The task of controlling inflation in any nation is the responsibility of the Monetary Authority of the country. This tight or expansionary monetary policy brings some costs related to economic activity. According to Friedman (1976), the essential objective of monetary policy is to maintain a stable relationship between inflation and output. Low inflation has been considered a beneficial condition for the economy and it is also concluded that disinflation policies cause output losses. i.e., SR is significantly positive.

In the last thirty years, price stability has been the main objective of central banks all over the world, it has a crucial place in the monetary policy framework. To achieve price stability, central banks use different tools, in which inflation targeting is an important strategy for output stabilization. Price stability is a necessary condition for sustainable growth and employment opportunities. According to empirical literature, a low inflation rate is an important determinant of long-run growth and minimum welfare loss (Okun, 1978). Because bringing inflation down to its normal value leads to short-run output losses (Ball, 1994), that's why it's crucial for the central bank to consider the trade-off between inflation and output, while formulating the monetary policy. The output losses are the opportunity cost of inflation targeting and that's why the policymaker is always keen to measure the cost of disinflation. So, it is important to calculate SR for effective monetary policy.

In the literature, various attempts are made by different authors for the estimation of SR. These attempts are classified into two major groups: Time-invariant SR (Cecchetti & Rich, 2001; Gordon & King, 1982 and Okun, 1978) and episode-specific method (Zhang 2005 and Ball 1994). In Time invariant SR various methodologies like the Phillips Curve, structural vector autoregressive, and the new Keynesian Phillips curve are used to estimate the SR. Ball (1994) criticized Phillip's Curve approach on the basis that output and inflation trade-offs remain the same during the process of disinflation as well as during the process of accelerating inflation. He proposed a new methodology for the estimation of SR based on episode identification. Ball (1994) identified the disinflation episode by the trend inflation. After the identification of the disinflation episodes, Ball (1994) estimates the sum of the deviation of differences between actual output and potential (trend) output and then estimates SR associated with disinflation episodes. Ball (1994) assumed that potential output in disinflation episodes grows linearly. Secondly, Ball (1994) also assumed that at the beginning of the disinflationary episode, the output must be at its potential level and after deviation due to disinflationary policy, it goes back to its potential level four quarters after the termination of the disinflationary episodes. After 1994 the methodology proposed by Ball was adopted by many researchers whose objective was the estimation of the output cost of a disinflationary episode (Bernanke et al., 1999; Lunardelli & Nakane, 2019 & Caporale, 2008).

The limitation of Ball's methodology in terms of ignoring long-lived and persistent effects is criticized by Zhang (2005) that the cost of disinflation will be understated if long-lived effects are not taken into consideration while estimating SR. The assumption of Ball (1994) related to the potential output at the trough is relaxed by Zhang (2005). Ball (1997) argued that persistence effects or long-lived effects are much stronger than the standard assumptions of Ball. Hofstetter (2008) also followed the Zhang (2005) methodology, but he also considers inflation inertia.

These long-lived effects were analyzed by different researchers through the VAR methodology. Dolado and Lopez Salido (1996), Gereziher, & Nuru, (2021), Bhatti & Qayyum (2016) and Cetinkaya & Yavuz (2002), and Ikwor et al. (2024) checked the effects of Monetary shocks through the structural VAR for the economy and stated that these monetary shocks had long term costs for the economy. Cecchetti & Rich (2001) criticize the way Ball identifies the disinflation episode, which he assumes is because of contractionary monetary policy but he ignores the effects of other variables.

In the case of Pakistan, monetary tightening not only hurts economic activity through the traditional channel, it has fiscal consequences as well. Owing to financial sector reforms, monetary policy became market-based which resulted in a high cost of borrowing. This has fiscal consequences which in turn affect fiscal space and hence hampers long-run growth potential. The worth of this study is to estimate the fiscal consequences of disinflationary policy. To decrease inflation, the central bank will increase the interest rate, which will increase the cost of borrowing and ultimately debt burden. So, measuring SR through only the traditional methods as discussed above will underestimate the true cost of contractionary monetary policy, because in these the supply side effects of fiscal contraction are ignored. The inflation targeting policy increased the cost of borrowing both for the private sector and the government sector, which will affect long-term growth.

Keeping in view the empirical literature related to the methodology of SR and the importance of trade-offs between output and inflation in the monetary policy framework, This study calculates the sacrifice ratio (SR) by examining both how reduced demand and limited fiscal space affect the economy. We argue that the long-term gains from price stability are outweighed by the overall costs measured through these two channels.

