Learning About Consumer Uncertainty from Qualitative Surveys: As Uncertain As Ever

Transcription

1 Learning About Consumer Uncertainty from Qualitative Surveys: As Uncertain As Ever Santiago Pinto, Pierre-Daniel Sarte, Robert Sharp Federal Reserve Bank of Richmond October 2016 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

2 Introduction Information compiled by statistical agencies (e.g. BLS, BEA) on state of economic activity, involves lags, i.e. published with at least a one-month lag, and subject to 3-month and 1-year revisions S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

3 Introduction Information compiled by statistical agencies (e.g. BLS, BEA) on state of economic activity, involves lags, i.e. published with at least a one-month lag, and subject to 3-month and 1-year revisions is not comprehensive, e.g. regional information on certain series are not compiled S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

4 Introduction Information compiled by statistical agencies (e.g. BLS, BEA) on state of economic activity, involves lags, i.e. published with at least a one-month lag, and subject to 3-month and 1-year revisions is not comprehensive, e.g. regional information on certain series are not compiled A growing number of institutions and government agencies produce diffusion indices constructed from survey data Michigan Survey of Consumers indices of consumer sentiment, Institute of Supply Management index of manufacturing production, National PMIs (CES ifo Business Climate Index, etc.) S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

5 Introduction Information compiled by statistical agencies (e.g. BLS, BEA) on state of economic activity, involves lags, i.e. published with at least a one-month lag, and subject to 3-month and 1-year revisions is not comprehensive, e.g. regional information on certain series are not compiled A growing number of institutions and government agencies produce diffusion indices constructed from survey data Michigan Survey of Consumers indices of consumer sentiment, Institute of Supply Management index of manufacturing production, National PMIs (CES ifo Business Climate Index, etc.) Federal Reserve Banks regional indices - Atlanta, Dallas, Kansas City, New York, Philadelphia, Richmond S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

6 Introduction Quantitative Survey Data Properties of inflation expectations - Coibion and Gorodnichenko (2012), Coibion, Gorodnichenko and Kumar (2015),... Disagreement among forecasters - D Amico and Orphanides (2008), Sill (2012),... S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

7 Introduction Quantitative Survey Data Properties of inflation expectations - Coibion and Gorodnichenko (2012), Coibion, Gorodnichenko and Kumar (2015),... Disagreement among forecasters - D Amico and Orphanides (2008), Sill (2012),... Qualitative Survey Data Forecasting - Nardo (2003), Pesaran and Weale (2006),... Assessing the state of economic activity - Bram and Ludvigson (1998), Bachmann and Elstner (2013), Bachmann, Elstner and Sims (2013),... S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

8 Introduction Summarizing qualitative survey data in the form of a diffusion index: ( ) n u µ n nd + κ = µd + κ n ISM: µ = 1/2, κ = 1/2, Richmond: µ = 1, κ = 0 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

9 Introduction Summarizing qualitative survey data in the form of a diffusion index: ( ) n u µ n nd + κ = µd + κ n ISM: µ = 1/2, κ = 1/2, Richmond: µ = 1, κ = 0 Aggregate growth may arise in different ways: e.g. IP, a few sectors doing well while others muddle through, all sectors doing moderately well, etc. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

10 Introduction Summarizing qualitative survey data in the form of a diffusion index: ( ) n u µ n nd + κ = µd + κ n ISM: µ = 1/2, κ = 1/2, Richmond: µ = 1, κ = 0 Aggregate growth may arise in different ways: e.g. IP, a few sectors doing well while others muddle through, all sectors doing moderately well, etc. Diffusion indices summarize the direction of change in a set of disaggregated series: the breadth of change S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

11 Introduction The BLS gives us employment, and hence employment growth, by sector from which we can construct aggregate employment growth. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

12 Introduction The BLS gives us employment, and hence employment growth, by sector from which we can construct aggregate employment growth. The BLS also publishes a diffusion index of employment in its monthly statistical release, covering roughly 260 sectors (4-digit NAICS). S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

13 Actual change and the breadth of change x t = 1 n n u t i=1 x u i,t } {{ } xt u 1 n n d t i=1 x d, i,t } {{ } xt d where x u i,t = x i,t if x i,t 0, and x d i,t = x i,t if x i,t < 0 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

14 Actual change and the breadth of change x t = 1 n n u t i=1 x u i,t } {{ } xt u 1 n n d t i=1 x d, i,t } {{ } xt d where x u i,t = x i,t if x i,t 0, and x d i,t = x i,t if x i,t < 0 x t = nu t n µu t nd t n µd t S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

