. The t-statistics for significance of the coefficient of the lagged FCIs, the adjusted R², and the incremental adjusted R² over the AR estimates reported in Table 4 reveal the following. First, the coefficients of the lagged FCIs are positive and significant, and inclusion of FCIs leads to all significant improvement in the explanatory power over the AR equations, indicating that these indices help in explaining the near-term GDP growth. Second, purging the influence of economic activity from the FCIs, particularly in VAR-based FCIs, leads to reduction in the predictive power. This finding shows that the suggestion made in the literature that FCI should be purged from the influence of past economic activity to reflect only the exogenous shifts in financial variables can conflict with the usefulness of a FCI which is measured by its predictive ability of future economic activity. Third, the incremental explanatory power over the AR equation rises as the forecast horizon increases from 3 to 9 months for all FCIs, except non-standardised VAR-based FCI where a decline is shown. Further, in VAR-based FCI, the predictive power of FCI is significantly higher when financial variables are standardised than when not standardised. This highlights the importance of normalising the influence of magnitude of measurement of financial variables in constructing FCI, which is mostly ignored in VAR-based approach in the literature. Fourth, VAR-based FCIs perform better than PCA-based FCI for forecast horizon of three months only, but that too only when the financial variables are standardised. While PCA-based FCIs outperforms CLI in all the three forecast horizons, for the VAR-based FCI they are better only up to 6 months when financial variables standardised, and only up to 3 months when not standardised. Overall, PCA-based FCI outperform VAR-based FCI over the longer forecast horizon.

Table 4.

In-sample Forecast

FCI	Three Months Ahead		Six Months Ahead		Nine Months Ahead
	t-stats	R²	Δ R² over AR (%)	t-stats	R²	Δ R² over AR (%)	t-stats	R²	Δ R² over AR (%)
AR	6.40*	0.23	0.00	4.72*	0.14	0.00	4.00*	0.10	0.00
FCI_var_m	8.53*	0.50	118	6.60*	0.35	152	5.53*	0.27	166
FCI_var_m_p	8.37*	0.49	117	5.53*	0.31	126	4.84*	0.25	149
FCI_var	6.63*	0.42	82	3.88*	0.22	60	2.73*	0.14	43
FCI_var_p	6.23*	0.40	76	3.14*	0.21	52	2.18**	0.15	43
FCI_pc	7.27*	0.44	94	7.05*	0.37	168	8.09*	0.40	296
FCI_pc_p	7.24*	0.44	94	7.04*	0.37	167	8.07*	0.40	295
FCI_average	7.44*	0.46	101	7.12*	0.39	177	8.05*	0.41	304
CLI	3.37*	0.28	24	4.98*	0.30	116	6.31*	0.31	206

Source: Authors’ estimates.

Note: * and ** denote significance at 1% and 5% levels, respectively.

To compare the dynamic out-of-sample forecast, equation 7 estimated for the period 2009:3 to 2012:12 was used to forecast for the remaining sub-sample 2013:1 to 2014:9, and the forecast error measured by RMSE was compared with the corresponding RMSE obtained from the forecast based on AR process of GDP growth over the corresponding period.⁸ With relative RMSE of less than one indicating a better forecast performance, the results presented in Table 5 show that PCA-based FCI has a much better out-of-sample forecast ability than the other FCIs, with relative forecast error for the 3-month horizon lower by almost 50.0 percent. As in in-sample forecast, purging leads to significant reduction in out-of-sample forecast ability of FCIs, particularly for VAR-based FCIs. Non-standardisation of financial variables also leads to marked deterioration in the out-of-sample forecast performance of FCIs. In fact, purged and non-standardised VAR-based FCI do not contribute much to the out-of-sample forecast, with a higher RMSE than that of AR forecast in all the three forecast horizons. Only PCA-based FCIs and VAR-based FCI which is not purged and standardised (FCI_var_m) have better out-of-sample forecast performance than that of CLI in all the three forecast horizons. Averaging of FCI does not lead to any noticeable improvement in the forecast. Overall, PCA-based FCI without purging has the best out-of-sample forecast in all the three forecast horizons.

Table 5.

Out-of-sample Forecast

FCI	Three Months Ahead		Six Months Ahead		Nine Months Ahead
	RMSE	RMSE as % of AR	RMSE	RMSE as % of AR	RMSE	RMSE as % of AR
AR	0.03		0.03		0.03
FCI_var_m	0.02	0.55	0.02	0.62	0.02	0.68
FCI_var_m_p	0.03	0.94	0.03	0.90	0.03	0.88
FCI_var	0.02	0.81	0.03	0.88	0.03	0.92
FCI_var_p	0.04	1.27	0.03	1.11	0.03	1.05
FCI_pc	0.01	0.47	0.01	0.51	0.01	0.51
FCI_pc_p	0.01	0.50	0.02	0.57	0.02	0.56
FCI_average	0.01	0.47	0.01	0.51	0.01	0.51
CLI	0.03	0.89	0.02	0.85	0.02	0.76

Source: Authors’ estimates.

