348 U.S. 121 (1954)
Petitioners, husband and wife, stand convicted under § 145 of the Internal Revenue Code1 of an attempt to evade and defeat their income taxes for the year 1948. The prosecution was based on the net worth method of proof, also in issue in three companion cases2 and a number of other decisions here from the Courts of Appeals of nine circuits. During the past two decades this Court has been asked to review an increasing number of criminal cases in which proof of tax evasion rested on this theory. We have denied certiorari because the cases involved only questions of evidence and, in isolation, presented no important questions of law. In 1943 the Court did have occasion to pass upon an application of the net worth theory where the taxpayer had no records. United States v. Johnson, 319 U. S. 503.
In recent years, however, tax-evasion convictions obtained under the net worth theory have come here with increasing frequency and left impressions beyond those of the previously unrelated petitions. We concluded that the method involved something more than the ordinary use of circumstantial evidence in the usual criminal case. Its bearing, therefore, on the safeguards traditionally provided in the administration of criminal justice called for a consideration of the entire theory. At our last Term a number of cases arising from the Courts of Appeals brought to our attention the serious doubts of those courts regarding the implications of the net worth method. Accordingly, we granted certiorari in these four cases and have held others to await their decision.
In a typical net worth prosecution, the Government, having concluded that the taxpayer’s records are inadequate as a basis for determining income tax liability, attempts to establish an “opening net worth” or total net value of the taxpayer’s assets at the beginning of a given year. It then proves increases in the taxpayer’s net worth for each succeeding year during the period under examination and calculates the difference between the adjusted net values of the taxpayer’s assets at the beginning and end of each of the years involved. The taxpayer’s nondeductible expenditures, including living expenses, are added to these increases, and if the resulting figure for any year is substantially greater than the taxable income reported by the taxpayer for that year, the Government claims the excess represents unreported taxable income. In addition, it asks the jury to infer willfulness from this understatement, when taken in connection with direct evidence of “conduct, the likely effect of which would be to mislead or to conceal.” Spies v. United States, 317 U. S. 492, 499.
Before proceeding with a discussion of these cases, we believe it important to outline the general problems implicit in this type of litigation. In this consideration we assume, as we must in view of its widespread use, that the Government deems the net worth method useful in the enforcement of the criminal sanctions of our income tax laws. Nevertheless, careful study indicates that it is so fraught with danger for the innocent that the courts must closely scrutinize its use.
One basic assumption in establishing guilt by this method is that most assets derive from a taxable source, and that when this is not true the taxpayer is in a position to explain the discrepancy. The application of such an assumption raises serious legal problems in the administration of the criminal law. Unlike civil actions for the recovery of deficiencies, where the determinations of the Commissioner have prima facie validity, the prosecution must always prove the criminal charge beyond a reasonable doubt. This has led many of our courts to be disturbed by the use of the net worth method, particularly in its scope and the latitude which it allows prosecutors. E. g., Demetree v. United States, 207 F. 2d 892, 894 (1953); United States v. Caserta, 199 F. 2d 905, 907 (1952); United States v. Fenwick, 177 F. 2d 488.
But the net worth method has not grown up overnight. It was first utilized in such cases as Capone v. United States, 51 F. 2d 609 (1931) and Guzik v. United States, 54 F. 2d 618 (1931), to corroborate direct proof of specific unreported income. In United States v. Johnson, supra, this Court approved of its use to support the inference that the taxpayer, owner of a vast and elaborately concealed network of gambling houses upon which he declared no income, had indeed received unreported income in a “substantial amount.” It was a potent weapon in establishing taxable income from undisclosed sources when all other efforts failed. Since the Johnson case, however, its horizons have been widened until now it is used in run-of-the-mine cases, regardless of the amount of tax deficiency involved. In each of the four cases decided today the allegedly unreported income comes from the same disclosed sources as produced the taxpayer’s reported income and in none is the tax deficiency anything like the deficiencies in Johnson, Capone or Guzik.