15 Actual change and the breadth of change Define µ u = T 1 T t=1 µu t, ϕu = T 1 T t=1 nu t /n, S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

16 Actual change and the breadth of change Define µ u = T 1 T t=1 µu t, ϕu = T 1 T t=1 nu t /n, Then... ( n xt u u ) ( = t n n ϕu µ u + ϕ u (µ u t µ u u ) ) + t n ϕu (µ u t µ u ), S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

17 Actual change and the breadth of change Define µ u = T 1 T t=1 µu t, ϕu = T 1 T t=1 nu t /n, Then... ( n xt u u ) ( = t n n ϕu µ u + ϕ u (µ u t µ u u ) ) + t n ϕu (µ u t µ u ), Similarly, let µ d = T 1 T t=1 µd t, ϕd = T 1 T t=1 nd t /n, S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

18 Actual change and the breadth of change Define µ u = T 1 T t=1 µu t, ϕu = T 1 T t=1 nu t /n, Then... ( n xt u u ) ( = t n n ϕu µ u + ϕ u (µ u t µ u u ) ) + t n ϕu (µ u t µ u ), Similarly, let µ d = T 1 T t=1 µd t, ϕd = T 1 T t=1 nd t /n, Then... x d t = ( ) ( ) nt d n ϕd µ d + ϕ d (µ d t µ d n d ( ) t ) + n ϕd µ d t µ d, S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

19 Actual change and the breadth of change Decomposing an expansion/contraction, x t ϕ u (µ u t µ u ) ϕ d (µ d t µ d ) }{{} Change in how much or intensive margin + µ u D t }{{}, Change in how many or extensive margin S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

20 Actual change and the breadth of change Decomposing an expansion/contraction, x t ϕ u (µ u t µ u ) ϕ d (µ d t µ d ) }{{} Change in how much or intensive margin + µ u D t }{{}, Change in how many or extensive margin Overall growth arises from: the difference between how fast up sectors grew and how badly down sectors declined, the difference between the proportion of sectors that expanded versus those that declined, the breadth of the expansion S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

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22 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

23 Actual change and the breadth of change Using plant-level data from Chile and the U.S., we show that investment spikes are highly pro-cyclical, so much so that changes in the number of establishments undergoing investment spikes (the extensive margin) account for the bulk of variation in aggregate investment. Gourio and Kashyap (2007) S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

24 Measuring the breadth of change using qualitative surveys A sample of n survey participants, drawn randomly from a population at a point in time, is surveyed e.g. overall business conditions? S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

25 Measuring the breadth of change using qualitative surveys A sample of n survey participants, drawn randomly from a population at a point in time, is surveyed e.g. overall business conditions? Possible answers: A ={1,2,...,r}. Answers are indexed by a A, e.g. a A ={u,d,s} S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

26 Measuring the breadth of change using qualitative surveys A sample of n survey participants, drawn randomly from a population at a point in time, is surveyed e.g. overall business conditions? Possible answers: A ={1,2,...,r}. Answers are indexed by a A, e.g. a A ={u,d,s} Number of respondents associated with answer a A, is n a, where r a=1 na = n. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

27 Measuring the breadth of change using qualitative surveys A sample of n survey participants, drawn randomly from a population at a point in time, is surveyed e.g. overall business conditions? Possible answers: A ={1,2,...,r}. Answers are indexed by a A, e.g. a A ={u,d,s} Number of respondents associated with answer a A, is n a, where r a=1 na = n. Answers of type a are assigned a value of ω a [ω,ω], e.g. ω u = 1, ω s = 0, and ω d = 1. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

28 Measuring the breadth of change using qualitative surveys The answers are summarized in a diffusion index D = r ω a na n. a=1 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

29 Measuring the breadth of change using qualitative surveys The answers are summarized in a diffusion index D = r ω a na n. a=1 Then, we have that ω D ω. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

30 Measuring the breadth of change using qualitative surveys The answers are summarized in a diffusion index D = r ω a na n. a=1 Then, we have that ω D ω. An expansion in, say spending no durable goods, if D > (1/r) r a=1 ωa, and no change or contraction otherwise. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

31 Measuring the breadth of change using qualitative surveys p a is the probability that a participant s answer is a A = {1,2,...,r}, with r a=1 pa = 1 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

32 Measuring the breadth of change using qualitative surveys p a is the probability that a participant s answer is a A = {1,2,...,r}, with r a=1 pa = 1 Survey process: n random participant draws, each leading to a success for exactly one of r types of responses, each answer type having success probability p a S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