As mentioned above, usefulness of a FCI lies in it being a good leading indicator of economic activity or business cycle. Given the above reasonably satisfactory forecast performance of the estimated FCI, dynamic forecasts of GDP growth were performed for the next three quarters beyond the sample period viz., for December 2014 to June 2015, with the focus of the projections being the turning points rather than the absolute numbers. For the same, equation 7 was estimated for the entire sample period 2003:3 to 2014:9 using FCI_var_m and FCI_pc. Based on these estimates, forecasts were generated for 3, 6, and 9 months. The forecasts for first three months were obtained from the 3-month forecast, for the fourth to sixth month from the 6-month forecast and seventh to ninth month from the 9-month forecast. These monthly projections were then converted back to quarterly projections by adding the corresponding months of the respective quarters. The projections based on the two FCIs show a turnaround in GDP growth over the next three quarters starting from quarter ended—December 2014 to June 2015 (Figure 7).

Figure 7.

Source: Authors’ estimates.

5. Summary and Conclusion

The article estimates financial conditions indices for India employing two alternative approaches—VAR and principal component analysis—using a larger dataset of higher frequency that extend to more recent period than the comparable earlier works on India, and employing an interpolated monthly GDP series. Using a number of tests, the predictive power of the estimated FCIs on future economic activity is assessed and compared vis-à-vis to that of OECD CLI. In doing so, the importance of standardising the financial variables, that is, removing the influence of unit of measurement, and purging the influence of past economic activity from the FCIs is also analysed.

The estimated FCIs indicate that much of the pre-crisis period in the 2000s was characterised by easy financial conditions, which tightened substantially with the global financial crisis and continued to remain so barring a brief phase coinciding with economic recovery during 2010–11. Both the approaches show exchange rate, equity prices, bank credit, money supply, and spread between 10-year G-sec yield in India and the US are important determinants of overall financial conditions. The FCIs are highly correlated with GDP growth and the causality is unidirectional running from the FCIs to GDP growth, except when VAR-based FCIs are purged from the influence of past economic activity. The performance of aggregate FCI, both in terms of its correlation with and the predictive ability of future GDP growth, is much better than the individual FCIs forming the aggregate. This suggests the importance of combining the information contained in the individual financial variables that joint movement in financial variables has more information about future economic activity than individual financial variables.

All the FCIs have a reasonable predictive ability of future economic activity, much higher than that of CLI, except for VAR-based FCIs derived from non-standardised financial variables and are purged from the influence of past economic activity. In both in-and out-of-sample forecast of GDP growth, PCA-based FCIs in general outperform VAR-based FCIs in all the near-term forecast horizons.

Thus, unlike in the literature, the estimates suggest the need to standardise or remove the influence of unit of measurement from the financial variables as that leads to marked improvement in forecasting ability of VAR-based FCIs. Further, the estimates indicate that capturing of only the exogenous financial developments by purging the influence of past economic activity can, instead of enhancing as suggested in the literature, lower the forecasting ability of FCI about future business cycle. Last but not the least, the forecasts from the preferred FCIs from among the estimates suggest a turnaround in GDP growth in India in the next three quarters from December 2014 to June 2015.

Footnotes

Data Sources

Sr. No.	Variable	Data Source
1	GDP	Database on Indian Economy (DBIE), Reserve Bank of India
2	IIP	Database on Indian Economy (DBIE), Reserve Bank of India
3	NEER	Database on Indian Economy (DBIE), Reserve Bank of India
4	REER	Database on Indian Economy (DBIE), Reserve Bank of India
5	Money Supply (M3)	Database on Indian Economy (DBIE), Reserve Bank of India
6	NFC	Database on Indian Economy (DBIE), Reserve Bank of India
7	Capital raised by corporate	Securities and Exchange Board of India
8	Sensex Index	Bloomberg
9	Yield on 10-year Indian Government bond	Bloomberg
10	Yield on 10-year US Treasury	Bloomberg
11	3-month T-Bill for India	Bloomberg
12	Weighted Average Call Rate (WACR)	Database on Indian Economy (DBIE), Reserve Bank of India
13	Yield on 10-year AAA corporate bond in India	Bloomberg

Chow and Lin Method of Temporal Disaggregation

Chow and Lin (1971) introduced in their seminal paper a general methodology for interpolation, distribution, and extrapolation of time series by related series as in the following. Suppose ‘Y’ is quarterly a series of ‘n’ observations. The objective is to find out the monthly series say Y* of 3*n observations such that monthly series aggregates to quarterly series. The fundamental assumption made in this method is that it is possible to write the series to be constructed as a linear stochastic function of some observed monthly time series x as

(1)

Y * = x β + \in

where β represents a vector of parameters and ϵ is a vector of stochastic disturbances with covariance matrix V.

Let C be a nx3n aggregation matrix that converts monthly series into its quarterly values by pre-multiplication so that

Y = C Y * = C x β + C ε

Then, this method provides the monthly series of variable of interest by using estimate of β from equation 1 (i.e., based on quarterly series) and distributing the errors from equation 1 according to aggregation matrix C.

Notes

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