The net worth method, it seems, has evolved from the final volley to the first shot in the Government’s battle for revenue, and its use in the ordinary income-bracket cases greatly increases the chances for error. This leads us to point out the dangers that must be consciously kept in mind in order to assure adequate appraisal of the specific facts in individual cases.
In this connection, the taxpayer frequently gives “leads” to the Government agents indicating the specific sources from which his cash on hand has come, such as prior earnings, stock transactions, real estate profits, inheritances, gifts, etc. Sometimes these “leads” point back to old transactions far removed from the prosecution period. Were the Government required to run down all such leads it would face grave investigative difficulties; still its failure to do so might jeopardize the position of the taxpayer.
As we have said, the method requires assumptions, among which is the equation of unexplained increases in net worth with unreported taxable income. Obviously such an assumption has many weaknesses. It may be that gifts, inheritances, loans and the like account for the newly acquired wealth. There is great danger that the jury may assume that once the Government has established the figures in its net worth computations, the crime of tax evasion automatically follows. The possibility of this increases where the jury, without guarding instructions, is allowed to take into the jury room the various charts summarizing the computations; bare figures have a way of acquiring an existence of their own, independent of the evidence which gave rise to them.
Although it may sound fair to say that the taxpayer can explain the “bulge” in his net worth, he may be entirely honest and yet unable to recount his financial history. In addition, such a rule would tend to shift the burden of proof. Were the taxpayer compelled to come forward with evidence, he might risk lending support to the Government’s case by showing loose business methods or losing the jury through his apparent evasiveness. Of course, in other criminal prosecutions juries may disbelieve and convict the innocent. But the courts must minimize this danger.
When there are no books and records, willfulness may be inferred by the jury from that fact coupled with proof of an understatement of income. But when the Government uses the net worth method, and the books and records of the taxpayer appear correct on their face, an inference of willfulness from net worth increases alone might be unjustified, especially where the circumstances surrounding the deficiency are as consistent with innocent mistake as with willful violation. On the other hand, the very failure of the books to disclose a proved deficiency might indicate deliberate falsification.
In many cases of this type, the prosecution relies on the taxpayer’s statements, made to revenue agents in the course of their investigation, to establish vital links in the Government’s proof. But when a revenue agent confronts the taxpayer with an apparent deficiency, the latter may be more concerned with a quick settlement than an honest search for the truth. Moreover, the prosecution may pick and choose from the taxpayer’s statement, relying on the favorable portion and throwing aside that which does not bolster its position. The problem of corroboration, dealt with in the companion cases of Smith v. United States, post, p. 147, and United States v. Calderon, post, p. 160, therefore becomes crucial.
The statute defines the offense here involved by individual years. While the Government may be able to prove with reasonable accuracy an increase in net worth over a period of years, it often has great difficulty in relating that income sufficiently to any specific prosecution year. While a steadily increasing net worth may justify an inference of additional earnings, unless that increase can be reasonably allocated to the appropriate tax year the taxpayer may be convicted on counts of which he is innocent.
While we cannot say that these pitfalls inherent in the net worth method foreclose its use, they do require the exercise of great care and restraint. The complexity of the problem is such that it cannot be met merely by the application of general rules. Cf. Universal Camera Corp. v. Labor Board, 340 U. S. 474, 489. Trial courts should approach these cases in the full realization that the taxpayer may be ensnared in a system which, though difficult for the prosecution to utilize, is equally hard for the defendant to refute. Charges should be especially clear, including, in addition to the formal instructions, a summary of the nature of the net worth method, the assumptions on which it rests, and the inferences available both for and against the accused. Appellate courts should review the cases, bearing constantly in mind the difficulties that arise when circumstantial evidence as to guilt is the chief weapon of a method that is itself only an approximation.
With these considerations as a guide, we turn to the facts.