The existing literature on the estimation of SR cites different methodologies, which are discussed below. First methodology for SR from the monetary side is discussed and then the same from the fiscal side is explained.

Phillips Curve Methodology

The trade-off between output and inflation has been studied in the literature extensively, by the pioneer work of Okun (1978) and Gordon and King (1982). The measurement of SR is based on expectations augmented Phillips Curve.

(1)

Where , and ? measure actual output, potential output, and inflation rate and measure the cost of disinflation.

Ball’s Methodology

The disadvantage associated with Phillips's curve methodology is that the SR estimated remains the same within the disinflation episode as well as within the inflationary situation (Ball, 1994). Ball's (1994) methodology is based on the identification of disinflationary episodes. Ball (1994) defines SR as:

(2)

In equation 2, the numerator measures the sum of the difference between the actual output and potential level of output during disinflationary episodes and the denominator measures the change in inflation rate at the start and end of the disinflation episode. Following the work of Ball for the identification of disinflationary episodes this study brings a little bit of change in the definition of trend inflation because here the data available is in annual format. For episodes' identification, we define trend inflation "t" as a centered three-year moving average between t-1 and t+1. The study identified a disinflation episode with inflation peaks and inflation troughs. An inflation peak is a point where the trend inflation at time period t is at a higher level as compared to the trend inflation at time period t-1 and at time period t+1. An inflation trough is the point where the trend inflation at time period t is lower than the trend inflation at time period t-1 and time period t+1. The disinflation episodes are the episodes that begin with peak inflation and end with trough inflation. And the trend inflation in disinflation episodes decreases by at least 1.5 percent.

The next is the calculation of the potential output which is the most elusive issue. Because a very little difference in fitted trends can cause very huge differences for the SR. Ball (1994) defines the potential level of output based on the given assumption: i.e., at the inflation peak the output is to be assumed at a potential level, and after the four quarters of inflation trough output is to be assumed to return to its natural level. When the trend output and actual output are equal between the two points, the trend output is assumed to grow linearly. Geometrically, trend output is the straight line connecting these two points (Ball, 1994; Partow et al, 1998; and Jordan & Thomas, 1997). The first assumption stated that the inflation and potential level must be stable at the start of the episode. The second assumption states that there are no hysteresis effects which can cause a strong persistence effect. The hysteresis effects only occur when disinflation and contractionary monetary policy affect the potential output permanently. Ball (1994) assumes that trend output is at its potential level during the disinflation episode. The trend output grows log linearly in the disinflation episode.

The third method was used by Zhang in 2005, the modified version of Ball (1994). Zhang (2005) criticizes Ball's methodology as it ignores the persistence and hysteresis effect when output comes back to its potential level after the disinflation episode. Through this approach, the HP filter of the real GDP was calculated. Then, the growth rate of the HP filter was calculated. Thirdly it is assumed that potential output grows at the rate found by the series of HP filters.

Structural VAR Methodology

The fourth methodology used for the determination of SR is the Structural VAR Methodology used by Cecchetti and Rich (2001) to calculate the SR. Ball's (1994) and Zhang's (2005) methodologies of SR do not identify the monetary policy shocks. Cecchetti and Rich's (2001) structural VAR methodology is appropriate to find the effect of monetary policy on the output-inflation trade-off. This study used bivariate unrestricted VAR and to calculate the SR, the structural response functions are estimated for a log of GDP and inflation rate. It is assumed that, in the long run, aggregate demand shocks have no permanent effect on the level of output. The SR is calculated over a time horizon (?), where the numerator measures the output loss and the denominator measures the difference in the level of inflation.

SR(?)= (?_(j=0)^??(??y?_(?+j)/(????_t^? )) )/((????_(t+?)/(????_t^? )) )= ((?_(i=0)^???_j^i?a_12^i ))/((?_(i=0)^??a_22^i ) ) (3)

There are also limitations associated with this kind of methodology i.e., it is difficult to identify the shocks i.e., anticipated, and unanticipated shocks and restrictions due to theoretical constraints due the which results are not stable ( Dar & Nain 2023, Jean-Jacques,2003 and Mohan & Verma, 2018). The data is taken from World Development Indicators for the period of 1960 to 2020. For the inflation rate, the study uses the GDP deflator and Consumer Price index with the base year 2015. For output, the real GDP with base year 2015 is used in log form and measured in million US dollars.