33 Measuring the breadth of change using qualitative surveys p a is the probability that a participant s answer is a A = {1,2,...,r}, with r a=1 pa = 1 Survey process: n random participant draws, each leading to a success for exactly one of r types of responses, each answer type having success probability p a f (n 1,...,n r ;n,p 1,...,p r ) = n! Π r a=1 na! Πr a=1 (p a ) na S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

34 Measuring the breadth of change using qualitative surveys p a is the probability that a participant s answer is a A = {1,2,...,r}, with r a=1 pa = 1 Survey process: n random participant draws, each leading to a success for exactly one of r types of responses, each answer type having success probability p a f (n 1,...,n r ;n,p 1,...,p r ) = n! Π r a=1 na! Πr a=1 (p a ) na E(n a ) = np a, Var(n a ) = np a (1 p a ), Cov(n a,n a ) = np a p a for answers of types a A and a A S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

35 Measuring the breadth of change using qualitative surveys p a = n a /n, the proportion of answers of type a A, p a = 1 n n i=1 x a i, where xi a takes on the value 1 when survey participant i answers a, zero otherwise S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

36 Measuring the breadth of change using qualitative surveys p a = n a /n, the proportion of answers of type a A, p a = 1 n n i=1 x a i, where xi a takes on the value 1 when survey participant i answers a, zero otherwise p a then has the interpretation of a sample Bernoulli mean S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

37 Uncertainty in the measure of direction of change The multivariate Central Limit Theorem immediately gives n p 1 p 1 p 2 p 2... p r 1 p r 1 D N , p 1 (1 p 1 ) p 1 p 2... p 2 p 1 p 2 (1 p 2 ) p r 1 p 1 p r 1 p 2... S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

38 Uncertainty in the measure of direction of change The multivariate Central Limit Theorem immediately gives n p 1 p 1 p 2 p 2... p r 1 p r 1 D N , p 1 (1 p 1 ) p 1 p 2... p 2 p 1 p 2 (1 p 2 ) p r 1 p 1 p r 1 p 2... D, is a linear combination of sample Bernoulli means, r a=1 ωa p a S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

39 Uncertainty in the measure of direction of change The multivariate Central Limit Theorem immediately gives n p 1 p 1 p 2 p 2... p r 1 p r 1 D N , p 1 (1 p 1 ) p 1 p 2... p 2 p 1 p 2 (1 p 2 ) p r 1 p 1 p r 1 p 2... D, is a linear combination of sample Bernoulli means, r a=1 ωa p a Then ( ) ) r n ( D D a N 0,( (ω a ) 2 p a D ), 2 a=1 where D = E( D) = r a=1 ωa p a. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

40 Uncertainty in the survey-measured direction of change Richmond indices: A ={u,d,s}, and ω u = 1, ω s = 0, ω d = 1 D = ( p u p d ) and ) ( n ( D D D N 0,(1 p s ) D 2). S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

41 Uncertainty in the survey-measured direction of change Richmond indices: A ={u,d,s}, and ω u = 1, ω s = 0, ω d = 1 D = ( p u p d ) and ) ( n ( D D D N 0,(1 p s ) D 2). Uncertainty in the measured direction of change... decreases with the square root of the sample size decreases with the diffusion index itself, D decreases with the degree of polarization, 1 p s S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

42 Distinguishing between different categories of participants D = J r j=1 a=1 ω a na j n = D = where J j=1 na j = n a, and J j=1 n j = n J n j n j=1 r a=1 ω a na j n j } {{ } D j S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

43 Distinguishing between different categories of participants D = J r j=1 a=1 ω a na j n = D = where J j=1 na j = n a, and J j=1 n j = n J n j n j=1 r a=1 ω a na j n j } {{ } D j One may choose to rescale the weights, say by γ j, D = J j=1 γ j n j n r ω a na j n a=1 j S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

44 Distinguishing between different categories of participants D = J r j=1 a=1 ω a na j n = D = where J j=1 na j = n a, and J j=1 n j = n J n j n j=1 r a=1 ω a na j n j } {{ } D j One may choose to rescale the weights, say by γ j, D = J j=1 γ j n j n ( ) r n ( D D a N 0,( r ω a na j n a=1 j J a=1 j=1 ( ω a γ j ) 2 p a j ) D 2 ) S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

45 The Distribution of Composite Indices n survey participants responding to questions concerning k economic conditions - e.g. household conditions, overall business conditions, spending on big ticket items S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

46 The Distribution of Composite Indices n survey participants responding to questions concerning k economic conditions - e.g. household conditions, overall business conditions, spending on big ticket items Answers a k, confined to a set A k, each comprising r possible types of responses, {1,2,...,r}. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