The indictment returned against the Hollands embraced three counts. The first two charged Marion L. Holland, the husband, with attempted evasion of his income tax for the years 1946 and 1947. He was found not guilty by the jury on both of these counts. The third count charged Holland and his wife with attempted evasion in 1948 of the tax on $19,736.74 not reported by them in their joint return. The jury found both of them guilty. Mrs. Holland was fined $5,000, while her husband was sentenced to two years’ imprisonment and fined $10,000.
The Government’s opening net worth computation shows defendants with a net worth of $19,152.59 at the beginning of the indictment period. Shortly thereafter, defendants purchased a hotel, bar and restaurant, and began operating them as the Holland House. Within three years, during which they reported $31,265.92 in taxable income, their apparent net worth increased by $113,185.32.3 The Government’s evidence indicated that, during 1948, the year for which defendants were convicted, their net worth increased by some $32,000, while the amount of taxable income reported by them totaled less than one-third that sum.
Use of Net Worth Method Where Books Are Apparently Adequate.
As we have previously noted, this is not the first net worth case to reach this Court. In United States v. Johnson, supra, the Court affirmed a tax-evasion conviction on evidence showing that the taxpayer’s expenditures had exceeded his “available declared resources.” Since Johnson and his concealed establishments had destroyed the few records they had, the Government was forced to resort to the net worth method of proof. This Court approved on the ground that “to require more . . . would be tantamount to holding that skilful concealment is an invincible barrier to proof,” 319 U. S., at 517-518. Petitioners ask that we restrict the Johnson case to situations where the taxpayer has kept no books. They claim that § 41 of the Internal Revenue Code,4 expressly limiting the authority of the Government to deviate from the taxpayer’s method of accounting, confines the net worth method to situations where the taxpayer has no books or where his books are inadequate. Despite some support for this view among the lower courts (see United States v. Riganto, 121 F. Supp. 158, 161, 162; United States v. Williams, 208 F. 2d 437, 437-438; Remmer v. United States, 205 F. 2d 277, 286, judgment vacated on other grounds, 347 U. S. 227), we conclude that this argument must fail. The provision that the “net income shall be computed . . . in accordance with the method of accounting regularly employed in keeping the books of such taxpayer,” refers to methods such as the cash receipts or the accrual method, which allocate income and expenses between years. United States v. American Can Co., 280 U. S. 412, 419. The net worth technique, as used in this case, is not a method of accounting different from the one employed by defendants. It is not a method of accounting at all, except insofar as it calls upon taxpayers to account for their unexplained income. Petitioners’ accounting system was appropriate for their business purposes; and, admittedly, the Government did not detect any specific false entries therein. Nevertheless, if we believe the Government’s evidence, as the jury did, we must conclude that the defendants’ books were more consistent than truthful, and that many items of income had disappeared before they had even reached the recording stage. Certainly Congress never intended to make § 41 a set of blinders which prevents the Government from looking beyond the self-serving declarations in a taxpayer’s books. “The United States has relied for the collection of its income tax largely upon the taxpayer’s own disclosures .... This system can function successfully only if those within and near taxable income keep and render true accounts.” Spies v. United States, 317 U. S., at 495. To protect the revenue from those who do not “render true accounts,” the Government must be free to use all legal evidence available to it in determining whether the story told by the taxpayer’s books accurately reflects his financial history.
Establishing a Definite Opening Net Worth.