Methodology for SR from the Fiscal Side

As discussed above the prime objective of the monetary policy is price stability. And to bring inflation down by one percent, the central bank must increase the interest rate. This will increase the cost of borrowing and will shrink the capacity of borrowers i.e., public, and private, which will affect the potential of the economy. So, to calculate the effect of disinflation on output first the relationship between interest rate and inflation is estimated through the cumulative impulse response function by applying the structure VAR model. Based on this, the present value of the change in interest payment on domestic debt on floating rate and fixed rate for a period of 2022 to 2031 is calculated due to the change in interest rate because of one percent disinflation. The logic behind the selection of this period is that in 2031 almost all existing domestic debt will mature. Similarly, the change in the present value of domestic debt for the projected federal deficit is calculated from 2022-23 to 2031-32. Now to find the impact of this change in domestic debt on output, the government expenditure multiplier is calculated through the ordinary least square technique. After this, the present value of change in domestic debt is multiplied by the government expenditure multiplier and is divided by the nominal GDP of 2020-21 to calculate the SR from the supply side.

Identification of Disinflation Episodes

The first and the major step for the estimation of SR is the identification of disinflation episodes. For the identification of disinflationary episodes, peaks, and troughs were identified. The disinflation episode is the episode that begins with trend inflation peaks and terminates with trend inflation troughs. The study identified disinflationary episodes by utilizing annual data from Pakistan from 1961 to 2020. The study identified five disinflation episodes by utilizing annual inflation data of CPI through a centered three-year moving average as shown in Table 1. Based on the GDP deflator there are six disinflationary episodes as shown in Table 2. In both tables, the length of the episode is shown to be in the range of 3 years to 7 years. The maximum decline in trend inflation is almost 13.5 percent in the case of CPI and GDP deflator as shown in Table 1 and Table 2.

After identification of the disinflationary episodes the next step was the measurement of SR by three methods. The first method is the one used by Ball in 1994. The trend output grows log linearly in the disinflation episode. The output loss is calculated by taking the summation of the difference between the potential level of output and the actual level of output as explained in Ball's methodology. The SR for annual GDP data is obtained for all disinflationary episodes in Pakistan identified through CPI and GDP deflators. The results of SR measured through Ball's method are given in Table 3. The table shows that SR is different and positive in all episodes with reasonable magnitude. The average value of SR for all episodes is 3.22 using CPI and 2.41 using the GDP deflator for episode identification. According to Table 3, a one percent reduction in inflation leads to a 2.41 to 3.22 percent fall in the real GDP.

The above section only calculates the effects of contractionary monetary policy through a decrease in output mainly because of a change in aggregate demand. This way of measuring the cost of disinflation underestimates the decrease in output because of contractionary monetary policy because it only considers the short-run effects and ignores the long-run supply-side effects from the fiscal side. To decrease the inflation rate, the central bank uses contractionary monetary policy tools using mostly the interest rate. This increase in interest rate will increase the cost of borrowing both for the private and public sectors, the expected interest payment on domestic debt will increase, which will shrink the investment capabilities and will affect the potential level of output. So, to quantify the relationship between interest rate and inflation, accumulated impulse responses are estimated through a vector autoregressive model for interest rate, inflation rate, and real GDP as shown in Table 6. According to Table 6, to decrease the inflation rate by one percentage point, the central bank has to increase the interest rate by 1.4 percent.

At present the challenge faced by the Central Banks of developing countries is to implement the best controlling contractionary policies to enjoy low output cost in the region. SR is estimated to check the impact of disinflationary policies on Output Growth. This study estimated SR through three different methods available in the literature. These different methods gave the same results, which support the assumptions of Ball (1994), Zhang (2001), and structural VAR methodology by Cecchetti (2001). The study concludes that SR is positive in the Pakistan Economy for all episodes in the case of all methods, however, the magnitude of SR n is sensitive to different methods. Furthermore, the study found that the change in interest payment on existing domestic debt and projected federal deficit for the years 2022-23 and 2023-24 is significant and high and leads to the shrinking of fiscal space. The effect of disinflation on the demand side and supply side may offset the benefits of price stability. The study finds SR that is two times more as compared to previous studies. Our study implies that fiscal consequences of monetary policy must be considered before monetary policy decisions. The study suggests that disinflation brings significant output losses both in the short run and long run, so disinflation is not in favor of the economy. The analysis suggests that contractionary monetary policy has high welfare loss and comparatively large SR. We also suggest future research to estimate the benefits of price stability so that the benefit-cost ratio can be estimated for disinflationary policies.