47 The Distribution of Composite Indices n survey participants responding to questions concerning k economic conditions - e.g. household conditions, overall business conditions, spending on big ticket items Answers a k, confined to a set A k, each comprising r possible types of responses, {1,2,...,r}. Participants answers across all components, k = 1,..., k, are collected in a k tuple a = (a 1,...,a k ) that lives in the set A = Π k k=1 A k. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

48 The Distribution of Composite Indices n survey participants responding to questions concerning k economic conditions - e.g. household conditions, overall business conditions, spending on big ticket items Answers a k, confined to a set A k, each comprising r possible types of responses, {1,2,...,r}. Participants answers across all components, k = 1,..., k, are collected in a k tuple a = (a 1,...,a k ) that lives in the set A = Π k k=1 A k. Consider an example with 3 components, each comprising 3 possible responses, A = A 1 A 2 A 3 = {u,d,s} {u,d,s} {u,d,s} = {uus, uud, uus, duu, ddu, dsu, suu, sdu, ssu,...} has 27 elements, in general r k. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

49 The Distribution of Composite Indices The Composite Index where 0 < δ k < 1. D = k δ k Dk, k=1 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

50 The Distribution of Composite Indices The Composite Index where 0 < δ k < 1. D = k δ k Dk, k=1 D k = r ω a a=1 n(ak =a,a k ) n a k A\A k = r ω a na k n, a=1 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

51 The Distribution of Composite Indices The Composite Index where 0 < δ k < 1. D = k δ k Dk, k=1 D k = r ω a a=1 n(ak =a,a k ) n a k A\A k = r ω a na k n, a=1 Uncertainty in D will need to take account of pairwise covariances between individual indices, say D k and D l - i.e. how participants answers compare/comove across different categories S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

52 The Distribution of Composite Indices nkl aa - the number of survey participants answering a k = a and a l = a for the components k and l, nkl aa = n (a k =a,a l=a,a {k,l}), k = l, a {k,l} A\A k A l S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

53 The Distribution of Composite Indices nkl aa - the number of survey participants answering a k = a and a l = a for the components k and l, nkl aa = n (a k =a,a l=a,a {k,l}), k = l, a {k,l} A\A k A l The number of participants answering a given response a for component k satisfies n a k = a A l n aa kl S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

54 The Distribution of Composite Indices nkl aa - the number of survey participants answering a k = a and a l = a for the components k and l, nkl aa = n (a k =a,a l=a,a {k,l}), k = l, a {k,l} A\A k A l The number of participants answering a given response a for component k satisfies n a k = a A l n aa kl Let p k a = na k /n, and paa kl = naa kl /n, S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

55 The Distribution of Composite Indices nkl aa - the number of survey participants answering a k = a and a l = a for the components k and l, nkl aa = n (a k =a,a l=a,a {k,l}), k = l, a {k,l} A\A k A l The number of participants answering a given response a for component k satisfies n a k = a A l n aa kl Let p k a = na k /n, and paa kl = naa kl /n, Individual indices are given by D k = r ω a p k a = a=1 r a=1 ω a p kl aa, a A l S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

56 The Distribution of Composite Indices pkl aa - the joint probability of observing a k = a and a l = a for the components k and l, p aa kl = a {k,l} A\A k A l p (a k =a,a l=a,a {k,l}), k = l, where (a k = a,a l = a,a {k,l} ) distinguishes between answers for component k, component l, and all other components, {k,l} S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

57 The Distribution of Composite Indices pkl aa - the joint probability of observing a k = a and a l = a for the components k and l, p aa kl = a {k,l} A\A k A l p (a k =a,a l=a,a {k,l}), k = l, where (a k = a,a l = a,a {k,l} ) distinguishes between answers for component k, component l, and all other components, {k,l} p kl - the vector comprising all pairwise joint probabilities, pkl aa given components k and l, where the dimension of p kl is r 2. for S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

58 The Distribution of Composite Indices pkl aa - the joint probability of observing a k = a and a l = a for the components k and l, p aa kl = a {k,l} A\A k A l p (a k =a,a l=a,a {k,l}), k = l, where (a k = a,a l = a,a {k,l} ) distinguishes between answers for component k, component l, and all other components, {k,l} p kl - the vector comprising all pairwise joint probabilities, pkl aa given components k and l, where the dimension of p kl is r 2. for Each element p aa kl, in the vector p kl, is the sample mean of a Bernoulli distribution n( pkl p kl ) D N (0,Σ pkl ). S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