We agree with petitioners that an essential condition in cases of this type is the establishment, with reasonable certainty, of an opening net worth, to serve as a starting point from which to calculate future increases in the taxpayer’s assets. The importance of accuracy in this figure is immediately apparent, as the correctness of the result depends entirely upon the inclusion in this sum of all assets on hand at the outset. The Government’s net worth statement included as assets at the starting point stock costing $29,650 and $2,153.09 in cash.5
The Hollands claim that the Government failed to include in its opening net worth figure an accumulation of $113,000 in currency and “hundreds and possibly thousands of shares of stock” which they owned at the beginning of the prosecution period. They asserted that the cash had been accumulated prior to the opening date, $104,000 of it before 1933, and the balance between 1933 and 1945. They had kept the money, they claimed, mostly in $100 bills and at various times in a canvas bag, a suitcase, and a metal box. They had never dipped into it until 1946, when it became the source of the apparent increase in wealth which the Government later found in the form of a home, a ranch, a hotel and other properties. This was the main issue presented to the jury. The Government did not introduce any direct evidence to dispute this claim. Rather it relied on the inference that anyone who had had $104,000 in cash would not have undergone the hardship and privation endured by the Hollands all during the late 20’s and throughout the 30’s. During this period they lost their café business; accumulated $35,000 in debts which were never paid; lost their household furniture because of an unpaid balance of $92.20; suffered a default judgment for $506.66; and were forced to separate for some eight years because it was to their “economical advantage.” During the latter part of this period, Mrs. Holland was obliged to support herself and their son by working at a motion picture house in Denver while her husband was in Wyoming. The evidence further indicated that improvements to the hotel, and other assets acquired during the prosecution years, were bought in installments and with bills of small denominations, as if out of earnings rather than from an accumulation of $100 bills. The Government also negatived the possibility of petitioners’ accumulating such a sum by checking Mr. Holland’s income tax returns as far back as 1913, showing that the income declared in previous years was insufficient to enable defendants to save any appreciable amount of money. The jury resolved this question of the existence of a cache of cash against the Hollands, and we believe the verdict was fully supported.
As to the stock, Mr. Holland began dabbling in the stock market in a small way in 1937 and 1938. His purchases appear to have been negligible and on borrowed money. His only reported income from stocks was in his tax returns for 1944 and 1945 when he disclosed dividends of $1,600 and $1,850 respectively. While the record is unclear on this point, it appears that during the period from 1942 to 1945 he pledged considerable stock as collateral for loans. There is no evidence, however, showing what portions of this stock Mr. Holland actually owned at any one time, since he was trading in shares from day to day. And, even if we assume that he owned all the stock, some 4,550 shares, there is evidence that Mr. Holland’s stock transactions were usually in “stock selling for only a few dollars per share.” In this light, the Government’s figure of approximately $30,000 is not out of line. In 1946 Holland reported the sale of about $50,000 in stock, but no receipt of dividends; nor were dividends reported in subsequent years. It is reasonable to assume that he sold all of his stock in 1946. In fact, Holland stated to the revenue agents that he had not “fooled with the stock market” since the beginning of 1946; that he had not owned any stocks for two or three years prior to 1949; that he had saved about $50,000 from 1933 to 1946, and that in 1946 he had $9,000 in cash with the balance of his savings in stocks.6
The Government’s evidence, bolstered by the admissions of petitioners, provided convincing proof that they had no stock other than the amount included in the opening net worth statement. By the same token, the petitioners’ argument that the Government failed to account for the proceeds of stock sold by them before the starting date must also fail. The Government’s evidence fully justified the jury’s conclusion that there were no proceeds over and above the amount credited to petitioners.
The Government’s Investigation of Leads.
So overwhelming, indeed, was the Government’s proof on the issue of cash on hand that the Government agents did not bother to check petitioners’ story that some of the cash represented proceeds from the sales of two cafés in the 20’s; and that in 1933 an additional portion of this $113,000 in currency was obtained by exchanging some $12,000 in gold at a named bank. While sound administration of the criminal law requires that the net worth approach — a powerful method of proving otherwise undetectable offenses — should not be denied the Government, its failure to investigate leads furnished by the taxpayer might result in serious injustice. It is, of course, not for us to prescribe investigative procedures,7 but it is within the province of the courts to pass upon the sufficiency of the evidence to convict. When the Government rests its case solely on the approximations and circumstantial inferences of a net worth computation, the cogency of its proof depends upon its effective negation of reasonable explanations by the taxpayer inconsistent with guilt. Such refutation might fail when the Government does not track down relevant leads furnished by the taxpayer — leads reasonably susceptible of being checked, which, if true, would establish the taxpayer’s innocence. When the Government fails to show an investigation into the validity of such leads, the trial judge may consider them as true and the Government’s case insufficient to go to the jury. This should aid in forestalling unjust prosecutions, and have the practical advantage of eliminating the dilemma, especially serious in this type of case, of the accused’s being forced by the risk of an adverse verdict to come forward to substantiate leads which he had previously furnished the Government. It is a procedure entirely consistent with the position long espoused by the Government, that its duty is not to convict but to see that justice is done.
In this case, the Government’s detailed investigation was a complete answer to the petitioners’ explanations. Admitting that in cases of this kind it “would be desirable to track to its conclusion every conceivable line of inquiry,” the Government centered its inquiry on the explanations of the Hollands and entered upon a detailed investigation of their lives covering several states and over a score of years. The jury could have believed that Mr. Holland had received moneys from the sale of cafés in the twenties and that he had turned in gold in 1933 and still it could reasonably have concluded that the Hollands lacked the claimed cache of currency in 1946, the crucial year. Even if these leads were assumed to be true, the Government’s evidence was sufficient to convict. The distant incidents relied on by petitioners were so remote in time and in their connection with subsequent events proved by the Government that, whatever petitioners’ net worth in 1933, it appears by convincing evidence that on January 1, 1946, they had only such assets as the Government credited to them in its opening net worth statement.
Net Worth Increases Must be Attributable to Taxable Income.
Also requisite to the use of the net worth method is evidence supporting the inference that the defendant’s net worth increases are attributable to currently taxable income.
The Government introduced evidence tending to show that although the business of the hotel apparently increased during the years in question, the reported profits fell to approximately one-quarter of the amount declared by the previous management in a comparable period;8 that the cash register tapes, on which the books were based, were destroyed by the petitioners; and that the books did not reflect the receipt of money later withdrawn from the hotel’s cash register for the personal living expenses of the petitioners and for payments made for restaurant supplies. The unrecorded items in this latter category totaled over $12,500 for 1948. Thus there was ample evidence that not all the income from the hotel had been included in its books and records. In fact, the net worth increase claimed by the Government for 1948 could have come entirely from the unreported income of the hotel and still the hotel’s total earnings for the year would have been only 73% of the sum reported by the previous owner for the comparable period in 1945.
But petitioners claim the Government failed to adduce adequate proof because it did not negative all the possible nontaxable sources of the alleged net worth increases — gifts, loans, inheritances, etc. We cannot agree. The Government’s proof, in our view, carried with it the negations the petitioners urge. Increases in net worth, standing alone, cannot be assumed to be attributable to currently taxable income. But proof of a likely source, from which the jury could reasonably find that the net worth increases sprang, is sufficient. In the Johnson case, where there was no direct evidence of the source of the taxpayer’s income, this Court’s conclusion that the taxpayer “had large, unreported income was reinforced by proof . . . that [for certain years his] private expenditures . . . exceeded his available declared resources.” This was sufficient to support “the finding that he had some unreported income which was properly attributable to his earnings . . . .” United States v. Johnson, 319 U. S., at 517. There the taxpayer was the owner of an undisclosed business capable of producing taxable income; here the disclosed business of the petitioners was proven to be capable of producing much more income than was reported and in a quantity sufficient to account for the net worth increases. Any other rule would burden the Government with investigating the many possible nontaxable sources of income, each of which is as unlikely as it is difficult to disprove. This is not to say that the Government may disregard explanations of the defendant reasonably susceptible of being checked. But where relevant leads are not forthcoming, the Government is not required to negate every possible source of nontaxable income, a matter peculiarly within the knowledge of the defendant. See Rossi v. United States, 289 U. S. 89, 91-92.
The Burden of Proof Remains on the Government.