59 The Distribution of Composite Indices ) n ( D D a N 0, k k=1 ) δk 2 ( Dk Var + 2 δ k δ l Cov ( Dk, D ) l, 1 k<l k S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

60 The Distribution of Composite Indices ) n ( D D a N 0, k k=1 ) δk 2 ( Dk Var + 2 δ k δ l Cov ( Dk, D ) l, 1 k<l k where D = k r δ k k=1 a=1 ω a p a k, S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

61 The Distribution of Composite Indices ) n ( D D a N 0, k k=1 ) δk 2 ( Dk Var + 2 δ k δ l Cov ( Dk, D ) l, 1 k<l k where D = k r δ k k=1 a=1 ω a p a k, {( ) } ) Var ( Dk = 1 r n (ω a ) 2 pk a (D k ) 2, a=1 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

62 The Distribution of Composite Indices ) n ( D D a N 0, k k=1 ) δk 2 ( Dk Var + 2 δ k δ l Cov ( Dk, D ) l, 1 k<l k where D = k r δ k k=1 a=1 ω a p a k, {( ) } ) Var ( Dk = 1 r n (ω a ) 2 pk a (D k ) 2, a=1 Cov ( Dk, D ) l = 1 n ω a ω a (a,a ) A k A l pkl aa pkl ab pb a kl (b,b ) A k A l. S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

63 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

64 An Application: The Michigan Survey of Consumers Monthly survey of Consumers (about 500 interviews) conducted by the Survey Research Center, University of Michigan S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

65 An Application: The Michigan Survey of Consumers Monthly survey of Consumers (about 500 interviews) conducted by the Survey Research Center, University of Michigan Index of Current Conditions D 1 : Would you say that you (and your family living there) are better off or worse off financially than you were a year ago? D 5 : Generally speaking, do you think now is a good or bad time for people to buy major household items? ICC = D 1 + D S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

66 An Application: The Michigan Survey of Consumers Index of Consumer Expectations D 2 : Do you think that a year from now, you will be better off financially, or worse off, or just about the same as now? D 3 : In the country as a whole do you think that during the next twelve months we ll have good times financially, or bad times, or what? D 4 : In the country as a whole, will we have continuous good times during the next five years or so, will we have periods of widespread unemployment or depression, or what? ICE = D 2 + D 3 + D S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

67 An Application: The Michigan Survey of Consumers Index of Consumer Expectations D 2 : Do you think that a year from now, you will be better off financially, or worse off, or just about the same as now? D 3 : In the country as a whole do you think that during the next twelve months we ll have good times financially, or bad times, or what? D 4 : In the country as a whole, will we have continuous good times during the next five years or so, will we have periods of widespread unemployment or depression, or what? ICE = D 2 + D 3 + D Index of Consumer Sentiment (headline number) ICS = D 1 + D 2 + D 3 + D 4 + D S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

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74 Conclusions Diffusion indices: S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

75 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

76 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest are linear combinations of Bernoulli averages and, therefore, approximately Normally distributed S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

77 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest are linear combinations of Bernoulli averages and, therefore, approximately Normally distributed variance of diffusion index reflects polarization or disagreement across responses S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

78 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest are linear combinations of Bernoulli averages and, therefore, approximately Normally distributed variance of diffusion index reflects polarization or disagreement across responses in Composite Indices, uncertainty in the index also reflects coincidence in polarization across individual indices S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

79 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest are linear combinations of Bernoulli averages and, therefore, approximately Normally distributed variance of diffusion index reflects polarization or disagreement across responses in Composite Indices, uncertainty in the index also reflects coincidence in polarization across individual indices In Michigan Survey of Consumers: S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

80 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest are linear combinations of Bernoulli averages and, therefore, approximately Normally distributed variance of diffusion index reflects polarization or disagreement across responses in Composite Indices, uncertainty in the index also reflects coincidence in polarization across individual indices In Michigan Survey of Consumers: steady rise in uncertainty around consumer sentiment starting in the late 1990s S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33

81 Conclusions Diffusion indices: are estimates of change in quasi-extensive margin - can account for bulk of variation in aggregate series of interest are linear combinations of Bernoulli averages and, therefore, approximately Normally distributed variance of diffusion index reflects polarization or disagreement across responses in Composite Indices, uncertainty in the index also reflects coincidence in polarization across individual indices In Michigan Survey of Consumers: steady rise in uncertainty around consumer sentiment starting in the late 1990s uncertainty around consumer sentiment, six years removed from the Great Recession, at its highest level since 1978 S. Pinto P.-D. Sarte R. Sharp Uncertainty and Qualitative Surveys October / 33