Nor does this rule shift the burden of proof. The Government must still prove every element of the offense beyond a reasonable doubt though not to a mathematical certainty. The settled standards of the criminal law are applicable to net worth cases just as to prosecutions for other crimes. Once the Government has established its case, the defendant remains quiet at his peril. Cf. Yee Hem v. United States, 268 U. S. 178, 185. The practical disadvantages to the taxpayer are lessened by the pressures on the Government to check and negate relevant leads.
Willfulness Must be Present.
A final element necessary for conviction is willfulness. The petitioners contend that willfulness “involves a specific intent which must be proven by independent evidence and which cannot be inferred from the mere understatement of income.” This is a fair statement of the rule. Here, however, there was evidence of a consistent pattern of underreporting large amounts of income, and of the failure on petitioners’ part to include all of their income in their books and records. Since, on proper submission, the jury could have found that these acts supported an inference of willfulness, their verdict must stand. Spies v. United States, supra, at 499-500.
The Charge to the Jury.
Petitioners press upon us, finally, the contention that the instructions of the trial court were so erroneous and misleading as to constitute grounds for reversal. We have carefully reviewed the instructions and cannot agree. But some require comment. The petitioners assail the refusal of the trial judge to instruct that where the Government’s evidence is circumstantial it must be such as to exclude every reasonable hypothesis other than that of guilt. There is some support for this type of instruction in the lower court decisions, Garst v. United States, 180 F. 339, 343; Anderson v. United States, 30 F. 2d 485-487; Stutz v. United States, 47 F. 2d 1029, 1030; Hanson v. United States, 208 F. 2d 914, 916, but the better rule is that where the jury is properly instructed on the standards for reasonable doubt, such an additional instruction on circumstantial evidence is confusing and incorrect, United States v. Austin-Bagley Corp., 31 F. 2d 229, 234, cert. denied, 279 U. S. 863; United States v. Becker, 62 F. 2d 1007, 1010; 1 Wigmore, Evidence (3d ed.), §§ 25-26.
Circumstantial evidence in this respect is intrinsically no different from testimonial evidence. Admittedly, circumstantial evidence may in some cases point to a wholly incorrect result. Yet this is equally true of testimonial evidence. In both instances, a jury is asked to weigh the chances that the evidence correctly points to guilt against the possibility of inaccuracy or ambiguous inference. In both, the jury must use its experience with people and events in weighing the probabilities. If the jury is convinced beyond a reasonable doubt, we can require no more.
Even more insistent is the petitioners’ attack, not made below, on the charge of the trial judge as to reasonable doubt. He defined it as “the kind of doubt . . . which you folks in the more serious and important affairs of your own lives might be willing to act upon.” We think this section of the charge should have been in terms of the kind of doubt that would make a person hesitate to act, see Bishop v. United States, 71 App. D. C. 132, 137-138, 107 F. 2d 297, 303, rather than the kind on which he would be willing to act. But we believe that the instruction as given was not of the type that could mislead the jury into finding no reasonable doubt when in fact there was some. A definition of a doubt as something the jury would act upon would seem to create confusion rather than misapprehension. “Attempts to explain the term ‘reasonable doubt’ do not usually result in making it any clearer to the minds of the jury,” Miles v. United States, 103 U. S. 304, 312, and we feel that, taken as a whole, the instructions correctly conveyed the concept of reasonable doubt to the jury.
Petitioners also assign as error the refusal of the trial judge to give instructions on the wording of the criminal statute under which they were indicted, even though the judge fully and correctly instructed the jury on every element of the crime. The impossibility of pointing to any way in which defendants’ rights were prejudiced by this, assuming it was error, is enough to indicate that the trial judge was correct, see United States v. Center Veal & Beef Co., 162 F. 2d 766, 771. There is here no question of the jury’s duty to apply the law to the facts. That operation implies the application of a general standard to the specific physical facts as found by the jury. The meanings of standards such as willfulness were properly explained by the trial judge in no greater particularity than necessary, and thus the jury’s function was not invaded.
In the light of these considerations the judgment is
Affirmed.